48 sets of forks Vani could buy for the restaurant to have enough forks.
What is inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.
Given Data
The restaurant needs at least 795 forks. There are currently 315 forks.
If each set on sale contains 10 forks
(10 ×(x)) ≥ (795-315)
10x ≥ 480
x ≥ 48
48 sets of forks Vani could buy for the restaurant to have enough forks.
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In a factory, the production hours t and output y are having linear relationship. When the
factory operates for 5 hours per day, it may have the number of outputs of 2000 units and 3500
units for 8 hours of operation.
(a) Model an equation that gives the outputs, y, in terms of operation hours, t, per day.
(b) If the factory wants to have 4500 units of production per day, how long it should operate?
(c) Draw the graph in excel of the production against operation hours t up to first 20 hours.
Considering the linear relationship between the variables, we have that:
a) The function is: y = 500t - 500.
b) The factory should operate for 10 hours to have a production of 4500 units.
c) The graph for the first 20 hours of the function is given at the end of the answer.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For the given linear relationship, we have two points, as follows:
(5,2000) and (8,3500).
The slope is given by change in y divided by change in x, hence:
m = 1500/3 = 500.
Then:
y = 500t + b.
When t = 5, y = 2000, hence we solve for the intercept as follows:
2000 = 500(5) + b
b = -500.
Then the function is:
y = 500t - 500.
For 4500 units, the time is found as follows:
4500 = 500t - 500
500t = 5000.
t = 5000/500
t = 10 hours.
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Two cars start moving from the same point. One travels south at 16 mi/h and the other travels west at 12 mi/h. At what rate (in mi/h) is the distance between the cars increasing three hours later?
Answer:
20 mi/h
Step-by-step explanation:
You want the speed of separation after 3 hours between two cars that started from the same point. One is moving at 16 mi/h south, the other is moving at 12 mi/h west.
Velocity vectorsSince both cars started from the same point, the speed of separation is the magnitude of the difference between the respective velocity vectors. A graphical representation of the velocity vectors shows them to be the legs of a right triangle. Their difference is the length of the hypotenuse, which can be found using the Pythagorean theorem.
s = √(16² +12²) = √(256 +144) = √400
s = 20
The speed of separation is a constant 20 mi/h.
__
Additional comment
If the cars did not start at the same point, then the speed of separation would be changing with time. It could be found using the derivative of the distance between the cars, or by considering the car speeds in the direction each car is from the other at the time of interest.
We note that the problem here makes use of a 3-4-5 right triangle, with a multiplier of 4 mph.
I added a picture of my question need answer quickly please
The statements that are true regarding the temperature include:
1. At noon, the temperature is - 9 1/2°F.
2. The temperature at 5pm is - 15 3/4°F.
3. The change in temperature from noon to 5pm is - 6 1/4°F.
How to calculate the temperature?From the information, the temperature at 6A.M is -14°D and the temperature increases at an average of 3/4°F each hour until noon. Then it drops at 1 1/4°F until 5P.M.
The temperature at noon will be:
= -14 + (3/4 × 6)
= -14 + 4.5
= -9.5°F
The temperature at 5pm will be:
= -9.5 - (1 1/4 × 5)
= -9.5 - 6.25
= -15.75
The total change in temperature will be:
= Ending temperature - Starting temperature
= -15.75°F - (-14°F)
= 1.75°F
The temperature change from noon to 5 pm will be:
= -15.75 - (-9.5)
= -6.25 = 6 1/4°F
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what is the value of (-20.16)+( -3.9)?
A. 16.26
B. - 24.06
C. 24.06
D. -16.26
Answer:
24.06................
Answer:
B
Step-by-step explanation:
[tex]( - 20.16) + ( - 3.9) \\ [/tex]
=
[tex] - 20.16 - 3.9[/tex]
=
[tex] \frac{ - 1203}{50} or - 24.06[/tex]
Show your work, due today
1. x = 8 -8 When the number that is the sum or answer, the number that is in the lines is usually the same but is the opposite, os if it is positive, then it is negative.
2. x = 7, -7
3. A = 6, -10 8 - 2 = 6 8 + 2 = 10 Switch it up, put the negative sign with the 10.
This is all that I can do right now I hope this helped I will try to answer more later.
Help me please it’s due today please help me please help me please help me please help me please help me?
The results of the logical expressions are
¬ q v p: false if q is true and p is false¬ p ∧ ¬ q: true if q is false and p is falseWhat are logical expressions?Logical expressions are expressions that have a result of true or false.
These results are generally classified as boolean values
How to solve the logical expressions?We start by solving the first expression
Logic expression (3)
¬ q v p
The above expression uses the or operator
The rule of the or operator is that:
It evaluates to true, if at least one of the terms is trueOtherwise, it is falseThis means that the expression ¬ q v p evaluates to false if q is true and p is false; otherwise, it evaluates to true
Logic expression (4)
¬ p ∧ ¬ q
The above expression uses the and operator
The rule of the and operator is that:
It evaluates to true, if both terms are trueOtherwise, it is falseThis means that the expression ¬ p ∧ ¬ q evaluates to true if q is false and p is false; otherwise, it evaluates to false
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Answer:The results of the logical expressions are¬ q v p: false if q is true and p is false¬ p ∧ ¬ q: true if q is false and p is falseWhat are logical expressions?Logical expressions are expressions that have a result of true or false.These results are generally classified as boolean valuesHow to solve the logical expressions?We start by solving the first expressionLogic expression (3)¬ q v pThe above expression uses the or operatorThe rule of the or operator is that:It evaluates to true, if at least one of the terms is trueOtherwise, it is falseThis means that the expression ¬ q v p evaluates to false if q is true and p is false; otherwise, it evaluates to trueLogic expression (4)¬ p ∧ ¬ qThe above expression uses the and operatorThe rule of the and operator is that:It evaluates to true, if both terms are trueOtherwise, it is falseThis means that the expression ¬ p ∧ ¬ q evaluates to true if q is false and p is false; otherwise, it evaluates to false
Step-by-step explanation:
Please help :(((
Question 1(Multiple Choice Worth 2 points)
(Proportional Relationships MC)
Determine if the table shows a proportional relationship.
Time (hours) 0 6 12 18 24
Pay (dollars) 0 72 144 216 288
Yes, it is proportional because the ratios for dollars per hour are all equivalent to 12 dollars per hour.
Yes, it is proportional because the ratios for dollars per hour are all equivalent to 13 dollars per hour.
No, it is not proportional because 72 over 6 does not equal 216 over 18.
No, it is not proportional because 216 over 18 does not equal 288 over 24.
Question 2(Multiple Choice Worth 2 points)
(Proportional Relationships MC)
The graph of a proportional relationship is shown.
graph of a line beginning at point 0 comma 0 and continuing to the right going through points 5 comma 700 and 6 comma 840 and 7 comma 980
Create a table from the graph.
x 1 2 3
y 140 280 420
x 14 28 42
y 1 2 3
x 1 2 3
y 14 28 42
x 140 280 420
y 1 2 3
Question 3(Multiple Choice Worth 2 points)
(Proportional Relationships MC)
Three different recipes each make a different number of cookies and require a different amount of flour.
Recipe 1: 2 dozen cookies; 1.5 cups of flour
Recipe 2: 3 dozen cookies; 3 cups of flour
Recipe 3: 4 dozen cookies; 4.5 cups of flour
Determine if the three recipes use a proportional amount of flour.
Yes, it is proportional because the cookies increase by 1 dozen for every 1.5 cups of flour.
Yes, it is proportional because the ratios between the number of cookies and cups of flour are all equivalent.
No, it is not proportional because the number of cookies and cups of flour could not be zero at the same time.
No, it is not proportional because the ratios between the number of cookies and cups of flour are not all equivalent.
Question 4(Multiple Choice Worth 2 points)
(Proportional Relationships MC)
Determine if the table shows a proportional relationship.
x 36.5 23.2 63.3
y 18.25 11.6 21.1
Yes, it is proportional because the ratios for y over x are all equivalent to one half.
Yes, it is proportional because the ratios for y over x are all equivalent to one third.
No, it is not proportional because 18.25 over 36.5 is not equal to 23.2 over 11.6.
No, it is not proportional because 18.25 over 36.5 is not equal to 21.1 over 63.3.
Question 5(Multiple Choice Worth 2 points)
(Proportional Relationships LC)
Determine if the graph shows a proportional relationship.
Graph with x axis labeled distance miles and y axis labeled time hours. A line begins at point 0 comma 0 and continues to the right.
No, it is not proportional because the line does not intersect with the origin.
No, it is not proportional because the x-axis and y-axis are not labeled correctly.
Yes, it is proportional because it is a line that intersects with the origin.
Yes, it is proportional because the x-axis and y-axis are labeled correctly.
Question 6(Multiple Choice Worth 2 points)
(Proportional Relationships MC)
The table shows a proportional relationship.
Workout (hours) 1 2 3
Calories Burned 190 380 570
Create a description in words for the table.
The number of calories burned is dependent on the number of hours working out. For every 190-hour workout, there is 1 calorie burned, and for every 380-hour workout, there are 2 calories burned.
The number of calories burned is dependent on the number of hours working out. For a one-hour workout, there are 190 calories burned, and for a two-hour workout, there are 380 calories burned.
The number of hours working out is dependent on the number of calories burned. For every 190-hour workout, there is 1 calorie burned, and for every 380-hour workout, there are 2 calories burned.
The number of hours working out is dependent on the number of calories burned. For a one-hour workout, there are 190 calories burned, and for a two-hour workout, there are 380 calories burned.
Question 7(Multiple Choice Worth 2 points)
(Proportional Relationships MC)
A group of hikers tracked how long it took to hike a 15-mile trail. They hiked 3.5 miles in 2 hours, 8.75 miles in 5 hours, and 12.25 miles in 7 hours.
Determine if the relationship between the hikers' distance and time is proportional.
Yes, it is proportional because the ratios for miles per hour are all equivalent to 1.75 miles per hour.
Yes, it is proportional because the ratios for miles per hour are all equivalent to 0.6 miles per hour.
No, it is not proportional because 3.5 miles in 2 hours is not equivalent to 8.75 miles in 5 hours.
No, it is not proportional because 8.75 miles in 5 hours is not equivalent to 12.25 miles in 7 hours.
The relationship between the input and output variables in the given table of values are;
Question 1
Yes, it is proportional, because the ratio of Dollar per hour are all equivalent to 12 dollar per hour
Question 2;
x; 1, 2, 3, 4, 5
y; 140, 280, 420, 560
Question 3
No it is not proportional because the ratio between the number of cookies, and the cups of flour are not equivalent
Question 4
No, it is not proportional because 18.26/36.5 ≠ 21.1/63.3
Question 5
Yes, it is a proportional relationship because it is a line that intersects with the origin
Question 6
The number of calories burned is dependent on the number of hours worked out. For a one–hour work out, 190 calories are burned, and for a two–hours work out, there are 380 calories burned
Question 7
Yes because the ratio of the miles per hour are all equivalent to 1.75
What is a proportional relationship?A proportional relationship is one in which the input and output have a constant ratio, and in which the graph passes through the origin.
Question 1
A proportional relationship is one that has the x and y –intercept as the origin, (0, 0) and in which the ratio of the values at each point, y/x is a constant
Given (0, 0) is a data point and 72/6 = 144/12 = 216/18 = 12
Therefore; Yes it is proportional because the ratio for Dollar per hour are all equivalent to 12 dollar per hour
Question 2;
The points on the graph are;
(0, 0), (5, 700), (6, 840), (7, 980)
Therefore;
y = (5/700)•x = (1/140)•x
The table is therefore;
x; 1, 2, 3, 4
y; 140 280 420 560
Question 3;
The ratio of the dozens of cookies to cups of flour, gives;
Recipe 1; R = 2/1.5 dozen per cup of flour
Which gives;
Approximately 1.33 dozens per cup of flour
Recipe 2, R = 3/3 dozens per cup of flour
Which gives;
Recipe 3, R = 4/4.5 dozens per cup of flour
Therefore;
No it is not proportional because the ratios between the number of cookies and the cups of flour are not all equivalent
Question 4
The ratio of the terms are;
18.26/36.5 = 11.6/23.2 = 1/2 ≠ 21.1/63.3 = 1/3
Therefore;
No it is not proportional because 18.26/36.5 is not equal 21.1/63.3
Question 5
Given that the graph is a straight line that passes through the origin, it is a proportional relationship with which gives;
Yes, it is a proportional relationship because, it is a line that intersects with the origin
Question 6
The number of calories burned is dependent on the number of hours worked out. For a one–hour work out 190 calories are burnt, and for a two–hours work out there are 380 calories burned
Question 7
The relationship is proportional, given that 3.5/2 = 8.75/5 = 12 .25/7 = 1.75
Therefore; Yes, because the ratios for miles per hour, are all equivalent to 1.75
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Answer:
The relationship between the input and output variables in the given table of values are;
Question 1
Yes, it is proportional, because the ratio of Dollar per hour are all equivalent to 12 dollar per hour
Question 2;
x; 1, 2, 3, 4, 5
y; 140, 280, 420, 560
Question 3
No it is not proportional because the ratio between the number of cookies, and the cups of flour are not equivalent
Question 4
No, it is not proportional because 18.26/36.5 ≠ 21.1/63.3
Question 5
Yes, it is a proportional relationship because it is a line that intersects with the origin
Question 6
The number of calories burned is dependent on the number of hours worked out. For a one–hour work out, 190 calories are burned, and for a two–hours work out, there are 380 calories burned
Question 7
Yes because the ratio of the miles per hour are all equivalent to 1.75
What is a proportional relationship?
A proportional relationship is one in which the input and output have a constant ratio, and in which the graph passes through the origin.
Question 1
A proportional relationship is one that has the x and y –intercept as the origin, (0, 0) and in which the ratio of the values at each point, y/x is a constant
Given (0, 0) is a data point and 72/6 = 144/12 = 216/18 = 12
Therefore; Yes it is proportional because the ratio for Dollar per hour are all equivalent to 12 dollar per hour
Question 2;
The points on the graph are;
(0, 0), (5, 700), (6, 840), (7, 980)
Therefore;
y = (5/700)•x = (1/140)•x
The table is therefore;
x; 1, 2, 3, 4
y; 140 280 420 560
Question 3;
The ratio of the dozens of cookies to cups of flour, gives;
Recipe 1; R = 2/1.5 dozen per cup of flour
Which gives;
Approximately 1.33 dozens per cup of flour
Recipe 2, R = 3/3 dozens per cup of flour
Which gives;
Recipe 3, R = 4/4.5 dozens per cup of flour
Therefore;
No it is not proportional because the ratios between the number of cookies and the cups of flour are not all equivalent
Question 4
The ratio of the terms are;
18.26/36.5 = 11.6/23.2 = 1/2 ≠ 21.1/63.3 = 1/3
Therefore;
No it is not proportional because 18.26/36.5 is not equal 21.1/63.3
Question 5
Given that the graph is a straight line that passes through the origin, it is a proportional relationship with which gives;
Yes, it is a proportional relationship because, it is a line that intersects with the origin
Question 6
The number of calories burned is dependent on the number of hours worked out. For a one–hour work out 190 calories are burnt, and for a two–hours work out there are 380 calories burned
Question 7
The relationship is proportional, given that 3.5/2 = 8.75/5 = 12 .25/7 = 1.75
Therefore; Yes, because the ratios for miles per hour, are all equivalent to 1.75
Step-by-step explanation:
I need to learn how to do equations with variable on both side
I will give an example on an equation with variables on both sides, then explain.
Example : 20-x = 5x - 4
→the first step in solving an equation with a variable on both sides is to get the variable on one side. This is done by reversing the addition or subtraction of one of the terms with the variable.
20-x =
Divide.
−10 ÷ −2
Drag and drop the correct number into the box to complete the sentence.
I'm not sure what the correct answers is, heh..please help me
Given expression is
[tex]\sqrt[4]{2}=2^{\frac{1}{4}}[/tex]Among the given options the simplication that applies the power rule is
[tex](2^{\frac{1}{4}})^4=2^{\frac{1}{4}}.2^{\frac{1}{4}}.2^{\frac{1}{4}}.2^{\frac{1}{4}}[/tex]This can be simplified as
[tex]2^{\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}}=2^{\frac{4}{4}}=2[/tex]Hence the corresponding simplification is D.
−67b+6≤9b+43minus, 67, b, plus, 6, is less than or equal to, 9, b, plus, 43
The variable "b" is greater than or equal to −37/76.
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.The inequality to be solved is given below :−67b+6 ≤ 9b+43Move the like terms to one side of the inequality.6−43 ≤ 9b+67bSimplify and merge the terms.−37 ≤ 76bSeparate the constant and the variable in the inequality.−37/76 ≤ bOur final result is obtained.The variable "b" is greater than or equal to −37/76.To learn more about inequalities, visit :
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please help this is due today
Carlos sells coupon booklets for $5.50 apiece. He makes $60.50. Monica sells the same books for $4.75 each and makes $57. Who sells more booklets? How many more?
Answer:
Monica sells one more book (12) than Carlos (11).
Step-by-step explanation:
Carlos: $60.50/$5.50 = 11
Monica: $57.00/$4.75 = 12
Monica sells one book more than Carlos.
Manuela is making a banner for a school dance. She makes one angle 116°. What should she make the measures of angles B and D so that the banner is a parallelogram?
64°
116°
128°
244°
Answer: 64
Step-by-step explanation:
If angle A is 116, then the angle C is also 116. As the sum of the angles of a parallelogram is 360, the sum of B and D should be 360 - 2*116 = 132. Hence, the angles B and D should be each 132/2 = 64
pls help i will give brainliest etc
Answer:
Quotient = 58.5
Step-by-step explanation:
Long division is a method used to divide large numbers by breaking the division down into multiple steps.
Parts of long division:
The dividend is the number that is divided by the divisor.The divisor is the number that divides the dividend. The quotient is the result obtained by the division.The remainder is the number left over.The divisor is placed to the left of the parenthesis.
The dividend is placed to the right of the parenthesis.
The quotient is placed above the dividend and separated from it by a bar.
To finish the given long division, subtract 64 from 68:
⇒ 68 - 64 = 4
Now divide the result by the divisor:
⇒ 4 ÷ 8 = 0.5
Finally, add 0.5 to 58 to give the final quotient:
⇒ 58 + 0.5 = 58.5
[tex]\large \begin{array}{r}58.5\\8{\overline{\smash{\big)}\,468\phantom{))}}}\\{-~\phantom{(}\underline{40\phantom{))..}}\\68\phantom{))}\\-~\phantom{()}\underline{\phantom{)}64\phantom{))}}\\4\phantom{))}\\-~\phantom{()}\underline{\phantom{)}\phantom{)}4\phantom{))}}\\0 \phantom{))}\\\end{array}[/tex]
Therefore, from inspection of the given long division:
The dividend is 468.The divisor is 8.The quotient is 58.5.A straight road named Planet Drive will connect the diner and the community garden.What is the equation of the line that represents Planet Drive? Show your work
As the line intersected the y-axis at x = 4, the equation of the line which represents planet Drive to the community garden is x = 4.
How is line equation represented?The shortest distance that separates two points is represented by a line. A line can be horizontal, slanted, or straight. A equation of a line in slope-intecept form has been expressed as:
y = mx + b
where,
m is called the slope
b is the y-intercept
From the graph shown, you recognize that the planet drive line is a horizontal as well as the general equation of the a horizontal line is represented as x = a where;
'a' is indeed the x-intercept of a line, which is the point at which the line intersects the y-axis.
Because, the line intersected the y-axis at x = 4, the equation of the line which reflects planet Drive to community garden is x = 4.
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Write an equation for the function graphed.
PLEASE SHOW WORK THANK YOU
Answer:
you nrriebr dhdhxbe ahowe a grap by doing your work
Combine like terms, if possible. Write the result with descending powers.
6x³ + 5x³+4x5
Select the correct choice below and, fill in the answer box to complete your choice.
OA. The polynomial cannot be simplified. The polynomial written in descending powers is__
OB. The polynomial can be simplified. 6x³ + 5x³+4x5=__
B. The polynomial can be simplified. 6[tex]x[/tex]³ + 5[tex]x[/tex]³ + 4[tex]x[/tex] + 5 = 11[tex]x^3[/tex] + 4[tex]x[/tex] + 5
What is the value of y? (20 points)
{question in image}
Answer:
Step-by-step explanation:
I will use cross multiplication to answer this question.
[tex]4(2y)=3y+10\\8y=3y+10\\8y-3y=10\\5y=10\\\frac{5y}{5} =\frac{10}{5} \\y=2[/tex]
I hope this helps!!!!!!!
The table represents a quadratic function. Write an equation of the function in
standard form.
X- -3,-2,-1,0
An equation of the function in standard form for the given table of values is equal to -2x² - 7x - 6 = 0.
The standard form of a quadratic equation.In Mathematics, the standard form of a quadratic equation is given by;
y = f(x) = ax² + bx + c = 0
In order to write an equation of the quadratic function in standard form, we would formulate a system of equations from the data provided in the table above as follows:
-6 = a(-3)² + b(-3) + c ⇒ -6 = 9a - 3b + c .......equation 1.
0 = a(-2)² + b(-2) + c ⇒ 0 = 4a - 2b + c .......equation 2.
-2 = a(-1)² + b(-1) + c ⇒ -2 = a - b + c .......equation 3.
From equation. 2, we derive:
c = -4a + 2b .....equation 4.
Substituting equation 4 into equation 1 and 3, we derive the following equations:
-2 = a - b - 4a + 2b ⇒ -2 = -3a + b
-6 = 9a - 3b - 4a + 2b ⇒ -6 = 5a - b
By using the elimination method, the value of a is given by:
[-2 + (-6) = (-3a + 5a) + (b + (-b)]
-2 - 6 = -3a + 5a + b - b
-8 = 2a
a = -4
Next, we would determine the value of b as follows:
-2 = -3a + b
b = -2 + 3a
b = -2 + 3(-4)
b = -2 - 12
b = -14
For the value of c, we have:
c = -4a + 2b
c = -4(-4) + 2(-14)
c = 16 - 28
c = -12.
Substituting the respective values of a, b and c into the standard form of a quadratic equation:
ax² + bx + c = 0
-4x² - 14x - 12 = 0
Dividing all through by 2, we have the following quadratic function:
-2x² - 7x - 6 = 0
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Complete Question:
The table represents a quadratic function. Write an equation of the function in standard form.
X -3, -2, -1, 0
f(x)-6, 0, -2, 0
Kim bought 0.32 pounds of ham and 0.832 pounds of turkey How many pounds did she buy altogether?
A. 1.152 pounds
B. 1.052 pounds
C. 0.864 pounds
D. 0.152 pounds
Answer: A. 1.152 pounds.
Step-by-step explanation:
Add vertically
0.320
+0.832
[tex]2+0=2[/tex]
0.320
+0.832
2
[tex]2+3=5[/tex]
0.320
+0.832
52
Since [tex]3+8=11[/tex] , the one Carries Over to the ones place.
1
0.320
+0.832
.152
[tex]1+0+0=1[/tex]
1
0.320
+0.832
1.152
Therefore, 1.152 pounds is the correct answer.
Aisha drew a square that had a side length of 2 inches. What is the perimeter of 's Aisha square ?
Compare the sides and angles by filling in the blank with a < or > symbol.
Q: 23The side opposite to larger angles is always larger than angle oppostie to smaller side.
a sideangle the
Since side opposite to angle 68 is AB and side opposite to angle 65 is CD. The angle of measure 68 is more than angle 65. So,of measure
[tex]AB>CD[/tex]In a bag there are 2 red buttons, 3 green buttons, and 4 purple buttons. A student writes the ratio for the number of purple buttons to green buttons as 3:4. Is this student correct? Explain why or why not.
Answer:
No
Step-by-step explanation:
No because it says purple to green buttons and the student put green to purple so the answer would be 4:3 not 3:4
A restaurant decides to include a 16% tip automatically in all customers’ bills. The restaurant will apply the 16% tip after applying a 5% sales tax. If the total cost of a meal is c dollars, write two different expressions that represent the total bill, including both tax and tip.
Two different expressions that represent the total bill, including both tax and tip for the meal sold by the restaurant, are:
c dollars + 5% of c dollars + 16% of c dollarsc dollars + 21% of c dollarsWhat expressions can we get for the total amount to be paid by the customer?To arrive at the amount to be paid by the customer, we first have to get the original amount that they should pay for the meal. Next, they are meant to apply the 16% tip for the total meal and this is gotten by calculating 16% of the total meal.
Next, we ought to get 5% of the sales tax which will also be applied to the total bill. When all of these are summed up, we will arrive at the total amount to be paid by the customer. Another way will be, to sum up, all of the percentages and apply them to the total bill.
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PLS ANSWER THIS MATH PROBLEM!!
For the linear function y = 2/3x + 1, we have that:
a) The slope is of 2/3 and the intercept is of 1.
b) The y-intercept is marked at y = 1 on the y-axis.
c) Using the slope and the intercept, point (3,3) is the second point used to graph the function.
d) The graph of the linear function y = 2/3x + 1 is given at the end of the answer.
What is the definition of a linear function in slope-intercept format?A linear function, in slope-intercept format, is modeled as follows:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For this problem, the function is:
y = 2/3x + 1.
Then, form item a, we have that:
The slope is of m = 2/3.The intercept is of b = 1.For item b, the y-intercept of b = 1 means that the function crosses the y-axis at b = 1.
For item c, we have to consider that the slope is of 2/3, meaning that when y increases by 2, x increases by 3. Point (0,1) is on the graph of the function, hence point (3,3) will also be, as x increases by 3 from 0 to 3 and y increases by 2 from 1 to 3.
Considering the discussion above, the graph of the function is given at the end of the answer, with the intercept and point (3,3) labeled.
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What are the next numbers on the ratios chart
The equivalent ratios are 14:56 and 5 : 20 .
A ratio in mathematics shows how many times one number appears in another. For instance, if there were eight oranges and six lemons on a fruit platter, the ratio of oranges to lemons would be eight to six.
By dividing each quantity by the sum of all the numbers' common components, ratios can be reduced (much like fractions are). The fraction is said to be in its simplest form when the ratio's numbers are the tiniest practical integers.
A and B are frequent names for the ratio's antecedent and consequent, respectively.
The given ratios are 2 : 8 and 7 : 28 . which when simplified given the ratio 1 : 4 .
Now we know that 1 / 4 = k which is the common ratio.
Hence 14 / x = k = 1 / 4
or , x = 56
Again 5 / y = k = 1 / 4
or , y = 20
Therefore the equivalent ratios are 14:56 and 5 : 20 .
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the ratio of the number of miles run to the number of miles biked is equavlent for each row in the table
When the ratio of the number of miles run to the number of miles biked is equivalent for each row in the table, the value for A is C. 2 3/4.
How to illustrate the information?It should be noted that based on the information, the table has been given and the appropriate figures have been put into it.
The constant rate will be:
7 / 3 1/2 = 2
Now we can then write the relationship and this is illustrated as:
B = 2R
where B is the distance biked
R = the distance that's run.
We want to find the missing value of A. This is illustrated as:
5 1/2 = 2 × A
2A = 5 1/2
A = 2 3/4
Therefore, based on the information given, the correct option is C.
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The ratio of the number of miles run to the number of miles biked is equivalent for each row in the table.
Complete the table for A
A 2 1/4
B 2 2/4
C 2 3/4
D 3 3/4
Angel placed a rectangular photograph on a page of the yearbook.
Rectangle ABCD, shown on the coordinate grid below, represents the location of
the photograph on the yearbook page.
The points plotted in the cartesian plane are:
A( - 6 , 8 )
B( -2 , 8 )
C( - 2 , 2 )
D( - 6 , 2 )
What is a cartesian plane?The intersection of two perpendicular lines forms a cartesian plane. The X-axis is the horizontal line, and the Y-axis is the vertical line.
1st Quadrant - x > 0 and y > 0. Thus, the sign = ( +, +).
2nd Quadrant - x < 0 and y > 0. Thus, the sign= ( -, +).
3rd Quadrant - x < 0 and y < 0. Thus, the sign = ( -, -).
4 th Quadrant - x > 0 and y < 0. Thus, the sign= ( +, -).
In this given question all the points lie in the second quadrant that is all the point are of the form ( - x, y)
Thus the points are A( - 6 , 8 )
B( -2 , 8 )
C( - 2 , 2 )
D( - 6 , 2 )
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Write an equation of a line that passes through (-1,3)and (1,4)
SOLUTION
We want to write an equation of a line that passes through (-1,3) and (1,4)
First, let us find the slope m of the line for the points (-1,3) and (1,4)
We have
[tex]\begin{gathered} m=\frac{4-3}{1-(-1)} \\ m=\frac{1}{1+1} \\ m=\frac{1}{2} \end{gathered}[/tex]Now, equation of a line in point slope form becomes
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ (x_1,y_1)=(-1,3) \end{gathered}[/tex]plugging in the values, we have
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-3=\frac{1}{2}(x-(-1) \\ y-3=\frac{1}{2}(x+1) \\ y-3=\frac{1}{2}x+\frac{1}{2} \\ y=\frac{1}{2}x+\frac{1}{2}+3 \\ y=\frac{1}{2}x+\frac{7}{2} \end{gathered}[/tex]Hence the answer becomes
[tex]y=\frac{1}{2}x+\frac{7}{2}[/tex]The yearly profits of a company is $25,000. The profits have been decreasing by 6% per year.a. What is the initial value? $ b. What is the decay factor? c. What will be the profits in 8 years? Round your answer to the nearest dollar
The initial value is the initial profits of the company, so:
Answer a: $25,000
The decay factor is the percentage in what the profits have been decreasing, so:
Answer b: 6% or 0.06
Finally, the profits every year can be calculated as:
[tex]\begin{gathered} \text{profits}=InitialValue(1-0.06)^t \\ \text{Profits}=25,000(1-0.06)^8 \\ \text{Profits}=25,000(0.609) \\ \text{Profits}=15,239 \end{gathered}[/tex]Answer c: $15,239