jane used $68 more than two fifths of her last paycheck to purchase a new surfboard. If the surfboard cost $289, find the amount of her paycheck.
Answer: Let x be the amount of Jane's paycheck.
We know that:
surfboard cost = $289
and jane used $68 more than two fifths of her last paycheck to purchase a new surfboard.
So we can set an equation as:
surfboard cost = 2/5 x + $68
289 = 2/5 x + 68
Now we can substitute the known value in the above equation:
289 = 2/5 x + 68
221 = 2/5 x
x = (2215) / 2 = 115 = 55
So the amount of her paycheck is $55.
Therefore, jane's last paycheck was $55.
Step-by-step explanation:
the set {...,-2,-1,0,1,2...} is called what?
Answer: Set of integers
Integers are positive and negative whole numbers, with 0 included.
Answer: Set of Integers
Step-by-step explanation:
{...,-2,-1,0,1,2...}
since we can see that here is a zero as well as positive and negative numbers, therefore, we call this set, a set of integers.
hope that helps...
Ques below: please answer that
Angle X and angle Y are complementary angles. The measure of angle Y is 6 less than twice the measure of angle X. What is the measure of each angle?
The measure of each angle X and Y are x = 32 degrees and y = 58 degrees
How to determine the measure of each angleFrom the question, we have the following parameters that can be used in our computation:
Angle X and angle Y are complementary angles. The measure of angle Y is 6 less than twice the measure of angle X.The above statements mean that
x + y = 90
y = 2x - 6
Substitute the known values in the above equation, so, we have the following representation
x + 2x - 6 = 90
Evaluate the like terms
3x = 96
Divide both sides by 3
x = 32
Substitute x = 32 in the equation y = 2x - 6
y = 2 * 32 - 6
Evaluate the equation
y = 58
Hence, the measure of the angle y is 58 degrees
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A linear function as a rule shown
The equation that represents the linear function is y = 11 + 7x.
What is the solution to the linear equation?
The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
We have given the rules:
x: a number
y: 11 more than 7 times x.
Linear equations are the equations of degree 1. It is the equation for the straight line.
The standard form of the linear equation is ax+by+c =0,
where a ≠ 0 and b ≠ 0.
From the given conditions we can form the linear equation:
That is,
y = 11 + 7x,
Hence, the equation that represents the linear function is y = 11 + 7x.
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A moving sidewalk carries people at a rate of 400 feet per minute. How long is this moving sidewalk if it takes 4 minutes to travel from one end to the other?
A 25 feet
B 100 feet
C 404 feet
D 1600 feet
*process
I'm not sure what I did wrong here, I only have one try at this question, please help!
LMNP is a rectangle. Find the value of x and the length of each diagonal.
The value of x is equal to 3.
The length of diagonal LN is equal to 18 units.
The length of diagonal MP is equal to 15 units.
What is a diagonal?In Mathematics, the diagonal of a rectangle can be defined as a line segment that connects any two (2) of its non-adjacent vertices together while dividing the rectangle into two (2) equal parts.
This ultimately implies that, the length of each diagonal of a rectangle is always equal to each other. Therefore, the diagonals of any rectangle is always equal to one other.
How to determine the value of x?We would determine the value of x by equating the length of each diagonal as follows;
LN = MP
7x - 3 = 4x + 3.
7x - 4x = 3 + 3
3x = 6
x = 6/2
x = 3.
Next, we would calculate length of each diagonal as follows;
LN = 7x - 3
LN = 7(3) - 3
LN = 21 - 3
LN = 18 units.
MP = 4x + 3.
MP = 4(3) + 3.
MP = 12 + 3
MP = 15 units.
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Complete Question:
LMNP is a rectangle. Find the value of x and the length of each diagonal.
LN = 7x - 3 and MP = 4x + 3.
The volume of a rectangular box is x^3+x^2-4x-4 cubic inches. If the length of the box is x+1 inches and the width is x-2 inches, what is the height , in inches, off the box in terms of x
The volume of a rectangular box can be found by multiplying the length, width, and height of the box together. So if the volume of the box is x³+x²-4x-4 cubic inches, the length is x+1 inches, and the width is x-2 inches, we can set up the equation h = (x³+x²-4x-4) ÷ (x²-x-2).
The formula for the volume of a rectangular box is V = l × w × h, where l is the length, w is the width, and h is the height of the box. This formula can also be written as V = l×w×h.
In the question you provided, the volume of the rectangular box is given as x³+x²-4x-4 cubic inches, and the length and width are given as x+1 inches and x-2 inches, respectively. With this information, we can set up an equation using the formula for the volume of a rectangular box:
(x+1)(x-2)(h) = x³+x²-4x-4
where h is the height of the box in inches. To solve for h, we can divide both sides of the equation by (x+1)(x-2) to get:
h = (x³+x²-4x-4) ÷ (x+1)(x-2)
And Now we can simplify the expression using standard algebraic operations.
h = (x³+x²-4x-4) ÷ (x²-x-2)
You can now substitute any value of x to find the height of the box.
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pls help, last question. the one circled in red
On solving the provided question, we can say that - in the linear equation y = 1/2x + 5, slope, m = 1/2
What is a linear equation?The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
here,
in the linear equation =>
y = +1/2x + 5
on comparing with y = mx +c
slope, m = 1/2
and, c= +5
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Find the length of side xx in simplest radical form with a rational denominator. 3
The length of x is 6 in simplest radical form.
What is a right-angled triangle?'A triangle in which one of the interior angles is 90° is called a right-angled triangle. The longest side of the right triangle, which is also the side opposite the right angle, is the hypotenuse and the two arms of the right angle are the perpendicular and the base.'
According to the given ,
Perpendicular = 3
Hypotenuse = x
We know,
sin∅ = 3/x
∅ = 30°
⇒ sin30 = 3/x
⇒ 1/2 = 3/x [ sin30 = /2 ]
⇒ x = 3 * 2
⇒ x= 6
Hypotenuse = 6
Applying Pythagoras theorem:
Hypotenuse² = Perpendicular² + Base²
6² = 3² + Base²
6² - 3² = Base²
Base² = 25
Base = √25
Base = 5
We can conclude the value of x to be 6.
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Complete the table as you answer the multiple choice questions below.
Complete the table with values 3, 2, 24 and 10 respectively
How to complete the table?
The constant of proportionality is the ratio of the y value to the x value i.e.
constant of proportionality (k) = y/x
The table can be completed by determining the constant of proportionality. That is:
k = y/x
where y = hours and x = magnets
k = 4/12 = 1/3
when y = 1:
1/3 = 1/x
x = 3
when x = 6:
1/3 = y/6
y = 2
when y = 8:
1/3 = 8/x
x = 24
when x = 30:
1/3 = y/30
x = 10
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Find the length of AB.
The length of AB in the line segment is 21 units.
How to find the length of a line segment?A line segment is bounded by two distinct points on a line. In other words, a line segment is a part of a line that connects two points which are considered to be its endpoints.
Therefore, let's find the length AB, in the line segment AC.
Hence,
AC = AB + BC
AC = 23
AB = 2x + 7
BC = 3x - 19
Therefore,
23 = 2x + 7 + 3x - 19
23 = 5x - 12
23 + 12 = 5x
35 = 5x
divide both sides by 5
x = 35 / 5
x = 7
Therefore,
AB = 2x + 7 = 2(7) + 7 = 14 + 7 = 21
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y to the -3 power
pls help!!!!!!!!!
Answer:
any number goes down 3 places
Step-by-step explanation:
EX:10 to the power of -3 = 0.001
hazar is having 4 friends over to play video games. Each person will spend $6 on game rental and $4 on drinks and snacks, Write two expressions for the total cost for hazar and his friends
Answer: Here are two possible expressions for the total cost for Hazar and his friends:
The first expression is to add the cost of game rental and drinks and snacks for all the four friends
6x + 4x =10x where x is the number of friends
Second expression is to calculate the cost for each of the 4 friends and then add it together
(6 + 4) * 4 = 40
Both the expressions represent the same outcome, that is the total cost of $40 for Hazar and his friends to play video games.
It's depend on how you want to represent it, both are correct and represents the same outcome.
Step-by-step explanation:
Solve 7 cos(2x) = 7 cos² (x) - 4 for all solutions
value of x for all solution is 49.11° or 50° and 230°
Which trigonometry topics should I learn first?Before mastering trigonometry, you should have a working knowledge of algebra and geometry. You ought to be able to work with algebraic expressions and equations without any trouble. The Pythagorean theorem, similar triangles, and a few other concepts from geometry should be familiar to you, but not a lot.
7 cos(2x) = 7 cos² (x) - 4
7 cos² (x) - 7 (2cos² (x)-1)- 4=0
7 cos² (x)- 14 cos² (x)+7-4=0
cos² (x)= 3/7
range given from 0 to 360°.
x=49.11° or 50° and 230°
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Find the distance between the points.
(-2.5,3), (5,3)
The distance is
Answer:
7.5 units
Step-by-step explanation:
5-(-2.5)=7.5
Moya is moving to a new house and packing up. She has 70 kilograms of books and 127 kg kilograms of clothing to send through the postal service. How much more do her clothes weigh than her books? How much is her shipping cost of sh has to pay $80 per kg of books and $200 per kg of clothing?
The amount that her clothes weigh more than her books would be = 57kg
The amount for the shipping cost for her school would be = 5600+25400 = $31000
What is postal service?Postal service is the type of service that helps.in the delivery of goods from one location to another when the goods are properly registered.
The mass of Moya's books = 70 kilograms
The mass of Moya's clothing = 127 kg
The difference between the bothe masses = 127 - 70 = 57kg
The cost per kg for books = $80 per kg
The cost per kg of clothing = $200
Therefore, the amount for the shipping cost for her school would be = (70×80) + (127 ×200)
= 5600+25400 = $31,000.
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Pls help with my math
This is the hard question for me
Thnx
Find the slope of the line passing through the points (3, 4) and (8, -3).
Answer: -7/5
Step-by-step explanation:
Mary bought 5 pounds of grapes for $19. Mark bought 4 pounds of grapes for $16. Complete the statement comparing Mary's unit rate with Mark's unit rate.
Mary paid $3.80 per pound and Mark paid $4.00 per pound.
19 ÷ 5 = 3.80
16 ÷ 4 = 4
Mary's unit rate is less than Mark's unit rate.
How to calculate expression?To compare the unit rate of Mary and Mark, we need to find how much each of them paid per pound of grapes.
Mary paid $19 for 5 pounds of grapes, so her unit rate can be calculated as:
The unit rate of Mary = Total cost of grapes / Total amount of grapes purchased
= $19 / 5 pounds
= $3.80 per pound
Mark paid $16 for 4 pounds of grapes, so his unit rate can be calculated as:
The unit rate of Mark = Total cost of grapes / Total amount of grapes purchased
= $16 / 4 pounds
= $4.00 per pound
Comparing the unit rate of Mary and Mark, we can see that Mary paid less per pound of grapes than Mark did.
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Percent | Word Problems
1) Mrs. Smith has covered 50 miles of a 125-mile journey. What percentage of the
journey has been covered by her?
Answer:
40%
Step-by-step explanation:
50/125×100%
=40%
Mr Smith has covered 40 percent of the journey
Answer:
40%
Step-by-step explanation:
50/125 ×100= 40%
5) Is y = x^3 a function. Why or why not; please use complete sentences.
Yes, the expression; y = x³ is a function because it passes the vertical line test.
What is function?Function from a set x to a set y assigns to each element of x exactly one element of y. The set x is called the domain of the function and the set y is called the codomain of the function.
There are 4 types of functions:
Functions with arguments and return values Functions with arguments and without return valuesFunctions without arguments and with return valuesFunctions without arguments and without return valuesOn this note, the set containing all possible values of x is called the domain of the function and the set y is called the co-domain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity.
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Can someone solve this please
Answer:
u=37
Step-by-step explanation:
u+41= u+4 + u (sum of 2 interior angles is equal to exterior angle)
u+41= 2u+4
2u-u= 41-4
u=37
If you need to measure the length of a run of pipe from a house to the water main on the street using metric system, which of the following units would you likely use? A. Centimeters, B. Kilometers, C. Metics D. Millimeters
Answer:
C. meters
Step-by-step explanation:
how are algebraic expressions used to represent and solve problems
Answer:
How are algebraic expressions used to represent and solve problems?
The purpose of solving an algebraic expression in an equation is to find the unknown variable. When two expressions are equated, they form an equation, and therefore, it becomes easier to solve for the unknown terms. To solve an equation, place the variables on one side and the constants on the other side.
Step-by-step explanation:
How can you use algebraic expressions to solve problems?
To solve an algebraic word problem:
1. Define a variable.
2.Write an equation using the variable.
3.Solve the equation.
4.If the variable is not the answer to the word problem, use the variable
to calculate the answer.
How are algebraic expressions applied in real life situations?
utilizing linear algebra, and this uniqueness starts to expose a lot of applications. Other real-world applications of linear algebra include ranking in search engines, decision tree induction, testing software code in software engineering, graphics, facial recognition, prediction and so on.
What is algebraic expression why it is used in mathematics?
In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). For example, 3×2 − 2xy + c is an algebraic expression.
s/4 +5=13
How do i solve thissssssss
[tex]\dfrac{s}{4} +5=13[/tex]
Simplify:
[tex]\dfrac{1}{4} s+5=13[/tex]
Subtract 5 from both sides:
[tex]\dfrac{1}{4} s+5-5=13-5[/tex]
[tex]\dfrac{1}{4} s=8[/tex]
Multiply both sides by 4:
[tex]4\times(\dfrac{1}{4} s)=4\times(8)[/tex]
[tex]\fbox{s = 32}[/tex]
s = 32.
Step-by-step explanation:1. Write the expression.[tex]\frac{s}{4} +5=13[/tex]
2. Subtract 5 from both sides of the equation.[tex]\frac{s}{4} +5-5=13-5\\ \\\frac{s}{4} =8[/tex]
3. Multiply by "4" on both sides of the equation.[tex]\frac{s}{4}*4 =8*4\\ \\s=32[/tex]
4. Verify.If the result is correct, then the equation should return the same value of both sides of the equal symbol (=) when we substitute the variable "s" by it's calculated value, 32.
[tex]\frac{(32)}{4} +5=13\\ \\8+5=13\\ \\13=13[/tex]
As you can tell, the same number appears on both sides of the equal symbol, this means that the result is correct!
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The morning temperature is -29.8 degrees. The temperature rose 33.2 degrees during the day.
What is the new temperature in degrees?
Answer:
Step-by-step explanation:use a calculator
Answer:
Step-by-step explanation:
-29.8+33.2=3.4
The patient’s weight is 245 lbs. If the patient loses 1 kg every week for 5 weeks:
a. How much will the patient weight in pounds?
b. How much will the patient weight in kilograms?
a) The patient weight in pounds is 234 lbs.
b) The patient weight in kilograms is 106.36 Kg.
What is Unit Conversion?The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.
Given:
The patient’s weight is 245 lbs.
Each week patient loses = 1 Kg
So, In 5 week patient loses = 5 Kg
As, 1 kg = 2.2 lbs
In 5 week patient loses = 11 lbs
a) The weight of the patient after 5 weeks = 245 lbs. - 11 lbs.
= 234 lbs.
b) The weight of the patient after 5 weeks = 234 lbs.
The weight of the patient after 5 weeks in Kg
= 234 lbs x 1 kg per 2.2 lbs.
= 106.36 kg
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The numerical coefficient of 3xy2 is 2 true or false
Answer:
false
Step-by-step explanation:
[tex]3xy^{2}[/tex]
The coefficient is 3
Hope this helps