[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ 2}(x-\stackrel{x_1}{(-2)}) \implies y -6= 2 (x +2) \\\\\\ y-6=2x+4\implies {\Large \begin{array}{llll} y=2x+10 \end{array}}[/tex]
If you add Alex’s and bobs pie total together, they ate 22 pies, while bobs and chucks pies sum to 24. When you add Alex and chucks pie together, you find that they are 16 total. How many pies did each individual eat?
The number of pie each got-
Alex -7Bob - 15Chuck - 9What is the method of elimination?To create an equation in one variable, use the elimination method and can either add or subtract this same equations. Whenever the coefficients with one variable are opposites, the equations are added to eliminate a variable; when the coefficients with one variable are equal, the equations are subtracted to eliminate a variable.For the given question;
Let the number of pie eaten by Alex be 'a'.
Let the number of pie eaten by Bob be 'b'.
Let the number of pie eaten by Chuck be 'c'.
Then, for the given condition.
If you add Alex’s and bobs pie total together, they ate 22 pies,
a + b = 22 .....eq 1.
Bobs and chucks pies sum to 24.
b + c = 24 .......eq 2
Alex and chucks pie together be 16.
a + c = 16 .......eq 3
Solving equation 1 and 3 by elimination.
Subtract eq 3 from 1.
c = b - 6 .....eq 4
Solving equation 4 and 2.
b = 15
Put in eq 4
c = 9
Put the values of b and c in eq 1.
a = 7
Thus, the number of pie shared by Alex, Bob and Chuck are 7, 15 and 9 respectively.
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Question
What numbers are a distance of 23 unit from 12 on a number line
Answer:
distance: 11
there are 11 points between 12 and 23, they are:
12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 and 23.
Step-by-step explanation:
PLEASE HELP THIS IS DUE❗️❗️❗️❗️❗️
Answer:
Step-by-step explanation:x=-2x
if c=4 work out the value of
c/2 + 6
Using arithmetic operations, If the value of c = 4 then the value of (c/2) + 6 is 7
The given expression is (c/2) + 6
The value of c = 2
To find the value of (c/2) + 6 we have to do the suitable arithmetic operation after substituting the value c in the expression
Substitute the value of c in the given expression (c/2) + 6
(c/2) + 6 = (2/2) + 6
Divide 2 by 2 first
(2/2) + 6 = 1+6
Add one and six
1+6 = 7
Hence, by using the arithmetic operation, if the value of c = 4 then the value of (c/2) + 6 is 7
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please look at the pic
By using internal angles of the triangles and the definition of supplementary angles, the measure of the angle MNP is equal to 54°.
How to determine a missing angle in a geometric systemHerein we find a geometric system formed by two common semirrays with a common vertex at point N and a line segment MP such that triangle MPN is a right triangle. By Euclidean geometry we know that the sum of the measures in the internal angles equals 180°:
m ∠ NMP + m ∠ MNP + m ∠ MPN = 180° (1)
And the two angles at point P are supplementary angles:
24 · x + m ∠ MPN = 180° (2)
Then, by (1):
90° + 9 · x + m ∠ MPN = 180°
m ∠ MPN = 90° - 9 · x
By (1) in (2):
24 · x + 90° - 9 · x = 180°
15 · x = 90°
x = 6
Then, the measure of the angle MPN is equal to:
m ∠ MNP = 9 · x
m ∠ MNP = 9 · 6
m ∠ MNP = 54°
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Which number sentence is true? OA. 2 3/4 >2.68 2² OB. 7.895 x 10² > 5.43 x 10³ OC. √63>811 OD. 1-151> 13.21
All the expressions like (a), (b) and (c) are true sentences in the form of inequality.
What is inequality expression?
The inequality expression in a sentence consist of two algebraic expression with the inequality symbols. And the solution of an inequality is a number which when substituted for the variable to makes the inequality as a true statement.
According to the question, the given inequality expressions in the form of the sentence is as follows:
(a) 2(3/4) > 2.68;
(b) 7.895 x 10² > 5.43 x 10³;
(c) √63 > 8.11;
(d) |-1.5| > |3.2|
In this, all the expressions like (a), (b) and (c) are true sentences in the form of inequality.
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G(x)=-x^2/4+7
Over which interval does have a negative average rate of change?
Answer: [tex](-\infty, 0][/tex]
Step-by-step explanation:
This is a parabola that opens down (because of the negative leading coefficient).
So, the average rate of change (i.e., the slope of the secant) is negative when the function is decreasing.
The function is decreasing to the left of the vertex, which is at (0, 7).
So, the function has a negative average rate of change for [tex](-\infty, 0][/tex].
Note that although there is a stationary point at x = 0, and that the graph isn't decreasing at this point, the average rate of change is still negative when considering a point to the left.The sum of twice a number and eight is 20. What is the number?
Answer:
6
Step-by-step explanation:
let the number be equal to x
The sum of twice a number= 2x
2x+8=202x=20-82x=122x/2=12/2x=6there are 10 boys and 15 girls. The teacher chooses a student by random. Eric says that the probability for a boy to be chosen is 0.5. Jenny says he is wrong. Who is correct. Give reasons
In a case whereby there are 10 boys and 15 girls and the teacher chooses a student by random, then the probability that a boy will be chosen is 2/5 which means Jenny is right.
How can the probability be calculated?Since there are there are 10 boys and 15 girls, then the total number of the population will be (10+15)=25
Then the probability of that a boy will be chosen if one of them is been chosen at random will then be =10/25 = 2/5
Therefore, Jenny is very correct because the probability of that a boy will be chosen if one of them is been chosen at random will then be 2/5.
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Trevor tutors French for $15 and hour and scoops ice cream for $10 an hour. He iS going to work 15 hours
this week. How many hours does Trevor need to tutor to make at least $180?
hours
Inequality - Trevor needs to tutor more than 6 hours in order to make at least $180.
What is inequality?
inequality, A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to. Either questions or theorems can be used to express inequality problems, and both can be solved using methods similar to those used to solve equations. The triangle inequality, for instance, states that the length of the remaining side of a triangle is greater than or equal to the sum of the lengths of any two of its sides. Many of these inequalities, including the Cauchy-Schwarz inequality, are used by mathematical analysis to prove some of its most significant theorems.
Total number of hours = 15
Let the hours spent tutoring French is x
Therefor, hours spent in scooping ice cream = (15-x)
Tutoring French is $15 an hour, total for x hours = 15x
Scooping ice cream is $10 an hour, 10×(15-x)= 150-10x
To make more than $180,
= 15x+ (150-10x)> 180
= 15x+150-10x>180
=15x-10x>180-150
=5x>30
=x>6
So, Trevor needs to tutor more than 6 hours.
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Arrange the numbers 1 to 9 so that the sum of the three numbers in any straight line = 15
Answer:
1 8 6
9 4 2
5 3 7
Step-by-step explanation:
1) When solving problems like this it is best to start with the smallest number. In this case the smallest number was 1, so that was placed in the top left corner.
2) The smallest number must be next to the two largest numbers so, 8 and 9 can be placed on its sides
1 8
9
3) solve for the final spots in the first row and the first column.
Row:
1 + 8 = 9
15 - 9 = 6
Column:
1 + 9 = 10
15 - 10 = 5
So,
1 8 6
9
5
3) Looking at the largest unused number, number 7, we can see that it is too large to go in the second row or the second column. This means it must be placed in the lower right corner
1 8 6
9
5 7
4) At this point you have enough information to solve for the rest of the numbers using simple addition and subtraction
34= -w/7 solve for w
Hey! Your question was incomplete because I have double-checked my work, and even checked reliable sources to see if I missed something in my work, but I keep getting –238. I did play around with the question by switching the negative symbol around in the equation to see if I would get a balanced answer. I say this because when you solve the question you posted, the answer I got was w = –238, but when I went back to check my work by plugging that number in as the value of w, I got –238 ≠ 238 (or something like that. The number is the same, but the signs are not). If the signs and numbers don't both equal each other something is wrong with the problem. I believe I figured out where your question went wrong. Instead of the question being 34 = –w/7, I believe that the correct question should have been –34 = w/7. What I think happened was that when you typed your question, you swapped the negative on the 34 with the variable of w. If I am incorrect, and you typed your question correctly, I am sorry in advance because my work wasn’t matching what I got for w. But for now, I will solve what I think the question should have said. Again, sorry in advance. Solve for w in the following equation: –34 = w/7.
Write the equation:
–34 = w/7
Multiply both sides by 7:
7 × –34 = w/7 × 7
Multiply:
–238 = 1w
Divide:
–238/1 = 1w/1
–238 = w or w = –238
Check your work by plugging –238 back into the equation as w:
–34 = w/7
–34 = –238/7
Multiply both sides by 7:
–34 × 7 = –238/7 × 7
–238 = –238 ✔
Thus, w = –238
Hope that helps! Have an amazing rest of your day!! :)
A cash discount of 8% is allowed on an item which costs £45. How much money is saved if a customer decides to pay in cash?
If a costumer decides to pay in cash then saved £3.6.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
A cash discount of 8% is allowed on an item which costs £45.
Now, The amount of Saved money calculated as;
Since, A cash discount of 8% is allowed on an item which costs £45.
Hence,
Saved money = 8% of £45
= 8 x 45 / 100
= 3.6
Thus, Saved money = 3.6
Therefore, If a costumer decides to pay in cash then saved £3.6.
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Write an equation for the line through the points (6, 10) and (3, 5) in point-slope form.
y =
+
Point slope form of the equation through the points (6, 10) and (3, 5) is y - 5 = 5/3 (x - 3)
Point slope form:
The point slope form of equation is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point.
The general form of the equation is
(y - y1) = m (x - x1)
y = y coordinate of second point
y1 = y coordinate of point one
m = slope
x = x coordinate of second point
x1 = x coordinate of point one
Given,
Here we have the points (6, 10) and (3, 5).
Through the given points we have to find the point slope form of the equation.
To find the point slope of the equation, first step is to find the slope of those points,
It can be calculated using the formula,
m = (y2 - y1)/(x2 - x1)
Where the values of (x1,y1) is (6,10) and the values of (x2,y2) is (3,5).
Then the value of slope after applying the values,
m = (5 - 10)/(3-6)
m = -5/-3
m = 5/3
Use the slope and a given point (3,5) to substitute for x1 and y1 in the point-slope form
y−y1=m(x−x1),
which is derived from the slope equation.
Then we get the equation as,
y - 5 = 5/3 (x - 3)
Therefore, the point slope form equation is y - 5 = 5/3 (x - 3).
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2-b/3= -5/2 if you guys can help me thank you very much.
Answer:
b = 13.5
Step-by-step explanation:
2-b/3 = -5.2Multiply both sides of the equation by 6, the least common multiple of 3,212 - 2b = -15Subtract 12 from both sides-2b = -15 - 12Subtract 12 from -15 to get -27-2b = -27Divide both sides by -2b = -27/-2You can simplify -27/-2 by dropping off the negative sings making it b = 27/2Divide 27/2 to get 13.5 Or you can just simplify 27/2 to 13 1/2There are different ways you can solve this equation. Let me know if you'd like to know a different way.
Have a Good Rest of Your Day.
Do the ratios 9 6 and 12 8 form a proportion?
The ratios 9:6 and 12:8 does not form a proportion, since the products of the two are not equal.
Given we have two ratios:
9:6 and 12:8
An equation in mathematics that shows that two ratios expressed in fraction form are equivalent is known as a proportion. The rule that says a/b= c/d if and only if ad=bc allows us to assess whether two ratios, a: b and c: d, constitute a proportion.
To determine if 9:6 and 12:8 form a proportion, we use the rule of proportion.
That is, 9/12 = 8/6
If only if 9×6=12×8
Therefore, 9×6=54
and 12×8=96
since these two products are not equal, we have that 9:12 and 8:6 do not form a proportion.
Hence the ratios 9:6 and 12:8 are not in proportion.
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-2x + 3y = -6 and -3x - 2y = 11
Step-by-step explanation:
-2x + 3y = -6
-3x - 2y = 11
-5x + y = 5
y = 5 + 5
y = 10
-2x + 3(10) = -6
-2x + 30 = -6
-2x = -6 - 30
-2x = -36
x = -18
i have no idea
Exercises
Write an algebraic expression for each verbal expression.
Four times a number?
The mathematical expression is as follows.
1) 4(v +3)
2) 15v -7
What is algebraic expression?An algebraic expression is one that has been constructed using integer constants, variables, and algebraic operations. A good example of an algebraic expression is 3x 2 2xy + c.
Given Data
Suppose the number is v
1) To obtain: four times the product of v and 3.
Accordingly, we must first add v and 3, and then multiply the result by 4.
The mathematical expression is as follows.
= 4(v+3)
2) Assume that v is the given integer.
What we're aiming for is: 7 less than 15 times v.
This calls for multiplying the v by 15 and then taking 7 out of the result.
The expression in algebra would be as follows:
= 15v - 7
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A cylindrical container is to be constructed so that the sum of its height and its diameter is 15 feet.
a) Write an equation relating the height of the cylinder, h, to its radius, r. Solve the equation for h in terms of r.
b) The volume of a cylinder is given V=πr^2h. Use your answer in part A to express the volume of the cylindrical container in terms of r alone. Leave your expression in factored form so that it will be easier to analyze.
c) What are the values of r for which this problem makes sense? Explain.
From the characteristics of the given cylinder, we have that:
a) The equation is h = 15 - 2r.
b) The volume of the cylinder is of V = πr²(15 - 2r).
c) The values of r should be in the range of 0 < r < 7.5.
What is the volume of a cylinder?The volume of a cylinder of radius r and height h is given according to the following equation:
V = πr²h.
The sum of the height and the diameter is of 15 feet, hence:
h + d = 15.
The diameter is twice the radius, hence:
h + 2r = 15.
For item a, the solution of h in terms of r is:
h = 15 - 2r.
Hence, in item b, the equation is:
V = πr²h.
V = πr²(15 - 2r).
For item c, there are two constraints, as follows:
r > 0, as the radius of a cylinder cannot be negative nor zero.r < 7.5, as the height must be positive.More can be learned about the volume of a cylinder at https://brainly.com/question/9554871
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-1 1/3 - 1/6 subtract using number line
The addition of the two negative numbers has a result of -3/2, and is illustrated on the number line given at the end of the answer.
How to add two negative numbers?To add two negative numbers, we keep the negative signal and then we add the quantities, that are represented by the numbers without the signal.
For this problem, the numbers are given as follows:
-4/3, which is the mixed number -1 and 1/3, given by -1 - 1/3 = -3/3 - 1/3 = -4/3.The fraction -1/6.Hence the addition of the negative numbers is given as follows:
-4/3 - 1/6 = -8/6 - 1/6 = -9/6 = -3/2.
The result is of -3/2.
As for the number line, we have two negative numbers, hence each increment is to the left of the number line. The sum of the two increments, starting at zero, of 1/6 and of 4/3, combine to 3/2, as given by the image at the end of the answer.
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TASK E5.1
1 The length, width and height of the cuboid are
measured to the nearest cm.
volume = length x width x height
What is the lowest possible value
of the volume of the cuboid?
Main Book Page 139
7 cm-
4cm
9cm
The length, width and height of the cuboid are measured to the nearest cm, volume = length x width x height, the lowest possible value of the volume of the cuboid is [tex]cm^{3}[/tex].
What is volume?Volume is measurement of three-dimensional space that is occupied. Numerous imperial units or the SI-derived units, such as the cubic meter and liter, are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). Volume and length (cubed) have symbiotic relationship. The volume of a container is typically thought of as its capacity, not as amount of space it takes up. In other words, volume is the amount of fluid (liquid or gas) that the container may hold.
Volume was initially measured using naturally occurring vessels of a comparable shape and then with standardized containers. Arithmetic formulas can be used to quickly calculate volume of several straightforward three-dimensional shapes. If a formula for the shape's boundary is known, it is possible to use integral calculus to determine volumes of more complex shapes. No object in the dimensions of zero, one, or two has volume; in the dimensions of four and above, the hypervolume is a concept similar to the standard volume.
Volume = 7cm*4cm*9cm = 252[tex]cm^{3}[/tex]
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Suppose sin a + cos b = -0.2 while sin b + cos a = 1.6. What is the value of sin(a+b)?
The value of the trignometric expression sin(a+b) is 0.3.
Given the trignometric equations sin a + cos b = -0.2 and sin b + cos a = 1.6
So, squaring both equations and adding them
we have
[tex](sin a + cos b)^2 = -0.2^2\\(sin a + cos b)^2 = 0.04\\sin^2a+cos^2b + 2 sina cos b= 0.04\\(sin b + cos a)^2 = 1.6^2\\sin^2b+cos^2a + 2 sinb cos a= 2.56\\\\[/tex]
adding both equations
[tex]sin^2a+cos^2b + 2 sina cos b + sin^2b+cos^2a + 2 sinb cos a= 0.04+2.56\\[/tex]
1+1+2( sina cos b + cos a sin b)= 2.6
2( sina cos b + cos a sin b) = 0.6
( sina cos b + cos a sin b) = 0.3
We know that sin(a+b)= ( sina cos b + cos a sin b)
So,
sin(a+b)=0.3
Therefore, the value of sin(a+b) = 0.3
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Identify which graph can be used to solve each equation. Enter the letter of the correct graph next to the
equation.
Pleaseee help me
is Figure C a scaled copy of Figure D (Thank you!)
Answer:
Step-by-step explanation:
Figure D is a dialation of Figure C.
Each of the sides of Figure D is proportionate to Figure C
The scale factor is 1.5
3:2 = 4.5:3 = 3:2=3:2
what is 1+1x3/2+10x3450/2+300-500 I don't know what is it
Answer:
17052 1/2
You're Welcome
100 Points!!
Activity
A submarine is at a depth of 100 feet below sea level. Then it starts to dive at a rate of 50 feet per minute. Use this information to answer the following questions.
Question 1
Part A
For this situation, what is the independent variable (include units)?
Part B
What is the dependent variable (include units)?
Part C
What is the slope of the line that models this situation?
Part D
What is the y-intercept of the line that models this situation?
Question 2
Write the equation of the line that models the situation using the slope and y-intercept found in parts C and D of question 1.
Answer:
See below.Step-by-step explanation:
The initial depth is 100 feet below sea level or 100 ft.
Diving rate is 50 feet per minute or 50 ft/min.
Question 1Part AThe diving rate is the independent variable, which is:
50 ft/minPart BThe depth at any point is the dependent variable, which is different after number of minutes, in ft.
Part CThe slope is the diving rate in this situation.Part DThe initial depth is the y-intercept, the starting point.Question 2The equation of the line is:
y = mx + b, substituting the values,y = 50x + 100Answer:
Independent variable: Time in minutes
Dependent variable: The elevation in feet
Slope: -50
Y-Intercept: -100
Step-by-step explanation:
Just did the assignment
find the compound interest on $1500 for 2years at 2%per annum compounded anually
Answer:
$1560.60
Step-by-step explanation:
PV (1+V)^n
= 1500 (1+2%)² = 1560.6
step by step 9 divided by 1557
Answer:
0.00578034682
Step-by-step explanation:
9/1557
keep on adding .0 to the end of your number.
You will eventually get the answer.
Answer:
173.
Step-by-step explanation:
multiply 2^3x^3.6^3x^3
The expression is multiplied to give 1728x^6
What are index forms?Index forms are simply defined as the power or exponent of a variable, number or element.
It is also seen as an arithmetic method of writing numbers that are too large or too small into simpler forms.
The rules of exponents are;
Add the powers if they are being multiplied the bases are the sameSubtract the exponents if they are divided and have the same base.Multiply the exponents when the bases of the forms are the sameGiven the expression;
2^3x^3.6^3x^3
We have to determine the product of the index forms
First, we have to multiply the numbers, we have;
2^3 = 2 × 2 × 2 = 8
6^3 = 6 × 6 × 6 = 216
Now, substitute the values
8x³ × 216x³
Multiply through
1728x^3 + 3
1728x^6
Thus, the value is 1728x^6
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a researcher is interested in the travel time of utrecht university students to college. a group of 50 students is interviewed. their mean travel time in 16.7 minutes. for this study the mean of 16.7 minutes is an example of a:
For this study, the mean of 16.7 minutes is an example of a (B) Statistic.
What do we mean by Statistic?As opposed to methods for gathering statistical data, mathematical statistics is the application of probability theory, a subfield of mathematics, to statistics. Mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory are some of the specific mathematical methods used in this. Due to the abstract concepts and ideas that you will encounter later in your study, statistics stands out as the more challenging area of math. When you actually try to understand what's happening in a statistics equation or problem, you'll discover that the concepts are very challenging.So, the appropriate choice is an option (B).
In this case, a researcher is interested in how long it takes Utrecht University students to get to class. For this study, a sample of 50 students was gathered, and the sample mean for travel time was found to be 16.7 minutes.Since the sample means is a sample statistic, option (B) is the right choice.Therefore, for this study, the mean of 16.7 minutes is an example of a (B) Statistic.
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The correct question is given below:
A researcher is interested in the travel time of Utrecht University students to college. A group of 50 students is interviewed. Their mean travel time in 16.7 minutes. For this study, the mean of 16.7 minutes is an example of a(n)
A. Parameter
B. Statistic
C. Population
D. Sample.