matt and brian were solving a system of equations. they both noticed that the two lines had the same slope. brian said that because each line in the system had the same slope, the two lines had to be parallel, which meant the solution to the system was "no solution" matt disagreed, and said they should also look at the y-intercepts before determining how many solutions there were. who is correct?

Question 1:

For this case we have that by definition, the area of a circle is given by:

[tex]A = \pi * r ^ 2[/tex]

Where:

r: It is the radius of the circle.

They tell us that the diameter is 9 inches, then the radius is 4.5 inches. substituting we have:

[tex]A = \pi * (4.5) ^ 2\\A = \pi * 20.25\\A = 63.59[/tex]

Thus, the area of the circle is[tex]63.59 \ in ^ 2[/tex]

ANswer:

Option C

QUestion 2:

For this case we have that by definition, the volume of a cylinder is given by:[tex]V = \pi * r ^ 2 * h[/tex]

Where:

r: It's the radio

h: It's the height

According to the data we have to:

[tex]r = 6.8 \ meters\\h = 14 \ meters[/tex]

Substituting in the formula:

[tex]V = \pi * (6.8) ^ 2 * 14\\V = \pi * 46.24 * 14\\V = 2032.71[/tex]

Finally, the volume of the cylinder is [tex]2032.71 \ m ^ 3[/tex]

Answer:

Option C

Question 3:

For this case we have that by definition, the volume of a cylinder is given by:

[tex]V = \pi * r ^ 2 * h[/tex]

Where:

r: It's the radio

h: It's the height

According to the data we have to:

[tex]r = \frac {5} {2} = 2.5 \ feet\\h = 7.4 \ feet[/tex]

Substituting in the formula:

[tex]V = \pi * (2.5) ^ 2 * 7.4\\V = \pi * 6.25 * 7.4\\V = 145.23[/tex]

Finally, the volume of the cylinder is [tex]145.23 \ ft ^ 3[/tex]

Answer:

Option B

Question 4:

For this case we have that the volume of the bricks comes given by:

[tex]V = 11 * 5 * 3\\V = 165[/tex]

The volume of each brick is [tex]165 \ in ^ 3.[/tex]

On the other hand, we have that the volume of the crate is also obtained by multiplying its three dimensions, that is:

[tex]V = 55 * 20 * 12V = 13,200[/tex]

Thus, the volume of the crate is [tex]13,200 \ in ^ 3[/tex]

We divide the volume of the crate between the volume of the brick to know the quantity:

[tex]\frac {13,200} {165} = 80[/tex]

Thus, 80 bricks fit.

Answer:

Option A

Answer:

5).  Option C.  63 inches

6). Option C.  2032.71 m³

7). Option b.  145.23 ft³

8). Option a.  80

Step-by-step explanation:

To find the answers

Question 5

Here r = 9/2 = 4.5

Area of circle = πr²

 = 3.14 * 4.5²

 = 63.585 ≈ 63

Option c is the correct answer

Question 6

Here r = 6.8 m and h = 14 m

Volume of cylinder = πr²h

 = 3.14 * 6.8² * 14

 = 2032.71 m²  Option C

Question 7

Here r = 6.8 m and h = 14 m

Volume of cylinder = πr²h

 = 3.14 * 5² * 7.4

 = 145.23 feet²  Option b

Question 8

Volume of one brick = lbh

 = 11 * 5 * 3

Volume of crate = 55*20*12

number of briks = Volume of crate /Volume of one brick

 = (55*20*12)/(11 * 5 * 3)

= 80   Option a

Answer:

The width should be more than 5 m. So it can be  6,7 ...

Step-by-step explanation:

The length of a flower garden is = 9 m

The width of a flower garden is   = w

The area of a flower garden > 45 sq. m

The area of a flower garden  = l * b

l * b > 45

9 * b > 45

the width should be more than 5 m. So it can be  6,7 ...

Answer:

w > 36

Step-by-step explanation:

i got it right on edgeinuity

There are three types of correlation.

1) Positive correlation: Two variables are said to be positively correlated when one variable increase then other variable will also increase or one is decrease then other will also decrease.

2) Negative correlation between two variables means when x is increasing but y is decreasing or vice versa.

3) No correlation: When the is scattred and we won't be able to find any distinct relationship then there will be no relation.

Notice in the first and third graph it has positive slope which means if x is increasing then y is also increasing. So, first and third graph is positively correlated.

Whereas in the second graph if x is increasing then y is decreasing. So, second graph is negatively correlated.

But in the last graph there is no such relationship as the data scattered randomly everywhere in the graph. So, it's shows no correlation.

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The last graph shows no correlation.

Option D is the correct answer.

Correlation is a statistical measure that indicates how strongly two variables are related or associated with each other.

It is a way of expressing the degree to which one variable is related to another variable.

We have,

The correlation is of different types.

- Positive correlation:

As one variable increases, the other variables also increase.

- Negative correlation:

As one variable increases, the other variables also increase.

- No correlation:

The variable increase and decrease as one variable increases.

Now,

We see that,

The last graph shows no correlation.

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Answer:

So it's B.

Step-by-step explanation:

Because 2a+3b, a= -1 and b = 0

so, 2(-1) + 3(0)

        -2 + 0 = -2

Hope my answer has helped you and if not i'm sorry.

By using the principles of similar triangles and setting up a ratio based on the given information, we can determine that the tree is approximately 22.22 feet tall.

We can solve this problem using similar triangles. In this case, the person (Mac) and his shadow form one triangle, while the tree and its shadow form another triangle. It's given that Mac is 5 feet tall and casts a 4 foot 6 inch (or 4.5 feet) shadow. At the same time, a nearby tree casts a 20 foot long shadow. The question asks, how tall is the tree?

What we need to do here is simple: set up a proportion using the ratios of the lengths of the sides of these two triangles. The ratio is height to shadow. So, let's use the information given:

Equating both ratios gives us: 5/4.5 = T/20. Solving this equation for 'T' will give us the height of the tree in feet.

Therefore, to compute 'T', cross multiply to get: T = (5*20)/4.5 = 22.22 feet approximately.

So, the tree is approximately 22.22 feet tall.

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Add the cost of the three items:

8 + 5 + 15 = $28

Subtract that amount from the total:

29.82 - 28 = $1.82 ( amount he paid in tax)

Divide the tax amount by the cost of the items:

1.82 / 28 = 0.065

Multiply that by 100:

0.065 x 100 = 6.5% sales tax rate

Answer:

50.

Step-by-step explanation:

the range is the lowest number subtracted from the highest; in this case, 93-43.

Answer:

54

Step-by-step explanation:

Given:

[tex]3(a + b + c) 2[/tex]

Input the numbers provided into the equation

3(2 + 3 + 4)2

Add all of the numbers inside the parentheses

3(9)2

Multiply

3 * 2 = 6

6 * 9 = 54

Hey there! :)

3(a + b + c)2 ; when a = 2, b = 3, c = 4

In order to evaluate this, we simply need to plug everything in then simplify/

3(2 + 3 + 4)2

Simplify everything inside the parenthesis first.

3(9)2

Simplify.

27 × 2

Simplify.

54 is our final answer.

Hope this helped! :)

Answer:

Third option: 80 people.

Step-by-step explanation:

Let be "x" the number of people that were surveyed.

You know that 48 people chose winter as their favorite season and these amount of people are the 60% of those questioned.

Knowing this,  you can calculate  the number of people that were surveyed with this procedure:

[tex]x=\frac{(48\ people)(100\%)}{60\%}\\\\x=(48\ people)(\frac{5}{3})\\\\x=80\ people[/tex]

Therefore, 80 people were surveyed. This matches with the third option.

Answer:

The first glass

Step-by-step explanation:

I believe that first, you must find the ratio of lemonade to water in each glass.

[Remember that you can write a ratio in 3 ways (assume that x and y are numbers):

x : y

x / y

x  to  y

Now, our first glass of lemonade can be written as 5/8. If you were to write 5/8 as a decimal, you'd get 0.625.

Now, our second glass of lemonade can be written as 3/7. If you were to write 3/7 as a decimal, you'd get 0.428 (I rounded it to the nearest thousandth.)

0.625 > 0.428

0.625 is greater than 0.428, so therefore, the first glass had a stronger lemon flavor.

I hope this helps! :)

Step-by-step explanation:

The first glass has a total volume of 5 oz + 8 oz = 13 oz.  Of the 13 oz, 5 oz is lemon juice, so the fraction of lemon is 5/13.

The second glass has a total volume of 3 oz + 7 oz = 10 oz.  Of the 10 oz, 3 oz is lemon juice, so the fraction of lemon is 3/10.

We need to compare these fractions.  To do that, we need to find the common denominator.  In this case, 10×13 = 130.

5/13 = 50/130

3/10 = 39/130

So the first glass has the stronger lemon flavor.

bearing in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-2}{2-(-3)}\implies \cfrac{-1}{2+3}\implies -\cfrac{1}{5} \\\\\\ \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-2=-\cfrac{1}{5}[x-(-3)]\implies y-2=-\cfrac{1}{5}(x+3)[/tex]

[tex]\bf y-2=-\cfrac{1}{5}x-\cfrac{3}{5}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{5}}{5\left(y-2 \right)=5\left( -\cfrac{1}{5}x-\cfrac{3}{5} \right)}\implies 5y-10=-x-3 \\\\\\ 5y=-x+7\implies x+5y=7[/tex]

Answer:

3.95m + 8.95b = 47.65

Step-by-step explanation:

From this problem, you get quite a handful of information.

The variable "m" represents the # of magazines Hugh bought.

The variable "b" represents the # of books Hugh bought.

One magazine [m] cost $3.95

One book [b] cost $8.95

The total cost of books and magazines is $47.65

Based on the information, you can create an equation with two variables, representing the total cost and how many of each magazine and book Hugh bought.

If one magazine cost $3.95, the amount of money he spent on magazines can be represented by 3.95m.

If one book cost $8.95, the amount of money he spent of magazines can be represented by 8.95b.

And lastly, if the total cost of magazines and books Hugh bought is $47.65, the following equation can be made:

3.95m + 8.95b = 47.65

So, "3.95m + 8.95b = 47.65" is the correct equation. I hope this helps! :)

Answer:

32%

Step-by-step explanation:

The given table in the correct format is attached in the image below. We need to tell what percentage of students from the grades 9 - 10 like rap music.

Total number of students in grades 9 - 10 = 125

Number of students in grades 9 - 10 who like rap music = 40

Percentage of students in grades 9 - 10 who like the rap music will be calculated as:

[tex]\frac{\text{Number of students in grades 9-10 who like rap music}}{\text{Total number of students in grades 9-10}} \times 100 \%[/tex]

Using the given values in above expression we get:

[tex]\frac{40}{125} \times 100\%\\\\= 32\%[/tex]

This means 32% of the students in grades 9 - 10 like rap music

Answer:

B: 32% I got it Correct on my test.

Step-by-step explanation:

Hope this helps :)

Step-by-step explanation:

To find the LCM, we must check and find the value that all four denominators can divide without a remainder.

Let's take 48

Therefore: 48/8= 6

48/16= 3

48/3= 16

48/2= 24

So, we can see that clearly 48 is our LCM

Therefore; 6(3/8)+3(5/16)+16(2/3)+24(1/2)

=18/48+15/48+32/48+24/48

=(18+15+32+24)/48

=89/48

Answer:

Its 48 to clarifiy instead of a long paragraph

Step-by-step explanation:

Answer:

She can double the base length of the base so that the new volume is 120 cubic inches

Step-by-step explanation:

The method she can use to double the volume of triangular pyramid is she can double the base length of the base so that the new volume is 120 cubic inches.

A tetrahedron, also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ordinary convex polyhedral and the only one that has fewer than 5 faces.  

Volume of triangular pyramid :

Volume of triangular pyramid = 1/3 × Base Area × Height

According to the question

Naomi made a triangular pyramid from cardboard.  

The triangular base has a height = 4 inches

The triangular base has a base length = 15 inches

The height of the pyramid = 6 inches  

Therefore,

Base area of triangular pyramid

= [tex]\frac{1}{2} * Base\ of\ triangle * Height\ of\ triangle[/tex]

= [tex]\frac{1}{2} * 15 * 4[/tex]

= 30 [tex]inches ^{2}[/tex]

So,

Volume of triangular pyramid = 1/3 × Base Area × Height

                                                   = [tex]\frac{1}{3}[/tex] × 30 × 6

                                                   = 60  [tex]inches ^{3}[/tex]

Now,

Naomi wants to double the volume of the triangular pyramid

i.e

New Volume of triangular pyramid = 120 [tex]inches ^{3}[/tex]

Which can be obtain if she can double the base length of the base  

Hence, the method she can use to double the volume of triangular pyramid is she can double the base length of the base so that the new volume is 120 cubic inches.

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Check the picture below.

so the vertex at the bottom is exactly half-way of the opposite side, and equidistant from the other two vertices, meaning the two slanted sides are twins, and thus this is an isosceles triangle.

Answer:

[tex]f(x)=7(b)^{x}-2[/tex]

[tex]f(x)=-5(b)^{x}+10[/tex]

Step-by-step explanation:

we know that

The y-intercept is the value of y when the value of x is equal to zero

Verify each case

case 1) we have

[tex]f(x)=7(b)^{x}-2[/tex]

so

For x=0

[tex]f(0)=7(b)^{0}-2[/tex]

[tex]f(0)=7(1)-2=5[/tex]

therefore

The function has a y-intercept of (0,5)

case 2) we have

[tex]f(x)=3(b)^{x}-5[/tex]

so

For x=0

[tex]f(0)=3(b)^{0}-5[/tex]

[tex]f(0)=3(1)-5=-2[/tex]

therefore

The function does not have a y-intercept of (0,5)

case 3) we have

[tex]f(x)=5(b)^{x}-1[/tex]

so

For x=0

[tex]f(0)=5(b)^{0}-1[/tex]

[tex]f(0)=5(1)-1=4[/tex]

therefore

The function does not have a y-intercept of (0,5)

case 4) we have

[tex]f(x)=-5(b)^{x}+10[/tex]

so

For x=0

[tex]f(0)=-5(b)^{0}+10[/tex]

[tex]f(0)=-5(1)+10=5[/tex]

therefore

The function has a y-intercept of (0,5)

case 5) we have

[tex]f(x)=2(b)^{x}+5[/tex]

so

For x=0

[tex]f(0)=2(b)^{0}+5[/tex]

[tex]f(0)=2(1)+5=7[/tex]

therefore

The function does not have a y-intercept of (0,5)

Answer:

The answer is 7 hours

Step-by-step explanation:

20 times 7 is 140 and 15 times 7 is 105 so 105 plus 35 is 140 hence the answer is 7 hours.

The number of hours that each man works will be 7 hours. Then the correct option is A.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Kenji and Antwan have jobs that pay differently. Antwan gets paid an hourly wage of $20. Kenji gets paid an hourly wage of $15 and receives $35 a day in tips.

Both men worked h hours on Tuesday and earned the same amount of money. If the equation 20h = 15h + 35 models this situation.

Then the solution to the equation will be

20h = 15h + 35

5h = 35

h = 7 hours

The number of hours that each man works will be 7 hours. Then the correct option is A.

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There are two ways to solve this question:

1. The quickest way to solve this question is perhaps to try substitute an x-value from the table into each of the possible answer equations and seeing if it returns the same y-value as in the table.

Let us use point (0, 2) from the table:

A. y = 12x - 5

if x = 0: y = -5

The value we wanted is 2, therefor A is not correct

B. y = -5x + 2

if x = 0, y = 2

This is correct, however to check if it really is this equation we should substitute a few more points in.

if x = -2: y = -5(-2) + 2 = 12 (correct)

if x = -1: y = -5(-1) + 2 = 7 (correct)

Given that the first three values are correct, we can say that the answer is B. y = -5x + 2.

To make sure even further however we may also substitute x = 0 into C. and D.

C. y = 10x - 5

if x = 0: y = -5 (not correct)

D. y = -2x + 2

if x = 0: y = 2 (this is correct so we must try substituting another value from the table)

if x = -2: y = -2(-2) + 2 = 6 (the value from the table for x = -2 is y = 12, therefor this is not correct)

Thus the answer is B. y = -5x + 2

2. The second method is to find the equation of the line itself without testing points. The first step is to find the gradient. We can do this using any two points, (x1, y1) and (x2, y2), and the formula for the gradient of a straight line:

m = (y2 - y1)/(x2 - x1)

Let's use the first two points from the table (-2, 12) and (-1, 7). Thus:

m = (7 - 12)/(-1 - (-2))

m = (-5)/1

m = -5

Now we can substitute this and one point (let's take (0, 2) into the formula for a straight line y - y1 = m(x - x1), where (x1, y1) is our point. Thus:

y - 2 = -5(x - 0)

y - 2 = -5x

y = -5x + 2

Therefor, looking at the possible answers, we can see that this matches answer B.

Answer:

B

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, 12) and (x₂, y₂ ) = (- 1, 7) ← 2 ordered pairs from table

m = [tex]\frac{7-12}{-1+2}[/tex] = - 5

note that (0, 2) is where the graph crosses the y- axis ⇒ c = 2

y = - 5x + 2 → B

Answer:

f(x) = [tex]e^{x}[/tex]

Step-by-step explanation:

The only function that has it;s derivative equal to the function is the exponential function.

That is f(x) = f'(x) = [tex]e^{x}[/tex]

[tex]A=100\pi\text{ ft}^2\\V=?\\\\V=\dfrac{4}{3}\pi r^3\\r=?\\\\100\pi=4\pi r^2\\r^2=25\\r=5\text{ ft}\\\\V=\dfrac{4}{3}\pi \cdot 5^3=\dfrac{500}{3}\pi \text { ft}^3[/tex]

the cheap answer is simply

(x-5)(x²+4x-2)

we can simply multiply the terms on one by the terms of the other and then add like-terms and simplify.

[tex]\bf (x-5)(x^2+4x-2)\implies \begin{array}{cllll} x^2+4x-2\\ \times x\\ \cline{1-1}\\ x^3+4x^2-2x \end{array}+ \begin{array}{cllll} x^2+4x-2\\ \times -5\\ \cline{1-1}\\ -5x^2-20x+10 \end{array} \\\\\\ x^3+4x^2-2x-5x^2-20x+10\implies x^3+4x^2-5x^2-2x-20x+10 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill x^3-x^2-22x+10~\hfill[/tex]

Answer:

51x

Step-by-step explanation:

Answer:

The Total including sales tax would equal $1.04.

Step-by-step explanation:

The total tax added is $0.08.

Answer:

$1.04

Step-by-step explanation:

.96*.08=.08

.08+.96=1.04

Final answer:

The quadratic expression 3x²-8x+5 is factored by finding two numbers that multiply to 15 and sum to -8, resulting in the factorization (3x-5)(x-1).

Explanation:

The factorization of the quadratic expression 3x²-8x+5 can be found by looking for two numbers that multiply to give the product of the coefficient of x² (which is 3) and the constant term (which is 5), and also sum to give the coefficient of x (which is -8). These numbers are -5 and -3, as (-5) × (-3) = 15 (which is 3 × 5) and (-5) + (-3) = -8. Therefore, the expression can be factored as (3x-5)(x-1).

Answer:

(9,2)

Step-by-step explanation:

(1,2) is reflected over vertical line x=3 which means since (1,2) is 2 units over from x=3 that the reflection is going to be 2 units over in the other direction from x=3 so the first image is (5,2)

Now the last image is processed by a reflection through vertical line x=7

(5,2) is 2 units from x=7 so the reflection will also be 2 units from the vertical line x=7 so the final image is (9,2).

Answer (9,2)

Answer:

(9, 2 )

Step-by-step explanation:

Under a double reflection in 2 parallel vertical lines

The y- coordinate remains unchanged

The x- coordinate is twice the difference of the parallel lines added to the original x- coordinate, that is

image = (1 + 2(7 - 3), 2 ) = (1 + 8, 2) = (9, 2 )

[tex]x=-2.08\overline{3}\\100x=-208.\overline{3}\\1000x=-2083.\overline{3}\\1000x-100x=-2083.\overline{3}-(-208.\overline{3})\\900x=-1875\\x=-\dfrac{1875}{900}=-\dfrac{25}{12}[/tex]

Answer:

A. f(x) = x²

Step-by-step explanation:

Observing the values

when x= -2..............f(x)= 4..................this is x²............-2²= 4

when x= -1..............f(x)= 1......................this is x²............ -1² = 1

when x= 0..............f(x)=0.....................this is x².......... 0²= 0

when x= 1.............f(x)= 1........................this is x²........ 1²= 1

When x=2........... f(x) = 2...................... this is x²........ 2² = 4

⇒The first option is correct.

ANSWER

The correct answer is A.

EXPLANATION

We can see from the table that:

[tex]f( - 2) = {( - 2)}^{2} = 4[/tex]

[tex]f( - 1) = {( - 1)}^{2} = 1[/tex]

[tex]f(0) = {(0)}^{2} = 0[/tex]

[tex]f(1) = {( 1)}^{2} = 1[/tex]

[tex]f(2) = {(2)}^{2} =4[/tex]

In general we can conclude that,

[tex]f(x) = {( x)}^{2} = {x}^{2} [/tex]

Therefore the parent function represented by the table is

[tex]f(x) = {x}^{2} [/tex]

Answer:

Step-by-step explanation:

Two points define a straight line (look at the picture #1).

Three non-collinear points define a plane (look at the picture #2).

Four points not lying in one plane, define space (look at the picture #3).

Answer:

-2 = x

Step-by-step explanation:

4(1-x)+3x = -2(x+1)      Distribute

4 - 4x + 3x = -2x -2    Combine Like Terms (On the same sides of the equal sign)

4 -x = -2x -2               Combine Like Terms (On different sides of the equal sign)

4 = -3x - 2                   Solve

6 = -3x                        

-2 = x

Final answer:

The solution to the equation 4(1-x) + 3x = -2(x + 1) is found to be x = -6, after simplifying and checking by substitution back into the original equation, which confirms the solution by resulting in an identity.

Explanation:

To solve the equation 4(1-x) + 3x = -2(x + 1), we need to expand and simplify our equation:

4 - 4x + 3x = -2x - 2

4 - x = -2x - 2

Adding 2x to both sides we get:

4 + x = -2

Now subtracting 4 from both sides, we obtain:

x = -6

We then check this solution by plugging it back into the original equation, confirming that it simplifies to an identity. Therefore, x = -6 is the correct solution.