The graph represents the balance on Harrison’s car loan in the months since purchasing the car.


Which statement describes the slope of the line?

The loan balance decreases $500 per month.
Harrison makes a monthly payment of $250.
The loan balance increases $250 per month.
Harrison increases his monthly payment by $500 each month.

(5x - 2 - g(x))(x)

(5x - 2 -(2x + 1)

(5x - 2 - (2x + 1) : 3x - 3

= 3x - 3

Mila reads at a rate of 2 paragraphs per minute. After reading for 3 minutes, she had read a total of 6 paragraphs.

This situation can be represented with a linear equation written in point-slope form,  

Let 'x' represents the number of minutes and,

y represents the number of paragraphs.  

In one minute Mila reads 2 paragraphs .

So, y=2x

Let x=1 then y=2

x=2 then y =4

Here slope of equation is 2

Let( x1, y1) and (x2,y2) be the two point the equation y=2x the ,

we can write, (y2 - y1) = m(x2 - x1)

or (y2 - y1) = 2(x2 - x1)

Answer:

(3,6)

Step-by-step explanation:

Given that Mila reads at a rate of 2 paragraphs per minute. After reading for 3 minutes, she had read a total of 6 paragraphs.

This situation can be represented with a linear equation written in slope-intercept form,  as

[tex]y=2x[/tex]

where 'x' represents the number of minutes and,

y represents the number of paragraphs.  

Since y intercept is 0 i.e. 0 paras in 0 minutes we have the equation as

[tex]y=2x[/tex]

Since no of minutes or paragraphs cannot take negative values this line is defined only in the I quadrant where both x and y are positive

Out of the points given as follows:

(3,6) (2,3) (-3,6) or (-2,6) ,

we can remove last two since they have negative x which is impossible.

Consider  (3,6) (2,3)

Out of these only I point  (3,6) satisfies  [tex]y=2x[/tex] and second point   (2,3) does not satisfy

[tex]y=2x[/tex]

Hence answer is (3,6)

false , w = 147

multiply both sides by - 7 to eliminate the fraction

w = - 7 × - 21 = 147

The solution to the equation w/-7=-21 is not 3 but 147. Therefore, the original statement is false.

The equation in question is w/-7 = -21. To solve this equation, we multiply both sides by -7.

When we do this, the equation simplifies to w = -(-21)*7. As -(-21) turns to 21, and 21*7 is equal to 147, we find that the solution to the equation w/-7=-21 is w=147, and not w=3.

Therefore, the statement 'The solution to w/-7=-21 is 3' is false.

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median = $28

the median is the middle value of the data arranged in ascending order

rearrange the data in ascending order

13 26 28 31 34

the middle entry is 28

hence median = $28

The median is the middle value so put the numbers in order from smallest to largest.

13,26,28,31,34

The middle value is 28, so the median value is 28

note that 5π /4 is in the third quadrant where the cos is negative

the related acute angle to 5π /4 is π/4, thus

cos( 5π /4 ) = - cos (π/4 ) = - √2/2

We can also evaluate using the addition formula for cosine

• cos (x + y ) = cosxcosy - sinxsiny

note that 5π /4 = (π + π/4 )

cos(5π /4 ) = cos (π + π/4 )

= cos(π)cos(π/4) - sin(π)sin(π/4)

= - 1 √2/2 - 0 = - √2/2

solution = (4, - 2 )

substitute x = 4 into - y = [tex]\frac{1}{2}[/tex] x

- y = [tex]\frac{1}{2}[/tex] × 4 = 2 ( multiply both sides by - 1 )

y = - 2

solution is ( 4, - 2 )

Answer:

I think it is (4,-2)

Try this option (note, this is not the shortest way!), the additional elements are shown by green colour.

Answers: ∠1=∠2=50°; ∠3=82°

The distance MN is 9/(9+1) = 9/10 of the distance MP, so is

... MN = (9/10)×MP = (9/10)×2 = 9/5

The distance MK is 1/4 that, so is ...

... MK = (1/4)×(9/5) = 9/20 . . . . . matches selection (C)

Answer:

C

Step-by-step explanation:

the answer is C. give the person the brainly :) ignore this answer

The naming of similar triangles has corresponding vertices in the same order in the name. That means segment QS corresponds to segment AC. We note that QS = 6 cm is 1/10 the length of AC = 60 cm.

Side AB is given as 50 cm, so the corresponding side QR will be 1/10 that value.

... QR = 5 cm

The given equation can be simplified to ...

... x² +2x = 5

This is a quadratic equation. The highest-degree term has degree 2. (TRUE)

300000000+400000+50000+300+90= 300450390

Hope this helped! :)

How do you write 300450390 in expanded form ?

300000000+ 400000+ 50000+ 300+ 90= 300450390

Hope this helps. If it does, please mark me brainiest! <3

the answer would be 103 students

6/7 and 12/17 all the other have to be reduced

These are the proper fractions

6/7

12/17

6/25

These are improper fraction

5/3

9/5

11/4

Answer:

i am pretty sure that it is .2,

Step-by-step explanation:

first, you would do .5 divided by 5 which is 0.1. Then you would do 0.1 divided by 0.5 and you would get 0.2

By rounding to the nearest whole numbers and estimating, it is confirmed that Ruben's answer of 96.52 ÷ 12.7 equals 7.6 is indeed reasonable.

To assess if Ruben's answer that 96.52 ÷ 12.7 equals 7.6 is reasonable, let's consider the magnitude of the numbers involved. Firstly, we can simplify our estimation by rounding the numbers to the nearest whole digits, which gives us approximately 97 ÷ 13. By using division, we see that 13 goes into 97 about 7 times with some remainder, since 13 x 7 is 91, which is close to 97.

Now, 7.6 is indeed close to our estimation, so we can determine that Ruben's answer is within a reasonable range. Thus, the correct response to whether Ruben's calculation is reasonable would be:

D. Yes, Ruben's answer is reasonable.

3(x + 12) does not, and never will, equal 3(x + 5)

We can solve the equation to verify.

3(x + 12) = 3(x + 5)

Distributive property.

3x + 36 = 3x + 15

Subtract 15 from both sides.

3x + 21 = 3x

Cancel like terms.

21 = 0 × this is incorrect.

If we consider the first half mile to be charged at $0.30 per tenth also, that half-mile costs $1.50 and the charges amount to a fixed fee of $2.00 and a variable fee of $0.30 per tenth mile.

After you subtract the $2 tip and the fixed $2 fee from the trip budget amount, you have $11.00 you can spend on mileage charges. At 0.30 per tenth mile, you can travel

... $11.00/$0.30 = 36 2/3 . . . . tenth-miles

The trip is measured in whole tenths, so you can ride ...

... 36 × 1/10 = 3.6 miles

_____

If you want to see this in the form of an equation, you can let x represent the miles you can travel. Then your budget amount gives rise to the inequality ...

... 3.50 + 0.30((x -.50)/0.10) + 2.00 ≤ 15.00

... 3.50 + 3x -1.50 +2.00 ≤15.00 . . . . . . . eliminate parentheses

... 3x ≤ 11.00 . . . . . . . . . . . . . . . . . . . . . . . . collect terms, subtract 4

... x ≤ 11/3 . . . . . . . . . . . . . . . . . . . . . . . . . . divide by 3

... x ≤ 3.6 . . . . . rounded down to the tenth

since y varies directly with y then

y = kx ( k is the constant of variation )

to find k use y = 3 when x = 2

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{3}{2}[/tex]

equation is : y = [tex]\frac{3}{2}[/tex] x

When x = 1 then y = [tex]\frac{3}{2}[/tex] × 1 = [tex]\frac{3}{2}[/tex]

[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we also know that}~~ \begin{cases} y=3\\ x=2 \end{cases}\implies 3=k2\implies \cfrac{3}{2}=k \\\\\\ therefore\qquad \boxed{y=\cfrac{3}{2}x} \\\\\\ \textit{when x = 1, what is \underline{y}?}\qquad y=\cfrac{3}{2}(1)\implies y=\cfrac{3}{2}[/tex]

y=4/3x+4

are you in k12 i tookthat test already

y = [tex]\frac{4}{3}[/tex] x + 4

the equation of a line in slope- intercept form is

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

to calculate m use the gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4 ) and (x₂, y₂ ) = (-3, 0 ) ← 2 points on line

m = [tex]\frac{x0-4}{-3-0}[/tex] = [tex]\frac{-4}{-3}[/tex] = [tex]\frac{4}{3}[/tex]

the line crosses the y-axis at (0, 4 ) → c = 4

y = [tex]\frac{4}{3}[/tex] x + 4 ← in slope-intercept form

D

Substitute the coordinates of the given points into the inequalities and if both are true then the point is a solution to the system.

A(1, 1 ) : 4 + 2 = 6 and 1 - 1 = 0 not a solution

B(8, 4 ) : 32 + 8 = 40 and 8 - 4  = - 4 not a solution

C(3, 9 ) : 12 + 18 = 30 and 3 - 9 = - 6 not a solution

D(9, 1 ) : 36 + 2 = 38 and 9 - 1 = 8 is a solution

the point (9, 1 ) is the only point that makes both inequalities true

When you factor out -1, you get ...

... -(2 4/5 - 6/7)

Answer:

Dad made 90 steps during that period.

Step-by-step explanation:

Let x,y,z be the steps made by dad,Anna and Todd.

Given that while dad made 3 steps, Anna made 5 steps.

That is [tex]\frac{x}{y}= \frac{3}{5}[/tex]

           [tex]y=\frac{5x}{3}[/tex]

And for every 3 steps Anna made, Todd made 5 steps.

That is [tex]\frac{y}{z}= \frac{3}{5}[/tex]

            [tex]z=\frac{5y}{3} =\frac{5(\frac{5x}{3}) }{3} =\frac{25x}{9}[/tex]

It is also given that total number of steps made by Anna and Todd is 400.

That is y+z=400

let us plugin y and z in terms of x.

       [tex]\frac{5x}{3} +\frac{25x}{9} =400[/tex]

        [tex]\frac{15x}{9} +\frac{25x}{9}=400[/tex]

       [tex]\frac{40x}{9}=400[/tex]

       [tex]x=400X\frac{9}{40} =90steps[/tex]

Hence Dad made 90 steps during that period.

Answer:

4. 73

5. 40°

Step-by-step explanation:

The sum of the angles in a triangle is 180°. The sum of angles in a linear pair is 180°.

4. 45° +62° + k° = 180°

... 107 +k = 180 . . . . . collect terms, divide by °

... k = 180 -107 = 73 . . . . . subtract 107

_____

5. ∠STR = ∠SRT = 20°

... ∠STR +∠STU = 180°

... 20° + 4x = 180°

... 4x = 160° . . . . . . . . subtract 20°

... x = 40° . . . . . . . . . . divide by the coefficient of x

if (x - 5 ) is a factor of f(x ) then x = 5 is a root of f(x) and f(5) = 0

Answer:

[tex]f(5) = 0[/tex]

Step-by-step explanation:

A function [tex]f[/tex] can be simplified by it's roots.

For example, a second order function expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0.[/tex]

Can be expressed in function of it's roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = (x - x_{1})*(x - x_{2})[/tex].

Is [tex]x-5[/tex] is a factor of f, this means that f can be expressed in function of [tex]x - 5[/tex], that is, x = 5 is a root of the equation.

This means that:

[tex]f(5) = 0[/tex]

The 2-point form of the equation of a line can be written as ...

... y = (y2-y1)/(x2-x1)·(x -x1) +y1

For your points, this is ...

... y = (1-5)/(3-6)·(x -6) +5

... y = (4/3)(x -6) +5

It can also be written as

... y -5 = (4/3)(x -6)

Answer: The required equation is y= 4x/3 - 3

Step-by-step explanation:

Given points (6,5) and (3,1)

Two point slope equation is  given as

[tex]y - y1 = \frac{y2-y1}{x2-x1}(x-x1)[/tex]

where (x1, y1) and (x2,y2) are the points respectively

∴ [tex]y-5 =\frac{1-5}{3-6}(x-6)[/tex]

[tex]y-5 =\frac{-4}{-3} (x- 6)[/tex]

[tex]y -5 =\frac{4}{3} (x-6)[/tex]

[tex]y - 5 =\frac{4}{3}x - 8[/tex]

[tex]y = 5 +\frac{4}{3} x - 8[/tex]

[tex]y = \frac{4}{3}x -3[/tex]

It can also be written as

[tex]y -5 =\frac{4}{3}(x -6)[/tex]

In a scatter plot with two sets of data, the independent variable is the variable that was controlled by the researchers and is represented on the x-axis.

In a scatter plot with two sets of data, the independent variable is the variable that was controlled by the researchers. The independent variable is typically represented on the x-axis of a scatter plot. It is the variable that is manipulated or changed to observe its effect on the dependent variable, which is plotted on the y-axis.

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Saturn takes 17.6 more years than Jupiter, so 17.6 + 11.9 will get you how long Saturn will take to orbit the sun, which would give you 29.5 years.

The time it takes Saturn to orbit the sun can be calculated by adding Jupiter's orbit time to the additional time Saturn takes after Jupiter. Saturn takes approximately 29.5 years to complete one orbit around the sun.

To find out how long it takes Saturn to orbit the sun, we know that Jupiter takes 11.9 years and Saturn takes 17.6 more years than Jupiter. So, Saturn takes 11.9 + 17.6 = 29.5 years to orbit the sun.