suppose y varies directly as x. suppose also that y=34 when x=17. find y when x=56.

Answer:

y=1/3x-4

Step-by-step explanation:

The point where the line intercepts the y-axis is the y-intercept and where the digit -4 comes from

1/3 comes from how many times the line rises (1) and run (3)

Hope this helps!

Step-by-step explanation:

x⁴ + 4x³ - 5x² + x - 3 ÷ x² + x - 3 = x² + 3x - 5

- x⁴ + x³ - 3x²

-------------------------

0 3x³ - 2x² + x - 3

- 3x³ + 3x² - 9x

-------------------------------

0 - 5x² + 10x - 3

- - 5x² - 5x + 15

-------------------------------------

0 15x - 18

the result is therefore

x² + 3x - 5 + (15x - 18)/(x² + x - 3)

Answer:

D im pretty sure

Step-by-step explanation:

If each line is 20 x 3 = 60 12 dots 60 + 12 = 72 divided by 3 circles = 24

Answer: 9.75

Step-by-step explanation: i just added

Answer:

less

Step-by-step explanation:

The system of equations is consistent and dependent and it can be determined by using the properties of the equation.

Given that,

[tex]\rm y=4x-4\\y=-4x+4[/tex]

We have to determine,

The system of equations is consistent and independent, consistent and dependent, or inconsistent.

According to the question,

When a system has at least one solution, it's called consistent. When it has only one solution, it's called independent.

[tex]\rm y=4x-4\\y=-4x+4[/tex]

On adding both the equation,

[tex]\rm y+ y=4x-4+(-4x+4)\\\\2y = 4x-4-4x+4\\\\2y = 0\\\\ y = 0[/tex]

Substitute y = 0 to evaluate the value of x.

[tex]\rm y = 4x-4\\\\(0)= 4x-4\\\\ 4x=4\\\\ x = \dfrac{4}{4}\\\\x = -1[/tex]

The solution of the equation is (1, 0).

Hence, The system of equations is consistent and dependent.

To know more about the System of equations click the link given below.

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Answer:

[tex]y=\frac{6}{13}x+\frac{107}{13}[/tex]

Step-by-step explanation:

(x1, y1) = (-7, 5)

(x2, y2) = (6, 11)

The firs thing to do is fine the slope. That is the distance between the y-coordinates divided by the distance between the x-coordinates:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

I marked the points above as points 1 and 2, so you can plug those numbers into the formula:

[tex]m=\frac{11-5}{6--7}\\\\m=\frac{6}{13}[/tex]

That fraction can't be simplified any further, so the slope of this line is 6/13. The next thing to do is to find the y-intercept.

[tex]y=mx+b[/tex]

Plug the slope and any point of your choice into the equation. I'll use point b:

[tex]11=(\frac{6}{13})6+b[/tex]

Now, solve for b:

[tex]11=\frac{36}{13}+b\\\\11-\frac{36}{13}=b\\\\\frac{143}{13}-\frac{36}{13}=b\\\\\frac{107}{13}=b\\\\b=\frac{107}{13}[/tex]

They're far from clean, but those are the correct slope and y-intercept. Using those, the equation for this line is:

[tex]y=\frac{6}{13}x+\frac{107}{13}[/tex]

You can confirm that this is the correct equation by checking it with one of the points. Plug in one of the known values of x and make sure it gives the correct value of y:

[tex]y=\frac{6}{13}(-7)+\frac{107}{13}\\\\y=\frac{-42}{13}+\frac{107}{13}\\\\y=\frac{65}{13}\\\\y=5[/tex]

That works out.

Answer:

-45xj-9xk

Step-by-step explanation:

-9x(5j+k)

Multiply -9x with 5j

Multiply -9x with k

-9x times 5j is -45xj

-9x times k is -9xk

So the equivalent expression is

-45xj-9xk

Hope this helps!

The distance from the stadium to Pine Avenue is [tex]13.4miles[/tex], (to the nearest tenth)

The stadium is on Hazel Street(the green line). Pine Avenue is the blue line. The distance from the stadium to Pine Avenue will be the distance on the graph (in miles) from the point representing the stadium, to the point of intersection between Hazel Street and Pine Avenue.

We know the location of the stadium, [tex]S=(-6,6)[/tex]

The point of intersection can be obtained by solving the simultaneous equations

[tex]y=-\dfrac{1}{2}x+3\\y=2x-12[/tex]

since both equations are set equal to [tex]y[/tex], set them equal to each other, to eliminate [tex]y[/tex], and solve for [tex]x[/tex]

[tex]-\dfrac{1}{2}x+3=2x-12\\\\x=6[/tex]

Substitute this value of [tex]x[/tex], into the equation for Pine avenue

[tex]y-2x-12\\=2(6)-12\\=0[/tex]

The point of intersection between Hazel Street and Pine Avenue is [tex]I=(x,y)=(6,0)[/tex]

To compute the distance between the stadium and Pine Avenue, we find the distance between the two points [tex]S[/tex] and [tex]I[/tex]. So,

[tex]d=\sqrt{(6-(-6))^2+(0-6)^2}\\\\=\sqrt{12^2+(-6)^2}\\\\=6\sqrt5\approx13.4\text{ (to the nearest tenth)}[/tex]

The distance is [tex]13.4miles[/tex]

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Answer:

A

Step-by-step explanation:

Answer:

y = 3x + 18

Here's how I got that:

- You first assign the points -

     (-9, -9) → x1 = -9, y1 = -9

     (-6, 0) → x2 = -6, y2 = 0

- Now you plug those points into slope formula and solve-

                          [tex]s=\frac{y2-y1}{x2-x1}[/tex]

                                   ↓

                       (0 - (-9))/((-6) - (-9))

                                   ↓

                                  9/3

                                   ↓

                           slope = 3

- Now we plug the numbers we got into intercept formula -

                            b = y1 − s ⋅ x1

                                      ↓

                             -9 - (3) · (-9)

                                      ↓

                           y-intercept = 18

           - Put everything together and you get.. -

                                 y = 3x + 18

~That's all folks~

-Siascon

Answer:

y = 3x + 18

Step-by-step explanation:

Answer:  

O = (1,-1)

N = (1,-2)

M = (3,-2)

L = (3,-1)

Step-by-step explanation:

Answer:

B) 6

Step-by-step explanation:

If this is similar triangles:

x:42=6:42

Well you could also just

bigger triangle is isosceles

so x=6

Answer:

Step-by-step explanation:

What you have here is called "the difference of two squares"

Difference means subtraction and both 100x2 and 49 are perfect squares.

The factored form of 100x2-49 is

(10x+7)(10x-7)

Because 10x times 10x is 100x2 and 7 times 7 is 49

One factor has a + and

One factor has a -

It is a pattern worth memorizing!

So 10x + 7 is the factor you're looking for.

Answer:

8

Step-by-step explanation:

g(x) = 2x + 2

g(3) = 2*3 + 2             Substitute 3 for x.

g(3) = 6 + 2                 Multiply.

g(3) = 8                       Add.

Answer:

g(3) = 11

Step-by-step explanation:

Substitute x = 3 into g(x) , that is

g(3) = 3² + 2 = 9 + 2 = 11

Answer:

  (c)  multiplication property of equality

Step-by-step explanation:

Both sides of the equation can be multiplied by the same number without changing the values of any variables. This is the multiplication property of equality.

Using the tables to answer the question, the correct option is D.

Only table B represents a function

A relation/table will represent a function if each value of x is attached to a unique value of y.

That is, no value of x must be mapped to more than one value of y.

By considering the tables represented

Set A = {(-5, 2), (-8, 5), (-5, 8)}

As clearly shown above, when x = -5, y = 2 and 8. This means that there are more than 1 value of y for a single value of x, therefore, table A does not represent a function.

Set B = {(-5, 2), (-8, 5), (-11, 2)}

As shown above, all values of x have different values of y. Therefore, table B represents a function.

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Answer:

42 months

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

|-12|= 12

this means that it represents a positive number. Each answer represents a positive number other than the town that lies -12 feet below sea level. (sorry if I'm wrong)

Answer: Guilty of or involving betrayal or deception.

Step-by-step explanation:

====================================================

Explanation

x = measure of angle 1

y = measure of angle 2

x = 2y+18, since angle 1 is 18 more than twice that of angle 2

Assuming this is a parallelogram, the adjacent angles are supplementary. So,

x+y = 180

2y+18+y = 180

3y+18 = 180

3y = 180-18

3y = 162

y = 162/3

y = 54

This leads to,

x = 2y+18

x = 2*54+18

x = 108+18

x = 126

Note that x+y = 126+54 = 180

Another useful fact about parallelograms is that the opposite angles are the same measure. So angle 1 = angle 3 = 126 degrees

The measure of angle 3, if The measure of ∠1 is 18 more than twice the measure of ∠2 is 126°

In geometry, a polygon is any closed curve made up of a collection of continuous line segments (sides) without any intersections. Triangles (three sides), quadrilaterals (four sides), and pentagons are the three simplest polygons (five sides).

Given:

The measure of angle 1 = 2 × The measure of the angle 2 + 18

Write an equation for the above statement,

x = 2y + 18

Here, x is a measure of angle 1 and y is the measure of angle 2,

As you can see from the figure it is a parallelogram then,

x + y = 180  (The sum of supplementary angle)

Solve the equation by elimination method,

y = 54, x = 2 × 54 + 18 = 126

The opposite angle of a parallelogram are equal,

Measure of angle 3 = Measure of angle 1 = 126

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Answer:

C   y = 1/5x - 1

Step-by-step explanation:

Slope intercept form: y = mx + b where m = slope and b = y-intercept.

Substitute into the slope intercept form m= 1/5 and b = -1

y = 1/5x - 1

Answer:

7 people

Step-by-step explanation:

The equations and inequality expresses the relationship between the variables.

The correct responses are;

Reasons:

First part;

The difference between y-values following a change in 2 units of the x-value is a constant, and is equal to 1;

The rate of change of the function, m, is therefore;

[tex]\displaystyle m = \frac{2 - 1}{6 - 4} = \frac{1}{2} = 0.5[/tex]

The slope and intercept form of the equation of the function is therefore;

y - 3 = 0.5·(x - 8) = 0.5·x - 4

y = 0.5·x - 4 + 3 = 0.5·x - 1

The rule that represent the function is; y = 0.5·x - 1

Second part;

2·n represent twice the number

The difference between twice the number and 6 = 2·n - 6

At least 35 = ≥ 35

Therefore, the inequality is; 2·n - 6 ≥ 35

Third part;

The given quadratic equation is; a·x² + b·x + c = 0

Therefore;

[tex]\displaystyle \underline{b = \frac{-c - a\cdot x^2}{x}}[/tex]

Fourth part;

The best correct option is table 4, given that the table is as follows;

[tex]\begin{tabular}{|c|cc|}In&&Out\\Not clear&&\\9&&17\\10&&19\end{array}\right][/tex]

Fifth part;

The y-intercept of the graph is -0.5

The slope is -4 ÷ 8 = -0.5

Therefore, the equation is; y = -0.5·x - 4

The shaded area is the area lower than the y-values, with broken lines (indicating < relationship) which gives, the correct inequality as follows;

[tex]\displaystyle \underline{y < -\frac{1}{2} \cdot x - 4}[/tex]

Sixth part;

The amount Jordan part-time job pays = $75

The amount he has already saved = $55

The cost of the iPhone = $400

Let w represent the number of weeks Jordan works, at his part-time job to purchase the iPhone, we have;

75·w + 55 ≤ 400

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Answer:

8 1/3 liters

Step-by-step explanation:

create a proportion from water : yard

let 'y' = water for entire yard

5/3 ÷ 1/5 = y ÷ 5/5

5/3 · 5/1 = y/1

25/3 = y/1

3y = 25

y = 8 1/3

Answer:

Step-by-step explanation:

x + 4y = 8

-x           -x

4y = -x + 8

divide by 4

y= -1/4x + 2

then graph

Answer:

Step-by-step explanation:

y = 4/3x

you can see the line passes through (0,0)

the next point it passes through is (3,4)

(y2-y1)/(x2-x1)

(4 - 0)/(3 - 0)

4 / 3

the slope = 4/3

meaning it goes up 4 and right 3 from point to point