What is the value of y in the solution to the system of equations?
3x + 4y = 30
3x + 5y = 33

Answer:

a. (7, 27) Polly was incorrect.

b. (3, 1) Polly was correct.

Step-by-step explanation:

a.

y = 4x - 1

2x - y = -13

We can solve this by substitution. Our first equation gives us y. Plug that into our second equation for each instance of y.

2x - y = -13

2x - (4x - 1) = -13

First distribute the negative sign across the parentheses.

2x - 4x + 1 = -13

Combine like terms.

-2x + 1 = -13

-2x = -14

Divide both sides by -2.

x = 7

Now that we know x, plug its value into one of our original equations.

y = 4x - 1

y = 4(7) - 1

Solve.

y = 28 - 1

y = 27

Our solution is (7, 27).

Let's check our answer by plugging both values into one of our original equations.

2x - y = -13

2(7) - 27 = -13

Solve.

14 - 27 = -13

-13 = -13

Your solution is correct.

Polly's solution was (-2, -9), which is incorrect.

b.

3x + 6y = 15

-2x + 3y = -3

Let's solve this by elimination. To solve by elimination means to eliminate a variable from the equation.

We have 3x & -2x and 6y & 3y. Notice that 6 and 3 can be simplified easily. To eliminate y, we want to multiply each factor of the second equation by -2.

-2x + 3y = -3

-2(-2x + 3y = -3)

4x - 6y = 6

Write the equations together.

3x + 6y = 15

4x - 6y = 6

Now we can see that the y variable will cancel out.

Apply the elimination method.

3x + 6y = 15

4x - 6y = 6

________

7x = 21

Divide both sides by 7.

x = 3

Now that we know x, plug its value into one of our original equations.

3x + 6y = 15

3(3) + 6y = 15

Solve.

9 + 6y = 15

6y = 15 - 9

6y = 6

y = 1

Our solution is (3, 1).

Let's check our answer by plugging both values into one of our original equations.

-2x + 3y = -3

-2(3) + 3(1) = -3

Solve.

-6 + 3 = -3

-3 = -3

Your solution is correct.

Polly's solution was (3, 1), so she was correct.

Hope this helps!

Answer:

g(x) = -x²

Step-by-step explanation:

By looking at the graph and equation of the blue quadratic line, you know the y-intercept is 4. When you look at the red one you can see the y-intercept is 0 so then the equation should be g(x) = -x²

Answer:

Answer B

Step-by-step explanation:

If both the function have the same shape, it means that the function f(x) is just shifted downwards to obtain function g(x).

The function f(x) is given as,

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

Shifting the curve downwards by 4 unites, the function g(x) is obtained,

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

I think option B is the correct choice.

Answer:

Option A

Step-by-step explanation:

Just substitute each value of x in the graph to find the correct function.

When be graph the functions given, we find that option A is correct.

To graph a function, you have to select x-values and plug them into the equation. Once you plug those values into the equation, you will get a y-value. Your x-values and your y-values make up your coordinates for a single point. Keep plugging in x-values to get coordinates to plot more points on the graph, and then you will see your graphed function once the dots are connected.

Using the graph,

For x < = -2, y = 5.

For -2 < x < 1, the function is a polynomial.

We have two options, either [tex]y = x^{2} -5\ or\ y = x^{2} +5[/tex]

The polynomial must have the point (0,-5) on it.

For [tex]y = x^{2} -5[/tex] , when x = 0, y = -5.

Hence, it is the correct option.

For x >= 1,

Using graph, we see that when y = 0, x lies between 3 and 4.

For equation, [tex]y = 2^{(x-2)} - 2\\[/tex], when y = 0, x = 3, so it is not correct.

For equation, [tex]y = 2^{(x-2)} - 3\\[/tex], when y = 0, x = 3.584, hence it is correct.

Learn more about graphing a function here

https://brainly.com/question/27757761

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Answer:

3

Step-by-step explanation:

5 + 4 = 9

12 - 9 = 3

In order to find the missing length you will need to add up the given lengths then subtract that from the total perimeter.

Answer:

C) H

Step-by-step explanation:

It can only be a function when every y has a different x. There cannot be an x with multiple y’s

Step-by-step explanation:

i forgot sorry

Answer:

6.52 i took the test

Step-by-step explanation:

Answer:

Geographic Features of Ancient Greece

Step-by-step explanation:

Greece has all these attributes on the list

Answer:

Geographic Features of Ancient Greece

Step-by-step explanation:

plzzzzzzzzzzzzzzzzzzzzzzzz give brain alist

Answer:

-

He spent 1 hour in total

-

1 hour

There's two Xs on the graph indicating that he had two 1/2 hour hikes, so you just add that up. And that's 1 hour woo

Answer:

a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).

Step-by-step explanation:

Answer:

A regular polygon has 5 sides

Answer:

BC ≈ 4.17

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos43° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{BC}{5.7}[/tex] ( multiply both sides by 5.7 )

5.7 × cos43° = BC , then

BC ≈ 4.17 ( to 3 sf )

Answer:

19/4 =12

Step-by-step explanation:

The 19/4 is a fraction, 19 being the top (numerator)

and 4 being the bottom (denominator)

Answer:

Option B --> (8, -5)

Step-by-step explanation:

To find the midpoint, we use the equation-

[tex]\frac{x1 + x2}{2} , \frac{y1 + y2}{2}[/tex]

The coordinates given were (8, -2) (8, -8)

x1= 8,

x2 = 8

y1 = -2

y2= -8

Substituting these values in the equation:-

[tex]\frac{8+ 8}{2} , \frac{-2 + -8}{2}[/tex]

[tex]\frac{16}{2} , \frac{-10}{2}[/tex]

Coordinates of midpoint will be ---> (8, -5)

Answer:

B

Step-by-step explanation:

4x-8y=16

add 8y to both sides, so you get

8y+16=4x

then subtract 16 from both sides

8y=4x-16

divide by 8 on both sides

y=1/2x-2

Answer:

6

Step-by-step explanation:

60 = 12+8 divided 2 times height

60 = 20/2 x H

60 = 10 x H

60/10 = h

6 = H

Answer:

c. Real, rational and unequal

Answer:

time in weeks

Step-by-step explanation:

Answer:

One solution.  

Step-by-step explanation:

X=2/3 or x=2.6666

Answer:

x=2/3

Step-by-step explanation:

3x + 7 = 9x + 3

Collect like terms (subtract 3x from both sides and subtract 3 f4=rom both sides)

The resulting equation will look like this:

 4=6x

=6x=4

Divide be 6 on both sides:

x=4/6

Simplify:

x=2/3 :-)

option ( C )

5

...........

Answer:

C. 5

Step-by-step explanation:

The degree is the highest exponent in the polynomial and in the polynomial given, 3x^5 has the highest exponent, being 5, so that would be the degree.

Hope this helps :)

Answer:

1/3

Step-by-step explanation:

y = mx + b

m is the slope and b is your y-intercept.

Answer:

m = 1/3

Step-by-step explanation:

Answer:

110 square centimeters.

Step-by-step explanation:

The area for a trapezoid can be figured out with the equation (a + b)h/2.

(9 * 5) + (9 + 4)10/2 {Work inside the parentheses first.}

45 + (13)10/2 {Divide 10 by 2 to get 5.}

45 + 13(5) {Multiply 13 by 5 to get 65.}

45 + 65 {Add 45 & 65 to get 110.}

110 square centimeters.

The area of the figure is 110 square centimeters.

Answer:

There are so many!

For circumference use = 2 pi r

For area use = pi r²

I have told only formula, else you may lack practice. try to solve yourself

Answer:

Step-by-step explanation:

The value of y varies directly with x. When y = 75, x = ½ . What is the value of y when x is 2 ¼ ? A. 168.75 C. 66.67 B. 16.67 D. 337.5

y ∝x

y = kx

k = y/x

Answer:

420

Step-by-step explanation:

volume = length x width x height

12 x 5 x 7 = 420

Answer:

1 A. 1080°

1 B. 142°, 74°,74°, 125°, 125°

Step-by-step explanation:

1A.

The sum of the measure of the interior angle of a convex octagon is given as

S = (n-2)180°................. Equation 1

Where n = 8 sides

S = (8-2)180°

S = 6×180°

S = 1080°

1B.

The sum of the angle of a convex pentagon is given as

S = (5-2)180°

S = 3×180°

S = 540°

From the diagram,

2x+142+2x+(3x+14)+(3x+14) = 540

10x+170 = 540

10x = 540-170

10x = 370

x = 37°

Hence,

∠H = ∠K = 2(37) = 74°,

∠M = ∠L= (3×37)+14 = 111+14 = 125°

Answer:

2.5 feet

Step-by-step explanation:

Answer:

2.5 feet

Step-by-step explanation:

[tex] \frac{30}{12} = 2.5[/tex]

Answer:

12 ft

Step-by-step explanation:

Given data

Area= 84 ft^2

Length= 7ft

The expression for the area is

Area= L*W

substitute

84=7*W

W= 84/7

W= 12ft

Hence the width is 12 ft

Answer:12ft

Step-by-step explanation:

Answer:

Just put it in Geogebra classic. It's an app that helps very much with functions!

Answer:

150

Step-by-step explanation:

Answer:

Step-by-step explanation:

Your y= -x2 -10x +1 should be written as y = -x^2 -10x +1.  This is a quadratic function.  Because the coefficient (-1) of the x^2 term is negative, we know immediately that the graph (a parabola) opens down, and thus has a maximum.