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Natali [406]
3 years ago
13

The archway of the main entrance of a university is modeled by the quadratic equation

Mathematics
1 answer:
Scilla [17]3 years ago
3 0

Answer:

B. (1,5) and (5.25, 3.94)

Step-by-step explanation:

The answer is where the 2 equations intersect.

We need to solve the following system of equations:

y = -x^2 + 6x

4y = 21 - x

From the second equation:

x = 21 - 4y

Plug this into the first equation:

y = -(21 - 4y)^2 + 6(21 - 4y)

y = -(441 - 168y + 16y^2)+  126 - 24y

y = -441 + 168y - 16y^2 +  126 - 24y

16y^2 + y - 168y + 24y + 441 - 126 = 0

16y^2 - 143y + 315 = 0

y = [-(-143) +/- sqrt ((-143)^2 - 4 * 16 * 315)]/ (2*16)

y = 5, 3.938

When y = 5:

x = 21 - 4(5) = 1

When y = 3.938

x = 21 - 4(3.938) = 5.25.

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Brent created a mural, 4/5 of which he painted in shades of blue. Three eighths of the blue area is sky blue. What portion of th
Snezhnost [94]

Answer: \frac{3}{10} of the mural is sky blue.


Step-by-step explanation:

Let x be the full portion of mural.

Since, \frac{4}{5} of mural is painted in shades of blue.

Therefore, the blue portion=\frac{4}{5}x

Also, Three eighths of the blue area is sky blue.

Therefore, the portion of the mural is sky blue=\frac{3}{8}\times\frac{4}{5}x

The portion of the mural is sky blue=\frac{12}{40}x

Simplify, by dividing numerator and denominator by 4, we get

The portion of the mural is sky blue=\frac{3}{10}x


5 0
3 years ago
in one month you had both a raise and a $250 bonus for exceeding your goals by 10%. your old paycheck gross was 2300 with a net
maks197457 [2]
Backing out the bonus, we get 2711 - 250 = 2461, which is 161 more than his last check 

<span>So 161 / 2300 = 0.07, or 7%</span>
3 0
4 years ago
I need help with problem
pychu [463]

Answer:

f(x)=4x(x-3)

Vertex=3/2, -9

Step-by-step explanation:

First, factorize it.

That is equal to 4x(x-3)

Therefore, x intercepts are 0 and 3, as  at least one of them need to be 0.

To find the vertex, first find the x of the vertex, which you can do by finding the average of the x intercepts, so it will be 3/2

Then, find the y, by making x in the original equation equal 3/2. This will give us -9 as the y.

The vertex will by 3/2, -9

4 0
2 years ago
Which equation is it? plz help ​
zvonat [6]

Answer:

In the pic

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below ÷)

8 0
3 years ago
What are the solutions to m^2 – 9 = 0? a. m = –9 and m = 0 b. m = –3 and m = 3 c. m = –3 d. m = 9
marysya [2.9K]
2 ways
zero product property
easy way

zero product
factor perfect square
m^2-3^2=0
(m-3)(m+3)=0
set each to zero
m-3=0
x=3

m+3=0
m=-3

m=-3 or 3

easy way
add 9 to both sides
m^2=9
sqrt both sides remember to take postive and negative roots
m=+/-3
m=-3 or 3


B is answer

5 0
3 years ago
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