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3 years ago

Write each relation in standard form and then find the y-intercept for each relation:

Mathematics

1 answer:

tresset_1 [31]3 years ago

4 0

Answer:

In standard form, the relation is $y = 5x^2 + 100x + 507$

The y-intercept is y = 507.

Step-by-step explanation:

Quadratic equation:

In standard form, it is written as:

$y = ax^2 + bx + c$

The y-intercept is c.

a) y = 5(x+10)^2 +7

We open the binomial to write in standard form. So

$y = 5(x + 10)^2 + 7$

$y = 5(x^2 + 20x + 100) + 7$

$y = 5x^2 + 100x + 500 + 7$

$y = 5x^2 + 100x + 507$

In standard form, the relation is $y = 5x^2 + 100x + 507$

The independent term, c, is 507, so the y-intercept is y = 507.

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3 years ago

A teenager who is 5 feet tall throws an object into the air. The quadratic function LaTeX: f\left(x\right)=-16x^2+64x+5f ( x ) =

tia_tia [17]

Answer:

At approximately x = 0.08 and x = 3.92.

Step-by-step explanation:

The height of the ball is modeled by the function:

$f(x)=-16x^2+64x+5$

Where f(x) is the height after x seconds.

We want to determine the time(s) when the ball is 10 feet in the air.

Therefore, we will set the function equal to 10 and solve for x:

$10=-16x^2+64x+5$

Subtracting 10 from both sides:

$-16x^2+64x-5=0$

For simplicity, divide both sides by -1:

$16x^2-64x+5=0$

We will use the quadratic formula. In this case a = 16, b = -64, and c = 5. Therefore:

$\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Substitute:

$\displaystyle x=\frac{-(-64)\pm\sqrt{(-64)^2-4(16)(5)}}{2(16)}$

Evaluate:

$\displaystyle x=\frac{64\pm\sqrt{3776}}{32}$

Simplify the square root:

$\sqrt{3776}=\sqrt{64\cdot 59}=8\sqrt{59}$

Therefore:

$\displaystyle x=\frac{64\pm8\sqrt{59}}{32}$

Simplify:

$\displaystyle x=\frac{8\pm\sqrt{59}}{4}$

Approximate:

$\displaystyle x=\frac{8+\sqrt{59}}{4}\approx 3.92\text{ and } x=\frac{8-\sqrt{59}}{4}\approx0.08$

Therefore, the ball will reach a height of 10 feet at approximately x = 0.08 and x = 3.92.

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3 years ago

Please help if good

Mariana [72]

Answer:

a=formula : Sum of all side

= 3+5+3

=11 ans

Step-by-step explanation:

formula is sum of all side

so add 3+5+3 ans =11

this is simple method

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3 years ago

Please help I will give you brainliest!!!!

VikaD [51]

Answer:

63.25sqft

Step-by-step explanation:

semi circle:

a= $\pi$ r^2

a= $\pi$ (5)^2 (radius is 5 bc diameter is 10 so you divide it by 2)

a=25 $\pi$

a=78.5/2=39.25 (divide by 2 bc its a semi circle)

triangle:

a=1/2bh

a=1/2(6x8)

a=1/2(48)

a=24

area:

39.25+24=63.25

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3 years ago