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3 years ago

A right triangle has a leg of 11 and a hypotenuse of 16. Find the missing leg (in simplest radical form)

Mathematics

1 answer:

wel3 years ago

6 0

Answer: d

Step-by-step explanation:

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4. Gloria the grasshopper is working on her hops.

aivan3 [116]

The path that Gloria follows when she jumped is a path of parabola.

The equation of the parabola that describes the path of her jump is $\mathbf{y = -\frac{5}{49}(x - 14)^2 + 20}$

The given parameters are:

$\mathbf{Height = 20}$

$\mathbf{Length = 28}$

<em>Assume she starts from the origin (0,0)</em>

The midpoint would be:

$\mathbf{Mid = \frac 12 \times Length}$

$\mathbf{Mid = \frac 12 \times 28}$

$\mathbf{Mid = 14}$

So, the vertex of the parabola is:

$\mathbf{Vertex = (Mid,Height)}$

Express properly as:

$\mathbf{(h,k) = (14,20)}$

A point on the graph would be:

$\mathbf{(x,y) = (28,0)}$

The equation of a parabola is calculated using:

$\mathbf{y = a(x - h)^2 + k}$

Substitute $\mathbf{(h,k) = (14,20)}$ in $\mathbf{y = a(x - h)^2 + k}$

$\mathbf{y = a(x - 14)^2 + 20}$

Substitute $\mathbf{(x,y) = (28,0)}$ in $\mathbf{y = a(x - 14)^2 + 20}$

$\mathbf{0 = a(28 - 14)^2 + 20}$

$\mathbf{0 = a(14)^2 + 20}$

Collect like terms

$\mathbf{a(14)^2 =- 20}$

Solve for a

$\mathbf{a =- \frac{20}{14^2}}$

$\mathbf{a =- \frac{20}{196}}$

Simplify

$\mathbf{a =- \frac{5}{49}}$

Substitute $\mathbf{a =- \frac{5}{49}}$ in $\mathbf{y = a(x - 14)^2 + 20}$

$\mathbf{y = -\frac{5}{49}(x - 14)^2 + 20}$

Hence, the equation of the parabola that describes the path of her jump is $\mathbf{y = -\frac{5}{49}(x - 14)^2 + 20}$

See attachment for the graph

Read more about equations of parabola at:

brainly.com/question/4074088

7 0

3 years ago

An orbiting satellite has seven solar cells, which function independently of each other. During a mission, each cell fails with

Makovka662 [10]

The due date is 2pm, dolololo

4 0

4 years ago

HELP ASAPPPP!!!BRAINLEST WILL BE GIVEN!!!

liraira [26]

Answer:

30 days

Step-by-step explanation:

The common multiples of 15 and 6 are 30, 60, 90 etc and because it increases by 30 each time we can find out that he will play both football and basketball together in thirty days!

8 0

3 years ago

Which number line represents the solution to -3x ≤ -36?

seraphim [82]

Answer:

x ≥12

Step-by-step explanation:

-3x ≤ -36

Divide each side by -3, remembering to flip the inequality

-3x/-3 ≥ -36/-3

x ≥12

4 0

3 years ago

PLEASE ANSWER ASAP FOR BRANLEST!!!!!!!!!!!!!!!

adoni [48]

Answer:

t = 8

Step-by-step explanation:

8 0

3 years ago