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2 years ago

Hi can someone help me with this geo question please thanks

Mathematics

1 answer:

IrinaVladis [17]2 years ago

7 0

Answer:

x = 24 , y = 19

Step-by-step explanation:

(2x + 13) and 47 + 3x are same- side interior angles and sum to 180° , so

2x + 13 + 47 + 3x = 180 , that is

5x + 60 = 180 ( subtract 60 from both sides )

5x = 120 ( divide both sides by 5 )

x = 24

Then 3x = 3 × 24 = 72

5y - 23 and 3x are corresponding angles and are congruent , then

5y - 23 = 72 ( add 23 to both sides )

5y = 95 ( divide both sides by 5 )

y = 19

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

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

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Express properly as:

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

A point on the graph would be:

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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

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