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3 years ago

Graph the line with slope 3/4 passing through the point (3, - 3) .

Mathematics

1 answer:

Svetlanka [38]3 years ago

4 0

Answer:

The line in slope-intercept form is y=3/4x-5.25.

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

2 years ago

Use the function rule to complete the table<br> -10x + y = 4

alexgriva [62]

Plug in the given numbers (x) to the equation. For example, let's take the first value it gives us. -10(-2) +y=4 20+y=4 y=-16 Then you would put that on the table, and plug in the next value(s). Hope this helped!

8 0

3 years ago

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Mhm help please! quarantine got me

Karolina [17]

The answer would be 9.4

3 0

3 years ago

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If the geometric mean of a and 28 is 16 sqrt 7 find a

kozerog [31]

Answer:

a = 64

Step-by-step explanation:

The geometric mean of 2 numbers a and b is $\sqrt{ab}$ , then

$\sqrt{28a}$ = 16 $\sqrt{7}$ ( square both sides )

28a = (16 $\sqrt{7}$ )² = 1792 ( divide both sides by 28 )

a = 64

8 0

2 years ago

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A 3cm×10cm rectangle sits inside a circle with radius of 12. Find the area of the shaded region

kolezko [41]

Answer:

422.4cm²

Step-by-step explanation:

area of circle is pi x 12² which is 144 pi

144pi subtract 30 is 422.4

6 0

2 years ago