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2 years ago

11. The speed limit in a residential neighborhood is 35 miles per hour. This is one half

Mathematics

2 answers:

tatuchka [14]2 years ago

6 0

Answer:

35*2 = 70

70 mph on the Major Highway

Step-by-step explanation:

sweet-ann [11.9K]2 years ago

4 0

Answer:

Step-by-step explanation:

if 35 is half of x (x being the speed of a major interstate highway a few miles away) then this means $\frac{x}{2} =35$ you multipliy both sides by 2 to get x by its self and now have x=70

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2 years ago

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2 years ago

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

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2 years ago

A retangle has a perimeter (p) of 58 inches. The length (L) is one more than 3 times the width (W)

worty [1.4K]

The rectangle has a perimeter P of 58 inches.The length l is one more than 3 times the width w.write and solve a system of linear equations to find the length and width of the rectangle?

Answer:

Length(L)=22 inches

Width(W) = 7 inches

Step-by-step explanation:

GIven:-

Perimeter (p)=58 inches,

Length(L)= one more than 3 times the width(W)

Let, W=x ---------------------------------(equation 1

$L=3x+1$ -----------------------(equation 2)