E

Mathematics

1 answer:

Shtirlitz [24]3 years ago

3 0

Answer:

Point (6, -1) = (x, y)

Slope = -3

The proper linear equation is written in following form: y = mx + b (where m is slope, and b is y-intercept). Since we already have the slope, we need to find the y-intercept, b

So we plug in what we have:

y = mx + b

-1 = (-3)(6) + b, where we solve for b

-1 = -18 + b

b = 17

Finally, the equation of the line that passes through point (6, -1) and has a slope of -3 is y = -3x + 17

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Evaluate the function rule to find the range of each function for the domain {-3, 0, 5}. f(x) = x² − 6x + 4

harina [27]

Range is output for given input

domain is D={-3,0,5}
input -3,0 and 5 for x

f(-3)=(-3)^2-6(-3)+4
f(-3)=9+18+4
f(-3)=31

F(0)=(0)^2-6(0)+4

f(0)=0-0+4

f(0)=4

f(5)=(5)^2-6(5)+4

f(5)=25-30+4

f(5)=-1

Domain={-3,0,5}

Range={31,4,-1}

5 0

3 years ago

Pretty Pavers company is installing a driveway. Below is a diagram of the driveway they are

prohojiy [21]

Answer:

The most correct option is;

(B) 958.2 ft.²

Step-by-step explanation:

From the question, the dimension of each square = 3 ft.²

Therefore, the length of the sides of the square = √3 ft.

Based on the above dimensions, the dimension of the small semicircle is found by counting the number of square sides ti subtends as follows;

The dimension of the diameter of the small semicircle = 10·√3

Radius of the small semicircle = Diameter/2 = 10·√3/2 = 5·√3

Area of the small semicircle = (π·r²)/2 = (π×(5·√3)²)/2 = 117.81 ft.²

Similarly;

The dimension of the diameter of the large semicircle = 10·√3 + 2 × 6 × √3

∴ The dimension of the diameter of the large semicircle = 22·√3

Radius of the large semicircle = Diameter/2 = 22·√3/2 = 11·√3

Area of the large semicircle = (π·r²)/2 = (π×(11·√3)²)/2 = 570.2 ft.²

Area of rectangle = 11·√3 × 17·√3 = 561

Area, A of large semicircle cutting into the rectangle is found as follows;

$A_{(segment \, of \, semicircle)} = \frac{1}{4} \times (\theta - sin\theta) \times r^2$

Where:

$\theta = 2\times tan^{-1}( \frac{The \, number \, of \, vertical \, squrare \, sides \ cut \, by \ the \ large \, semicircle}{The \, number \, of \, horizontal \, squrare \, sides \ cut \, by \ the \ large \, semicircle} )$