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Sergeu [11.5K]
3 years ago
13

A new sidewalk will be 5 feet​ wide, 100 feet​ long, and filled to a depth of 3 inches ​(0.25 ​foot) with concrete. How many cub

ic yards of concrete are​ needed?
Mathematics
1 answer:
GarryVolchara [31]3 years ago
4 0

Answer:

4.63 cubic yard.

Step-by-step explanation:

Given,

The length of sidewalk, l = 100 feet,

Width, w = 5 feet,

Depth, h = 3 inches = 0.25 feet,

Thus, the volume of the concrete needed for making the sidewalk,

V=l\times w\times h

=100\times 5\times 0.25

= 125 cubic feet,

∵ 1 cubic yard = 27 cubic feet,

⇒ 1 cubic feet = \frac{1}{27} cubic yard,

Thus, the quantity of concrete needed = \frac{125}{27} ≈ 4.63 cubic yard.

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The curve with equation y = f ( x ) is stretched so that the point (-3,-5) moves to the point (-3,-10). State in terms of f ( x
Leviafan [203]

Answer:

The transformed function is g(x) = 2\cdot f(x), \forall\,x \in \mathbb{R}.

Step-by-step explanation:

Let be f(x) and g(x) continuous functions in x. In this case, the stretch factor consist on multiplying f(x) by a scalar factor, so that:

g(x) = k \cdot f(x), \forall\, k\in \mathbb{R}, k \neq 0

The stretch factor is:

k = \frac{g(x)}{f(x)}, \forall\, x \in \mathbb{R}

If f(-3) = -5 and g(-3) = -10, then:

k = \frac{g(-3)}{f(-3)}

k = \frac{-10}{-5}

k = 2

The transformed function is g(x) = 2\cdot f(x), \forall\,x \in \mathbb{R}.

5 0
4 years ago
6(a)If the gradient of the straight line
tensa zangetsu [6.8K]

Answer:

(i) k =1

(ii) y-intercept is 7

Step-by-step explanation:

<u>Given line:</u>

  • ky = kx + x + 7

<u>Divide all terms by k to get slope-intercept form of the line</u>

  • y = (1 + 1/k)x + 7/k

<u>Since the gradient (slope) of the line is 2:</u>

  • 1 + 1/k = 2
  • 1/k = 1
  • k = 1

<u>The equation is now:</u>

  • y = 2x + 7

<u>y - intercept is found when x = 0</u>

  • x = 0 ⇒
  • y = 2*0 + 7
  • y = 7

5 0
3 years ago
Everett drove his motorcycle 16 miles in 4/5 of an hour. If he continue to drive at this rate how many miles would he drive in a
Elenna [48]

Answer:

20 miles in an hour.

Step-by-step explanation:

4/5=0.8

16/0.8=x/1

cross product

0.8*x=16*1

0.8x=16

x=16/0.8

x=20

4 0
3 years ago
A living room will be painted with white trim. The ratio of the blue surface area between the walls is 1:10. Of 2 gallons of blu
bija089 [108]

Answer:

20 gallons

Step-by-step explanation:

The living room is made up of white trim and blue surface area between the walls. Since the ratio of the blue surface area between the walls to the white trim is given by 1 : 10.

Also 2 gallons of blue paints are used for the walls, let x represent the number of white paint used in gallons. Hence:

number of white paint in gallons = [1 / (1 + 10)] * total number of paints = 1 / 11 * total number of paints

2 = 1/11  * total number of paints used

total number of paints  = 22 gallons

number of white paint (x) = [10 / (1 + 10)] * total number of paints = 1 / 11 * total number of paints

x = 10/11 * 22

x = 20 gallons

Therefore 20 gallons of white paint was used

7 0
3 years ago
The slope of the line containing the points (6, 4) and (-5, 3) is: <br> A. 1/11 <br> B. 1 <br> C. -1
svetoff [14.1K]

\bf (\stackrel{x_1}{6}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{3}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3-4}{-5-6}\implies \cfrac{-1}{-11}\implies \cfrac{1}{11}

5 0
3 years ago
Read 2 more answers
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