Construction crew is using heavy equipment to dig a hole in which the foundation of a house will be built. The whole will be in the shape of a right rectangular prism with dimensions of 4 feet in depth, 100 feet long, and 50 feet wide. The soil will be removed using a truck that can hold a maximum of 40,000 pounds. The soil weighs 90 pounds per cubic foot. What is the least number of truckloads needed to remove all of the soil ?

Answer: [tex]75.47\ ft[/tex]

Step-by-step explanation:

Given

String of the kite is [tex]l=100\ ft[/tex]

Angle of elevation [tex]\theta=49^{\circ}[/tex]

suppose altitude of the kite is h

from the figure, we can write

[tex]\Rightarrow \sin 49^{\circ}=\dfrac{h}{100}\\\\\Rightarrow h=100\sin 49^{\circ}\\\\\Rightarrow h=75.47\ ft[/tex]

Thus, the altitude of the kite is [tex]75.47\ ft[/tex]

Answer:

Step-by-step explanation:

Given,

Vertex (h, k ) = (1,0)

Now,

We know,

f(x) = a(x-h)²+k

Since, it passess through (2, −17)

Put x = 2 and  y = - 17

or, -17 = a(2 - 1)² + 0

or, -17 = a

Now,

f(x) = a(x - h)² + k

     = -17(x - 1)² + 0

     = -17x² + 34x - 17

Answer:

3/4 cups

Step-by-step explanation:

Adding the fractions

1/4 + 1/2 + 1/4 + 3/4 + 1 + 1 1/2 + 1/2 + 1 3/4 + 1/2 + 1/2

And the the L.C.M to be 4

=30/4

=15/2

Mean = 15/2 ÷ 10

=15/2 × 1/10

3/4

Answer:

Option (2)

Step-by-step explanation:

Given geometric sequence is,

2, 5, 12.5, 31.25, 78.125......

First term = a₁ = 2

Common ratio of the sequence = r = [tex]\frac{5}{2}[/tex]

                                                          = 2.5

Recursive formula of a geometric sequence is given by,

[tex]a_n=a_{n-1}(r)[/tex]

Here, [tex]a_n=[/tex] nth term of the sequence

[tex]a_{n-1}=[/tex] (n - 1)th term

r = common ratio

Therefore, recursive formula for the given sequence will be,

[tex]a_1=2[/tex]

[tex]a_n=a_{n-1}(2.5)[/tex]

Explicit formula of a geometric sequence is given by,

[tex]a_n=a_1(r)^{n-1}[/tex]

Therefore, explicit formula of the sequence will be,

[tex]a_n=2(2.5)^{n-1}[/tex]

Option (2) will be the correct option.

Answer:

The required solution: (a, u) = (5, [tex]\frac{35}{2}[/tex])

Step-by-step explanation:

Answer:

Hello! answer: 252

Step-by-step explanation:

To find parelogram area you do base × height so... 21 × 12 = 252 therefore 252 is the area Hope that helps!

The exact value of cot A will be 0.857.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The co-secant of angle A is √85 / 6. And that angle A is in Quadrant I.

Then the value of angle A will be

csc A = √85 / 6

1 / cos A = √85 / 6

cos A = 6 / √85

A = 49.4°

Then the exact value of cot A will be

cot A = cot 49.4°

cot A = 0.857

The exact value of cot A will be 0.857.

More about the trigonometry link is given below.

https://brainly.com/question/22698523

#SPJ2

Answer:

$3.75

Step-by-step explanation:

Answer:1832

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

like the guy above me said

Answer:

well you answered the question in your question: you have Area = 136 square units. How you got it, you need to be more specific. Maybe it's because the side lengths are 2 * 68 for example. If anything provide more info. tried to help the best I can

Step-by-step explanation:

1,873

Step-by-step explanation:

Answer:

The answer is 188/15

Hope this helps!

Brainliest??

Answer:

[tex]6[/tex]

[tex]16[/tex]

Step-by-step explanation:

[tex] \frac{x}{12} + \frac{y}{3} = 2[/tex]

[tex] \frac{y}{3 } = 2 - \frac{x}{12} [/tex]

[tex]y = 3( 2 - \frac{x}{12} )[/tex]

[tex]y = 6 - \frac{x}{4} [/tex]

[tex]y = - \frac{x}{4} + 6[/tex]

[tex] {x}^{2} - 8x + c[/tex]

[tex] {x}^{2} + c - 18[/tex]

To find the c value ,

[tex]c = ( \frac{b}{2} {)}^{2} [/tex]

divide the coefficient of x by 2 and square the result.

[tex]( - 1 \times 4 {)}^{2} [/tex]

[tex]( - 4 {)}^{2} [/tex]

[tex]16[/tex]

Answer:

A

Step-by-step explanation:

look at how the sign are set +-can't be correct so b is out c some of the equation is missing d in d the equation is different e you can't have--1 that's wrong

Answer:

-40

Step-by-step explanation:

y−27−13

=y+−27+−13

Combine Like Terms:

=y+−27+−13

=(y)+(−27+−13)

=y + −40

Answer:

The angle SQR is half the intercepted arc SR which is 43°

Answer:

n= 12     m=5

Step-by-step explanation:

Because it is a parallelogram, the parallel sides are equal in length.  So n = side length 12.  n = 12

For the other one, m + 1 = 6

Be careful to solve for m, not m+1.

m=6-1

m=5

Answer:

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

(0, 0) Is not a answer because ithe point does not fall within the shaded area

Answer:

70

Step-by-step explanation:

180-80-30=70

Answer:

7x+3=8x+1[corresponding angle are equal]

3-1=8x-7x

x=2 is a required answer.

Answer:

[tex]7x + 3 = 8x + 1[/tex]

[tex]x = 2[/tex]

Answer:

Radius = 11.85yd

Step-by-step explanation:

Volume of a Cone formula: V = πr²(h/3)

We know that;

V = Volume

r = radius

π = pi (this is a sign located on your calculator)

h = height

We are given that;

V = 4,410

r = unknown

h = 30

Let's substitute the values in:

=> V = πr²(h/3)

=> 4,410 = πr²(30/3)

=> 4,410 = πr²(10)

=> 4,410 / 10 = πr²

=> 441 = πr²

=> 441 / π = r²

=> 140.37 = r²

=> [tex]\sqrt{140.37}[/tex] = r

=> 11.85 = r

Therefore, the radius of the cone = 11.85yd

Hope this helps!

Answer:

141.3 pounds of seeds

Step-by-step explanation:

1 acre = 4.5 lbs

31.4 acres = 141.3 lbs

Answer:

Amount Charli paid for the car = $9,450

Step-by-step explanation:

Amount Carter paid for the car = $21,000

Sienna paid 75% of what Charli paid

Amount Sienna paid for the car = 75% of $21,000

= 75/100 * $21,000

= 0.75 * $21,000

= $15,750

Amount Sienna paid for the car = $15,750

Charli paid 60% of what Sienna paid

Amount Charli paid for the car = 60% of $15,750

= 60/100 * 15,750

= 0.60 * 15,750

= $9,450

Amount Charli paid for the car = $9,450

Answer:

91.5

Step-by-step explanation:

If the table is asking for the amount of miles travelled on 3 gallons of gas, you get 3 * 30.5 = 91.5

This is because one gallon gives 30.5 miles and if you have three gallons, you get 30.5 + 30.5 + 30.5 which is the same as 3 * 30.5