Calculate the volume in litres of the cuboid shown above ​

Answer:

5668.3

Step-by-step explanation:

The problem can be represented as a right angled triangle as shown below.

The angle of depression is equivalent to the angle inside the triangle (alternate angles) and it is 34°.

The altitude of the balloon is 2999 feet. (opposite)

Using trigonometric function, SOHCAHTOA, we can solve this:

[tex]sin(34) = \frac{opposite}{hypotenuse}\\ \\sin(34) = \frac{altitude}{distance}\\\\sin(34) = \frac{2999}{distance}\\\\distance = \frac{2999}{sin34}\\\\distance = 5668.3 feet[/tex]

The pilot is 5668.3 feet far away from the house.

Answer:

f(0) = 3

Step-by-step explanation:

Step 1: Distribute

f(x) = -3x + 3

Step 2: Plug in

f(0) = -3(0) + 3

f(0) = 3

Answer:

f(0) = 3

Step-by-step explanation:

f(x) = -3(x-1)

Put x as 0 and solve.

f(0) = -3(0-1)

Solve the brackets.

f(0) = -3(-1)

Multiply both terms.

f(0) = 3

Answer:

4/15

Step-by-step explanation:

Answer:

let number of bags of popcorn = b

let number of drinks = d

at most = maximum

b + d ≤ 12

Answer:

51

Step-by-step explanation:

Multiplying 5.1 by 10^1 shifts the decimal point 1 place to the right.  We get 51.

Answer:

342/6 = 57

Step-by-step explanation:

Just basic division

Answer:

x=-6.5

Step-by-step explanation:

[tex]7\frac{1}{4} - 13\frac{3}{4}=-6\frac{1}{2}=-6.5[/tex]

Step-by-step explanation:

8x(7y+2)-4(7y+2)

=56xy+16x-28y-8

Answer:

56xy+16x-28y-8

Step-by-step explanation:

you have to use the FOIL method to solve this is problem which is

F-First

O-Outer

I-Inner

F-Last

Answer:

y - x = - 5

Step-by-step explanation:

Applying the rule gives

x = [tex]\frac{1}{3}[/tex] × 36 + 9 = 12 + 9 = 21

y = [tex]\frac{1}{3}[/tex] × 21 + 9 = 7 + 9 = 16

Thus

y - x = 16 - 21 = - 5

Answer:

Option C

Step-by-step explanation:

=> 4p + 2 = 8

Subtracting 2 to both sides

=> 4p = 8-2

=> 4p = 6

Dividing both sides by 4

=> p = 1.5

Answer:

The answer is C.

Step-by-step explanation:

First, you have to subtract 2 to both sides :

[tex]4p + 2 = 8[/tex]

[tex]4p + 2 - 2 = 8 - 2[/tex]

[tex]4p = 6[/tex]

Next, you have to divide it by 4 :

[tex]4p = 6[/tex]

[tex]p = 6 \div 4[/tex]

[tex]p = 3 \div 2[/tex]

[tex]p = 1.5[/tex]

Answer:

-6

Step-by-step explanation:

15/4 ÷ -5/8

Copy dot flip

15/4 * -8/5

Rewrite

15/5 * -8/4

3 * -2

-6

Answer:

-6

Step 1) Do keep change flip if your beginner

After you do that

you get 15/4x-8/5 multiply and simply get -6

Answer:

-1.67

Step-by-step explanation:

Answer:

area of the original square = 144 cm²

Step-by-step explanation:

You didn't include the whole question, but nonetheless this is the answer.

Take care. (:

Answer:

144 cm^2

Step-by-step explanation:

Answer: Not a solution of the System

Step-by-step explanation:

Plug in 0 for x and 2 for y for both equations.

Note, if only one of the equations is a true statement

(0.2) is not a solution. If either one of the equation is not true, the ordered pair is not a solution.

0+3(2)=4

3*2=6

0+6=6

6≠4

This was only the first equation but it was not true.

The equation is not true, so (0, 2) is not a solution of the second equation.  Therefore, (0, 2) is not a solution of the system of equations.

To determine graphically whether the ordered pair (0, 2) is a solution of the system of equations, we can plot the two equations on a graph. If the point (0, 2) lies on both lines, then it is a solution of the system.

The first equation is x + 3y = 4.  To plot this equation, we can first solve for y:

y = -(1/3)x + 4/3

This equation has a slope of -1/3 and a y-intercept of 4/3.  So, the line will rise 1 unit for every 3 units it moves to the left.  The y-intercept is 4/3, so the line will pass through the point (0, 4/3).  Three units to the left of (0, 4/3) is (-3, 7/3), so the line will also pass through this point.

The second equation is 3x + y = -2.  To plot this equation, we can first solve for y:

y = -3x - 2

This equation has a slope of -3 and a y-intercept of -2.  So, the line will fall 3 units for every 1 unit it moves to the right.  The y-intercept is -2, so the line will pass through the point (0, -2).  One unit to the right of (0, -2) is (1, -5), so the line will also pass through this point.

We can  check this algebraically.  Substituting (0, 2) into the first equation, we get:

0 + 3× 2 = 4

6 ≠ 4

This equation is not true, so (0, 2) is not a solution of the first equation.  Substituting (0, 2) into the second equation, we get:

3  × 0 + 2 = -2

2 = -2

This equation is also not true, so (0, 2) is not a solution of the second equation.  Therefore, (0, 2) is not a solution of the system of equations.

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Answer:

78 red apples

Step-by-step explanation:

Set up the equations

r + y + g = 130

y = 3g

r = 2y

If r = 2y and y = 3g, then r = 6g

Plug in the two equations, y = 3g, and r = 6g

6g + 3g + g = 130

10g = 130

g = 13

Plug in 13 as g in the equation r = 6g

r = 6(13)

r = 78

There were 78 red apples

Step-by-step explanation:

Simple Interest = PTR/100

=1000* 30* 6/100

=1800.

Amount= Principal + Interest

= 1000+1800

= $2800

The amount of money that has at the of 30 years is $​2800.

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time.

Unlike compound interest, which adds the interest from the principal of prior years to determine the interest of the following year, the principal amount in simple interest remains constant.

As per the given,

Principle amount P = $1000

Rate of interest R = 6%

Time span T = 30 years.

Total amount = Principle amount + Interest

Total amount = P + (PRT)/100

Total amount = $1000 + (1000 x 6 x 30)/100

⇒ $2800

Hence "The amount of money that has at the of 30 years is $​2800".

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Answer:

A. 72

Step-by-step explanation:

Determinant of a 2x2 matrix: ad - bc

In that case,

24(18) - 30(12)

432 - 360

72

And we have our answer.

Answer:

160J

Step-by-step explanation:

I think this is the answer

Answer:

35 acres

Step-by-step explanation:

We have 15.8 happys per acre and the we have exactly 553 happys living in happy land.

To calculate the number of acres, we just need to divide the number of happys we have by the number by the number of happys per acre

Mathematically, that would be 553/15.8 = 35 acres

Happyland have 35 acres of Land.

Given to us:

Population of Happyland = 553 Happys

Population of Happyland per acre = 15.8 Happys per acre,

Land with Happyland in acres:

[tex]\rm {Land with Happyland in acres =\dfrac{ Total\ number\ of\ Happys}{Population\ of\ Happyland\ per\ acre}}[/tex]

Putting in the value we get,

[tex]\rm {Land with Happyland in acres =\dfrac{ Total\ number\ of\ Happys}{Population\ of\ Happyland\ per\ acre}}\\\\\rm {Land with Happyland in acres =\dfrac{553}{15.8}}\\\\\rm {Land with Happyland in acres = 35 acres[/tex]

Hence, Happyland have 35 acres of Land.

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Answer:

60

Step-by-step explanation:

The sum of interior angles in a triangle is 180

180-90-30=60

Answer:

- 156250

Step-by-step explanation:

Find the ratio of the geometric sequence.

-10/2 =  -5

50/-10 = -5

The common ratio is -5.

Apply the formula.

an = ar^(n-1)

Where a is the first term and r is the ratio.

a8 = 2(-5)^(8-1)

a8 = 2(-5)^7

a8 = 2(-71825)

a8 = -156250

Answer:

1953125

Step-by-step explanation:

Step 1: Simplify

(5x5x5) x (5x5x5x5x5x5) = [tex]5^3(5^6)[/tex]

Step 2: Combine exponents

[tex]5^3(5^6)[/tex] = [tex]5^9[/tex]

Step 3: Evaluate

[tex]5^9[/tex] = 1953125

Answer:

15750

Step-by-step explanation:

First you calculate the first bracket (it is equal to 125), then you calculate the second bracket (it is equal to 15625), and then you multiply the 2 numbers.

Answer:

34/95

Step-by-step explanation:

Since 38 students choose football and 23 students chose tennis, then 95 - 38 - 23 = 34 students chose running. The probability is 34 / 95.

Answer:

(-1, 5), (2, -1), (0, 3)

Answer: 1324.12 sq. cm.

Step-by-step explanation:

A=2πrh+2πr2

A = 2π x 8.2 x 17.5 + 2π x 8.2^2

A = 2π x 143.50 + 2π x 67.24

A= 1324.12

Answer:

SA = 1324.1 cm²

Step-by-step explanation:

Surface Area of Cylinder = [tex]2\pi rh+2\pi r^2[/tex]

Where r = 8.2 cm, h = 17.5 cm

=> SA = [tex]2(3.14)(8.2)(17.5)+2(3.14)(8.2)^2[/tex]

=> SA = [tex]901.6+2(3.14)(67.24)[/tex]

=> SA = 901.6 + 422.5

=> SA = 1324.1 cm²

Answer:

I think it might be the second one or maybe the first one

Step-by-step explanation:

Im not quite sure so dont blame me if its wrong

Answer:

87th term is 497

Step-by-step explanation:

first, you have to find the nth term:

figure out the difference between your set of numbers (in our case +6)

that means that is 6n. next, the nth term is basically the 0th term so you have to find the 0th term. all you have to do is do the inverse of 6n (-6n or -6), which gives us -25.

nth term= 6n-25

now replace n with 87.

final step:

87*6 (6n and n=87) and that gives you 522. then, you have to do 522-25, due to the equation. 522-25=497

497 is your 87th term.

Answer:

Step-by-step explanation:

[tex]a = -19\\d = T_{2} -T_{1} \\d = -19-(-13)\\d = -19+13\\d = -6\\T_{n}= a+(n-1)d \\\\T_{87} = -19+(87-1)-6\\T_{87} = -19+(86)*-6\\T_{87} = -19-516\\T_{87} = -535[/tex]

Answer:

A= BEP and BCG

Because they aree the only triangle

C= about 600 to 750

Step-by-step explanation:

Answer:

The measure of angle a is 43 degrees.

Step-by-step explanation:

Angle P is congruent to Angle R. A triangle's angles add up to 180 degrees. 47*2=94. 180-94=86 degrees. 86/2=43 degrees.

Answer: 43°

Step-by-step explanation:

The degree of a triangle adds up to 180. We are given an angle of 47 and there is a right angle of 90

We now have 90 + 47 + a = 180

137 + a = 180

a = 43

Answer:

[tex] - x + x 2 - 6[/tex]

that's it hope its helpful