An architect drew plans for an office building.
The building will have the dimensions shown.

Building is made up of 2 cuboids. First cuboid has length as 10 ft, height as 12 ft and width as 10ft. Second cuboid has length as 10 ft, height as 30 ft and width as 10 ft.

Part A
Which is an expression for the total volume of the building?
A. (20 × 10 × 30) + (12 × 10 × 10)
B. (10 × 10 × 30) + (10 × 10 × 12)
C. (30 × 10 × 10) + (10 × 10 × 20)
D. (10 × 20 × 30) + (10 × 12 × 20)
Part B
What is the volume of the building? Enter your answer in the box.

ft3

Answer:

15a^5b^15

Step-by-step explanation:

3*5 = 15

when multiplying exponents with the same base, you just add the exponents together. so 2+3 = 5 and 7+8 = 15

Answer:

15a⁵b¹⁵

Step-by-step explanation:

( 3a²b⁷)(5a³b⁸)

remove unnecessary parantheses

using exponent rule

calculate the product

Answer:

(10, 4, -3)

Step-by-step explanation:

z = -3

y + z = 1

y - 3 = 1

y = 4

x + y - z = 17

x + 4 - -3 = 17

x + 4 + 3 = 17

x + 7 = 17

x = 10

(10, 4, -3)

Answer:

(10,4,-3)  

Step-by-step explanation:

(x,y,z)

z= -3 given

y+z = 1 (equation 2)

y-3 =1

y=4 (solve 2 after substation)

eq #1 : x + 4 - (-3) = 17

x+4+ 3 = 17

x+ 7 = 17

x=10

(10,4,-3)  

Answer:

B) $3 per gallon

Step-by-step explanation:

You can see on the graph that for 1 gallon of gasoline, it is $3.

Hope this helped!

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Answer: "C"

roots would make the function "0"

so just plug in the numbers...

with a + 12 you need minuses to cancel out...

B & C can not be the answer...

A is -i -3 + 4i - 12 which also is not 0

C is :  8i -12 -8i +12 WHICH DOES = 0

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

.....

Kathy is 18 and Kaity is 6. In six years, Kathy will be 24 and Kaity will be 12.

Good luck :)

Answer:

Katie is 6; Cathy is 18!

Happy learning!

--Applepi101

First term = a= -10

common difference=d= -8+10 = 2

n= 98

the 98th term = a+(n-1)d = -10+ (98-1)2

= -10+(97)2 = -10 +194

=184

98th term of the given arithmetic sequence is 184.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.

The given arithmetic sequence is -10, -8, -6,......

Here, a=-10, d=-8-(-10) = 2

So, aₙ=-10+(n-1)×2

aₙ=-10+2n-2

aₙ=2n-12

a₉₈=2×98-12

a₉₈=184

Therefore, 98th term of the given arithmetic sequence is 184.

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Answer:

[tex]1) y=-6[/tex]

[tex]2)x=3[/tex]

[tex]3) y=8[/tex]

[tex]4)a=8[/tex]

Step-by-step explanation:

[tex]4y+24=0[/tex]

subtract 24 from both sides

[tex]4y=-24[/tex]

divide both sides by 4

[tex]y=-6[/tex]

---------->>>>

[tex]15+3=6x[/tex]

combine like terms

[tex]18=6x[/tex]

divide both sides by 6

[tex]3=x[/tex]

---------->>>>

[tex]9y-72=0[/tex]

add 72 to both sides

[tex]9y+72[/tex]

divide both sides by 9

[tex]y=8[/tex]

---------->>>>

[tex]8a=75-11[/tex]

combine like terms

[tex]8a=64[/tex]

divide both sides by 8

[tex]a=8[/tex]

--------------------------------------------

Hope this is helpful.

Answer:

area: 454.2 sq.cm

perimeter: 77.7 cm

Step-by-step explanation:

to find area, find the area of all the separate shapes and add them together:

semi-circle:

radius is 12 cm

area = [tex]\frac{\pi (12)^2\\}{2}[/tex] = 226.2 sq.cm

separate the trapezoid into two right triangles and a rectangle.

area for triangles:

[tex]\frac{1}{2}[/tex](5)(12) = 30

30 x 2 = 60 sq.cm (since there are two triangles)

area for rectangle:

12 x 14 = 168 sq.cm

area of whole shape: 226.2 + 60 + 168 = 454.2 sq.cm

for perimeter, just add the length of the exterior sides together.

we have some unknown sides, such as the semicircle and the sides of the trapezoid

we can find the hypotenuse of the triangles we used earlier to find the sides of the trapezoid with pythagorean theorem

[tex]5^2 + 12^2 = c^2[/tex]

[tex]25 + 144 = c^2[/tex]

[tex]169 = c^2[/tex]

[tex]\sqrt{169} =\sqrt{c^2}[/tex]

c = 13 cm

to find the outside perimeter of the semi-circle, solve as if you were finding the circumference of a normal circle and divide it in half

[tex]\frac{2\pi12}{2}[/tex] = 37.7 cm

now add it all up:

14 + 13 + 13 +37.7 = 77.7

Answer:

- 7/2

Step-by-step explanation:

Answer:

x=22

Step-by-step explanation:

x+14=5x-74 (being corresponding angles and correcponding angles are always equal)

14+74=5x-x

88=4x

88/4=x

22=x

Answer:

The number of candy which can be bought for 20 dollars is 16 candies. Hence, the required answer is 16. The number of candy bars that can be bought for $20 are 16.

16 candy bars can be bought for 20 dollars. Hence, the correct answer is C.

An expression is a mathematical representation or statement that combines variables, constants, and mathematical operations. It does not contain an equals sign (=) and does not make a statement of equality or inequality. Instead, an expression represents a value or a computation.

To determine how many candy bars can be bought for 20 dollars, we need to use the given information that 4 candy bars can be purchased for $5.

To find the cost of one candy bar, we divide $5 by 4:

Cost of one candy bar = $5 / 4 = $1.25

Now, we can calculate how many candy bars can be bought for $20 by dividing 20 by the cost of one candy bar:

Number of candy bars = $20 / $1.25 = 16

Therefore, 16 candy bars can be bought for 20 dollars. Hence, the correct answer is 16 bars.

To know more about an expression follow

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Answer:

The length of each piece is 13 m.

Step-by-step explanation:

Maria bought 78 meters of rope, she divided the rope into 6 equal parts on Tuesday, May 8, How many meters is each piece?  

a) Each piece measures 312m

c) Each piece measures 13m

d) each piece mites 92m

b) Each piece measures 9m and 75cm

Total length, L =  78 m

Number of pieces, n = 6

length of each piece,

d = L/n = 78/6 = 13 m

So, the correct option is (c).  

Answer:

35 cm

Step-by-step explanation:

A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs

Characteristics of a trapezoid

It has 4 vertices and edges

If both pairs of its opposite sides of a trapezoid are parallel, it becomes a parallelogram

Area of a trapezoid =   x (sum of the lengths of the parallel sides) x height

h = 147x2 / (5.3 + 3.1) = 35cm

Answer:

$30

Step-by-step explanation:

$12/6=$2/can

$2/can x 15 cans=$30

Answer:

You will need to study and get the answer using

Step-by-step explanation:

a link: https://brainly.com/question/16261743. Taking a rescoruce. i surely think that you can do it

Answer:

the answer is (d)!! hope this helps

Step-by-step explanation:

Answer:

4x² - 10x - 6

Step-by-step explanation:

(x-3)(4x+2)

4x² + 2x - 12x - 6

4x² - 10x - 6

Answer:

146 adult tickets were sold

Step-by-step explanation:

subtract 73 from 573 which = 500

then you'll take away 500 from 73 =427

then you will subtract 427 from 573= 146

Answer:

21 is the answer

Step-by-step explanation:

from the figure it can be seen that

angle G = angle J

angle H = angle K and

angle I = angle L

thus triangle GHI is similar to triangle JKL and in 2 similar triangles the ratio of their corresponding sides is same. that means

[tex] \frac{hi}{kl} = \frac{gi}{jl} \\ \frac{18}{30} = \frac{x}{35} \\ x = \frac{18}{30} \times 35 \\ x = \frac{3}{5} \times 35 \\ x = 3 \times 7 \\ x = 21[/tex]

Answer:

A) y=4+x

Step-by-step explanation:

Since the initial amount was 4 gallons, any additional fuel added will be in addition to that.

Answer:

sin of 90 is 1

Step-by-step explanation:

sin is the y axis coordinate and the coordinates of 90° on unit circle is (0,1)

Answeni ideAA{

}

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

D. 5

Step-by-step explanation:

Applying,

cos∅ = adjacent/Hypotenuse

From the diagram,

Given: ∅ = 45°, adjacent = s, hyptenuse = 5√2

Therefore,

cos45° = s/5√2

make s the subject of the equation

s = cos45°×5√2

s = (1/√2)(5√2)

s = 5

Hence the right answer is D. 5

Answer:

(24x^2 + 14x – 20) /(3x+5) =  h

Step-by-step explanation:

The area of a trapezoid is given by

A =1/2 (b1+b2) h

12x^2 + 7x – 10 = 1/2 ( x+3+ 3x+2)h

Multiply each side by 2

24x^2 + 14x – 20 =  ( x+3+ 3x+2)h

Combine like terms

24x^2 + 14x – 20 =  ( 4x+5)h

Divide each side by (4x+5)

(24x^2 + 14x – 20) /(4x+5) =  ( 4x+5)h/(4x+5)

(24x^2 + 14x – 20) /(4x+5) =  h

Answer:

See Explanation

Step-by-step explanation: