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given that,

54 offices are currently rented

and it represent 30% of the total unit

to get the total offices in the building

let the total offices be x

30% of x = 54

30/100 X x = 54

cross multiply

30x = 5400

dividing both sides by 30

30x/30 = 5400/30

x = 5400/30

x = 180

therefore the total offices in the building is 180

EXPLANATION

Using a composite figure to approximate the area of the figure will give us the needed surface,

The area of the composite is approximately the area of the squares:

Area of square:

A= base * height = 1.0*1.0 = 1 cm^2

Since we have approximately 22 squares inside the figure, the approximate area will be as follows:

Therefore, the solution is approximately 22 square units.

Given,

The equation orr inequalities are,

A) In the expression,

7 - 2 = 5

Hence, 7-2 =6 is incorrect.

B) In the expression,

7 - 2 = 5,

Hence,

Option B is correct.

C) In the expression,

7 - 2 = 5

7 - 2 < 5 is incorrect

Hence, 7 - 2 =< 5 is incorrect.

D)In the expression,

7 - 2 = 5

Hence, 7 - 2 =< -5 is incorrect.

Hence, option B is correct.

A triangle is a shape that has a total angle of 180°.

It's important to note that a triangle is a shape that has three sides and the total sum is equal to 180°.

In this case, we have 2x + 6 and 42°. The other angle isn't given and this can't be solved further

The sides will have been illustrated as:

= a + b + c = 180

The expression given will then be allocated for each side to solve it further.

Note that an overview was given as the information is incomplete.

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Equation of the line passing through the point (-6,-3) and perpendicular to  the line passing through (-2,7) and (6,5) is y = 4x -19.

First we will find the slope of the line passing through (-2,7) and (6,5).

Slope of the line = (5-7)/(6-(-2)) = -2/8 = -1/4.

We know that,

Product of the slopes of two perpendicular lines = -1.

Let the equation of the line we have to find be y = mx + c.

Slope will be m.

Hence, we can write,

m*(-1/4) = -1

m = -1*(-4/1)

m = 4

Putting (6,5)  and m = 4 in y = mx + c , we get

5 = 4*(6) + c

5 = 24 + c

c = 5 - 24 = -19

Hence, the equation of the line is:-

y = 4x -19

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The length of segment AB as required in the task content is; 36.

It follows from the task content that the length of the line segment AB which is a side of the square ABCD is to be determined.

Since the perimeters of triangle EFG and square ABCD are equal as given;

Let the length of segment AB = x.

Therefore, EF = x + 12.

Therefore, the perimeter of the equilateral triangle = 3(x +12).

While the perimeter of square ABCD is; 4x.

Therefore, since the perimeters are equal;

3(x + 12) = 4x

3x + 36 = 4x

36 = x.

On this note, thee Length of line segment AB is; 36.

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Let's begin by listing out the given information:

The commutative property states that for addition, the order in which we add numbers does not change their sum & for multiplication, the order in which we multiply does not change their product.

Mathematically expressed as:

Therefore, the commutative property of this is:

Therefore, Option D is the correct answer

In the given triangle :

The coordinate of T is ( 2, 10 )

Triangle TUV will be dilated by a scale factor of 2

Thus, multiply the coordinates of TUV by 2

T' = 2 x T

T' = 2 x ( 2, 10 )

T' = ( 2x2, 2x10)

T' = ( 4, 20 )

So, T' will be located at ( 4, 20 )

Issac says that T' will be located at (4,20)

Answer : Issac says that T' will be located at (4,20)

Let:

x = Number of sodas purchased

y = Number of hamburgers purchased

The food truck charges $3 for sodas, so the total cost for sodas will be:

3*x=3x

also, it charges $8 for each hamburger, hence, the total cost for hamburgers will be:

8*y = 8y

Since Jack wants to spend no more than $30, the total cost must be less or equal than $30:

Answer:

Each of the workouts plans lasts 45 minutes.

Explanation:

Let the duration for Plan A workout = x

Let the duration for Plan B workout = y

Friday

• Plan A --> 3 clients

• Plan B --> 5 clients

• Kala trained her Friday clients for a total of 6 hours

Saturday

• Plan A --> 9 clients

• Plan B --> 7 clients

• Kala trained her Saturday clients for a total of 12 hours

The system of equations is solved simultaneously.

Multiply equation (1) by 3 in order to eliminate x.

Subtract.

Substitute y=0.75 into equation (2) to solve for x.

x=y=0.75 hours = 45 minutes,

Each of the workouts plans lasts 45 minutes.

ANSWER:

A rotation of 90° and then a translation left 2, up 4.

STEP-BY-STEP EXPLANATION:

Since r (90, 0) is the first and means a 90 ° rotation and that T (-2, 4) is a translation of 2 units to the left (because it is negative) and 4 units up (because it is positive) , the answer is the option "A rotation of 90° and then a translation left 2, up 4."

They are located 8 units away, so one has to be away in the left direction and the other one in the right direction

So, C and D are located at -10 and 6

Explanation:

This is a function defined by parts. When x is not 3, the function has the equation on top, but when x is 3, the function has one value: 2.

Answer:

f(3) = 2

From the given figure, let's select the rays given in the option.

A ray can be said to be a straight line which starts from a point and goes to infinity at the other end.

From the given figure, the rays are:

• NK

• NJ

• NL

• NM

Therefore, from the list the, the ray is NK.

ANSWER:

NK

SOLUTION

The terms below make an A.P. Now we are told to find the sum of the AP.

Sum of an AP is given by

Where S = sum of the AP, a = first term = 9, d = -5, n= ?

So we have to find n first before we can find the sum. The nth term which is the last term = -536. So we will use it to find the number of terms "n"

Now let's find the sum

Therefore, the sum = -31735

The total distance of the fun run is 7 9/10 miles and it can be written in the simplest fraction form.

Fraction:

The fraction is the part of the whole thing.

For example, a cake is divided into four equal pieces, then each piece is represented by ¼.

Given,

A school is organizing a fun run. The fun run involves a 4 1/2 mile run around the field, then a 3 2/5 mile run back to the school.

Now, we need to find the total distance of the fun run and we have to write it as simplest form.

First we have to convert the given fraction into simplest fraction then we get,

=> 4 1/2 = 9/2

=> 3 2/5 = 17/5

Now , we have to add these to fraction in order to get the total distance,

=> 9/2 + 17/5

The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD(9/2, 17/5) = 10

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

=> 45/10 + 34/10

=> 79/10

While we convert this into mixed number then we get,

=> 79/10 = 7 9/10

Therefore, the total distance is 7 9/10 miles.

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The most appropriate choice for tangent to a curve will be given by-

[tex]3x + 2y = 73[/tex] is the required equation of tangent.

What is tangent to a curve?

Tangent to a curve at a point is the straight line that just touches the curve at that point.

Equation of tangent to a curve at a point [tex](x_1, y_1)[/tex] is given by

[tex]y - y_1 = \frac{dy}{dx}|_{(x_1,y_1)} (x - x_1)[/tex]

Here,

y = B(x), B(25) = -1, B'(25) = -1.5

Equation of tangent =

[tex](y - (-1)) = -1.5(x - 25)[/tex]

[tex]y + 1=-1.5x +37.5\\y + 1 = -\frac{3}{2}x + 37.5\\2y + 2 = -3x + 75\\3x+2y = 75-2\\3x+2y=73[/tex]

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For a function, every element in the domain must have a unique image in the range.

On checking the domain and range provided in the question, we can see that there are two images for the range when the domain equals -2:

Therefore, the given domain and range violate the property of a function.

The relation is NOT a function.

Explanation:

The relation between liters and milliliters is:

we have to multiply the liters by 1000

Answer:

The answer is 950 milliliters

Let:

x = Colored markers

y =

Fundamental counting principle.

It is also called the counting rule, applying this principle we can know the number of outcomes by multiplying the options of each event together.

Given:

A coral reef grows 0.15 m every week.

Coral reefs grow 13 times 0.15m for 13 weeks.

We need to convert m into cm.

Multiply 1.95m by 100, we get

Hence a coral reef grows 195cm in 13 weeks.

Answer

The amount invested at

Step-by-step explanation:

The total amount invested is $5000

Let x be the investment at 5%

Let y be the investment at 15%

Mathematically, this can be expressed as

x + y = 5000 -- equation 1

Since the first part of the investment is invested at 5% and the second part is at 15%

0.05x + 0.15y = 540 --------- equation 2

The systems of equations can be solved simultaneously using the substitution method

x + y =5000 ----- equation 1

0.05x + 0.15y = 540 ------ equation 2

Isolate x in equation 1

x = 5000 - y

Substitute the value of x into equation 2

0.05(5000 - y) + 0.15y = 540

Open the parenthesis

250 - 0.05y + 0.15y = 540

Collect the like terms

-0.05y + 0.15y = 540 - 250

0.1y = 290

Divide both sides by 0.1

0.1y/0.1 =290/0.1

y = $2900

Recall that equation 1 is

x + y = 5000

y = $2900

x = 5000 - y

x = 5000 - 2900

x = $ 2100

Hence, the investment at 5% is $2100 and the investment at 15% is $2900

Explanation:

From the given question, we can sketch the pattern observed

The figure above helps show how the number of people increases

Initially, Jan tells 2 more people, then the two people tell two more people, then they also tell two more people

Thus

we can see that the model is given by

In order to have at least 700 (it also means a minimum of 700), we will have the equation

We then solve for n

Taking the log of both sides

So that

So, the number of days will be at least 10 days (Rounded to the nearest whole day )

Using mathematical operations, we know that P(Red and Small) is 4/3.

So, simple form of P(Red and Small):

Then, P(Red and Small):

Therefore, using mathematical operations, we know that P(Red and Small) is 4/3.

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Given:

Cut a 10-foot (ft.) long piece of wood into two pieces so that one piece is 2 ft longer than the other.

Required:

Which of the following equations depicts the given situation?

Explanation:

Let 10 feet long piece of wood cut into two pieces of length x(smaller piece) and

x+2 larger piece.

So, the equation will be

x + x + 2 =10

2x + 2=10

Answer:

Option C is correct.

Answer:

13 hours

Step-by-step explanation:

Let y = the total cost

let x = hours

y = 4x + 5      5 = the one time fee of the jacket  and the parking

57 = 4x + 5  Subtract 5 from both sides

52 = 4x  Divide both sides by 4

13 = x

Given:

x+2y = 8

x=2, y=0

Substitute x=2 then find value of x as,

2+2y=8

2y=6

y=3

(x,y) = (0,3)

Now, substitute y=0 then find value of y as,

x+2(0)=8

x=8

(x,y) = (8,0)

It is given that P = x+3y

(x,y) = (0,3) then P= 0+3x3

P=9

The maximum valu P=9 and vertiex (0,3)

(x,y) = (8,0) then P=8+0= 8

The mininmum val

The dimensions of the rectangular prism of 6 cm by 3 cm by 2 cm and the dimension of the cube of 3 cm gives the amount the surface area of the prism is greater than the cube as 18 cm²

A rectangular prism is a six faced solid hexahedron.

The given dimension of the rectangular prism are:

Length = 6 cm

Height = 3 cm

Width = 2 cm

The side length of the cube = 3cm

The surface area of the rectangular prism is therefore:

[tex]A_p[/tex] = 6 × 3 × 2 + 6 × 2 × 2 + 3 × 2 × 2 = 72

The surface area of the rectangular prism is 72 cm²

The surface area of the cube: [tex]A_c[/tex] = 6 × 3² = 54

The surface area of the cube, [tex]A_c[/tex] = 54 cm²

The amount by which area of the rectangular prism is greater than the area of the cube is therefore: [tex]A_p[/tex] - [tex]A_c[/tex] = 72 cm² - 54 cm² = 18 cm²

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