A library building is in the shape of a rectangle. Its floor has a length of (3x + 5) meters and a width of (5x − 1) meters. The expression below represents the area of the floor of the building in square meters: (3x + 5)(5x − 1) Which of the following simplified expressions represents the area of the floor of the library building in square meters? (5 points)

Hey there! I'm happy to help!

A militia is a local army. During the Battle of Lexington and Concord, the local militia (called minutemen), the militia outnumbered the British at Concord and chased them all the way back to Boston. The militia aided in many American victories during the Revolutionary War.

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Answer:

A. 183 meters

Step-by-step explanation:

Building A and building B are 500 meters apart. There is no road between them, so to drive from building A to building B, it is necessary to first drive to building C and then to building B. About how much farther is it to drive than to walk directly from building A to building B? Round to the nearest whole number. A) 183 meters B) 250 meters C) 366 meters D) 683 meters

Find distance BC

Cos (60°)=BC / AB (Adjacent divided by the hypotenuse)

Cos (60°)=1/2

BC=a

AB=500

Cos (60°)=BC / AB

1/2=a/500

1/2 * 500=a

250=a

a=250m

Find distance AC

Sin(60°)=AC/AB (opposite side divided by hypotenuse)

Sin(60°)=√3/2

AC=b

AB=500

Sin(60°)=AC/AB

√3/2=b/500

√3/2 * 500=b

250√3=b

b=433m

Distance AC and BC=AC+BC

433m+250m=683m

Subtract the distance AB from AC+BC

= 683m - 500m

=183m

Answer is A. 183 meters

Answer:

A. 183 meters

Step-by-step explanation:

sin(60) = x/500

= 433

tan(60) = 433/x

= 250

This is the driving distance. 433+250= 683. Directly walking (using hypotenuse distance) is 500.

683-500=183!

Answer:

A. R=0.86; strong correlation

Step-by-step explanation:

The correlation coefficient of 0.29 indicates that the correlation is a weak positive correlation. Thus option (D) is the correct answer.

"Correlation is a statistical tool that studies the relationship between two variables. Data sets have a positive correlation when they increase together, and a negative correlation when one set increases as the other decreases".

For the given situation,

Correlation coefficient = 0.29

Positive correlation: the two variables change in the same direction.

Negative correlation: the two variables change in opposite directions.

No correlation: there is no association or relevant relationship between the two variables.

The correlation coefficient lies between 0 to 0.3 indicating that the correlation is a weak positive correlation.

Hence we can conclude that option (D) weak positive correlation is the correct answer.

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Answer: (-6,8)

Step-by-step explanation:

Translation rules are

Left c units : [tex](x,y)\to(x-c,y)[/tex]

Down c units : [tex](x,y)\to(x,y-c)[/tex]

The image point of (-5,9) after a translation left 1 unit and down 1 unit will be:

[tex](-5,9)\to(-5-1,9-1)=(-6,8)[/tex]

Hence, the image point is (-6,8).

Answer:

4

Step-by-step explanation:

Answer:

-26, and -36

Step-by-step explanation:

(-2) (-3) + (4) (-8)

        6 + -32 = -26

(3) (-6) - 18

       -18 + -18 = -36

Answer:

Step-by-step explanation:

Given two coordinates (x₁, y₁) and (x₂, y₂), the coordinate of their midpoint is equivalent to X = (x₁+x₂)/2 and Y = (y₁+y₂)/2.

Given the coordinate of Sally's house and  her school to be (5, −1) and  (−9, 7) respectively, the midpoint of Sall's house and school is expressed as shown;

from the coordinates, x₁ = 5, y₁ = -1, x₂ = -9 and y₂ = 7

X = (5+(-9))/2

X = 5-9/2

X = -4/2

X = -2

Y = -1+7/2

Y = 6/2

Y = 3

The coordinate of the midpoint of Sally's house and school will be expressed as (X, Y) which is equivalent to (-2, 3).

Answer:

y = -10.375x + 126.125

Step-by-step explanation:

(12-95)/(11-3) = -83/8 = -10.375

y = mx + b

12 = -10.375(11) + b

12 = -114.125 + b

b = 126.125

y = -10.375x + 126.125

The solution is, y = -10.375x + 126.125,  is the equation of a trend line that passes through the points (3, 95) and (11, 12).

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

given that,

a trend line that passes through the points (3, 95) and (11, 12).

so, the slope is,

(12-95)/(11-3) = -83/8 = -10.375

now, we have,

y = mx + b

12 = -10.375(11) + b

12 = -114.125 + b

b = 126.125

so, we get,

y = -10.375x + 126.125

Hence, The solution is, y = -10.375x + 126.125,  is the equation of a trend line that passes through the points (3, 95) and (11, 12).

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Answer:

8

Step-by-step explanation:

If we have anything to the third power, we are multiplying the number by itself 3 times.

If x = 2, then the expression is [tex]2^3[/tex].

[tex]2\cdot2\cdot2=8[/tex]

Hope this helped!

Answer:

8

Step-by-step explanation:

Exponents is repeated multiplication, so what we are doing in this problem is that we are multiplying 2 by itself 3 times.

2 * 2 = 4

4 * 2 = 8

Answer:

OPTION A is correct

39 ounces

Step-by-step explanation:

Given:

The amount of water in the pitcher= 32 ounces

The amount of lemon juice in the pitcher = 7.15 ounces

We were to calculate the most reasonable estimate for the amount of liquid in the pitcher

To do this we need to sum up the Amount of water and Amount of lemon juice in the pitcher because the water is a liquid as well as the lemon juice which is

32 ounces + 7.15 ounces

=39.15 ounces

Therefore, the Estimated amount of liquid in the pitcher is approximately 39 ounces

If 11 is subtracted from 3 times the number, the result is the square of 5 less than the number. What are the set of numbers that satisfy

Answer:

[tex]\boxed{57ft 10in}[/tex]

Step-by-step explanation:

Hey there!

Well if the length is 18 and 3 inches we need to find the sum of both lengths,

18ft 3in + 18ft 3in = 36ft 6in

Width- 10ft 8in + 10ft 8in = 20ft 16 in -> 21ft 4in

l + w = 57ft 10in

Hope this helps :)

Answer:  20

Step-by-step explanation:

Given: Total students at the dinner = 100

Number of fish entrees = 40

Number of pasta entrees = 60

Number of students chose neither entree = 20

Now , Number of students chose either fish or pasta = (Total students) - (Number of students chose neither entree)

= 100-20

= 80

Now , Number of students chose either fish or pasta = (Number of fish entrees) + (Number of pasta entrees)- (Number of students chose both)

⇒ Number of students chose both = (Number of fish entrees) +(Number of pasta entrees)-(Number of students chose either fish or pasta)

= 40+60-80

= 20

Hence, the number of students were served two entrees = 20

20 students were served two entrees.

Given,

total student pass through cafeteria line and were served meal is 100.

No. of students choose fish entries is 40.

No. of students choose pasta entrees is 60.

No. of student choose neither entree is 20.

We have to calculate the no. of students served two entrees.

Now Number of students chose either fish or pasta will be,

[tex]N=100-20[/tex]

[tex]N=80[/tex]

Now no. of students choose both will be,

[tex]N=(fish\ entree+\ pasta \ entree )-Entree\ either \ pasta \ or \ fish[/tex]

[tex]N=60+40-80[/tex]

[tex]N=20[/tex]

Hence 20 students were served two entrees.

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Answer:

30/11 (hours)

Step-by-step explanation:

Pipe A can fill the tank until it is full in 3 hours.

=> In 1 hour, pipe A can fill 1/3 of tank

Pipe B can fill the tank until it is full in 5 hours.

=> In 1 hour, pipe A can fill 1/5 of tank

Pipe C can empty the full tank in 6 hours.

=> In 1 hour, pipe A can empty 1/6 of tank

Assume that we open 3 pipes A, B, and C at the same time.

Then, in 1 hour, the amount of water in tank is:

A =  1/3 + 1/5 - 1/6 = 10/30 + 6/30 - 5/30 = 11/30 (tank)

=> The time to fill up the tank is:

T = 1/A = 1/(11/30) = 30/11 (hours)

Answer:

30/11

Step-by-step explanation:

Imagine the tank can hold x litre of water

So,A can fill x/3 litre water per hour

And B can fill x/5 litre water per hour

And C can reduce x/6 litre of water per hour which is filled by A and B.

So the gross calculation per hour is:

(x/3+x/5)-x/6

=11x/30

Now suppose it tooks 'a' hour to fill the tank.

So, a(11x/30)=x

⇨ a= (30/11x)x

⇨a=30/11

Hello!

Answer:

[tex]\huge\boxed{x = 27}[/tex]

Given:

3x - 4y = 65 where y = 4;

Substitute in 4 for "y":

3x - 4(4) = 65

Simplify:

3x - 16 = 65

Add 16 to both sides:

3x - 16 + 16 = 65 + 16

3x = 81

Divide both sides by 3:

3x/3 = 81/3

x = 27.

Hope this helped you! :)

Answer:

x=27

Step-by-step explanation:

3x-4y=65

Let y=4

3x - 4(4) = 54

3x -16 = 65

Add 16 to each side

3x -16+16 = 65+16

3x = 81

Divide each side by 3

3x/3 =81/3

x =27

Answer:

The number is 3,552

15⅝% of 3,552 is 555

Step-by-step explanation:

15⅝% of a number is 555.

To determine what number it is, let the number be x.

Thus,

15⅝%*x = 555

[tex] \frac{125}{8}*\frac{1}{100}*x = 555 [/tex]

[tex] \frac{125}{800}*x = 555 [/tex]

[tex] \frac{125*x}{800} = 555 [/tex]

Multiply both sides by 800

[tex] \frac{125*x}{800}*800 = 555*800 [/tex]

[tex] 125*x = 444,000 [/tex]

Divide both sides by 125

[tex] \frac{125*x}{125} = \frac{444,000}{125} [/tex]

[tex] x = 3,552 [/tex]

The number = 3,552

15⅝% of 3,552 is 555

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▹ Answer

A ≈ 201.06 mm²

▹ Step-by-Step Explanation

A = πr²

Radius = 1/2d

Radius = 1/2(16)

Radius = 8

Substitute:

A = π8²

A ≈ 201.06 mm²

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

Step-by-step explanation:

Area of a circle is given by πr²

where r is the radius

To find the radius we use the formula

radius = diameter / 2

From the question

diameter = 16mm

radius = 16 / 2 = 8mm

So the area of the circle is

π(8)²

= 64π

= 201.061

= 201 mm² to the nearest whole number

Hope this helps you

Answer:

the slope of the line represented by the table is y = 2/11x

Step-by-step explanation:

y = mx + b

slope: (y² - y¹) / (x² - x¹)

(4 - 2) / (22 - 11) = 2/11

plug in an x and y value to find b

y = 2/11x + b

2 = (2/11)(11) + b

2 = 2 + b

b = 0

the y-intercept is 0

your equation is y = 2/11x

Answer:

$18

Step-by-step explanation:

$18.02 rounds to $18

Answer:

  $17

Step-by-step explanation:

Rounded, the listed numbers are ...

  12 + 5 -1 +3 -2 = 17

The estimate of total cost is $17.

Answer:

$22

Step-by-step explanation:

Beth=$5.00 for 2 rounds

Zane=$12 for 5 rounds

Tina=$x for 9 rounds

Find x

9 rounds=5 rounds + 2 rounds + 2 rounds

5 rounds costs =$12

2 rounds costs=$5

2 rounds costs=$5

Then,

5 rounds + 2 rounds + 2 rounds= $12 + $5 + $5

9 rounds=$22

It will cost Tina $22 to go on 9 rounds

Answer: Infinitely many solutions

Step-by-step explanation:

There are many solutions because the lines lies on top of each other.

i dont know the exact answer but its not  

One solution

Two solutions

so its most likely

Infinitely many solutions

Answer:

91.125

Step-by-step explanation:

Each term is multiplied by 1.5 to get the next term.

12,18,27,40.5, 60.75, 91.125

Hope that helped!!! k

Answer:

91.125

Step-by-step explanation:

We know that this is a geometric sequence. By definition, this means that each subsequent term divided by the previous one is a common ratio r.

Here, divide 18 by 12 to get:

18/12 = 3/2 = 1.5

Divide 27 by 18 to check if it's also 1.5:

27/18 = 3/2 = 1.5

Indeed, the common ratio is 1.5. Now, we simply multiply 27 by 1.5 to get the 4th term:

27 * 1.5 = 40.5

Multiply 40.5 by 1.5 to get the 5th term:

40.5 * 1.5 = 60.75

Finally, multiply 60.75 by 1.5 to get the 6th term:

60.75 * 1.5 = 91.125

Our answer is thus 91.125.

~ an aesthetics lover

Answer:

1

Step-by-step explanation:

[tex]cot^4x-cot^2x=1\\cot^4x=1+cot^2x\\cot^4x=cosec^2x\\ cos^4xsin^2x=sin^4x\\cos^4x=\frac{sin^4x}{sin^2x}\\cos^4x=sin^2x[/tex]------- (1)

Putting the value of [tex]cos^4x[/tex] in the equation:

[tex]cos^4x+cos^2x\\sin ^2x +cos^2x\\1[/tex]            (Using the identity [tex]cos^2x +sin^2x=1)[/tex]

Answer:

a = 53.13

b = 42.76

c= 0

Step-by-step explanation:

as the question said i was supposed to use a calculator which i did

Step-by-step explanation:

so 2.3 + 5.7 is 8.0 is the answer

Answer:

A triangle with angles:

"45°, 45°, 90°"

Is a triangle rectangle, with two catheti of equal length.

Now, there is a lot of problems that you can solve with this:

"Suppose that you want to find the height at which you need to attach a wire in a tree, such that the distance between the tree and the ground is 18ft, and the distance between the base of the tree and the two points where the wire is fixed is exactly the same"

Well, here we have a triangle rectangle with a hypotenuse of 18 ft, with cathetus of equal length (the catheti are the tree and the distance between the base of the tree and the point where the wire is attached at the ground)

And because the catheti are equal, then the angles are 45°, 45° and 90°.

Answer:

M (-3, -5/2)

N (3, -1)

Step-by-step explanation:

Solve the first equation for x.

4y = x − 7

x = 4y + 7

Substitute into the second equation.

x² + xy = 4 + 2y²

(4y + 7)² + (4y + 7)y = 4 + 2y²

Simplify.

16y² + 56y + 49 + 4y² + 7y = 4 + 2y²

18y² + 63y + 45 = 0

2y² + 7y + 5 = 0

Factor.

(y + 1) (2y + 5) = 0

y = -1 or -5/2

Plug back into the first equation to find x.

x = 4(-1) + 7 = 3

x = 4(-5/2) + 7 = -3

M (-3, -5/2)

N (3, -1)

Answer: 35%

Step-by-step explanation: It grows 3.5% every year. A decade is 10 years. 10 x 3.5% = 35% because you move the decimal one point to the right.

The population grows 41.1% per decade. Therefore, option B is the correct answer.

If a constant rate of growth be R% per annum, then population after n years = P(1+R/100)ⁿ.

Given that, a population grows 3.5% per year.

Now, D(n)=P(1+R/100)ⁿ

Let P=1

So, D(1)=1(1+0.035)¹

D(1)=1.035

Similarly per 10 years with the same rate

D(10)=1(1+0.035)¹⁰

= (1.035)¹⁰

= 1.41059

= 1.411-1 (Initial population is 1)

= 0.411

= 0.411×100

= 41.1%

The population grows 41.1% per decade. Therefore, option B is the correct answer.

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Answer:

Can you solve #18 from practice test 5 calculator section? ... years old and a pin oak tree with a diameter of 12 inches is ... because on the test you would have figured these mechanics out on ... Now, note that the concept of a “growth factor” as provided in the table ... That's a difference of about 1.3 inches.

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

I just got it correct on a.p.e.x :)

The solution to the equation [tex]\log_5(2x - 3) = 2[/tex] is x = 14

The equation is given as:

[tex]\log_5(2x - 3) = 2[/tex]

Convert the equation to an exponential equation

2x - 3 = 5^2

Evaluate the exponent

2x - 3 = 25

Add 3 to both sides

2x = 28

Divide both sides by 2

x = 14

Hence, the solution to the equation [tex]\log_5(2x - 3) = 2[/tex] is x = 14

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