31. ABCD has area equal to 28 sq. unit. BC is parallel to AD and BA perpendicular to AD. If BC = 6 and AD = 8,
then value of CD =
B.213
A. 2 12
C.4
D. 275

Answer:

Step-by-step explanation:

∠QRT and ∠SRT are supplementary angles,

therefore m∠QRT + m∠SRT = 180°.

(45x)° + m∠SRT = 180°            subtract (45x)° from both sides

m∠SRT = 180° - (45x)°

We know: the sum of the measures of the angles of the triangle is equal to 180 °. Therefore we have the equation:

(180 - 45x) + (57 + x) + 25x = 180         combine like terms

(-45x + x + 25x) + (180 + 57) = 180

-19x + 237 = 180             subtract 237 from both sides

-19x = -57             divide both sides by (-19)

x = 3

Answer:

240

Step-by-step explanation:

200 divided by 100, to get the amount per percent, then multiply it by 120, to get 240.

Answer:

Step-by-step explanation:200 multipled by 120%

200 • 120/100

Reduce the numbers with the greatest common divisor 100

2 • 100

2 •120

Multiply the numbers

THE ANSWER IS 240

Answer:

a=1

Step-by-step explanation:

2a + 3(a + 1) = 8

Distribute

2a +3a +3 = 8

Combine like terms

5a +3 =8

Subtract 3 from each side

5a+3-3=8-3

5a = 5

Divide by 5

5a/5 = 5/5

a=1

Answer:

(x-10)(x-2)

Formula:

a^{2} - b^{2} = (a-b)(a+b)  

Explanation:  

(x-6)^2-4^2

Then we can simplify to, (x-6-4)(x-6+4)

Which comes to your answer,  (x-10)(x-2)

Answer:

Step-by-step explanation:

x² − 12x − 20 = 0

a = 1;  b = (-12);  c = (-20)

b²-4ac = (-12)² - 4 * 1 * (-20) = 144 + 80 = 224

√b²-4ac = √ 224 = √ 2*2*2*2*2*7 = 2*2*√(2*7) = 4√14

delta = -b ± √b²-4ac / 2a

         = -(-12) ± 4√14

                    2 * 1

          = (12 ± 4√14)/2

           = 2 ( 6 ± 2√14) / 2

           =  6 ± 2√14

x =   6 + 2√14;  x =  6 - 2√14

Answer:

720/1681

Step-by-step explanation:

First quadrant so everything is positive for a trig function of just the angle.  I would suggest just drawing a right triangle using tan(x)=40/9 (opp/adj). Find the hypotenuse which is sqrt(40^2+9^2)=sqrt(1600+81)=sqrt(1681)=41.  So sin(x)=40/41 and cos(x)=9/41.

Therefore sin(2x)=2sin(x)cos(x)=2(40/41)(9/41)=720/1681

Answer:

the answer is B

Step-by-step explanation:

75 is a one time payment. 25 is the amount that you will pay permonth

Answer:

C=25m+75

Step-by-step explanation:

Aloha! My name is Zalgo and I am here to be of assistance to you today. The GCF (Greatest Common Factor) of 14 and 60 would be 12. To the GCF of 24, you need to multiply 2^3 by 3. In order to get the GCF of 60, you need to multiply 2^2 by 3 times 5.

I hope that this info helps! :P

"Stay Brainly and stay proud!" - Zalgo

(By the way, do you think you could mark me as Brainliest? I'd greatly appreciate it! Mahalo! XT)

The greatest common factor of 24 and 60 is 12.

To get the greatest common factor, we will list the factors of each number and find the largest one that they have in common.

The factors of 24 are:

1, 2, 3, 4, 6, 8, 12, and 24.

The factors of 60 are:

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

The largest factor that 24 and 60 have in common is 12.

Read more about common factor

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Answer:

4 x  [tex]10^{12}[/tex])

Step-by-step explanation:

(6 x [tex]10^{8}[/tex]) / (1.5 x [tex]10^{-4}[/tex])

=  ([tex]\frac{6}{1.5}[/tex] x [tex]10^{8}[/tex]) / ([tex]10^{-4}[/tex])

=  ([tex]\frac{6}{1.5}[/tex] x [tex]10^{8}[/tex]) x ([tex]10^{4}[/tex])

=  [tex]\frac{6}{1.5}[/tex] x [tex]10^{12}[/tex]

=  4 x  [tex]10^{12}[/tex]

Step-by-step explanation:

6*10^8 /1.5*10^-4

6/1.5 * 10^8/10^-4

4 * 10^8-(-4)

4*10^8+4

4*10^12

a sequence is a function whose domain is the set of natural numbers.

natural numbers are all the negative and positive integers

A sequence exists as a function whose domain is the set of natural numbers.

A sequence exists as a function whose domain is the set of natural numbers or a subset of the natural numbers. Usually use the symbol a to describe a sequence, where n is a natural number and a stands for the value of the function on n. Intuitively, a sequence exists just as an ordered list of (possibly infinitely many) numbers.

To learn more about Sequence refer to:

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Answer:

The best cluster would be Philadelphia which percentage of 27% is nearly close to 28% of the whole united states population percentage.

Step-by-step explanation:

The correct option for the city which would be considered as the best cluster is B. Miami,  16% of the population are MyBook users.

A survey is a means of gathering information from a sample of people using pertinent questions with the goal of understanding populations as a whole.

Now given that,

Amount of population that are MyBook users = 28%

Thus,

Amount of population that do not uses MyBook = 100% - 28% = 72%

Thus, Philaldephia and Denver cannot be percentage of the population who are MyBook users.

Thus, the correct option for the city which would be considered as the best cluster is B. Miami, 16% of the population are MyBook users.

To learn more about survey :

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Answer:

(2, 9)

Step-by-step explanation:

We've been given the exponential function;

f(x) = 25(3/5)^x

We need to determine the value of f(x) when x = 2, that is;

f(2) = 25(3/5)^2

Using a calculator we obtain

f(2) = 9

Thus the next point she plots on the graph will be (2, 9)

Answer: 0.167 is the part of the hall that was not occupied. Or 16.7 %

Step-by-step explanation:

300-250=50 this is the number of seats not occupied since 250 is the amount occupied.

So, 50/300=5/30 which can be converted to a number which is 0.1666666667. It says to round to the thousandths place, which is the 3rd number. That is 0.167

Answer:

0.167 part of the hall was not occupied

Step-by-step explanation:

Given :In a concert hall, 250 seats out of 300 were occupied.

To Find :To the nearest thousand, what part of the hall was not occupied?

Solution:

Total seats = 300

Occupied seats = 250

Unoccupied seats = 300-250 = 50

So, The part of the hall was not occupied = [tex]\frac{\text{unoccupied seats}}{\text{total seats}}[/tex]

                                                                     = [tex]\frac{50}{300}[/tex]

                                                                     = [tex]0.167[/tex]

Hence 0.167 part of the hall was not occupied

Answer:

The second alternative is correct

Step-by-step explanation:

We have been given the expression;

[tex](x^{27}y)^{\frac{1}{3}}[/tex]

The above expression can be re-written as;

[tex](x^{27})^{\frac{1}{3}}*y^{\frac{1}{3}}\\\\(x^{27})^{\frac{1}{3}}=x^{27*\frac{1}{3}}=x^{9}[/tex]

On the other hand;

[tex]y^{\frac{1}{3}}=\sqrt[3]{y}[/tex]

Therefore, we have;

[tex]x^{9}\sqrt[3]{y}[/tex]

Answer:

Option 2: [tex]x^{9}(\sqrt[3]{y})[/tex]

Step-by-step explanation:

Given

[tex](x^{27}y )^{\frac{1}{3} }[/tex]

The exponent power will be multiplied with the powers inside the bracket

So,

[tex](x^{27 * \frac{1}{3}} y^{\frac{1}{3}})[/tex]

[tex]= x^{\frac{27}{3}} y^{\frac{1}{3} }[/tex]

[tex]= x^{9} y^{\frac{1}{3}}[/tex]

Writing in radical form will give us:

[tex]x^{9}(\sqrt[3]{y})[/tex]

So,

Option 2 is the correct answer ..

Answer:

Possible values of x are   50 < x < 110.

Step-by-step explanation:

Consider the perimeter of the field:

2x + 2(x + 30) < 500

2x + 2x + 60 < 500

4x < 440

x < 110.

Consider the area of the field:

x(x + 30 ) > 4000

x^2 + 30x - 4000 > 0

(x - 50)(x + 80) > 0

The critical values are x = -80 and 50.

As x is a width it must be positive so x > 50.

ANSWER

[tex] \frac{5\pi}{3} + 2\pi \: n[/tex]

EXPLANATION

Coterminal angles are angles that have the same terminal side in standard position.

We want find all angles that are coterminal with

[tex] \frac{5\pi}{3} \: \: radians[/tex]

We add or subtract multiples of 2π radians to this angle to obtain all angles that are coterminal with this angle.

The coterminal angles are:

[tex] \frac{5\pi}{3} + 2\pi \: n[/tex]

where n is an integer.

Answer:

-7 Pi/3, -Pi/3, 11 Pi/3

Step-by-step explanation:

Answer:

cam bought 12 books 7 at $0.35 and 5 at $0.50

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

12 - 3 = 9

Hello :D

Answer:

[tex]\boxed{9}\checkmark[/tex]

The answer has a positive sign.

Step-by-step explanation:

Order of operations

PEMDAS

Parenthesis

Exponents

Multiply

Divide

Add

Subtract

Left to right

[tex]|-12|-|3|[/tex]

[tex]12-3=9[/tex]

[tex]\boxed{9}[/tex], which is our answer.

Hope this helps! :D

Step-by-step explanation:

There can be two situations

1. When maggie is older

The equation becomes x = y + 3

It can also be expressed as y = x - 3

2. When maggie is younger

The equation becomes y = x + 3

Table of possible values

1. x    y          2. x    y

  5   2              2   5

  6   3              3   6

Answer:

The required equation is [tex]|y-x|=3[/tex]. If maggies is elder, then [tex]y_1=x-3[/tex] and if maggies is younger, then [tex]y_2=x+3[/tex].

Step-by-step explanation:

Let the x represents maggies age and y represents terrance age, make a table of possible values for x and y.

It is given that the difference between maggies age and terrance age is 3.

It means

[tex]|y-x|=3[/tex]

On simplification, we get

[tex]y-x=\pm 3[/tex]

[tex]y=x\pm 3[/tex]

Case 1: If maggies is elder.

[tex]y_1=x-3[/tex]

Case 2: If maggies is younger.

[tex]y_2=x+3[/tex]

The table of values is

x      y₁      y₂

-3    -6      0

0    -3      3

3     0      6

The graph of both functions are shown below.

Answer:

-x(x^2 +3x +4)

Step-by-step explanation:

-x^3-3x^2-4x

Factor out a -x

-x(x^2 +3x +4)

We cannot factor inside the parentheses, so this is complete

A is the answer.  (0,5) (2,20)

Step-by-step explanation:

This is the correct graph on Desmos, the other user forgot to add x as an exponent.

(0,5) (2,20)

Answer:

8.15

Step-by-step explanation:

Step-by-step explanation:

1.9+6.25=8.15

   1.9  

+ 6.25

______

  8.15

Final answer:

To park for $30 in a parking garage that charges $22.50 for the first hour and $2.50 for each additional hour, you can park for 4.2 hours.

Explanation:

The parking garage charges $22.50 for the first hour and $2.50 for each additional hour. Let's use 'x' to represent the number of hours. To find how many hours you can park for $30, we need to write and solve the equation.

Total cost equation:

$22.50 + $2.50(x-1) = $30
$22.50 + $2.50x - $2.50 = $30
$2.50x = $10.50
x = 4.2 hours

Therefore, you can park for 4.2 hours for $30 in the garage.

Question 1:

For this case we have that by definition, the volume of a prism is given by:

[tex]V = a * b * c[/tex]

Where:

a: It is the long

b: It is the width

c: It is the height

According to the data we have:

[tex]a = 18m\\b = 9m\\c = 6m[/tex]

Substituting:

[tex]V = 18 * 9 * 6\\V = 972[/tex]

Thus, the volume of the building is[tex]972 \m ^ 3[/tex]

Answer:

Option B

Question 2:

For this case we have that by definition, the volume of a prism is given by:

[tex]V = a * b * c[/tex]

Where:

a: It's the long

b: It is the width

c: It is the height

According to the data we have:

[tex]a = 26in\\b = 14in\\c = 18in[/tex]

Substituting:

[tex]V = 26 * 14 * 18\\V = 6552[/tex]

Thus, the volume of the tank is [tex]6552 \in ^ 3[/tex]

Answer:

Option A

Question 3:

For this case we have that by definition, the volume of a cube is given by:

[tex]V = l ^ 3[/tex]

Where:

l: It's the side of the cube

According to the data we have that the cube side is 7.2ft.

Substituting we have:

[tex]V = (7.2) ^ 3\\V = 373.25[/tex]

Rounding off we have that the volume of the cube is [tex]373.25 \ ft ^ 3[/tex]

Answer:

Option B

Question 4:

For this case we have that by definition, the volume of a cube is given by the following formula:

[tex]V = l ^ 3[/tex]

Where:

l: It's the side of the cube

According to the data we have that the cube side is 4.5 yards.

Substituting we have:

[tex]V = (4.5) ^ 3\\V = 91.125[/tex]

Rounding off we have the cube volume is[tex]91.13 \ yd ^ 3[/tex]

Answer:

Option C

Answer:

the answer will 100 percent be A

Answer:

The correct option is B.

Step-by-step explanation:

Let x is the  air conditioning unit's actual capacity and y is the maximum variance in British thermal units (Btu).

It is given that an air conditioning unit promises to have a cooling capacity of 6,000 British thermal units (Btu).

It means the maximum variance is less than or equal to absolute difference of actual capacity and 6,000.

[tex]y\leq |x-6000|[/tex]

The related equation of this inequality is a V-shaped curve with vertex (6000,0) and y-intercept (0,6000). Related curve is a solid curve because the points on curve included in the solution set.

The shaded region lie below the curve because the sign of inequality is ≤.

Therefore the correct option is B.

Answer:

{-5,-4,2}

Step-by-step explanation:

The domain is the inputs and the range is the outputs

The outputs are the y values

{ -5,2,-4,2}

We only list them once and in order from smallest to largest

{-5,-4,2}

I am not sure but I think the probability of a circle being chosen first is 4/13

because 13 is the amount of shapes in total, and 4 is the amount of circles. I hope you found this helpful.

Answer:

The answer is [tex]\frac{4}{13}[/tex].

Step-by-step explanation:

There are five squares, two triangles, two ovals, and four circles.

So, total shapes are = [tex]5+2+2+4=13[/tex]

The probability that the first chosen shape will be a circle is given by :

[tex]\frac{possible outcomes}{total number of outcomes}[/tex]

= [tex]\frac{4}{13}[/tex]

Note: 4 because any 1 out of 4 can be selected.

Answer:

[tex]( {a}^{2} - b)(5 {a}^{2} + 6b) \\ 5 {a}^{4} + 6 {a}^{2} b - 5 {a}^{2} b - 6 {b}^{2} \\ = 5 {a}^{4} + {a}^{2} b - 6 {b}^{2} [/tex]

Final answer:

By repeating the perpendicular line segment construction twice using paper folding, one can effectively find the midpoint of a line segment, demonstrating the application of geometric principles and theorems related to perpendicular constructions.

Explanation:

If you repeat the perpendicular line segment construction twice using paper folding, you can construct the midpoint of a line segment. This is based on the principle that constructing perpendiculars at the ends of a given line segment and then erecting a third perpendicular midway between them will intercept the line segment at its midpoint. This is affirmed by the theorems that explain the geometrical properties and relationships of constructing perpendicular lines and their midpoints.

To elucidate, let's take a line segment AB of a certain length, and fold the paper to construct a perpendicular line at point A. Next, repeat the same action at point B. Now, fold the paper to find the midpoint of AB, and erect a perpendicular line at this midpoint. This results in the third perpendicular intersecting AB exactly at its midpoint, demonstrating that this method is effective for finding the midpoint of a line segment, thereby validating option A.

You can construct: The midpoint of a line segment.

The correct option is (A).

Paper folding constructions can be used to create geometric shapes and lines based on certain properties. Let's break down each of the given options and see if they can be achieved by repeating the perpendicular line segment construction twice:

A. The midpoint of a line segment: Yes, this can be achieved. Folding a line segment in half will give you its midpoint. By repeating the perpendicular line segment construction twice, you fold the line segment once to find a point equidistant from both endpoints (which is the midpoint), and folding it again should confirm that the resulting point is indeed the midpoint.

B. An angle congruent to a given angle: No, this cannot be achieved. The perpendicular line segment construction does not involve creating or manipulating angles, so it cannot be used to construct an angle congruent to a given angle.

C. A parallel to a line through a point not on the line: No, this cannot be achieved. The perpendicular line segment construction does not involve creating parallel lines.

D. An angle bisector: No, this cannot be achieved. Again, the perpendicular line segment construction does not involve manipulating angles, so it cannot be used to construct an angle bisector.

Therefore, the correct option is:

A. The midpoint of a line segment.

Answer:

There are no solutions to the inequality.

Step-by-step explanation:

|x - 3| < x – 3

1. Separate the inequality into two separate ones.

(1) x – 3 < x – 3

(2) x – 3 < -(x – 3)  

2. Solve each equation separately

(a) Equation (1)

[tex]\begin{array}{rcl}x - 3 & < & x - 3\\x & < & x\\\end{array}\\\text{This is impossible. No solutions exist.}[/tex]

(b) Equation (2)

[tex]\begin{array}{rcl}x - 3 & < & -(x - 3)\\x - 3 & < & -x + 3\\x & <& -x + 6\\2x & < & 6\\x & < & 3\\\end{array}\\\text{This is impossible. No solutions exist}[/tex]

For example, if x = 0, we get  

|0 - 3| < 0 - 3 or

3 < -3

Answer:

Step-by-step explanation:

Look at the picture.

The range: -6 ≤ y ≤ 9

The domain: x ≤ 0