A town planner wants to build two new streets, Elm Street and Garden Road, to connect parallel streets Maple Drive and Pine Avenue. Trapezoid E F G H is shown. F G is Maple Drive, G H is Garden road, E H is Pine avenue, and E F is Elm Street. Sides F G and E H are parallel. Angle G is 108 degrees. In trapezoid EFGH, EF ≅ HG. What is the measure of the angle between Elm Street and Pine Avenue? 54° 72° 108° 144°

Answer:

[tex] x = 11 [/tex]

Step-by-step explanation:

Given that ∆CDE ~ ∆FGH

CD = 25

DE = 35

FG = 65

GH = 8x + 3

Therefore,

[tex] \frac{CD}{FG} = \frac{DE}{GH} [/tex]

(Similarity Theorem)

[tex] \frac{25}{65} = \frac{35}{8x + 3} [/tex]

Cross multiply

[tex] 25(8x + 3) = 35*65 [/tex]

[tex] 200x + 75 = 2275 [/tex]

[tex] 200x + 75 - 75 = 2275 - 75 [/tex]

[tex] 200x = 2200 [/tex]

[tex] \frac{200x}{200} = \frac{2200}{200} [/tex]

[tex] x = 11 [/tex]

Answer:

C. 11

Step-by-step explanation:

x = 11

Answer:

210

Step-by-step explanation:

10x9x8x7x6x5x4x3x2x1 divided by 6x5x4x3x2x1x4x3x2x1=

(Take out 1 through 6 on both sides)

10x9x8x7 divided by 4x3x2x1=

5040 divided by 24=

210

Dance instructor can chose 4 students out of 10 if order doesn't matter in 210 ways

A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected.

For example, suppose we have a set of three letters: A, B, and C. We might ask how many ways we can select 2 letters from that set. Each possible selection would be an example of a combination.

Formula of combination:

[tex]C_{n} ^{r} = \frac{n!}{r! (n-r)!}[/tex]

Where

nCr is   the selection of objects from a group of objects where order of objects does not matter.

n is the total number of objects

r is the number of selected objects.

According to the question

A dance instructor chose four of his 10 students to be on stage for a performance and order does not matter .

i.e,

if we have to chose and order does not matter that means we have to use combination .

[tex]C_{n} ^{r} = \frac{n!}{r! (n-r)!}[/tex]

Total number of students (n)= 10

Number of selected students (r) = 4

[tex]C_{n} ^{r} = \frac{n!}{r! (n-r)!}[/tex]

[tex]C_{n} ^{r} = \frac{10!}{4! (6)!}[/tex]

[tex]C_{n} ^{r} = \frac{10*9*8*7}{4*3*2*1 }[/tex]

[tex]C_{n} ^{r} = \frac{5040}{24 }\\[/tex]

[tex]C_{n} ^{r} = 210[/tex]

Hence, Dance instructor can chose 4 students out of 10 in 210 ways

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Answer:

It should be noted that the p.f of X and Y when they are independent can be obtained by multiplying together their marginal probability function.

Step-by-step explanation:

Two discrete random variables X and Y are said to be statistically independent if and only if , for all possible values ( xi, yi) the joint probability function f(x,y) can be expressed as the product of two marginal functions. That is X and y are independent if

f(x,y) = P(x=xi  and Y =yi)

          =  P(x=xi) P(Y =yi)         for all i and j

            = g(x)h(y)

It should be noted that the p.f of X and Y when they are independent can be obtained by multiplying together their marginal probability function.

The values of marginal probabilities are often written in the margins of the joint table as there are rows and columns totals in the table. The probabilities in each marginal probability function add to 1.

Answer:

Find every possible factors of 32, and pair them

Step-by-step explanation:

if the same value for width/length cant be repeated, 3 total possible values is possible

1 × 32 = 32

2 × 16 = 32

4 × 8 = 32

if the value of width/length can be repeated, 6 total different values.

1 × 32 = 32

2 × 16 = 32

4 × 8 = 32

32 × 1 = 32

16 × 2= 32

8 × 4= 32

you can easily find all factors using online factor calculator

Answer:

x=2

Step-by-step explanation:

-7/2x + 3/2 + 2 =-7/2

Add the numbers

3/2+2

2=2/1=4/2

3/2+4/2=7/2

-7/2x+7/2=-7/2

Subtract 7/2 from both sides

-7/2x=-14/2

Multiply both sides by 2

-7x=-14

Divide both sides by -7

x=2

Answer:

Options (C), Option (D), Option (E), Option (F).

Step-by-step explanation:

It's given in the question,

ΔTUV ≅ ΔWXY

Therefore, corresponding sides and angles will be congruent.

∠T ≅ ∠W

∠U ≅ ∠X

∠V ≅ ∠Y

TV ≅ WY

UV ≅ XY

TU ≅ WX

By these properties, following options will be the correct options.

Option (C). ∠V ≅ ∠Y

Option (D). TV ≅ WY

Option (E). UV ≅ XY

Option (F). ∠X ≅ ∠U

Answer:

C,D,E, and F are correct

Step-by-step explanation:

In order to solve problems like this, you need to see which angles and segment correspond. Also, you would need to make sure that the order is the same on both sides of the equal side. For example, the first angle on one side of the equal sign will be congruent to the FIRST angle on the other side of the equal side.

Answer:

x = -9

Step-by-step explanation:

To solve these types of questions,

a). If both the sides of the equation are different,

    2x + 3 = 3x - 6

   There will be exactly one solution.

b). If the coefficient of variable 'x' is same in both the sides of the equation,

    x - 3 = x - 6

    Solution set will be 'none'.

c). If both the sides of the equation are exactly same then equation will have infinite solutions.

   2x + 3 = x + x + 3

In the given equation,

6x - (5x + 5) = -8 - 2(x + 12)

Further simplify the equation,

(6x - 5x) - 5 = - 8 - 2x - 24

x - 5 = -2x - 32

x + 2x = 5 - 32

3x = -27

x = -9

The statement which is true about the slope of the given graphed line is that the slope is positive.

Slope is the proportion of decrease or increase in variable y due to increase and decrease in variable x. The formula of calculating slope is as under:

Slope=[tex](y_{2} -y_{1}) /(x_{2} -x_{1})[/tex]

We have to find the slope of the graphed line and for that we have to first take two points which lie on the line whose slope we have to find.

Take the points (0,4) and (-5,2) and calculating slope we get:

slope=(2-4)/(-5-0)

=-2/-5

=2/5

Hence the statement which is true is that the slope is positive.

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Answer:

[tex]x=6[/tex]

Step-by-step explanation:

So we have the equation:

[tex]3(x+1)=9+2x[/tex]

Distribute the left side:

[tex]3x+3=9+2x[/tex]

Subtract 2x from both sides. The right side cancels:

[tex](3x+3)-2x=(9+2x)-2x\\x+3=9[/tex]

Subtract 3 from both sides:

[tex](x+3)-3=(9)-3\\x=6[/tex]

So, x is 6.

Answer:

2x

Step-by-step explanation:

Factor both terms given to simplest terms:

8x = 2 * 2 * 2 * x

22xy = 2 * 11 * x * y

Note that in each case, there is the factor of 2 & x that is shared by both. These are what is used to find the Greatest Common Factor. Multiply both terms together:

2 * x = 2x

2x is your GCF.

~

First find the greatest common factor of 8 and 22.

To find the greatest common factor of 8,

begin by dividing 8 by all the numbers you can.

8 ÷ 1 = 8

8 ÷ 2 = 4

Notice that I stopped here because if I continued

dividing, I would be dividing 8 by 4 which is 2.

Make sure to stop dividing when you see numbers repeat.

So the factors of 8 are 1, 2, 4, and 8.

Now do the same thing for 22.

22 ÷ 1 = 22

22 ÷ 11 = 2

So the factors of 22 are 1, 2, 11, and 22.

Now look for the largest number shared by the two lists.

In this case, the largest number is 2.

Now let's move to the variables.

To qualify for the Greatest Common Factor,

the variable must appear in every monomial.

Since the y doesn't appear in every monomial, it doesn't qualify.

However, notice that the x does appear in every monomial.

If the variable does appear in every monomial, the Greatest

Common Factor will use the smallest power on that variable.

Since the smallest power for x in both monomials is x, we use x.

So our greatest common factor is 2x.

Answer:

[tex]mean = \frac{9 + 4 + 4 + 1 + 0 + 6 + 4}{7} = \frac{28}{7} = 4[/tex]

[tex]mean \: deviation = \frac{ |9 - 4| + |4 - 4| + |4 - 4| + |1 - 4| + |0 - 4| + |6 - 4| + |4 - 4| }{7} = \frac{5 + 0 + 0 + 3 + 4 + 2 + 0}{7} = \frac{14}{2} = 7[/tex]

Answer:

Discount = Original Price x Discount %/100

Discount = 2.88 × 1/100

Discount = 2.88 x 0.01

You save = $0.03

Final Price = Original Price - Discount

Final Price = 2.88 - 0.0288

Final Price = $2.85

Answer:

[tex]\sqrt[3]{x^2}[/tex]

x ^( 1/8)

Step-by-step explanation:

x ^ (5/6)  ÷ x ^ (1/6)

We know that a^ b ÷ a ^c = a^ ( b-c)

x^ ( 5/6 - 1/6)

x^ (4/6)

x ^ 2/3

[tex]\sqrt[3]{x^2}[/tex]

[tex]\sqrt{x}[/tex][tex]\sqrt[\\4]{x}[/tex]

x ^ 1/2 * x ^ 1/4

We know that a^ b * a ^ c = a^ (b*c)

x ^ (1/2 * 1/4)

x ^( 1/8)

Answer:

[tex]\huge \boxed{\sqrt[3]{x^{2} } } \\ \\ \huge \boxed{x^{\frac{3}{4} } }[/tex]

Step-by-step explanation:

Part 1:

x^(5/6) ÷ x^(1/6)

Applying exponent rule : a^b ÷ a^c = a^(b-c)

x^(5/6-1/6)

x^(4/6)

Simplifying the exponent.

x^(2/3)

Converting to simplest radical form.

(x^2)^(1/3)

[tex]\sqrt[3]{x^{2} }[/tex]

Part 2:

[tex]\sqrt{x} \times \sqrt[4]{x}[/tex]

Converting to exponent form.

x^(1/2) × x^(1/4)

Applying exponent rule : a^b × a^c = a^(b+c)

x^(1/2+1/4)

x^(2/4+1/4)

x^(3/4)

Answer:

Assuming you mean (6^2/3)^6, the exponent 6 2/3 in the simplification should be replaced with 4

Step-by-step explanation:

Apply the power rule and multiply exponents.

6 ^2 /3  * 6

Cancel the common factor of  3

6 ^2 *2

Multiply  2  by  2 .

6 ^4

Answer:

-2, 2 and 3.

Step-by-step explanation:

each of the brackets could be zero.

So for example x + 2 = 0 gives x = -2.

Answer:

x=-2   x=2   x=3

Step-by-step explanation:

g(x) = (x + 2)(x − 2)(x − 3)

Set the function equal to 0

(x + 2)(x − 2)(x − 3) =0

Using the zero product property

x+2 =0  x-2 =0  x-3 =0

Solve each equation

x=-2   x=2   x=3

These are the zeros

Answer:

[tex] \boxed{ \bold{ \boxed{ \sf{ - 5 {x}^{5} + 2 {x}^{3} - 6x}}}}[/tex]

Step-by-step explanation:

[tex] \sf{( {x}^{5} + {x}^{3} ) - (6x - {x}^{3} + 6 {x}^{5}) }[/tex]

When there is a ( - ) in front of an expression in parentheses , change the sign of each term.

Also, remove the parentheses

⇒[tex] \sf{ {x}^{5} + {x}^{3} - 6x + {x}^{3} - 6 {x}^{5} }[/tex]

Collect like terms

⇒[tex] \sf{ {x}^{5} - 6 {x}^{5} + {x}^{3} + {x}^{3} - 6x}[/tex]

⇒[tex] \sf{ - 5 {x}^{5} + 2 {x}^{3} - 6x}[/tex]

Hope I helped!

Best regards!!

Answer: B. a savings account earns interest

Step-by-step explanation: Money loses value over time as the rate of inflation increases. In this scenario, when you have some money to spare, the ideal is to seek some kind of investment that earns interest.

Saving is one such option. The money in savings earns interest and is highly liquid, meaning it can be used at any time. In addition, saving is a very...

Answer:

B

Step-by-step explanation:

Answer:

Place Value

Step-by-step explanation:

To Find:in a multi-digit number, the number place that a digit is in determines it's?

Solution :

The number place that a digit is in determines it's PLACE VALUE

Definition of place value : Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.

Thus in a multi-digit number, the number place that a digit is in determines it's PLACE VALUE.

Eg . 389

Since the digit 8 is on tens place

So, it makes us to determine its place value

Place value of 8 is 80

Hence in a multi-digit number, the number place that a digit is in determines it's PLACE VALUE.

h= number of hours

m= number of miles

Formula: 4h=12m

(4 hours equals 12 miles)

Divide 4 on each side.

h= 3m

3 miles per hour.

Then, convert miles to feet. And hours to minute.

To do this simultaneously,

Convert miles to feet and hours to minutes.

There should be 3 "fractions" to multiply.

The first should be the original problem:

3miles/1 hour. (3 miles per hour).

The second should be 1 hour/60min. (1 hour per 60 min).

The third should be 5280 ft/1 mile. (5280 feet per mile).

The second and the third fractions are to convert miles to feet and the hours to minutes.

Answer:

I got 2 as an answer

Step-by-step explanation:

[tex]( {3x}^{4} ) - 5 = 43 \\ ( {3x}^{4} ) = 43 + 5 \\ ( {3x}^{4} ) = 48 \\ \frac{ {3x}^{4} }{3} = \frac{48}{3} [/tex]

[tex] {x}^{4} = 16 \\ \sqrt[4]{ {x}^{4} } = \sqrt[4]{16} \\ x = 2[/tex]

Answer: A

Step-by-step explanation:

L=Length W=Width

3W=2L+2

4L=2L+2W+12

2L=2W+12

Option A

Hope this helps!! :)

Please let me know if you have any question or need further explanation

Answer:

In a standard normal distribution;

The mean of the population is going to be zero and the population standard deviation is automatically one.

In a nonstandard normal distribution;

The mean of the population is not equal to zero and the population standard deviation is not equal to one.

Step-by-step explanation:

When looking at a  normal distribution: There are three major keys we need  to understand:

The major difference between a standard normal distribution and a nonstandard normal distribution is that:

In a standard normal distribution, there are two additional things attached.

The mean of the population is going to be zero and the population standard deviation is automatically one.

In a nonstandard normal distribution;

The mean of the population is not equal to zero and the population standard deviation is not equal to one.

Answer:

Step-by-step explanation:

(r/s)(x) is the quotien of r(x) = 3x - 1 and s(x) = 2x + 1:

  r            3x - 1

(-----)(x) = ----------

  s            2x + 1

Answer:

A. 9

Step-by-step explanation:

54/6 = 9

Answer:

9

Step-by-step explanation:

The scaling factor for this image is 9.

Notice that 54/6 = 9 and 108/12 = 9.

Cheers.

Answer:

$450

Step-by-step explanation:

Let R be the hourly pay rate in dollars per hour. Hannah worked 10 hours and Zach worked 9 hours for a total of $950, so we get the equation:

10R + 9R = 950

Solve for R:

19R = 950

R = 50

Zach worked for 9 hours, so the total he earned is:

9 hours * 50 dollars/hour = $450

Equation to represent amount of money Jerry has after working x hours is

y = $7x + $20

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Given,

Jerry makes $7 per hour

He has $20.

Jerry works for x hours

Amount Jerry made working x hours = $7x

Then, equation for total amount y Jerry has after working x hours

y = $7x + $20

Hence, y = $7x + $20 is equation that represents the total amount of money Jerry has after working x hours.

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Answer:

at N ≥ 6

Step-by-step explanation:

Error permissible = 0.001

The series = infinity  

at ( N + 1 ) ! > 1000  the inequality N ≥ 6 is valid and holds

attached below is the detailed solution using alternating series remainder

Answer:

m<VRU = 80°

m<URW = 15°

Step-by-step explanation:

<SRW and <VRT are vertical opposite angles. Vertical opposite angles are equal. Therefore:

[tex] 2x + 15 = 85 [/tex]

Use this expression to solve for the value of x

[tex] 2x + 15 - 15 = 85 - 15 [/tex]

[tex] 2x = 70 [/tex]

[tex] \frac{2x}{2} = \frac{70}{2} [/tex]

[tex] x = 35 [/tex]

Find m<VRU by plugging in the value of x in the expression for its angle given.

m<VRU = [tex] 2x + 10 [tex]

[tex] 2(35) + 10 = 70 + 10 = 80 [tex]

m<VRU = 80°

FIND m<URW.

m<URW = 180° - (m<VRU + m<SRW) (angles on a straight line is 180°)

m<URW = 180 - (80 + 85)

= 180 - 165

m<URW = 15°