Pentagon RSTUV is circumscribed about a circle. What is the value of x if RS = 8, ST = 12, TU = 15, UV = 9, and VR = 12?

Answer:

1010

Step-by-step explanation:

There are a whole class of questions that rely on the method to this one.

First add up what you know

1270 + 1150 + 870 + 1450 = 4740

Now add on the 5th month (which you don't know. Call it x)

4740 + x

Divide by 5

(4740 + x)/5 = 1150 and that is your equation    

Solution

Multiply both sides by 5

5*(4740 + x) / 5 = 1150 * 5

4740 + x = 5750

Subtract 4740 from both sides

4740 - 4740 + x = 5750 - 4740

x = 1010

Which seems kind of low, but that's what the numbers come to.

The equation that represents the line passing through the points (-1, 2) and (3, 1) is  [tex]\[ x + 4y = 7 \][/tex]

The correct option is (B).

To find the equation of the line that passes through the points (-1, 2) and (3, 1), we need to determine the slope of the line and use the point-slope form of the equation of a line, which is [tex]\( y - y_1 = m(x - x_1) \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( (x_1, y_1) \)[/tex] is a point on the line.

First, let's calculate the slope [tex]\( m \)[/tex] using the two given points [tex]\( (x_1, y_1)[/tex]= [tex](-1, 2) \) and \( (x_2, y_2) = (3, 1) \)[/tex]:

[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

Let's compute the slope.

The slope \( m \) of the line that passes through the points (-1, 2) and (3, 1) is [tex]\( -0.25 \)[/tex].

Next, we'll use one of the points and the slope to write the equation of the line in point-slope form and then convert it to slope-intercept form[tex]\( y = mx + b \)[/tex]. Let's use the point (-1, 2) to find the equation of the line.

The equation of the line in slope-intercept form is [tex]\( y = -0.25x + 1.75 \)[/tex].

Now let's convert this to the standard form of the line equation, [tex]\( Ax + By = C \),[/tex] and compare it with the given options.

To get the standard form, we will multiply through by 4 to eliminate the decimals and then rearrange the terms:

[tex]\[ y = -0.25x + 1.75 \][/tex]

[tex]\[ 4y = -x + 7 \][/tex]

[tex]\[ x - 4y = -7 \][/tex]

This standard form equation needs to be matched with one of the given options by comparing coefficients. Let's do this by checking which of the given options has the same ratio of coefficients for[tex]\( x \) and \( y \)[/tex] as the equation we found.

The equation that represents the line passing through the points (-1, 2) and (3, 1) is given by option B, which is:

[tex]\[ x + 4y = 7 \][/tex]

Choose the equation that represents a line that passes through points (-1,2) and (3,1)

A. 4x-y=6

B.x+4y=7

C. x-4y =-9

D.4x+y=2​

Using the rule that any non-zero number raised to the power of zero equals one, the equation 3 • 4^0 / a^0 simplifies to 3.

The problem seems to be a little bit confusing, so let's format it more clearly. I believe that you're looking to simplify: 3 • 4^0 / a^0.

There's a rule in mathematics stating that any number raised to the zeroth power equals one. In other words, if x is a non-zero number, then x^0 = 1. In this case, 4^0 = 1 and a^0 = 1.

Apply that rule to your problem and it becomes 3 • 1 / 1, or simply 3.

So, according to the rules of exponents, the simplified form of 3 • 4^0 / a^0 is 3.

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Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]f\left(x\right)=\left|x+3\right|-5[/tex]

Obtain the function g(x)

[tex]g(x)=-\frac{1}{5} f(x)[/tex]

substitute

[tex]g(x)=-\frac{1}{5} [\left|x+3\right|-5][/tex]

[tex]g(x)=-\frac{1}{5}\left|x+3\right|+1[/tex]

using a graphing tool

The graph in the attached figure

The vertex is the point (-3,1)

The x-intercepts are the points (-8,0) and (2,0)

The y-intercept is the point (0,0.4)

Answer:

n

Step-by-step explanation:

Answer:

C. [tex] \frac{3}{2} [/tex]

Step-by-step explanation:

To find the value f b, we need to compare the exponents.

The given exponential equation is:

[tex]( {x}^{2} {y}^{3} )^{3} = ( {x} {y}^{a} )^{b}[/tex]

Recall and apply the following rule of exponents.

[tex] ( {x}^{m} )^{n} = {x}^{mn}[/tex]

We apply this rule on both sides to get:

[tex]{x}^{2 \times 3} {y}^{3 \times 3} = {x}^{b} {y}^{ab}[/tex]

Simplify the exponents on the left.

[tex]{x}^{6} {y}^{9} = {x}^{b} {y}^{ab}[/tex]

Comparing exponents of the same variables on both sides,

[tex]b = 6 \: and \:\: ab = 9[/tex]

[tex] \implies \: 6b = 9[/tex]

Divide both sides by 6.

[tex]b = \frac{9}{6} [/tex]

[tex]b = \frac{3}{2} [/tex]

Answer:

Area =  16 units²

Step-by-step explanation:

Points to remember

Distance formula

The distance between two points (x1, y1) and (x2, y2) is given by

Distance = √[(x2 - x1)² + (y2 - y1)²]

To find the length and breadth of rectangle

Let the points be  (1, 7) , (5, 3)

Distance = √[(x2 - x1)² + (y2 - y1)²]

 = √[(5 - 1)² + (3 - 7)²]

 =  √[(4)² + (-4)²]

 = √32 = 4√2

If the points be  (5, 3) , (3, 1)

Distance = √[(x2 - x1)² + (y2 - y1)²]

 = √[(3 - 5)² + (1 - 3)²]

 =  √[(-2)² + (-2)²]

 = √8 = 2√2

Length = 4√2 and breadth = 2√2

To find the area of rectangle

Area = Length * Breadth

 = 4√2 * 2√2

 = 16 units²

Answer:

16 units

Step-by-step explanation:

i have answered ur question

Answer:

1) 95

2) -12

3) 7

4) 1,700

5) 57

6) 3,070

Answer:

C. y=x^2-6x+8

Step-by-step explanation:

We have to check each functions in options with the given point

So,

The point is (3,-1)

For A:

[tex]y = x^2+6x+8\\Putting\ the\ point\\-1 = (3)^2+6(3)+8\\ -1=9+18+8\\-1 \neq 35[/tex]

For B:

[tex]y=x^2-2x-8\\-1 = (3)^2-2(3)-8\\-1=9-6-8\\-1\neq -5[/tex]

For C:

[tex]y = x^2 - 6x+8\\-1 =(3)^2-6(3)+8\\-1= 9-18+8\\-1=-1[/tex]

The given point satisfies the third function. Therefore, Option C is the correct answer ..

Answer:

82%

Because O.34 + O. 48 = .82 and .82 • 1OO=82

So 82% Can swim

i got it right on Aoex

The percentage of people cannot swim is 18%.

Relative frequency can be defined as the number of times an event occurs divided by the total number of events occurring in a given scenario.

Given that, in a survey, 250 adults and children were asked whether they know how to swim.

From table cannot swim = 0.06+0.12

= 0.18

In percentage = 0.18×100

= 18%

Therefore, the percentage of people cannot swim is 18%.

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Answer:

Step-by-step explanation:

The number of customers carrying cash=45% = 0.45

The number of customers carrying checks= 44% =0.44

The number of customers carrying both = 31% = 0.31

So,

To find the probability we will write the expression:

cash+checks-cash or checks(both)=cash and checks

0.45+0.44-both=0.31

0.45+0.44-0.31=both

0.58=both....

Answer:

$1720.00

Step-by-step explanation:

55.75 + 9.65 = 65.40

65.40 x 26.3 = 1720.02

Answer:

C. 1307 ft

Step-by-step explanation:

Given:

Angle = 48.4 degrees

Height, opposite side= 1472 feet

his distance from the Empire State Building, base=x

Now as per the trigonometric ratios:

Tan∅= Opposite/base

tan(48.4)= 1472/x

x=1472/(1.13)

x=1302.65

his distance from the Empire State Building is 1302.65 feet!

Answer:

The correct answer is option C.

Step-by-step explanation:

Height of Empire State Building = 1,472 feet

Angle formed by the line segment from the point of ground on which Dante is positioned to the top of the building is  48.4°.

Distance of Dante from the Empire State Building =?

In the fig ,ΔABC

AB = 1,472 feet, BC = ? , θ= 48.4°

[tex]\tan\theta =\frac{Perpendicular}{base}[/tex]

[tex]\tan 48.4^o=\frac{AB}{BC}[/tex]

[tex]BC=\frac{AB}{\tan 48.4^o}=\frac{1,472 feet}{1.1263}=1,306.9 feet\approx 1,307 feet[/tex]

Distance of Dante from the Empire State Building is 1,307 feet.

Answer: Choice A

Step-by-step explanation:

-

Answer:

A

Step-by-step explanation:

Given :

2x + 4y = 14  ---------- eq 1

4x + y = 20 ---------- eq 2

if you multiply eq 2 by -4 on both sides, you get

-4 (4x + y = 20) = -4 (20)

-16x -4y = -80 --------- eq3

we can see that eq. 1 and eq 2 together forms the system of equations presented in option A, Hence A is equvalent to the orginal system of equations given in the question.

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}2x+4y=14&(1)\\4x+y=20&(2)\end{array}\right\\\\\left\{\begin{array}{ccc}2x+4y=14&(1)\\4x+y=20&\text{multiply both sides by (-4)}\end{array}\right\\\left\{\begin{array}{ccc}2x+4y=14&(1)\\-16x-4y=-80&(2)\end{array}\right\to \boxed{A.}[/tex]

B.

[tex]\left\{\begin{array}{ccc}2x+4y=14&(1)\\4x+y=20&\text{change the signs}\end{array}\right\\\\\left\{\begin{array}{ccc}2x+4y=14&(1)\\-4x-y=-20&\text{it's different to (2)}\end{array}\right[/tex]

C.

[tex]\left\{\begin{array}{ccc}2x+4y=14&\text{multiply both sides by 2}\\4x+y=20&(2)\end{array}\right\\\left\{\begin{array}{ccc}4x+8y=28&\text{different to (1)}\\4x+y=20&(2)\end{array}\right[/tex]

D.

[tex]\left\{\begin{array}{ccc}2x+4y=14&\text{change the signs}\\4x+y=20&(2)\end{array}\right\\\left\{\begin{array}{ccc}-2x-4y=-14&\text{different to (1)}\\4x+y=20&(2)\end{array}\right\\\\A.[/tex]

Answer:

x^2-16 goes with (x+4)(x-4)

x^2+10x+16 goes with (x+8)(x+2)

Step-by-step explanation:

The first one you got wrong is known as a difference of squares.

To factor a difference of squares, a^2-b^2, you just write it as (a-b)(a+b) or (a+b)(a-b) would work too.

So x^2-16=(x-4)(x+4) or (x+4)(x-4).

Let's check (x+4)(x-4) using foil!

First: x(x)=x^2

Outer: x(-4)=-4x

Inner: 4(x)=4x

Last: 4(-4)=-16

----------------------Add

x^2-16

Bingo! (x+4)(x-4) definitely corresponds to x^2-16.

Here are more examples of factoring a difference of squares:

Example 1:  x^2-25  = (x+5)(x-5)

Example 2: x^2-81   = (x+9)(x-9)

Example 3: x^2-100 =(x+10)(x-10)

Onward to the next problem:

x^2+10x+16

When the coefficient of the leading term of a quadratic is 1, all you have to do is find two numbers that multiply to be c=16 and add up be b=10.

Those numbers would be 8 and 2

because 8(2)=16 and 8+2=10.

So the factored form of x^2+10x+16 is (x+2)(x+8) or (x+8)(x+2).

Here is another example of when the leading coefficient of a quadratic is 1:

Example 1:  x^2+5x+6=(x+2)(x+3) since 3(2)=6 and 3+2=5.

Example 2: x^2-x-6=(x-3)(x+2) since -3(2)=-6 and -3+2=-1.

Answer:

Step-by-step explanation:

Yes it’s parallel because the lines do not meet

Answer: 2:45

Step-by-step explanation:

1 hour and 15 minutes plus 30 minutes equal an hour and 45 minutes. We subtract 1 hour and 45 minutes from 4:30 and get 2:45.

So she started shopping at 2:45.

Answer:

18

Step-by-step explanation:

A rectangular prism has four parallel edges along its length, four parallel edges along its width, and four parallel edges along its height.

We want to know how many different pairs of parallel edges there are.  Starting with the length, the number of unique pairs is:

₄C₂ = 6

The same is true for the width and height.  So the total number of different pairs of parallel edges is:

3 × 6 = 18

Answer:

-4x-1

Step-by-step explanation:

-1(2x + 3) -2 (x - 1)

Distribute the -1 and the -2

-2x - 3 -2 x  +2

Combine like terms

-4x-1

[tex]\huge \boxed{-4x-1}[/tex], you can use the distributive property of [tex]\displaystyle a(b+c)=ab+ac[/tex].  

Multiply from left to right.

[tex]\displaystyle 1\times(2x+3)=2x+3[/tex]

[tex]\displaystyle -(2x+3)-2(x-1)[/tex]

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

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

[tex]\Large\textnormal{Solve to find the answer.}[/tex]

[tex]\displaystyle-2x-3-2x+2=-4x-1[/tex]

[tex]\large \boxed{-4x-1}[/tex], which is our answer.

Answer:

see explanation

Step-by-step explanation:

Calculate the distance (d) using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (0, -4) and (x₂, y₂ ) = (3, - 1)

d = [tex]\sqrt{(3-0)^2+(-1+4)^2}[/tex]

  = [tex]\sqrt{3^2+ 3^2}[/tex]

  = [tex]\sqrt{9+9}[/tex]

  = [tex]\sqrt{18}[/tex] = 3[tex]\sqrt{2}[/tex] ≈ 4.24 ( to 2 dec. places )

Answer:

$8,000 to the nearest hundred.

Step-by-step explanation:

A depreciation of 15% means that after each year the car is worth 0.85 of it's value the previous year.

So after 7 years the values of the car is 25,000(0.85)^7

= 8,014

The value of a car that depreciates at a rate of 15% per year after 7 years is $10,400, after rounding to the nearest hundred.

The question is asking for the value of the car after 7 years when it depreciates at a rate of 15% per year. To find the car's value after each year, we can multiply the current value at the end of each year by 85% (which is 100% - 15%), because the car is losing 15% of its value. The formula to calculate the depreciation is P(1 - r)^t, where P is the initial principal (the initial value of the car), r is the depreciation rate, and t is the time in years.

Using this formula, the car's value after 7 years would be: $25,000 x (1 - 0.15)^7. Calculating this gives a value of $25,000 x 0.417709 = $10,442.73.

After rounding to the nearest hundred, the value is approximately $10,400.

ANSWER

The exact solution are:

[tex]y = \frac{ - 6 - 2 \sqrt{6} }{5} \: \: or \: \: y = \frac{ - 6 + 2 \sqrt{6} }{5} [/tex]

EXPLANATION

The given quadratic equation is

[tex] {(5y + 6)}^{2} = 24[/tex]

We use the square root method to solve for y.

We take square root of both sides to get:

[tex] \sqrt{{(5y + 6)}^{2}} = \pm\sqrt{24} [/tex]

This gives us:

[tex]5y + 6 = \pm 2 \sqrt{6} [/tex]

Add -6 to both sides to get:

[tex]5y = - 6 \pm 2 \sqrt{6} [/tex]

Divide through by 5:

[tex]y = \frac{ - 6 \pm2 \sqrt{6} }{5} [/tex]

[tex]y = \frac{ - 6 - 2 \sqrt{6} }{5} \: \: or \: \: y = \frac{ - 6 + 2 \sqrt{6} }{5} [/tex]

Answer:

A person drinks 4.52 cups per hour

Step-by-step explanation:  

No of work days = 5

No of hours in day = 10

No of hours in week = 10*5= 50 hours

Total cups consumed = 226

No of cups consumed per hour = Total no of cups/ Total week  hours            

                                                     = 226/50

                                                     = 4.52 cups/ hour

Answer:

8 x^6 + x + 14

Step-by-step explanation:

Simplify the following:

7 x^6 + x^6 + x + 5 + 9

Grouping like terms, 7 x^6 + x^6 + x + 5 + 9 = (x^6 + 7 x^6) + x + (9 + 5):

(x^6 + 7 x^6) + x + (9 + 5)

x^6 + 7 x^6 = 8 x^6:

8 x^6 + x + (9 + 5)

9 + 5 = 14:

Answer: 8 x^6 + x + 14

For this case we must find the sum of the following polynomials:

[tex]x ^ 6 + x + 9\ and\ 7x ^ 6 + 5[/tex]

We have:

[tex](x ^ 6 + x + 9) + (7x ^ 6 + 5) =[/tex]

We eliminate parentheses:

[tex]x ^ 6 + x + 9 + 7x ^ 6 + 5 =[/tex]

We add similar terms:

[tex]x ^ 6 + 7x ^ 6 + x + 9 + 5 =\\8x ^ 6 + x + 14[/tex]

Finally we have that the sum of the polynomials is:[tex]8x ^ 6 + x + 14[/tex]

Answer:

[tex]8x ^ 6 + x + 14[/tex]

Answer:

A 18%

Step-by-step explanation:

I believe it should be A because there is no specific type a marble specified therefore if you do

12/33--> 0.36 times 100= 36 % which isn't an option

15/33->0.45 times 100= 45 % which also isn't an option

6/33= 0.18 times 100= 18% this is the only option given

Answer:

B. 82%

Step-by-step explanation:

From the question; A marble is randomly selected from a bag containing 15 black, 12 white, and 6 clear marbles. Find P(not clear).

To find p(not clear), we use this formula;

P(not clear) = 1 -  p(clear)

To proceed we first have to find p(clear) and the minus it from 1

But,

probability =  Required outcome/ all possible outcome

In the question, since what we are looking for now is probability of clear, so our 'required outcome' is the number of marble which is 6,

all possible outcome is the number of all the marbles; 15 + 12 + 6 = 33

We can now proceed to find the probability of clear marble, hence;

probability =  Required outcome/ all possible outcome

p(clear marble) = 6/33

Now, we go ahead to find the probability of 'not clear marble'

P(not clear) = 1 -  p(clear)

                   =   1 - 6/33

                    = 1 -   0.181818

                     =0.818182

P(not clear) = 0.818182

But the question says we should round our answer to the nearest percent, so we will multiply our answer by 100%

p(not clear)  = 0.818182 ×  100%

p(not clear) = 82% to the  nearest percent

Answer:

A

Step-by-step explanation:

If you reflect over line A both pentagons are equally spaced in proportion to the line

The pentagon is reflected over the line A.

Reflection is a type of geometric transformation where the figure is flipped. In other words, a figure when undergoes reflection becomes it's mirror image.

Here given are two pentagons on left and right.

The pentagon on the left is a reflection of the pentagon on the right.

This means that both the pentagons should be proportionally spaced from the line.

If we consider the line of reflection as B, the the pentagon on the right is nearer to the line compared to that on the left.

If we consider line D as the line of reflection, then pentagon on the left is nearer to the line compared to that on the right.

So if line A is the line of reflection, the both pentagons are equally spaced from the line.

Hence line A is the line of reflection.

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Answer:

168.558

Step-by-step explanation:

       168.58

34√5731.0

    -34 ↓3

     23 3

    -204 ↓1

       28  1

     - 272 ↓0

       19  0

       -170  ↓0

         20 0

        -170  ↓0

           30 0

          -272 ↓0

            28  0

and just goes on..

Answer:

The points C(1,2) and E(2,2) make both inequalities true

Step-by-step explanation:

we have

[tex]y < 5x+2[/tex] -----> inequality A

The solution of the inequality A is the shaded area below the dashed line

[tex]y\geq \frac{1}{2}x+1[/tex] ------> inequality B

The solution of the inequality B is the shaded area above the solid line

The solution of the system of inequalities is the shaded area between the dashed line and the solid line

see the attached figure

Remember that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities and the point lie on the shaded area of the solution

Plot the points and verify if lie on the shaded area

Let

[tex]A(-1,3),B(0,2),C(1,2),D(2,-1),E(2,2)[/tex]

see the attached figure

The points C(1,2) and E(2,2) lie on the shaded area

Note

The points A(-1,3) and B(0,2) satisfy inequality B but don't satisfy inequality A

The point D(2,-1) satisfy inequality A but don't satisfy inequality B

therefore

The points C(1,2) and E(2,2) make both inequalities true

Answer:

c and e

Step-by-step explanation:

The probability that the number is formed greater than 600 is [tex]\frac{1}{2}[/tex].

Probability is the chance that something will happen, or how likely it is that an event will occur.

The formula for the probability is

[tex]P(E) = \frac{number \ of \ favorable \ outcomes }{Total\ number\ of\ outcomes}[/tex]

Where,

P(E) is the probability of any event.

A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.

The formula for the permutation is given by

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

Where,

[tex]^{n} P_{r}[/tex] is the permutation

n is the total number of objects

r is the total number of objects to be selected

According to the given question.

We have total four numbers 2, 4, 6, 7.

So,

The total number of three digits can be formed using these four numbers = [tex]^{4} P_{3}[/tex] = [tex]\frac{4!}{(4-3)!} =\frac{4\times 3\times 2\times 1}{1}[/tex][tex]=24[/tex]

Now, for making three digits number which are greater than 600 by using 2, 4, 6, 7 without repetition is given by

Number of ways for filling hundred place is 2 (either 6 or 7).

Number of ways for filling tens place is 3 (if 6 is placed at hundred place then remaining numbers are 7, 2, 4 and if 7 is place at hundred place then remaining numbers are 6, 2, 4).

Number of ways for filling one place is 2(because only 2 number are left).

Therefore, the total numbers of three digits can be formed by using these numbers 2, 4, 6, and 7

[tex]= 2\times 3\times 2\\=12[/tex]

So,

the probability that the number is formed greater than 600

= [tex]\frac{total\ three\ digits\ numbers\ which\ are \ formed \ by\ using\ 1,\ 2, \ 3, \ and\ 4\ which\ are\ greater\ than\ 600 }{Total \ three\ digits\ numbers\ formed\ by \ using \ 1,\ 2,\ 3,\ and \ 4}[/tex]

[tex]= \frac{12}{24}[/tex]

[tex]= \frac{1}{2}[/tex]

Therefore, the probability that the number is formed greater than 600 is [tex]\frac{1}{2}[/tex].

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Answer:

The option A,D and E are correct.

Step-by-step explanation:

Given: 2x^3-250x^2

Factor : 2x^2(x-125)

So, GCF = 2x^2

Now a = 1 and b= 5

we know that a^3-b^3 = (a-b)(a^2+ab+b^2)

(x)^3 - (5)^3 = (x-5)(x^2+5x+25)

So, the option A,D and E are correct.