Draw the graph for y=2x-3 for -2<=x<=3

a) Equation for length and width of the rectangular rug be [tex]x^{2}[/tex] + 8x - 42 = 0

b) Width of the rectangular rug be 3.5 feet

c) Diagonal of the rectangle is 12.5 feet

What is the area of the rectangle?

The area of ​​a rectangle is the area occupied by the rectangle within its four sides or boundaries.

The area of ​​a rectangle depends on its sides. Basically, the formula for area is equal to the product of the length and width of a rectangle. The perimeter of a rectangle is equal to the sum of all its four sides

It is given that area of a rectangular rug id 42 square feet. The rug is 8 feet longer than its wide

a) Let the width of the rectangular rug be x feet

Length of the rectangular rug = (x+8) feet

area of rectangular rug = Length × width = x × (x + 8) = [tex]x^{2}[/tex] + 8x

area of rectangular rug = 42

[tex]x^{2}[/tex] + 8x = 42

[tex]x^{2}[/tex] + 8x - 42 = 0

Therefore, equation for length and width of the rectangular rug be [tex]x^{2}[/tex] + 8x - 42 = 0

b) If the length of the rectangle is 12 feet

Area of rectangle = 42 square feet

length × width = 42 square feet

12 × width = 42 square feet

width = 42/12 = 3.5

Therefore, width of the rectangular rug be 3.5 feet

c) Length of the diagonal of the rectangle = [tex]\sqrt{length^2+width^2}[/tex]

= [tex]\sqrt{12^2+3.5^2}=\sqrt{144+12.25}=\sqrt{156.25}= 12.5[/tex]

Therefore, diagonal of the rectangle is 12.5 feet

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Answer:see below

Step-by-step explanation:

a+4<b+4

40% is  the percent markup.

What does math mean by percentage?

A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a percentage. Divide the number by the total and multiply by 100 to find the percent of a given number. , a.

                    an a, the in the an in the an in the an in the an in the Per 100 is what the word percentage signifies.

= 1 - 4800 /20 ÷ 400

= 1 - 12/20

= 1 - 3/5

= 5 - 3/5

= 2/5

Multiply a number to both the numerator and the denominator

       2 *20/5 *20

 = 40/100

 = 40%

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Answer:

JSHKAKSBKSBAK?

Step-by-step explanation:

The surface area of this cylinder is 118.378 square yards. 3.6 yard is the height.

The quantity of space enclosing a three-dimensional shape's exterior is its surface area.

For instance, the surface area of a cube is its surface area if we need to determine how much paint is needed to paint it. Square units are used to measure it at all times.

The terms "lateral surface area," "curved surface area," and "total surface area" refer to three different forms of surface area.

Surface area and volume are the cylinder's two main characteristics because it is a three-dimensional form. The area of the two circular bases combined with the cylinder's curved surface area equals the cylinder's overall surface area. Its volume is the three-dimensional area that a cylinder takes up.

Given that,

Surface area (A) of the cylinder = 118.378 square yards.

radius (r) = 2.9 yard

As we know, A = 2πrh + 2πr²

putting the values we get -

or, 118.378 = 2πr (h + r)

or, 118.378 = 2 × 3.14 ×2.9 × (h + 2.9)

or, 118.378 = 18.212 × (h + 2.9)

or, 6.5 = h + 2.9

or, h = 6.5 - 2.9

or, h = 3.6 yard

Thus, 3.6 yard is the height of the cylinder.

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Answer:

[tex]y=2-\frac{3}{4} y[/tex]

Step-by-step explanation:

Slope intercept form is y=mx+b

m is the slope; b is the y-intercept

Therefore, we need to isolate the y variable first

3x + 4y = 8

-3x          -3x

4y=8-3x                Divide both sides by 4 to leave y by itself.

/4    /4

[tex]y=2-\frac{3}{4} y[/tex]

Answer: 50 existing members

11 days are required to rent a car at both locations at the same price.

What is a System of Equations?

A system of equations in algebra is made up of two or more equations that are solved together. "A group of equations satisfied by the same set of variables are called a system of linear equations. Finding the values of the variables employed in the system of equations is the first step towards solving it. While maintaining the balance of the equations on both sides, we compute the values of the unknown variables. Finding a variable whose value makes the condition of all the given equations true is the primary goal of solving an equation system.

1st equation: 61+24x=y

Equation 2: 105+ 20x Equals y

Eq. 1 - 2 - subtracted

105-61+20x-24x= 0

44-4x= 0

4x = 44

4 divided by both sides

x= 44/4

x= 11 days

Hence, 11 days are required to rent a car at both locations at the same price.

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The expected value of these outcomes are  $262.5, $496 and $648 respectively

You should know that the expected value are the proportion of the values when valued with the percentages

The given values are $210, $320 and $540

The given percentages are 25%, 55% and 20%

The expected values are

0.25*210 = $52.5+210=$262.5

0.55*320=176+320=$496

0.20*540=108+540=$648

Therefore the projected values of the project are  $262.5, $496 and $648 respectively

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Answer:

n<1

Step-by-step explanation:

3n<3
/3. /3

n<1
hopes this helps

Answer:

n < 1

Step-by-step explanation:

3/3 n < 3/3

n < 1

Answer: 2 times!

Step-by-step explanation:

(-1,0)

(4/3, 0)

Answer:

C.2

Step-by-step explanation:

See attached: the graph of your function

Answer: Y=112

Step-by-step explanation: Add all of the interior angles you have to get 248 and subtract 248 from 360.

67+80+101 = 248.

360-248 = 112

Answer:

4

Step-by-step explanation:

First we need to get some definitions out of the way

Definition of a turning point

Definition of degree of polynomial

Answer:

6 + 2x

Step-by-step explanation:

5 + 5x - 3x + 1

add 5 + 1

6 + 5x - 3x

collect like terms 5x -3x

6 + 2x

Step-by-step explanation:

Please follow me the answer is 6+2x

or 2x+6

As per the congruency theorem, the two triangles are congruent.

Congruency theorem:

Congruency theorem states that "if all the three sides of one triangle are equal to all the three sides of another triangle, then both the triangles are congruent to each other."

Given,

Here we need to prove that  congruency theorem can be used to prove that △wut ≅ △vtu.

Let us consider triangles WUT and VTU.

And in these triangles:

=> WU≅VT

And in those one, ∠T≅∠U,

Therefore, m∠T = m∠U = 90°

Here the side TU is common.

Now, we have to note that triangles WUT and VTU are right triangles, because m∠T = m∠U = 90°.

Then the side TU is common leg and sides WU and VT are hypotenuses.

Therefore, the HL theorem states: if the hypotenuse (WU) and one leg  (TU) of a right triangle (ΔWUT) are congruent to the hypotenuse (VT) and one leg (TU) of another right triangle (ΔVTU), then the triangles are congruent.

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Answer: HL

Step-by-step explanation:

The expression |ab^3| if a>0 and b>0 is even.

What is Parity Definition?

Even Function: A function is even if f(-x)=f(x) for all [tex]$x \in \mathbb{R}$[/tex] Odd Function: A function is odd if f(-x)=-f(x) for all [tex]$x \in \mathbb{R}$[/tex]

[tex]f(a): \quad|a|\left|b^3\right|[/tex]

[tex]f(-a): \quad|a|\left|b^3\right|[/tex]

[tex]-f(a):-|a|\left|b^3\right|[/tex]

Check parity of [tex]$|a|\left|b^3\right|$[/tex]

Check if Even: True

Check if Odd: False

Even

The expression |ab^3| if  b>0

[tex]$$\begin{aligned}& f(a): \quad|a| b^3 \mid \\& f(-a): \quad|a|\left|b^3\right| \\& -f(a): \quad-|a| b^3 \mid\end{aligned}$$[/tex]

Check parity of [tex]$|a|\left|b^3\right|$[/tex]

Check if Even: True

Check if Odd: False

Even

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The total area of the shaded region is solved to be 154.93 cm²

The diameter is solved using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

x² = 8² + 15²

x² = 289

x = √289

x = 17

Work out the area of the triangle using the formula

= 1/2 *  base * height

base = hypotenuse or diameter

height = radius = diameter/2

= 0.5 * 17 * 8.5

= 72.25 cm²

Area of the circle

= Π * radius²

= 22/7 * 8.5²

= 226.98 cm²

shaded portion

= Area of the circle - area of the triangle

= 226.98 - 72.25

= 154.93 cm²

the area of the shaded portion is 154.93 cm²

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American adults believes in alien for the  given 95% confidence interval and sample surveyed is in the interval range of ( 0.66 , 0.78 ).

As given in the question,

Sample of American adults surveyed 'n' = 200

Percent of people believes in aliens are success  'p'= 72%

                                                                                      = 0.72

Percent of people who don't believes (failure) in aliens ' 1 - p'  = 1 - 0.72

                                                                                          = 0.28                                                                                    

95% Confidence interval that represents Americans adults who believes in aliens

value of z - score for 95% confidence interval = ± 1.96

Margin of error 'MOE'= (z-score)√p ( 1- p) /n

                                   = ( 1.96)√(0.72 × ( 1 - 0.72 )/ 200

                                   = 1.96 ( √0.2016 / 200)

                                   = 1.96 ×√0.001008

                                   = 0.063

Lower limit = p - MOE

                 = 0.72 - 0.063

                 = 0.66

Upper limit =  p + Margin of error

                 = 0.72 + 0.063

                 = 0.78

Therefore, 95% confidence interval with sample size of the Americans adults who believes in alien are in the interval of ( 0.66 , 0.78 ).

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Even though A and B are both square, AB always equals BA.

Could someone please assist me in demonstrating that b=c follows from ab=ac and a does not equal 0. You can only apply the field axioms. Here is my try.

ab=ac then, ab-ac=0

a(b-c)=0

a(0)=0 Since a cannot equal zero (this has already been shown), (b-c) must also equal zero, leaving us with...

b-c=0

b=c

The only issue I have with the above is that I presupposed that a did not equal 0. I'm not sure if this is okay because the original theorem I'm attempting to prove includes the claim that "a does not equal 0."

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The factored form of f(x) is f(x) =  (x+2) (x+2)(x+4)      

What is a factor?

A factor is a number/expression that divides another number/expression, leaves zero remainder . In other words, if multiplying two numbers/expressions gives us a product, then the numbers/expressions we are multiplying are factors of the product because they are divisible by the product.

f(x) = x³ +8x² + 20x + 16

The value of x at which f(x) is zero, is the root

x= -2 is a root

so, ( x- (-2) ) = ( x+2) is a factor

Divide the polynomial  x³ +8x² + 20x + 16  by  ( x+2)  using long division method:

x+2)  x³ +8x² + 20x + 16  ( x² + 6x + 8

        x³ + 2x²

_______________________

               6x² + 20x + 16

                6 x² + 12x

____________________________

                            8x + 16

                            8x + 16

__________________________

                                00

f(x)= (x+2) (x² + 6x + 8 )

Factors of (x² + 6x + 8 ) are (x+2)(x+4)      

f(x) =  (x+2) (x+2)(x+4)      

Thus, the factored form of f(x) is f(x) =  (x+2) (x+2)(x+4)      

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Answer:

a) Solving by factoring, you move 225 to the left side by subtracting then making the equation equal to 0.

b) x = -15

x = 15

Step-by-step explanation:

1. x^2 -225=0

2. Find what two numbers equal to -225 then factor by using the expression a^-b^2=(a-b)(a+b)

In this case, -15(15)=-225

(x-15)(x+15)=0

3. Find x

x-15=0

x+15=0

This equation has 2 solutions

x=-15

x=15

To check answer, one of the solutions into X

Answer: y = 3/4x

Step-by-step explanation:

(100, 75)

(200, 150)

find slope

150 - 75 / 200 - 100

75 / 100 = 3/4

plug values into formula y=mx+b to find y-intercept

y = 3/4x + b

75 = 3/4(100) + b

75 = 75 + b

b = 0

think about this conceptually first. The difference between their rates of work is going to be the total speed at which the chalk board fills up (speed of writing - speed of erasing).

Ok, so we need to find the speed that Bart is writing, and the speed at which Nelson is erasing.

Bart: 50 minutes/ 1 board

However, we want to find his speed, which will be in boards/minute. Flip the fraction to get 1 board/50 minutes. Then multiply top and bottom by 1/50 in order to get 1/50 board per minute.

Bart's Speed = 1/50 board per minute

Do the same for Nelson, to get 1/80 board per minute (erasing).

The difference between these will be 1/50 - 1/80 = 3/400 board per minute

Since we want to know how long it will take to fill the board at this rate, we multiply 1 board * 1/(3/400) minute per board - this is the same as 1 * 400/3

So, the answer is 400/3 minutes, or 133.33 minutes, or 2 hours, 13 minutes.

#2

This is the same idea as #1. His speed without the headwind is 2000 miles/5 hours = 400miles/hour.

His speed with the headwind is 2000 miles/8 hours = 250 miles/hour.

400m/h - 250m/h = 150m/h

The speed of the wind is 150 miles/hour.

Answer:

14

Step-by-step explanation:

To find g(f(3)), you will need to first find f(3) and then substitute that value into the function g(x).

To find f(3), substitute 3 for x in the equation for f(x):

f(3) = 3(3) - 2 = 9 - 2 = 7

Now substitute the value of f(3) into the equation for g(x):

g(f(3)) = g(7) = 2(7) = 14

Therefore, g(f(3)) = 14

Answer:

f(3)=7  g(3)=6

Step-by-step explanation:

f(x)=3x-2

f(3)=3(3)-2

f(3)=9-2

f(3)=7

g(x)=2x

g(3)=2(3)

g(3)=6

Answer:

x=2

Step-by-step explanation:

1. Set the proportions equal: 5/2x-3 = 15/27

2. Butterfly method: 27x5 = 3x-3 x 15

3. Continue solving: 135 = 45x-45

4. Break it down: 45x = 90

5. Solution: 2 because 45 x 2 is equal to 90

Answer:

x=4

Step-by-step explanation:

[tex]\frac{3x-3}{5}=\frac{24+3x}{20}[/tex]          Original equation. A proportion can be set up so that

                              you can find x. One proportion can be one side over the

                              other side of one of the smaller triangle set equal

                              to the total length of the larger triangle. 27 and -3 can

                              combine forming 24, which continues to be added to 3x.

                              15 and 5 can be combined to become 20.

20(3x-3)=5(24+3x) Now, cross multiply. This involves the distribution of one

                               term to the terms it's multiplied by. 20*3x=60x and

                               20*-3=-60. 5*24=120 and 5*3x=15x.

60x-60=120+15x     Now, the goal is to get x alone on one side. You can do

                                this by combining like terms. Subtract 15x from both

                                sides and add 60 to both sides.

45x=180                   Then, divide by 45 to get x by itself.

x=4                            This is your answer.

Answer:

117

Step-by-step explanation:

13 yards = 468 inches

468 ÷ 4 = 117