The perimeter of a rectangle is 44. The length is 5 less than double the width. Find the dimensions

Answer:

H(G(x)) = 12x - 52

Step-by-step explanation:

We are given the following two functions:

[tex] H ( x ) = - 6 x + 8 [/tex]

[tex] G ( x ) = 1 0 - 2 x [/tex]

And we are to find the value of H(G(x)).

For that, we will apply the function of H on the function of G.

[tex]H(G(x))=H(10-2x)[/tex]

[tex] H ( G ( x ) ) = - 6 ( 1 0 - 2 x ) + 8 [/tex]

[tex]H(G(x))=-60+12x+8[/tex]

H(G(x)) = 12x - 52

Answer:

3.6

Step-by-step explanation:

For the 20-deg angle, x is the opposite leg, and 10 cm is the adjacent leg. The trig ratio that relates the opposite leg to the adjacent leg is the tangent.

[tex] \tan A = \dfrac{opp}{adj} [/tex]

[tex] \tan 20^\circ = \dfrac{x}{10~cm} [/tex]

[tex] x = (10~cm)\tan 20^\circ [/tex]

[tex] x = 3.6~cm [/tex]

Answer:

Potential roots:  [tex]\frac{9}{4},\frac{9}{2},9,\frac{3}{4},\frac{3}{2},3, \frac{1}{4},\frac{1}{2},1[/tex]

Step-by-step explanation:

Simply put, the rational roots theorem tells us that if there are any rational roots of a polynomial function, they must be in the form

±  [tex]\frac{FactorsOfa_{0}}{FactorsOfa_n}[/tex]

Where

a_n is the number before the highest power of the polynomial, and

a_0 is the constant in the polynomial

From the polynomial shown, we have a_n = 9 and a_0 = 4

The factors of 9 are 9, 3, 1

and

The factors of 4 are 4,2,1

So, if there are any rational roots, they would be:

±  [tex]\frac{FactorsOfa_{0}}{FactorsOfa_n}[/tex]

±  [tex]\frac{9,3,1}{4,2,1}[/tex]

Which is  ±   9/4, 9/2, 9/1, 3/4, 3/2, 3/1, 1/4, 1/2, 1/1

or

[tex]\frac{9}{4},\frac{9}{2},9,\frac{3}{4},\frac{3}{2},3, \frac{1}{4},\frac{1}{2},1[/tex]

Using the Rational Root Theorem, the polynomial f(x) = 9x^4 - 2x^2 - 3x + 4 has potential rational roots which are ±4, ±2, ±1, and their counterparts divided by 3. In the complex number system, every nth-order polynomial can be factored into n roots, including imaginary roots for equations that lack real solutions.

Rational Root Theorem and Potential Roots

The Rational Root Theorem is a useful tool for identifying all potential rational roots of a polynomial equation. When applying this theorem to the given polynomial f(x) = 9x^4 - 2x^2 - 3x + 4, we note that the potential rational roots are the divisors of the constant term (in this case, 4) divided by the divisors of the leading coefficient (in this case, 9). Therefore, the potential roots are ±4, ±2, ±1, and their counterparts divided by 3, which are ±4/3, ±2/3, and ±1/3. To determine which of these are actual roots, each must be tested in the polynomial equation.

The concept of complex number system further elaborates on polynomials by stating that every nth-order polynomial can have up to n roots, factored into linear factors in accordance with the fundamental theorem of algebra. In the case of second-order polynomials, the real number system may not yield roots for equations like x² + 1, but in the complex number system, such polynomials do have roots and can be factored as (x - i)(x + i), for instance.

Answer:

[tex]\frac{-2x-12}{x^2-16}[/tex]

Step-by-step explanation:

We want to find the difference;

[tex]\frac{x}{x^2-16}-\frac{3}{x-4}[/tex]

The first denominator can be rewritten as;

[tex]x^2-16=(x+4)(x-4)[/tex]

Therefore the least common denominator is [tex]x^2-16[/tex]

We collect LCD to obtain;

[tex]\frac{x-3(x+4)}{x^2-16}[/tex]

Expand the parenthesis to obtain;

[tex]\frac{x-3x-12}{x^2-16}[/tex]

[tex]\frac{-2x-12}{x^2-16}[/tex]

Answer:

b

Step-by-step explanation:

Answer:

If the number of miles is 6

Step-by-step explanation:

Since they vary with different rates ($/mile in our case), such equality can only be true for a specific amount of miles.  Less miles and the left part ($2.50...) would be higher, more miles and the right part ($1.00...) would be higher because it grows faster.

So, that's the number of miles for which the equation is true?

2.50 + 0.50m = 1.00 + 0.75m

Let's regroup similar terms:

1.50 = 0.25m

the isolate m

m = 6

So, if the ride covers 6 miles, the equation is true:

2.5 + 0.5 (6) = 1.00 + 0.75 (6)

2.5 + 3 = 1 + 4.50

5.5 = 5.5

Answer:

One cab charges an initial fee of $2.50 and then $0.50 for every mile. The other cab company charges an initial fee of $1.00 and then $0.75 for every mile.

Step-by-step explanation:

Hey!

-------------------------------------------------

Writing scientific notation in numeral is solving for the equation.

Multiply 10 to 6.4 seven times.

6.4 x 10 = 64

64 x 10 = 640

640 x 10 = 6,400

6,400 x 10 = 64,000

64,000 x 10 = 640,000

640,000 x 10 = 6,400,000

6,400,000 x 10 = 64,000,000

-------------------------------------------------

Hope This Helped! Good Luck!

Answer:

64,000,000

Step-by-step explanation:

Answer

how many sides are there to the spinner?

Step-by-step explanation:

i need to knowhow many there are in order to give you a probibility

Answer:

ti guarantee it is 45 degree

Step-by-step explanation:

first the opposite angle of 39 will be 39

then 39 plus 42 is 81. a triangle is 180 so the third angle is 99.

so since supplementary angles also equal to 180 the other side is 81.

same with 126 the other side is 54.

now the triangle where x is we have found 2 angles 81 and 54 so the last one will be... drumroll... 45 since a triangle equals tk 180 degree.

Answer:

Step-by-step explanation:

45

2*(l+b)

So,

2*(21+15)

2*36

=72

Answer:

Perimeter of rectangle is 72 feet.

Step-by-step explanation:

We need to find the perimeter of rectangle where

Length = 21 feet

Width = 15 feet are given.

The formula used will be: Perimeter of rectangle = 2(Length + Width)

So, Perimeter of rectangle is:

Perimeter of rectangle = 2(Length + Width)

                                      = 2 ( 21+15)

                                      = 2(36)

                                      = 72 feet.

So, perimeter of rectangle is 72 feet.

Answer:

∠1 and ∠8 are alternate exterior angles

∠4 and ∠6 are same side interior angles

∠3 and ∠6 are alternate interior angles

Step-by-step explanation:

Verify each case

case 1) ∠1 and ∠8 are alternate exterior angles

The relationship is correct

case 2) ∠4 and ∠6 are same side interior angles

The relationship is correct

case 3) ∠5 and ∠7 are vertical angles

The relationship is incorrect

Because ∠5 and ∠7 are supplementary angles

case 4) ∠2 and ∠8 are  corresponding angles

The relationship is incorrect

case 5) ∠3 and ∠6 are alternate interior angles

The relationship is correct

Answer:

A) ∠1 and ∠8 are alternate exterior angles

B) ∠4 and ∠6 are same side interior angles

E) ∠3 and ∠6 are alternate interior angles

Step-by-step explanation:

Let's check the each options.

A) ∠1 and ∠8 are alternate exterior angles

The exterior angles are ∠1, ∠2, ∠7 and ∠8.

This is correct.

B) ∠4 and ∠6 are same side interior angles.

∠4 and ∠6 are inside the line m and n, they are in the same side, you can see it on the figure.

This is correct

C) ∠5 and ∠7 are vertical angles

∠5 and ∠7 are supplementary angles.

This is not correct.

D) ∠2 and ∠8 are  corresponding angles

These are same side of exterior angles.

This is not correct.

E) ∠3 and ∠6 are alternate interior angles

These are interior angles and alternative to each other.

This is correct.

For this case we have that by definition, the total surface area of a right prism is given by:[tex]SA = ph + 2B[/tex]

Where:

p: Perimeter of the base

h: It's the height

B: It is the area of the base

So:

[tex]B = 6 * 2\\B = 12 \ cm ^ 2\\p = 6 + 6 + 2 + 2 = 16 \ cm[/tex]

So, we have:

[tex]SA = 16 * 5 + 2 (12)\\SA = 80 + 24\\SA = 104 \ cm ^ 2[/tex]

Answer:[tex]104 \ cm ^ 2[/tex]

Answer:

[tex](120\degree,-180\degree)[/tex]

Step-by-step explanation:

The given parametric equation is

x=2t  

y= -3t

The coordinates of any point lying on this curve can be obtained by substituting the parameter value.

Given the parameter value, t=60

We have

[tex]x=2(60\degree)=120\degree[/tex]

and

[tex]y=-3(60)=-180\degree[/tex]

Therefore the point[tex](120\degree,-180\degree)[/tex]

lie on this parametric curve.

The income tax bracket fall into 28%.

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Answer:

- 1

Step-by-step explanation:

To evaluate substitute p = - 2 into f(p)

f(- 2) = (- 2)² + 3(- 2) + 1 = 4 - 6 + 1 = - 1

The answer should be -1

Answer:

option c

x + 4 = 64

and

option e

x = 60  

Step-by-step explanation:

Given in the question an expression

3∛x+4 = 12

∛x + 4 = 12/3

∛x + 4 = 4

Take cube on both sides of the equation

∛(x + 4)³ = 4³

x + 4 = 64

x = 64 - 4

x = 60  

Answer:

The third and the fifth equations are equivalent.

Step-by-step explanation:

First of all, you must find [tex]x[/tex] from [tex]3\cdot \sqrt[3]{x+4}=12[/tex] and check during the procedure what expressions from the options are equivalent.

The process is shown below:

From step 3, it could be said that the first, the second and the fourth options ARE NOT equivalent equations because when the left side is [tex]\sqrt[3]{x+4}[/tex], the right side must be [tex]+4[/tex], and these three options don't meet the condition.

From step 5, it could be said that the third option IS an equivalent equation because it is the same expression.

From step 7, it could be said that the fifth option IS an equivalent equation because it is the same expression.

Thus, the third and the fifth equations are equivalent.

Answer: George McClellan did

Step-by-step explanation:

Answer:

D McClellan

Step-by-step explanation:

In 1862, president Abraham Lincoln decided to relieve General George McClellan of his command after the Battle of Antietam. The reason is McClellan was unable to concentrate his forces effectively, so the Confederate army shifted his defenders to block each of three Union thrusts. Besides, he was unable to employ his large reserved forces to ensure success.

Answer:

The area of the sector is [tex]37.68\ in^{2}[/tex]

Step-by-step explanation:

step 1

Find the area of the circle

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=12/2=6\ in[/tex] ----> the radius is half the diameter

substitute

[tex]A=(3.14)(6)^{2}[/tex]

[tex]A=113.04\ in^{2}[/tex]

step 2

Find the area of a sector with a central angle of (2pi/3)

Remember that

The area of [tex]113.04\ in^{2}[/tex] subtends a central angle of [tex]2\pi \ radians[/tex]

so

by proportion

Let

x----> the area of the sector

[tex]\frac{2\pi}{113.04}=\frac{(2\pi/3)}{x}\\ \\x=113.04*(2\pi/3)/(2\pi)\\ \\x=37.68\ in^{2}[/tex]

Answer: X = 2.4

Step-by-step explanation:

The first step should be to isolate x or get x alone. This means we should get rid of the divided by 2 on the left by multiplying both sides by 2. This would get us to 2 * X/2 = 1.2 * 2. The multiplying X/2 would simplify to just X, and the 1.2 * 2 = 2.4. Therefore the final equation would become X = 2.4.

To check, you would plug in 2.4 into where X is in X/2 = 1.2. Since 2.4/2 = 1.2, we know that X = 1.2 from checking.

x = 2.4

You want to get x by itself, so you need to get rid of the division on the left side of the equals sign. The way to undo division is to multiply. So, multiply both sides of the equation by 2. This gives you x = 2.4, so now you have your answer.

Now, since the problem wants us to check our answer, we just put 2.4 back into the equation as x. This gives us 2.4 / 2 = 1.2. Now, we just simplify to see if the equation is true. If it is true, the answer is correct. 2.4 divided by 2 is 1.2, so 1.2 = 1.2, which means our answer is correct.

Answer:

both option (A) & (B) is description of given distribution.

Step-by-step explanation:

The outlier is a point which lies differently or far away from rest points in datasets or distribution.

Here we can self-time for one apple on the 10th day is outlier present in the distribution. Thus Option (A) is correct.

We divide the heterogeneous group into many homogeneous groups, these homogeneous group is known as Cluster. It can be seen naturally.

Also, here distribution is divided into many clusters and we can see given distribution has many clusters and one of them is from 4 to 6 days. Thus Option (B) is also a correct option here.

here are my analyses of the possible answer choices based on the image you sent:  The distribution clusters around 4-6 days and has a few potential outliers above 8 days.

here are my analyses of the possible answer choices based on the image you sent:

(A) The distribution has an outlier.

There are a few data points that are higher than the rest of the distribution, so in that sense, yes, there are outliers. However, it is important to consider what an outlier is in the context of the data. If the data is normally distributed, then outliers are data points that fall more than two standard deviations away from the mean. In this case, it is difficult to say for sure whether the data is normally distributed, so it is also difficult to say for sure whether there are outliers. However, there are a few data points that are higher than the rest of the distribution.

(B) The distribution has a cluster from 4 to 6 days.

There is a cluster of data points from 4 to 6 days, so yes, this statement is accurate.

In conclusion, the accurate descriptions of the distribution are:

Answer:

[tex]\boxed{\text{\$810.78}}[/tex]

Step-by-step explanation:

If regular pay = $14.35/h, then

Overtime pay = 1.5 × $14.35/h = $21.525/h

[tex]\begin{array}{rcr}\text{First 40 h at \$14.35/h}& = & \$574.00\\\text{Next 11 h at \$21.525/h} & = & 236.78\\\text{Gross pay}& = & \mathbf{\$810.78}\\\end{array}\\\\\text{Rob's gross pay for the week will be }\boxed{\textbf{\$810.78}}[/tex]

Answer:

G=Seven

Step-by-step explanation:

-two=g-nine

two=nine-?

two=nine-seven

-two=seven-nine

Answer:

Step-by-step explanation:

The cosine of angle Ф is √(1 - sin²Ф), which is positive if our angle 81 degrees is in Quadrant I.

sin 81° = 0.9877, so (sin 81°)² = 0.9755, and

cos 81° = 1 - 0.9755 = 0.0245

To find the cosine of 81 degrees in terms of sine, we use the identity cos(Ф) = sin(90° - Ф), giving us cos(81°) = sin(9°).

To find the cosine of 81 degrees in terms of sine, we use the trigonometric identity that relates sine and cosine for complementary angles. The cosine of 81 degrees is the same as the sine of 9 degrees, because 81 and 9 add up to 90 degrees. The trigonometric identity is cos(Ф) = sin(90° - Ф).

Using this identity:

cos(81°) = sin(90° - 81°)

= sin(9°).

Therefore, the cosine of 81 degrees is equal to the sine of 9 degrees.

Answer: Town 1- 5.42%, Town 4- 5.86%, Town 3- 6.63%, Town 2- 7.11%

Step-by-step explanation:

Download the app PhotoStudy it’s helpful

Final answer:

To find the amount Carl and Linda Munson will have accumulated in 10 years, you can use the formula for compound interest. Plugging in the given values, their 401k retirement account will have approximately $3,639.48 after 10 years.

Explanation:

To find the amount Carl and Linda Munson will have accumulated in 10 years, we can use the formula for compound interest:

A = P(1+r)^n

Where:

A = amount accumulated after n years

P = principal amount

r = interest rate (in decimal form)

n = number of years

Using the given information, P = $2,100, r = 8% (or 0.08), and n = 10. Plugging these values into the formula:

A = $2,100(1+0.08)^10

Simplifying the expression:

A = $2,100(1.08)^10

Calculating the value:

A ≈ $3,639.48

Therefore, Carl and Linda Munson will have approximately $3,639.48 accumulated in their 401k retirement account after 10 years.

Answer:

As of 2021, for this question, the answer is "The range is positive real numbers (y>0)

Step-by-step explanation:

Hope this helps somebody!

The range is all real numbers is not a characteristic of the absolute value parent function.

Hence, the option which is not a characteristic of the absolute value parent function is The range is all real numbers.

Therefore, Option A is the correct answer.

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Answer:

B. Add the two equations.

Step-by-step explanation:

Lets solve our system of equations step-by-step

Step 1. Add the two equations

2x – 2y = 5 +

5x + 2y = 9

----------------

7x         = 14

Step 2. Solve for x in the resulting equation

7x = 14

[tex]x=\frac{14}{7}[/tex]

x = 2

Step 3. Replace the value of x in any of the original equations

2x – 2y = 5

2(2) – 2y = 5

4 – 2y = 5

-2y = 5 - 4

-2y = 1

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

We can conclude that the correct answer is: B. Add the two equations.

Answer:

The number per hour = 5400 ÷ 8 = 675 action figures

Step-by-step explanation:

* Lets explain how to solve the problem

- A toy manufacturer uses 90 pints of plastic to make 600 action figures

- they use 810 pints of plastic in an 8 hour shift

- To find how many action figures are made per hour we must to find

  how many action figures in an 8 hour shift and then find the number

  of the action figures per hour

∵ The toy manufacture  uses 90 pints of plastic to make 600 action

   figures

∵ They use 810 pints

- Lets find how many action figures are made by this numbers of pints

∴ 90/600 = 810/x ⇒ x is the number of action figures

- Use the cross multiplication to find x

∴ 90 x = 810 × 600

∴ 90 x = 486000 ⇒ divide both sides by 90

∴ x = 5400

∴ They will use 810 pints to make 5400 action figures

∵ They use 810 pints in an 8 hour shift

∴ They make 5400 action figures in 8 hours

- To find the number of the action figures per hour divide the number

  of them in 8 hours by 8

∴ The number per hour = 5400 ÷ 8 = 675 action figures

Answer:

[tex]\frac{1}{8}[/tex]

Step-by-step explanation:

P(Black) = [tex]\frac{1}{2}[/tex]

[tex]\frac{1}{2}*\frac{1}{2}*\frac{1}{2}=\frac{1}{8}[/tex]

P(Black 3/3) = [tex]\frac{1}{8}[/tex]

The probability it will land on the black all three times out of three spins is 1/8.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

Given the probability of the spinner landing on black is 1/2. Therefore, the probability it will land on the black all three times out of three spins is,

Probability = (1/2) × (1/2) × (1/2) = 1/8

Hence,  the probability it will land on the black all three times out of three spins is 1/8.

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Answer:

fd akkkkcm

Step-by-step explanation:

The measure of arc CB is 236°.

find the measure of the indicated arc in circle O.

Given information:

-[tex]\(m\angle DOC = 44°\)[/tex]

- [tex]\(m\angle COB = 80°\)[/tex]

We want to find the measure of arc CB.

1. Calculate the central angle containing arc CB:

  - The sum of the central angles [tex]\(m\angle DOC\) and \(m\angle COB\)[/tex]gives the measure of the entire circle.

  - Total degrees in a circle = 360°

  - Central angle containing arc CB = [tex]\(m\angle DOC + m\angle COB\)[/tex]

   [tex]\[m\angle DOC + m\angle COB = 44° + 80° = 124°\][/tex]

2. Find the measure of arc CB:

  - Subtract the central angle from 360° to get the measure of arc CB.

[tex]\[m\text{ arc CB} = 360° - 124° = 236°\][/tex]

Therefore, the measure of arc CB is 236°.

Answer:

G > 2

Step-by-step explanation:

Answer:

6+2g >10

6-6+2g>10-6

2g>4

divide by 2

2g/2> 4/2

g>2

Answer is g>2