A regular pentagon with a perimeter of 18 centimeters is dilated by a scale factor of 3 2 32 to create a new pentagon. What is the perimeter of the new pentagon?

Answer:

A. 1 rational root and 2 complex roots

Step-by-step explanation:

The equation [tex]x^3+x^2=x-1[/tex] has the expression [tex]x^3+x^2[/tex] in the left side and the expression [tex]x-1[/tex] in the right side.

when ypu plot the graphs of the functions [tex]y=x^3+x^2[/tex] and [tex]y=x-1,[/tex] the number of intersection points shows the number of real solutions. These two graphs intersect only once, so the equation has one real solution. The third power equation should have three solutions, thus, two remaining solutions are complex.

Answer:

The answer is A

Step-by-step explanation:

4x + 7 = 31

    -7    -7

4x = 24

/4     /4

x = 6 (Answer)

Prove.

4(6) + 7 = 31

24 + 7 = 31

31 = 31

True.

The solution to the given equation 4x + 7 = 31 is x = 6, which is determined by subtraction.

The equation is given as follows:

4x + 7 = 31

To solve the equation 4x + 7 = 31 for x, we want to isolate the variable x on one side of the equation.

First, we can begin by subtracting 7 from both sides of the equation:

4x + 7 - 7 = 31 - 7

Simplifying, we get:

4x = 24

Next, we want to isolate x, so we divide both sides of the equation by 4:

4x/4 = 24/4

This simplifies to:

x = 6

Therefore, the solution to the equation 4x + 7 = 31 is x = 6.

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Answer:

it look like B but I'm not sure

Answer:

Step by step explanation

the equation is 225=27x-18

the first step is to add the 18 to the other side to get

243=27x

now divide by 27 on both sides

243/27=27x/27

solve to get

9=x

Answer:

2 nickels 3 dimes 5 quarters

Step-by-step explanation:

We know it cannot be the second option because there are only 7 coins and Kim has 10. It also cannot be the first option because the coins add up to $1.60, and Kim has $1.65. It could not be the last option either because the coins add up to $1.15, and Kim has $1.65.

Answer: Third option

Why? The third option has a total of $1.65, which is what Kim has. There are 10 coins all together, which is also what Kim has. And the number of nickels and dimes combined (5) is equal to the number of quarters (5).

Answer:

3

Step-by-step explanation:

3/4 divided by 1/4=0.75/0.25=3

Answer:

3

Step-by-step explanation:

Think:  "3/4" reads "three fourths," and thus we have 3  fourths.

Answer:

[tex]\frac{10x^2+6x}{6x^2}[/tex] and [tex]\frac{21x}{6x^2}[/tex].

Step-by-step explanation:

The given expression is:

[tex]\frac{5x+3}{3x}[/tex] and [tex]\frac{7x}{3x^2}[/tex].

The least common denominator is: [tex]6x^2[/tex].

We collect  LCM for the denominator to obtain;

[tex]\frac{2x(5x+3)}{6x^2}[/tex] and [tex]\frac{3(7x)}{6x^2}[/tex].

We multiply out the parenthesis to obtain;

[tex]\frac{10x^2+6x}{6x^2}[/tex] and [tex]\frac{21x}{6x^2}[/tex].

Therefore the correct answer is B or the second option.

Answer:

B) {x|-13 < x < 13}

C) {x|x < -4 or x > 4}

Step-by-step explanation:

Given in the question,

Remove the absolute value term.

If your absolute value is less than a number, then set up a three-part compound inequality that looks like this:

-(number on other side) < (quantity inside absolute value) < (number on other side)

-13 < x < 13

If your absolute value is greater than a number, then set up an "or" compound inequality that looks like this:

(quantity inside absolute value) < -(number on other side)

OR

(quantity inside absolute value) > (number on other side)

x < - 4 or x > 4

Answer:

Step-by-step explanation:

A]

The center is the average values of the 2 endpoints (which is also the diameter).

x:(-10 + 4)/2 = -6/2 = -3

y:(-2 + 6)/2 = 4/2 = 2

Center(-3,2)

B]

The radius is the distance from the center to one of the end points.

r^2 = (-3 - 4)^2 + (2 - 6)^2

r^2 = (-7)^2 + (-4)^2

r^2 = 49 + 16

r^2 = 65

r = sqrt(65)

C]

(x + 3)^2 + (y - 2)^2 = 65

Graph

The graph has been included so that you can see that the center I have calculated is between (-10,-2) and (4,6)

Further, it shows the the circle goes the two end points of the diameter.

Answer:

262 m³

Step-by-step explanation:

The volume (V) of a cone is calculated as

V = [tex]\frac{1}{3}[/tex] πr²h ( r is the radius of the base and h the height )

here diameter = 10 m, hence radius = 5 m

V = [tex]\frac{1}{3}[/tex]π × 5² × 10

   = [tex]\frac{1}{3}[/tex] π × 250 = [tex]\frac{250\pi }{3}[/tex] ≈ 262 m³

Okay, so there are nickels and pennies in this jar.

So, let's call the number of pennies X

Since there are 161 coins altogether, the number of nickels is (161 - X)

So now we solve the equation:

.01X + .05(161 - X) = 3.09

.01X + 8.05 - .05X = 3. 09

4.96 = .04X

124 = X

So, there are 124 pennies

Therefore, there are 161 - 124 = 37 nickels

Let's check our answer:

124 x .01 + 37x .05 = 1.24 + 1.85 = 3.09

It works!

I think it is 18

nickels for $3.09

Answer:

A = $784.00

Step-by-step explanation:

This is the answer

The current value of the coin is $990.38 if the Conner's coin collection, which was worth $400 eight years ago, has been increasing in value by 12% per year since then.

It is defined as the interest on the based on the principal amount, it does not include the compounded amount. The interest calculate on the initial amount or borrowed amount.

We have formula:

A = P(1 + r)^t

Here P = $400

r = 12% = 0.12

t = 8 years

A = 400(1+0.12)^8

A = 400(2.47596)

A = $990.38

Thus, the current value of the coin is $990.38 if the Conner's coin collection, which was worth $400 eight years ago, has been increasing in value by 12% per year since then.

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Answer:

A) Δ RQP ↔ ΔUTS

Step-by-step explanation:

Answer:

Option A) is correct

Step-by-step explanation:

Given : [tex]\Delta PQR \leftrightarrow  \Delta STU[/tex]

We need to find which correspondence is equivalent to [tex]\Delta PQR \leftrightarrow  \Delta STU[/tex] .

Solution :

One to one correspondence means measure of each side and each angle of one triangle is equal to the side and angle of the other triangle .

Here, we observe that option A) is equivalent to [tex]\Delta PQR \leftrightarrow  \Delta STU[/tex] as explained below :

As per [tex]\Delta PQR \leftrightarrow  \Delta STU[/tex] ,

[tex]PQ=ST\,,\,QR=TU\,,\,PR=SU\\\angle P=\angle S\,,\,\angle Q=\angle T\,,\,\angle R=\angle U[/tex]

Also, as per [tex]\Delta RQP \leftrightarrow  \Delta UTS[/tex] , we have

[tex]PQ=ST\,,\,RQ=UT\,,\,PR=SU\\\angle P=\angle S\,,\,\angle Q=\angle T\,,\,\angle R=\angle U[/tex]

Therefore,

[tex]\Delta RQP \leftrightarrow  \Delta UTS[/tex] is equivalent to [tex]\Delta PQR \leftrightarrow  \Delta STU[/tex]

So, option A) is correct .

ANSWER

[tex]\theta = \frac{\pi}{2} ,\frac{3\pi}{2},\frac{\pi}{4} , \frac{5\pi}{4} [/tex]

EXPLANATION

We want to solve the equation;

[tex] \cos( \theta) - \tan( \theta) \cos( \theta) = 0[/tex]

We factor to get:

[tex] \cos\theta(1 - \tan\theta) = 0[/tex]

Either

[tex]\cos\theta = 0[/tex]

Or

[tex]1 - \tan \theta = 0[/tex]

For

[tex]\cos\theta = 0[/tex]

We gave

[tex] \theta = \frac{\pi}{2} ,\frac{3\pi}{2}[/tex]

When

[tex]\tan \theta = 1[/tex]

Then,

[tex] \theta = \frac{\pi}{4} , \frac{5\pi}{4} [/tex]

Therefore the solution on the interval

[tex]0 \leqslant \theta \: \leqslant 2\pi[/tex]

is

[tex]\theta = \frac{\pi}{2} ,\frac{3\pi}{2},\frac{\pi}{4} , \frac{5\pi}{4} [/tex]

Answer:

a.<55, -27>

Step-by-step explanation:

The given vectors are u = <7, -3>, v = <-9, 5>.

We want to find 4u - 3v.

We substitute the vectors and multiply by the scalars.

4u - 3v=4<7, -3>-3 <-9, 5>.

4u - 3v=<28, -12>- <-27, 15>.

4u - 3v=<28--27, -12-15>

4u - 3v=<55, -27>

Answer:

B. 330

Step-by-step explanation:

The question indicates the order doesn't matter, so it's a combination and not a permutation.

The combinations are calculated using this formula:

[tex]C(n,r) = \frac{n!}{r! (n-r)!}[/tex]

In this case we have a population of 11 (n = 11) and a selection of 4 (r=4), so...

[tex]C(11,4) = \frac{11!}{4! (11-4)!} = 330[/tex]

So, there are 330 different combinations that can be made of 4 paintings out of a selection of 11.

Answer:

The correct answer is option B.  330

Step-by-step explanation:

It is given that,There are 11 paintings at an art show. Four of them are chosen randomly to display in the gallery window.

To find the possible ways

There are total 11 paintings.

We have to choose 4 of them

Possible number of ways = 11C₄

 = (11 * 10 * 9 )/(1 * 2* 3 * 4)

 = 330 ways

Therefore the  correct answer is option B.  330

Answer:  D) -2 |x| - 2

Step-by-step explanation:

A v-shaped graph is an absolute value graph.  

The general form of an absolute value equation is: y = a |x - h| + k

where (h, k) represents the vertex and "a" represents the vertical stretch (aka slope).  

The vertex of the given graph is (0, 2), however the graph is inverted (upside-down) which is a reflection across the x-axis.  Therefore,

It would have to be 3/5

Answer:

We use the combination formula:

combinations = n! / r! * (n-r)!

n = 5 and r =3

combinations = 5! / 3! * 2!

combinations = 5! / 12

combinations = 5 * 4 * 3 * 2 * 1 / 12

combinations = 5 * 2 = 10

Step-by-step explanation:

Answer:

400

Step-by-step explanation:

Just take 10% of 4,000 flashlights.  400 flashlights are likely to be defective.

The answer is a okay

Answer:

A and D

Step-by-step explanation:

The customers were chosen at random, so the sample is not biased.  However, the question is biased.  "Extra time and effort" is phrased to get a No response.

A and D.

I believe it’s 245 I believe I did this before I don’t know

Answer:

399.6 miles²

Step-by-step explanation:

The area (A) of the major sector is

A = area of circle × fraction of circle

   = πr² × [tex]\frac{255}{360}[/tex]

   = π × 13.4² × [tex]\frac{255}{360}[/tex]

   = [tex]\frac{13.4^2(255)\pi }{360}[/tex] ≈ 399.6 miles²

Answer:

This is the answer : (answer given in the picture)

Answer:

vertex = (- 3, 24)

Step-by-step explanation:

Given a quadratic in standard form y = ax² + bx + c : a ≠ 0, then

The x- coordinate of the vertex is

[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]

y = - x² - 6x + 15 ← is in standard form

with a = - 1, b = - 6, thus

[tex]x_{vertex}[/tex] = - [tex]\frac{-6}{-2}[/tex] = - 3

Substitute x = - 3 into the function for corresponding value of y

y = - (- 3)² - 6(- 3) + 15 = - 9 + 18 + 15 = 24

vertex = (- 3, 24)

Answer:

Option C.(–∞, 2] ∪ (8, ∞)

Step-by-step explanation:

we know that

The solution of the inequality [tex]x > 8[/tex] Is the interval (8,∞)

The solution of the inequality [tex]x\leq 2[/tex] Is the interval (-∞,2]

therefore

The solution of  [tex]x > 8[/tex] or [tex]x\leq 2[/tex] is equal to

(-∞,2] U (8,∞)

Final answer:

The correct interval notation for the inequality x > 8 or x ≤ 2 is (−∞, 2] ∪ (8, ∞), which represents all numbers less than or equal to 2 and all numbers greater than 8.

Explanation:

The question asks to describe the set of numbers using interval notation for the inequality x > 8 or x ≤ 2. Interval notation is a concise way of writing sets of numbers, using brackets to include endpoints and parentheses for exclusive limits. For an inequality like x > 8, we use the notation (8, ∞) to indicate all numbers greater than 8 but not including 8 itself. Likewise, for x ≤ 2, the interval notation is [−∞, 2] which includes all numbers less than or equal to 2. When we combine these with the union because of the 'or' condition, the correct interval notation is (−∞, 2] ∪ (8, ∞). Therefore, the correct answer is C. (8, ∞) indicates all the numbers larger than 8, and (−∞, 2] includes all the numbers up to and including 2.

Answer:

step one: product of powers

step 2:power of powers

step 3: quotient of powers

Step-by-step explanation:

The rule of exponents was applied in each step will be multiplication rule,division rule and inverse of exponent rule.

Arithmetic is a branch of mathematics that studies numbers and the many operations that may be applied to them. The four basic math operations are addition, subtraction, multiplication, and division.

The given expression is;

[tex]\frac{(2)^3(2)^4}{2^{10}}[/tex]

Step 1; Multiplication rule of exponents;

[tex]\frac{(2)^3(2)^4}{2^{10}} \\\\ \frac{2^{3+4}}{2^{10}} \\\\\frac{2^7}{2^{10}}[/tex]

Step 2;Division rule of exponents;

[tex]\frac{2^7}{2{10}} \\\\ (2)^{7-10}\\\\ (2)^{-3}[/tex]

Step 2;Inverse rule of exponents;

[tex](2)^{-3}\\\\ \frac{1}{2^3} \\\\\frac{1}{8}[/tex]

Hence, the rule of exponents was applied in each step will be multiplication rule,division rule and inverse of exponent rule.

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The data item in this distribution that corresponds to the given z-score of 2 is 580.

Given:

Mean = 500

z score = 2

standard deviation = 40

To find the data item corresponding to a given z-score in a normally distributed data set, use the formula:

[tex]X = \mu + (z * \sigma)[/tex]

where X is the data item, μ is the mean, z is the z-score, and σ is the standard deviation.

Plugging the values into the formula, we have:

[tex]X = 500 + (2 * 40)[/tex]

[tex]X = 500 + 80[/tex]

[tex]X = 580[/tex]

Therefore, the data is 580.

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In a data set with a mean of 500 and standard deviation of 40, the data item that corresponds to the z-score of 2 is 580. This is computed by multiplying the standard deviation by the z-score and adding the product to the mean.

This question is dealing with z-scores and the standard normal distribution in statistics. The z-score is a measure of how many standard deviations an element is from the mean. In a standard normal distribution, the mean is 0 and the standard deviation is 1.

When you are given a z-score of 2 for a data set with a mean of 500 and a standard deviation of 40, it means the data item you're looking for is 2 standard deviations above the mean. You compute this by multiplying the z-score by the standard deviation and adding the product to the mean. So in this case, 500 + 2*40 = 580. Therefore, the data item in this distribution that corresponds to the z-score of 2 is 580.

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Answer:

11.820 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that ...

Sin = Opposite/Hypotenuse

The length of the ladder is the hypotenuse of a right triangle with 52° as the base angle. The side opposite is the height up the building where the top of the ladder rests. So, you have the relation ...

sin(52°) = height/(15 ft)

Multiplying by the denominator gives you ...

height = (15 ft)·sin(52°) ≈ 11.820 ft

___

You may need to round this number appropriately.

Final answer:

The equation 4x + 3 = 7 is solved algebraically by subtracting 3 from both sides and then dividing by 4 to find x = 1. There is no need for logarithms or the change of base formula to solve this linear equation.

Explanation:

The equation 4x + 3 = 7 is a linear equation and can be solved using simple algebraic manipulations rather than the change of base formula for logarithms. However, to show how logarithms could hypothetically be used (even though it's over-complicating this particular problem), we can take the following steps:

Divide both sides by 4: x = 1.

Therefore, the solution to the equation is x = 1. There is no need to round to the nearest thousandth as the solution is a whole number. The change of base formula, logb y = (log y) / (log b), is not necessary for this equation.

The solution to the equation [tex]\(4x + 3 = 7\) is \(x = 1\),[/tex] obtained by isolating [tex]\(x\)[/tex]

Step-by-Step Solution:

1. Write down the equation:

[tex]\[ 4x + 3 = 7 \][/tex]

2. Isolate the term with the variable [tex]\(x\):[/tex]

  - To do this, we need to remove the constant term on the left side by subtracting 3 from both sides of the equation.

[tex]\[ 4x + 3 - 3 = 7 - 3 \][/tex]

  - Simplify both sides:

[tex]\[ 4x = 4 \][/tex]

3. Solve for [tex]\(x\):[/tex]

  - To isolate [tex]\(x\)[/tex], divide both sides of the equation by 4:

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

- Simplify both sides:

[tex]\[ x = 1 \][/tex]

Conclusion:

The solution to the equation [tex]\(4x + 3 = 7\)[/tex] is:

[tex]\[x = 1\][/tex]

Answer:

√85

Step-by-step explanation:

See image

Distance formula can be used to find the distance between two points.

[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}  }[/tex]

Answer: Second option

[tex]d=\sqrt{85}[/tex]

Step-by-step explanation:

The formula to find the distance between two points is:

[tex]d=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]

In this problem the points are C(0, 4), T(-6, -3)

This is

[tex]x_1=0\\\\x_2=-6\\\\y_1=4\\\\y_2=-3[/tex]

So the distance is:

[tex]d=\sqrt{((-6)-0)^2 + ((-3)-4)^2}[/tex]

[tex]d=\sqrt{(-6)^2 + (-7)^2}[/tex]

[tex]d=\sqrt{36 + 49}[/tex]

[tex]d=\sqrt{85}[/tex]

Answer:

Line = To get a Unique line you need two distinct points.

In the given figure PQ is a line.

A plane is either a two dimensional or three dimensional surface such that if you take any two points on it ,the line joining these two points will completely lie on it.

You can name a plane by Single Alphabet or Set of Alphabet.

So,the plane can be Named as: P,Q,R , S→Single Alphabet or

P Q,PS,SR, R Q,→Using two Alphabet,

→ P QR, P Q S,......,P Q RS.