The surface area of a triangular prism is dilated at a scale factor of _3_. How is 2
the surface area of the dilated prism related to the surface are of the original cylinder?

Answer:

19 - 3(x - 2)²

Step-by-step explanation:

7 + 12x - 3x² ( rearrange terms in x )

7 - 3x² + 12x ( factor out - 3 from each of the x- terms )

= 7 - 3(x² - 4x)

using the method of completing the square on x² - 4x

add/subtract ( half the coefficient of the x- term )² to x² - 4x

= 7 - 3(x² + 2(- 2)x + 4 - 4)

= 7 - 3(x - 2)² - 3(- 4)

= 7 - 3(x - 2)² + 12

= 19 - 3(x - 2)² ← in the form a + b(x + c)²

with a = 19 , b = - 3 , c = - 2

Answer:6c+2y=4.5i

Step-by-step explanation:

i am pretty sure it that answer is because you cant add 2 variables in a problem well 2 different variable

hope its right

The equation that has the solutions [tex]\frac{-3 \pm \sqrt{3}i }{2}[/tex] will be a) 2x² + 6x + 9

Here we have to find the equation which has roots

[tex]\frac{-3 \pm \sqrt{3}i }{2}[/tex]

This means that the factors of the roots will be

[tex]x+\frac{3 + \sqrt{3}i }{2}[/tex] and [tex]x+\frac{3 - \sqrt{3}i }{2}[/tex]

Now since all our options are quadratic equations, they have to be a product of these 2 factors and ONLY an additional numerical co-efficient

Hence we get

[tex][x+\frac{3 + \sqrt{3}i }{2}][x+\frac{3 - \sqrt{3}i }{2}][/tex]

rearranging this will give us

[tex][x+\frac{3}{2} + \frac{ \sqrt{3}i }{2}][x+\frac{3}{2} - \frac{ \sqrt{3}i }{2}][/tex]

using the formula

a² - b² = (a + b)(a - b) we get

(x + 3/2)² - (√3i/2)²

= x² + 9/4 + 3x + 9/4                                                                  [since i² = -1]

Hence we get x² + 3x + 9/2

= a) 2x² + 6x + 9

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Correct Question

Which equation has the roots

[tex]\frac{3 \pm \sqrt{3}i }{2}[/tex]

a) 2x² + 6x + 9 = 0

b) x² + 3x + 12 = 0

c) x² + 3x + 3 = 0

d) 2x² + 6x + 3 = 0.

The required equation of transformation from figure V to figure W is (-x, y+3).

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.

Here,
From the figure, it is clearly seen that first the figure gets mirrored on the y-axis, so the translation in the horizontal direction is given as -x. Now after forming the image across the y-axis the figure is translated up by 3 units so vertical translation is given as y +3.
Combine translation is given as {-x, y+3}

Thus, the required equation of transformation from figure V to figure W is (-x, y+3).

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There are 2,848 calories in two pounds of a certain ice cream.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

There are 623 calories in seven ounces of a certain ice cream.

Since, We know that;

⇒ 1 pound = 16 ounces

Hence, We get;

⇒ 2 pounds = 32 ounces

Here, Amount of ice cream in 7 ounces = 623 calories

Hence, Amount of ice cream in 32 ounces = 623 × 32 / 7

                                                                   = 2,848 calories

Thus, Amount of ice cream in 1 pounds = 2,848 calories

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A representative sample is one that is drawn at random from the population and is large enough to provide accurate data.

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Answer:

6,562.5 miles

Step-by-step explanation:

The proportion is 1,875 miles/1 hour.

At that speed, the distance can be calculated when the time is known, which is 3.5 hours in this case:

  (1,875 miles/hr)*(3.5 hr) = 6562.5 miles

Answer:

Step-by-step explanation: He can get 150 worth of clothes

He can buy 3 new shirts and 3 pairs of new pants!

Her checking account balance at every given time is represented by the linear function 175 + 8.75t

In this situation, the checking account offers simple interest at a rate of 5% annually. Her account has $175 in it.

The amount of money in the account at anytime will be:

= 175 + (PRT/100)

P = principal

R = rate

T = time

= 175 + [(175 × 5 × t)/100]

= 175 + 8.75t

The function is 175 + 8.75t

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The range of the data on the boxplot is 12

From the question, we have the following parameters that can be used in our computation:

The box plot

The range is calcilated as

Range = Maximum - Minimum

From the plot, we have

Maximum = 12

Minimum = 0

Substitute the known values in the above equation, so, we have the following representation

Range = 12 - 0

Evaluate

Range = 12

Hence, the range is 12

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The number of images formed by two mirrors kept at an angle of 72° are;

5 images, If the object is positioned symmetrically between the mirrors

4 images if the object is placed asymmetrically between the mirrors

The formula that can be used to find the number of images formed, n, when two mirrors are placed at a specified angle, θ, to each other is presented as follows;

If [tex]\dfrac{360^{\circ}}{\theta}[/tex] is an even number, the number of images formed is obtained using the formula;

If [tex]\dfrac{360^{\circ}}{\theta}[/tex] is an odd number, the number of images formed is obtained using the formula;

If [tex]\dfrac{360^{\circ}}{\theta}[/tex] is an odd number, and the position of the object is asymmetric, the number of images formed is obtained using the formula;

When θ = 72°, we get;

[tex]n = \dfrac{360^{\circ}}{72^{\circ}} = 5[/tex], which is an odd number, therefore;

If the object is placed symmetrically between the two mirrors, the number of images formed is therefore;

[tex]n = \dfrac{360^{\circ}}{72^{\circ}}-1 = 4[/tex]

If the object is placed asymmetrically between the two mirrors, the number of images formed is [tex]n = \dfrac{360^{\circ}}{72^{\circ}} = 5[/tex]

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The cost of a family pack of 45 chicken nuggets = 6.75 dollars

Given that Burger Mania sells 10 chicken nuggets for $1. 50

First we find the cost of one chicken nugget.

10 chicken nuggets = 1. 50 dollars

So, 1 chicken nugget = (1.50) / 10 dollars

                                  = 0.15 dollars

                                  = 15 cents

We need to find the cost of 45 chicken nuggets.

Using Unitary method the cost of 45 chicken nuggets would be,

45 × 0.15 = 6.75 dollars

Therefore, at given rate a family pack of 45 chicken nuggets must be 6.75 dollars

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Let's assume that the reaction is taking place between alkyl bromide and the nucleophile is OH- , then the formula for substitution reaction will be , R-Br + OH− => R-OH + Br− .

Nucleophiles are known as organisms that are strongly linked to an area of positive charge in the form of an ion or a molecule. These are believed to be fully charged or to have negative ions on a molecule. Cyanide ions, water, hydroxide ions, and ammonia are common examples of nucleophiles.

Electrophiles are compounds which are involved in the electrophilic substitution process. They are the molecules that transfer a pair of electrons during the creation of a covalent bond.

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Step-by-step explanation:

[tex]\frac12(8k+12k^2+6k^3)\\=4k+6k^2+3k^3\\[/tex]

Rearrange into descending order:

[tex]\boxed{3k^3+6k^2+4k}[/tex]

Answer:

Hence, your answer will be:

P  ≈  $54900

Step-by-step explanation:

Owen is going to invest in an account paying an interest rate of 5.7% compounded continuously. How much would Owen need to invest, to the nearest hundred dollars, for the value of the account to reach $122,000 in 14 years?

Compounded Continuously:

A  =  Pe^rt

Given Values:

A = 122000     t = 14    r = 0.057

Plug In:

122000 = Pe^0.057(14)

Plug In:

122000 = Pe^0.798

Evaluate In Calculator Using e Button:

122000 = P(2.221094295)

Divide By: 2.221094295

122000 / 2.221094295  =  P(2.221094295) / 2.221094295  

Use Calculator:

54927.87959894 = P

Round to The Nearest Hundred Dollars:

P  ≈  $54900

Answer: It seems that the missing step in this proof would be option "OB" ZBDE ZDEB ZADE ZDEC,

Step-by-step explanation:  

It's showing that the angles are equal and the angles are congruent. The reason is that by definition, congruent angles have the same degree measure and by using the Angle-Angle Similarity Criterion we can prove that if two angles of one triangle are congruent to two angles of another triangle, the two triangles are similar.

It is important to note that this statement can only be used when the two figures are similar and it is not sufficient for congruency. Therefore, a missing step in this proof would be to prove that the figures are similar before using the Angle-Angle Similarity Criterion.

The statement given is "AABC with = CB" and the conclusion is "DE AC." The question is asking for the missing step in the proof that shows how these two statements are related.

The value of the given expression is -4.25

Expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

Given that, an expression, -1.5 - 2.75

= -1.5 - 2.75

= -1.5 + (-2.75)

= -4.25

Hence, the correct expression is -1.5 + (-2.75) = -4.25

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The additive inverse of 3/2 is -3/2 as the sum of both value is 0 which is additive identity.

An additive inverse of a number is the number that when added to the original number, results in a sum of zero. In other words, it is the opposite of the original number on the number line. In the case of a fraction, the additive inverse is found by multiplying the numerator and denominator by -1. The additive inverse of 3/2 is -3/2 because 3/2 + (-3/2) = 0. This is true for any number in any form, whether it be an integer, a decimal, or a fraction.

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Complete question:

what is additive inverse of 3/2?

An interior angle of a regular decagon is given by the formula (n-2) * 180 / n, where n is the number of sides. Since a decagon has 10 sides, the measure of each interior angle is (10-2) * 180 / 10 = 160 degrees.

The measure of each exterior angle of a regular polygon is given by the formula 360 / n, where n is the number of sides. So in the case of a decagon, each exterior angle measures 360 / 10 = 36 degrees.

The required equation that represents the relationship between b and e exists m<b + m<e = 180.

Two angles are called supplementary when their measures add up to 180 degrees.

If the sum of two angles is 180 degrees then they are said to be supplementary angles, which form a linear angle together. Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.

The required equation that represents the relationship between b and e exists m<b + m<e = 180

From the given diagram, we can see that the line x and y are cut by a transversal. This shows that the following statements exists true;

m<b and m<g exists supplementary

i.e m<b + m<g = 180

Also m<b and m<f are equal (alternate interior angle)

m<b = m<d (vertically opposite angle)

Also, since m<d and m<e are supplementary angles (angle on a straight line), then m<b and m<e are also supplementary.

Therefore, the required equation that represents the relationship between b and e exists m<b + m<e = 180.

The complete question is:

Lines x and y are parallel. Write an equation that represents the relationship between b and e. Explain how you know this equation is always true. Your explanation should use AT LEAST TWO of the following terms: vertical angles, corresponding angles, congruent, supplementary.

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No, it depends upon the size of the bottle but it's not enough for a normal bottle to make 6 frozen juice bars.

No, 2 cups of orange juice is not enough to make 6 frozen juice bars. Each frozen juice bar typically requires a certain amount of juice, and it is likely that 6 bars would require more than 2 cups of juice. To be sure, you would need to check the recipe or packaging for the frozen juice bars to determine the exact amount of juice required per bar.

It is also important to note that even if the juice is enough to make 6 bars, it might not yield the same taste as desired because of the lack of enough juice, also the freezing process might not work as well as it should because of the small quantity of juice.

Therefore, It is not enough as it depends upon the size of the bottle but it's not enough for a normal bottle to make 6 frozen juice bars.

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The point's x and y coordinates may be switched to create the point's image around the line y=x. As an illustration, consider the picture of the point (a,b) about the line y=x: (b,a).

A main image's spatial reference is specified by an image coordinate system. No distortions appear when a main picture is presented in its own image coordinate system, and secondary images and features can be projected onto the primary image using its image coordinate system.

The point B(l,m) is the point that corresponds to the point P in the line mirror ax+by+c=0 such that PB is perpendicular to ax+by+c=0 and the midpoint L of PB falls on the line ax+by+c=0.

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The equation in point-slope form for the line passing through (3, -8) with a slope of -3 is y = -3x + 1

What is the slope?

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

The point-slope form of the equation of a line is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope.

We are given that the line passes through the point (3, -8) and has a slope of -3, so we can substitute these values into the point-slope form:

y - (-8) = -3(x - 3)

Simplifying the equation, we get:

y + 8 = -3x + 9

Subtracting 8 from both sides, we get:

y = -3x + 1

Therefore, the equation in point-slope form for the line passing through (3, -8) with a slope of -3 is:

y - (-8) = -3(x - 3)

which simplifies to:

y + 8 = -3x + 9

or in slope-intercept form:

y = -3x + 1

Hence, the equation in point-slope form for the line passing through (3, -8) with a slope of -3 is y = -3x + 1

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The image of the point (-3,-4) after a dilation with a scale factor of 4 centered at the origin is (12,-16).

Generally, Dilation is a method for producing figures with a similar appearance.

By multiplying the distances between each point with the scale factor, each point is extended outwards from the center point D.

(Towards the outside in the event that the scale factor is greater than 1) To alter the profile of the triangle, move the points A, B, and C respectively.

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Answer:(-12, -16)

Step-by-step explanation:

I took the test

The solution of the inequality are n  ≤ -7 and n ≥ -12.

A compound inequality is an inequality that combines two simple inequalities.

Therefore, let's solve the compound inequality individually.

n + 2 ≤ −5 and  n + 6 ≥ −6

Hence,

n + 2 ≤ − 5

subtract 2 from both sides of the inequality

n + 2 - 2 ≤ − 5 - 2

n  ≤ -7

n + 6 ≥ −6

subtract 6 from both sides of the inequality

n + 6 ≥ −6

n + 6 - 6 ≥ −6 - 6

n ≥ -12

Therefore, n  ≤ -7 and n ≥ -12

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r represents the sample correlation coefficient.

p represents the population correlation coefficient.

A statistical concept known as the correlation coefficient helps in establishing a relationship between expected and actual values gained through statistical experimentation.

The estimated correlation coefficient's value explains how much the expected and actual values match.

The correct answers are

r represents the sample correlation coefficient

The interpretation of sample correlation coefficient (r) depends on how the sample data are collected.

A statistical concept known as the correlation coefficient helps in establishing a relationship between expected and actual values gained through statistical experimentation.

p represents the population correlation coefficient.

With a large simple random sample, the sample correlation coefficient is an unbiased estimate of the population correlation coefficient (p)

A correlation coefficient of 1 is perfect positive correlation

A correlation coefficient of -1 is perfect negative correlation

A correlation coefficient of 0 indicated the variables do not have any direct relationship.

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Discuss the difference between r and p. Choose the correct answers below.

r represents the _____

1. sample correlation coefficient thing

2. critical value for the correlation coefficient.

3. population correlation coefficient.

p represents the _____

1. critical value for the correlation coefficient.

2. population correlation coefficient.

3. sample correlation coefficient.

Finding a number's square root is the equivalent as squaring it, or the opposite process. When you multiply the square root of a given integer by itself, you get the original number. Since 8 x 8 equals 64, as fact, 8 is the square root of 64.

It is possible to multiply an integer by its square root in order to obtain the original value. Square root of, end square root is the symbol for this mathematical concept. Contrary to squaring, finding a number's square root is the reverse. For instance, 3 is squared at 9, 32, and its square root at 9, which is 9, is equal to 3. It is simple to multiply by 9 since it is a perfect square.

Thus, there is a reverse relationship between squaring and getting the square root.

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The unit rate of miles/hour taken by the van is 66.67 miles/hr.

Here given that,

The records of the trip of three vehicles are:

Van:500 miles in 7.5 hours

Truck:300 miles in 5 hours

Car:400 miles in 5.5 hours

We have to find unit rate miles/hour of the van.

So ,

Van covers 500 miles in 7.5hrs.

To find the unit rate,

Unit rate = total distance covered / total time taken

By substituting the values,

unit rate = 500/7.5

              = 66.67 miles/hr

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