Clare says, "We know that if we dilate a cube by a factor of k, the cube's volume is multiplied by k³. It seems like that must apply to all solids, but I'm not sure how to prove it."
Elena says, "Earlier in the unit, we showed that we can cover any two- dimensional shape with rectangles, so the property that area changes by k² when we dilate a figure by k applies to all shapes, not just rectangles. Can we do something similar here?"

1. Use Elena's line of reasoning to argue that for any solid, if it's dilated by a
factor of k, the volume is multiplied by k³.

2. Suppose a triangular prism has surface area 84 square centimeters and volume 36 cubic centimeters. The prism is dilated by scale factor k=4. Calculate the surface area and volume of the dilated prism.

The sοlutiοns in οrder frοm least tο greatest are:

Lesser x = -4

Greater x = 1

Ascending οrder refers tο the arrangement οf numbers in which the smallest number cοmes befοre the largest.

Tο sοlve fοr x in the equatiοn [tex]x^2 + 3x - 4 = 0[/tex], we can use the quadratic fοrmula:

[tex]x= \frac{(-b+\sqrt{b^{2} -4ac} )}{2a} \\[/tex]

where a, b, and c are the cοefficients οf the quadratic equatiοn[tex]ax^2 + bx + c = 0.[/tex]

In this case, a = 1, b = 3, and c = -4. Substituting these values intο the quadratic fοrmula, we get:

[tex]x = (-3\± \sqrt{(3^2 - 4(1)(-4)))} / 2(1)\\\\x = (-3 \± \sqrt{(25))} / 2\\\\x = (-3 \± 5) / 2[/tex]

This gives twο pοssible sοlutiοns:

x1 = (-3 - 5) / 2 = -4

x2 = (-3 + 5) / 2 = 1

Therefοre, the sοlutiοns in οrder frοm least tο greatest are:

Lesser x = -4

Greater x = 1

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The length of the altitude of the equilateral triangle with side lengths of 28 meters is 14[tex]\sqrt{3}[/tex] meters.

Define equilateral.

Equilateral is an adjective used to describe a geometric figure, such as a triangle, that has all sides of equal length. In an equilateral triangle, all three sides are of equal length, and all three angles are also equal, measuring 60 degrees each.

To find the altitude of an equilateral triangle, we can use the following formula:

altitude = ([tex]\sqrt{3}[/tex]/2) x side length

Since the side length of the equilateral triangle is 28 meters, we can substitute it in the formula and simplify:

altitude = ([tex]\sqrt{3}[/tex]/2) x 28

= 14[tex]\sqrt{3}[/tex] meters (rounded to two decimal places)

Therefore, the length of the altitude of the equilateral triangle is approximately 14.00 meters.

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To find:-

Answer:-

To find out the equation of the line , we need to find out the slope first. It can be calculated as ,

[tex]\implies m =\dfrac{\Delta y}{\Delta x }=\dfrac{y_2-y_1}{x_2-x_1} \\[/tex]

And here ,

On substituting the respective values, we have;

[tex]\implies m =\dfrac{25-20}{8-3} \\[/tex]

[tex]\implies m=\dfrac{5}{5}\\[/tex]

[tex]\implies m=\boxed{1} \\[/tex]

Hence the slope of the line is 1 . Now we may use point slope form of the line to find out the equation of the line. Point slope form of the line is,

[tex]\implies y - y_1 = m(x-x_1) \\[/tex]

Take any of the given two points. Here i am taking (3,20) . So here we have;

On substituting the respective values, we have;

[tex]\implies y - 20 = 1(x - 3) \\[/tex]

[tex]\implies y -20 = x - 3 \\[/tex]

[tex]\implies x - 3 - y +20 = 0 \\[/tex]

[tex]\implies \underline{\underline{\green{ x - y +17=0}}}\\[/tex]

Hence the equation of the line in standard form is x - y + 17 = 0 .

and we are done!

When a data line on a graph slopes down as it goes to the right, it is depicting that the relationship between the variables on the graph is inverse.

An inverse relationship is a kind of correlation between two variables, in which one variable decreases while the other increases, or vice versa. An inverse relationship happens when one variable increases while the other decreases, or when one variable decreases while the other increases.

On a graph, when a data line slopes down as it goes to the right, this is an indication that the relationship between the variables on the graph is inverse. As the values of x increase, the values of y decrease. Therefore, we can conclude that there is an inverse relationship between x and y.

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The length of Line FG is 13.5 inch

A parallelogram is a four-sided, geometric form in two dimensions. It is a quadrilateral, which means it has four vertices (corners) and four angles.

Area of parallelogram = base × height

As per given diagram, base, GH = 9inch and height, FP = 12inch

So, Area of parallelogram = 9 × 12 = 108 inch²

and also, Area of parallelogram = EQ × FG

put values here, 108 = 8 × FG

FG = 13.5 inch

Therefore, the length of Line FG is 13.5 inch

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The contrapositive of the given statement is "If it is not a cat, then it is a lion."

The contrapositive of the statement "If it is not a lion, then it is a cat" can be obtained by negating the original statement and switching the positions of the antecedent (the "if" part) and the consequent (the "then" part).

The contrapositive takes the form:

"If it is not a cat, then it is a lion."

So, the contrapositive of the given statement is "If it is not a cat, then it is a lion."

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The linear approximation error when using the linear approximation to estimate the cube root of 8.25 is 0.0593.

When we want to find the linear approximation error, we can use the formula

Error = f(x) - L(x),

Where `f(x)` is the actual value of the function at `x`, and `L(x)` is the linear approximation of the function at `x`.

The linear approximation of a function f(x) near x=a is given by:

L(x) = f(a) + f'(a)(x-a)

In this case, we want to find the linear approximation of the function f(x) = cube root of x near x=8. To do so, we first need to find the value of f(8) and f'(8).

f(8) = cube root of 8 ⇒ 2

To find f'(8), we take the derivative of f(x) with respect to x:

f(x) = x^(1/3)

f'(x) = (1/3)x^(-2/3)

So, f'(8) = (1/3)(8)^(-2/3) ⇒ 1/12

Therefore, the linear approximation of f(x) near x=8 is:

L(x) = 2 + (1/12)(x-8)

Now, we want to use this linear approximation to estimate the value of the cube root of 8.25. To do so, we substitute x=8.25 into the linear approximation:

L(8.25) = 2 + (1/12)(8.25-8) ⇒ 2.0208

The actual value of the cube root of 8.25 is:

∛8.25 ⇒ 2.0801

So, the error in the linear approximation is:

2.0801 - 2.0208 ⇒ 0.0593

Therefore, the linear approximation error when using the linear approximation to estimate a cube root of 8.25 is approximately 0.0593.

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The first game brought in more money than the last game.

Any number of equal parts is represented by a fraction, which also symbolizes a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many pieces of a particular size there are when spoken in everyday English.

According to question:

The baseball team made more money at their first game because 6/7 is less than 1. This means that they made less money at their last game than at their first game. For example, if they made $100 at their first game, then they made 6/7 x $100 = $85.71 at their last game, which is less than $100.

Therefore, the first game brought in more money than the last game.

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Since only 25% of the variability in y is explained, Julie's actual score could have been much higher than the predicted value.

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. When the standard deviation is low, the data are concentrated around the mean, and when it is large, the data are widely dispersed.

(a) Slope, b = r*(sy/sx) = 0.5*(8/40) = 0.1

Intercept = y - bx = 75 - 0.1*280 = 47

The regression equation is:

y = 47 + 0.1*x

(b) Put x = 300

y = 47 + 0.1*300

y = 77

(c) r2 = 0.5*0.5 = 0.25

Since only 25% of the variability in y is explained, Julie's actual score could have been much higher than the predicted value.

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There are 720 different choices if order matters and there are 120 different choices if order does not matter.

a) If order matters,

The player can choose the first number in 10 ways (any of the digits 0-9), the second number in 9 ways (since one digit has already been chosen), and the third number in 8 ways (since two digits have already been chosen).

So the total number of choices is:

10 x 9 x 8 = 720

Therefore, there are 720 different choices if order matters.

b) If order does not matter,

We need to divide the number of choices by the number of ways the three numbers can be arranged.

Since there are 3 numbers, they can be arranged in 3! = 6 ways.

So the number of choices when order does not matter is:

(10 x 9 x 8) / 6 = 120

Therefore, there are 120 different choices if order does not matter.

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ANSWER:

The Pythagorean theorem is used to find the hypotenuse of a triangle.

=> AC² = AB² + BC²

In squares, the length of the side can be calculated by finding the square root of the area.

You can use the distributive property of multiplication over addition and the fact that 18 is thrice of 6.

The given expression is equivalent to

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

[tex]a(b+c)=a\times b+a\times c[/tex]

(remember that many times, when using letters or symbols, we hide multiplication and write two things which are multiplied, close to each other. As in [tex]2\times x=2x[/tex])

The given expression is [tex]6g-18h[/tex]

We know that we can write

[tex]6=2\times3[/tex]

[tex]18=2\times9=3\times6[/tex]

Thus,

[tex]6g-18h=6\times g-6\times 3h=6(g-3h)=-6(-g+3h)[/tex]

[tex]6g-18h=2\times 3g-2\times 9h=2(3g-9h)=-2(-3g+9h)[/tex]

[tex]6g-18h=3\times 2g-3\times 6h=3(2g-6h)=-3(-2g+9h)[/tex]

All of the above forms are obtained from the same expression without altering its value but only forms, so their simplified forms are same so they are equivalent expressions.

Thus,

The given expression is equivalent to

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Answer:C & D

Step-by-step explanation:

Answer:

0% (0/40)

Step-by-step explanation:

I feel like this is a trick question. since chicken is not indicated on the graph, I believe chicken is nobodies favorite food

a. S = {(1, -1), (2, 1)}Let's begin by calculating the determinant of the matrix composed of the vectors of S, and checking if it is equal to 0. Because the two vectors are not colinear, they should span R2.|1 -1||2 1| determinant is not 0, therefore S spans R2. No geometric description is required for this example.

b. S = {(1, 1)} The set S contains one vector. A set containing only one vector cannot span a plane because it only spans a line. Therefore, S does not span R2. Geometric description: S spans a line that passes through the origin (0, 0) and the point (1, 1).c. S = {(0, 2), (1, 4)} Let's again begin by calculating the determinant of the matrix composed of the vectors of S, and checking if it is equal to 0.|0 2||1 4| determinant is 0, thus S does not span R2. In this scenario, S only spans the line that contains both vectors, which is the line with the equation y = 2x.

Geometric description: S spans a line that passes through the origin (0, 0) and the point (1, 2).

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There will be a total of 28 handshakes when the 3 late members arrive.

The first n-1 positive integers are added together using the formula n(n-1)/2, where n is the total number of terms being added together.

The number of combinations or arrangements of a given collection of items may be determined using this formula, which can be obtained using the process of mathematical induction. It is often used in combinatorics and discrete mathematics. For instance, the formula was used to determine how many times a group of individuals shook hands in the scenario above. It might also be used to determine the number of pathways in a network of nodes or vertices or the number of ways to choose a portion of an object set from a bigger set in other settings.

Given that, 3 members arrive late, and 5 members are already present.

The total members are 5 + 3 = 8.

Now, using the sum of positive integer formula:

n(n-1)/2

We can determine the number of handshakes.

8(8-1)/2 = 28

Hence, there will be a total of 28 handshakes when the 3 late members arrive.

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Answer:

9.5 decimal

espero y te ayude

To create opposite x terms, we need to multiply the first equation by -5.

How to choose what term to multiply the first equation?

To choose what term to multiply the first equation, we need to consider the coefficients of the variable that we want to eliminate (in this case, the x variable) in both equations. Our goal is to create opposite terms for that variable in the two equations, so that when we add or subtract the equations, that variable will be eliminated.

Determining the number to multiply the first equation by to form opposite terms for the x-variable :

In this case, the coefficient of x in the first equation is 2/5, and the coefficient of x in the second equation is -2.

To create opposite terms for x, we need to find a constant that, when multiplied by the first equation, will result in a coefficient of x that is the negative of the coefficient of x in the second equation (i.e., -2).

To do this, we can divide the coefficient of x in the second equation by the coefficient of x in the first equation, and then multiply the entire first equation by the resulting constant.

In this case, we have:

[tex](-2)/(2/5) = -5[/tex]

Multiplying the first equation by -5 gives:

[tex]-5(2/5)x + (-5)6y = -5(-10)[/tex]

which simplifies to:

[tex]-2x - 30y = 50[/tex]

Now we have two equations with opposite x terms:

[tex]-2x - 4y = 40[/tex]

[tex]-2x - 30y = 50[/tex]

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The option in the question that is equivalent to 3/8 is 2/5.

We can simplify 3/8 and 2/5 so that they have a common denominator:

3/8 = 3*(5/5)/(85/5) = 15/40

2/5 = 2(8/8)/(5*8/8) = 16/40

Since 15/40 and 16/40 have the same denominator, we can compare their numerators to see which is larger:

15/40 < 16/40

Since 16/40 is larger, we can conclude that 2/5 is greater than 3/8.

Therefore, the option that is equivalent to 3/8 is 2/5.

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Answer:

9.5x + 8 = 65

Step-by-step explanation:

Let x = number of sandwiches.

The cost of x sandwiches is 9.5x.

The delivery fee is $8.

The total cost of an order is the price of the sandwiches, 9.5x plus the delivery fee, 8.

In this case, the total cost is $65.

9.5x + 8 = 65

Answer:

$65

Step-by-step explanation:

X=9.50 because you add the $8 delivery fee to equal 65 in total.

The histogram that most likely represents a country with a declining population growth rate is one where the bars to the right (representing higher numbers of births or deaths) are lower than the bars to the left.

A declining population growth rate means that the rate at which the population is growing is decreasing, which suggests that the number of births is decreasing or the number of deaths is increasing.

In other words, the shape of the histogram would be skewed to the left, with a long tail on the left-hand side and shorter bars on the right-hand side. This shape suggests that there are fewer births or more deaths, leading to a declining population growth rate.

It is worth noting that a histogram alone may not provide enough information to make definitive conclusions about population growth rates. Other factors such as migration rates and changes in life expectancy can also affect population growth. Therefore, it is important to consider multiple sources of data and statistical methods when analyzing population trends.

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The Rico ride his bike at a speed of 6 miles per hour.

Speed is a measure of how quickly an object moves, calculated as the distance traveled per unit of time.

Let's take Rico's speed on his bicycle is 'r'.

So, Luis's speed can be expressed as 4r.

Time = Distance / Speed

For Luis, the time it takes to travel 24 miles is:

Time = 24miles / 4r

For Rico, the time it takes to travel 24miles is:

Time = 24miles / r

Since Rico takes 3 hours longer than Luis to travel the same distance (24miles), we can set up an equation:

24miles / r = (24miles / 4r) + 3hour

Simplifying this equation, we get:

⇒ 24 = 6 + 3r

⇒ r = 6

Therefore, Rico can ride his bike at a speed of 6 miles per hour.

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The iron wrecking ball weighs roughly 191184 grams, which is equivalent to 191.184 kilograms.

To calculate the mass of the iron wrecking ball, we need to use the formula:

mass = density x volume

The density of iron is given as 7.8 g/cm3. The volume of the wrecking ball can be calculated using the formula for the volume of a sphere:

volume = (4/3) x π x radius³

Plugging in the given radius of 18 cm, we get:

volume = (4/3) x π x (18 cm)³

volume = 24488.48 cm³

Now, we can use the formula for mass:

mass = density x volume

mass = 7.8 g/cm³ x 24488.48 cm³

mass = 191183.94 g

Therefore, the mass of the iron wrecking ball is approximately 191184 g or 191.184 kg.

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Answer:392

Step-by-step explanation:

a) It would take one machine 392 minutes.

b) It would take one machine 49 minutes.

Two ratios are said to be equal when a proportion is stated. When comparing two quantities, ratios are used to divide one quantity by the other.

a) Here given that, to produce a batch of newspaper 7 printing machines needed 56 minutes.

Using this relationship, we can set up a proportion:

as given, 7 printing machine needed = 56 minutes

So, 1 printing machine needed = 7 × 56 minutes = 392 minutes

Therefore, it would take one machine 392 minutes to produce the same batch of newspapers.

b) Similarly, to find out for 8 machines to produce the same batch of newspapers, we can use the same relationship:

1 printing machine needed = 392 minutes

So, 8 printing machine needed = (392 / 8) minutes = 49 minutes

Therefore, it would take one machine 49 minutes to produce the same batch of newspapers.

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Answer:

The observer deck of a ship is located at the origin of a coordinate system. Find the bearing of an object located at the point (5, 5).

Step-by-step explanation:

To find the bearing of an object located at the point (5, 5) relative to the observer deck at the origin of a coordinate system, we need to find the angle between the positive x-axis and the line connecting the observer deck to the object.

First, we calculate the slope of the line connecting the observer deck at (0, 0) to the object at (5, 5):

slope = (change in y) / (change in x)

= (5 - 0) / (5 - 0)

= 1

Next, we use the inverse tangent function to find the angle whose tangent is equal to the slope:

angle = arctan(slope)

= arctan(1)

= 45°

Therefore, the bearing of the object located at (5, 5) relative to the observer deck at the origin is 45 degrees.

Answer:

45° north of east

Step-by-step explanation:

tan⁻¹(y/x) = tan⁻¹(5/5) = tan⁻¹(1) = 45°

The rate of change in candies sold per month is 3 hundred candies.

The momentum of a variable is conveyed by the rate of change, which is used for expressing the percentage change in value over a particular amount of time.

To find the rate of change in candies sold per month, it is necessary to find the slope of the line connecting the two points.

The slope formula is given by: Δ[tex]\frac{y}{x}[/tex][tex]\frac{y2-y1}{x2-x1}[/tex]

Using the coordinates of the points, [tex]\frac{8-2}{6-4} =\frac{6}{2} =3[/tex]

The slope is 3. This means that for every month, the store sells 300 more candies.

Therefore, the rate of change, in candies sold per month is 300.

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Answer:

Step-by-step explanation:

Kind of like rema from the song calm down calm down!!

you an find it on youtub

Answer:

X = 3

Step-by-step explanation:

I can't really draw the diagram for you.

$9 is always charged so just add that to the end of your equation.

x is what they charge for skates and their are 7 skates so 7x

$30 is the total

7x + 9 = 30

subtract 9 from both sides

7x = 21

divide by 7 on both sides

x = 3

Answer:

x=15°,  ∠A=75°,  ∠B=60°,  ∠C=45°

Step-by-step explanation:

As we know that sum of the angle of a triangle is 180°

Therefore ∠A+∠B+∠C=180°

                5x+4x+3x=180°     {  ∵ ∠A=5x   ∠B=4x ∠C=3x   }

              ⇒   12x=180°

              ⇒      x=15°

Hence ∠A=5x=5×15°=75°

           ∠B=4x=4×15°=60°

and      ∠C=3x=3×15°=45°

to verify your answer 75°+60°+45°=180°