A rectangle that is 2 inches by 3 inches has been scaled by a factor of 7.

1. What are the side lengths of the scaled copy?

2. Suppose you want to scale the copy back to it's original size. What scale factor should you use?

Step-by-step explanation:

x is the depth. put the given depths in the given formula and then find their difference.

T1=4500/1000=4.5°C

T2=4500/2500=1.8°C

now the difference:

∆T=T2-T1

∆T=1.8-4.5= -2.7°C

Answer:

20

Step-by-step explanation:

add 3ft+3ft+11ft+3ft and that's your answer

Answer:

12.5

Step-by-step explanation:

the radius of a circle is half of the diameter

Answer:

1372 ft^3

Step-by-step explanation:

Volume of sphere =\(\frac{4}{3}\)πr^3

here π is 3 and radius = 7

4/3 * 3 * 7^3

1372ft^3

Answer:

14ft

Step-by-step explanation:

Answer:

5, and 20

Step-by-step explanation:

5+20=25

reciprocal of 5 is 1/5 and reciprocal of 20 is 1/20 so 1/5=4/20 and 4/20 + 1/20 = 5/20. 5/20 = 1/4

Answer:

  C. RP = 4.5

Step-by-step explanation:

You want to know what condition is sufficient to show ∆ABC ~ ∆QPR, given  three sides and 2 angles in ∆ABC, and 2 sides in ∆QPR.

Similarity can be shown if all three sides are proportional, or if two angles are congruent.

The offered answer choices only list one angle, so none of those will work. The answer choice that makes the third side of ∆QPR be in the same proportion as the corresponding side of ∆ABC is the condition of interest.

  C. RP = 4.5

__

Additional comment

The side ratios in the two triangles are ...

  AB : BC : CA = 10 : 9 : 6

  QP : PR : RQ = 5 : PR : 3

For these ratios to be the same, PR must be half of BC, just as the other segments in ∆QPR are half their counterparts in ∆ABC.

Answer :

32b + 63

Hope this help!

The amount that you will have in 3 years, given the interest rate and the amount won, is 1, 195, 618. 17 currency units

To find the amount earned in three years as a result of your lottery being invested, use the future value formula which is:

= Amount won x ( 1 + periodic  rate ) ^ number of periods

Periodic rate :

= 6 % / 4 quarters per year

= 1. 5 %

The number of periods is:

= 3 years x 4 quarters per year

= 12 quarters

The amount you will have in 3 years is:
= 1,000,000 x ( 1 + 1. 5 %) ¹²

= 1, 195, 618. 17 currency units

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The circumference of the given circle is approximately 47.3 inches.

Since the length of the arc KL and the measure of the central angle ∠KOL are known, we can use the formula for arc length to find the circumference of the circle:

arc length = (central angle / 360°) x circumference

Plugging in the known values, we have:

4.6 in = (35° / 360°) x circumference

Solving for the circumference, we get:

circumference = 4.6 in / (35° / 360°)

circumference = 4.6 in x (360° / 35°)

circumference ≈ 47.3 in (rounded to the nearest tenth)

Therefore, the circumference of the circle is approximately 47.3 inches.

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Answer:

zero

Step-by-step explanation:

This flat horizontal line is Y=1 has a slope (rate of change) of zero.

Answer:

The letter "x" is often used in algebra to mean an unknown value. It is often called a "variable".

Example:

In x + 5 = 12, x is a variable, but we can work out its value if we try!

See the attached picture:

Answer:Yes

Step-by-step explanation:His complaint is valid.

Answer:

1 is the like term in a series as there is nothing common

.sorry if mistake.

like terms =

2x,-6x,

5y²,-9x²,18y²

7 is the mode of this dataset since, as we can see, it appears twice.

The most common occurrence of a number, or the one that does so most frequently.

Example: The mode of the digits 4, 2, 4, 3, and 2 is the number 2, which appears three times, more than any other number.

The mode computation is a rather straightforward procedure.

Calculate the frequency with which each number appears in the group after arranging the numbers in the set in any order—from lowest to highest or highest to lowest.

The most frequent mode is the one that appears.

So, we have the dataset:

3, 6, 8, 7, 2, 4, 5, 10, 7, 14

A number of terms repeated:

3 = 1

6 = 1

8 = 1

7 = 2

2 = 1

4 = 1

5 = 1

10 = 1

14 = 1

Since we can see that 7 is repeated twice then, 7 is the mode of this dataset.

Therefore, 7 is the mode of this dataset since, as we can see, it appears twice.

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Correct question:

The gym offers multiple exercise classes per day. The number of people in an exercise class this week is represented in the list.

3, 6, 8, 7, 2, 4, 5, 10, 7, 14

What is the value of the mode for this data set?

A. 14

B. 8

C. 7

D. 3

Answer:

4 rows of 28 kids

Step-by-step explanation:

Answer:

the function f(x) = -3x^2 + 12x - 9 has a maximum value of 3, which occurs at x = 2.

Step-by-step explanation:

To determine whether the function f(x) = -3x^2 + 12x - 9 has a maximum or minimum, we can use the fact that a quadratic function has a maximum at the vertex if the coefficient of x^2 is negative, and a minimum at the vertex if the coefficient of x^2 is positive.

In this case, the coefficient of x^2 is -3, which is negative, so the function has a maximum at the vertex. The x-coordinate of the vertex is given by -b/2a, where a is the coefficient of x^2 and b is the coefficient of x. Using the formula, we get:

x = -b/2a = -12/(2*(-3)) = 2

So the vertex of the parabola is at x = 2. To find the corresponding y-coordinate (i.e. the maximum value of the function), we can substitute x = 2 into the function:

f(2) = -3(2)^2 + 12(2) - 9 = -3(4) + 24 - 9 = 3

Therefore, the function f(x) = -3x^2 + 12x - 9 has a maximum value of 3, which occurs at x = 2.

Answer:

\(d=9.21954\)

Step-by-step explanation:

Distance Formula: \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Simply plug in the 2 coordinates into the distance formula to find distance d:

\(d=\sqrt{(-1-5)^2+(9-2)^2}\)

\(d=\sqrt{(-6)^2+(7)^2}\)

\(d=\sqrt{36+49}\)

\(d=\sqrt{85}\)

\(d=9.21954\)

The incorrect statement is

In mathematics, dilation can be defined as a transformation which alters the size of an object, though its shape remains unchanged. It is described as a specific similarity transformation where all dimensions associated with the given object (i.e. height, width and length) are increased or decreased uniformly by a particular scale factor.

A dilation thus produces an alteration in size, with the figure being either magnified or diminished while keeping its unique shape intact.

The scale factor used in the dilation is 9/7 instead of 7/3.

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Answer:

When a denominator has a higher root, multiplying by the radicand will not remove the root. Instead, to rationalize the denominator we multiply by a number that will yield a new term that can come out of the root. For example, with a cube root multiply by a number that will give a cubic number such as 8, 27, or 64.

Answer:

3.1) Para calcular la mediana de la lista de datos, primero debemos ordenarlos de menor a mayor:

2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 10, 10, 10, 10, 10, 10

Como la lista tiene un número impar de elementos (35), la mediana es el valor central de la lista, es decir, el elemento en la posición 18. En este caso, el valor de la mediana es 6.

3.2) Para calcular la media y la mediana mediante una tabla de frecuencias, primero debemos determinar las frecuencias de cada valor en la lista:

Valor Frecuencia

2 5

4 8

6 9

8 5

10 8

La media se calcula sumando todos los valores y dividiendo entre el número total de elementos:

media = (25 + 48 + 69 + 85 + 10*8) / 35 = 5.8

Para calcular la mediana, primero debemos determinar el valor que ocupa la posición central de la lista. Como el número total de elementos es impar, ese valor es el que ocupa la posición (n+1)/2, donde n es el número total de elementos. En este caso, ese valor es el que ocupa la posición (35+1)/2 = 18.

Luego, debemos encontrar el valor que ocupa la posición 18 contando los valores de la tabla de frecuencias. Podemos hacer esto sumando las frecuencias hasta alcanzar o superar la posición 18:

Valor Frecuencia Frec. Acumulada

2 5 5

4 8 13

6 9 22

8 5 27

10 8 35

Como la posición 18 está dentro del intervalo correspondiente al valor 6, la mediana es 6.

The expression which shows how many grams of raisins are in the bowl will be

(0.01x) * 150 + (0.01y) * 250

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

The expression which shows how many grams of raisins are in the bowl will be:

= (x% × 150) + (y% × 250)

= (0.01x) * 150 + (0.01y) * 250

This equation represents the total grams of raisins in the bowl by multiplying the weight of the Oreana's bag by the percentage of raisins in it, and adding that to the product of the weight of Brandon's bag and the percentage of raisins in it. The "0.01" is used to convert the percentages from x and y to decimal form.

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Representing the quantity by an integer : a loss of 14 pounds will be -14.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the corresponding positive numbers are the negative numbers.

An integer is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043.

In this case, the quantity by an integer : a loss of 14 pounds will be -14. This is because a loss is negative.

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Convert \(-1+i\) to polar form.

\(z = -1 + i \implies \begin{cases}|z| = \sqrt{(-1)^2 + 1^2} = \sqrt2 \\\\ \arg(z) = \pi + \tan^{-1}\left(\dfrac1{-1}\right) = \dfrac{3\pi}4 \end{cases}\)

By de Moivre's theorem,

\(\left(-1+i\right)^7 = \left(\sqrt2 \, e^{i\,\frac{3\pi}4}\right)^7 \\\\ ~~~~~~~~ = \left(\sqrt2\right)^7 e^{i\,\frac{21\pi}4} \\\\ ~~~~~~~~ = 8\sqrt2 \, e^{-i\,\frac{3\pi}4} \\\\ ~~~~~~~~ = 8\sqrt2 \left(\cos\left(\dfrac{3\pi}4\right) - i \sin\left(\dfrac{3\pi}4\right)\right) \\\\ ~~~~~~~~ = 8\sqrt2 \left(-\dfrac1{\sqrt2} - \dfrac1{\sqrt2}\,i\right) \\\\ ~~~~~~~~ = -8 (1 + i)\)

QED

Answer:

10 ounces

Step-by-step explanation:

5 pounds equals 80 ounces, so 80 divided by 8 is 10

Answer: False

Step-by-step explanation:

We can write tan(x) = sin(x)/cos(x)

if cos(x) tends to 1, and sin (x) tends to 0 (this happens aronund the point x = 0)

then we have:

Tan(x) = 0/1 = 0

Then the statement is false, as cos(x) approaches 1 and sin(x) approaches 0, tan(x) also approaches 0.

From the given triangle, x has a value of 35°.

As a result, one of the triangle's sides has been stretched to create an exterior angle of 125° outside angle.

Angles that are always located near one another, sharing a similar vertex and common side but not overlapping, are said to be adjacent angles.

According to the above figure, the tringle's exterior angle is 125°, and y is an adjacent angle to that.

Now, 125°+ y =180°

y = 180°-125°

y = 55°

As a result, the supplied triangle's value for y is 55°.

The sum of the triangle law,

55°+ 90° + x  = 180°

x = 35°

Therefore the value of x = 35°

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Answer:

2.5 cm

Step-by-step explanation:

From the first 4 bounces, we find that the height of the lacrosse ball after each bounce is 1/4 the height that it was after the previous bounce. Therefore, since the 7th bounce is 6 bounces after the first bounce, we can set up an equation to find the balls height (y), after some number of bounces after the first one:

\(y=10240*(\frac{1}{4})^x\).

Plug-in 6 for x to get 2.5.

Hope this helps :)