Line segment CD is 5 inches long. if line segment CD is dilated to form line segment C'D' with a scale factor of 0.6, what is the length of line segment C'D'.

Answer: 1 1/40.

Step-by-step explanation:

Answer:

t>15

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Only 1 right angle can be in any triangle.

Answer:

1,600,000

Step-by-step explanation:

100,000x2x2x2x2

Answer:160000

Step-by-step explanation:

,

Answer:

17+3b+5c

Step-by-step explanation:

9-4b+(8+7b+5c)

9-4b+8+7b+5c

9+8-4b+7b+5c

17+3b+5c

Answer:

-3/4 is plotted 3 little tabs left of 0

5/4 is plotted 1 little tab right of 1

Answer:

f(200) =116

f(200) is the cost to rent the moving van and drive it 200 miles

Step-by-step explanation:

f(x) = 90 + 0.13x

Let x = 200

f(200) = 90+ .13(200)

          =90+26

          =116

f(200) is the cost to rent the moving van and drive it 200 miles

72 = l . w . h

72 = x . (x - 1) . (x + 9)

72 = (x² - x) . (x + 9)

72 = x³ + 9x² - x² - 9x

72 = x³ + 8x² - 9x

0 = x³ + 8x² - 9x - 72

0 = x² (x + 8) - 9 (x + 8)

0 = (x² - 9)(x + 8)

0 = (x - 3)(x + 3)(x + 8)

x = 3 or x = -3 or x = -8

so, x = 3

length = x = 3

width = x - 1 = 2

height = x + 9 = 12

Final answer:

To find the dimensions of the rectangular prism, set up an equation using the volume formula and solve for x. The dimensions of the box are 3 feet, 2 feet, and 12 feet.

Explanation:

To find the dimensions of the box, we need to set up an equation using the volume formula for a rectangular prism. The volume of a rectangular prism is given by V = length x width x height.

So, we have the equation x(x - 1)(x + 9) = 72.

Simplifying this equation, we get x³ + 8x² - 9x - 72 = 0.

Using factoring or synthetic division, we find that x = 3 is a solution to the equation. Therefore, the length of the box is 3 feet, the width is 2 feet, and the height is 12 feet.

Answer:

Step-by-step explanation:

(4x^2-2x+8)+(x^2+3x-2)

Collect like terms

5x^2+x+6

5x^2+x+6 dont know if you need to siplify it any more

Answer:

He is incorrect

If there was 2 sides of 6 inches, the base can be 5 inches and it could be an isoscles triangle

Step-by-step explanation:

He is incorrect, the third side could be 5.

The correct answer is [tex]\( x = \frac{\ln(1.5)}{4\ln(1.05)} \).[/tex]

Let's analyze the given equation step by step:

Given the equation [tex]\( 1000(1+0.05)^4 \cdot x = 1500 \)[/tex], we want to solve for [tex]\( x \).[/tex]

First, simplify the left side of the equation by calculating

[tex]\( (1+0.05)^4 \):\( (1+0.05)^4 = (1.05)^4 \).[/tex]

Now, the equation becomes:

[tex]\( 1000 \cdot (1.05)^4 \cdot x = 1500 \).[/tex]

Next, divide both sides by [tex]\( 1000 \cdot (1.05)^4 \) to isolate \( x \):[/tex]

[tex]\( x = \frac{1500}{1000 \cdot (1.05)^4} \).[/tex]

Simplify the right side by dividing 1500 by 1000:

[tex]\( x = \frac{1500}{1000} \cdot \frac{1}{(1.05)^4} \),[/tex]

[tex]\( x = 1.5 \cdot \frac{1}{(1.05)^4} \).[/tex]

Now, to express [tex]\( x \)[/tex] in terms of natural logarithms, we take the natural logarithm of both sides:

[tex]\( \ln(x) = \ln(1.5 \cdot \frac{1}{(1.05)^4}) \).[/tex]

Using the property of logarithms that [tex]\( \ln(ab) = \ln(a) + \ln(b) \)[/tex], we can split the right side:

[tex]\( \ln(x) = \ln(1.5) - \ln((1.05)^4) \).[/tex]

Applying the power rule of logarithms, [tex]\( \ln(a^b) = b\ln(a) \)[/tex], we get:

[tex]\( \ln(x) = \ln(1.5) - 4\ln(1.05) \).[/tex]

To solve for [tex]\( x \)[/tex], exponentiate both sides to remove the natural logarithm:

[tex]\( e^{\ln(x)} = e^{\ln(1.5) - 4\ln(1.05)} \),[/tex]

[tex]\( x = e^{\ln(1.5)} \cdot e^{-4\ln(1.05)} \),[/tex]

[tex]\( x = 1.5 \cdot \frac{1}{e^{4\ln(1.05)}} \),[/tex]

[tex]\( x = 1.5 \cdot \frac{1}{(e^{\ln(1.05)})^4} \),[/tex]

[tex]\( x = 1.5 \cdot \frac{1}{(1.05)^4} \).[/tex]

Now, we have arrived back at the expression we had for [tex]\( x \)[/tex] earlier:

[tex]\( x = 1.5 \cdot \frac{1}{(1.05)^4} \).[/tex]

To find the numerical value of [tex]\( x \)[/tex], we can use the expression involving natural logarithms:

[tex]\( x = e^{\ln(1.5) - 4\ln(1.05)} \).[/tex]

This is equivalent to:

[tex]\( x = \frac{e^{\ln(1.5)}}{e^{4\ln(1.05)}} \),[/tex]

[tex]\( x = \frac{1.5}{1.05^4} \).[/tex]

Finally, to express [tex]\( x \)[/tex] as a single logarithm, we can use the change of base formula for logarithms:

[tex]\( x = \frac{\ln(1.5)}{\ln(1.05^4)} \),[/tex]

[tex]\( x = \frac{\ln(1.5)}{4\ln(1.05)} \).[/tex]

This is the correct expression for [tex]\( x \)[/tex] in terms of natural logarithms. The mistake in the original attempt was likely in the manipulation of the logarithms, where the properties of logarithms were not correctly applied. The correct step is to use the quotient rule of logarithms, [tex]\( \ln(\frac{a}{b}) = \ln(a) - \ln(b) \)[/tex], and the power rule, [tex]\( \ln(a^b) = b\ln(a) \)[/tex], to arrive at the correct expression for [tex]\( x \).[/tex]

Answer:74

Step-by-step explanation:

Since RP is 72, you would divide 72 by 2. The quotient you would get is 36. So then Q=38, you would add 36+38 and get 74.

Answer:

116.9FT

Step-by-step explanation:

Answer:

7/8

Step-by-step explanation:

Simplify the following:

(1 + 3/4)/2

Put 1 + 3/4 over the common denominator 4. 1 + 3/4 = 4/4 + 3/4:

(4/4 + 3/4)/2

4/4 + 3/4 = (4 + 3)/4:

((4 + 3)/4)/2

4 + 3 = 7:

(7/4)/2

7/4×1/2 = 7/(4×2):

7/(4×2)

4×2 = 8:

Answer:  7/8

Answer:

4π(2r)² = 4π(4r²) = 4(4πr²)

Doubling the radius of a sphere increases the surface area by a factor of 4.

The correct factor is 4. Doubling the radius of a sphere increases the surface area by a factor of 4.

To understand why the surface area increases by a factor of 4 when the radius is doubled, let's consider the formula for the surface area of a sphere, which is given by:

[tex]\[ A = 4\pi r^2 \][/tex]

where A is the surface area and [tex]\( r \)[/tex] is the radius of the sphere.

Now, if we double the radius, the new radius becomes [tex]\( 2r \)[/tex]. Substituting this into the formula for surface area, we get:

[tex]\[ A_{\text{new}} = 4\pi (2r)^2 \][/tex]

[tex]\[ A_{\text{new}} = 4\pi \cdot 4r^2 \][/tex]

[tex]\[ A_{\text{new}} = 16\pi r^2 \][/tex]

To find out how much the surface area has increased, we take the ratio of the new surface area to the original surface area:

[tex]\[ \text{Factor of increase} = \frac{A_{\text{new}}}{A} \][/tex]

[tex]\[ \text{Factor of increase} = \frac{16\pi r^2}{4\pi r^2} \][/tex]

[tex]\[ \text{Factor of increase} = 4 \][/tex]

Therefore, when the radius of a sphere is doubled, the surface area increases by a factor of 4.

Answer:

0.00132450331

Step-by-step explanation:

just divide lol

To solve 8 divided by 6040, perform the division, resulting in approximately 0.0013245.

To solve the problem of 8 divided by 6040, follow these steps:

Answer:

2h+3 Because they bought 2 hot dogs and h represents the amount they cost. And the 3 represents the drink he purchased

Final answer:

To factor the quadratic expression 8x² – 18x – 5 completely, one finds factors of the coefficient product (–40) that sum to the x coefficient (–18). These factors are -20 and +2, which are used to rewrite and group the middle term, allowing us to factor by grouping into (4x + 1)(2x – 5).

Explanation:

To factor the quadratic expression 8x2 − 18x − 5 completely, we need to find two binomials that when multiplied together give us the original quadratic expression. This process generally involves finding two numbers that multiply to give us the product of the coefficient of x2 term (8) and the constant term (-5) and also add to give the coefficient of the x term (-18).

The product of the coefficient of x2 and the constant term is -40 (8 × -5). We need to find factors of -40 that will add up to -18. After testing several combinations of factors, we see that -20 and 2 work since -20 + 2 = -18. Now we rewrite the middle term using these two numbers:

8x² − 20x + 2x − 5

Next, we group the terms to facilitate factoring by grouping:

=(8x² − 20x) + (2x − 5)

Now we factor out the common factors from each group:

=4x(2x − 5) + 1(2x − 5)

At this point, we have a common binomial factor (2x − 5) that can be factored out:

=(4x + 1)(2x − 5)

This is the expression factored completely.

Answer:

-1/3

Step-by-step explanation:

2/3 times -1 is -1/3

It is -2/3 or negative two thirds

Answer:A. 36

Step-by-step explanation:2x+16=×+20 x=4

4+8=12. 4+20=24

12+24=36

1. Collect like terms

(7x + 4x) + 2

2. Simplify

11x + 2

Answer:

25 and

9

Step-by-step explanation:

Let the number of males be A and that of females be B

Total number of students = 34

Number of females B = A - 16

Remember males and females = 34

That’s

A + B = 34

We now have two equations

Equation one:B = A - 16

Equation two: A + B = 34

Substitute A - 16 for B in equation 2

We have,

A + B = 34

A + A - 16 = 34

2A - 16 = 34

Add 16 to both sides

2A - 16 + 16 = 34 + 16

2A = 50

Divide both sides by 2

2A/2 = 50/2

A = 25

Now put 25 as A in any of the equations to get B

Using equation one , we have

B = A - 16

B = 25 - 16

B = 9

There are 25 males and 9 females in the class

Answer:

The correct answer is 32.5

Answer:

151 trays, 1 left over

Step-by-step explanation:

907/6 = 151 remainder 1

The Bake Stars could sell 151 trays of caramel apples with 1 apple left over.

The Bake Stars picked 907 apples and sold them in trays of 6.

To determine how many trays they can sell, divide the total number of apples by the number of apples in each tray:

907 apples / 6 apples per tray = 151 trays with 1 apple remaining (since 907 = 151 * 6 + 1).

Answer:10.68

Step-by-step explanation:

3.1 + 1.35 = 4.45 4.45 × 2.4 = 10.68

Answer:

10.68

Step-by-step explanation:

i worked it out on a piece of paper but this is my answer

The resulting coordinate of X is (0, -2)

Given the coordinate point X (-3, -2). If the coordinate is translated using the rule (x, y) = (x+3, y + 4), the resulting coordinate will be (-3+3, -2+4) = (0, 2)

In conclusion, the resulting coordinate of X is (0, -2)

Learn more on translation here: https://brainly.com/question/1046778

After translation and reflection, the coordinate of X" is (0, -2).

To find the coordinate of X" after a translation and reflection, we need to first apply the translation rule to point X (-3, -2). Using the rule (x, y) = (x+3, y + 4), we add 3 to the x-coordinate and add 4 to the y-coordinate:

x' = -3 + 3 = 0

y' = -2 + 4 = 2

After the translation, the new coordinates are (0, 2). To reflect over the x-axis, we change the sign of the y-coordinate, giving us the final coordinate of X" as (0, -2).

https://brainly.com/question/37212834

#SPJ3

Answer:

see explanation

Step-by-step explanation:

1

The area of a rectangle = length × width

2

To find the width, divide the area by the length

3

width = [tex]\frac{area}{length}[/tex] = [tex]\frac{3x^2+9x}{3x}[/tex]

To simplify divide each term on the numerator by 3x

= [tex]\frac{3x^2}{3x}[/tex] + [tex]\frac{9x}{3x}[/tex] = x + 3 ← width

Answer:

I think it is 8.5

Step-by-step explanation:

The height of the triangle is 8.5 feet

To find the height of a triangle when the area and the base are known, we use the formula Area = 1/2 x base x height, where A is the area, b is the base, and h is the height. Given that the area of the triangle is 93.5 square feet and the base measures 22 feet, we can rearrange the formula to solve for h: h = 2 × Area/Base

h = 2×93.5/22

h=187/22

h = 8.5 feet

Therefore, the height of the triangle is 8.5 feet.

Answer:

1 + 2i and 1 – 2i