So every week in my class we do a riddle and if you’re able to solve 3 of these correctly in a row you get a prize (homework pass, money or candy etc) and this would be my 3rd one correct in a row but I want to make sure my answer is right. Please help!

1. Collect like terms

(7x + 4x) + 2

2. Simplify

11x + 2

Answer:

1 + 2i and 1 – 2i

Answer:

-1/3

Step-by-step explanation:

2/3 times -1 is -1/3

It is -2/3 or negative two thirds

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

Answer:

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

5/4 is plotted 1 little tab right of 1

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:

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:

1

Step-by-step explanation:

Only 1 right angle can be in any triangle.

Answer:

The correct answer is 32.5

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:

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 true inequalities are √5 < 3, 2.2 < √5 < 2.3, and 3.6 > √13 > 3.7. The false inequalities are √8 > 3 and √13 = 3.6. The truth value of √8, √13 is inconclusive due to the incomplete expression. These comparisons highlight the relative magnitudes of square roots in the given range of numbers.

The given numbers √5, √8, and √13 can be compared using various inequalities to determine their relative magnitudes. First, √5 is less than 3, as √5 is approximately 2.24. However, √8 is not greater than 3, as it is approximately 2.83, rendering the second inequality false.

The inequality √8, √13 is incomplete, making it impossible to determine its truth value without a specific comparison operator. Moving on, √13 is not equal to 3.6; in fact, it is approximately 3.61, making the statement false.

On the other hand, the range-based inequality 2.2 < √5 < 2.3 holds true, as √5 is approximately 2.24, falling within the given range. Similarly, the range-based inequality 3.6 > √13 > 3.7 is true since √13 is approximately 3.61, falling within the specified range.

In summary, √5 < 3, 2.2 < √5 < 2.3, and 3.6 > √13 > 3.7 are true inequalities, while √8 > 3, √13 = 3.6, and √8, √13 are inconclusive or false based on the provided information. These comparisons highlight the relative sizes of square roots within the given numerical context.

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:

1,600,000

Step-by-step explanation:

100,000x2x2x2x2

Answer:160000

Step-by-step explanation:

,

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

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:

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

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:

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:

5v +30

Step-by-step explanation:

[tex]5(v + 6) \\ = 5v + 5 \times 6 \\ = 5v + 30[/tex]

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: 1 1/40.

Step-by-step explanation:

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

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Answer:A. 36

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

4+8=12. 4+20=24

12+24=36

Answer:

t>15

Step-by-step explanation:

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: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: