Which choice represents the fraction below as a single exponential expression?

8^2/8^16

a. 8^-12
b. 8^12
c. 1/4
d. 8^4

Answer:

100

Step-by-step explanation:

Answer:

1/5

Step-by-step explanation:

5y = x - 3

To find the slope of a line, we need to get the equation in the form y= mx+b where m is the slope and b is the y intercept

5y = x - 3

Divide each side by 5

5y/5   = x/5 - 3/5

y = 1/5 x - 3/5

The slope is 1/5 and the y intercept is -3/5

Answer:

1/5

Step-by-step explanation:

Answer:

[tex]g = \frac{48}{4}[/tex]

Step-by-step explanation:

[tex]Average = \frac{\text{Sum of all observations}}{\text{No. of observations}}[/tex]

[tex]Average = \frac{\text{Total score}}{\text{Total no. of games}}[/tex]

Since we are given that Dylan scored a total of 48 points in first 4 games of the basketball season.

So,[tex]Average = \frac{48}{4}[/tex]

Let the average be g

So, [tex]g = \frac{48}{4}[/tex]

Hence The equation can be used to find g, the average number of points he scores per game is [tex]g = \frac{48}{4}[/tex]

11. y - y₁ = m(x - x₁)

y - 4 = ²/₃(x - 3)

y - 4 = ²/₃x - 2

y = ²/₃x + 2

12. y - y₁ = m(x - x₁)

y - 0 = ⁻¹/₅(x - 5)

y - 0 = ⁻¹/₅x + 1

y = ⁻¹/₅x + 1

The correct equation for the given scenario is 38m + 150 = 3,000. Solving this equation, we find that it will take Paula approximately 75 minutes to finish her essay.

The question involves calculating how much time Paula needs to complete her essay based on her typing speed and desired essay length. Paula needs to write 3,000 words, but she already has 150 written. Therefore, she needs to write 3,000 - 150 = 2,850 more words. If she types at a rate of 38 words per minute, the number of minutes, represented as m, can be found using the equation 38m = 2,850. Therefore, the correct equation from the options is 38m + 150 = 3,000. Solving this equation for m gives m = 2,850 / 38 ≈ 75 minutes. Thus, option c) 38m + 150 = 3,000; m = 75 minutes is the correct answer.

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Given that the product of two numbers will be smallest when the two numbers are equal, the numbers closest to this rule given the condition of having a fixed difference of 44 are -22 and 22.

This problem falls under the branch of Mathematics called optimization problems in calculus. In this case, we are asked to find two numbers differing by 44 whose product is smallest. Remember that the product of two numbers that are a fixed difference apart will be smallest when the two numbers are equal. But since we can't have that according to the problem's conditions, we will have to get the closest possible which is making the two numbers as close to each other as possible.

Let's denote the smaller number as 'x'. Consequently, the larger number will be 'x + 44'. The product of these two numbers (which we want to minimize) is given by the function f(x) = x * (x + 44). To find the minimum, you would typically take the derivative of this function, set it equal to zero, and solve for 'x'. However, since we're dealing with a quadratic function, we know the graph is a parabola that opens upwards, and thus the minimum point is at the vertex. In a quadratic function given in the form of f(x) = a*(x - h)² + k, the vertex is at the point (h, k). Comparing this with our quadratic function, we can see by inspection that our 'h' is '-22'. Therefore, the two numbers are -22 and 22.

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The smallest product of two numbers differing by 44 is -484. These numbers are -22 and 22.

This problem is solvable using the principle of quadratic minimum. Let's denote the two numbers as x and x + 44. Their product equals x(x + 44) = x2 + 44x.

This is a quadratic function with a positive leading coefficient (x2), therefore, it will yield a minimum value. The x-value for this minimum can be found using the formula -b/2a for any quadratic ax2 + bx + c, where a = 1 and b = 44. Calculating, -b/2a = -44/2 = -22.

This means that the product will be smallest when x = -22. However, since we're looking for two numbers that differ by 44, the necessary pairs are -22 and 22. The product of these two numbers, (-22)(22), equals -484, which is indeed the smallest possible product for two numbers differing by 44.

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Since b = c, the angles B and C also equal

 so you get
180 - 45 = 135
135/2 = =67.5 for each angle

now we know 2 sides and all 3 angles, use the law of sines to find a

b/sin B = a/sin A

4/(sin 67.5) = a/(sin 45)

a = 4(sin 45)/(sin 67.5)

a^2 = (4(sin 45)/(sin 67.5))^2

a^2 = 9.37

 Answer is C

Jesse’s annual premium would be $175.50. The correct option is A.

An annual premium is the amount of money paid by an insurance policyholder each year in order to keep their coverage.

It is usually paid all at once, but it can also be paid in installments throughout the year.

The amount of the premium is determined by factors such as the type of insurance, the level of coverage, and the policyholder's risk profile.

The face value of the policy is $75,000. Since the annual premium rate is $2.34 per $1000 of face value, the annual premium Jesse would have to pay is:

$75,000 / $1000 = 75

75 x $2.34 = $175.50

Therefore, Jesse’s annual premium would be $175.50. The correct option is a.

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Answer:

7.

Step-by-step explanation:

2/5x -3

If we plug in 25, we get:

2/5(25) - 3 =

50/5 - 3 =  

10 - 3

7

Answer:

[tex]base=\frac{4x+16}{height}[/tex]   which is the required expression.

Step-by-step explanation:

We have been given the area of parallelogram which is (4x+16)

And the formula for area of parallelogram is [tex]base\cdot height[/tex]

Hence, when we substitute the value if area of parallelogram in the formula we get:

[tex]4x+16=base\cdot height[/tex]

Now, rearranging the terms so, as to get the expression for the base or value of base in terms of height and area we get:

[tex]base=\frac{4x+16}{height}[/tex]   which is the required expression.

Reflexive Property of Congruence justifies the following statement ∠AOB ≅ ∠AOB. Option B is correct.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,
∠AOB ≅ ∠BOB
It can be obtained, only by when the angle gets reflected.
So by the reflexive Property of Congruence justified.

Thus, the reflexive Property of Congruence justifies the following statement ∠AOB ≅ ∠AOB. Option B is correct.

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