find the product of quotient using only positive exponents

The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. The correct option is B.

The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. It is given by the formula,

\(c =\sqrt{a^2 + b^2 -2ab\cdot Cos\theta}\)

where

c is the third side of the triangle

a and b are the other two sides of the triangle,

and θ is the angle opposite to the third side, therefore, opposite to side c.

The length of the sidelink b using the cosine rule can be written as,

\(b = \sqrt{a^2+c^2-2ac\cos(\angle B)}\\\\b = \sqrt{4^2+5^2 - 2(4)(5)(\cos 60^o)}\\\\b = \sqrt{16+25-20}\)

Hence, the correct option is B.

The complete question is:

Consider ABC with the measure of angle B equal to 60 degrees, and side lengths a=4 and c=5. Which option lists an expression that is equivalent to the length of side b?

Options are given in the image below.

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the new coordinates of the triangle MNP will be  M'(4, -2), and N' (8, -6). P'(2, -6).

Horizontal translation: g(x)=f(x+c).

The graph is translated c units to the left if c>0 and c units to the right if c<0. Vertical translation: g(x)=f(x)+k.

The graph is translated k units upward if k>0 and k units downward if k<0.

Given, Graph the image of ΔMNP after a dilation with a scale factor of 1/2 centered at the origin.

The origin (0, 0) is the center of dilation in the coordinate plane.

Given, MNP is a triangle in the coordinate plane. The points in the coordinate planes are M(4, -2), N (8, -6). P(2, -6)

If the scale factor is 1/2, then every coordinate point of the original triangle is multiplied by the scale factor 1/2.

Therefore, the dilated triangle will be A’B’C’ and the coordinate points obtained are  M(2, -1), N (4, -3). P(1, -3)

Dilation with scale factor 2, then multiply by 2.

(x, y) → (2x, 2y)

Therefore, the new coordinates of the triangle MNP will be  M'(4, -2), and N' (8, -6). P'(2, -6).

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Answer: B

Step-by-step explanation:

Answer:

Step-by-step explanation:

If Robert is 7 1/2 months old you need to multiply 7 1/2 by 12 because there are 12 months in a year.  

7x12=84  

1/2x12=6

6+84=90

The total volume is the one in option C, 708 cubic centimeters.

We know that this prism can be divided into two prisms, and remember that the volume of a prism is equal to the product between its dimensions.

Then the volume of the first prism is:

V = 8cm*6cm*13cm = 624 cm³

And the volume of the second prism is:

v' = 3cm*4cm*7cm = 84 cm³

Adding that we will get:

total volume =  624 cm³+  84 cm³ = 708 cm³

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Answer:

90% probability that she has at least one marble of each color

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the marbles are selected is not important. So we use the combinations formula to solve this question.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

What is the probability that she has at least one marble of each color?

Desired outcomes:

Two red(from a set of 2) and one yellow(from a set of 3)

Or

One red(from a set of 2) and two yellows(from a set of 3).

So

\(D = C_{2,2}*C_{3,1} + C_{2,1}*C_{3,2} = \frac{2!}{2!(2-2)!}*\frac{3!}{1!(3-1)!} + \frac{2!}{1!(2-1)!}*\frac{3!}{2!(3-2)!} = 3 + 6 = 9\)

Total outcomes:

Three marbles, from a set of 3 + 2 = 5. So

\(T = C_{5,3} = \frac{5!}{3!(5-3)!} = 10\)

Probability:

\(p = \frac{D}{T} = \frac{9}{10} = 0.9\)

90% probability that she has at least one marble of each color

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

Answer:

the driver tried to fix it by lighting up the engine thinking it would start again. it didnt and the entire engine set on fire. the bus doors were closed and everyone was trapped inside. everybody inside burnt to a crisp as the fire spread and local residents heard their screams as their skin melted. the end...

number one take the second

Answer:

4.85 ÷ 5 = 0.97

hope this helps

Therefore, the quotient when x³ - x² - 3x + 2 is divided by x - 2 is x² - 2x - 5 with a remainder of -3.

To find the quotient when x³ - x² - 3x + 2 is divided by x - 2, we will use the long division method. Here is the solution:  

Step 1: The first term of the quotient is x². Multiply x² by x - 2 to get x³ - 2x². Subtract this product from x³ - x² to get: x² - 3x² = -2x²

Step 2: Bring down the next term of the dividend, which is -3x. The new dividend is -2x² - 3x.

Step 3: The second term of the quotient is -2x. Multiply -2x by x - 2 to get -2x² + 4x. Subtract this product from -2x² - 3x to get -5x.

Step 4: Bring down the last term of the dividend, which is +2. The new dividend is -5x + 2. Step 5: The third term of the quotient is -5. Multiply -5 by x - 2 to get -5x + 10. Subtract this product from -5x + 2 to get -3.

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If principal is $2,658 and rate of interest 9% then the value of  the account balance is approximately $10,253 by using continuous compound interest formula.

Recurring interest is interest calculated on principal plus all interest and other interest. The idea is that lenders always receive interest, not individually at specific times.

The formula for continuous compound interest :

  A=    Peˣⁿ                          

Where,

A =Amount of money  after a certain amount of time

P= principal or the amount of money you start with

e =Napier's number, which is approximately 2.7183

x =Interest rate

n =Amount of time in years.

Use the continuous compound interest formula :

Given  P= 2658

x =9% =   = 0.09

n = 15

e = 2.7183

By using

A=    Peˣⁿ  

A= (2658)(2.7183)⁰°⁰⁹¹⁵

A =10,253 (approximately)

Hence, the value of account balance after 15 years is approximately $10,253

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Answer:

y = x + 1

Step-by-step explanation:

Parallel lines have same slope.

y = x - 1

Compare with the equation of line in slope y-intercept form: y = mx +b

Here, m is the slope and b is the y-intercept.

m =1

Now, the equation is,

         y = x + b

The required line passes through (-3 ,-2). Substitute in the above equation and find y-intercept,

        -2 = -3 + b

  -2 + 3 = b

         \(\boxed{b= 1}\)

    Equation of line in slope-intercept form:

                  \(\boxed{\bf y = x + 1}\)      

The equation is :

Solution:

If two lines are parallel to each other, then their slopes are equal. The slope of y = x - 1 is 1. Hence, the slope of the line that is parallel to that line is 1.

We shouldn't forget about a point on the line : (-3, -2).

I plug that into a point-slope which is :

\(\sf{y-y_1=m(x-x_1)}\)

Slope is 1 so

\(\sf{y-y_1=1(x-x_1)}\)

Simplify

\(\sf{y-y_1=x-x_1}\)

Now I plug in the other numbers.

-3 and -2 are x and y, respectively.

\(\sf{y-(-2)=x-(-3)}\)

Simplify

\(\sf{y+2=x+3}\)

We're almost there, the objective is to have an equation in y = mx + b form.

So now I subtract 2 from each side

\(\sf{y=x+1}\)

Answer: you’re welcome

Step-by-step explanation:

The probability for the given case is ⁰C₈(0.8)⁸(0.3)². The correct option is (c).

The binomial distribution is based on the binomial theorem which can be written as (a + b)ⁿ = ⁿC₀aⁿb⁰ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b²+ ....+ ⁿCₙa₀bⁿ.

In order to use in the probability, there should be events independent of each other and the sum of there probabilities is 1.

Given that,

The probability of making free-throw is 70% = 70/100 = 0.7

Then, the probability of not making free-throw is 1 - 0.7 = 0.3.

The exact 8 free-throws out of 10 implies that there will be 2 throws that are not free.

So, this case belongs to the binomial distribution which can be written as,

ⁿCₓpˣqⁿ⁻ˣ, where p is the probability of success and q is the probability of failure, n is the total number of trials and x is the number of favorable trials.

Now, in order to find the probability of exact 8 free-throws out of 10 can be found using binomial distribution as follows,

P (exact 8 throws) = ¹⁰C₈(0.8)⁸(0.3)²

Hence, the probability of getting exact 8 free-throws out of 10 is  ¹⁰C₈(0.8)⁸(0.3)².

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Answer:

Step-by-step explanation:

area of a triangle = 1/2 base * height

where area = 10 units²

        height = x units

          base = 4

plugin values into the formula:

10 = 1/2 * 4 * x

x = 10 (2)

        4

x = 5 units

Answer:

it is too blury to read

Step-by-step explanation:

1) All of these questions are about evaluating those functions for each input.

9) So, let's check them out evaluating each one.

10)

11)

12)

Answer:

2

_

3

Step-by-step explanation:

i think at least hopefully

Answer:

24°

Step-by-step explanation:

For an n-sided regular polygon, the sum of internal angles = (n-2)×180°

Since all internal angles are equal, the internal angle can is given as:

Here, it is given that the polygon has 15 sides.

So n = 15

So each internal angle is 156°.

Internal and external angles are always supplementary. So the sum of the internal and external angles is 180°.

So external angle = 180° - 156° = 24°.

The measure of each external angle is 24°.

=============================================================

Explanation:

Let's say the shed comes in 40 equal pieces. Each piece takes the same amount of time to assemble. Why am I picking 40? Because 8*5 = 40.

This will allow us to rewrite the fractions with a common denominator.

So Jack can build 8/40 of the shed in the same amount of time Kyle can build 25/40 of the shed.

Instead of writing fractions (which honestly are a pain to deal with), I'm going to write "8 pieces" and "25 pieces" to represent "8/40" and "25/40" respectively. Just keep in mind that there are 40 pieces total.

So again, Jack can assemble 8 pieces in the time it takes Kyle to assemble 25 pieces.

---------------

The ultimate goal is to have Kyle assemble 40 pieces while Jack puts together some unknown number of pieces (some number between 8 and 40). Let's say it's x.

We can then form this proportion

\(\frac{\text{Jack's initial 8 pieces}}{\text{x pieces}}=\frac{\text{Kyle's initial 25 pieces}}{\text{goal of 40 pieces}}\)

which simplifies or cleans up to

5/x = 25/40

-----------------

Let's solve for x using cross multiplication

8/x = 25/40

8*40 = x*25

320 = 25x

25x = 320

x = 320/25

x = 12.8

So in the time it takes Kyle to assemble all 40 pieces, Jack can put together 12.8 pieces of the shed. However, we can't have Jack put together some fractional piece, because each "piece" is as small as it gets. We can't get any smaller. It would be like saying a fractional part of an atom or a lego block.

So we'll round 12.8 down to 12.

Jack can assemble 12 pieces in the time it takes Kyle to assemble 40 pieces.

Let's then convert this back to fraction form

12 pieces = 12/40 of a shed = 3/10 of a shed.

Answer:

-2

Step-by-step explanation:

\(3x^2 + x -2x^3 -10 \\\\3x^2 + x + (-2)x^3 + (-10)\)

Answer:

-2.

Step-by-step explanation:

-2x^3 is the third degree term.

Answer:

x =45

Step-by-step explanation:

This is a parallelogram with opposite sides that are parallel and equal in length. Let's label the points as A, B, C, and D, where AB and CD are parallel and equal in length, and AD and BC are parallel and equal in length.

Let's draw a diagonal of the parallelogram, such as AC. We can see that this diagonal divides the parallelogram into two congruent triangles, ∆ABC and ∆ACD.

Since opposite sides of a parallelogram are parallel, we know that the angles ∠ABC and ∠ADC are equal because they are corresponding angles. Similarly, we know that the angles ∠ACB and ∠CAD are equal because they are corresponding angles.

Let's call the measure of each of these angles x. Since the sum of the angles in a triangle is 180 degrees, we know that:

x + x + 90 = 180

Simplifying this equation gives:

2x + 90 = 180

Subtracting 90 from both sides gives:

2x = 90

Dividing both sides by 2 gives:

x = 45

Therefore, each of these angles has a measure of 45 degrees.

Since opposite angles of a parallelogram are equal, we know that the measure of each of the angles ∠BAD and ∠BCD is also 45 degrees. Therefore, we have shown that all four angles of the parallelogram are equal, and each has a measure of 45 degrees.

Answer:

\(600, 900, 1350\)

Step-by-step explanation:

Given

\(a = 400\) -- initial subscribers

\(b = 1.5\) -- growth factor

Required

Determine the number of subscribers in the next three months

To do this, we make use of:

\(y = ab^x\)

In this case:

x is the number of months

y is the number of subscribers

So:

when x = 1;

\(y = ab^x\)

\(y = 400 * 1.5^1\)

\(y = 400 * 1.5\)

\(y = 600\)

when x = 2

\(y = 400 * 1.5^2\)

\(y = 400 * 2.25\)

\(y = 900\)

when x= 3

\(y = 400 * 1.5^3\)

\(y = 400 * 3.375\)

\(y = 1350\)

So, the next three number of subscribers is:

\(600, 900, 1350\)

Answer:

192 is the answer

Step-by-step explanation:

Answer:

SA = 272 sq in

Step-by-step explanation:

SA = 2(8 x 2) + 2(8 x 12) + 2(2 x 12)

= 2(16) + 2(96) + 2(24)

= 32 + 192 + 48

= 272 sq in

The direct labor cost included in the Preble Company's flexible budget for March is $819,000.

To find the direct labor cost included in the company's flexible budget for March, we shall estimate the actual direct labor cost incurred during the period.

Given:

Actual production and sales =n26,600 units

Actual direct labor rate = $13.00 per hour

Actual direct labor hours worked = 63,000 hours

Direct labor cost = Actual direct labor rate × Actual direct labor hours worked

Direct labor cost = $13.00/hour × 63,000 hours

Direct labor cost = $819,000

Hence, the direct labor cost included in the company's flexible budget for March would be $819,000.

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Answer:

Answer:

1

Step-by-step explanation:

The GCF of 15 : 1, 3, 5, 15

The GCF of 647 : 1, 647

The only GCF that was on both lists was 1