Fill in the blanks to correctly complete the sentence.To perform the division x-3)x³ + 6x² + 4x, begin by writing the synthetic division problem shown below.0)1040

[tex]t^3=-\cfrac{27}{343}\implies t^3=-\cfrac{3^3}{7^3}\implies t^3=-\left( \cfrac{3}{7} \right)^3\implies t^3=-\left( \cfrac{3}{7} \right)\left( \cfrac{3}{7} \right)\left( \cfrac{3}{7} \right) \\\\\\ t^3=+\left( -\cfrac{3}{7} \right)\left( -\cfrac{3}{7} \right)\left( -\cfrac{3}{7} \right) \implies t^3=+\left( -\cfrac{3}{7} \right)^3 \\\\\\ t^3=\left( -\cfrac{3}{7} \right)^3\implies t=-\cfrac{3}{7}[/tex]

In order to calculate the percent of one nurse over the other, we can divide both payments and then convert the result to a percentage value.

So we have:

Therefore the California nurse earns 122.22% of the Washington State nurse's pay.

So the volume of a cube is given by:

Where r is the length of its sides. By finding r we can find the length of the cube:

So the cube is 4 feet long.

Answer:

B,C,D:)

Step-by-step explanation:

i got 100%

Given three numbers x, y and z

The average of the numbers = A

We will complete the given table

When : x = 7 , y = 12 , z = 8

When x = 23 , y = 17 , z = 2

For the last case,

x = 4 , y = 11 , A = 6

Solve for z, multiply both sides by 3

[tex] \frac{2a + 6}{ 2{a}^{2} - 18} \\ = \frac{2(a + 3)}{2( {a}^{2} - 9)} \\ = \frac{a + 3}{(a + 3)(a - 3)} \\ = \frac{1}{a + 3} [/tex]

ATTACHED IS THE SOLUTION

Answer:

m∠FGD = 132°

Step-by-step explanation:

Corresponding Angles Postulate

When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.

Therefore, as AB is parallel to CD, and line EH intersects them:

⇒ m∠EFB = m∠FGD

Substitute the given expressions for the angles and solve for x:

⇒ (3x - 120)° = (x + 48)°

⇒ 3x - 120 = x + 48

⇒ 3x - 120 - x = x + 48 - x

⇒ 2x - 120 = 48

⇒ 2x - 120 + 120 = 48 + 120

⇒ 2x = 168

⇒ 2x ÷ 2 = 168 ÷ 2

⇒ x = 84

Substitute the found value of x into the expression for m∠FGD:

⇒ m∠FGD = (84 + 48)°

⇒ m∠FGD = 132°

The following are the options Victoria's been thinking of in installing a circular window in her basement.

a.) Three small windows, each with a 2 ft radius.

b.) One large window with a 4 ft radius.

Since Victoria wants to let in as much light as possible, she wants to use the option with the greater area.

We must determine which options have the greater area.

Let's

Answer:

Explanation:

We were given that:

SOLUTION

Since the rectangles are similar,

The ratio of their perimeter is thus

Ratio of their areas become

To solve find the percentage of people that said Spider-Man was their favorite superhero

We will simply write

=12%

Therefore; 12% of the people said Spider-Man was their favorite superhero

Answer: 3x16=48

Step-by-step explanation: Multiplying is just like adding multiple times, so this is 16x3, or adding 16 three times. 16+16+16=48 I hope this helps!

Answer:

First Solution: 8.5mL

Second Solution: 42.5 mL

Explanation:

Let us call x the number of mL of the first solution and y the number of mL of the second solution.

Now, from the fact that the final solution is 51 mL, we know that

Furthermore, from the fact that the final solution 40% carbonated water, meaning there are in total

of carbonated water in the love potion.

Now, the first solution contributes 15/100 * x mL of carbonated water in the solution whereas the second solution contributes 45/100 * y mL. Since all 20.4 mL of carbonated water in the solution is coming from solution 1 and 2, then it must be that

Thus we have two equations and two unknowns

We solve the above system by elimination.

First multiplying the second equation by 0.15 gives

which simplifies to give

Subtracting the first equation from the second gives

Finally, dividing both sides by 0.30 gives

With the value of y in hand, we now put it into x+ y = 51 and solve to x to get

subtracting 42.5 from both sides gives

Hence, to conclude the needed amounts of the solution are:

First Solution: 8.5mL

Second Solution: 42.5 mL

step 3 ------> distributive property of multiplication

step 5 ----> subtraction property of equality

step 2 ----> addition property of equality

step 1 ----> multiplication property of equality

step 4 ---> division property of equality

The correct order is

3-5-2-1-4

The explanation of the geometric shape known as an angle is made by three students. The matching answer is 1-1, 2-2,3-3.

Given that,

The explanation of the geometric shape known as an angle is made by three students.

We have to match the definitions to the teacher's comments.

Step1: definition of angle

Step2: teachers comments

1- Ruby's definition: The amount of turn between two straight lines that have a common vertex.

1-Bingo! you got it.

2-Shriya's definition: Two lines that come together.

2- Were you thinking of intersecting lines?

3- Abhishek's definition: A figure composed of two rays sharing a common endpoint. The common endpoint is known as vertex.

3-You seem to be getting at the idea of the measure of an angle,

not the definition of the angle itself.

Therefore, The matching answer is 1-1, 2-2,3-3.

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X E  (10,12]

Isolate the Variable by dividing each side by factors i.e 2 that don't contain the variable.

12<2x-8

6<x-4

10<x

Inequality Form:

x>10

Interval Notation:

(10,∞)

Isolate the variable by dividing each side by factors i.e 2 that don't contain the variable.

16>=2x-8

8>=x-4

12>=x

Inequality Form:

x≤12

Interval Notation:

(−∞,12]

Combining Both : X E  (10,12]

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They both together do the job is 6 hours.

It is given that Alain did the job in 10 hours.

We have to determined that how much time is take for Parc alone to do the job.

For this problem you have to derive the equation given:

If we derive y again we notice that y''=-36 that means that a maximum is reached for x=1, then the maximum height of the ball is

y= 18 feet

Given the general rule for the division of fractions:

in this case, we can use the formula in the following way:

therefore, the answer is 55/48

we make a ratio between the number of the selected snakes and the total of snakes

selected snakes

are 3 feet long or bright orange

4 are 3 feet long and 6 are orange, but 2 oranges are 3feet long too, then we count

Ben end up paying $3279.12 over the course of five years with rate of interest 5.5% for a principal of $2500.

In the question, we are given the following information:

P = $2500

r = 5.5% = 0.055

t = 5 years

n = 2

The compound interest is calculated as follows:

A = [tex]P(1 + r/n)^{nt}[/tex]

where A denotes the amount, p denotes the principal, r denotes the interest rate, t denotes the time in years, and n denotes the type of compound interest.

A= 2500( 1 + 0.055/2)¹⁰

  = 3279.12 ≈ $3279

A = $3279.12

Ben will end up paying $3279.12 at the end of 5 years for n = 2.

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Answer:

48

Step-by-step explanation:

40 yards /  10 quilts = 4 yards per quilt

12 * 4 = 48

Hope this helps.  

Answer:

48 yards

Step-by-step explanation:

Hey there!

To find the answer, we must first find how much yards of yarn she needs for 1 quilt

we do, 40/10 which is 4

Meaning, she needs 4 yards of yarn to make 1 quilt

Now we multiply 4 by 12 since we are making 12 quilts

4 x 12 = 48

So, Natalie needs 48 yards of yarn to make 12 quilts

The area of a circle is given by the following formula:

where r is the lenght of the circle's radius.

In this case, we have a radius of 12 units, so the area will be

We are however, asked to find the area of the shaded region, which is encased within a square. From the image we can see that the circle's radius is half the length of a side of the square. In other words, the square's sides measure 24 units.

The area of a square is given by

where s is the lenght of the sides of the square. In this case,

Now, in order to determine the area of the shaded region, we subtract the area of the circle from the area of the square:

So the area of the shaded region is 123.84 square units.

Answer:

Domain: A, [1, 7]

Range: A, [-4, 2]

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

Beacuse to both sides of the equation you distribute the number that is outside the parentheses when making the product.

Then, you operate on both sides of the equation -7x, that is, you use the additive inverse of 7x

Then, you operate on both sides of the equation 4, that is, you use the add inverse of -4

Finally,

Solution:

Let the cost of a tray of club sandwiches be s, and the cost of a tray of vegetarian sandwiches be v.

Then, the first order was for 6 trays of club sandwiches and 3 trays of vegetarian sandwiches at a cost of $75. We have;

Also, the second order was for 9 trays of club sandwiches and 9 trays of vegetarian sandwiches at a cost of $144. We have;

We would solve the two equation simultaneously, using elimination method.

Multiply equation 1 by 9 and equation 2 by 3.

Subtract equation 5 from equation 4. We have;

Substitute the value of s in equation 1. We have;

Thus;

FINAL ANSWER: A tray of club sandwiches costs $9, and a tray of vegetarian sandwiches costs $7

We are given the final value of the house after its price was increased by 24%

We must go back to the original price knowing the final price. It's called inverse percentage calculation

To calculate the 24% of the value, we multiply by 24 and divide by 100, that is

value * 24 / 100 = 0.24 * value

The original price of the house is 100%, the increase is 24%, thus the final value of the house is 100% + 24% = 124%

What we were given as data is 124% of the original price of the house

As we did above, to compute 124% of a value, we multiply by 124 and divide by 100. Being P the original price of the house, then the final value is

P * 124% = P * 124 / 100 = 1.24 * P

We know this value:

1.24 * P = $527,000

Divide by 1.24 both sides of the equation

P = $527,000 / 1.24 = $425,000

The original price of the house was $425,000

Let's check it out:

Original price: $425.000

Increase: 0.24 * 425,000 = $102,000

Final Price: $425,000 + $102,000 = $527,000

The condition is met and the question is answered

The general binomial theorem can be expressed as:

Now, for this problem we identify:

(a)

Then, using the general form:

(b)

The combination operator for this sum:

Then, the simplified terms of the expansion are:

We are given a set of data, 5, 12, 14, 19, 19, 21, 25, 29, 33

Firstly, we need to find the mean of the data

We have a line with slope -1 and y-intercept of 8.

We can write the equation of this line as:

Then, we can test the values for each x-coordinate and see if it matches the y-coordinate indicated by the point:

Point (3,5)

Point (2,10)

Answer: the point (2,10) is not on the line.