Which is the correct simplified version ofthe expression -7(2x - 3)?a. - 14x + 21b. - 14x - 21c. -5x – 10d. -14% - 10

[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]

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

The height of the object based on the information is 1963 feet.

It should be noted that a function is important to show the relationship between the variables given in the data.

In this case, the function given for the height of the object is given as:

h = 16t² + 1899

where t = time

When the time is 2 seconds, the height will be:

h = 16t² + 1899

h = 16(2)² + 1899

h = 64 + 1899

h = 1963

The height is 1963 feet.

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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

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.

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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[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

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%

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

SOLUTION

Since the rectangles are similar,

The ratio of their perimeter is thus

Ratio of their areas become

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

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

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.

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.

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:

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

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

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.

Answer:

Explanation:

We were given that:

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

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 correct combination of vectors is:

This comes from the fact that we need to multiply the x component by i and the y component by j.

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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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.

The value of x based on the multiplication in 90 × x = 9000 is 100.

Multiplication simply means the product of numbers given. This is illustrated with the sign given as ×.

In this case, 90 × x = 9000

Multiply 90 by x which equates to 9000

90x = 9000

Divide by 90

90x / 90 = 9000 / 90

x = 100

The value of x is 100.

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Answer: 62.33

The ratio of the real length to the shadow is 6:11. to make the first ratio 34 then I could multiply both sides by 34/6 which would make 34:374/6. When 374 is divided by 6 it equals 62 1/3 which also equals 62.33333... Then I would round it to 62.33.

Step 1

Given;

Required; To simplify the question.

Step 2

Answer;

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

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