if the area of a rectangle is x^2-9 and one dimension is x-3. what would be the other dimension?

The original height  of the water in a pool is 5 ft , Option B is the correct answer.

An equation can be defined as a mathematical statement when two algebraic expressions are equated using an equal sign.

It is given in the question that

A leak in a pool causes the height of the water to decrease by 0.25 foot over 2 hours.

the height of the water is 4.75 feet.

The equation

4.75 = x + (negative 0.25)

can be used to find x, the original height of the water in a pool.

4.75 = x - 0.25

x = 5

Therefore the original height  of the water in a pool is 5 ft , Option B is the correct answer.

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Answer:

B

Step-by-step explanation:

A mathematically indication example would be to solve the equation 3x + 2 = 14 for the value of x. The solution would be 4.

Looking for a mathematically indication example, we can consider a simple mathematical equation with one variable and solve it.

The equation would be 3 x + 2 = 14.

So we can solve for the equation to be :

3x + 2 - 2 = 14 - 2

3x = 12

3 x / 3 = 12 / 3

x = 4

In conclusion, the mathematically indication example would be 3x + 2 = 14 and the value of x would be 4.

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just deal with the power of the x , multiply and simplify

\(( { {x}^{ \frac{3}{2} }})^{6} = {x}^{ {9} } \)

Answer:

29

Step-by-step explanation:

Answer:

The answer is 29

The practical domain of the situation is [0, ∞].

The practical range of the situation is [0, 100].

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [0, ∞] or 0 ≤ x ≤ ∞.

Range = [0, 100] or 0 ≤ y ≤ 100.

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3. The factored polynomial is p(x) = (x - 1)(x - 5)

4. The factored polynomial is p(x) = (x + 3)²

A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.

3. To factorize the polynomial using the graph, we see that the polynomial cuts the x - axis at x = 1 and x = 5.

This implies that its factors are (x - 1) and (x - 5)

So, the factored polynomial is p(x) = (x - 1)(x - 5)

4. To factorize the polynomial using the graph, we see that the polynomial touches the x - axis at only one point x = -3. So,it has repeated roots

This implies that its factors are (x - (-3)) = (x + 3) twice

So, the factored polynomial is p(x) = (x + 3)²

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Answer:

31 days

Step-by-step explanation:

155/5=31

Answer: 31

Step-by-step explanation:

155 divided by 5 equals 31

Answer:

28 days

Step-by-step explanation:

Day 1  = 3 m,  day 1 end = 3 - 1 = 2 m

Day 2 end = 2 + 3 -2 = 3m

Day3 end = 3 + 3- 2 = 3 +1 = 4m

On 27th day end = 26+ 3 - 2 = 27 m

On 28th day =27 + 3 = 30 m

Answer

The client would make a call of 400 minutes for the cost of the two plans to be equal

Step-by-step explanation:

Let C be the cost

Let x be the number of minutes of call

For the first plan

The company charge $0.18 for each minute

Let the total cost

C = 0.18 * x

C = 0.18x -------------- equation 1

The second plan

The second plan has a monthly charge of $20 and an additional $0.13 for each minute call

C= 20 + 0.13 * x

C = 20 + 0.13x -------------------- equation 2

To know the number of minutes that will make the cost of the plan equal, then, we need to combine the two equations

0.18x = 20 + 0.13x

Subtract 0.13x from both sides

0.18x - 0.13x = 20 + 0.13x - 0.13x

0.05x = 20

Isolate x by dividing through by 0.05

0.05x / 0.05 = 20/0.05

x = 400 minutes

Hence, the client would make a call of 400 minutes for the cost of the two plans to be equal

Answer:

3y(2x-1)(x-4y)

Step-by-step explanation:

Apply exponent rule:

6x^2y-3xy-24xyy+12yy

Rewrite 12 as 4*3

Rewrite -24 as 8*3

Rewrite 6 as 2*3

2*3x^2y-3xy+8*3xyy+4*3yy

Factor out common term 3y:

3y(2x^2-x-8xy+4y)

Factor 2x^2-x-8xy+4y:

3y(2x-1)(x-4y)

Your Answer Is 3y(2x-1)(x-4y)

Answer:

40=x x h

Step-by-step explanation:

The rate of change in the total amount charged with respect to the time spent on the service call is $40 per hour.

The mathematical concept of rate of change describes how much one quantity changes in relation to another. It is calculated as the difference between the change in the output (the dependent variable) and the change in the input (independent variable).

The rate of change, in other words, informs us of how quickly or slowly something is changing through time or in relation to another variable. When tracking the distance an automobile travels over time, for instance, the rate of change would be the car's speed, which is calculated as the distance traveled divided by the time required.

Slope, which is the ratio of the vertical change (rise) to the horizontal change (run) between two points on a graph, is a common way to depict the rate of change. The rate of change of the dependent variable with respect to the independent variable is depicted by the slope of a straight-line graph.

The rate of change in the total amount charged with respect to the time spent on the service call represents the slope of the graph. We can find the slope of the graph by taking any two points on the line and calculating the change in y (total amount) divided by the change in x (time spent on the service call).

Looking at the graph, we can choose two points: (2, 130) and (8, 370). The change in y is:

370 - 130 = 240

And the change in x is:

8 - 2 = 6

Therefore, the slope (rate of change) of the graph is:

240/6 = 40

So the rate of change in the total amount charged with respect to the time spent on the service call is $40 per hour.

Therefore, the correct option is $40 per hour.

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Step-by-step explanation:

-6 = 2/9 x

2/9x = -6

x = (-6)×9/2

= -27

Answer:

3/9

Step-by-step explanation:

The gallons of a 80​% antifreeze solution must be mixed with 70 gallons of ​25% antifreeze to get a mixture that is ​70% ​antifreeze is  x=315

Use a weighted average........ let x = an unknown number of gallons of the 80​% solution.

then     {x(80​%) + 70 (25%)}/{x +70} =70% ​

{x*\(\frac{80}{100}\) + 70*\(\frac{25}{100}\)}/{x +70} =70% ​

{\(\frac{4x}{5}\) +17.50}/{x +70} =70% ​

\(\frac{4x+87.5}{5x+350}\) = \(\frac{70}{100}\)

40x+875 = 35x + 2450

40x-35x = 2450-875

5x = 1575

x=315

Keep in mind that the substance with the highest concentration is the solvent.

There are numerous varieties of solutions. A solute, for instance, could be a gas, a liquid, or a solid. Additionally, solvents can be solids, liquids, or gases.

The behavior of several types of solutions at the microscopic level is depicted in the following illustrations. You'll see that the solute particles are evenly spaced out among the solvent particles in each instance.

A solution is a homogeneous mixture of one or more solutes dissolved in a solvent. solvent: the substance during which a solute dissolves to produce a homogeneous mixture. solute: the substance that dissolves during a  solvent to produce a homogeneous mixture. The solute is the substance that is being dissolved, while the solvent is the dissolving medium. Solutions are often formed with many different types and forms of solutes and solvents.

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Equation of the line

The equation of a line can be expressed in slope-intercept form as follows:

y = mx + b

Where m is the slope of the line and b is the y-intercept.

We are given the equation of a line:

y = -5x + 3

This line as a slope of m=-5 and the intercept with the y-axis is y=3

We are required to find the equation of another line that is parallel to the given line. Parallel lines have the same slope. Thus the slope of our new line is also m=-5.

We are also given the y-intercept of the new line (0,4). This means the value of b is 4.

Knowing the values of m and b, we can write the equation of the required line as:

y = -5x + 4

Answer:

Yes 4/5 is greater than 2/3

Step-by-step explanation:

Because

4/5 = 0.8

2/3 = 0.667

Then, we compare the two decimal numbers to get the answer.

0.8 is greater than 0.667.

Therefore, 4/5 is greater than 2/3 and the answer to the question "Is 4/5 greater than 2/3?" is yes.

Answer:

Step-by-step explanation:

is the base of the triangle 30?

To fins the linear equation you shoul use two of the points to find the slope

a=(-2,6) b=(4,9)

and use the formula for the slope in this way

after you have the slope you can use whichever point you want to find b

y=mx+b

lets use point (-2,6)

the equation should be

to check if the answer is correct we can replace in the equation with one of the point; lets use (-4,5)

with this we can conclude the equation is correct.

3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

To express 3 1/2 cups as a multiplication expression using the unit "1 cup" as a factor, you can write it as:

3 1/2 cups = (3 + 1/2) cups = 3 cups + 1/2 cup

Since there are 1 cup in each term, we can rewrite it as:

3 cups + (1/2) cup

Now, we can express each term as a multiplication expression:

3 cups = 3 * 1 cup = 3

(1/2) cup = (1/2) * 1 cup = 1/2

Putting it all together, the multiplication expression is:

3 * 1 cup + (1/2) * 1 cup = 3 + 1/2

Therefore, 3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

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The angle PMR in the quadrilateral is 32 degrees.

The angle PMR can be found as follows;

The line AP is an angle bisector of angle RPM. Therefore, the following relationships are formed.

∠RPM ≅ ∠WPM

Hence,

∠RPM ≅ ∠WPM = 58 degrees

Therefore,

∠WPM = 58 degrees

∠PWM = 90 degrees

Let's find ∠PMR as follows

∠PMR = 180 - 90 - 58

∠PMR = 90 - 58

∠PMR  = 32 degrees

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Answer:

Option 4

Step-by-step explanation:

Area of a trapezoid = \(\frac{1}{2}(b_1+b_2)h\)

Here, \(b_1\) and \(b_2\) are the bases and 'h' is the height between the bases.

Area of the composite figure = Area of two trapezoids given

                                                = \(\frac{1}{2}(12+12)14+\frac{1}{2}(25+31)11\)

                                                = \(\frac{1}{2}(24)(14)+\frac{1}{2}(56)(11)\)

                                                = 168 + 308

                                                = 476 square ft

Option 4 is the answer.

The probability that a simple random sample of 50 unemployed individuals will provide a sample mean within 1 week of the population mean is 0.92

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Let X the random variable that represent the avergae number of weeks an individual is unemployed of a population, and for this case we know the distribution for X is given by:

X = N(17.5)

Where μ = 17.5 and σ = 4

Since the distribution for X is normal then, the distribution for the sample mean  is given by:

X = N(17.5, σ/√n)

X =N(17.5.4/√50) = 0.566

We select a sample of n =50 people. And we want to find the following probability

P(16.5 < X < 18.5) = P((16.5 -17.5)/(4/√50) < Z < (16.5 -17.5)/(4/√50) )

And using the normal standard table or excel we find the probability:

P(-1.768 < Z 1.768) = P(Z < 1.768) - P(Z< -1.768) = 0.961 - 0.039 = 0.92

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Step-by-step explanation:

Look at the points  (0,-3)  and  ( 3,0)

slope,  m = rise / run =   3 / 3 =  1  

Answer:

1

Step-by-step explanation:

y=x+3

Answer:

True

Step-by-step explanation:

Supplementary angles always equal to 180 degrees, and the sum of 130 and 50=180 degrees.