Factor the expression using the GCF 7+14

Answer:

i'd say D

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

The difference between the largest and smallest geometric numbers is 840.

Assume that the largest geometric number starts with a 9.

We know that the common ratio must be a rational of the form k/3 for some integer k, because a whole number should be attained for the 3rd term as well. When k = 1, the number is 931.

When k = 2, the number is 964. When k = 3, we get 999, but the integers must be distinct.

By the same logic, the smallest geometric number is 124.

The largest geometric number is 964 and the smallest is 124. Thus the difference is 964 - 124 = 840.

Hence, the difference between the largest and smallest geometric numbers is 840.

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At the instant when the diameter of the dam is 20 m and the water level is 6 m, the rate at which the volume of water in the dam is changing is approximately 8.948 cubic meters per hour.

To determine the rate at which the volume is changing, we need to use the given formula and calculate the derivatives with respect to time. Let's denote the volume as V, the diameter as d, and the water level as h. The formula for the volume of water in the dam is V = 2πh^2(3d - 3h).

We are given that the water level is increasing at a rate of 0.06 m/hr, which means dh/dt = 0.06 m/hr. Additionally, the diameter is increasing at a rate of 0.25 m/hr, which gives us dd/dt = 0.25 m/hr.

We need to find dV/dt, the rate at which the volume is changing. To do this, we can apply the chain rule of differentiation. Taking the derivative of V with respect to time, we have:

dV/dt = (dV/dd) * (dd/dt) + (dV/dh) * (dh/dt)

Now, let's calculate the partial derivatives. Taking the derivative of V with respect to d, we get:

dV/dd = 2πh^2(3 - 3h)

And taking the derivative of V with respect to h, we get:

dV/dh = 2πh(6d - 6h)

Substituting the given values of d = 20 m and h = 6 m into the expressions for dV/dd and dV/dh, we can evaluate these partial derivatives. Plugging in the rates of change dh/dt = 0.06 m/hr and dd/dt = 0.25 m/hr, we can now calculate dV/dt:

dV/dt = (2π(6^2)(3(20) - 3(6)) * 0.25 + (2π(6)(6(20) - 6(6)) * 0.06

Simplifying this expression yields dV/dt ≈ 8.948 cubic meters per hour. Therefore, the rate at which the volume is changing at the instant when d = 20 m and h = 6 m is approximately 8.948 cubic meters per hour.

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The factor of the given expression 2x²+13x+15 will be (2x+3)(x+5).

To express equivalent expressions of some expressions, we can either make it look more complex or simple. Usually, we simplify it.

We need to factor the expression into an equivalent form 2x²+13x+15

This expression could also be given by;

2x²+13x+15

We know that if D≥0, then trinomial 'ax²+bx+c' can be written in form a(x-x1)(x-x2),

where x1 and x2 - roots of ax²+bx+c=0.

Then D=b²-4ac=13²-15*2*4=49,

2x²+13x+15

Factor =2(x+5)(x+1.5)

The answer is: (2x+3)(x+5).

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Answer: D) -20.99

Step-by-step explanation:

-4.97-2.36+-5.19-8.47 = -20.99

Answer:

I think no. Because degree is the sum all variables in first equation degree. Is14 but second equation degree not 14.

Answer:

10

Step-by-step explanation:

32 - 12 (because C is 12 years younger) = 20

20 / 2 (because twice Anna's age, so we do the inverse) = 10

Anna is 10 years old.

Hope this helps!

Answer:44

Step-by-step explanation:

a. For the conversion, the chief should multiply 8 by 5,280 to convert the 8 miles to feet. The Option C is correct

b. It will take the crew 440 minutes to paint 8 miles.

One mile is equal to 5280 feet. So, to convert our miles to feet, we need to multiply the length or distance in miles times 5280.

To convert miles to feet, the chief should multiply number of miles by the conversion factor of 5,280 feet per mile.

The measurement in feet will be:

= 8 miles * 5,280 feet/mile

= 42,240 feet.

B. If the crew can paint 96 feet in one minute, we will use unit rate of feet per minute to determine how long it will take to paint 42,240 feet which is:

= 42,240 feet /96 feet

= 440 minutes.

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Answer:

Step-by-step explanation:

Given the question

A rope is 24 feet long. It is cut into two pieces such that one piece is half the length of the other. Find the lengths of the two pieces of rope.

Options

The stated solution is correct (lengths of 16 feet and 8 feet).

Based on the way the variable is defined, the equation should be x + 2x = 24.

The equation is written correctly, but there is an error in solving the equation.

The way the variable is defined, and because x=16, the longer piece of rope would be 32 feet, which is not possible.

2

Let the length of one piece be x (shorter piece) and the other be y.

If the rope is cut into two pieces and 24ft long, then;

x+y = 24.......... 1

If one piece is half the length of the other, then x = y/2..... 2

substitute equation 2 into 1

y/2 + y = 24

take the LCM

y+2y/2 = 24

3y/2 = 24

cross multiply

3y = 48

Divide both sides by 3;

3y/3 = 48/3

y = 16 feet

Since x = y/2

x = 16/2

x = 8 feet

Based on the calculation above, I can conclude that;

- The student stated solution is correct (lengths of 16 feet and 8 feet)

- The way the variable is defined, and because x=16, the longer piece of rope would be 32 feet, which is not possible.

- Based on the way the variable is defined, the equation should be x + 2x = 24.

Answer:

The line's slope equals the difference between points' y-coordinates divided by the difference between their x-coordinates. Select any two points on the line of best fit. These points may or may not be actual scatter points on the graph. Subtract the first point's y-coordinate from the second point's y-coordinate.

Step-by-step explanation:

Question 6)

Radius=8

Center (6, -3)

Question 3)

On

Question 4)

outside the circle.

Question 2)

All circles are similar to all other circles.

The last question.

1 , center at (0,-3) radius of 6

2 , Radius of√6 center at (3, -2)

3 , Radius of √6 center at (-3,2)

4 , Radius of 6 center at (-3,0)

5 , Radius of 6 center at (3, -2)

If the ratio of the dimensions is 4:7 and the shorter dimension is 10ft, we know that the 10ft corresponds to the 4 in this scenario. We can set up the equation as follows:

\(\frac{4}{7} =\frac{10}{x}\)

You have to multiply by 2.5 to get from 4 to 10. And since we want to make sure we are maintaining the ratio, we have to multiply the denominator, 7, by 2.5 as well.

\(\frac{4}{7}*\frac{2.5}{2.5}=\frac{10}{17.5}\)

This means your shorter side has a length of 10ft and your longer side has a length of 17.5ft.

AREA

The formula for the area of a rectangle is: \(w*l\)

So we can plug our dimensions into the formula: \(10*17.5=175\)

So 175 is our area. But we can't forget about units! Since this is area and we multiplied our units together, our units would be squared. That means our answer is 175 square feet.

PERIMETER

The formula for the perimeter of a rectangle is: \(2(w+l)\)

We can plug our dimensions into the formula: \(2(10+17.5)=55\)

So 55 is our perimeter. Of course, we can't forget about our units. Because this is perimeter, we only added our units together, so they don't change. That means our answer is 55 feet.

Answer:

97

Step-by-step explanation:

< LMN = 33

The sum of the interior angles equal 180

180 - 92 - 55 = 33

<QM (can't read the last letter 50

180 - 45 - 85 = 50

<LMQ This is a straight angle and straight angles are 180

180 - 33 -50 = 97

Answer:

4 hours

Step-by-step explanation:

is 40 is two hours then 80 must be 4 hours

Answer:

See picture for steps.

Step-by-step explanation:

Answer:

parallel segments in order: CB, CA, CO, AN, BA, NO

Answer:

24 1/2

Step-by-step explanation:

Every 1/2 is 2 gallons.

1/2 x 2 gallons = 4 gallons.

The whole number in 6 1/2 is 6.

1 x 6 = 6.

Now, we multiply 6 by 4 because each 1 = 4 gallons.

6 x 4 = 24.

There is still an 1/2 left in 6 1/2.

You add that.

Your answer is 24 1/2.

Hope this helps you!

Answer:

2/5

Step-by-step explanation:

there are 5 lines starting at point 1 and ending at 2. point c is on the second line which makes it 2/5ths

The position of C on the number line below is 7/5 or 1 2/5.

The number line is a horizontal line where all the integers are placed at equal intervals. The number line is extended to infinity on both sides.

Also, the line segment between two integers also divided into subparts to represent the rational number.

here given in the number line there are two integers 1 and 2 in which point C is situated.

The line segment between 1 and 2 is divided into 5 parts.

every subpart in line segment between 1 and 2 will be= the length of the subpart / total number of division

= (2-1)/5= 1/5

C point is present at a distance of 2 subparts from integer 1.

So the position of C will be = 1+(2)(1/5)= 1+(2/5)= 7/5 or 1 2/5

Therefore The position of C on the number line below is 7/5 or 1 2/5.

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3.749 9.9 24.62 9.798

Okay, so take this with a grain of salt

Answer:

\(2x^{2} - 7x - 4\)

Step-by-step explanation:

Give Me Brainllest

Answer:

Your welcome ;)

Step-by-step explanation:

The expression is,

On solving, we have,

Thus, the required answer is 20.

The x- coordinate of the vertex P is  -4  and the y coordinate is -3. The coordinates of the image of vertex P is thus,  (-4, -3).

Coordinates are numbers describing the position of a point or shape in a line or particular space. We can represent a line or shape in the space between number lines with both positive and negative coordinates.

The vertical axis in the number line is called y-axis and the horizontal axis is called the x- axis. The coordinate of a point is written as (x, y). The x, y represents the numbers on x-axis and y -axis touched at which the point lies in the graph.

For the given vertex P, the vertex lies on the point -4 on x-axis and on -3 in y axis. Hence, the coordinate of P is (-4, -3).

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The option (a) 12 ounces of beer (360ml) contain more alcohol

Alcohol content is something that is important to understand, especially if you are of legal drinking age. It can affect your health and your ability to make sound decisions.

First, let's start with 12 ounces of beer. A typical beer has an alcohol content of around 5%, which means that 12 ounces of beer contains 0.6 ounces (18 ml) of alcohol. This is the same as the fourth option.

Next, let's consider 4 ounces of wine. The alcohol content of wine varies depending on the type and brand, but a typical wine has an alcohol content of around 12%. This means that 4 ounces of wine contains 0.48 ounces (14.2 ml) of alcohol.

Finally, we have 1.5 ounces of spirits. The alcohol content of spirits is generally higher than beer and wine, with a typical range of 40-50%. For the sake of this comparison, let's assume the spirits have an alcohol content of 40%. This means that 1.5 ounces of spirits contains 0.6 ounces (18 ml) of alcohol, the same amount as 12 ounces of beer.

So, in summary, 12 ounces of beer and 1.5 ounces of spirits contain the same amount of alcohol, which is 0.6 ounces (18 ml). 4 ounces of wine contains less alcohol, with 0.48 ounces (14.2 ml).

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Answer:

Perpendicular

Answer:

See below

Step-by-step explanation:

Step 2 and Step 3

Mistake #1: From step 1 to step 2 the 32 randomly changed to 9

Mistake #2: According to PEMDAS multiplication and division comes before addition and subtraction.

During step 3, 8 was added to -6 before 8 was multiplied by 7 which is incorrect as the multiplication should come first.

The real answer should be....

-6 +8(11 - 4)+ 32

Evaluate using PEMDAS

Parenthesis

Exponents

Multiplication and division (left to right)

Addition and Subtraction (left to right)

-6 +8(11 - 4)+ 32

First do the operations inside of the parenthesis. ( Subtract 4 from 11 )

-6 + 8(7) + 32

There are no exponents so we go to the next step.

Next is multiplication.

Multiply 8 and 7

- 6 + 56 + 32

Finally we do the addition and subtraction going left to right.

First add 56 to -6

50 + 32

Then add 50 and 32

= 82

Answer: Step 2 and Step 3.

From step 1 to step 2 the "32" unexpectedly changes into a "9" for no reason.

Step 3 also has a mistake due to misusing PEMDAS, as 6 is removed from the 8(7) to get 2. The 6 should be removed from the 32 instead.

Correct step-by-step explanation:

\(-6 + 8(11-4) + 32\\=-6+8(7)+32\\=-6+8(7)+32\\=8(7)+26=56+26\\=82\)

The change in Jane's total pay for each copy of "History is Fun" she sells is $70, and if she doesn't sell any copies, her total pay is $2200.

1. What is the change in Jane's total pay for each copy of "History is Fun" she sells?

According to the equation given, y = 2200 + 70x, the coefficient of 'x' is 70. This means that for every additional copy of "History is Fun" that Jane sells, her total pay increases by $70. Therefore, the change in Jane's total pay for each copy sold is $70 (positive).

2. What is Jane's total pay if she doesn't sell any copies of "History is Fun"?

If Jane doesn't sell any copies of "History is Fun," the equation y = 2200 + 70x helps us calculate her total pay. By substituting x = 0 into the equation, we find:

y = 2200 + 70(0)

y = 2200 + 0

y = 2200

Thus, if Jane doesn't sell any copies of "History is Fun," her total pay would still be $2200.

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Answer:

y=500x+100

Step-by-step explanation:

y=mx+b is slope-intercept form where m is the slope and b is the y-intercept.

Fara has to pay $100 to set the tent up, so b is 100.

Fara has to pay $500 per hour, so m is 500.

So, the equation is y=500x+100

The equations are x - 5 = 7, x - 7 = 5 and x - 4 = 8

The solution to the equation is given as

x = 12

The subtraction property of equality states that if we subtract the same number from both sides of an equation, the equation remains true.

Using the above as a guide, we have the following:

Each of these equations is equivalent to x = 12, since we have simply subtracted the same value from both sides of the equation.

Hence, the solution to each of these equations is x = 12.

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