Simplify.

Rewrite the expression in the form k • x^n

(4x)^2

Final answer:

Sam completed math questions at a rate of 0.5 questions per minute and took 2 minutes per question.

Explanation:

To find the unit rates of math questions per minute and minutes per math question, we use the information given: Sam completed 12 math questions in 24 minutes.

These unit rates provide us with an understanding of Sam's pace when completing the questions.

Simplify √-y to √yi

3+ 2y = √yi

Square bot sides

(3 + 2y)^2 = -y

Expand

9 + 12y + 4y^2 = -y

Move all terms to one side

9 + 12y + 4y^2 + y = 0

Simplify 9 + 12y + 4y^2 + y to 9 + 13y + 4y^2

9 + 13y + 4y^2 = 0

Split the second term in 9 + 13y + 4y^2 into two terms

4y^2 + 9y + 4y + 9 = 0

Factor out common terms in the first two terms, then in the last two terms

y(4y + 9) + (4y + 9) = 0

Factor out the common term 4y + 9

(4y + 9)(y + 1) = 0

Solve for y

y = -9/4, -1

Check solution

when y = -9/4, the original equation; 3 + 2y = √-y does not hold true. We will drop y = -9/4 from the solution set.

Therefore,

y = -1

Answer:

(6*6*6*6)*(6*6*6)

Step-by-step explanation:

6^4 = 6.6.6.6.

6^3= 6.6.6

Then

(6^4)(6^3) =(6*6*6*6)*(6*6*6)

Best regards

Answer:

6*6*6*6*6*6*6 = 6^7

Step-by-step explanation:

The third expression is equivalent to 6^4*6^3, or 6^7.

6 is used as a factor 4 + 3, or 7, times.

Answer:

You have to divided by 1000

Best regards

Answer:

[tex]\large\boxed{\text{For}\ x>6\to x\in(6,\ \infty)}[/tex]

Step-by-step explanation:

[tex]2(1+x)>x+8[/tex]                 use distributive property

[tex]2+2x>x+8[/tex]       subtract 2 from both sides

[tex]2x>x+6[/tex]           subtract x from both sides

[tex]x>6[/tex]

Skewed right, if its data is mostly on the left it’s skewed right, if it’s data is mostly on the right it’s skewed left

Answer: skewed right

Step-by-step explanation:

Answer:

[tex]\boxed{\bold{2y^2-4y-24}}[/tex]

Step By Step Explanation:

Expand [tex]\bold{3\left(2y-8\right): \ 6y-24}[/tex]

[tex]\bold{6y-24-2y\left(5-y\right)}[/tex]

Expand [tex]\bold{-2y\left(5-y\right): \ -10y+2y^2}[/tex]

[tex]\bold{6y-24-10y+2y^2}[/tex]

Simplify [tex]\bold{6y-24-10y+2y^2}[/tex]

[tex]\bold{2y^2-4y-24}[/tex]

Answer:

C. 40

Step-by-step explanation:

There are 3 sectors that are labeled five, which is out of 12. So the chance of landing on one of it is 3/12, or 1/4.

So, a reasonable estimate is that out of 150 spins, 1/4 of them will land on five. The number of spins can be found out by multiplying 150 by 1/4. 150 * 1/4 is equal to 37.5, which is about 40.

Answer:

The aqnswer is 30

Step-by-step explanation:

the answer is 30

Multiply the numerator of the left-hand fraction by the denominator of the right-hand fraction. ...

Multiply the numerator of the right-hand fraction by the denominator of the left-hand fraction. ...

Set the two products equal to each other. ...

Solve for the variable.

Answer:

Cross multiplying is literally what you do multiplying diagonally.

Step-by-step explanation:

Here you would multiply 12 by 100% and x by 10.

We convert the percents into decimals first.

So 12 * 1 = 12 and x * 0.1 = x/10

So x/10 = 12

Then we multiply each side by 10.

x = 120.

Answer: Option A; cos(28°) = 15/17

Step-by-step explanation:

You must remember that for a triangle rectangle we have that:

Sin( angle) = (opposite cathetus)/hypotenuse

cos(angle) = (adjacent cathetus)/hypotenuse

tan(angle) = (opposite cathetus)/(adjacent cathetus)

We want to find the cos(28°), then we can use the second relation, where the adjacent cathetus is 15 units long, and the hypotenuse is 17 units.

cos(28°) = 15/17

Then the correct option is A.

The value of cos(28) = 15/17.

Based on the diagram, the cosine of angle 28 degrees can be determined using the given information. In a right triangle, cosine is defined as the ratio of the length of the adjacent side to the hypotenuse.

Given that the base of the triangle is 15 units and the hypotenuse is 17 units, we can conclude that the adjacent side is the base. Therefore, the adjacent side has a length of 15 units.

Now, we can apply the cosine formula: cos(angle) = adjacent/hypotenuse. Plugging in the values, we have cos(28) = 15/17.

Hence, the cosine of angle 28 degrees, with a base of 15 units and a hypotenuse of 17 units, is approximately 0.882.

Learn more about right triangle here

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Answer:

Just like x, but -4. x on a graph means that the graph will always be (x, x) instead of (x, y)

Used desmos.com to create this.

Step-by-step explanation:

Look at picture below.

Answer:

What is the equation of the line parallel to the given line with an x-intercept of 4?

y = 4 x +  -16

Step-by-step explanation:

The resulting equation is y = x - 4.

Firstly, a line that is parallel to another line has the same slope. Since the given line is in the form y = mx + b, we need the slope (m) from this equation. Let's assume it is y = x + c, then the slope (m) is 1 since no explicit value is provided for c.

Next, we need the equation of a new line that has the same slope (which is 1) and an x-intercept of 4. An x-intercept of 4 means the line passes through the point (4, 0).

Therefore, the equation of the line parallel to the given one with an x-intercept of 4 is y = x - 4.

Answer:

C

Step-by-step explanation:

No explanation required

From your rules from SOHCAHTOA, you can solve for a using the cosine of B. See picture attached.

The formula for I in terms of P and R is [tex]I = \sqrt{\frac PR}[/tex]

The formula is given as:

P = I^2R

To rewrite the formula for I in terms of P and R, we start by dividing both sides by R.

So, we have:

I^2 = P/R

Take the square root of both sides

[tex]I = \sqrt{\frac PR}[/tex]

Hence, the formula for I in terms of P and R is [tex]I = \sqrt{\frac PR}[/tex]

Read more about expressions at:

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The formula for I in terms of P and R is 2) I = [tex]\sqrt ( PR)[/tex]

How to rewrite the formula for I

The formula is given as:

[tex]P = I^2R[/tex]

To rewrite the formula for I in terms of P and R, we start by dividing both sides by R.

So, we have:

[tex]I^2 = P/R[/tex]

Take the square root of both sides

[tex]I = \sqrt( PR)[/tex]

Hence, the formula for I in terms of P and R is 2)  [tex]I = \sqrt (PR)[/tex]

Answer:

916 in.

Step-by-step explanation:

Step by Step.

5*10 = 50, and 50*2 = 100

10*4 = 40, and 40 * 2 = 80

(4*6)/2 = 12, and 12 * 2 = 24

10*10 = 100, and 100 * 2 = 200

16*16 = 256, and 256 * 2 = 512

Adding this together, we get: 916 inches.

Answer:

she worked 17 hours

Step-by-step explanation:

first you subtract 256-40

then you get 216 and divide by 8

then you get 27 as an answer

Answer:

2 Cups of water

Step-by-step explanation:

To find the amount of water that Arjun will need to make 3 pancakes for each family member in a family of 6, we first need to know what our current ratio of pancake mix to water is.

2/3 water : 1 pancake mix = 6 to 7 pancakes

Now we need to know how much pancakes Arjun needs to make.

6 family members

3 pancakes each

So we multiply the number of family members to the number of pancakes each

Total number of pancakes = 6 x 3

Total number of pancakes = 18

So we need at least 18 pancakes for the family to have 3 pancakes each.

Since we know that the combination of water and pancake mix will make around 6 to 7 pancakes, we simply multiply the entire amount by 3.

2/3 (3) : 1 (3) = 6 (3) to 7 (3)

2 Cups of water : 3 pancake mix = 18 to 21 Pancakes

With a combination of 2 cups of water and 3 pancake mix. We will get 18 to 21 pancakes.

So Arjun will need 2 cups of water to get 18 to 21 pancakes for the family of 6.

To create a word problem for the equation '1/2 x + 6 = 81', we can imagine a student earning points on a quiz and receiving additional points, with the task to find out how many points they initially earned.

To create a word problem for the equation 1/2 x + 6 = 81, we can consider a real-world scenario. Imagine that a teacher tells a student that they will receive double the number of points they earn on a special quiz and an additional 6 points for their efforts in the classroom. The total points would then put their score at 81 points for the semester. The question is, how many points did the student earn on the special quiz?

To solve the problem, we follow these steps:

The student earned 150 points on the special quiz before the additional points were added.

Answer:

Step-by-step explanation:

7

A proportion looks like this:

[tex]a\div b = c\div d[/tex]

It means that the quantity a,b,c and d are in the same proportion: the ratio between a and b is the same ratio between c and d.

They are particularly useful in situation when you have an example given, and you want to extrapolate the relationship for another couple.

For example, you can think of the following problem: "Five apples cost 2 dollars. How much will 8 apples cost?"

You can build the proportion

[tex]5\div 2 = 8\div x[/tex]

And then solve it for x:

[tex]\dfrac{5}{2}=\dfrac{8}{x} \iff 5x=16 \iff x = \dfrac{16}{5} = 3.2[/tex]

You switch the sign of the y coordinate for point b, so the new b coordinate is (-2,1)

Answer:

(-2,1)

Step-by-step explanation:

The point  b (-2,-1) lies in the third quadrant. A reflection over the x-axis will map the point in the second quadrant. In this quadrant, y is positive while x will still be negative. so we end up with;

(-2,1)

Answer:

larger number : 24

smaller number : 10

Step-by-step explanation:

Final answer:

To find the two numbers whose sum is 34 with one being 14 less than the other, equations were set up and solved. The larger number is 24, and the smaller number is 10.

Explanation:

The sum of two numbers is given as 34, and it is known that the smaller number is 14 less than the larger number. To find these numbers, we can set up a system of equations. Let's denote the larger number as L and the smaller number as S. According to the problem, we have two equations:

Substituting the second equation into the first one gives us:

L + (L - 14) = 34

Combining like terms, we get:

2L - 14 = 34

Adding 14 to both sides, we obtain:

2L = 48

Dividing both sides by 2 gives us the value of L:

L = 24

Now that we have the larger number, we can find the smaller number by subtracting 14 from L:

S = 24 - 14

S = 10

The numbers are 24 and 10, with 10 being the smaller number.

Answer:

15[tex]\sqrt{5}[/tex]

Step-by-step explanation:

[tex]3\sqrt{125}=3\sqrt{25*5}\\ =3\sqrt{25}*\sqrt{5}\\ =3*5*\sqrt{5}\\ =15\sqrt{5}[/tex]

( x - 2) ( x + 5/7 )

Answer:

Since I did this on Odyssey, the answer is (7x+5)(x-2)

Answer:

A segment

Step-by-step explanation:

A line is a straight path that is infinitely long.  

A line segment is a section of a line. It consists of two points, which mark the beginning and the end of the segment, and all points in between.

In the diagram, the segment consists of the points A and B and all the points between them.

The line itself extends infinitely both  left and right.

A line segment is the part of a line that encompasses two points and every point between them. It is defined by its extremities, and its characteristic property is that for any three distinct points on it, one must lie between the other two.

The part of a line that contains two points and all other points between them is known as a line segment. Essentially, if you have two points, A and B, the line segment AB includes every point that lies between point A and point B on the straight line that passes through them both. This is captured in geometry by saying that A and B are the extremities of the segment AB and any point C that lies between A and B is part of that segment.

Important properties of a line segment:

If A and C are points on a straight line, there will always be at least one point B such that B lies between A and C.

For any three points situated on a straight line, one of them will always be between the other two.

If four points are considered, they can be arranged in such a way that one of them invariably lies between any two others.

Answer:

[tex]f^{-1}(x)=-\frac{x+9}{5}[/tex];

Step-by-step explanation:

The given linear function is;

[tex]f(x)=-5x-9[/tex]

Let [tex]y=-5x-9[/tex];

Interchange [tex]x[/tex] and [tex]y[/tex] to get;

[tex]x=-5y-9[/tex];

Solve for [tex]y[/tex].

[tex]x+9=-5y[/tex]

Divide both sides by -5

[tex]\frac{x+9}{-5}=y[/tex];

This implies that;

[tex]f^{-1}(x)=-\frac{x+9}{5}[/tex];

Answer:

f⁻¹(x) =  -(x+9) / 5

Step-by-step explanation:

We have given a function.

f(x) = -5x -9

We have to find inverse of given function.

Let y = f(x)

y = -5x-9

Solving above equation for x, we have

x = -(y+9) / 5

Putting x = f⁻¹(y) in above equation ,we have

f⁻¹(y) =  -(y+9) / 5

Replacing y by x, we have

f⁻¹(x) =  -(x+9) / 5 which is the answer.

Answer:

0.23

Step-by-step explanation:

The first spot to the right of the decimal is the tenths place. Ex. .0

The second spot to the right of the decimal is the hundredths place. Ex. .00

The third spot to the right of the decimal is the thousandths place. Ex. .000

Since you are trying to round to the nearest hundredth you look at the thousandths place. If it is 5 or higher you round up. If it is under 5 you round down.

0.232

Since the 2 is the thousandths place the hundredths stays the same and you drop the thousandths place.

0.23

Answer:

D is the answer

Step-by-step explanation:

This question requires a calculator

Answer:

N, the verticle lines are are parallel

Step-by-step explanation:

Answer:

N

Step-by-step explanation:

Note to the wise:  It's letter, not leffer.  

Only N has 2 parallel lines.