Which of the following functions is a direct variation?

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]

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]

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: 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.

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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]

Answer:

g(x) = (4/5)x^2 - 2

Step-by-step explanation:

f(x) = (2/5)x^2 - 2 is the equation of a parabola with vertex at (0, -2).

Applying a vertical stretch of factor 2 to f(x) requires multiplying both the slope (2/5) and the y-intercept (-2) by 2:

g(x) = (2)(2/5)x^2 - 4, or

g(x) = (4/5)x^2 - 4.

its A. look at the other percents when considering about the question.

hope this helps!!

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

Answer:

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

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

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:

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.

Answer:

x^2 - 5x - 6  =  (x - 2)(x - 3).

Step-by-step explanation:

f(x) = x^2 - 5x - 6

We need 2 numbers whose product is - 6 and whose sum is -5. They are   -3 and -2:

The factors are x- 2  and x - 3.

Final answer:

The factors of the expression x²-5x-6 are (x-6)(x+1).

Explanation:

This question demands basic understanding of methods of factorization and finding solutions of an equation.

The method to find factors of an equation, ax² + bx + c = 0, find two numbers that multiply to get c and add to give b.

To find the factors of the expression x²-5x-6, we need to factorize it. We look for two numbers that multiply to give -6 and add to give -5. The numbers -6 and 1 fit these conditions.

So, x²-5x-6

=> x² - 6x + x- 6

=> x(x - 6) +1(x - 6)

=> (x - 6)(x + 1)

Therefore, the factors of the expression are (x-6)(x+1).

There are 10 crosses, which means that there are 10 trees in total. If we distribute 5 gallons among 10 trees, we give each tree

5/10=1/2=0.5 gallons

Answer:

Each tree will get 0.5 gallons of Syrup redistributed to it.

Step-by-step explanation:

According to the line graph shown in the picture there are 10 trees in total.  We have 5 gallons of syrup that needs to be distributed equally among all ten trees. We can solve this by simply dividing the amount of syrup by the amount of trees that will be sharing the syrup.

5/10 = 0.5 gallons each

So each tree will get 0.5 gallons of Syrup redistributed to it.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

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:

Step-by-step explanation:

1 case = $7

81*7=$567

81 case = $567

76*7=$532

76 case = $532

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷ 90 is an integer, and the closest others are 89 and 91

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

TROLLER

Hence, the nearest integer to [tex]90[/tex] is the closest others are [tex]89[/tex] and [tex]91[/tex].

What are the integers?

Integers are the collection of whole numbers and negative numbers. Similar to whole numbers, integers also does not include the fractional part.

Here given that,

The nearest integer to [tex]90[/tex] is the closest others are [tex]89[/tex] and [tex]91[/tex].

Hence, the nearest integer to [tex]90[/tex] is the closest others are [tex]89[/tex] and [tex]91[/tex].

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Answer:

Step-by-step explanation:

7

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.

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)

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:

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.

The product −(1/4⋅1/4⋅1/4⋅1/4) can be written as exponents as - (1/4)⁴.

Exponents are the method of writing numbers, especially large numbers, in terms of a base and an exponent, which is written as the power of base.

Given expression is,

−(1/4⋅1/4⋅1/4⋅1/4)

We have to write the expression using exponents.

Taking the minus sign as such, it is given that three are 4 times 1/4 is repeating.

So, −(1/4⋅1/4⋅1/4⋅1/4) = - (1/4)⁴.

Hence the exponent form of the given expression is - (1/4)⁴.

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Final answer:

The expression −(1/4· 1/4· 1/4· 1/4) is written using exponents as −(1/4)⁴.

Explanation:

The expression −(1/4· 1/4· 1/4· 1/4) can be rewritten using exponents by recognizing that we are multiplying 1/4 by itself four times. Converting a repeated multiplication into exponential form means we use a base (which is 1/4 in this case) and an exponent (the number of times we multiply the base by itself). Thus, we write the expression as −(1/4)⁴. The negative sign just indicates that the result should be taken as the opposite (negative) value of (1/4)⁴.

When x = -1, f(x) = 0 because

(-1)^4 - 2(-1)^2 + 1 = 1 - 2 + 1 = 0.

Answer:

see explanation

Step-by-step explanation:

In order to determine the end behaviour, we only need to look at the term of highest degree, that is the leading term in standard form.

Given

f(x) = [tex]x^{4}[/tex] - 2x² + 1

So the term of highest degree is [tex]x^{4}[/tex]

Which is of even degree with positive coefficient

As a result the end behaviour is

As x approaches positive infinity, f(x) approaches positive infinity

As x approaches negative infinity, f(x) approaches positive infinity

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Substitute x = - 2 into f(x)

f(- 2) = [tex](-2)^{4}[/tex] - 2(- 2)² + 1 = 16 - 8 + 1 = 9 ≠ 0

Substitute x = - 1 into f(x)

f(- 1) = [tex](-1)^{4}[/tex] - 2(- 1)² + 1 = 1 - 2 + 1 = 0

Thus x = - 1 is a root of f(x) and (x + 1) is a factor of f(x)

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:

You have to divided by 1000

Best regards

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.

The correct answer is 104 fl oz = 13 c

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.

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:

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