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Answer:

y = kx

Step-by-step explanation:

You'll need to share the possible answer choices in all future posts.  

A function in which y varies directly with x has the form

y = kx, where k is the constant of proportionality.

With more data, it'd be possible for you and me both to identify this constant.

To identify if a function represents a direct variation relationship between \( y \) and \( x \), we need to determine if the function can be written in the form \( y = kx \), where \( k \) is a non-zero constant known as the constant of variation.
Here are the steps to determine if a function shows that \( y \) varies directly with \( x \):
1. Have a function \( f(x) \) to test. The function should be expressed in terms of \( x \).
2. Attempt to write the function in the form \( y = kx \).
3. Analyze the function:
  - If there are no constant terms (that is, no term without \( x \)) and the only term is a multiple of \( x \), then the function shows direct variation. The coefficient of \( x \) is the constant \( k \).
  - If there is a constant term not involving \( x \) (other than when \( x = 0 \)), or if \( x \) is raised to a power other than 1, then \( y \) does not vary directly with \( x \).
Let's look at a few examples:
**Example 1**: \( f(x) = 3x \)
This function is in the form \( y = 3x \), which matches the direct variation form \( y = kx \). Here \( k = 3 \). Therefore, \( y \) varies directly with \( x \).
**Example 2**: \( g(x) = 5x^2 \)
\( g(x) \) does not show direct variation because it does not have the form \( y = kx \); instead, \( x \) is raised to the second power, so it cannot represent a direct variation.
**Example 3**: \( h(x) = -2x + 1 \)
\( h(x) \) has a constant term, \( +1 \), which means it does not match the form \( y = kx \) for direct variation since \( y \) should have no constant term other than the coefficient of \( x \). Thus \( y \) does not vary directly with \( x \).
**Example 4**: \( j(x) = \frac{1}{4}x \)
\( j(x) \) reflects a direct variation. The function can be written as \( y = \frac{1}{4}x \), so \( y \) varies directly with \( x \) with a constant of variation \( k = \frac{1}{4} \).
In conclusion, to determine if \( y \) varies directly with \( x \) within a given function, you only need to inspect the function's form to ensure it is a linear equation with a slope \( k \) and no constant term (other than 0 when \( x = 0 \)).

The total number of students surveyed = 44 students

The answer is option D.

According to the given graph, the total number of students is equal to the sum of all the students in each vertical column.

∴tota students surveyed=12+8+9+15=44 students answer.

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it would be 2.00 it’s closer to 2.00 than 3.00

Answer:

-44

Step-by-step explanation:

√x²+49=x+5

X+49=x+5

x-x=5-49

=-44

Answer:

x = 12/5

Step-by-step explanation:

[tex]\sqrt{x^{2}+49 } = x +5[/tex]

Square both sides: ([tex]\sqrt{x^{2} +49}[/tex])[tex]^{2}[/tex] = (x+5)[tex]^{2}[/tex]

[tex]x^{2} + 49 = (x+5)(x+5)\\[/tex]

[tex]x^{2} +49[/tex] = [tex]x^{2} + 10x + 25\\[/tex]

49 = 10x + 25

24 = 10x

[tex]\frac{12}{5}[/tex] = x

Answer:

(x, y) = (0, 4)

Step-by-step explanation:

The two lines intersect at their y-intercept: (x, y) = (0, 4).

Final answer:

Dimensional analysis, also known as the factor-label method, is a mathematical process related to factors, specifically used for unit conversions and complex computations to ensure correct units are obtained in the results.

Explanation:

The basic calculation or process in mathematics that relates to factors is known as dimensional analysis or the factor-label method. This method is integral in solving problems involving unit conversions and more complex computations, where the orientation of factors according to their units is essential to ensure that quantities cancel out or combine correctly to give a result with the desired units.

Through the factor-label method, we can transform quantities into different units by multiplying by conversion factors, which are ratios that equal one, to achieve the intended units for the result. This approach ensures that we conduct operations on the units of the quantities in the same way we do on the numbers.

For example, if we want to convert meters into inches, we multiply the quantity in meters by a conversion factor that expresses the number of inches in a meter. This factor, being a ratio of inches to meters, aligns the units so that 'meters' cancel out, leaving only 'inches' in the result.

If you rotate the triangle so that the 6 is on the bottom, the two sides are both 6.2.

Because the two sides are equal the two angles at the bottom would also be equal. One is given as 61 degrees, so the other bottom angle is also 61 degrees.

The three inside angles of a triangle need to equal 180, so X would equal 180 minus the two bottom angles.

X = 180 - 61 - 61 = 58 degrees.

Answer:

x= 31/5  (Exact form)

x= 6.2  (Decimal Form)

x= 6 1/5 (Mixed number form)

Step-by-step explanation:

Answer:tan 30 = 5/b

Step-by-step explanation:

From the diagram line BC is opposite to the angle 30 and line AC is adjacent to that same angle

From trigonometric ratios

Tan 30 = opposite /adjacent

Answer:

The correct answer is first option

Step-by-step explanation:

Points to remember

Trigonometric ratio

Tan θ = Opposite side/Adjacent side

From the figure we can see that a right angled triangle ABC

BC = 5 cm, <A = 30° and <C = 90°

To find the correct equation

We have,

Tan θ = Opposite side/Adjacent side

Tan 30 =BC/AC

Tan 30 = 5/b

The correct answer is first option.

Answer:

  a = ±b

Step-by-step explanation:

The vertical bars are the symbol for "absolute value", so the equation is saying, "the absolute value of 'a' is equal to the absolute value of 'b'." The absolute value is the magnitude of a number, so, for example, |-3| = 3.

If the magnitudes of two numbers are the same, they may be the same value, or they may differ in sign.

Answer:

See below.

Step-by-step explanation:

The 2 vertical lines about  the letters mean ' the absolute value of' . That is if a  or b have negative values then the absolute value will be the positive . For example if a = -4 then |a| = 4. The absolute value is always positive.

Therefore, for example, if a is 2 and b = -2 then |a| will be equal to |b|, because they both have a value of 2.

Answer:

y = x - 4

Step-by-step explanation:

y - 4 = x - 8

y = x - 4

Answer:

slope-intercept form of the equation for this line is [tex]y=x -4[/tex]

Step-by-step explanation:

The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y – 4 = (x – 8).

To find slope intercept form of a equation of a line we solve for y

[tex]y - 4 = (x - 8)[/tex]

We remove the parenthesis

[tex]y -4 =x - 8[/tex]

To get y alone, we need to add 4 on both sides

[tex]y -4+4=x - 8+4[/tex]

[tex]y=x -4[/tex]

slope-intercept form of the equation for this line is [tex]y=x -4[/tex]

The answer is D. 6cm*8cm because the cross section is exactly parallel to the side with those exact dimensions.

Hope this helps!

6cm*8cm because the cross section is exactly parallel to the side with those exact dimensions.

A cross section is the non-empty intersection of a solid body in three dimensions with a plane in geometry and science, or its equivalent in higher dimensions. Multiple parallel cross-sections are produced when an item is cut into slices.

Given,

6cm*8cm because the cross section is exactly parallel to the side with those exact dimensions.

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Final answer:

Among 4 1/2, 4 1/6, and 4.85, the number 4.85 has the greatest value as it has the highest decimal portion when all numbers are expressed in decimal form.

Explanation:

To find which number has the greatest value among 4 1/2, 4 1/6, or 4.85, we need to compare them directly. The number 4 1/2 converts to 4.5 in decimal form, 4 1/6 converts to approximately 4.17, and 4.85 is already in decimal form. Comparing these three numbers, it's clear that 4.85 has the greatest value because it has the highest decimal portion.

Answer:

15

Step-by-step explanation:

Complementary angles mean the two angles add up to 90 degrees. So the step by step would look like this;

3x + 10 + 2x + 5 = 90

5x + 15 = 90

5x = 90 - 15

5x = 75

x = 75/5

x = 15 :)

If the angles A and B are complementary then the value of x is 15.

Complementary angles are two angles whose sum is 90 degrees. In this case, angle A and angle B are complementary, so we can set up an equation based on their measures:

(3x + 10) + (2x + 5) = 90

Now, combine like terms:

3x + 2x + 10 + 5 = 90

Combine the x terms and constants:

5x + 15 = 90

Next, isolate the x term:

5x = 90 - 15

5x = 75

Finally, solve for x by dividing both sides by 5:

x = 75 / 5

x = 15

Therefore, the value of x is 15.

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The perimeter is 21 cm.

thanks

Answer:

12 + √74 cm

Step-by-step explanation:

The perimeter (literally meaning "around measure") is the length around an area, shape, or boundary. Here, we have a right triangle, and the legs of that right triangle measure 5 cm and 7 cm. Using the Pythagorean theorem, we can find the hypotenuse (we'll call it h):

[tex]5^2+7^2=h^2\\25 + 49=h^2\\74=h^2\\\sqrt{74}=h\\[/tex]

Adding all the lengths together, we find a perimeter of

5 + 7 + √74 = 12 + √74 cm

Answer:

1/3

Step-by-step explanation:

Look up on google "how to find slope" and your answer will be right at the top

The answer is x=3 since its a vertical line. hope this helps.please add brainliest

Do a part over whole fraction

98% is a part of 100%

343 is a part of the number of mules who were surveyed in an unknown quantity.

You can set what you know into two proportions equal to each other:

[tex]\frac{98}{100} =\frac{343}{x}[/tex]

***x is the unknown value

Now you can cross multiply/butterfly

98x = 34300

Isolate x by dividing 98 to both sides of the equation

98x/98 = 34300/98

x = 350

This means that a total of 350 mules were surveyed

Hope this helped!

~Just a girl in love with Shawn Mendes

The answer is A. A secured loan, hope this helps!

Answer:A, a secured loan

Step-by-step explanation:

I hope this helps please tell me if it doesn’t

Answer:

5

Step-by-step explanation:

2² + 4² = 4 + 16 = 20

20 ÷ 2² = 20/4 = 5

option A, D, and E

I just took it on edge

The true statement regarding the shape are:

Base: The bottom surface of a pyramid is a polygonal shape, such as a square, rectangle, triangle, or any other polygon. The base is typically larger in area compared to the other faces.

Faces: Pyramids have triangular faces that slope inward from the edges of the base to a single point at the apex. The number of faces depends on the number of sides of the base polygon.

Vertices: A pyramid has several vertices where the edges of the base meet the triangular faces, and one vertex where all the triangular faces converge at the apex.

Edges: The edges of a pyramid are the lines where the faces intersect. For example, a square pyramid has 8 edges (4 from the base and 4 connecting the base to the apex).

Answer:

26+c

Step-by-step explanation:

The given expression 2-(-8c)+24-7c simplifies to 26 + c by removing the parenthesis, changing the sign of -8c to +8c, combining like terms, and adding the constants.

The equation 2-(-8c)+24-7c simplifies by applying the distributive property and combining like terms. We first remove the parentheses and change the sign of the term inside, which is -8c, to a positive. Then we combine the like terms, -8c and -7c. The equation simplifies to:

2 + 8c + 24 - 7c = 2 + 24 + (8c - 7c) = 26 + c

So, the given expression simplifies to 26 + c.

Answer:

B infinitely many solutions

Step-by-step explanation:

8x+9y = -5

-8x-9y =5

Add the two equations together

8x+9y = -5

-8x-9y =5

-------------------

0 = 0

This is always true, so we have infinite solutions

Answer: B

Step-by-step explanation:

There are infinite ways to solve this solution. If you plug it in, you can get the answer of infinite.

Answer:

Option A is correct.

Step-by-step explanation:

The polynomial with factors with zeros at 0,-3 and 4 means

x=0 and x =-3 and x=4

this can be written as:

x=0, x+3 =0 and x-4=0

or

x(x+3)(x-4) =0

or

f(x) = x(x+3)(x-4)

So, Option A is correct.

Answer:

Step-by-step explanation:

Average rate of change is Δy / Δx.

For f(x):

[ f(1) - f(0) ] / (1 - 0)

(1 - 3) / (1 - 0)

-2

For g(x):

[ g(1) - g(0) ] / (1 - 0)

(4 - 3) / (1 - 0)

1

Answer: 0.00604

Step-by-step explanation: 10^-3 would be 0.001. If you multiply that by 6.04, you will get 0.00604

I hope that helps! :D

Answer:

x= -19

Step-by-step explanation:

6-2(x+5)=42

6-2x-10=42

-4-2x=42

-2x=38

x= -19

6e + 3(e - 1)

6e + 3e - 3

9e - 3

Answer: Equivalent expression would be 9e-3.

Step-by-step explanation:

Since we have given that

[tex]6e+3(e-1)[/tex]

As we need to simplify the above expression:

First we open the brackets :

[tex]3(e-1)=3e-3[/tex]

Now, add it to 6e.

So, it becomes,

[tex]6e+3e-3\\\\=9e-3[/tex]

Hence, equivalent expression would be 9e-3.

Answer: An output is the function

Step-by-step explanation:

The most appropriate domain to calculate the cost of downloading songs is whole number greater than or equal to one.

Whole numbers include all natural numbers and 0. They are real numbers that do not include fractions, decimals, and negative integers.

It is most appropriate since numbers of songs downloaded cannot be a negative or part quantity.

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The most appropriate domain for calculating the cost to download songs after paying a membership fee is whole numbers greater than or equal to one, as you cannot download fractional or negative numbers of songs.

The most appropriate domain for calculating the cost to download songs, given the information that an online company charges a $5 membership fee and then $0.99 for each song, would be option 2, which is whole numbers greater than or equal to one. The domain is referring to the number of songs you can download after the initial membership fee. Since you cannot download a fraction of a song or a negative number of songs, whole numbers make the most sense in this context. The cost for downloading songs would be the membership fee plus the cost per song times the number of songs downloaded, which is a linear relationship.