Use the graph to solve the problem.
12) Find the equation of the line in standard and slope-intercept form from the graph given.
Make sure the standard form of the equation is written with whole numbers.
-10
K
5
10--axis.
10-
5
x-axis
Y
10

The graph that represents the situation on the gymnast paying membership for yoga is Graph C.

The equation given for the amount spent in total by the gymnast is y = 10 + 20 x. What this means is that even if the gymnast takes no classes, he still has to pay the monthly fee of $ 10.

The graph should therefore begin at $10. If the gymnast takes 1 class, then the total cost for the month is:

= 10 + 20 ( 1 )

= $ 30

This is shown in the third graph so this is the correct graph.

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Answer:

Step-by-step explanation:

2790.47619048

Answer:

2790.47619048

Step-by-step explanation:

To solve 5,860 ÷ 2.1, we are finding how many times 2.1 goes into 5,860.

We start by dividing 5,860 by 2.1 and keep dividing until the result can no longer be divided evenly.

5,860 ÷ 2.1 = 2790.47619048

The result, 2790.47619048, is the number of times 2.1 goes into 5,860. So, the answer to 5,860 ÷ 2.1 is 2790.47619048.

For the given equation, we can complete the statements below:

Ariel is correct. For any value of y, the statement -12 = 3 is always true.

The equation has no solutions.

What is an equation?

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

The first part of the question is as given below.

Ariel simplifies the equation 3y - 12 = 3(y+1) and says it has no solution.

We are asked to complete the statements based on the above information.

Simplifying the equation,

 3y - 12 = 3(y+1)

3y - 12 = 3y + 3

-12 = 3

Since the y term in the above equation is not present, the given equation has indeed no solution.

Also if we take any value of y, the final answer will always be -12 = 3.

Therefore we can complete the statements as below:

Ariel is correct. For any value of y, the statement -12 = 3 is always true.

The equation has no solutions.

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Answer: Ariel is correct. For any value of y the statement -12=3 is always false and it’s no solution

Step-by-step explanation:

Answer:

the answer is foot/hour

The closest number to 320 that can be made using these cards is 327.5

From the question, we have the following parameters that can be used in our computation:

5 27

FIVE

7 3

TWO

SEVEN

THREE

DECIMAL POINT

To get this number, place the decimal point between the 7 and 5

We also make use of the card with "THREE" and add the number "TWO".

The resulting number is 327.5.

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Another way to write the division expression 34 divided by 8 is 34/8 or 4.25, where 4.25 is the result of the division.

What is a mathematical expression?

A mathematical expression consists of a statement, at least two variables or integers, and one or more arithmetic operations. It is possible to multiply, divide, add, or subtract values with this mathematical operation. The following is the structure of an expression: Expression: (Number/Variable, Math Operator, Math Operator)

Another way to write the division expression 34 divided by 8 is 34/8 or 4.25, where 4.25 is the result of the division.

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Answer: it's less than 6.87...

Answer:

e = 190

Step-by-step explanation:

Rearrange to:

e/(-95)+6-(4)=0

Now we simplify, and get this:

(e/-95 + 6) - 4 = 0

Rewrite the equation to get this:

6 = 6/1 = 6x(-95)/-95

after adding fraction with a common denominator we get:

(570 - e)/95 - 4 = 0

Rewrite the whole as an equivalent fraction:

4 = 4/1 = 4x95/95

After adding fractions with a common denominator we get:

190-e/95 = 0

Now we must get the numerator to equal 0:

190-e/95 x 95 = 0 x 95

We get:

190 - e = 0

So we solve:

-e + 190 = 0

Subtract 190 from both sides:

-e = -190

Multiply both sides by (-1):

e = 190

The expression to represents the phrase: "6 times a number plus 3." is:

6n + 3

Here, "n" represents an unknown number, and "6" and "3" are constants. The expression means that 6 is being multiplied by "n" to get an intermediate result, and then 3 is being added to that result to get the final answer.

For example, if n = 2, then the expression would evaluate to 6 * 2 + 3 = 12 + 3 = 15. So, the expression "6n + 3" represents the mathematical relationship between the unknown number "n" and the final result.

Therefore, the expression "6 times a number plus 3" can be represented as "6n + 3".

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Answer: 3,2

Step-by-step explanation: The degree represents the highest exponent in the function. In this case, there is a cubed term which has an exponent of 3. The leading coeffient represents the number before x that makes that highest exponent and in this case its 2.

The answer is:

A frequency distribution for a collection of data is shown in the accompanying table.

The intervals or ranges of the data are displayed in the left column of the table, and the frequency or number of observations within each interval is displayed in the right column.

For instance, the first row demonstrates that 3 observations fall within the range of 10 to 19, the second demonstrates that 5 observations fall within the range of 20 to 29, and so on.

We only combine the frequencies to determine the total number of observations:

Total observations are equal to 3 + 5 + 7 + 4 + 1 = 20.

By averaging the bottom and upper interval bounds, we can also determine each interval's midpoint. As an illustration, the first interval's midway (10-19) is as follows:

Midpoint: (14.5) (10 + 19) / 2

This may be done for each interval, and to display the midpoints, we can add a third column to the table.

The cumulative frequency, which is the overall frequency as we progress from the shortest interval to the longest interval, can then be calculated. The cumulative frequency can be displayed in the table by using a fourth column.

The finished table is shown here:

Interval Frequency Midpoint Cumulative Frequency

Oct-19 3 14.5 3

20-29 5 24.5 8

30-39 7 34.5 15

40-49 4 44.5 19

50-59 1 54.5 20

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The two numbers are 3 and 6. We can then solve for y using the quadratic formula:y = [9 ± √(81 - 120)]/2 , y = 3 or 6

The sum of two numbers (x + y) = 9

The product of two numbers (x * y) = 30

We can solve for x and y using the following equations:

x + y = 9

x * y = 30

We can solve for x by dividing both sides of the equation by y:

x = (30/y)

We can then substitute this into the first equation:

(30/y) + y = 9

We can then solve for y by subtracting 30/y from both sides:

y = 9 - (30/y)

We can then solve for y by multiplying both sides by y:

y^2 = 9y - 30

We can then solve for y using the quadratic formula:

y = [9 ± √(81 - 120)]/2

y = 3 or 6

Therefore, the two numbers are 3 and 6.

the complete question is :

What are the two numbers has a sum of 9 and a product of 30 ?

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53.9 degree is the angle of the compass direction of a line connecting your starting point to your final position measured from north of west.

A compass is a tool for orientation and navigation that displays direction in relation to the four cardinal directions of the earth (or points). The directions north, south, east, and west are typically represented on the compass face as initialised abbreviations in a design called a compass rose. The rose can be aligned with the corresponding geographic directions when the compass is employed; for instance, the rose's "N" mark points northward. Compass roses are frequently joined with (or occasionally replaced by) marks indicating angles in degrees. East is 90° degrees, south is 180° degrees, and west is 270° degrees, with north being 0° and the angles increasing clockwise.

Here,

You started by travelling west to north.

Your entire distance from the beginning location is your hypotenuse.

[tex]H^{2}= P^{2}+ B^{2} \\\\H^{2}= 17.5^{2}+ 24^{2}\\\\H^{2}= 306.25+ 576\\\\H=\sqrt{882.25} \\\\=29.7 meters[/tex]

You are moving in the northwest.

Use trigonometry now:

[tex]sin\alpha =\frac{B}{H}\\\\sin\alpha =\frac{24}{29.70} \\\\=0.808\\\\\alpha =53.9 degree[/tex]

That's the angle of the compass direction.

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Solve the following problem using analytical techniques: Suppose you walk 17.5 m straight west and then 24.0 m straight north. How far are you from your starting point, & what is the compass direction of a line connecting your starting point to your final point?

To find the missing  sides of the special right angle,

The ratio for 45°,45°and 90°,   1:1:√2,

and for 60°, 30°, 90°,   1:√3:2.

Special right triangles are right triangles with three defined interior angles and fixed side ratios. If one side is known in these right-angled triangles, we can find the value of the two missing sides. The 45°- 45°- 90° triangle and the 30°- 60°- 90° triangle are additional names for the two exceptional right triangles.

Given finding the  missing sides of the special right angle,

Only right triangles with other internal angles of 30° and 60° or 45°and 45°. are valid according to this criteria. Furthermore, it makes no difference whatever side's length you know in order for the rule to function.

for 45°,45°and 90°.

The 45°,45°,90° theorem states that triangles with these angles will have sides in a ratio 1:1:√2,

where the side opposite 45° equates to 1 in the ratio and the side opposite to 90° equates to √2. To find the missing side, just put the given value in the following ratio and find the value.

For 60°, 30°, 90°

Similar to this, according to the 30°, 60°, 90° theorem, triangles with these angles will have sides in the ratio 1:√3:2,

where the side opposite to 30° equates to 1 in the ratio, the side opposite to 60° equates to √3, and the side opposite to 90° equates to 2 in the ratio. Simply enter the given amount into the following ratio to determine the value to discover the missing side.

Hence the ratios are for 45°,45°and 90°,   1:1:√2,

and for 60°, 30°, 90°,   1:√3:2.

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The initial graph shows [tex]f(x)= 2(3)^{x}[/tex]

A function is a mathematical object that assigns a unique output (or "value") to each input in its domain. It is a rule that takes an input (or "argument"), performs some operations on it, and returns a corresponding output. Functions are often written using the notation f(x), where x is the input, and f(x) is the corresponding output. For example, the function f(x) = x^2 maps the input value x to its square. Functions are a key concept in mathematics and are used to model various phenomena in science, engineering, economics, and more.

The function provided is,

[tex]f(x)= 2(3)^{x}[/tex]

making x = 1

[tex]f(x)= 2(3)^{1}=f(x)= 2(3)=6[/tex]

The point (1, 6) that is (x, f(x)) must therefore satisfy the condition or be on the curve of the function.

The point (1, 6) only lies on the curve in the first graph.

As a result, the first graph accurately depicts the function.

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The required system of equations equation besides y = 8x + 7 is y = 8x + 15  has no solution.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,

A system of equations has no solution when the equations describe lines that are parallel and do not intersect. In other words, there is no common solution for both equations, or in other words, there is no ordered pair that satisfies both equations.

If y = 8x + 7 is one of the equations, the other equation could be any line that is parallel to it and does not intersect it. This means that the other equation would have the same slope as y = 8x + 7, which is 8, but a different y-intercept.

For example, y = 8x + 15 is a line that is parallel to y = 8x + 7 and does not intersect it. Thus, the system of equations

y = 8x + 7 and y = 8x + 15 has no solution.

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The slope is negative three halves for option 2 and the y-intercept is 2. Hence option 2 is the correct answer.

A line's steepness and direction are determined by the line's slope. Without actually using a compass, determining a line's slope in a coordinate plane can aid in determining whether the line is parallel, perpendicular, or not.

Any two clearly separated points on a line can be used to calculate the slope of any line. Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined.

The y-intercept is obtained when the x coordinate is 0.

From the given options the y-intercept is 2 for option 1 and 2.

The slope is given as:

m = (y2 - y1) / (x2 - x1)

For option 1:

m = (0 - 2) / (3 - 0)

m = -2/3

For option 2:

m = (-1 - 2) / (2 - 0)

m = -3/2

So, the slope is negative three halves for option 2 and the y-intercept is 2. Hence option 2 is the correct answer.

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Answer:

Step-by-step explanation:

Mr. Adams will fill 21 plates, and he will have 5 extra cookies.

To find the number of plates filled by Mr. Adams, we need to divide 730 cookies by 35 cookies per plate:

730 ÷ 35 = 21

So, Mr. Adams will fill 21 plates.

To find the number of extra cookies, we use the modulo operator to find the remainder after dividing 730 by 35:

730 % 35 = 5

So, Mr. Adams will have 5 extra cookies.

The length, width, and height of the right square prism are all equal to 7units, i.e., 7units * 7units * 7units.

The volume of a right square prism can be expressed as the product of its length, width, and height. If the volume is 360 cubic units, and the prism is a square prism, then we can assume that its length, width, and height are all equal, so we can call them x. The volume formula can be expressed as:

V = x * x * x = 360

Taking the cube root of both sides of the equation, we get:

x = ∛(360) = 7.11

The cube root of 360 is approximately 7, so the length, width, and height of the square prism are all equal to 7 units.

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Answer: The equation 63 = 9k is correct.

To solve for k, you can divide both sides of the equation by 9:

63/9 = 9k/9

k = 7

So, k = 7 is the solution to the equation 63 = 9k.

Step-by-step explanation:

The value of k in the equation 63= 9k is 7

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

The equation 63 = 9k is a type of linear equations with one variable.. The variable here is K

To find k;

63 = 9k

divide both sides by 9

63/9 = 9k/9

k = 7

therefore the value of k is 7

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Answer:

y=4x-1

Explanation:

looking at the x row, as you can see, it goes up by 1 each time. In the y row, it goes up by 4, because -1+4=3, 3+4=7, etc. So your slope is 4, and in the funtion y=mx+b given, that would go in the “m” spot. Then for the “y” spot you need to figure out if x is 0, what is y. Well, that is given to you in the picture. It shows that when x=0, y=-1. So that is you y intercept, going into the b spot. If you put it together, it looks like this: “y=4x-1”.

a) The value of x is 20 cm

b) The area of cones that sought is 680π cm²

a) To find the length of x

Compare the ratio and height of the small cone with the large cone

4/x= 7/35

4.35=7x

x= 20 cm, x is the radius of the large cone

b) To calculate the area of the whole cone

The area you are looking for = (Area of the large cone - Area of the small cone) + area of the circle

The area sought = (π20.35 - π4.7) + 2π4

The area sought = 700π-28π+8π

Area sought = 680π cm²

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a) The measure of an interior angle is of 135º.

b) The polygon has 8 sides.

An interior angle is supplementary with it's exterior angle, meaning that the sum of their measures is of 180º.

Hence the measure of the interior angle of a polygon with exterior angle of 45º is given as follows:

180 - 45 = 135º.

The sum of the interior angle measures of a polygon with n sides is given by the equation presented as follows:

S(n) = 180 x (n - 2).

For a regular polygon, all the angles have the same measure, hence:

S(n) = 135n.

Then the value of n, representing the number of sides of the polygon, is obtained as follows:

135n = 180(n - 2)

135n = 180n - 360

45n = 360

n = 360/45

n = 8 sides.

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Among the 3 cards the probability of picking an odd number and then picking an odd number is 1/3.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The probability of picking a card with odd number is -

Probability = Favourable outcomes / Total outcomes

Substitute the values in the equation -

P(odd1) = Odd number of cards / Total number of cards

P(odd1) = [tex]\frac{^1C_1}{^3C_1}[/tex]

P(odd1) = 1/3

This is followed by picking up a second card without putting the first card back.

So, out of remaining two cards an odd card needs to be picked.

Probability = Favourable outcomes / Total outcomes

Substitute the values in the equation -

P(odd2) = Remaining odd number of cards / Remaining number of cards

P(odd2) = [tex]\frac{^0C_1}{^1C_1}[/tex]

P(odd2) = 0/1

P(odd2) = 0

The probability of both the events is -

P(odd1) + P(odd2)

1/3 + 0

1/3

Therefore, the probability value is 1/3.

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Answer:

$89 for each payment

Step-by-step explanation:

3,204 / 36 = 89

Answer: Each payment is 89 dollars

Step-by-step explanation:

Divide 3,204 by 36 to get how much each payment will be.

As the single fraction, we can write the expression as -

k/x.

Given is the expression as follows -

{(kx + k²)/x²} × {x/(x + k)}

The given expression is -

{(kx + k²)/x²} × {x/(x + k)}

{k(x + k)/x²} × {x/(x + k)}

k/x

Therefore, as the single fraction, we can write the expression as -

k/x.

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Answer:

you have it correct sir

Step-by-step explanation:

An expression which does not represent the perimeter of the rug in feet include the following: C. 2(6 7/8) + w.

Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;

P = 2(L + W) or P = 2L + 2W

Where:

Substituting the given parameters into the perimeter of a rectangle formula, we have the following expressions;

Perimeter, P = 2(6 7/8 + W)

Perimeter, P = 2(6 7/8) + 2W = 2W + 13 6/8

Perimeter, P = 6 7/8 + W + 6 7/8 + W

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The first ship with an angle of depression 9° has a 2399.23m distance from the shore. And the first and second ship are on a 1944.19m distance apart.

The angle of depression is an angle formed between the horizontal line and the line of sight when an observer looks downwards.

Considering the right triangle formed by the height of the cliff and the distance of the ships from the shore, we shall derive a complementary angle considering their respective angles of depression as:

90° - 9° = 81° for the first ship

90° - 5° = 85° for the second ship

such that;

tan 81° = distance of the first ship from the shore/380m {opposite/adjacent}

distance of the first ship from the shore = 380m × cos 81°

distance of the first ship from the shore = 2399.23m

tan 85° = distance of the second ship from the shore/380m {opposite/adjacent}

distance of the second ship from the shore = 380m × cos 85°

distance of the second ship from the shore = 4343.42

the ships distance apart = 4343.42m - 2399.23m

the ships distance apart = 1944.19m

Therefore, first ship with an angle of depression 9° has a 2399.23m distance from the shore. And the first and second ship are on a 1944.19m distance apart.

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Answer: (1/3, -1)

Step-by-step explanation: substitue 0 for x to find the y

y=-3x-1

y=-3(0)-1

y=-1

then substitue -1 in for y to find the x

3x-y=1

3x-(-1)=1

3x=1

x=1/3