Question 5(Multiple Choice Worth 2 points)
(Graphing Linear Equations MC)

A gymnast joined a yoga studio to improve his flexibility and balance. He pays a monthly fee and a fee per class he attends. The equation y = 30 + 10x represents the amount the gymnast pays for his membership to the yoga studio per month for a certain number of classes.

Which graph represents this situation?

A . graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 30 through the point 1 comma 20

B. graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 30 through the point 1 comma 40

C. graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point one third comma 0

D. graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point 1 comma 40

Answer:

multiply 2, 7 times

Step-by-step explanation:

2 x 2 x 2 x 2 x 2 x 2 x 2

= 128

The graph in option - B represents the correct alternative.

A function describes a relationship between a dependent and independent variable. Example -

y = f(x) = 5x + 9

Given is the function as -

f(x) = 12(1/3)ˣ

At {x = 0}, we get -

y = 12 x 1 = 12

The {y - intercept} would be at (0, 12).

It is a exponential function of the form -

y = A(B)ˣ.

Refer to the graph attached. We can conclude that option B is the correct graph.

Therefore, the graph in option - B represents the correct alternative.

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The x intercept shown in the table are -2 and 2

The y intercept shown in the table is -4

The x-intercept of a graph is the point at which the graph crosses the x-axis, i.e., the y-coordinate of the point is 0. In other words, it's the solution to the equation y = 0.

The y-intercept of a graph is the point at which the graph crosses the y-axis, i.e., the x-coordinate of the point is 0. In other words, it's the solution to the equation x = 0.

In the table x- and y-intercepts are the values where the y values and x value are zero

x intercepts = -2 and 2

y intercepts = -4

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Answer:

4/3

Step-by-step explanation:

to find slope just choose any two points on the line and subtract them. I prefer choosing points that lie on the grid for instance in #11

I will choose Point 1: (4,3) and Point 2: (1,-1) because the intersect the grid and I can do 'clean' subtractions.

Slope = rise/run

= change in y/change in x

= y2-y1/x2-x1

= ( -1 - 3 ) / ( 1 - 4 )

= - 4 / -3

= 4/3

Answer:

5

Step-by-step explanation

32 -12 =20 divided by

4= 5

The equation of the blue graph is option B. G(x) = (x - 4)² + 1.

Transformation of geometrical figures or points is the manipulation of a given figure to some other way.

The given function is f(x) = x².

From the figure, we can see that the graph of f(x) is shifted left to 4 units.

Then the function becomes (x - 4)².

Then the function is shifted up to 1 unit.

The resulting function is G(x) = (x - 4)² + 1.

Hence the correct equation of the graph is G(x) = (x - 4)² + 1.

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The best-fit line to represent the black data points is the blue line.

The plot of absorbance vs. concentration shows 8 data points with 3 lines drawn to represent the data. In order to determine the best-fit line, we need to evaluate the lines based on how well they represent the data points.

(a) The red line is the middle line and goes through 1 data point, with 3 data points above it and 4 data points below it. This line has a slope that is between the slopes of the other two lines. However, it doesn't go through many of the data points and the slope is not consistent with the majority of the data points.

(b) The green line is the top line and touches 3 of the data points, with the rest of the data points below it. This line has a steeper slope compared to the red line, but it doesn't touch many of the data points and has a significant deviation from the majority of the data points.

(c) The blue line is the bottom line and has 2 data points below it and 6 data points above it. This line has a slope that is more consistent with the majority of the data points, and it has the least deviation from the data points compared to the other two lines.

In mathematical terms, the blue line has the least sum of squared residuals, meaning it has the smallest difference between the observed values and the predicted values.

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Answer:

Multiply 1/4*3= 3/4. So a motorcycle can go 3/4 of a mile on 3 gallons of gas

Step-by-step explanation: Hope this helps!!, Mark me Brainliest, :)))

The mass of the vessel if it is made of metal of density 10 g/cm³ is 1993 g.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We know that;

Volume of sphere = 4/3 πr³

Hence, For internal;

⇒ Volume of sphere = 4/3 πr³

⇒ Volume of sphere = 4/3 × 3.14 × (6)³

⇒ Volume of sphere = 904.32 cm³

For external;

⇒ Volume of sphere = 4/3 πr³

⇒ Volume of sphere = 4/3 × 3.14 × (6.4)³

⇒ Volume of sphere = 1097.5 cm³

Thus, Volume of sphere between sphere is,

⇒ 1097.5 - 904.32

⇒ 193.2 cm³

Here,  it is made of metal of density 10 g/cm³.

Hence, the mass of the vessel is,

⇒ 193.2 × 10

⇒ 1932 g

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The required area of the circle with diameter 15.8 cm is 196.06 cm^2.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.

To find the area of a circle, we use the formula: pi * (radius)^2. The diameter of the circle is given as 15.8 cm,

so the radius can be calculated by dividing the diameter by 2,

giving us a radius of 15.8 cm / 2

= 7.9 cm.

Plugging the radius into the formula, we get:

pi * (7.9 cm)^2

= 3.14 * 62.41.

Finally, rounding the answer to the nearest hundredth, we get: 62.41 * 3.14

= 196.06 cm^2.

Thus, requi9red answer is 196.06 cm^2.

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Answer:

SOH-CAH-TOA, the rest are just reciprocals of these

Step-by-step explanation:

sinY= o/h = 6/√61
cosY= a/h = 5/√61
tanY =o/a = 6/5
cosecY = h/o = √61/6
secY = h/a = √61/5
tanY = a/o = 5/6

Answer:

Step-by-step explanation:

Sin = 6/[tex]\sqrt{61][/tex]

Cos=5/[tex]\sqrt{61[/tex]

tan=6/5

cosec=    [tex]\sqrt{61\\[/tex]/6

sec=[tex]\sqrt{61\\[/tex]/5

cot= 5/6

Answer:

The third angle is 60

Step-by-step explanation:

The interior angle of a triangle is equal to the 180 minus the exterior angle.

[tex]180-80= 100[/tex]

So one of the interior angles is equal to 100

All of the interior angles of a triangle add up to 180

[tex]180=100+20+x[/tex]

[tex]x=60[/tex]

Answer: The answer to this equation is 50.

Step-by-step explanation:

Evaluate the equation like this using PEMDAS.

2 x (1 + 4) ^2

2 x ( 5 ) ^ 2

2 x 25

 50

Hope this helps!

The measures of the arcs MN in the circles are 105, 100, 106 and 66

Circle 1

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

MN = PQ

This means that

2MN + 85 + 65 = 360

So, we have

2MN = 210

Divide by 2

MN = 105

Circle 2

Here, we have

MN = 2MP

Also, we have

MP + MQ = 180

So, we have the following equation

1/2MN + 130 = 180

So, we have

MN = 100

Circle 3

Here, we have

PR = 74

So, we have the following equation

MN + 74 = 180

So, we have

MN = 106

Circle 4

Here, we have

PN = PM = 147

So, we have the following equation

MN + 2 * 147 = 360

So, we have

MN = 66

Hence, the measures of the arcs are 105, 100, 106 and 66

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The value of the element t11 is 34 and the value of the element at d12 is 15.

Two matrices are equal if and only if their shapes are same, and they've got the same elements for each corresponding row and column positions.

M + W = Indoor= [26 55] Outdoor = [32 49]

The value indicates the sum of the indoor volunteers ages 18-39,\

34.

To create a matrix by subtracting the women's matrix from the mens matrix.

Now the difference;

M – W = Indoor = 8 15 Outdoor = -16 3

This value indicates the difference of the volunteers indoors 40 so

Therefore the value would be 15.

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A)

Gracie has 130 stamps after 3 months.

B)

The point (2, 100) represents that the number of stamps after 2 months is 100.

Option C is the correct answer.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

Coordinate grid labeled points (0, 40), (1, 70), (2, 100).

Each month Gracie adds 30 stamps to her collection.

So,

(3, 130)

Now,

A)

130 stamps after 3 months.

B)

(2, 100) represents that the number of stamps after 2 months is 100.

Thus,

130 stamps after 3 months.

(2, 100) represents that the number of stamps after 2 months is 100.

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There will be 130 stamps  Gracie have after 3 months,

and (2, 100) represents the number of stamps in the collection after 2 months is 100.

A coordinate grid has two perpendicular lines, or axes labeled just like number lines. The horizontal axis is usually called the x-axis. The vertical axis is usually called the y-axis. The point where the x- and y-axis intersect is called the origin.

Given Gracie's grandmother gave her 40 stamps.

Then, each month Gracie adds 30 stamps to her collection,

Coordinate grid labeled points (0, 40), (1, 70), (2, 100), and (3, ?)

A: since she adds 30 stamps each month,

stamps in 3rd month are 100 + 30 = 130.

130 stamps in 3rd month.

B: What does the point  (2, 100),

the graph is plotted between the number of stamps and months,

which gives the  change of stamp each month,

the coordinates (2, 100) say that Gracie has 100 stamps in 2 months.

so option B is correct.

Hence There will be 130 stamps  Gracie have after 3 months,

and The number of stamps Gracie added to her collection in 2 months is 100.

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Answer:

10

Step-by-step explanation:

2x - 7 = 13

+7. +7

2x = 20

20/2x = 10

The type of transaction described in the problem is called an installment purchase.

What is the simple interest?

Simple interest is a type of interest that is calculated on the principal amount of a loan or investment for a specific period of time.

The type of transaction described in the problem is called an installment purchase. In this type of transaction, a buyer pays a deposit at the time of purchase and then makes periodic payments, typically over a fixed period of time, until the full purchase price is paid off. In this case, the buyer pays a deposit of R999 and then pays off the remaining balance over a period of 3 years using simple interest.

To calculate the total amount that the buyer will pay over the 3-year period, we need to calculate the amount of interest that will be charged on the remaining balance. Since simple interest is being used, we can use the formula I = Prt, where I is the interest, P is the principal (the remaining balance), r is the interest rate, and t is the time period.

Assuming an annual interest rate of, for example, 5%, the interest charged on the remaining balance of R4000 (the original price minus the deposit) over 3 years would be:

I = Prt

I = 4000 * 0.05 * 3

I = R600

So the total amount that the buyer will pay over the 3-year period is:

R999 (deposit) + R4000 (remaining balance) + R600 (interest) = R5599

the total cost of the binoculars over the 3-year period will be R5599.

Hence, The type of transaction described in the problem is called an installment purchase.

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the ratio representing the above-described number are given as follows;

In mathematics, parity refers to whether an integer is even or odd. If an integer is a multiple of two, it is even; otherwise, it is odd. For instance, 4, 0, 82 are even because 3, 5, 7, and 21 are all odd numbers.

With regard to the above ratios:

1) Odd numbers to all numbers involved:

There are 10 odd numbers from 1 to 20 (1, 3, 5, 7, 9, 11, 13, 15, 17, 19). So, the ratio of odd numbers to all numbers involved is 10/20 = 1/2.

2) Numbers divisible by 5 to even numbers:

There are 4 numbers from 1 to 20 that are divisible by 5 (5, 10, 15, 20). Out of these 4 numbers, 2 are even (10, 20). So, the ratio of numbers divisible by 5 to even numbers is 4/2 = 2/5.

3) Numbers greater than 7 to numbers less than 12:

There are 4 numbers less than 12 (1 to 7) and 5 numbers greater than 7 (8 to 20). So, the ratio of numbers greater than 7 to numbers less than 12 is 5/4.

4) Even numbers greater than 5 but less than 17 to all numbers involved:

There are 6 even numbers greater than 5 but less than 17 (6, 8, 10, 12, 14, 16). So, the ratio of these even numbers to all numbers involved is 6/20 = 3/10 = 1/2 * 3/5 = 3/10.

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The

speed

indicated in kilometers per hour is 85 km/h, as shown on the circular scale of the automobile

speedometer

.

The automobile

speedometer

is an instrument that measures the speed of a vehicle. It has a circular

scale

that reads both miles per hour (mph) and kilometers per hour (km/h). To determine the

speed

in kilometers per hour, the user must first locate the needle on the scale. The needle should be pointing to a specific number that corresponds to both mph and km/h. For example, if the needle is pointing to 85, then the speed indicated in kilometers per hour is 85 km/h. It is important to note that if the needle is located between two

numbers

, the user should determine the approximate speed by interpolating the two numbers. To find the speed in miles per hour, the user can simply look at the number that corresponds to the needle on the scale. In this case, the speed indicated in miles per hour is 53 mph.

The complete question: An automobile speedometer with circular scales reading both miles per hour and kilometers por hour is shown. What speed is indicated in miles per hour? 100 120 140 80 160 *60 180 200 40 20 220 Own 240 Express your answer in miles per hour v.2 mph

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The number of possible seating arrangements depends on the conditions specified in the problem is 435,456,000

Permutation is the arrangement of objects in a specific order.

a. The mathematics majors occupy the first 6 seats:

The number of permutations of the mathematics majors is simply 6! (6 factorial), since they all have to sit together in a block. After the mathematics majors are seated, we have 12 chairs left for the chemistry and physics majors, who can be arranged in (5 + 7)! / (5! x 7!) ways.

Finally, the total number of permutations for the mathematics majors to occupy the first 6 seats is

=>  6! x (5 + 7)! / (5! x 7!).

=> 570240

b. The mathematics majors cannot occupy the first 6 seats:

In this case, the number of permutations of the mathematics majors is (18 - 6)! / (6! x (12 - 6)!). This is because they cannot occupy the first 6 seats and have to be arranged in the remaining 12 chairs.

Next, the number of permutations for the chemistry majors is (12 - 6)! / (5! x (12 - 6 - 5)!).

Finally, the number of permutations for the physics majors is (12 - 6 - 5)! / 7!.

The total number of permutations for this scenario is

=> (18 - 6)! / (6! x (12 - 6)!) x (12 - 6)! / (5! x (12 - 6 - 5)!) x (12 - 6 - 5)! / 7!.

=> 668250

c. Students with the same major sit in a block:

In this case, the number of permutations of the chemistry majors is simply 5! since they have to sit together in a block.

Similarly, the number of permutations of the mathematics majors is 6! and the number of permutations of the physics majors is 7!.

Finally, the total number of permutations for students with the same major to sit in a block is

=> 5! x 6! x 7!.

=> 435456000

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The persuasion technique that is being used in this case is the black-or-white technique.

This is a persuasion strategy or technique that implies showing the audience there are only two possibilities and the two possibilities are very different (black-or-white). This aims to show the audience they should choose a specific possibility because it is better than the other alternative.

This is the technique being implemented here because the speaker purposes two possibilities buying Mopster mop or having a dirty floor to encourage the audience to purchase this product.

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Answer:

The complete system of inequalities to model this scenario is s ≥ 0, l ≥ 0, 8s + 12l ≤ 160, and s - l < 30.

Step-by-step explanation:

Answer:  8s + 12l ≤ 160.

Step-by-step explanation: I would explain.. but I figured maybe I'd spare you the struggle and give you the answer. If you NEED steps, DM me.

Answer:

Below

Step-by-step explanation:

L x W = area

60 * W = 1800

W = 1800/60 = 30 ft

The value of q is -106 and the required equation is given by q=-106

In Algebra, the like terms are defined as the terms that contain the same variable which is raised to the same power. In algebraic like terms, only the numerical coefficients can vary. We can combine the like terms to simplify the algebraic expressions.

Given here: The statement of an equation" 336 is 230 decreased by q"

230 is decreased by q is equivalent to 230 substracted by q and the number obtained by the above operation is equal to 336

Thus we have the equation as follows

230-q=336

q=230-336

q=-106

Hence, The value of q is -106 and the required equation is given by q=-106

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Answer: The hypotenuse are both 13 cm

Step-by-step explanation:

The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

So, in this case:

c^2 = a^2 + b^2

c^2 = 5^2 + 12^2

c^2 = 25 + 144

c^2 = 169

c = √169

c = 13

So the length of the hypotenuse is 13 cm.

Next, we can use the Pythagorean theorem to find the length of the segments into which the bisector of the right angle divides the hypotenuse. Let's call the length of the segments x. Then, the segments form two right triangles with legs of length x and (13-x)/2.

Using the Pythagorean theorem on each triangle, we have:

x^2 + ((13-x)/2)^2 = 13^2

x^2 + (13-x)^2/4 = 169

x^2 + (13^2 - 2x(13) + x^2)/4 = 169

x^2 + (13^2 - 2x(13))/4 = 169

x^2 + (169 - 26x)/4 = 169

x^2 + 169 - 26x = 676

x^2 - 26x + 507 = 0

Now, we can use the quadratic formula to find x:

x = (-b ± √(b^2 - 4ac)) / 2a

a = 1, b = -26, c = 507

x = (26 ± √(26^2 - 4 * 1 * 507)) / 2 * 1

x = (26 ± √(676)) / 2

x = (26 ± 26) / 2

x = 26 / 2

x = 13

So, the lengths of the segments into which the bisector of the right angle divides the hypotenuse are both 13 cm, to the nearest tenth.