Which of the following situations represent direct variation?
y = -5x
2y = x
y/x = 12
x/y = 4

The number of buttons on each card from Elaine's grandmother is given as follows:

7 buttons.

The number of buttons on each card is obtained applying the proportions in the context of this problem.

Elaine sorted the buttons into 6 piles, putting 8 buttons in each pile, hence the total number is given as follows:

6 x 8 = 48.

Elaine had 6 buttons, hence the number donated is given as follows:

48 - 6 = 42.

6 cards were donated, hence the number of buttons in each card is given as follows:

42/6 = 7.

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1:4

it would be 1 to the ratio of 4 because its 4 numbers listed only once which means youll have a chance of one out of 4 to get one number four different times

There are 2 observations remaining in the data

The complete question is added as an attachment

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

The table of values

From the table of values. we have

Number of observations = 5

Observations with missing values = 3

So, we have

Remaining =5 - 3

Evaluate

Remaining = 2

Hence, the remaining observations is 2

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The linear function that predicts the number of cars that will be sold at a price of x dollars is y = -0.05x + 11580.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

To determine the linear function that predicts the number of cars sold we need to find the slope of the equation.

The two coordinated given are:

(x1, y1) = (52000, 8980)

(x2, y2) = (57000, 8730)

The slope of the equation is given by:

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

m = (8730 - 8980) / (57000 - 52000)

m = - 0.05

Substituting the value of the coordinates and slope in the point-slope form we have:

y - y1 = m (x - x1)

y - 8980 = -0.05(x - 52000)

y - 8980 = -0.05x + 2600

y = -0.05x + 11580

Hence, the linear function that predicts the number of cars that will be sold at a price of x dollars is y = -0.05x + 11580.

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The number of red jelly beans and blue jelly beans are 15 and 40 respectively.

Billy bought a bag of jelly beans from the store. Billy counted the jelly beans when he got home and counted a total of 55. The bag contained red and blue jelly beans. The number of blue jelly beans was 5 less than three times the number of red jelly beans.

Therefore, let's find the jelly beans of each colour.

Using equation,

let

x = number of blue jelly beans

y = number of red jelly beans

Therefore,

x + y = 55

x = 3y - 5

Therefore,

x + y = 55

-x + 3y = 5

add the equations

4y = 60

y = 60 / 4

y = 15

x = 55 - 15

x = 40

Therefore,

number of blue jelly beans = 40

number of red jelly beans = 15

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Answer:4x - 2 = 12

Step-by-step explanation:

Every output value for g is half the output value for f.

I would describe the transformation as a vertical compression by a factor of 1/2, since every y-value was cut in half.

g(x) = 1/2 · f(x)

The value of sin θ from the unit circle is sin θ = 0.9230769

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

The terminal side of angle θ intersects the unit circle in the first quadrant at ( 3√10/10,√10/10 )

So , the equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r²   be equation (1)

Substituting the values of x and y in the equation , we get

x = -5/13

And , y = 12/13

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

So , the value of cos θ = ( -5/13 ) and sin θ = ( 12/13 )

On simplifying the equation , we get

sin θ = ( 12/13 )

sin θ = 0.9230769

Hence , the value of sin θ = 0.9230769

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The measures of the interior angles of the triangle are: A=45°, B=110° and C=25°.

Triangles are geometric figures with three (3) sides. They can present different classifications regarding their sides or angles.

The sum of any triangle's angles will always be 180°, independent of its classification.

The question gives that the angles of the given  triangle are:

A=x

B= x+65°

C=25°

If A+B+C= 180° with the given values for angles B and C you can write:

x+x+65+25=180

2x+90=180

2x=180-90

x=90/2

x=45°

Thus, from the given information  you have:

A=45°

B= 45+65°=110°

C=25°

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The volume of the cylinder with a radius of 19 km and a height of 5 km is 5706 km³, using 3.14 for π.

What is the volume of a cylinder?

The cylinder's volume is given by the formula, πr²h, where r is the radius of the circular base and h is the height of the cylinder.

The formula for the volume of a cylinder is given by:

V = π * r²* h

Where r is the radius of the base and h is the height of the cylinder.

Given that the radius of the cylinder is 19 km and the height is 5 km, we can substitute these values into the formula:

V = π * 19² * 5

V = 3.14 * 361 * 5

V = 5706 km³

Therefore, the volume of the cylinder with a radius of 19 km and a height of 5 km is 5706 km³, using 3.14 for π.

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Answer:

[tex](3+\sqrt{7},7+2\sqrt{7})[/tex]

[tex](3-\sqrt{7},7-2\sqrt{7})[/tex]

Step-by-step explanation:

Given equations:

[tex]\begin{cases}y=2x+1\\y=x^2-4x+3\end{cases}[/tex]

Substitute the second equation into the first equation:

[tex]\implies x^2-4x+3=2x+1[/tex]

Rearrange so that the terms in x are on the left side of the equation and the constants are on the right:

[tex]\implies x^2-4x-2x=1-3[/tex]

[tex]\implies x^2-6x=-2[/tex]

Add the square of half the coefficient of the term in x to both sides:

[tex]\implies x^2-6x+\left(\dfrac{-6}{2}\right)^2=-2+\left(\dfrac{-6}{2}\right)^2[/tex]

[tex]\implies x^2-6x+9=-2+9[/tex]

[tex]\implies x^2-6x+9=7[/tex]

Factor the perfect square trinomial on the left side of the equation:

[tex]\implies x^2-3x-3x+9=7[/tex]

[tex]\implies x(x-3)-3(x-3)=7[/tex]

[tex]\implies (x-3)(x-3)=7[/tex]

[tex]\implies (x-3)^2=7[/tex]

Square root both sides of the equation:

[tex]\implies x-3=\pm \sqrt{7}[/tex]

Add 3 to both sides of the equation:

[tex]\implies x=3\pm\sqrt{7}[/tex]

To find the y-values, substitute the found x-values into the first equation:

[tex]x=3+\sqrt{7}\implies y=2(3+\sqrt{7})+1=7+2\sqrt{7}[/tex]

[tex]x=3-\sqrt{7}\implies y=2(3-\sqrt{7})+1=7-2\sqrt{7}[/tex]

Therefore, the solutions to the system of equations are:

The percent of the total calories in each brownie comes from fat is 34%

Percentage is described as a number or ratio expressed as a fraction of 100.

It is often represented with the percent sign, "%"

Abbreviations like "pct" and "pc" are used to denoted it.

Percentage is a dimensionless number, that is, it has no unit of measurement.

From the information given, we have that;

207 calories of fat/606 calories in a brownie × 100/1

Divide the values, we get;

0. 34 × 100/1

Multiply the values

34%

Hence, the value is 34%

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The area of the lawn that will be watered by the sprinkler is 191.1 square feet, rounded to the nearest tenth.

Area is a measurement of the size of a two-dimensional surface, such as a square, rectangle, or circle. It is calculated by multiplying the length of the surface by its width. Area can also be measured in terms of square units, such as square feet or square meters. Area is an important concept in mathematics and is used to measure the size of shapes and objects. It is also used to find the total area of a group of shapes.

To calculate the area, use the formula A = r2θ, where A is the area, r is the radius, and θ is the central angle in radians. In this scenario, the radius is 10 ft and the central angle is 30°, or π/6 radians. Plugging these numbers into the formula, we get A = (10 ft)2(π/6 radians), or 191.1 square feet.

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The equation, in slope-intercept form is y = 0.75x + 1.75

The equation for total cost can be represented in slope-intercept form as:

y = mx + b

where y is the total cost, x is the number of tacos,

m is the slope (the cost per taco), and b is the y-intercept (the cost of the drink).

So in this case,

m = 0.75 (the cost per taco),

b = 1.75 (the cost of the drink), and

x is the number of tacos.

So, the equation is:

y = 0.75x + 1.75

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Complete question

Chin is sells food at a local taco truck. She sells a soda which costs $1.75. Tacos cost $0.75 each.

What is the equation for Chin’s charges needed to solve the system and find the cost of the initial and additional hours?

The total number of cards is 192 cards

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

Initial number of cards = 144 cards.

Nicole pays for the:

9/27 = 1/3 of the set

so she gets proportional amount of cards:

1/3*144 = 48 cards

Total number of cards Nicole has now:

144 + 48 = 192

Hence, the total number of cards is 192

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Complete question

Nicole has 144 role-playing cards and $9

to buy more cards. She and her friends buy

another set that costs $27. They evenly

split the cost and the cards in the set. How

many cards does Nicole have after she buys

part of a set with her friends?

The slope-intercept form of the function described by this table?

x 0 1 2 3

y 3 8 13 18. is y = 5x + 3

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope of the line and b is the y-intercept. To find the equation that fits the table, we can use the two points (0, 3) and (1, 8) to calculate the slope and y-intercept.

First, calculate the slope:

m = (8 - 3) / (1 - 0) = 5

Next, use the point-slope form of a line to find the y-intercept:

y - 3 = 5(x - 0)

Expanding the right-hand side:

y - 3 = 5x

Adding 3 to both sides:

y = 5x + 3

So, the slope-intercept form of the function described by the table is:

y = 5x + 3

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Answer: 16.65

Step-by-step explanation:

Answer:

y=1/6x+3

Step-by-step explanation:

THe equation of the graph is y=mx+c

so,

m= { (-3)-(-4) } / (-1)-(-7) = 1/6

intercept = (0,y)

1/6= (y+3)/1

y=3

so, the equation ⇒y=1/6x+3.

so a and b are positive integer

so when we put the all options in place of a one by one in equation we will get

a+26=b²

10+26= b²

b=√36

b= 6

so a must be 10.

-14 is less than 16. All negative numbers are less than positives!

Answer:

Step-by-step explanation:

The equation of the line with the given points is y = 6x - 4. This can be derived by calculating the slope of the line, which is 6, and then using the point-slope form of the equation of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. In this case, the given points are (x1, y1) = (1, 10), so the equation of the line is y - 10 = 6(x - 1) or y = 6x - 4.

Answer y == 3

+7

Step-by-step explanation:

The graph of a linear relationship contains the points (1, 10) and (3, 16).

Write the equation of the line in slope-intercept fo

Step-by-step explanation:

the general slope-intercept form is

y = ax + b

a is the slope, which is the ratio of "y coordinate change / x coordinate change" when going from one point to another on the line.

b is the y-intercept - the y value when x = 0.

for the slope we see

x changes by +2 (from 1 to 3)

y changes by +6 (from 10 to 16)

so, the slope a is +6/+2 = 3

and the semi-ready equation is

y = 3x + b.

now we use one of the points in the equation to solve for b. I picked (1, 10) :

10 = 3×1 + b = 3 + b

b = 7

so, the full equation is

y = 3x + 7

The value of the variable x when y = 6 is 2

It is important to note that a proportional relationship between variables or events means that as one increases in its value, the other also increases in the same way.

From the information given, we have that;

The variable y and x is proportional

This is represented as;

y ∝ x

Find the constant value

k = y/x

Substitute the values

k = 12/4

k = 3

Then when y = 6, we get;

x = y/k

x = 6/3

x = 2

Hence, the value is 2

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R and S are points on the number line. If RS= 11 and S lies at 5, where could R be located 16 or -6.

A number line is a visual representation of numbers arranged in a continuous sequence along a straight line. It is used to represent the real numbers and to help visualize relative sizes and order of numbers. The numbers on a number line are placed at equal intervals, and the distance between two numbers represents the magnitude of the difference between them.

A typical number line starts from a specific number on the left, such as zero, and extends to the right, with positive numbers increasing as you move to the right and negative numbers decreasing as you move to the left. Points on the number line correspond to specific numbers, and the position of a point on the line represents the value of that number.

The number line is a useful tool in mathematics for solving problems, such as determining the solution to an equation, estimating the value of a decimal or fraction, or visualizing the magnitude of a negative or positive number. It is also used in geometry to represent the positions of points and to understand concepts such as distance and midpoint.

If S lies at 5 on the number line and RS = 11, then R could be located at either 5 + 11 = 16 or 5 - 11 = -6. So, R could be at either 16 or -6 on the number line.

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The cosine of the angle  θ  is √5/5  whose terminal side passes through the given point

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Given here: The terminal side goes through the point  (√5/5,2√5/5)

Thus we have cosθ =√5/5 and sin θ =-2√5/5

now tan θ =sinθ /cosθ

        tanθ    =-2√5/5 / √5/5

              θ = 63.434

Hence, cosθ =√5/5

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Using linear equations, the cost of each t - shirt is $8.

Consider how (0,5), (1, 4), (2, 3), etc. are all possible answers to the linear equation x + y = 5 to illustrate the infinite number of solutions to a linear equation with two variables. One solution that satisfies both solutions can exist for systems of two linear equations with two variables.

The only way to solve x + y = 5 and 2x y = 1 is to combine two equations with two variables into one equation with one variable, which is what we do when solving a system of equations. The two equations in the system can be added or subtracted to cancel out, or eliminate, one of the variables as each equation in the system has two variables.

Given,

Kathy pays 30 for 3 shirts and 2 caps.

marc pays 23 for 1 shirt and 5 caps.

Let us assume cost of t - shirt = x

cost of cap = y

⇒ 3x + 2y = 30

⇒ x + 5y = 23

on solving the equations using elimination method,

Multiply 2 equation by 3,

⇒ 3x + 2y = 30

⇒ 3x + 15y = 69

Now, subtract both equation -

⇒ - 13y = -39

⇒ y = 3

x = 30 - 2 × 3 / 3

x = 8

cost of each t - shirt = $ 8

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Answer:

(2, -5)

Step-by-step explanation:

-7x=y=-19

y=7x-19

-2x+3(7x-19)=-19

-2x+21x-57=-19

19x-57=-19

19x=38

x=2

-2(2)+3y=-19

-4+3y=-19

3y=-15

y=-5

The amount to be deposited for 10 years is $2000.

Given that,

Simple interest  is 5%

The amount to be in the account is $3000

The time period is 10 years.

The formula associated with these values is

A = P(1+rt)

where A = amount after 10 years

P = amount to be deposited in the account

r = rate of interest

t = time period

By applying the formula,

3000 = P (1+ (5% × 10))

3000 = P (1+ (0.05 × 10)

3000 = P (1 + 0.5)

3000 = P (1.5)

P = 3000/1.5

P = 2000 $

Therefore, $2000 should be deposited in an account in order to have $3000 in the account after 10 years.

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The given function

g(x)  =  (x√x)/(x - 6)²

is continuous at  x = 36,

In mathematics, The function is called as continuous at the particular value of x,  if right hand limit, left hand limit and the value of function at x all are equal.

RHL   = LHL  = F(x)

Limit exist and continuous

Given that,

F(x)  =   (x√x)/(x - 6)²

To check whether it is continuous at x = 36

First taking LHL,

[tex]\lim_{h \to \00}[/tex]    [(36-h)√(36-h)]/((36-h) - 6)²

[tex]\lim_{h \to \00}[/tex]  [(36-0)√(36-0)]/((36-0) - 6)²

⇒   (36 x 6)/30²

⇒    6/25

Now, taking RHL

[tex]\lim_{h \to \00}[/tex]    [(36+h)√(36+h)]/((36+h) - 6)²

[tex]\lim_{h \to \00}[/tex]  [(36+0)√(36+0)]/((36+0) - 6)²

⇒   (36 x 6)/30²

⇒    6/25

The value at x = 36

F(-1)  =  [(36)√(36)]/((36) - 6)²

⇒   (36 x 6)/30²

⇒    6/25

RHL = LHL = F(36)

Hence Proved,  the function is continuous at x = 36

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