Solve for y:
-3x+4y=28

The amount of coffee she bought is 5.16 pounds.

She received a $70 gift card for a coffee store.

She used it in buying some coffee that cost $8.36 per pound after buying a coffee she had $26.85 left.

Therefore, base on the card, the number of pounds of coffee she bought can be calculated as follows;

Hence,

let

the amount of coffee she bought in pounds = x

Hence,

70 = 8.36x + 26.85

70  - 26.85 = 8.36x

43.15 = 8.36x

divide both sides by 8.36

43.15 / 8.36 = x

x = 5.16148325359

Therefore, the amount in pounds is 5.16 pounds.

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We will determine the area of the green section as follows:

Here alpha is the angle [In radians] and r is the radius-

*First: We determine the angle:

Now, we transform it to radians:

*Second: We replace on the equation:

So, the area of the green sector is 69pi/5 square centimeters. [Approximately 43.4 square centimeters]

Answer:

A ≈ 43.4 cm²

Step-by-step explanation:

the area (A) of the green sector is calculated as

A = area of circle × fraction of circle

  given d = 12 then r = 12 ÷ 2 = 6 cm

the central angle of the green sector = 180° - 42° = 138°

then

A = πr² × [tex]\frac{138}{360}[/tex] ( simplify fraction by dividing numerator/denominator by 6 )

   = π × 6² × [tex]\frac{23}{60}[/tex]

   = 36π × [tex]\frac{23}{60}[/tex]

   = [tex]\frac{36\\pi (23) }{60}[/tex]

   ≈ 43.4 cm² ( to the nearest tenth )

Deterministic.

The relationship between the variables is deterministic. A deterministic relationship refers to a relationship in which the dependent variable does not depend on other elements (variables) other than the independent element classified in the relationship. The independent variable (element) in the relationship possesses an exact value. Hence deterministic relationship is also named as the exact relationship between variables.

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Each midpoint's coordinate is given by the mean of the respective coordinates of the two endpoints of the segment. Then, if we say M is the midpoint of that segment, we have:

Mx = (-4 + 4)/2 = 0/2 = 0

My = [6 + (-2)]/2 = (6 - 2)/2 = 4/2 = 2

Therefore, writing those coordinates as an ordered pair, we have:

M = (0, 2)

We will have the following:

Now, we corroborate with one of the expression, in our case we will analyze y = x^2:

So, the expression taht represents the value given is:

Answer:

(4,-5)

Step-by-step explanation:

A is 5 units above the x axis so a' will be 5 units below the x axis.

Answer: -27/40

Step-by-step explanation:

The figure above is a rectangle

The classifications of a rectangle are:

1. A rectangle has 4 sides and angles, therefore, it is a quadrilateral.

2. Each interior angle is a right-angle, that is 90⁰

3. The sum of the interior angles equals 360

4. The opposite sides are parallel

5. The opposite sides are equal

6. The diagonals bisect each other

7. The diagonals have the same length

Answer:

AD

Step-by-step explanation:

Given

x - y + (- z) where x and z are positive real numbers and y is a negative real number.

Find

i) What are the directions of motion for this calculation ?

ii) Is the final answer positive , negative , or undetermined ?

Explanation

i) as we have given

x - y + (- z)

x - y - z

(x - y) - z

right -left - left

ii) for this we take examples

let x = 2 , y = -1 and z = 2

2- (- 1) + (- 2) = 1 , positive

now

let x = 2 , y = -1 and z = 5

2 - (- 1) + (- 5) = 3 - 5 = -2 , negative

so , it is both negative or positive

hence it is undetermined

Final Answer

Hence , the correct option is

i) Right, left , left

ii) Undetermined

Answer:

Question 4

Answer: Alternative C - 0

Step-by-step explanation:

Since x→∞, we can substitute the values of x for values as 10, 100, 1000 and see the tendency of the function when the values are getting higher (closer to ∞):

For x = 10

f(10) = 0.5*10^(-3/4)

f(10) = 0.089

For x = 100

f(10) = 0.5*100^(-3/4)

f(10) = 0.016

For x = 1000

f(10) = 0.5*1000^(-3/4)

f(10) = 0.003

As we can see, when the x-values are getting closer to infinite, the y-values tends to zero. Thus, alternative C is correct.

If the coordinates of quadrilateral ABCD are A (-6,2) B (-5,3) C (7,3) D (0,4) and it is translated 4 units down and 3 units right, then the coordinates of the image is A'(-3,-2), B'(-2,-1), C'(10,-1) and D'(3,0)

The coordinates of the quadrilateral ABCD is

A (-6,2) , B(-5,3), C(7,3) and D(0,4)

The quadrilateral is translated 4 units down and 3 units right

After translation

A(x, y)⇒ A(x + a, y +b)

The value of a and b will be positive if the shift is right and up.

The value of a and b will be negative if the shift is left and down.

Therefore

a = 3, b = -4

The coordinates of A' =(-6+3,2-4)=(-3,-2)

The coordinates of B' =(-5+3,3-4)=(-2,-1)

The coordinates of C' =(7+3,3-4)=(10,-1)

The coordinates of D' =(0+3,4-4)=(3,0)

Hence, If the coordinates of quadrilateral ABCD are A (-6,2) B (-5,3) C (7,3) D (0,4) and it is translated 4 units down and 3 units right, then the coordinates of the image is A'(-3, -2), B'(-2, -1), C'(10, -1) and D'(3, 0)

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In terms of the calculation, the answer is 39/4 in improper fraction.

An improper fraction has a denominator that is greater than or equal to the numerator. Based on the numerator and denominator values, proper fractions and improper fractions are the two main types of fractions in mathematics.

A mixed fraction is a fraction formed by combining a natural number and a proper fraction. It is a shortened version of an improper fraction.

The given equation is [tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] .

Taking 4 as LCM from the above equation.

[tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] = (13/4) + (13/2)

[tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] = (13+26)/4

[tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] = 39/4

Now, since the solution must be proffered in an improper fraction.

Therefore, the obtained improper fraction is 39/4.

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Answer:

Hope this helps!!

Answer:

x = 32

Step-by-step explanation:

-6(x-18) = -84

Divide both sides by -6

x - 18 = 14

Add 18 to both sides

x = 32

Answer:

  y = -3x +6

Step-by-step explanation:

You want to solve the equation 6x +2y = 12 for y.

We can isolate the y-term by subtracting 6x from both sides.

  6x -6x +2y = -6x +12

  2y = -6x +12 . . . . . . . . . . simplify

Then we can get y by itself by dividing both sides by 2:

  2y/2 = -6x/2 +12/2

  y = -3x +6 . . . . . . . . . . . simplify

The expression for y is  y = -3x +6.

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Part a

The domain is the set of x-values, which is [tex][1, \infty)[/tex].

Part b

The range is the set of y-values, which is [tex][-3, \infty)[/tex].

Part c

As [tex]x \to \infty[/tex], [tex]y \to \infty[/tex].

Part d

The x-intercept is when y=0, which is [tex](2, 0)[/tex].

Part e

The absolute minimum is the lowest point, which has a y-coordinate of [tex]-3[/tex].

Part a

The domain is the set of x-values, which is .

Part b

The range is the set of y-values, which is .

Part c

As , .

Part d

The x-intercept is when y=0, which is .

Part e

The absolute minimum is the lowest point, which has a y-coordinate of

It is not possible to write a linear inequality such that the solution contains only positive values of x and y.

This happens because every line on the coordinate plane must have a y-intercept and/or an x-intercept. When the line crosses an axis, either the variable x or y changes its sign.

The following is not a step in a hypothesis test; d. if the sample data is located in the critical region, we reject the null hypothesis.

There are two hypotheses. The first one is called the null hypothesis and it is chosen such that it predicts nullity or no change in a thing. It is usually the hypothesis against which we do the test.

The hypothesis which substitutes the null hypothesis is an alternate hypothesis.

We know that the Null hypothesis is the one that researchers try to disprove.

The null hypothesis must be rejected if we choose the 99.7 percent of  confidence level.

The following is not a step in a hypothesis test; d. if the sample data is located in the critical region, we reject the null hypothesis.

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The equation for constant proportionality is y ∝ m .

1760 is a constant of proportionality.

The ratio of two proportional values at a constant value is the proportionality constant. When either the ratio or the product of two variables results in a constant, the connection between the two is proportional. The ratio between the two stated quantities affects the proportionality constant's value.

The formula y = 1760m describes the relationship between a distance in yards (y) and a similar value in miles (m).

As a result, the graph of the aforementioned equation will be a straight line with a constant slope of 1760 that passes through the origin (0, 0).

As a result, a measurement in yards and a measurement in miles have the same proportionality relationship.

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The value of g(a) + h(a) is a²-3a-2 or (a-2)(a-1) using addition of functions.

Given a collection of inputs X (domain) and a set of potential outputs Y (codomain), a function is more technically defined as a set of ordered pairings (x,y) where x belongs to X  and y belongs to Y, with the caveat that there can only be one ordered pair with the same value of x. The function notation f:XY can be used to express that f is a function from X to Y

Adding two functions-

g(a) = a²- 2

h(a) = -3a

Let h(a) be g(a) + h(a)

So h(a) = a² - 2 - 3a.

We can factorize the function into (a-2)(a-1).

So we get h(a) = (a-2)(a-1).

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Answer:

Surface area= 6(5·5)+6(3·3)-2(3·3)

Step-by-step explanation:

first figure out the surface area of both cubes

for the larger cube- 5 multiplied by 5 for the area of one side then multiplied by 6 for all faces

for the smaller cube- 3 multiplied by 3 for the area of one side then multiplied by 6 for all the faces.

the cubes are touching on one face, this is the whole area of one side of the 3 by 3 cube, meaning two of these faces must be subtracted to find the surface area of the whole shape

hope that helps

The number of students that enrolled = 3,500 students.

This is defined as the intake of individuals into an organism or students into an institution through adherence to specific orders given by the administrative department of the organisation.

The number of students that apply= 20,000 students

The percentage of students that are accepted= 70% of 20,000

That is, 70/100× 20,000

= 1400000/100

= 14,000 students.

The quantity of students that actually enroll = 25% of 14,000

That is, 25/100× 14000

= 350000/100

= 3,500 students.

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Given:

1. The sum of X and 96 equals half of X.

To determine the algebraic equation, we note that the sum of x and 96 would be:

x+96

Next, half of x must be like this:

x/2

Then, the phrase equals means we set x+96 equals to x/2.

Therefore, the answer is:

Based on the linear relationship between the ticket numbers and the total cost, the cost of one ticket can be found to be A. $10.50

First, find the rate of change in ticket pricing assuming the number of tickets is x and the total cost is y.

The rate of change is:

= Change in y / Change in x

= (67.50 - 46.50) / (5 - 3)

= $10.50

Then find the y-intercept:

y = Slope(x) + y-intercept

67.50 = 10.50(5) + y-intercept

y-intercept  = 67.50 - 52.50

y-intercept = 15

Linear equation is:

Total cost = Rate of change (Tickets) + y-intercept

A single ticket would cost $10.50 which is the rate of change.

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The required rate of change and slope of the given relationship is $10.50.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
The slope for the linear function is given as,
m = (y₂ - y₁) /  (x₂ - x₁)

From the table substitute the value in the above equation,
m = [67.50-46.50]/[5-3]
m = 21 / 2
m = 10.50

Thus, the required rate of change and slope of the given relationship is $10.50.

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The coordinates of the vertices of the image of the square are S'(x, y) = (- 1, - 4), T'(x, y) = (- 1, 1), U'(x, y) = (4, 1) and V'(x, y) = (4, - 4).

In this problem we need to make use of a translation on a geometric locus on a Cartesian plane, which is generated by four points representing the vertices of the square. The translation is a kind of rigid transformation, whose formula is shown below:

P'(x, y) = P(x, y) + t(x, y)

Where:

If we know that S(x, y) = (- 6, - 5), T(x, y) = (- 6, 0), U(x, y) = (- 1, 0) and V(x, y) = (- 1, - 5) and t(x, y) = (5, 1), then the locations of the vertices of the triangle are:

S'(x, y) = (- 6, - 5) + (5, 1)

S'(x, y) = (- 1, - 4)

T'(x, y) = (- 6, 0) + (5, 1)

T'(x, y) = (- 1, 1)

U'(x, y) = (- 1, 0) + (5, 1)

U'(x, y) = (4, 1)

V'(x, y) = (- 1, - 5) + (5, 1)

V'(x, y) = (4, - 4)

The location of the image of the square is shown below.

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The sum of  -1  and 3/4 and 2 and 1/2 is the same as the difference between 2 and 1/2 and 1 and 3/4.

First we will convert the mixed fractions into improper fractions.

-1 and 3/4 = -7/4

2 and 1/2 = 5/2

Sum of -1 and 3/4 and 2 and 1/2 = -7/4 + 5/2 = -7/4 + 10/4 = 3/4

Difference between  2 and 1/2 and 1 and 3/4 = 5/2 - 7/4 = 10/4 - 7/4 = 3/4

As both the values equal to 3/4 , we can say that the sum of  -1  and 3/4 and 2 and 1/2 is the same as the difference between 2 and 1/2 and 1 and 3/4.

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The missing value is 1/3 from the table that represents Judy's rate which is the correct answer that would be an option (C).

In mathematics, relations are used to describe the link between the components of two sets. They aid in mapping items from one set (known as the domain) to elements from another set (known as the range), resulting in ordered pairs of the form (input, output).

We have been given the rates of time taken by Judy and Sal to complete a puzzle.

Sal's rate is r, as we can see from the table. Judy is said to take 3 hours to solve a puzzle by herself. It barely takes them two hours to work with Sal.

Because Judy completes the task in three hours, the portion of the puzzle finished in one hour is 1/3.

Therefore, the missing value is 1/3 from the table that represents Judy's rate

Hence, the correct answer would be an option (C).

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By the concept of measurement of length we get the remaining length of the pipe 65 cm.

The total length of pipe before it was used by the plumber was 2.5 metre = (2.5 x 100)cm = 250cm.

Since,the plumber needs to cut lengths of 60cm, 35cm and 90cm

Thus,total Length of the pipe cut  by the plumber = 60cm + 35cm + 90cm = 185cm

After subtracting the length of pipe used by the plumber from the original length of the pipe, we get,

The remaining length of the pipe = 250 - 185 = 65cm

Hence, the remaining length of the pipe is 65 cm.

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