Select the correct answer.
Gas station A has posted a chart that shows the price of gasoline in terms of the number of gallons.

The value of x in the equation is 59/5

The equation is given as:

5x = 59

Divide both sides by 5

x = 59/5

This means that the value of x in the equation is 59/5

To know if the value is accurate, we simply multiply 5 by 59/5 and we get 59 as in 5x = 59

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Answer: B and C

Step-by-step explanation:

Let's start off with some definitions.

Supplementary Angles: Two angles that add up to 180°.

Right Angle: One angle equal to 90°. Also identified with a square on the angle.

Complementary Angles: Two angles that add up to 90°.

Straight Angle: A straight line, which equals to 180°.

Right off the bad, we can knock off A and D because there is no proof of those being seen.

The angle <EFH is a right angle because it is equal to 90°. If you pay close attention, the angles <EFG and <GFH both add up to 90°, making them complementary angles.

Therefore, the correct answers are B and C.

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ABC reports the liability on the balance sheet as a $1 million current liability, and a $4 million long-term liability.

A current liability is a liability that is payable within 12 months or one year.

On the other hand, a long-term liability is a liability that is payable after 12 months or one year.

Since $1 million is payable in each of the next five years, this implies $1 million is payable within one year while $4 million is payable after one year.

Therefore, ABC reports the liability on the balance sheet as a $1 million current liability, and a $4 million long-term liability.

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Answer:

1/4, 0.5, -4/6, 4.5, 1/3, 7/8

explanation: it is the ratio of two integers

a/b where b is not = to 0

Answer:

see below

Step-by-step explanation:

2: letter at the vertex,  placing a letter or number inside .... , or by using 3 letters

3:

WXY

WXZ

YXZ

4: X

In the given diagram, the length of OQ is 11

From the question, we are to determine the length of OQ

From the given information,

OP = 17

QP = 6

In the diagram, we can observe that

OQ + QP = OP

∴ OQ + 6 = 17

Subtract 6 from both sides

OQ + 6 - 6 = 17 - 6

OQ = 11

Hence, the length of OQ is 11

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[tex]\huge \boxed{\sf 11}\\\\\\\displaystyle \sf OP=OQ+QP\\\\OQ=OP-QP\\\\OQ=17-6\\\\OQ=11[/tex]

Answer:

-5 + 12 i

Step-by-step explanation:

(2 + 3i)^2   = 4  + 6i  + 6i  + 9i^2

                 =   4   + 12 i   + 9(-1)

                     = - 5 + 12 i

In the imaged attached, the most precise name for ABCD  is known to be rhombus.

Looking at the shape attached, one can see that the diagonals of a parallelogram are said to be bisecting one other and if it cross at right angles, it is said to be a rhombus.

Using the Diagonal midpoints of AC and BD, the equation will be:

(A+C)/2

(B+D)/2

To find if the midpoints are similar, then:

A +C = (3, 5) +(6, 2) = (9, 7)

B +D = (7, 6) +(2, 1) = (9, 7)

Therefore, from the solution above, the midpoints of the diagonals are the same, making the shape to be a parallelogram.

In terms of Diagonal vectors, the shape will be perpendicular when the figure is a rhombus. So:

 AC = C -A = (6, 2) -(3, 5) = (3, -3)

BD = D -B = (2, 1) -(7, 6) = (-5, -5)

So the lengths will be (3√2 vs 5√2).

Note also that the dot-product of these values need to be zero if they are perpendicular and as such:

 AC·BD = x1·x2 +y1·y2 = (3)(-5) +(-3)(-5) = -15 +15 = 0

Therefore, one can say that the diagonals are known to different length and are perpendicular bisectors, so the shape above is regarded as rhombus.

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A ratio shows us the number of times a number contains another number. The maximum amount of purple that Susan can make is 25 ml.

A ratio shows us the number of times a number contains another number.

Susan makes purple paint by mixing red and blue paint in a ratio of 2:3. Now, if Susan wants to use the complete red paint then,

Purple paint she can make = 2/3 × 6/6 = 12 ml of red paint / 18 ml of blue paint

If Susan wants to use the complete blue paint then,

Purple paint she can make = 2/3 × 5/5 = 10 ml of red paint / 15 ml of blue paint

As per the first condition 18ml of blue paint is needed which is not possible, therefore, the second case is possible.

Thus, Susan needs to mix 10 ml of red paint and 15 ml of blue paint. Therefore, the amount of paint that Susan will make is,

Total Paint = 10ml + 15ml = 25ml

Hence, the maximum amount of purple that Susan can make is 25 ml.

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Answer:

d. 93 [tex]m^{2}[/tex]

Step-by-step explanation:

4×3= 12, 12/2 =6, 6×4 = 24

5×3= 15, 15×4= 60

3×3=9,

24+60+9= 93

All the parts are answered , y =  6x + 5 represents the scatter data points given.

The complete question is

A coach is assessing the correlation between the number of hours spent practising and the average number of points scored in a game. The table shows the data:

Number of hours spent practising

(x) 0 0.5 1 1.5 2 2.5 3 3.5 4

Score in the game

(y) 5 8 11 14 17 20 23 26 29

Part A: Is there any correlation between the number of hours spent practising and the score in the game? Justify your answer. (4 points)

Part B: Write a function that best fits the data. (3 points)

Part C: What does the slope and y-intercept of the plot indicate? (3 points)

A function is a law that connects the y and x variable , i.e. the dependent and independent variable.

Part (A)

There is a positive correlation between the number of hours spent practising and the score in the game , as the time is increasing the scores is also seen to be increasing.

Part (B)

From the online scatter point equation calculator or by using three points which best fits the linear regression the equation can be determined

y =  6x + 5

x represents the timeline spent in practising

Part C:

slope = 6

When the time spent practising increases by 1 hour,  the average scores increases by 1 hour, the score in a game is predicted to increase by an average of 6 and

as intercept = 5

When no time is spent on the practice the score obtained is 5.

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The quadratic equation  is y = -0.15x² + 2x + 5.5 , Option D is the correct answer.

The complete question is

If a person who is 5.5 feet tall throws a baseball into the air, the path can be modelled using the table of values, where x represents the time in seconds and y is the height of the ball in feet.

(table is in the photo below)

Which quadratic equation models the data in the table?

y= −0.25x2 + 2x + 5.5

y= −0.35x2 + 2x + 5.5

y= −0.27x2 + 3x + 5.5

y= −0.15x2 + 2x + 5.5

The quadratic equation represented by the table is y = -0.15x² + 2x + 5.5

When  two algebraic expressions are linked with an equal sign , the expression formed is called an Equation.

The standard form of the Quadratic equation is

y = ax² + bx + c

here a, b and c are constants.

From the given data in the table

at point (0, 5.5)

5.5 = a(0)² + b(0) + c          

at point (1, 7.35)

7.35 = a(1)² + b(1) + c    

at point (2, 8.9)

8.9 = a(2)² + b(2) + c    

The system of equations will be solved to determine the value of a,b and c

a= -0.15, b = 2, c = 5.5

Therefore , The quadratic equation  is y = -0.15x² + 2x + 5.5 .

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Answer:

B) y= -0.25x^2 + 2x + 5

Step-by-step explanation:

I got it correct on test

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The value of x is 2 because the centroid of the triangle divides each median in the ratio of 2:1 option (C) is correct.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

RQ = 3x+2 ,QN = 2x and SM=3x

In the figure, the TM, Rn, and SL are medians of the triangle SRT and Q is the centroid.

The centroid of the triangle divides each median in the ratio 2:1

RQ/QN = 2/1

(3x+2)/2x = 2/1

After solving:

3x + 2 = 4x

x = 2

Thus, the value of x is 2 because the centroid of the triangle divides each median in the ratio of 2:1 option (C) is correct.

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Answer:

No

Step-by-step explanation:

To determine if a point is a solution to a system of equations, you need to determine if the point is a solution to both equations.

Is ( 2,10) a solution to -3x-4y = 4

Substitute into the equation and see if it is true

-3(2) -4(10) = 4

-6 -40 = 4

-46 =4

This is not true so it is not a solution

Answer:

No

Step-by-step explanation:

The solution(s) of a system is/are the point(s) (x, y) where the lines intersect.

The question asks if (2, 10) is a solution of the system. This means the "x" value is "2" and the "y" value is "10".

We can substitute those values into both of the equations.

[tex]-3x-4y=4\\-3(2)-4(10)=4\\-6-40=4\\-46=6 \Rightarrow Incorrect![/tex]

The "x" and "y" values must be true for both equations, therefore (2, 10) is not a solution of the system.

Answer:

Step-by-step explanation:

given

cos(30°) = [tex]\frac{adjacent}{hypotenuse} \\[/tex]

cos(30°) = [tex]\frac{b}{c} \\[/tex]

cos(30°)=[tex]\frac{b}{16}[/tex]

b = 16cos(30°)

b [tex]16(\frac{\sqrt{3} }{2})\\ = 8\sqrt{3}[/tex]

The fraction of their student loan will be left to spend is half of their loan.

A number expressed quotient, in which numerator is divided by denominator is called a fraction.

Let the loan amount be $100.

Expenses for food is given that two fifths of their loan

i.e.

= 2/5 × 100

= $40

Now,

Remaining part will be = $100- $40 = $60

So,

Expenses for travel are given that one sixth of their loan,

i.e.

= 1/6 × 60

= $10

So,

Remaining part will be = $60 - $10 = $50

Hence, the fraction of their student loan will be left to spend is half of their loan.

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Answer:

1.5kg

Step-by-step explanation:

The mean for the packages on day 1 will be:

= (1 + 8 + 1 + 12 + 1 + 11 + 7 + 6)/8

= 47/8

= 5.875

The mean for day 2 will be:

= (47 + 12)/8

= 59/8

= 7.375

The increase in mean:

= 7.375 - 5.875

= 1.5

Answer:

The factors are (x-7) and (x-4)

Step-by-step explanation:

We are finding the factors of a function from the zeros

The zeros are 7 and 4

We can use the zero product property which is

(x-b)(x-c) = 0  where b and c are the zeros

(x-7) (x-4) =0

The factors are (x-7) and (x-4)

1) The equation of the line passing through (−4, 4) and parallel to the line whose equation is 7x − 9y − 8 = 0 is; y - 4 =  ⁷/₉(x + 4)

1) We are told that the line passes through (−4, 4) and is parallel to the line whose equation is 7x − 9y − 8 = 0

Thus, let us rearrange to find the slope.

7x − 9y − 8 = 0

⇒ 9y = 7x - 8

⇒ y = ⁷/₉x - ⁸/₉

Slope; m = ⁷/₉

Now,  the point slope formula is;

y − y₁ = m(x − x₁)

where;

y₁ is the y-coordinate

x₁ is the x-coordinate

m is the slope

Thus the line Passing through (−4,4) is;

y - 4 =  ⁷/₉(x + 4)

2) The equation in general form is;

y = 4 + ⁷/₉x + ²⁸/₉

y = ⁷/₉x + ⁶⁴/₉

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Step-by-step explanation:

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Answer:

$90

Step-by-step explanation:

Answer:

probability; ( of choosing a yellow marble)

7 yellow marbles + 10 orange marbles = 17 in total

if the no of yellow marbles is 7 therefore = ⁷/10

so that is the probability ⁷/10

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The measure of the angle EFD will be 68 degrees. The correct answer is option B.

The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.

Given that:-

The arc angle is 68 degrees and we need to find the angle EFD.

As it is given in the question that the angle suspended by the arc is 68 degrees so the angle EFD will also be equal to 60 degrees.

Therefore the measure of the angle EFD will be 68 degrees. The correct answer is option B.

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=============================================

Work Shown:

[tex]\perp (q,r,s,t) = \frac{qr + s}{t}\\\\\perp (2,6,4,8) = \frac{2*6 + 4}{8}\\\\\perp (2,6,4,8) = \frac{12 + 4}{8}\\\\\perp (2,6,4,8) = \frac{16}{8}\\\\\perp (2,6,4,8) = 2\\\\[/tex]

Let m = 2 so we can use this result later.

[tex]\perp (q,r,s,t) = \frac{qr + s}{t}\\\\\perp (4,7,2,6) = \frac{4*7 + 2}{6}\\\\\perp (4,7,2,6) = \frac{28 + 2}{6}\\\\\perp (4,7,2,6) = \frac{30}{6}\\\\\perp (4,7,2,6) = 5\\\\[/tex]

Let n = 5 so we can use this result later.

Add the two results.

m+n = 2 + 5 = 7.0 is the final answer.

The pair of triangle formed are congruent using the side-side-side congruency theorem.

Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent.

Since the opposite sides of a parallelogram are congruent, if the parallelogram is cut through the diagonal, the pair of triangle formed are congruent using the side-side-side congruency theorem.

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The incorrect rounding for 53.864 is 53.87

The decimal to be approximated is as follows;

53.864

The first option rounded the decimal to 2 significant figures or a whole number.

The second option is incorrect because they rounded it wrongly to 2 decimal places. The correct 2 decimal round is 53.86.

The third option is approximated rightly to one decimal place.

The last option is rounded to the closes tens term.

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Answer:

≈5.3 feet,63.6 inches

Step-by-step explanation:

36+b²=64

-36 -36

b²=28

if we square root both sides we can get the radical/exact answer or the rounded one

radical: 4√7

rounded to the nearest tenth: 5.3 feet

Answer:

-104

Step-by-step explanation:

Completed by plugging 50 in the equation:

-2(50) - 4 =

-100 - 4 =

-104

The profit-maximizing price and resulting profits are $36 and $0 respectively.

The profit-maximizing price for the monopoly will be to produce at the quantity where marginal revenue is equal to marginal cost.

Therefore, suppose the average total cost is $36 when q = 24, the profit maximizing price is as follows:

when Q = 24 at average cost = $36,

Then,

profit-maximizing price = p = $36

Hence, the resulting profit is as follows;

resulting profit = 36 - 36 = $0

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A graph which represents the solution set for the compound inequality is shown in the image attached below.

In order to determine the graph which represents the solution set for the compound inequality, we would evaluate the given inequalities as follows.

Given the following inequalities:

⅓x + 10 ≥ 7

x - 10 ≥ 7

For the first inequality, we have:

⅓x + 10 ≥ 7

Multiply all through by 3;

x + 30 ≥ 21

x ≥ 21 - 30

x ≥ -9  ⇒ x < 9.

For the first inequality, we have:

x - 10 ≥ 7

x ≥ 7 + 10

x ≥ 17.

In conclusion, a graph which represents the solution set for the compound inequality is shown by using the number line in the image attached below.

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