Admission to the state fair is $8 for adults and $7 for students. Write two equivalent expressions if two adults and two students go to the fair. Then find the total admission cost.

Answer:

n = 100

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

given A = 40π , then

πr² × [tex]\frac{n}{360}[/tex] = 40π

π × 12² × [tex]\frac{n}{360}[/tex] = 40π

144π × [tex]\frac{n}{360}[/tex] = 40π ( divide both sides by π )

144 × [tex]\frac{n}{360}[/tex] = 40 ( multiply both sides by 360 to clear the fraction )

144n = 14400 ( divide both sides by 144 )

n = 100

Answer:

a) x = 1.5 or x = -0.3

b) x = 5 or x = -8

Explanation:

Quadratic formula:

[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad when \:\: ax^2 + bx + c = 0[/tex]

Here given equation: 5x² - 6x  - 2 = 0

Identify variable constants: a = 5, b = -6, c = -2

Putting these values into equation:

[tex]\sf x = \dfrac{ -(-6) \pm \sqrt{(-6)^2 - 4(5)(-2)}}{2(5)}[/tex]

[tex]\sf x = \dfrac{ 6 \pm \sqrt{36 + 40}}{10}[/tex]

[tex]\sf x = \dfrac{ 6 \pm \sqrt{76}}{10}[/tex]

[tex]\sf x = \dfrac{ 3\pm \sqrt{76}}{5}[/tex]

[tex]\sf x = \dfrac{ 3+ \sqrt{76}}{5} \quad or \quad \dfrac{ 3- \sqrt{76}}{5}[/tex]

In one decimal point:

[tex]\sf x = 1.5 \quad or \quad -0.3[/tex]

b) Here use "middle term split" method

⇒ x² + 3x = 40

relocate

⇒ x² + 3x - 40 = 0

The factors of 40 are 8 and 5

⇒ x² + 8x - 5x - 40 = 0

factor common terms

⇒ x(x + 8) - 5(x + 8) = 0

collect into groups

⇒ (x - 5)(x + 8) = 0

set to zero

⇒ x - 5 = 0 or x + 8 = 0

relocate

⇒ x = 5 or x = -8

Step-by-step explanation:

a) The quadratic formula can help find answers to a quadratic equation when it is equal to 0. The formula is [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex] for a quadratic equation of the form [tex]ax^2+bx+c=0[/tex].

In this question, a is 5, b is -6, and c is -2. Let's put them in the equation and solve.

[tex]x=\frac{6\pm\sqrt{(-6)^2-4(5)(-2)}}{2(5)}\\x=\frac{6\pm\sqrt{36+40}}{10}\\x=\frac{6\pm\sqrt{76}}{10}\\x=\frac{6\pm2\sqrt{19}}{10}\\x=\frac{3\pm\sqrt{19}}{5}[/tex]

This means that the value of x is both [tex]\frac{3+\sqrt{19}}5[/tex] and [tex]\frac{3-\sqrt{19}}5[/tex], since both values make x equal to 0. Putting both into the calculator, we get that [tex]x=1.5[/tex] or [tex]x=-0.3[/tex].

b) We can easily solve this equation using factoring, which turns a quadratic into two factors, and finds the solutions by setting both to 0. This will only work if the quadratic is equal to 0.

[tex]x^2+3x-40=0[/tex]

Now, we have to find two numbers that add to 3 and multiply to -40. The numbers 8 and -5 work, as 8-5=3 and 8*-5 is -40.

we can now make our factors x+8 and x-5

[tex](x+8)(x-5)=0[/tex]

If two numbers, say A and B, are being multiplied and equal 0, then either A is 0, or b is 0, or both. Similarly, if x+8 and x-5 are being multiplied and equal 0, either x+8 = 0, or x-5=0.

[tex]x+8=0\\x=-8[/tex]    [tex]x-5=0\\x=5[/tex]

This makes our solutions x=-8 and x=5.

If you are not familiar with factoring or the process I have went through above, I highly recommend learning about it.

By assuming that 1 + 1 = 3, we will reach an absurd.

To do this, we need to reach an absurd.

Let's assume that we are working with integer numbers, and let's assume that 1 + 1 is equal to 3.

Then we can write:

1 + 1 = 3

Now, if we subtract 1 in both sides, we get:

(1 + 1) - 1 = 3 - 1

1  = 2

Now we can subtract 1 again so we get:

1 - 1 = 2 - 1

0 = 1

This is an absurd, then the statement:

1 + 1 = 3

is false.

So we conclude that:

1 + 1 isn't 3.

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Answer:

Step-by-step explanation:

To check this, we need to know whether

2

1

​

=

3

2

​

We have,  

2

1

​

=

2×3

1×3

​

=

6

3

​

and  

3

2

​

=

3×2

2×2

​

=

6

4

​

We find that

6

3

​

<

6

4

​

, which means that  

2

1

​

<

3

2

​

.

Therefore, The ratio 1:2 is not equivalent to the ratio 2:3

Answer:

No, they aren't equal.

Step-by-step explanation:

Answer:

This would be true for a rectangle and a square.

Step-by-step explanation:

Rectangles and square have 90 angles.  The exterior angles would also equal 90 because 90 + 90 is 180.  An interior angle and the exterior angle are supplements (add together to 180).

Yes

See

3 contractors took 8hours

4 contractors took 6hours

We observe

So it's inverse variation

Answer:

[tex]\fbox {Yes}[/tex]

Step-by-step explanation:

An inverse variation can be seen when two factors are compared, if one factor is seen to be increasing, then naturally the factor should be decreasing.

Here, as the number of contractors increase, the time taken to complete the work decreases.

∴ Hence, this represents an inverse variation.

More likely -You are more likely to commit a Type I error

According to statement

we have to find the type 1 error by using the significant levels.

we are commit a MORE LIKELY to find the error by rejecting a true null hypothesis using the 0.05 level of significance than using the 0.01 level of significance.

So, More likely -You are more likely to commit a Type I error

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The inflation rate between 2017 and 2018 is 2.86%.

Inflation rate is used to determine the rate at which the general price levels in an economy is increasing with the passage of time.

The inflation rate = (2018 CPI / 2017 CPI) - 1

(180 / 175) - 1 = 0.0286 = 2.86%

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The equation of the line parallel to the line KL passing through the points (-6, 8) and (6, 0), and going through the point M (-4, -2) is 2x + 3y = -6. The point satisfying this equation is (-6, 2). Thus, the 2nd option is the right choice.

Slope of the line KL = (8 - 0)/(-6 - 6) = 8/(-12) = -2/3.

Using the formula of the slope of the line passing through the points (x₂, y₂) and (x₁, y₁), as m = (y₂ - y₁)/(x₂ - x₁).

The slope of the line parallel to the line KL will be equal to the slope of KL.

Thus, the slope of the required line is m = -2/3.

The required line also passes through point M (-4, -2).

Thus, the equation of the required line will be,

y - (-2) = (-2/3)(x - (-4)) {Using the equation of the line passing through the point (x₁, y₁) and a slope m, as y - y₁ = m(x - x₁)},

or, y + 2 = (-2/3)(x + 4),

or, 3(y + 2) = -2x - 8,

or, 2x + 3y = -6.

From the given points, only the point (-6, 2) satisfies the equation.

Thus, the equation of the line parallel to the line KL passing through the points (-6, 8) and (6, 0), and going through the point M (-4, -2) is 2x + 3y = -6. The point satisfying this equation is (-6, 2). Thus, the 2nd option is the right choice.

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The provided question is incomplete. The complete question is:

"On a coordinate plane, line K L goes through (negative 6, 8) and (6, 0). Point M is at (negative 4, negative 2). Which point could be on the line that is parallel to line KL and passes through point M?

(–10, 0)

(–6, 2)

(0, –6)

(8, –10)"

Answer:

[tex]\displaystyle \\\sum_{k=0}^4 45-2.5k=200[/tex]

Step-by-step explanation:

We start off with the term 45 and decrease by 2.5 each term, ending with four 2.5's subtracted from 45.

Therefore, our index starts at k=0 and ends at 4. The general term can be defined then as [tex]\displaystyle \\\sum_{k=0}^4 45-2.5k[/tex] and evaluating yields 200.

Answer:

the 4th answer option. W = 153°, P = 71°

Step-by-step explanation:

PQRS ~ TUVW

that means both figures are similar.

and that means that the angles at the corresponding vertexes are the same, and all 4 corresponding sides (and any other pair of corresponding lines like diagonals) have the same scaling factor.

we see due to the proportions of the different parts of the shapes

U corresponds to Q.

T corresponds to P.

W corresponds to S.

V corresponds to R.

therefore, as the angle at S = 153°, so is W.

and as the angle at T = 71°, so is P.

Answer:

1/7

Step-by-step explanation:

When 2 lines are perpendicular the gradient of one is the reciprocal of the other :

If the gradient of A was 2 the gradient of B would be 1/2.

If the gradient of a is 7 the gradient of b would be 1/7 .

Hope this helped and have a good day

The measure of the acute angles are 62° and 28° .

Let x represent the measure of one of the acute angles of the right angle triangle.

Let y represent the measure of the other acute angle of the right angle triangle.

One of the acute angles in a right triangle measures 22 degrees less than 3 times the other acute angle. This means that

x = 3y - 22

The sum of two acute angles in a right triangle is 90 degrees.

We write as

x + y = 90 - - - - - - - (1)

Substituting x = 3y - 22 into equation 1, it becomes

3y - 22 + y = 90

4y = 90 + 22= 112

y = 112/4 = 28

x = 90 - y = 90 - 28

x = 62

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Answer:

The answer is X=3/4 or -1/2

The equation which has the values as given in the task content is; y= x² -3x -5.

By convention, the general form representation of a quadratic equations is;

y = ax² + bx +c.

Hence, it follows that when the equation has an a-value of 1 a b-value of -3 and a c-value of -5, the equation is; y= x² -3x -5.

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The amplitude, Period, Horizontal Shift and Vertical Shift of both graphs are as detailed below.

3)a. Amplitude is the distance between the center line and the positive or negative peak of the graph. Thus, the amplitude is 0.5.

b. The period is the time it takes for the graph to repeat or complete one cycle and in this graph, it is 3.

c. Looking at the graph, ideally the coordinate (3, -1.5) should have been on the y-axis which is at (0, -1.5). This means it was shifted by 3 units to the right side.

d. The positive peak should be equal to the negative peak but in this case, it is not so and as such the center should be on the x-axis which means that the graph was shifted down vertically by 2 units.

4) a. Amplitude is the distance between the center line and the positive or negative peak of the graph. Thus, the amplitude is 3 - 1 = 2

b. The period is the time it takes for the graph to repeat or complete one cycle and in this graph, it is 6.

c. Looking at the graph, ideally the coordinate (4, -1) should have been on the y-axis which is at (0, -1). This means it was shifted by 4 units to the right side.

d. The positive peak should be equal to the negative peak but in this case, it is not so and as such the center should be on the x-axis which means that the graph was shifted up vertically by 1 unit.

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Answer: Joe's number is a negative number.

Since the number's opposite is greater in value, the number's value is in the negatives.

The set {h| 0 ≤ h ≤ 60} describe the domain of p(h).

According to the statement

We have given that the brenton gets paid $20 per hour for the first 40 hours he works in a week. For any hours above that, he is paid overtime at $30 per hour.

and we have to find that the those set which describes the domain of p(h).

So,for this purpose

In this case, the domain represents the set of hours he is permitted to work

From the question, we understand that he cannot work more than 60 hours

This means that, the least number of hours to work is 0, and the highest is 60

So, the domain is 0 to 60

When represented properly, the domain of P(h) is (b)  {h| 0 ≤ h ≤ 60}.

So, The set {h| 0 ≤ h ≤ 60} describe the domain of p(h).

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

Brenton’s weekly pay, P(h) , in dollars, is a function of the number of hours he works, h. He gets paid $20 per hour for the first 40 hours he works in a week. For any hours above that, he is paid overtime at $30 per hour. He is not permitted to work more than 60 hours in a week. Which set describes the domain of P(h)? {h| 0 ≤ h ≤ 40} {h| 0 ≤ h ≤ 60} {P(h)| 0 ≤ P(h) ≤ 1,400} {P(h)| 0 ≤ P(h) ≤ 1,800

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Answer:

B.{h|0<h<60}

Step-by-step explanation:

Answer:

D.10

Step-by-step explanation:

Mode is the number that is repeated the most as we can see the number 10 is there 3 times in the data. 13 isn't there, 14 is only there once and 16 is also not there

Answer:

396 gold bars

Step-by-step explanation:

first of all we will find numbers of gold bar 7*99

which is 693 and

we will find number of silver bars 11*99

which is 1089

then 1089-693=

396

the answer of this question is 38 and i hope it s  correct

Answer: 3/7

Step-by-step explanation:

Answer:

C) -9

Step-by-step explanation:

x + 19 must be half x + 29 because triangles RBC and RST are similar by SAS and RB is half of RS and RC is half of RT.

2(x + 19) = x + 29

2x + 38 = x + 29

x + 38 = 29

x = -9

The probability that the number chosen is divisible by 5 is; 1/5.

It follows from the task content that the number of possible outcomes in the probability event is; 100. Additionally, the number of required outcomes is 20 as only 20 numbers are divisible by 5.

Ultimately, the required probability is; 20/100 = 1/5.

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The location of the points on Cartesian plane are listed below:

Figure 1: A(x, y) = (0, 4), B(x, y) = (5, 0)

Figure 2: A(x, y) = (8.5, 4), B(x, y) = (2.5, 1.5)

A point on a Cartesian plane can be represented by rectangular system of coordinates with the form:

(x, y)

Where:

Now we proceed to represent each point:

Figure 1: A(x, y) = (0, 4), B(x, y) = (5, 0)

Figure 2: A(x, y) = (8.5, 4), B(x, y) = (2.5, 1.5)

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Answer:

Yes.

Step-by-step explanation:

Yes, the given line can be used to make reasonable predictions of the number of cheese pizzas that will be sold, since the scatter points clearly show a trend.

As time goes on, the number of pizzas sold is getting bigger, and the trend is what created the line.

The data was taken over 8 consecutive weeks, so we can assume that it can be used in our prediction.

Since the trend has been pretty consistent over periods of time, we can expect it to continue in the upcoming weeks.

Answer:

[tex]x=-3[/tex]

Step-by-step explanation:

Given equation:

[tex]\dfrac{2x}{x+1}+\dfrac{3(x+1)}{x}=5[/tex]

Make the denominators the same:

[tex]\implies \dfrac{2x}{x+1} \cdot\dfrac{x}{x}+\dfrac{3(x+1)}{x} \cdot \dfrac{x+1}{x+1}=5[/tex]

[tex]\implies \dfrac{2x^2}{x(x+1)}+\dfrac{3(x+1)^2}{x(x+1)} =5[/tex]

Combine the fractions:

[tex]\implies \dfrac{2x^2+3(x+1)^2}{x(x+1)} =5[/tex]

Multiply both sides by x(x+1):

[tex]\implies 2x^2+3(x+1)^2 =5x(x+1)[/tex]

Expand the brackets:

[tex]\implies 2x^2+3(x^2+2x+1) =5x^2+5x[/tex]

[tex]\implies 2x^2+3x^2+6x+3 =5x^2+5x[/tex]

Combine like terms:

[tex]\implies 5x^2+6x+3=5x^2+5x[/tex]

Subtract 5x² from both sides:

[tex]\implies 6x+3=5x[/tex]

Subtract 5x from both sides:

[tex]\implies x+3=0[/tex]

Subtract 3 from both sides:

[tex]\implies x=-3[/tex]

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