Drag a statement or reason to each box to complete the proof.

If 3(x−4)=x+4, then x=8.

an ice cream cone has a diameter of 8 cm and a slant height of 8.4 cm. find the lateral surface area of the cone then The lateral surface area of the cone is 105.2 cm².

What is lateral surface area?

The lateral surface area is the area of all the sides of a 3-dimensional object excluding its base and top.

Lateral surface area = πr√(h² + r²)

Where:

π = pi = 3.14

r = radius = 8/2 = 4cm

h = √8.4² - 4² = 7.38

3.14 x 4 x √(7.38² + 4²)

= 105.4 cm

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Percent of the games do not cost $1 or $2 is 35%.

A fraction of a number out of 100% is referred to as a percentage, sometimes known as a percent. Percentage refers to a portion of a total amount and signifies "per 100." For instance, 45% signifies 45% of the total or 45 out of 100.

By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.

Given,

games = 58

5/8 is 62.5%

2.5% + 62.5% = 65%

100%-65% = 35%

A third of the games (35%) are free.

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Complete question -

At a carnival, 58 of the games cost $1. Another 2.5% of the games cost $2. What percent of the games do not cost $1 or $2?

EXPLANATION

Given the circle, we can see the following facts:

Diameter= 24 ft ----> radius= 12 ft

Total arc length = 360°

The arc of a semi-circle is equal to 360/2 = 180 degrees

The red labeled arc is given by the difference between 360, the other 60 degrees and the semi-circle,

360° - 180° - 60° = 120°

So, representing this as a radian form:

Multiplying terms:

Simplifying:

So, the answer is 8π ft

If we reflect a triangle in a line, translate a triangle, rotate a triangle, and reflect it in a point result in an image that will be congruent to the original( pre-image) triangle.

This is a problem from triangular geometry. We can solve this problem by following a few steps.

Here a triangle ABC is given and the triangle is at first reflected and then translated, thereafter it rotates and is later reflected.

After all, these processes the value of ∠A, ∠B, and ∠ C remains the same as usual concerning ∠A''', ∠B''', ∠ and C'', as they just changes coordinates not geometric structures.

After all these processes the length of the triangle AB, AC, BD, and A'''B''', B'''C''', C'''A''' remains the same as usual.

∵ We can conclude that ΔABC ≅ ΔA'''B'''C'''

( As AB = A'''B''', BC = B'''C''', ∠ABC = ∠ A'''B'''C''' )

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Answer: 12%

Step-by-step explanation:

12%

Explanation:

If has 176 £1 coins then 176 drivers paid £1 and 20 p coins.

The rest of the driver paid with 20 p coins.

So the number of 20 p coins is:

320 - 176 = 144

Since £1 and 20 p need 6 coins of 20 p, the number of drivers who paid only for 20 p coins is:

144 / 6 = 24

The total number of drivers is:

176 + 24 = 200

The percentage of drivers who paid only with coins id 20 p is:

24 / 200 • 100% =

0.12 • 100% = 12%

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 9 5/8, where 9 is the quotient and 5 is the remainder.

Remain length = 13.2' = 13' 2 2/5 ".

Length of black steel pipe is 21'-0".

7' 9 5/8" =7.8 '

Remain length = 13.2' = 13' 2 2/5 ".

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Answer:

Nah

Step-by-step explanation:

This is an instance of conditional probability and the formula to use is;

Where:

P(A|B) = the probability of event A occurring given that event B occurred

P(A ∩ B) = the probability that both events A and B occur

P(B) = the probability of event B

Therefore, the probability that A occurs given that B occurs is 5/6

a)26 is not a possible value for x as the angle becomes a right angle and doesn't remain acute

An acute angle is one whose measure is less than 90 degrees. The given acute angle in the question is represented by (3x+12)°

if x=26 then the angle is 90°

if x= 21 then the angle is 75°

if x=23 then the angle is 81°

if x=25 then the angle is 87°

∴26 cannot be a possible value for x as the angle becomes 90 degrees (right angle) and doesn't remain acute any longer.

Thus the correct answer is option a)26

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The equation of line in point - slope form will be;

⇒ y + 2 = 10 (x - 1)

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line = (1, -2)

And, The slope of the line = 10

Now,

Since, The equation of line in point-slope form is;

⇒ y - y₁ = m (x - x₁)

Where, (x₁ , y₁) is the point on the line and m is slope of the line.

Hence, The equation of line in point-slope form passing through the points (1, -2)  with slope 10 is;

⇒ y - y₁ = m (x - x₁)

⇒ y - (-2) = 10 (x - 1)

⇒ y + 2 = 10x - 10

⇒ y = 10x - 10 - 2

⇒ y = 10x - 12

Thus, The equation of line in point - slope form will be;

⇒ y + 2 = 10 (x - 1)

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Answer: 9. y=[tex](x+4)^2-3[/tex]

10. y=[tex]-(x-5)^2+5[/tex]

11. y=[tex](x-2)^2+1[/tex]

12. y=[tex]x^2-3[/tex]  or y=[tex](x-0)^2-3[/tex]

Step-by-step explanation:

Step-by-step explanation:

-1 × -3/10

=> 3/10

Multiplicative Inverse/Reciprocal of 3/10 = 10/3

Answer:

−3.11×10^2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Question a: Solve for c

0.9c = 17.01 - 18.9r

c = 17.01-18.9r/0.9

c = 18.9 - 2.1r

Question b: Solve for r

18.9r = 17.01-0.9c

r =  9 - [tex]\frac{0.9}{18.9}[/tex]c

r = -10/21c + 9

(0.9/18.9 = 10/21)

Question c:

It will be best to use the equation that solves for c because this helps us determine how much chicken is bought.

c = 18.9 - 2.1r

Substitute r with 3.25

c = 18.9 - 2.1(3.25)

c= 18.9 - 6.825

c = 12.075

The equivalent expression is 54 divided by 18, and the quotient is 3.

The change that increases the loudness is a > 1

From the question, the equation of the function that represents the musical note is given as

y = a sin(1320πx)

Where

In sound, the sound loudness is directly proportional to the amplitude.

This means that an increment in the amplitude, would cause the note to become louder

This change is represented as a > 1

This is so because a represents the amplitude, and the initial value is 1

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The area of the hot tub to be installed for local spa is 6358.5 in².

For the given question;

The diameter of the hot tub to be installed for local spa is 90 inches.

Then, radius is 90/2 = 45 inches.

The area of the circle is;

Area = πr²

Where,  π = 3.14

Put the values;

Area = 3.14×45²

Area = 6358.5

Thus, the area of the hot tub to be installed for local spa is 6358.5 in².

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Given:

You plan to retire in 35 years and would like to have 1,000,000$ in investments.

So, the time = 35 years

And A = 1,000,000

compounded daily, n = 365

Rate of the interest = r = 7% = 0.07

We will find the initial investment = P

We will use the following formula:

Substitute with the values of A, r, n, and t

Solve the equation to find P

So, the answer will be $86,313.86

The angle x= 33 degree.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. It is not necessary for the angle to be in Euclidean space if it lies in the plane. Angles are referred to as dihedral angles if they are created by the intersection of two planes in a space other than Euclidean. The sign "" is used to denote angles. The Greek letter,,, etc. can be used to represent the angle measurement between the two rays. If different types of angles, such as a positive angle and a negative angle.

Positive Angle: If angle goes in counterclockwise, then it is called a positive angle.

Negative Angle: If angle goes clockwise direction, then it is called a negative angle.

360= 87*3+3x

360-261=3x

33=x

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The range of values, in interval notation is [-6,14] .

What is interval notation in math?

the values with a distance of 10 units from 4.

Maximum value to the right, 10 units from 4 is 4+10 = 14

Maximum value to the left, 10 units from 4 is 4 - 10 = -6

So, all the range of values, in interval notation is [-6,14]

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It will take 30 weeks to have to have the same amount of money as my sister if I have $60 and my sister has $120. I am saving $7 per week and my sister is saving $5 per week.

A mathematical sentence that uses the equal sign, =, to show that two expressions are equal is known as an equation. Look for key words or phrases such as "is," "the same as," or "equals" to determine where to place the equal sign when writing a word sentence as an equation. Make an equation out of the word sentence.

A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation. Linear equations are classified into three types: point-slope, standard, and slope-intercept.

The given condition,

You have $60 and your sister has $120. You are saving $7 per week and your sister is saving $5 per week.

Let x be the time period in weeks. So we need same amount of money.

60+7x=120+5x

This is the equation needed.

2x=60

x=30 weeks

If I have $60 and my sister has $120, it will take 30 weeks for me to have the same amount of money as my sister. I save $7 per week, and my sister saves $5 per week.

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Answer:

No

Step-by-step explanation:

Step-by-step explanation:

160 + 37x <= 900

37x <= 740

x <= 20

the custodian can move max. 20 boxes on the elevator at one time.

if he/she is always riding with the boxes.

if the custodian would climb the stairs and let the books ride alone, there could be

37x <= 900

x <= 900/37 = 24.32432432 ≈ 24

boxes on the elevator at one time.

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

Explanation:

x = number of hours

y = total cost

The equation is y = 25x+250 since 250 is the initial cost, aka y intercept, and 25 is the slope telling us how much the cost goes up per hour (aka rate of change).

I recommend making a table of values to help see how/why that equation works out.

Plug in y = 1275 and isolate x.

y = 25x+250

1275 = 25x+250

1275-250 = 25x

1025 = 25x

25x = 1025

x = 1025/25

x = 41 hours

----------------

Check:

If the customer rents the car for 41 hours, then they pay 25*41 = 1025 dollars on top of the initial fee of $250.

The total cost is therefore 1025+250 = 1275 dollars to confirm the answer.

----------------

Extra info:

41 hours = 24 hours + 17 hours = 1 day + 17 hours

41 hours = 41/24 = 1.70833 days approximately

[tex]x+146=546[/tex]

Subtract 146 from both sides:

[tex]x+146-146=546-146\\[/tex]

[tex]x=400[/tex]

Answer:

x = 400

Step-by-step explanation:

x + 146 = 546

We need to subtract 146 on both sides.

146 - 146 is equal to 0 so we cancel out. 546 - 146 is equal to 400.

So now x is alone and we have our answer.

x = 400

If the sum of two angles is 180 then the angles are supplementary.This is true.

Supplementary angles are those that total 180 degrees. Angles 130° and 50°, for example, are supplementary angles since the sum of 130° and 50° equals 180°.

If the total of two angles is 180 degrees, they are considered to be supplementary angles since they form a linear angle when combined. If the total of two angles is 90 degrees, they are considered to be complimentary angles since they produce a right angle when combined.

If two angles add up to 180 degrees, they are considered to be supplementary angles in geometry. For example, if A + B = 180°, A and B are referred to as supplementary angles. When supplementary angles are combined, they always yield a straight angle (180 degrees).

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Answer:

The answer is C

Step-by-step explanation:

The percentage of students that use the internet for more than 402 minutes =  16%

Percentage

Percentage, often referred to as percent, is a fraction of 100. Percentage means "per 100," and denotes part a total amount. For example, 45% represents 45 out of 100.

calculate the percentage-

The empirical rule states that

68% of the population lies within 1 standard deviation of the mean

95% of the population lies within 2 standard deviations of the mean

99.7% of the population lies within 3 standard deviations of the mean

Standard Deviation

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

The percentage will be illustrated in this:

P(X > 402) = P(X > 30 + 1 × 102)

= (1-0.68) / 2

= 0.32/2

= 16%

The percentage of students that use the internet for more than 402 minutes =  16%.

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