Angle 1 can be represented by the expression 6x + 30. Angle 2 can be
represented by the expression 16x - 10. If the two angles are congruent,
write an equation to find the value of x

To prove that n^2 - 7n + 12 is nonnegative whenever n is an integer with n ≥ 3, we can start by factoring the expression:
n^2 - 7n + 12 = (n - 4)(n - 3) . Since n ≥ 3, both factors in the expression are positive. Therefore, the product of the two factors is also positive.
(n - 4)(n - 3) > 0

We can also use a number line to visualize the solution set for the inequality:
n < 3: (n - 4) < 0, (n - 3) < 0, so the product is positive
n = 3: (n - 4) < 0, (n - 3) = 0, so the product is 0
n > 3: (n - 4) > 0, (n - 3) > 0, so the product is positive
Therefore, n^2 - 7n + 12 is nonnegative whenever n is an integer with n ≥ 3.
Alternatively, we can complete the square to rewrite the expression in a different form:
n^2 - 7n + 12 = (n - 3.5)^2 - 0.25
Since the square of any real number is nonnegative, we have:
(n - 3.5)^2 ≥ 0
Therefore, adding a negative constant (-0.25) to a nonnegative expression ((n - 3.5)^2) still yields a nonnegative result. This confirms that n^2 - 7n + 12 is nonnegative whenever n is an integer with n ≥ 3.

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Answer:

6:10

Step-by-step explanation:

Answer:

3: 23 feet and 4 inches wide

Answer:

the answer is 80000 is b

Answer:

(2, -4)

Explanation:

When we reflect a point across the x-axis, we change the coordinates as follows:

(x, y) -----> (x, -y)

Then, the image of the point (2, 4) reflected across the x-axis is:

(2, 4) ------> (2, -4)

The EOQ for premium tires, rounded to 2 decimal places is  468.06 tires.

To determine the Economic Order Quantity (EOQ) for the premium tires,  use the EOQ formula:

EOQ = √((2 ×D × S) / H)

where:

D = Annual demand (number of premium tires required annually) = 10,000

S = Ordering cost per order = $200 (since both products are ordered together)

H = Holding cost per unit = 20% of the cost of an item = 0.20 × $90 = $18

Substituting the values into the formula:

EOQ = √((2 × 10,000 × 200) / 18)

Calculating this expression us the EOQ for the premium tires. Rounding the answer to 2 decimal places:

EOQ ≈ 468.06

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We have that because the central angle is 90°, the sector represents 1/4 of a circle with a radius of 10 yd.

So, length of the safety rail is given by:

Where:

r = 10 yd

pi = 3.14

Substitute, we have:

The Answer is 15.7 yd

Next, area of the deck is given by:

Substitute the values:

The answer is 78.5 yd^2

anthesis pranatheseirame

We need to find the nature of the roots of the quadratic equation 2x² - 6x + 7 = 0 , and need to find the Discriminant

Now ,as we know that the Discriminant of any quadratic equation of the form ax² + bx + c = 0 , is D = b² - 4ac

So now ;

\({:\implies \quad \sf D=(-6)^{2}-4\times 2\times 7}\)

\({:\implies \quad \sf D=36-56}\)

\({:\implies \quad \bf \therefore \quad \underline{\underline{Discriminant=-20}}}\)

Now , as D < 0 ,So nature of roots will be imaginary

Answer:    Since the angles in a triangle sum up to 180 degrees, we can write:

m∠O + m∠P + m∠Q = 180

Substituting the given angle measures, we get:

(2x - 5) + (3x - 8) + (10x - 17) = 180

Simplifying and solving for x, we have:

15x - 30 = 180

15x = 210

x = 14

Now that we know x = 14, we can find the value of angle θ by substituting x into one of the angle measures:

m∠O = 2x - 5 = 2(14) - 5 = 23 degrees

Therefore, the value of angle θ is 23 degrees and the value of x is 14.

Step-by-step explanation: hope this helps (:

Minimum Increment operations to make Array unique

The UNIQUE function will return an array, which will spill if it's the final result of a formula. This means that Excel will dynamically create the appropriate sized array range when you press ENTER .

ArrayList is like an array behind the scenes as it’s backed by an array of type java.lang.Object in java.

Normally arrays are fixed in size which means the number of elements that can be added are fixed and cannot be increased once created. ArrayList can dynamically increase in size once the array that backs is full so, these way we won’t encounter runtime exceptions.

When we say list.get(0), it’s equivalent to array[0]. It can be said the ArrayList is a kind of more convenient way to use dynamic arrays.

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Answer:

  20

Step-by-step explanation:

The proceeds from the sale can be described by an equation involving the original number of computers.

__

Let n represent the number of computers the school originally had. Then n-5 is "all but 5" and is the number sold. Each is sold for ₹1200, and the value of the sale is ₹18000. This can be expressed by the equation ...

  (n -5)×1200 = 18000

__

This 2-step linear equation can be solved by dividing by the coefficient, and adding the opposite of the constant.

  n -5 = 18000/1200 = 15 . . . . . divide by 1200

  n = 15 +5 = 20 . . . . . . . . . . add the opposite of -5

The school originally had 20 computers.

Answer:

Part A

5 m

Part B

The maximum displacement of the Ferris wheel from the midline

Step-by-step explanation:

Part A

The amplitude is the largest displacement of a body, moving in an oscillatory, or vibrational motion from its position of equilibrium or central position about which the body vibrates

In the Ferris wheel, the central position is the midline, between the maximum height and the minimum height

Therefore, the amplitude is the maximum displacement from the midline = The maximum height - ((The maximum height - The minimum height)/2 + The minimum height)

∴ The amplitude = 11 m - ((11 m - 1 m)/2) + 1 m) = 5 m

Part B

The amplitude represents the maximum and minimum distances the Ferris wheel moves above the midline.

Answer:

B

Step-by-step explanation:

26% is close to 25%, which is equal to 1/4th.

You're adding to the number and removing from the percentage so it balances it out.

The estimation of 26% of 91 is  1/4 x 92.

The correct option is (B).

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

26% of 91

Now solving the above Quantity

= 26 /100 x 91

Now, We take 1 from 26 make it 25 and add that 1 to 91 make 92.

Then, 25 / 100 x 92

= 1/4 x 92

Hence, the estimation is 1/4 x 952.

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Answer:

3(x+5)

hope it helps you

The radius of a cylinder is 4 inches and the height is 5 inches. The surface area is equal to the sum of the areas of all the faces of a solid.

A cylinder has two circular bases, and each circular base has an area of πr² square units, where r is the radius of the base. The lateral area of a cylinder is the area of the cylinder's curved surface, which is the height of the cylinder multiplied by the cylinder's base perimeter. It is given by the formula: 2πrh. The surface area of the cylinder is obtained by summing the lateral area and two times the area of the base. Hence, we have:

Surface area = 2πrh + 2πr²

Let us calculate the area of the two bases by plugging the given values into the formula.

Area of one base = πr²= π (4)²= 16π square inches

Therefore, the area of the two bases is 2 × 16π = 32π square inches. Thus, statement 2 is correct

Lateral area of a cylinderLateral area = 2πrh= 2 × π × 4 × 5= 40π square inches.

Thus, statement 3 is correct.

The total surface area of the cylinderTotal surface area = Lateral area + 2 × Area of base= 2πrh + 2 × πr²= 2πr(h + r)= 2π × 4(5 + 4)= 72π square inches.

Therefore, statement 5 is correct.

Therefore, the following statements are correct:Statement 2: The area of the two bases is 32π square inches.Statement 3: The lateral area is 40π square inches.Statement 5: The total surface area is 72π square inches are true.Therefore, the correct statements are 2, 3, and 5.

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Answer:

\(-15 + 6x\)

Step-by-step explanation:

Given

\(Expression: 7 - 3(4 - 2x) - 10x\)

Required

Determine Jon's error and make corrections.

Also, give the equivalent of the expression

The question has missing details because Jon's workings is not listed.

One mistake student's make during multiplications that involves minus (-) and plus (+) is in the signs.

So, watch out for the signs to know where the error is.

However, I'll give an equivalent of the given expression

\(7 - 3(4 - 2x) - 10x\)

Open Bracket

\(7 - 12 + 6x - 10\)

Collect Like Terms

\(7 - 12 - 10 + 6x\)

\(-15 + 6x\)

Hence, the given expression is equivalent to \(-15 + 6x\)

Answer:

x=-3

Step-by-step explanation:

Answer:

x = -3

Step-by-step explanation:

2(x - 3) = 4x

2x - 6 = 4x

2x - 4x = 6

-2x = 6

x = -3

I hope this helps you :)

Answer:

I think it's the second one

Step-by-step explanation:

because you have four with a + and then seven with a -

Answer:

So far, so good. Remember the rocket goes up, and then comes back down again. What you have discovered so far is that the height is 528 feet 3 seconds after launch, and then it keeps going up. At some point it starts coming back down again, and at 11 seconds after launch it passes 528 feet again.

Part b is exactly the same problem, except that you use 0 instead of 528. You will get two roots for your equation again, one will be 0 because the rocket is on the ground at time 0, and the other will be the time it hits the ground on the way back down.

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Based on the information given the average speed for his trip is 64 miles.

Using this formula

d=rt

r=d/t

Where:

r=rate=?

d=distance=512 miles

t=time=8 hours

Let plug in the formula

r=512/8

r=64 miles

Inconclusion the average speed for his trip is 64 miles.

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Answer:

In order to solve this, we need to transform the equation into R = D/T

Plug in the numbers into this equation

R = 512/8

So after we divide these two numbers, we get an answer of 64 mph as Adam's average speed.

Three types of rigid transformations are Reflection, Rotation, and Translation. Rigid transformation, also called isometry.

A rigid transformation, also called isometry,  is a transformation that doesn't change the size or shape of a geometric figure. The following are 3 types of rigid transformation:

1. Reflection

→  is the act of shifting an object's coordinates that flip it across a line without changing its shape or size. Horizontal (draw a figure to the left or right) or vertical (draw a figure to the up or down) reflections are possible. The result of reflection is a mirror image of the figure itself.  

The figure is reflected across \(x-\) or \(y-\) axis, and then change \(x-\) or \(y-\) coordinate.

2. Rotation

→ is the non-modification of an object's size or shape by rotating it around an fixed point. A center of rotation is required to rotate an object. And the rotation did by using a degree.

The figure is rotated by a degree (ex: 90°), and then change \(x-\) or \(y-\) coordinate. Meanwhile, a point's center rotation stays at the same.

3. Translation

→ is sliding a figure in any direction without changing its size, shape, or orientation. Translation could be horizontal (make a figure left or right),  or vertical reflections (make a figure up or down).

Vertical translation is shifting the graph along  \(y-\) axis

Horizontal translation is shifting the graph along  \(x-\) axis.

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The scalar factors are (4,4)

Dilation is a type of transformation in which a shape or geometric figure's size is altered while maintaining its relative proportions and general shape.

Dilation is applied by the rule:

(x, y) → (kx, ky), where k is the scale factor

We have

(x, y) = (-2, 3) and (kx, ky) = (-8, 12)

Substitute and solve for k

-8 = -2k and 12 = 3k  ⇒ k = 4

So the rule is

(x, y) → (4x, 4y)

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Sarah's chocolate cake has 300 calories and 15 grams of fat. the percentage of calories from fat in Sarah's chocolate cake is 45%.

To calculate the percentage of calories that come from fat, we need to divide the number of fat calories by the total number of calories and then multiply by 100.

Since we know that 1 gram of fat contains 9 calories, we can calculate the number of fat calories by multiplying the number of grams of fat by 9.

Number of fat calories = 15 grams of fat * 9 calories/gram = 135 calories

Percentage of calories from fat = (Number of fat calories / Total calories) * 100

Total calories = 300 calories

Percentage of calories from fat = (135 calories / 300 calories) * 100

Percentage of calories from fat = 45%

Therefore, the percentage of calories from fat in Sarah's chocolate cake is 45%.

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The percentage of calories from fat in Sarah's chocolate cake is 45%. This calculation is based on the ratio of fat calories to total calories.

To find out the percentage of calories from fat in her cake, we need to divide the amount of total fat calories (15g x 9 calories/gram = 135 calories) by the total amount of calories in the cake (300 calories). We then multiply this ratio (135/300) by 100, which gives us the answer of 45%. Generally, it is recommended that a person's diet should not have more than 25-35% of its total calories from fat.

Therefore, Sarah's chocolate cake is too high in fat to be a part of a well- balanced diet. To reduce the amount of fat in her cake, she should either opt for a different cake recipe or use reduced-fat or low-fat ingredients when baking.

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The prediction model equation is constructed using outputs from an R script.

We are creating a regression model to accurately predict fuel economy using horsepower, quarter mile time, and rear axle ratio as predictors. We will include interaction terms for horsepower and quarter mile time, as well as for horsepower and rear axle ratio.

The prediction model equation is written below, based on the outputs obtained from the R script:

Fuel Economy = β0 + β1*Horsepower + β2*Quarter Mile Time + β3*Rear Axle Ratio + β4*Horsepower*Quarter Mile Time + β5*Horsepower*Rear Axle Ratio

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The probability that both will be married before the age of 18 is 0.0036. The probability that both will be married by the age of 25 is 0.25. Finally, the probability that both will be married by the age of 30 is 0.5476.

According to the brief report by NCHS, approximately 6% of women in the United States married for the first time before their 18th birthday, and 50% of women married by their 25th birthday. 74% of women married by their 30th birthday.The probability of a family with two daughters marrying at different ages is asked in the question. The probability that both daughters will be married by the ages of 18, 25, and 30 will be determined

The question requires finding the probability that both daughters of a family will be married by the ages of 18, 25, and 30 respectively. Since each daughter's wedding is a separate event, the individual probability of a daughter marrying at a given age will be determined separately and then multiplied together to get the probability of both daughters being married at the given age. So, let's find the probabilities of each daughter marrying at a given age:

Probability of one daughter getting married by 18 years:

As per the brief report, 6% of women in the United States married before the age of 18.

Therefore, the probability of one daughter getting married before the age of 18 is 0.06

Probability of one daughter getting married by 25 years:

As per the brief report, 50% of women in the United States get married by the age of 25. Therefore, the probability of one daughter getting married by 25 years is 0.5.

Probability of one daughter getting married by 30 years:

As per the brief report, 74% of women in the United States get married by the age of 30. Therefore, the probability of one daughter getting married by 30 years is 0.74.

The probability of both daughters getting married at the same age is the product of each daughter's probability of getting married at that age.

The probability that both daughters will get married before the age of 18 is:

P(both daughters married at 18 years) = P(daughter1 married at 18) × P(daughter2 married at 18)= 0.06 × 0.06= 0.0036

The probability that both daughters will get married by the age of 25 is:

P(both daughters married at 25 years) = P(daughter1 married at 25) × P(daughter2 married at 25)= 0.5 × 0.5= 0.25

The probability that both daughters will get married by the age of 30 is:

P(both daughters married at 30 years) = P(daughter1 married at 30) × P(daughter2 married at 30)= 0.74 × 0.74= 0.5476

The probability that in a family with two daughters, both will be married before the age of 18 is 0.0036. The probability that both daughters will be married by the age of 25 is 0.25. Finally, the probability that both daughters will be married by the age of 30 is 0.5476.

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Answer:

y=√6(-x)

Step-by-step explanation:

We can reflect the graph of any function about the y-axis by graphing y=f(-x). which is subsituting x as -x into the function.

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\( {x}^{2} - 7x + 18 = (x - 9)(x + 2) \\ \)

Thus the correct answer is the second one.

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