a) 8xy(1-2x+3y)=
b) (x^2-2)(4+2x^2+x^4)

Danielle ride her bike fast than Ariana because ride her bike 14mph.

Given,

In the question:

Ariana can go 5 mph faster than her sister

and, if it takes Danielle one hour longer than Ariana to go 53.2 miles.

To find the how fast can Danielle ride her bike?

Now, According to the question:

Let Ariana can go x mph and Danielle can go (x + 5) mph.

Therefore, Ariana can go 53.2 miles in 53.2/x  hours.

And Danielle can go 53.2 miles in 53.2/x +5 hours.

53.2/x - 53.2/x +5 = 1

=> 53.2\((\)\(\frac{5}{x(x+5)}\) \()\) = 1

=> 266 = x² + 5x

=> x² + 5x - 266 = 0

=> x² - 14x +19x -266 =0

=> x(x - 14) + 19(x - 14) = 0

=> (x - 14)(x +19)= 0

x = 14 or x = -19

But x can not be negative, so x = 14 mph

Therefore, Danielle ride her bike fast than Ariana because ride her bike 14mph.

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Answer: ?Once you find the value of your angle, subtract it from 180° to find the possible second angle. Add the new angle to the original angle. If their sum is less than 180°, you have two valid answers. If the sum is over 180°, then the second angle is not valid??????

Step-by-step explanation:

Third quartile Q₃ of the given data is 11

correct option is: b

What is the 75th percentile value?

0.675

For instance, the median represents the 50th percentile, the first quartile represents the 25th percentile, and the third quartile represents the 75th percentile.

What exactly is Q3?

Q3, the third quartile, is known as the 'upper quartile,' and represents the 75th percentile, which means that only 25% of the values in the set are greater than this value.

given data:

7,14,8,10,7,8,9,7,14,6.

In ascending, order data is 6,7,7,7,8,8,9,10,14,14.

number of terms N = 10

therefore, third quartile Q₃ = \(\frac{3}{4} (n + 1)\)

Q₃ = \(\frac{3}{4} (10 + 1)\)

Q₃ = 8.25th term

Q₃ = 8th term + 0.25 = 11

therefore, therefore, third quartile Q₃ of the given data is 10

correct option is: b

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Answer:

x =10

Step-by-step explanation:

In a parallelogram, opposite sides are congruent

QT = RS

2x - 10 = x

Add 10 to both sides

2x = x + 10

subtract 'x' from both sides

2x -x = 10

x = 10

The amount of postretirement expense for 2021 is $746,540.

The service cost is the portion of the postretirement benefit cost that represents the increase in the actuarial present value of the accumulated benefit obligation resulting from employee service during the period.

According to the given data;

Service cost: $704,000

Discount rate: 6%

EPBO, January 1, 2021: $6,527,000

APBO, January 1, 2021: $5,808,000

Average remaining service to full eligibility: 20 years

Average remaining service to expected retirement: 28 years

The amount of postretirement expense for 2021 is calculated as follows;

Postretirement expense = Service cost + Interest cost + Amortization of prior service cost ± Gain or loss - Expected return on plan assets

Where,

Service cost = $704,000

Discount rate = 6%

EPBO, January 1, 2021 = $6,527,000

APBO, January 1, 2021 = $5,808,000

Interest cost = (EPBO - APBO) x Discount rate

                     = ($6,527,000 - $5,808,000) x 6%

                     = $42,540

Amortization of prior service cost = $0

Gain or loss = $0

Expected return on plan assets = $0

Hence, the amount of postretirement expense for 2021 is;

$704,000 + $42,540 + $0 ± $0 - $0 = $746,540

Therefore, the correct answer is $746,540.

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The amount of post retirement expense for 2021 is $1,052,480

To calculate the post retirement expense for 2021, the formula is

Post retirement Expense = Service Cost + Interest Cost

Service cost = $704,000

Interest Cost = Beginning PBO × Discount Rate

The beginning PBO can be either the EPBO (Ending PBO of the previous year) or the APBO (Actuarial Present Value of Benefits Obligation) of the current year. In this case, since the beginning PBO is given as of January 1, 2021, we'll use the APBO as the beginning PBO.

Interest Cost = APBO × Discount Rate

Interest cost = = $5,808,000 × 0.06

= $348,480

So,

Post retirement Expense ( PRE) = Service Cost + Interest Cost

PRE = $704,000 + $348,480

= $1,052,480

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Answer:

Step-by-step explanation:

42.34

Answer:

True

Step-by-step explanation:

:) Hope this helps ! x

True,  A translation maps each point to its image along a vector called the translation vector.

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

A translation maps each point to its image along a vector called the translation vector

Example:

A = (2, 4) translated vertically up with 2 units.

The image of A = (2, 4 + 2) = (2, 6).

The translation vector is the 2 units.

Thus,

A translation maps each point to its image along a vector called the translation vector

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The thirty-fourth term of the arithmetic sequence is the thirty-second term plus the common difference, which is not equal to 0.

The thirty-fourth term of the arithmetic sequence is calculated by adding the common difference to the thirty-second term. The common difference is the amount by which each successive term increases or decreases. As the common difference is not equal to 0, the thirty-fourth term is not the same as the tenth or second terms. The second, tenth, and thirty-fourth terms form a geometric sequence, which means that the ratio between any two successive terms is always the same. This ratio is determined by the common difference of the arithmetic sequence, and the thirty-fourth term can be calculated by adding the common difference to the thirty-second term.

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Answer:

1.5 kilograms

Step-by-step explanation:

You need to convert grams to kilograms, this means you must divide the mass value by 1000 to find your answer.

1,500/1,000 = 1.5

Answer:

For 1500 grams in kilogram we get 1.5 kg

Step-by-step explanation:

to convert a gram into a kilogram we have to divide the gram term by 1000

Answer:

2049.2

Step-by-step explanation:

512.3÷ 0.25​= 2049.2

You can use a calculator... (or long division.)

Answer:

2,049.2

Step-by-step explanation:

Hope this helped!

o(*^▽^*)┛

Answer:

w = \(\frac{9}{r}\)

Step-by-step explanation:

=> \(9wr = 81\\\)

Dividing both sides by 9r

=> w = \(\frac{81}{9r}\)

=> w = \(\frac{9}{r}\)

Answer:

3 ten blocks and 4 one blocks, or 2 ten blocks and 14 one blocks, or 1 ten block and 24 one blocks, or 34 one blocks.

Step-by-step explanation:

The 32th term of the arithmetic sequence AP is found to be -146.

An arithmetic progression (AP) is a succession in which each successive term has the same distinctions.

Now, to answer the question;

The given sequence of the numbers is-

9,4,-1,-6,-11, ...........

There are total 32 terms in the series for which we have to find 32nd number.

Let the first term be 'a₁' = 9.

Let the second term be 'a₂' = 4

Let the third term be 'a₃' = -1.

The common difference of between the two consecutive terms is equal of an AP is 'd'.

d = a₂ - a₁  

Substitute the values in the above equation;

d = 4 - 9

d = -5

Now, the 32th term is calculated by the nth term formula;

Now, substitute all the value in the formula,

a₃₂ = a + (n - 1) d

a₃₂ = 9 + (32 - 1)(-5)

a₃₂ = 9 - 160 + 5

a₃₂ = -146.

Therefore, the 32nd term of the arithmetic sequence is estimated as -146.

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The cost of producing x units of a product is is approximately $19.79.

(A) The average cost function is obtained by dividing the total cost by the number of units produced:

c(x) = C(x)/x = (140 + 25x - 150 ln(x))/x

(B) To find the minimum average cost, we need to take the derivative of the average cost function and set it equal to zero:

c'(x) = (25 - 150/x - 140/\(x^2\)) / x

Setting c'(x) equal to zero and solving for x, we get:

25 - 150/x - 140/\(x^2\) = 0

Simplifying and solving for x, we get:

x = 10

To confirm that this is a minimum, we need to check the second derivative:

c''(x) = (150/\(x^2\) - 280/\(x^3\)) / x

Evaluating c''(10), we get:

c''(10) = 5/4

Since c''(10) is positive, we can conclude that x = 10 is a minimum for the average cost function.

Using a graphing utility, we can graph the average cost function and confirm that the minimum occurs at x = 10.

We can see from the graph that the minimum occurs at x = 10, and the minimum value is approximately $19.79 (rounded to two decimal places).

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Answer:

u = 3.8 cm

Step-by-step explanation:

Since these triangles are similar, we can use a proportion to solve:

\(\frac{8}{6}= \frac{5}{u}\)

Cross multiply:

8u = 30

Divide both sides by 8:

3.75 cm

Round to nearest tenth:

3.8 cm

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- Heather

A circle can be defined as a geometric shape consisting of all points in a plane that are equidistant from a given point, which is known as the center. The distance between the center of the circle and any point on the circle is referred to as the radius.

In order to find the center and radius of a circle, we need to have three points on the circle's circumference, and then we can use algebraic formulas to solve for the center and radius. Let's look at the given problem to find the center and radius of the circle that passes through the points (-1,5), (5,-3), and (6,4).

Center of the circle can be determined using the formula:

(x,y)=(−x1−x2−x3/3,−y1−y2−y3/3)(x,y)=(−x1−x2−x3/3,−y1−y2−y3/3)

Let's plug in the values of the given points and simplify:

(x,y)=(−(−1)−5−6/3,−5+3+4/3)=(2,2/3)

Next, we need to find the radius of the circle. We can use the distance formula to find the distance between any of the three given points and the center of the circle:

Distance between (-1,5) and (2,2/3) =√(x2−x1)2+(y2−y1)2=(2+1)2+(2/3−5)2=√10.111

Distance between (5,-3) and (2,2/3) =√(x2−x1)2+(y2−y1)2=(5−2)2+(−3−2/3)2=√42.222

Distance between (6,4) and (2,2/3) =√(x2−x1)2+(y2−y1)2=(6−2)2+(4−2/3)2=√33.361

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Answer:

Percent error is approx. 22%

Step-by-step explanation:

So to do this you need to know the formula for percent error, which is

percent error = l measured - theoretical / theoretical l * 100%

With this just plug in 18 (real) and 14 (measured).

percent error = l 14 - 18 / 18 l * 100%

percent error = l -4 / 18 l *100%

percent error = l -2/9 l *100%

You then do absolute value because the percent error must be positive not negative! So -2/9 becomes 2/9. You then divide 2/9 to get approx. 0.22... and you muliply by 100% to get 22%.

  The ant's entire distance travelled along its semicircular journey is its total distance travelled overall. The ant is travelling around a circle with radius R, thus the distance it has travelled is equal to half of the circle's circumference, πR.

The change in the ant's position is represented by a vector quantity called the displacement of the ant. The ant in this scenario begins at one end of the semi-circular path and moves 2R away from the beginning point to reach the other end. The direction of the displacement vector is from the starting point to the ending point, and the displacement's magnitude is equal to the 2R distance between the two points.

    So, the option c is most suitable option.

Therefore, πR and 2R are the ant's displacement and the distance travelled, respectively.

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Answer:

not a solution

Step-by-step explanation:

6(2) - 2(2) = 12 - 4 = 8.

8 does not equal 10 so it is not a solution

Answer:

probably 4 or 2? i mean they are smaller than 8 afterall

Step-by-step explanation:

The two numbers that could be x in x < 8 are 1 and 2 or 1 and 4.

Word problems with algebraic expression as the name implies include technical words used together with variables of an algebraic term.

From the given question;

We are to determine two numbers that could be x and which must be less than 8 as seen in the expression below;

The first thing to do is to look for the factors of 8 which are:

From there, the two numbers that could be x which are less than 8 are:

This is because the multiplication of those two numbers is still less than 8.

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Since the angle of 132 and the angle x are corresponding angles they are equal.

Therefore x=132 degrees.

Answer:75%

Step-by-step explanation:

15 out of 20 is 75%

If angle b is five times the size of angle c, the equation can be used to find the measure of angle is 5x+x=90°.

because complementary angles complete each other to 90 degrees.

These angles b and c add up to 90° because they are complementary.

Let's say angle C is named x.

angle b is five times the size of angle c, this can be written: 5x

Complementary angles add up 90°, so angle B add angle C equal 90°

the equation to find the measure of angle C is 5x+x = 90°.

Types of angles are one of the materials in mathematics that you always encounter at every level of education. Learning about angles is very important, because angles are always present in everyday life and need to be identified.

An angle is a shape formed by two rays having an endpoint at one point. In angles, terms such as the leg of the angle, vertex, and area of the angle are also found.

The legs of the angle are the lines forming the angle. The vertex is the point where the two legs of the angle intersect, and the area of the angle is the area bounded by the two legs of the angle.

Your question is incomplete but most probably your full question was:

Only Interaction Angle B and angle C are complementary: If angle B is five times the size of angle C which equation can be used to find the measure of angle C?

5x+x=180

5x = 180

5x+x=9

5x = 90

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