Solve for x given the info.
Ignore the pencil mark

The required values of exponent a, b, and c are 6, 8, and 9 respectively.

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.

Here,
Given expression,
[tex][x^{24}y^{32}]^{1/4} \times (x^{-3}z^{27})^{1/5} = x^ay^bz^c[/tex]

We have to determine the value of a, b, and c in the exponents, so in order to get the solution we have to simplify the given expression.

[tex][x^{7}y^{8}] \times (x^{-1}z^{9}) = x^ay^bz^c\\x^{7 -1}y^8z^9 = x^ay^bz^c\\x^{6}y^8z^9 = x^ay^bz^c[/tex]

Comparing the exponent across the equal sign we get,
a = 6
b = 8
z = 9

Thus, the required value of exponent a, b, and c are 6, 8, and 9 respectively.

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Step-by-step explanation:

Since u and w are orthogonal, their dot product is 0. Thus,

u · w = 0

Using the Pythagorean Theorem,

||u - w||^2 = ||u||^2 + ||w||^2 - 2(u · w)

Since u and w are unital (i.e., their lengths are 1), we have

||u||^2 = ||w||^2 = 1

Substituting these values and u · w = 0, we get

||u - w||^2 = 1 + 1 - 0 = 2

Taking the square root of both sides, we get

||u - w|| = √2

Therefore, we have shown that if u and w are unital orthogonal vectors, then ||u - w|| = √2.

Answer:

A reciprocal function can be written in the form of f(x) = a / (x-h) + k, where a is a constant, h is the x-value of the vertical asymptote, and k is the y-value of the horizontal asymptote.

Given that the vertical asymptote is located at x = -2 and the horizontal asymptote is located at y = 5, we can write:

f(x) = a / (x - (-2)) + 5

Simplifying this expression, we get:

f(x) = a / (x + 2) + 5

Therefore, an equation that could represent this reciprocal function is:

f(x) = a / (x + 2) + 5

Step-by-step explanation:

By analytic geometry, the equation of the line y = - (1 / 12) · x + 11 is perpendicular to the line y = 12 · x + 3.

In accordance with analytic geometry, lines are described by algebraic equations of the form:

y = m · x + b

Where:

The relationship between the slopes of two perpendicular lines:

m · m' = - 1

First, write the original line:

y = 12 · x + 3

Second, write the slope and the intercept of the original line:

m = 12, b = 3

Third, the slope and the intercept of the perpendicular line:

m = - 1 / 12, b = 11

Fourth, write the equation of the perpendicular line:

y = - (1 / 12) · x + 11

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Answer: H: (7, 1)

Step-by-step explanation: If the endpoints of A and B are (3, 5) and (11, -3), you just have to find the middle of the x and y coordinate for each endpoint. The middle of 3 and 11 is 7, and the middle of -3 and 5 is 1, therefore the middle point would be (7, 1).

Answer: question 1 is 62° and radius is 1.0821  

question 2 is 454.91794m

question 3 is 855.57622m

Step-by-step explanation:

Given c=969 and ∠α=28°,

a = 454.91794

b = 855.57622

∠β = 62° = 1.0821 rad

h = 401.6687

area = 194,608.48704

perimeter = 2,279.49416

inradius = 170.74708

circumradius = 484.5

im only in 8th grade so don't trust me on this but i think im right

The Tape diagram for 7/8 is shown below.

A tape diagram is a visual model that students can use to show a mathematical connection or to help them grasp a math idea. Tape diagrams can be used to solve a variety of arithmetic problems, although they are most typically employed to solve word problems.

Tape diagrams are graphic representations that use rectangles to depict the portions of a ratio. Drawing them requires attention to detail because they are a visual model. They simplify complex mathematical word problems by breaking them down.

Given:

Here we can divide the fraction 7/8 as

7/8

= 2/8 + 5/8

= 2/8 + 2/8 + 3/8

So, the tape diagram will have 8 out tapes out of which 7 are shaded.

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Answer:

[tex]625m^{2}[/tex]

Step-by-step explanation:

Amount of money do you need to save to purchase the home is  $15,000. The total amount the bank will be loaning you is $235,000.  You can expect to pay around $1,332.29 per month.

A down payment is a payment made upfront when purchasing a large ticket item, such as a home or a car. It is a percentage of the total purchase price that the buyer pays out of their own pocket, with the remainder of the price financed through a loan.

To calculate the down payment, we need to multiply the purchase price by the percentage:

Down payment = 0.03 x $250,000 = $7,500

To calculate the closing costs, we also need to multiply the purchase price by the percentage:

Closing costs = 0.03 x $250,000 = $7,500

So the total amount of money needed to purchase the home is the sum of the down payment and the closing costs:

Total cost = $7,500 + $7,500 = $15,000

The amount the bank will be loaning you is the purchase price minus the down payment and the closing costs:

Loan amount = $250,000 - $15,000 = $235,000

To calculate the monthly payments, we need to use the formula for a fixed-rate mortgage:

M = P [ i(1 + i)ⁿ ] / [ (1 + i)ⁿ⁻¹]

where:

M = monthly payment

P = loan amount

i = monthly interest rate (5.5% / 12 = 0.0045833)

n = total number of payments (30 years x 12 months = 360)

Plugging in the numbers, we get:

M = $235,000 [ 0.0045833(1 + 0.0045833)³⁶⁰ ] / [ (1 + 0.0045833)³⁶⁰ – 1]

M ≈ $1,332.29

So you can expect to pay around $1,332.29 per month for 30 years to pay off the mortgage.

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The correct inequality that represents how many video games he could buy is C. 15.99x + 9.99 ≤ 100.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

Let x be the number of video games Manny wants to buy.

The total cost will be the sum of the cost of the video games and the shipping charges:

Total cost = (number of video games) × (cost per game) + (shipping charges)

Total cost = 15.99x + 9.99

Since Manny can spend at most $100, we can write the inequality:

Total cost ≤ 100

15.99x + 9.99 ≤ 100

Therefore, the correct inequality that represents how many video games he could buy is C. 15.99x + 9.99 ≤ 100.

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Answer: They all have the same unit rate

Step-by-step explanation:

3:1 is the unit rate if you multiply it by 2, it's 6:2. If multiplied by 3, it is 9:3. Multiplied by 4, its 12:4

Answer:

60%

Step-by-step explanation:

The evaluation of the inequalities are presented as follows;

2. x ≤ -5

3. x  ≤ -14

4. x ≤ 4

5. x < -10

An  inequality is an expression or comparison of two expressions that posses different values using an inequality sign.

2. -14·x + 1 ≥ 71

-14·x + 1 - 1 ≥ 71 - 1

-14·x  ≥ 70

x ≤ 70/(-14) = -5

x ≤ -5

3. -3·x - 1 ≥ 41

-3·x - 1  + 1 ≥ 41 + 1 = 42

-3·x - 1  + 1 ≥ 42

-3·x  ≥ 42

x ≤ 42/(-3) = -14

x ≤ -14

4. (x/2) + 11 ≤ 13

(x/2) + 11  - 11 ≤ 13 - 11  = 2

x/2  ≤ 2

x ≤ 2 × 2

x ≤ 4

5. x/(10) - 6  < -7

x/(10)  - 6 < -7

x/(10) -6 + 6 < -7 + 6 = -1

x/(10) < -1

x  < -10

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The equation of the line passing through (3,4) whose slope is -1 will be y = - x + 7.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The slope of the line is -1. Then the equation is written as,

y = - 1x + c

The equation passes through (3, 4), then we have

4 = - 1(3) + c

4 = - 3 + c

c = 4 + 3

c = 7

The equation of the line passing through (3,4) whose slope is -1 will be y = - x + 7.

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Answer:

E

Step-by-step explanation:

Acellus

Answer: 59, 218

Step-by-step explanation:

5 ten thousands = 50,000

9 thousands = 9,000

2 hundreds = 200

1 ten = 10

8 ones = 8

50,000 + 9,000 + 200 + 10 + 8 = 59,218

Answer: 59,218

Step-by-step explanation:

The number that has 5 ten thousands, 9 thousands, 2 hundreds, 1 ten, and 8 ones is 59,218.

By using the properties of the diagonal of the parallelogram, we found the values of x and y as 2 and 7 respectively.

A parallelogram is a straightforward quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size. A parallelogram has adjacent angles that add up to 180 degrees.

A parallelepiped is a three-dimensional shape with parallelogram-shaped faces. The base (one of the parallel sides) and height (the distance from top to bottom) of the parallelogram determine its area. A parallelogram's perimeter is determined by the lengths of its four sides.

Here the diagonal of the parallelogram intersects each other.

According to the properties of the paralleogram, the diagonal bisects each other.

So,

2x = x + 2

x = 2

and

5y -5 = y + 23

4y = 28

y = 7

Therefore by using the properties of the diagonal of the parallelogram, we found the values of x and y as 2 and 7 respectively.

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Answer:

$36,500 per employee

Step-by-step explanation:

$730,000/20 employees

With the discount, each dresser would cost $450.

What is the discount?

A discount is a reduction in the price of a product or service that is offered by a seller to a buyer. It is a form of incentive that is used to encourage customers to purchase goods or services, often by making them more affordable or attractive.

To calculate the amount of discount off each item, we need to know the original price of each dresser and the percentage discount that is being offered. Let's assume that the original price of each dresser is $500, and the discount being offered is 10%.

To calculate the discount off each item, we can use the following formula:

Discount amount = Original price x Discount rate

where the discount rate is the percentage discount expressed as a decimal (e.g., 10% = 0.1).

So, for each dresser, the discount amount would be:

Discount amount = $500 x 0.1 = $50

Therefore, each dresser would be discounted by $50. This means that the new price for each dresser would be:

New price = Original price - Discount amount

New price = $500 - $50 = $450

Hence, with the discount, each dresser would cost $450.

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The line that the equation represents has a y-intercept of.

What is an example of a y-intercept?

Here are several y intercept instances. So we obtain y = 5(0)2 + 2 = 2 when we replace x = 0, so y-intercept of y Equal 5x2 + 2 is (0, 2). Because we obtain y = -5e0 = -5 when we try substituting x = 0, this same y-intercept of y Equal -5ex is (0, -5).

Y-intercept: Is it 0 or 1?

The point where a straight line intersects the X-axis is known as the Y interception. In the picture above, the line intersects the Value of y at 1. The point is shown by and the value of the Variable y is 1. (0,1). Remember that for the y-intercept, the point's such and such is always zero.

On this note, we must recall that the y-intercept of an equation is the value of when.

Therefore, we have;

-60(0) + 2y -120 = 0

2y = 120

y = 60

Hence, the y-intercept of the line represented by the equation is; 60.

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The complete question is:

Ernesto brings his dog to training classes. The equation -60x + 2y - 120 =0 relates y, the total cost of a pet's training, and x, the number of classes taken Ernesto states that the y-intercept of the line represented by the equation is 30. is he correct?

The single transformation that maps shape A onto shape C is a translation of 4 units to the right.

A single transformation is a mathematical operation that changes the position, orientation, or size of a geometric figure. It can be a translation, reflection, rotation, or dilation. It is a way to describe how a figure is transformed to obtain a new figure.

To map shape A onto shape C, we need to perform a sequence of transformations.

First, shape A is reflected in the line x = 2 to give shape B. This is a reflection in the vertical line passing through x = 2.

Next, shape B is reflected in the line x = 6 to give shape C. This is a reflection in the vertical line passing through x = 6.

To find the single transformation that maps shape A onto shape C, we can combine these two reflections into a single transformation.

The composition of two reflections in vertical lines is a translation.

In this case, the distance between the vertical lines x = 2 and x = 6 is 4 units. Since shape A is reflected in the first vertical line and shape C is reflected in the second vertical line, the movement is from the first line to the second line, which is to the right.

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Using expressions, we get that$836 will be paid in total throughout the first 12 months.

The combination of numerical variables and operations expressed by the addition, subtraction, multiplication, and division signs is known as a mathematical expression.

Given is that the starting balance is 62. As a result, the sum rises by 4%.

The time period is 12, but he will pay for 11 extra months, not including the first month's 62 dollars.

The formula is: y=62(1+0.11

y=62(1.04) ^11

The amount to be paid in the previous month is: y=95.45$

This geometric sequence has r equal to 1.04 in this case. The total will be determined as follows:

Sum = 62(1.04¹¹-1)/1.04-1

Sum = $836

Hence, $836 will be paid in total throughout the first 12 months.

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The trade discount rate for the wholesaler at the net price is 0.45 or 45%.

A trade discount is a cut in the list price of products or services provided by a seller to a customer who makes frequent or significant purchases of such items. A trade discount is intended to encourage the customer to make further purchases from the supplier. The discount might change depending on the volume or regularity of purchases and is often given as a percentage of the list price. Retailers or wholesalers that purchase products from producers or suppliers to resell to consumers frequently receive trade discounts.

The discount rate is given by the following formula:

Trade Discount Rate = (List Price - Net Price) / List Price

Substituting the given values, we get:

Discount Rate = (13600 - 7480) / 13600

Discount Rate = 0.45 or 45%

Hence, the trade discount rate for the wholesaler is 0.45 or 45%.

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The ratio as fraction is 36/ 55.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

We have to find the ratio for  3 feet to 55 inches.

So, 3 feet to 55 inches

= 3 feet/  55 inches

= 3 feet : 55 inches

= 3 x 12 inches : 55 inches

= 36 inches : 55 inches

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Answer:

am not sure

Step-by-step explanation:

I will help you but yeh so y=20

The value of all the integers are,

4, 5, 6

or, - 8, - 7, - 6

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Let three consecutive numbers are, (x - 1) , x , (x + 1).

Hence, By given condition we get;

⇒ (x - 1)² + 2 (x + x + 1) = 38

⇒ x² - 2x + 1 + 4x + 2 = 38

⇒ x² + 2x - 35 = 0

⇒ x² + 7x - 5x - 35 = 0

⇒ x (x + 7) - 5 (x + 7) = 0

⇒ (x - 5) (x + 7) = 0

⇒ x = 5 or x = - 7

When, x = 5

All the integers are,

x - 1 = 5 - 1 = 4

x = 5

x + 1 = 5 + 1 = 6

When x = - 7

All the integers are,

x - 1 = - 7 - 1 = - 8

x = - 7

x + 1 = - 7 + 1 = - 6

Thus, The value of all the integers are,

4, 5, 6

or, - 8, - 7, - 6

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Answer:

2x(1700%x4)+2=138

Step-by-step explanation:

2x2.00=4 2x17=34 34 per month plus the 2 that they already had. 34x4=136 there will be 136 plus 2 after the 4 months

The role of GCF, its placement and verification has been explained below. The solution has been obtained by using the concept of Greatest Common Factor.

The greatest common factor, or largest number, is the product of two or more numbers (GCF). The greatest number (factor) that separates them yields a natural number.

1. The GCF is a factor that all terms in a polynomial share.

For instance, if the polynomial has the form R * S + R * T, the GCF is R because both terms share the factor R.

2. The GCF is positioned in front of the remaining polynomials, outside of the parenthesis, once we have factored out the GCF.

R * S + R * T, given the prior example, is R (S + T).

3. By allocating the GCF to the polynomial enclosed in parenthesis, we can verify that our factoring is accurate.

Hence, the above stated is the role of GCF in factoring a polynomial.

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The solution is, the expression is -3+0i, so, a = -3 & b = 0.

In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation {\displaystyle i^{2}=-1}; every complex number can be expressed in the form a + bi, where a and b are real numbers.

here, we have,

So we have:

given that,

(2+6i) - (5+6i)

First, distribute:

2+6i - 5 -6i

Combine like terms:

2 - 5 + 6i - 6i

Add:

-3 + 0

So, in the a+bi format, we will have:

-3 + 0i

Hence, The solution is, the expression is -3+0i, so, a = -3 & b = 0.

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A) R = -19t + 1890 B) 11 years from now, the total oil reserves will be 1681 billions of barrels. C)  The world's oil reserves will be completely depleted (all used up) approximately 99.47 years from now.

The slope of a line represents the rate of change between the x and y variables, or the rise over the run. A positive slope means that the line is increasing from left to right, while a negative slope means that the line is decreasing from left to right. A slope of zero means that the line is horizontal, while an undefined slope means that the line is vertical.

A) The rate of decrease in oil reserves is 19 billion barrels per year, which can be represented as a slope of -19. The initial oil reserves are 1890 billion barrels, which is the y-intercept. Therefore, the linear equation for the total remaining oil reserves R, in terms of t (the number of years since now) is:

R = -19t + 1890

B) To find the total oil reserves 11 years from now, we can substitute t = 11 into the equation:

R = -19(11) + 1890

R = -209 + 1890

R = 1681 billion barrels

Therefore, 11 years from now, the total oil reserves will be 1681 billions of barrels.

C) If no other oil is deposited into the reserves, the reserves will be completely depleted when R = 0. We can use the linear equation to find how long it will take for the reserves to reach 0:

0 = -19t + 1890

19t = 1890

t = 99.47 years

Therefore, the world's oil reserves will be completely depleted (all used up) approximately 99.47 years from now, assuming no new reserves are discovered or added.

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