Simplify the radical: √32x

(I understand how to simplify radicals I just don’t know how to do it with an unknown variable in it)

On using unit conversion the value for 31.5 inches is obtained as 80.01 centimeters.

What is unit conversion?

Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding.

To convert inches to centimeters, we can multiply the number of inches by 2.54.

So to convert a 31.5 inch board to centimeters, use the arithmetic operation of multiplication.

We can multiply 31.5 by 2.54 -

31.5 inches × 2.54 centimeters/inch = 80.01 centimeters

Therefore, the board is 80.01 centimeters long.

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Answer:

Shirt = $20
Sweater = 30

Step-by-step explanation:

3sh + 2sw = 120

2sh + 4sw = 160

Multiply (3sh + 2sw = 120) by -2
-6sh + -4sw = -240  -> -6sh -4sw = -240
Add the two equations -6sh -4sw = -240 and 2sh + 4sw = 160 together. -4sh = -80
Shirt = 20
Substitude in 20
3 x 20 = 60 120 - 60 = 60 60/2=30

Based on the proportionate ratios of 1:6, the number of overs bowled if 120 balls are bowled is 20.

Proportion describes two ratios equated to each other.

Proportional values are like fractional values and can be depicted in percentages or fractions.

The ratio of one over and balls bowled = 1:6

This implies that for every 6 balls being bowled, one goes over.

Proportionately, for 120 balls bowled, the number of overs will be = 20 (120/6 x 1)

Thus, if one over consists of 6 balls being bowled, proportionately, the number of overs bowled if 120 balls are bowled is 20.

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Answer: 3

Step-by-step explanation:

The scale factor is 1.5. And the value of the variables 'x' and 'y' will be 9 and 10, respectively.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

The ratio of the corresponding sides will be constant. Then the scale factor is given as,

SF = 12 / 8

SF = 1.5

The equation is given as,

x / 6 = 12 / 8 = 15 / y

From the first two terms, then we have

x / 6 = 12 / 8

x = 9

From the last two terms, then we have

12 / 8 = 15 / y

y = 10

The scale factor is 1.5. And the value of the variables 'x' and 'y' will be 9 and 10, respectively.

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The number of hours till Ed and Julie were 875 miles apart was 7 hours.

Since Ed and Julie are traveling in opposite directions, we can think of their distances from Good Life City as two separate distances that are adding up to their total distance apart.

For Ed, his distance from Good Life City is:

= 60 t

For Julie :

=  65t

We want to know how many hours it took for their total distance to be 875 miles. So we can set up the equation:

875 = 60t + 65t

Simplifying, we get:

875 = 125t

t = 875 /  125

t = 7 hours

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hi

here is the answer

i hope it helps

good luck:))

The value of n for the equation (1/36)n= 216 is -1.5.

The following equation is solved by the use of exponent power rule.

The step by step explanation is given below:

convert the fraction into negative exponential form,

(36∧-1)n=216

simplify using the exponent power rule,

(a∧n)∧m = a∧n×m

Covert both sides of the equation in terms with the same base,

(6 ∧2)∧-n = 6 ∧3

Simplify the equation ,

6∧2.-n = 6∧3

Corresponding exponents are equal to ,

-2n = 3

Divide both side of the equation by 2 ,

-n= 3/2

n= - 3/2.

Therefore n = -1.5.

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Answer:

3.3.1 Approximations for trigonometric functions. 3.3.2 ... 7.2.1 Consistency for three simultaneous linear equations in two unknowns ... x : y : z =5:4:3;.

Answer: 48

Step-by-step explanation: 9p p=4 9*4=36 +18 = 48

By answering the above question, we may infer that As a result, (x, y) = is the answer to the system of equation (3, 0).

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

The equations in the system are:

x + 2y = 3 ... (1)

x - 3y = 3 ... (2)

We may use equation (2) to solve for x in terms of y:

x = 3 + 3y

If this value of x is substituted into equation (1), the result is:

(3 + 3y) + 2y = 3

If we simplify this equation, we get:

5y = 0

Hence, y = 0. Inputting y = 0 into the equation we found for x results in:

x = 3 + 3(0) = 3

As a result, (x, y) = is the answer to the system of equations (3, 0).

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The answer of the given question based on  regular octagon ,the area of the regular octagon with center O is approximately 232.98 square units.

Area is  measure of  amount of space inside  2-dimensional figure or shape, usually measured in square units like square centimeters or square meters. It is calculated by multiplying  length and  width of the figure or a shape.

To find the area of a regular octagon, we need to use the following formula:

A = 2(1 + √2) × s²

Since O is the center of the octagon, we can draw lines from O to each vertex of the octagon. This will divide the octagon into 8 congruent isosceles triangles.

Let's call the length of each side of the octagon "s". Then the base of each triangle will also be "s". We can use the Pythagorean theorem to find the length of the other sides of the triangle:

s²+ s² = (2s)²/2

2s² = 4s² - 4s²/2

2s² = 2s²/2

s² = s²/2

s = √2s/2

Now we can substitute this value of s into the formula for the area of the octagon:

A = 2(1 + √2) × s²

A = 2(1 + √2) × (√2s/2)²

A = 2(1 + √2) × 2s²/4

A = (1 + √2) × s²/2

A = (1 + √2) × (17/2)²/2

A ≈ 232.98 square units

Therefore, the area of the regular octagon with centre O is approximately 232.98 square units.

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Answer:

64%

Step-by-step explanation:

Convert a fraction to a decimal and move the decimal point to make a percent

According to the graphs, the most accurate conclusion is that a person who moved from Spain to Australia in 2010 would probably be alarmed by the high prices of homes in Australia (option A).

To select an appropriate conclusion that matches the information in the graphs we must carefully analyze the information in the graphs. Additionally, we can read each of the options and check them with the trends shown in the graphs.

In accordance with the above procedure, we can infer that the most accurate conclusion is that a person who moved from Spain to Australia in 2010 would probably be alarmed by the high prices of homes in Australia because the Residential real estate graph shows that In 2010 housing was more expensive in Australia than in Spain.

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Answer: To find the monthly payment for each option, we can use the following formula:

Monthly Payment = Total Cost * (Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))

For the option to finance at the store for 2 years at 14% interest:

Total Cost = $2,000

Monthly Interest Rate = 14% / 12 = 0.011667

Number of Months = 2 years x 12 months/year = 24 months

Substituting these values into the formula, we get:

Monthly Payment = $2,000 * 0.011667 / (1 - (1 + 0.011667)^(-24)) = $95.13

Therefore, the monthly payment for financing at the store for 2 years at 14% interest is $95.13.

For the option to use his credit card at 21% interest for 1 year:

Total Cost = $2,000

Monthly Interest Rate = 21% / 12 = 0.0175

Number of Months = 1 year x 12 months/year = 12 months

Substituting these values into the formula, we get:

Monthly Payment = $2,000 * 0.0175 / (1 - (1 + 0.0175)^(-12)) = $185.44

Therefore, the monthly payment for using his credit card at 21% interest for 1 year is $185.44.

To find the total repayment for each option, we can multiply the monthly payment by the number of months:

For the option to finance at the store for 2 years at 14% interest:

Total Repayment = $95.13/month x 24 months = $2,283.12

Therefore, the total repayment for financing at the store for 2 years at 14% interest is $2,283.12.

For the option to use his credit card at 21% interest for 1 year:

Total Repayment = $185.44/month x 12 months = $2,225.28

Therefore, the total repayment for using his credit card at 21% interest for 1 year is $2,225.28.

Step-by-step explanation:

The function y=3x+12 in factored form is (3x+12) and the zero of the function is -4.

A linear function is a polynomial of degree 1, or a mathematical expression that describes a relation between two variables. It is often written in the form y = mx + b, where m is the slope, x is the independent variable, and b is the y-intercept.

The factored form of a linear equation is the same as the standard form of the equation, with the exception that the coefficients of the variables are each expressed as a product of their prime factors. In the case of y=3x+12, the factored form is (3x+12). The zero of the function (also known as the root of the equation) is the value of the variable that will result in a value of 0 for the equation. To find the zero of the function, we need to set the equation equal to 0 and solve for the value of x. When we set y=0, we get 3x+12=0, which can be solved to get x=-4. Therefore, the zero of the function is -4.

The function y=3x+12 in factored form is (3x+12) and the zero of the function is -4.

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The vertex of the function is,

⇒ Vertex = (1, - 4)

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The function is,

⇒ f (x) = -x² + 2x - 5

Now,

We can change the quadratic function in the form,

⇒ f (x) = a (x - h)² + k

Hence, We get;

⇒ f (x) = - x² + 2x - 5

⇒ f (x) = - (x² - 2x + 1 - 1) - 5

⇒ f (x) = - (x - 1)² + 1 - 5

⇒ f (x) = - (x - 1)² - 4

Thus, The vertex of the function is,

⇒ Vertex = (1, - 4)

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The value of x, given the sides in the right - angled triangle, would be 31. 8 °.

We are given side that is opposite the angle, and we are also given the hypotenuse.

This means that we can use the operation of Sin which is :

Sin ( angle ) = Opposite / Hypotenuse

Opposite = 10 units

Hypotenuse = 19 units

The value of x is :

Sin ( x ) = 10 / 19

Sin ( x ) = 0. 5263

x = Sin ⁻ ⁵ ( 0. 5663 )

x = 31. 8 °

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Answer:

46

Step-by-step explanation:

27+4*5+8-7-2=

27+20+8-7-2=

47+8-7-2=

55-7-2=

48-2=

46

The equations that gives true value for x = -2 and x = 2 are option A: x² - 4 = 0 and option D: 4x² = 16.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The equations that are true for x = -2 and x = 2 are -

x² - 4 = 0 (when x = -2, this becomes 4 - 4 = 0; when x = 2, this becomes 4 - 4 = 0)

4x² = 16 (when x = -2, this becomes 4(4) = 16; when x = 2, this becomes 4(4) = 16)

The other options are not true for x = -2 and x = 2.

Specifically -

x² = -4 is not true for any real value of x, since the square of any real number is always non-negative.

3x² + 12 = 0 is not true for x = -2 or x = 2, since plugging in these values gives 12 ≠ 0.

2(x - 2)² = 0 is only true for x = 2, but not for x = -2, since plugging in x = -2 gives 2(16) ≠ 0.

Therefore, the options x² - 4 = 0 and 4x² = 16 are the correct ones.

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Step-by-step explanation:

for the function

�

(

�

)

=

2

�

2

−

8

g(x)=2x

2

−8

, q = 0, r = 2, s = 3, t = -3

The given function is:

�

(

�

)

=

2

�

2

−

8

g(x)=2x

2

−8

The inverse of

�

(

�

)

=

2

�

2

−

8

g(x)=2x

2

−8

for x ≥ 0 is

�

(

�

)

=

1

2

�

+

4

f(x)=

2

1

x+4

The inverse of

�

(

�

)

=

2

�

2

−

8

g(x)=2x

2

−8

for x ≤ 0 is

�

(

�

)

=

−

1

2

�

+

4

d(x)=−

2

1

x+4

For x = -8

�

(

−

8

)

=

−

1

2

(

−

8

)

+

4

�

(

−

8

)

=

0

d(−8)=−

2

1

(−8)+4

d(−8)=0

q = d(-8) = 0

r = f(0)

�

(

�

)

=

1

2

�

+

4

�

(

0

)

=

1

2

(

0

)

+

4

�

(

0

)

=

4

�

(

0

)

=

2

f(x)=

2

1

x+4

f(0)=

2

1

(0)+4

f(0)=

4

f(0)=2

r = 2

s = f(10)

�

(

�

)

=

1

2

�

+

4

�

(

10

)

=

1

2

(

10

)

+

4

�

(

10

)

=

9

�

(

10

)

=

3

f(x)=

2

1

x+4

f(10)=

2

1

(10)+4

f(10)=

9

f(10)=3

s = 3

t = d(10)

�

(

�

)

=

−

1

2

�

+

4

�

(

10

)

=

−

1

2

(

10

)

+

4

�

(

10

)

=

−

9

�

(

10

)

=

−

3

d(x)=−

2

1

x+4

d(10)=−

2

1

(10)+4

d(10)=−

9

d(10)=−3

Therefore, for the function

�

(

�

)

=

2

�

2

−

8

g(x)=2x

2

−8

, q = 0, r = 2, s = 3, t = -3

The value of variables are,

q = 0

r = 2

s = - 3

t = 3

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The function is,

g (x) = 2x² - 8

Now, We have;

For x ≥ 0;

The inverse function is,

⇒ f (x) = √1/2x + 4

And, For x ≤ 0;

The inverse function is,

⇒ d (x) = - √1/2x + 4

Hence, For x = - 8;

⇒ d (x) = - √1/2x + 4

⇒ q = - √1/2 × - 8 + 4

⇒ q = - √- 4 + 4

⇒ q = 0

For x = 0;

⇒ f (x) =  √1/2x + 4

⇒ r = √1/2 × 0 + 4

⇒ r =  √0 + 4

⇒ r = 2

For x = 10;

⇒ d (x) = - √1/2x + 4

⇒ t = - √1/2 × 10 + 4

⇒ t = - √5 + 4

⇒ t = - 3

For x = 10;

⇒ f (x) =  √1/2x + 4

⇒ s =  √1/2 × 10 + 4

⇒ s =  √5 + 4

⇒ s = 3

Thus, The value of variables are,

q = 0

r = 2

s = - 3

t = 3

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Answer:

To divide by a fraction, we can multiply by its reciprocal.

So,

4/9 /8 = 4/9 x 1/8 = 4/72 = 1/18

To determine whether the function f(x) = (x^2-2x-3)/(x^2+3x+2) has any holes, we can factor the numerator and denominator and simplify the expression. The numerator can be factored as:

x^2 - 2x - 3 = (x - 3)(x + 1)

And the denominator can be factored as:

x^2 + 3x + 2 = (x + 1)(x + 2)

Therefore, we can simplify the function as:

f(x) = [(x - 3)(x + 1)]/[(x + 1)(x + 2)]

The factor of (x + 1) appears in both the numerator and denominator, so we can simplify further by canceling it out:

f(x) = (x - 3)/(x + 2)

Since (x + 1) was canceled out, we have a hole in the graph of the original function at x = -1. To find the coordinates of the hole, we can evaluate the simplified function at x = -1:

f(-1) = (-1 - 3)/(-1 + 2) = -4

Therefore, the hole in the graph of the original function is located at the point (-1, -4).

Where the above conditions exist:

(a) To find the weight of each type of coffee in 800g of X, we can use the ratio of P coffee to Q coffee in the blend, which is 3:13.

Let the weight of P coffee in 800g of X be 3x, then the weight of Q coffee in 800g of X is 13x.

The total weight of X is 800g, so we have:

3x + 13x = 800

16x = 800

x = 50

Therefore, the weight of P coffee in 800g of X is:

3x = 3(50) = 150g

And the weight of Q coffee in 800g of X is:

13x = 13(50) = 650g

(b) To find the weights of type P coffee and type R coffee in 800g of Y, we can use the ratio of the three types of coffee in the blend, which is 1:7:12 by weight.

Let the weight of P coffee in 800g of Y be x, then the weight of Q coffee in 800g of Y is 7x and the weight of R coffee in 800g of Y is 12x.

The total weight of Y is 800g, so we have:

x + 7x + 12x = 800

20x = 800

x = 40

Therefore, the weight of P coffee in 800g of Y is:

x = 40g

And the weight of R coffee in 800g of Y is:

12x = 12(40)

= 480g

(c) To find the ratio of the three types of coffee in a third standard blend Z, formed by mixing equal weights of X and Y, we first need to find the total weight of X and Y that will be used to make Z. Since we are mixing equal weights of X and Y, the total weight of X and Y in Z will be:

800g + 800g = 1600g

The ratio of P coffee to Q coffee in Z can be found by adding the weights of P coffee in X and Y, and then dividing by the total weight of X and Y:

(150g + 40g) / 1600g = 0.1125

Similarly, the ratio of Q coffee to the total weight in Z can be found by adding the weights of Q coffee in X and Y, and then dividing by the total weight of X and Y:

(650g + 7(40g)) / 1600g = 0.5063

The ratio of R coffee to the total weight in Z can be found by adding the weights of R coffee in Y, and then dividing by the total weight of X and Y:

(12(40g)) / 1600g = 0.3

Therefore, the ratio of the three types of coffee in Z is approximate:

P : Q : R = 0.1125 : 0.5063 : 0.3

(d) To find the weight of type P coffee in 800g of Z, we can use the ratio of P coffee to the total weight in Z, which is 0.1125.

Therefore, the weight of P coffee in 800g of Z is:

0.1125 * 800g = 90g

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Full Question:

Two types of coffee, P and Q, are blended in the ratio 3:13 by weight to form a standard blend X. A second standard blend, Y, is formed by blending type P coffee, type Q coffee, and type R coffee in the ratio 1:7:12 by weight. Find:

a) The weight of each type of coffee in 800 g of X

b) The weights of type P coffee and type R coffee in 800 g of Y

c) The ratio of the three types of coffee in a third standard blend Z, formed by mixing equal weights of X and Y

d) The weight of type P coffee in 800 g of Z.

-2x - 4 is not greater than 14

Step-by-step explanation:

I don't understand the question but I hope this helps

(-2 × X) + (-2 × 2)

1. The finance charge on the loan is $9,920.

2. The total deferred payment price of the airplane is $39,120.

To find the finance charge on the loan, we need to first determine the amount financed. George Bell made a 15% down payment on the airplane, so the amount financed is:

= $29,200 - (0.15)($29,200)

= $29,200 - $4,380

= $24,820

The total amount of payments made over the life of the loan is:

= $579/month x 60 months

= $34,740

The finance charge on the loan is:

= $34,740 - $24,820

= $9,920.

The total deferred payment price of the airplane is the sum of the down payment and the total amount of payments made over the life of the loan. The down payment is 15% of the purchase price which is:

= 0.15 * $29,200

= $4,380

The total amount of payments made over the life of the loan is:

= $579/month * 60 months

= $34,740

The total deferred payment price of the airplane is:

= $4,380 + $34,740

= $39,120.

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Therefore , the solution of the given problem of ratio comes out to be 1:3 is the decreased loss-to-games-played ratio.

A collection of integers "a" as well as "b" that seem to be equal can be defined using the straightforward fraction calculation "a / b," at which "b" may be larger than zero. A ratio is created by combining two ratios. The ration would be 1:1 if there were just one male and three women. There are 1/4 guys and 3/4 women in the group. Portions can be a divide between different things, a number, or a specific portion of the volume of a component.

Here,

In events played, win:

Out of the 12 games contested, 8 were victories. We can split the numerator and denominator by 4 to decrease the ratio:

=> 8/12 = 2/3

The decreased win-to-games-played ratio is 2:3.

win to loss ratio

If a squad has 8 victories, they have 4 defeats (since they have played 12 games in total). As a result, the winning/losing split is as follows:

8:4, which is further diminished by multiplying the number and denominator by 4:

=> 2:1

The decreased win-to-loss ratio is 2:1.

Played events lost:

If a squad has 4 losses and has played a total of 12 games, the ratio of losses to games played is as follows:

=> 4/12 = 1/3

=> 1:3 is the decreased loss-to-games-played ratio.

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The diagram shows the quantity x is 13.

A tape diagram, also known as a bar model or a strip diagram, is a visual representation of a problem or situation that helps students to organize and solve mathematical problems. It involves drawing a rectangular strip or bar to represent a quantity or a value, and then dividing or labeling the strip to represent different parts of the problem.

The full completed question is related to an equation as shown in the below diagram (Check it).

Given equation is x+4 = 17

If we select part 'a' the diagram is shown in the below diagram, see it.

For part 'b' the quantity x can be represent by:

x+4 = 17

x = 17 - 4

x = 13

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Answer:

c

Step-by-step explanation:

60>30 since pi is 180 ........

The scale factor of the dilation for the rectangle ABCD is found as 3.

The ratio of the scale of an original thing to a new object that is a representation of it but of a varying design is known as a scale factor (bigger or smaller).

The rectangle A'B'C'D' is created by dilation of rectangle ABCD.

We shall calculate the ratio of the rectangle's lengths in order to get the scale factor.

A:(1,5) and B:(4,5).

Length of side AB = 4 - 1 = 3

And,

A':(3,15) and B': (12,15).

Length of the side A'B' = 12-3 = 9

Ratio of the sides

AB : A'B' = 3 : 9

AB : A'B' = 1 : 3.

Thus, the scale factor of the dilation for the rectangle ABCD is found as 3.

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