Find the unit price. Round your answer to the nearest cent.It costs $98.39 to rent a standard-size car for 4 days. Find the price per day to rent this car.Answer: $ _______________ per day

We can conclude that the equation of the circle is (x - 3)² + (y + 6)² = 32, where (3, -6) is the center and 4√2 is the radius. Option 3 and 6 are correct  options.

Based on the information given, we know that circle has its center at the point (3, -6) and a radius of 4√2. We also know that the point (-1, -2) and (4, -0.5) are on the circle.

Using the distance formula, we can confirm that the distance between the center of the circle and each of these points is indeed 4√2.

This equation can be simplified to x² - 6x + y² + 12y + 1 = 0 by expanding and combining like terms. This is the equation of circle , and any point that satisfies this equation will be on the circle. Option 3 and 6 are correct  options.

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Angle JKL has a measure of 24 degrees while angle LKM has a measure of 12 degrees

The possible question is added at the end of the solution and as an attachment

From the attached figure, we have the following angles

From the attached figure, we can see that:

Angle 1 is twice the measure of angle 2

This is so because, the angle 1 is the vertex angle of an isosceles triangle

While the angle 2 is half of it

So, we have

Angle 1 = 2 * Angle 2

Substitute the known values in the above equation

So, we have

2 * 3x = 5x + 4

Evaluate the product

So, we have

6x = 5x + 4

Evaluate the like terms

x = 4

Substitute x = 4 in the equations JKL=5x+4 and LKM=3x

So, we have

JKL= 5 x 4 + 4

LKM = 3 x 4

Evaluate the equations

So, we have

JKL= 24

LKM = 12

Hence, the measures of the angles are JKL= 24 and LKM = 12, respectively

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The correct proof of the equation is cos3θ =cos(2θ + θ) =  cos²θ - 3cosθsin²θ (Proved)

Given the trigonometry identity below:

cos3∅=cos²∅-3cos∅sin²∅

We are to prove that both sides of the equation are equal.

cos 3θ = cos(2θ + θ)

Using the double angle formula for cosine, we can expand the first term:

cos(2θ + θ) = cos2θ cos θ - sin2θ sinθ

Since cos2θ = cos²θ - sin²θ

cos(2θ + θ) =  cos²θ - sin²θ - 2cosθsinθsinθ

cos(2θ + θ) = cos²θ - sin²θ - 2cosθsin²θ

On simplifying, we can see that;

cos3θ =cos(2θ + θ) =  cos²θ - 3cosθsin²θ (Proved)

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Answer:

false

Step-by-step explanation:

A line can be a function as long as it passes the vertical line test. A few examples of a line that is a function but does not have constant slopes are sin(x), cos(x), (known as trig FUNCTIONS), \(x^{2} \\), and basically x to any power.

Answer:

should be tue since y is slope and the equation is always y=mx+b

1. Based on the producer theory, an increase in the demand for labor (L) would be caused by An increase in the productivity of labor, A decrease in the wage rate and A decrease in the rental rate of capital.

2. Missing variables in this simple producer theory would include The technology used to produce output, The preferences of consumers and Quality of labor and capital.

In the standard producer theory, a producer minimizes costs for a given level of output.

This involves choosing the optimal mix of inputs, such as labor (L) and capital (K), to produce the desired output (y).

The cost function is represented by C = wL + rK, where w is the wage rate (cost of labor) and r is the rental rate (cost of capital).

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The number of additional red marbles to be added to the total 24 marbles present in the bag is 16 marbles.

What is Probability?

From the question, it is given that the,

Number of Red marbles = 8

Number of Yellow marbles = 9

Number of Green marbles = 7

So, the total number of marbles = 8 + 9 + 7 = 24

Let \(x\) be the additional number of red marbles added to the bag.

The total number of red marbles after the addition of \(x\) red marbles into the bag = \(8+x\)

The total number of all marbles after the addition of \(x\) red marbles into the bag = \(24+x\)

The probability of randomly drawing a red marble is given as equal to \(\frac{3}{5}\)

We know that, the probability of randomly drawing a red marble is equal to the ratio of the total number of red marbles to the total number of all marbles.

---> P(R) = n(R)/n(T)

Substituting the given values, we get

3/5 = 8+x / 24+x
---> 5(8+x) = 3(24+x)
---> 40 + 5x = 72+3x

Solving, we get

5x - 3x = 72 - 40
---> 2x = 32
---> x = 16

Therefore, the additional number of red marbles to be added to obtain the required probability is equal to 16.

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Answer:

8.0 billion

Step-by-step explanation:

1.2÷100=0.012

0.012×6.5=0.078

2017-2001=16

0.078×16=1.248

6.5+1.248=7.748

nearest tenth 8.0

Answer:

254 R 6

Step-by-step explanation:

Answer:

256 7/16

Step-by-step explanation:

2308/9 = 256 7/16

Answer:

Because -4 is 4 units away from 0.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

To graph the function g(x) = 7x + 10, we shift the graph of f(x) = 7x vertically by adding a constant term of +10. This means every y-coordinate on the graph increases by 10 units. The slope of the line remains the same at 7. The resulting graph is a straight line passing through (0, 10) with a slope of 7.

To graph the function g(x) = 7x + 10, you need to make the following change to the graph of f(x) = 7x:
1. Translation: The graph of f(x) = 7x can be shifted vertically by adding a constant term to the equation. In this case, the constant term is +10.
Here's how you can do it step by step:
1. Start with the graph of f(x) = 7x, which is a straight line passing through the origin (0,0) with a slope of 7.
2. To shift the graph vertically, add the constant term +10 to the equation. Now, the equation becomes g(x) = 7x + 10.
3. The constant term of +10 means that every y-coordinate of the points on the graph will increase by 10 units. For example, the point (0,0) on the original graph will shift to (0,10) on the new graph.
4. Similarly, if you take any other point on the original graph, such as (1,7), the corresponding point on the new graph will be (1,17) since you add 10 to the y-coordinate.
5. Keep in mind that the slope of the line remains the same, as only the y-values are affected. So, the new graph will still have a slope of 7.
By making this change, you will have successfully graphed the function g(x) = 7x + 10.

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Answer:

(A) P = A/1 + rt

Step-by-step explanation:

A = P(1 +rt)

Divide both sides by (1 + rt)

A/(1 + rt) = P

P = A/(1 + rt)

The correct equations which is equivalent in terms of P is,

P = A / (1 + rt)

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

We have to given that;

The equation A = P(1 +rt) represents the formula to find the total amount owed on a loan, A,

where, P represents the principal amount borrowed, r is the rate of interest, and t is the time of period for which the loan is repaid.

Hence, We can simplify expression for P as;

A = P (1 + rt)

Divide both side by (1+rt);

A / (1 + rt) = P

P = A / (1 + rt)

Thus, The correct equations which is equivalent in terms of P is,

P = A / (1 + rt)

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Answer:

  A. D: 0 ≤ b ≤ 10 R: 0 ≤ W(b) ≤ 120

Step-by-step explanation:

Since b represents the number of birdhouses, it is reasonable for that to have non-negative values. The maximum material availability means that b > 10 is not of practical use. This eliminates choices B and D.

Since W represents the amount of wood required for b birdhouses, it is reasonable for the range of it to match 12 times the domain: 12·0 = 0 to 12·10 = 120. This eliminates choice C.

The appropriate choice is ...

  A. D: 0 ≤ b ≤ 10 R: 0 ≤ W(b) ≤ 120

Proved that, sin⁴x-cos⁴x/ sin²x-cos²x = 1​.

Here, we have,

given that,

the LHS is:

sin⁴x-cos⁴x/ sin²x-cos²x

now, we know that,

sin²x+cos²x = 1

and, we know that,

a² - b² = (a+b) (a-b)

so, we get,

sin⁴x-cos⁴x/ sin²x-cos²x

= (sin²x+cos²x) (sin²x-cos²x ) / sin²x-cos²x

=(sin²x+cos²x)

=1

= RHS

Hence, Proved that, sin⁴x-cos⁴x/ sin²x-cos²x = 1​

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Answer:

Step-by-step explanation:

(5 + 3)/(4 - 2) = 8/2 = 4

Answer:

2x^5+y^12*x^2/3

Step-by-step explanation:

Answer:

4(7 + 6)

Step-by-step explanation:

28 + 24

GCF of 28 and 24 is 4

4 (7 + 6)

I hope this helps!

Answer:

7

Step-by-step explanation:

hope t helps

Answer: D. 9.68

Step-by-step explanation:

145.2 oz/ 15 cups = 9.68 oz per cup

Value of x and y are -51 and 8 respectively

What is Algebra?

One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for using these symbols in formulas.

Let,

X+27+32 = 8

X+ 3y +32 = 10

X + 2y +42 = 9

Be, equation 1, 2 and 3 respectively

X+27+32 = 8 -----(1)

X+ 3y +32 = 10 -----(2)

X + 2y +42 = 9 -----(3)

From equation we can find the value of x

X+27+32 = 8

X + 59 = 8

X = 8 - 59

X = - 51

Substituting the value of x in equation 3

X + 2y +42 = 9

(-51) + 2y + 42 = 9

-51 + 42 + 2y = 9

-9 + 2y = 9

2y = 9 + 9

2y = 18

y = 18/2

y = 9

Hence, the value of x = -51 and y = 9

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Answer:

=7-6x

Step-by-step explanation:

7-x 4-2x

=7-6x

Solve for x.

2x + 9 = 33

2x = 24

x = 12

A. x = 7.5

B. x = 12

C. x = 21

D. x = 84

Answer:

\(2x + 9 = 33 \\ 2x = 33 - 9 \\ 2x = 24 \\ x = \frac{24}{2} \\ x = 12\)

Answer: For in the inequality to be true, X must be less than or equal to 1. That represented as an in equality is X < 1.

x<1 true

Step-by-step explanation:

3(1+x)<+6= 3×1+3×X<+6=3+3x<6 then3x=6-3 solution 3x=3 devide by 3 both sides the answer is x=1 hence x<1 verified

The angles in the triangle are;

A = 26.67°, B = 29.06°, C = 124.27°

We know that we have the triangle as ΔABC  and a-13.9, b-15.2, c-25.7

Using the Cosine rule;

a^2 = b^2 + c^2 - 2ac CosA

(13.9)^2 = (15.2)^2 + (25.7)^2 - 2(15.2 * 25.7)Cos A

193.21 = 891.35 - 781.28CosA

193.21 -  891.35 =  - 781.28CosA

Cos A = 193.21 -  891.35 /  - 781.28

A = Cos-1 (193.21 -  891.35 /  - 781.28)

A = 26.67°

Then;

c^2 = a^2 + b^2 - 2abCosC

(25.7)^2 = (13.9)^2 + (15.2)^2- 2(13.8 * 15.2)CosC

660.49 = 424.25 - 419.52CosC

660.49 -  424.25 = - 419.52CosC

C= Cos-1 (660.49 -  424.25 / - 419.52)

C = 124.27°

Then B;

180 - ( 26.67° + 124.27°)

= 29.06°

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scalar factor= 2, in order to find the scalar factor between two triangle  we need to get the ratio between any of thier side of both the triangle on same side

what is scalar factor?

In mathematics, a scalar factor is a numerical value that scales or stretches a vector or a matrix by a certain factor. In other words, a scalar factor is a constant that is multiplied to a given vector or matrix to change its size or magnitude.

In the given question,

In mathematics, a scalar factor is a numerical value that scales or stretches a vector or a matrix by a certain factor. In other words, a scalar factor is a constant that is multiplied to a given vector or matrix to change its size or magnitude.

For instance, if we have a vector v = (x, y, z), then multiplying it by a scalar factor k will result in a new vector kv = (kx, ky, kz), which is stretched or shrunk according to the value of k. Similarly, if we have a matrix A, multiplying it by a scalar factor k will result in a new matrix kA, where each element of A is multiplied by k.

in order to find the scalar factor between two triangle  we need to get the ratio between any of thier side of both the triangle on same side

scalar factor= opposite side of bigger triangle / opposite side of smaller triangle

scalar factor= 20/10

scalar factor= 2

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we have

y=-2x^2+8x-8

Looking at the graph

the number of real solutions in a quadratic equation is equal to the number of x-intercept

In this problem

the graph has only one x-intercept (2,0)

therefore

has only one real solution

Answer:

inverse

Step-by-step explanation:

If one variable increases in value and the other variable decreases in value, the variables have a(n) inverse relationship. Option B is correct.

Given that,

A statement " If one variable increases in value and the other variable decreases in value, the variables have a(n) ________ relationship." is given blank space to fill in the state from the option given.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense that are they directly proportional or inversely proportional to each other.

Here, when two variable are proportional to each other,

Case 1
The value of one variable increases as the value of another variable variable are directly proportional to each other

Case 2
The value of one variable decreases as the value of another variable increase implies variables are inversely proportional to each other.

Thus, If one variable increases in value and the other variable decreases in value, the variables have a(n) inverse relationship. Option B is correct.

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The coordinates of point B are (-3, 17).

The given equation is M = I₁ + I₂ = 31 + 32.

Now let's substitute in our given values:

(-2, 2) = ((-5 + x₂) / 2, (-5 + 2 + y₂) / 2)

We will now set up two equations to solve for our two unknowns, x₂ and y₂:

Equation 1: (-5 + x₂) / 2 = -4

Multiply both sides by 2:

-5 + x₂ = -8

Add 5 to both sides:

x₂ = -3

This gives us the x-coordinate of point B.

Equation 2: (-5 + 2 + y₂) / 2 = 7

Simplify:

(-3 + y₂) / 2 = 7

Multiply both sides by 2:

-3 + y₂ = 14

Add 3 to both sides:

y₂ = 17

This gives us the y-coordinate of point B.

Therefore, the coordinates of point B are (-3, 17).

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