What is the constant of variation, k, of the direct variation, y = kx, through (5, 8)?k = – k equals negative (8 Over 5).k = – k equals negative (5 Over 8 ).k = k equals (5 Over 8).k = k equals (8 Over 5 ).I dont understand how to solve this.

SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

The details of the proof are as follows:

Since

and

Then,

CPCTC means corresponding parts of congruent triangles are congruent

and

Thus,

VUTS is a parallelogram since diagonals of a parallelogram bisect each other

Given:

Option B is the final answer.

EXPLANATION

Let's see the facts:

Bike Price: $99

Sold Price: $117

The percentage is given by the following relationship:

Replacing terms:

Answer: The markup was 18.18%

Answer

Dealer's cost = $499

Explanation

The markup percent is given as

Markup percent = 10%

Selling Price = 548.90 dollars

Cost = ?

0.1 (Cost) + Cost = 548.90

1.1 (Cost) = 548.90

Divide both sides by 1.1

Cost = (548.90/1.1)

Cost = 499 dollars

Hope this Helps!!!

Given the expression:

8(x + 4)

Let's simplify using distributive property.

Use distributive property to distribute 8 into x + 4:

8(x) + 8(4)

Evaluate:

8x + 32

ANSWER:

8x + 32

Given the inequality:

• You can solve it as follows:

1. Apply the Addition Property of Inequality by adding 7 to both sides of the inequality:

2. Apply the Division Property of Inequality by dividing both sides of the inequality by -4 (since you are dividing both sides by a negative number, the direction of the inequality symbol changes):

• In order to graph the solution on the Number Line, you can follow these steps:

1. Since the symbol is:

You need to draw an open circle over the number -5.

2. Draw a line from the circle to the right.

Then, you get:

Hence, the answer is:

• Solution:

• Number Line:

EXPLANATION

Applying subtitution: u=ln(x)

By integral substitution definition

Substitute: u=ln(x)

Apply the common derivative:

Simplify:

Multiply fractions:

Cancel the common factor: x

Apply the Power Rule:

Substitute back u=ln(x)

Simplify:

Add the numbers: 96+1=97

Add a constant to the solution:

The answer is D:

Answer:

The length EI is;

The measure of angle IFE is;

Explanation:

Given the rectangle in the attached image.

Given;

Recall that the length of the diagonals of a rectangle are equal so;

solving for x, we have;

Since we have the value of x, let us substitute to get the length of diagonal EG;

Also, note that the diagonals of a rectangle bisect each other, so the length of EI would be;

Therefore, the length EI is;

To get the measure of angle IFE;

Reason: base angles of an isosceles triangle are equal.

So;

Reason: Complementary angles.

Substituting the value of angle IFG;

Therefore, the measure of angle IFE is;

An angle with its vertex on a circle and chord-shaped sides is said to be inscribed. The arc that is inside the inscribed angle and whose endpoints are on the angle is known as the intercepted arc.

A triangle's internal angles are always divisible by 180 degrees.

The central angle of one radian (s = r) subtends an arc length of one radius. One radian has the same value for all circles because they are all alike. The central angle of a circle is measured by its arc, which is 360 degrees, and its radian measure, which is 2π.

Circles:

A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent. A circle is also known as the location of points that are evenly spaced apart from the center. The radius of a circle is measured from the center to the edge. The line that splits a circle into two identical halves is its diameter, which is also twice as wide as its radius.

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Explanation:

The graph shows a ine crossing the parabola. The solution of the systems is the point where both system of equations intersect.

The line crosses the parabola at two point:

At x = 2, y = 2

This point is applicable to both. Since both have same values at this point, (2, 2) is one of the solution

At x = -2, y = -6

Both graphs have this point . This shows point (-2, -6) is also a solution

Hence, the solutions of the systems are (2, 2) and (-2, -6)

Answer

Explanation

The total charge on the car = (Charge based on number of days) + (Charge based on the number of miles)

Charge based on number of days = (23.95) (x) = (23.95x) dollars

Charge based on the number of miles = (0.08) (400) = 32 dollars

(The total charge on the car) ≤ 440

23.95x + 32 ≤ 440

23.95x + 32 - 32 ≤ 440 - 32

23.95x ≤ 408

Divide both sides by 23.95

(23.95x/23.95) ≤ (408/23.95)

x ≤ 17.04

Hope this Helps!!!

Answer:

its B

Step-by-step explanation: just took the test

Answer:

B. (19/24)

Step-by-step explanation:

 1          1          5

------ + ------ + -------

 4         8         12

 1(6)     1(3)     5(2)

------ + ------ + -------

 4(6)   8(3)     12(2)

 6         3        10         19

------ + ------ + ------- = -------

 24      24       24        24

I hope this helps!

A account 8% B account 12%

A+$450 = B (1)

Ax8% +Bx12%= $220

Ax0.08 + Bx0.12 = 220

Now we replace (1) on B:

Ax0.08 + (A+450)x0.12 = 220

Ax0.08 + Ax0.12 + 54 = 220

Ax0.2 = 166

A= 830.

Now we replace the value of A on equation (1):

830 + 450 = B

B = 1280

We will have the following:

The expression that best describes the information is:

*When viewing the data for tolling a one, as the number of rolls increases, the experimental probability becomes closer to equal to the theoretical probability.

We're told from the question that Sarah needs atleast $1975, that means that she can either have exactly $1975 or more but not less;

Let x represent the number times she mows a lawn;

Let y represent the number of times she walks a dog;

The inequality can be modelled thus;

a)

In order to find the list of all potential rational roots, let's find the factors of the division between the constant term and the leading term.

Since the constant term is zero, so the only potential rational root in the list is 0.

b)

Since the constant term is zero, so 0 is a root of the polynomial. Then, let's factor it to find the remaining roots:

Solving this quadratic equation using the quadratic formula, we have:

Therefore the actual roots of P(x) are:

0 (multiplicity 1) and -5 (multiplicity 2).

The Perimeter of a Rectangle

Given a rectangle of width w and length l, the perimeter is calculated as the sum of the side lengths, that is:

P = w + w + l + l

Or, equivalently

P = 2w + 2l

Hermann was calculating the perimeter of a rectangle and built the expression:

P = x + x + 4x + 4x feet

Note this expression is similar to the first one. This means that the width of the rectangle is x and the length is 4x.

a) We'll draw a rectangle with such dimensions:

b) Assuming the base is the length and the height is the width, the relationship between the base and the height is

4x / x = 4

This means the base is four times the height

c) We are given the perimeter as P = 60 feet.

We need to solve the equation

x + x + 4x + 4x = 60

Simplifying:

10x = 60

Dividing by 10:

x = 60/10

x = 6 feet

The base is 4x = 24 feet.

The base of Herman's rectangle is 24 feet

The height of Herman's rectangle is 6 feet

g(x) = x + 7 when x =< 2

g(x) = 8 - x when x > 2

g(-2) Evaluate the first function

g(-2) = -2 + 7

g(-2) = 5

g(2) Evaluate the first function

g(2) = 2 + 7

g(2) = 9

g(8) Evaluate the second function

g(8) = 8 - 8

g(8) = 0

Step 1

Given; The area of a rectangle is given by a=6x^2y+4y^2x and the width of the rectangle is w=2xy. what is the length, l, of the rectangle if l=a/w?

Step 2

Thus;

Answer;

To solve this problem we remember the following statement: a quadrilateral that has opposite sides that are congruent and parallel can be a parallelogram, rhombus, rectangle or square.

From the figure, we see a quadrilateral with congruent opposite sides. Relating this information to the statement above, we see that this quadrilateral can be a parallelogram, rhombus, rectangle or square. So we conclude that there is not enough information to conclude that the quadrilateral is a parallelogram.

Answer

d. Not enough information

We are given the following information

sin u = 5/13

cos v = -3/5

Where the angle u and v are in the 2nd quadrant.

Let us find cos u

Apply the Pythagorean theorem to find the 3rd side.

Cos u = 12/13

Now, let us find sin v

Apply the Pythagorean theorem to find the 3rd side.

Sin v = 4/5

Recall the formula for sin (A - B)

Let us apply the above formula to the given expression

Therefore, sin (u - v) = 33/65

Answer:

Frankie is incorrect.

Step-by-step explanation:

Change 4/5 to 8/10.

You are comparing 10 7/10 to 10 8/10.

10 4/5 (which is also 10 8/10) can be written as 10.8

10 7/10 can be written as 10.7

10.8 > 10.7, so 10 4/5 > 10 7/10 is correct,

and 10 7/10 > 10 4/5 is incorrect.

Frankie is incorrect.

On a number line, show 10 and 11.

Make 10 equal spaces between 10 and 11. Each space is 1/10.

10 7/10 is one space to the left of 10 4/5, so 10 7/10 is less than 10 4/5.

Hello there. To solve this question, we'll need to isolate a variable, substitute its expression into the other equation and find both values.

4x + 4y = 12

x = -2y + 8

Plug x = -2y + 8 in the first equation. Before doing so, divide both sides of the first equation by a factor of 4

x + y = 3

-2y + 8 + y = 3

Subtract 8 on both sides of the equation and add the values

-2y + y = 3 - 8

-y = -5

Multiply both sides of the equation by a factor of (-1)

y = 5

Plug this value into the expression for x

x = -2 * 5 + 8

Multiply the values

x = -10 + 8

Add the values

x = -2

These are the values we're looking for.

The solution for this system of equation is given by:

S = {(x, y) in R² | (x, y) = (-2, 5)}

Answer:

         x = -2

         y = 5

Step-by-step explanation:

      4x + 4y = 12

Divide the entire equation by 4,

        x + y = 3 -------------(I)

             x = -2y + 8 ------------(II)

Substitute x = -2y + 8 in equation (I)

      -2y + 8 + y = 3

      -2y + y + 8 = 3

Combine like terms,

           -y + 8    = 3

Subtract 8 from both sides,

                 -y   = 3 - 8

                -y    = - 5

Multiply the entire equation by (-1)

                 [tex]\sf \boxed{\bf y = 5}[/tex]

Substitute y= 5 in equation (II),

        x = -2*5 + 8

           = - 10 + 8

       [tex]\sf \boxed{\bf x = -2}[/tex]

Solution:

(a) Given the functions:

Then:

Similarly,

Two functions f and g are inverses of each other if and only if f(g(x))=x for every value of x in the domain of g and g(f(x))=x for every value of x in the domain of f.

ANSWER: f and g are inverse of each other.

(b) Given:

Then:

Also,

ANSWER: f and g are not inverses of each other.

Simplest form of the  radical expression 3 ∛2 a − 6 ∛2 a is given by -3∛2 a.

As given in the question,

Given radical expression is equal to :

3 ∛2 a − 6 ∛2 a

Simplify the given 3 ∛2 a − 6 ∛2 a radical expression to get the simplest form ,

3 ∛2 a − 6 ∛2 a

Write all the prime factors of the number we have,

= 3∛2 a - ( 3 × 2) ∛2 a

Take out the common factor from the given radical expression we have,

= 3∛2 a ( 1 - 2 )

= 3∛2 a (- 1)

= -3∛2 a

Therefore, simplest form of the  radical expression 3 ∛2 a − 6 ∛2 a is given by -3∛2 a.

The complete question is:

What is the simplest form of the radical expression? 3 ∛2 a − 6 ∛2 a

Please show the steps to help me understand this process.

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We are given the expression:

To get the answer, we will have to apply exponents rules

The rule is:

Thus

we will have

Therefore,

The answer is 4

The given situation can be illustrated as follow:

In order to determine the distance x between the roller coaster and the tower. Use the law of cosines, as follow:

By simplifying the previous expression, you obtain:

Hence, the distance between the tower and the roller coaester is approximately 469.5m

A. ∠4 is congruent to ∠5; True.

B. Two lines are parallel; True.

C. The measure of ∠6 = 90.5°; False.

D. ∠2 and ∠3; True.

For the give question;

Two line are cut by the transversal.

∠1 =  90.5° and ∠7  =  89.5°

Thus the result for the given statement are-

A. ∠4 is congruent to ∠5 because they are alternate interior angles; True.

B. Two lines are parallel; True.

C. The measure of ∠6 = 90.5°; False.

∠6 = ∠7 =  89.5°.(correct)

D. ∠2 and ∠3 are supplementary because they are same-side exterior Angeles; True.

Thus, the result for the given statement are found.

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(Question 3)

Because of the definition of a perpendicular bisector, we know that angle B is a right angle (90°) an that

Note that AB is a segment that is shared by both triangles in the image. By using SAS (Side-Angle-Side), we can find that both the triangles are congruent (they are equal). Therefore,

We know that

We'll just have to plug in the value of x we calculated to find the lenght of AE

Therefore, AE = 36

(Question 4)

Because of the definition of a perpendicular bisector, we know that XY splits TS right by the middle. So if TS = 10, RS would be worth half of that

Therefore, RS = 5