Simplify the following rational expression to determine if thegiven simplification is correct. If it is correct, select TRUE. If it isnot correct, select FALSE.6x48x556x47

Let:

y=2x+18 (1)

4x+5y=20 (2)

replace (1) into (2)

4x+5(2x+18)=20

Using distributive property:

4x+10x+90=20

Add like terms:

(4x+10x)+90=20

14x+90=20

subtract 90 from both sides:

14x+90-90=20-90

14x=-70

Divide both sides by 14:

14x/14=-70/14

x=-5

Finally, replace the value of x into (1)

y=2(-5)+18

y=-10+18

y=8

Let:

2x+2y=6 (1)

3x-5y=25 (2)

From (1) let's solve for x:

subtract 2y from both sides:

2x+2y-2y=6-2y

2x=6-2y

Divide both sides by 2:

x=(6-2y)/2

x=3-y (3)

Replace (3) into (2)

3(3-y)-5y=25

Using distributive property:

9-3y-5y=25

Add like terms:

9+(-3y-5y)=25

9-8y=25

subtract 9 from both sides:

9-8y-9=25-9

-8y=16

Divide both sides by -8:

(-8y)/(-8)=(16)/(-8)

y=-2

Finally, replace the value of y into (3)

x=3-(-2)

x=3+2

x=5

SOLUTION:

Case: Unit rates

Given: Brian split 4/5 pounds of candy among 5 people

Method:

The unit rate in pounds per person

Final answer:

The rate in pounds per person is:

4/25 pounds

To round to the nearest tenth, we must round it to the nearest hundredth first, we have

See that we have 1 at the last decimal, then we will keep the hundredth value, it means that we will round to

Now the last decimal is 8, it's above 5, then we must add one at the tenth and remove the hundredth

Therefore the nearest tenth is the letter C, 14.5

Answer:c

Step-by-step explanation:THIS SOOO CORRECT!

f(x-1) + 2 translates f(x) 1 unit to the right and 2 units up. Then, the graph of the new function is:

f(x) = x^2

To translate the function 2 units down (along the y axis) subtract 2

F(x) = x^2 -2

To translate the function 3 units to the right (along the x-axis) subtract 3 units inside the parentheses.

f(x) = (x-3)^2 - 2

An inequality which can be used to determine x the number of people who can go to the amusement park is: 15 + 25x ≤ 115

Also, approximately 4 people can go to the amusement park.

In the given question,

cost for admission parking = $15

Tickets = $25 per person

Let x be the number of people those who go to the amusement park.

On parking and admission spent not more than $115

So we get an inequality,

15 + 25x ≤ 115

We solve above inequality.

25x ≤ 115 - 15

25x ≤ 100

25x / 25 ≤ 100/25

x ≤ 4

This means that approximately 4people can go to the amusement park.

Therefore, an inequality which can be used to determine x the number of people who can go to the amusement park is: 15 + 25x ≤ 115

Also, approximately 4 people can go to the amusement park.

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We are asked to find the value of b that makes quadrilateral RSTU a parallelogram.​

We know from the properties of a parallelogram that the opposite angles are always equal.

Let us equate the angles and solve the equation for b.

Similarly,

For the given ques, the graph is mention in the question.

As, domain are the all set of values lying on the x-axis.

Thus,

A. Domain {-1 to infinity} (In integer or fraction form.)

B. Domain [-1, ∞), (interval notation; half closed half open)

Range of the relation of function are-

A. Range {- infinity to infinity} (In integer or fraction form.)

B. Range (- ∞, ∞), (interval notation open interval both sides)

Thus, the value of domain and range of the function are found.

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The value of c would be 49 and the factored form will be;

Here, we want to get the value of c that will make the expression a perfect square

We proceed as follows;

Divide the coefficient of x by 2 ;

That would be; -14/2 = -7

Now, square this value; that would be (-7)^2 = 49

The value 49 would make the expression a perfect square

Thus, we have the factored form as follows;

Answer:

First choice: 08:25

Step-by-step explanation:

Squared Clock is 5 minutes slower than the round clock
since the round clock is 10 minutes behind actual time, square clod is 15 minutes behind actual time

Time on square clock = 8:05
So actual time = 8:05 + 15 = 8:20

Rectangular clock is 5 minutes ahead of actual time
So time on rectangular clock is 8:20 + 05 = 8:25

Answer: First choice: 08:25

Answer:

11

Step-by-step explanation:

The answer would be 11, because when you add 5 and 6 together, you get 11. Pretend you had 5 cookies, and you got 6 more.

5 Cookies- O,O,O,O,O

6 More Cookies- O,O,O,O,O,O

If you add the cookies up, you get 11.

Given the line shown in the figure passes through the points (-3, -4) and (1, 2)

We will write the equation of the line.

First, we will find the slope of the line using the following formula:

Substitute with the given points:

The equation of the line in point-slope form will be as follows:

Convert tot he slope-intercept form, so, the equation will be:

Now, we will check the options to see the correct equations.

So, the answer will be, we will select the options:

A. y+4 = 1.5 (x+3)

B. y = 1.5x + 0.5

C. y - 2 = 1.5 (x - 1)

Answer:

Serbia

Step-by-step explanation:

Austria-Hungary declares war on Serbia, effectively beggining the first world war

The three transformations—rotations, reflections, and translations—can be combined to produce congruent shapes. The truth is that any pair of congruent shapes can be matched to one another by combining one or more of these three transformations.

Explain transformations.

A point, line, or geometric figure has four different transformations that can be applied to alter its appearance. While the term "Image" refers to the position and final shape of the object, "Pre-Image" refers to the object's shape before transformation.

Given Information

The size and shape of the figures are preserved during stiff transformations, as we already know (reflections, translations, and rotations). Always in harmony with one another is the pre-image.

These transformational skills are all possessed by Matt:

Reflection

The reason a reflection maintains its original form Comparable locations between the pre-image and the picture remain apart from the line of reflection.

Rotations as a Transformation of Congruence

When a figure rotates, it twists. Despite being the same size and shape, the figurine appears to have toppled over. A clock is an excellent example of how the globe rotates in reality. Every hour or every day, the connecting arms of a clock revolve around its axis. The degree of a rotation determines what kind of rotation it is; popular rotations include 90, 180, and 270 degrees. Before spinning around completely and going back to where it started, the figure rotates 360 degrees. the clockwise or counterclockwise direction in which a rotation is made. This data can be used to determine the degree, amount, a revolution's speed and direction.

Congruence translational transformation

When an object or shape is transferred from one location to another without altering its size, shape, or orientation, we refer to the transfer as a movement. A translation, often known as a slide, involves moving every point on an object or shape uniformly and in one direction.

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For 9 of games is the cost of these plans the same.

Moving the variables to one side of the equation and the numeric portion to the other allows us to solve a linear equation with one variable. As an illustration, the equation x - 1 = 5 - 2x can be resolved by transferring the numerical components to the right side of the equation while leaving the variables on the left. Therefore, we receive x + 2x = 5 + 1. Thus, 3x Equals 6. As a result, x = 2. The formula for a two-variable linear equation is Ax + By + C = 0, where A and B are the coefficients, C is a constant term, and x and y are the two independent variables, each with a degree of 1. A linear equation involving two variables, for illustration, is 7x + 9y + 4 = 0.

Consequently, you would multiply $9.45 and $4.45 by the same number (I selected 9 because there are only one or two possible answers), then add $85 to the result for the $4.45 amount.

9.45 x 9

= 85.05

4.45 x 9

= 40.05 +85

= 125.05

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Answer:

5 cups of flour.

Step-by-step explanation:

I know the wording of the problem may be confusing at first, but if you look at it a little bit, it's just multiplication and division.

To start,

12 biscuits require 2 cups of flour,

meaning that 6 biscuits (half of the original) only require 1 cup.

(12/2 = 6)

Next,

We need to find how much flour is in 30 biscuits.

We know that 1 cup is in 6 biscuits, and if you were to find how much was in 30 biscuits, you would just need to divide 30 by 6.

(30/6 = 5)

5 cups of flour would be your answer.

To put it mathematically,

(12/2 = 6), (30/6 = 5)

The total cost of leasing the truck for 3 years is $8644.

An equation is an expression that can be used to show the relationship between numbers and variables.

Let y represent the total cost of leasing the truck for x months.

y = 154x + 3100

In 3 years, number of months (x) = 3 * 12 months = 36 months

Total cost in 3 years is:

y = 3100 + 154(36) = 8644

Total cost is $8644

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We consider a vector with:

• initial point (x₁, y₁) = (4, 3),

• final point (x₂, y₂) = (-4, -1).

The magnitude of the vector is given by:

The angle of the vector is given by:

We have obtained a positive value of the angle θ'. But we see that our vector points in the negative direction. To take into account this, we must sum 180° to this result:

||v|| = 8.944, θ = 206.565°

There are 20 baby devils in 2013 on Maria Island

in 2014 200 % where born

the number of baby devils born in 2014 can be gotten by

20 -------- 100

x -----------200

by proper analysis x = (200 x 20)/100 = 4000/100 = 40

40 baby devils were born in 2014

The greatest common factor is the greatest number that divides both numbers.

The given numbers are 574 and 532.

First, let's decompose each number into their prime factors.

574 | 2

287 | 7

41 | 41

1

574 = 2*7*41

532 | 2

266 | 2

133 | 7

19 | 19

1

532 = 2*2*7*19

As you can observe, the common factors are 2 and 7, so the greatest common factor is 14 since that's the product between 2 and 7.

cosecant = hypotenuse / opposite side

Angle = 7pi/4

I suggest to convert radians into angles

180° ------------------------- pi rad

x ------------------------ 7pi/4

x = 315°

Use the calculator to find this value

Cosecant 315° = -1.41

This is the answer

In order to find any pair of points that have a midpoint of (4, -10), we can choose any two values p and q. Then, one of the endpoints will be (4+p, -10+q) and the other endpoint will be (4-p, -10-q).

For example, let's choose p = q = 2, so we have:

Therefore the ordered pairs (6, -8) and (2, -12) have a midpoint of (4, -10).

When we graph a linear equation we draw a line. When we want to graph a quadratic equation we draw a parabola, a parabola is a U-shaped curve. The graph of an exponential function grows or decays and has asymptotic values.

In this case, the first graph is a line, so it represents a linear equation.

The second graph is a U-shaped curve, then it represents a quadratic equation.

The third graph decays, then it represents an exponential equation.

Answer:

3, 8

Step-by-step explanation:

Let's make the first integer x and the second integer y.

Now, you take the information given and convert it into a system of equations:

xy = 24

x = 5y - 7

y = 24 / x

Now, we substitute:

(5y - 7) · y = 24

Distribute y

5y² - 7y = 24

Rearrange it into a quadratic equation:

ax² + bx + c = 0

5y² - y - 24 = 0

Use the quadratic formula (shown in image) and plug in the values:

x = (- (7) ± [tex]\sqrt{(-7^})^{2} -4(5)(-24)}[/tex] ) / 2(5)

[tex]\sqrt{(-7)^{2} -4(5)(-24)}[/tex] = [tex]\sqrt{49 - (-480)} = \sqrt{529} = 23[/tex]

Remember that ± means there are two y values

[tex]x = \frac{7+23}{10} = \frac{30}{10} = 3[/tex]

and

[tex]x = \frac{7-23}{10} = \frac{-16}{10} = -1.6[/tex]

Since y must be an integer, we know that y = 3

Now, plug in y:

5(3) - y = 24

15 - y = 24

- y = -24

y = 8

Let's check to see if we are right:

5y - 7 = 5(3) - 7 = 15 - 7 = 8

It works!

To find the composition we need, let's first find the general expression:

Hence:

Now we can evaluate when x=1/2:

Therefore:

In order to graph the functiom we need to identify the parent function and the vertical and horizontal shifts that might be done to the function.

In this case we see that the parent function is a cubic function since the greater degree is 3

this means that f(x) is a transformation of g(x)

then

the horizontal shifts since there is sum inside the parentheses the shift will be 1 unit to the left.

the vertical shift will be 1 unit up since there is a sum outside the parentheses.

and finally since there is a - it means that the function is reflected over the x-axis

the parent function will be the red line and the function #15 is the blue line.

In order to find points we can tabulate the values for given xs' and construct the graph.

Start by making a table like this:

now since the function is given we can replace x with the values and find y

then after tabulating values should look like this

Now looking at the graph on the blue function we can see that the function is decreasing until reaching x=-1, however after that the function will continue to decrease but at a different rate, which means that over the interval

the function will be decreasing

Answer:

See below.

Step-by-step explanation:

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Alternate Interior Angles Theorem

If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.

Transitive Property of Equality

If a=b and c=b, then a=c.

Proof that ∠1=∠2

[tex]\begin{array}{c|c}\sf Statement & \sf Reason\\\cline{1-2}\\ \angle 3 = \angle 4 & \textsf{Vertical Angle Theorem}\\\\AB \parallel CD & \textsf{Given}\\\\\angle 3 = \angle 2 & \textsf{Alternate Interior Angles Theorem}\\\\\angle 2 = \angle 4 & \textsf{Transitive Property of Equality}\\\\\angle 1 = \angle 4 & \textsf{Given}\\\\\angle 1 = \angle 2 & \textsf{Transitive Property of Equality}\\\\\end{array}[/tex]

the Let number of people = y

Let price = x

Gradient = -200

Revenue = price X number of people

Optimal item price = $3

In order to determine which vehicle gets better gas mileage, we need to determine which of the two vehicles consumes less gas for each mile travelled. The car consumes 1 gallon of gas for every 32 miles. We shall now determine how many miles the truck covers to consume 1 gallon of gas.

Therefore, the results shows that the truck gets better gas mileage