Simplify the complex rational expression. Type your answer in simplest form, multiplying any factors you may have in the numerator or denominator. When typing your answers, type your terms with variables in descending power and in alphabetical order without any spaces between your characters. If needed use the carrot key ^ (press shift and 6) to indicate an exponent.\frac{\left(\frac{2c}{c+2}+\frac{c-1}{c+1}\right)}{\frac{\left(2c+1\right)}{c+1}}

Answer: 9

Step-by-step explanation:

the value of -10 is 10 and the value of 19 is 19 s0 19 - 10

The width of the living room on the new blueprint is 15 feet.

Based on the information, the scale of the original blueprint will be:

= 2 in / 5 ft

The width of the original blueprint is 6 inches, the actual width of the living room will be:

2/5 = 6/x

where x = width of living room

Cross multiply

x = 5 × 6 / 2

x = 15 feet.

The width is 15 feet.

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Answer:

1/9

Step-by-step explanation:

-1/9  + 2/9

Since the denominator is the same, we can add the numerators

(-1+2)/9 = 1/9

Answer:

185 dimes and 73 quarters

Step-by-step explanation:

q + d = 258

25(q) + 10(d) = 3675

The ladder will not reach a window that is 21.5 feet above the ground if the length of the ladder is 25 feet.

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

From the data:

The right angle triangle can be drawn:

From the diagram:

Applying Pythagoras' theorem:

BC² = AB² +  AC²

25² = 15² +  AC²

After solving

AC = 20 feet

AC < 21.5 feet

Thus, the ladder will not reach a window that is 21.5 feet above the ground if the length of the ladder is 25 feet.

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Answer:

No, because the ladder will only reach 20 feet high

Step-by-step explanation:

I go it right on my quiz :]

If we solve for the value of x we find that x is any value which is greater than -36/11.

What are inequalities ?

When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.

It is given in question that a required number divided by 3 decreased by 7 is less than 4 times the number increased by 5.

Let's assume the number be x.

So , x divided by 3 is x / 3 and if we subtract it by 7 , we get :

x/ 3 - 7  

Also , this value is less than 4 times the number added with 5.

i.e.,

4x + 5

So , the inequality can be written as :

[tex]\frac{x}{3}[/tex] - 7 < 4x + 5

or

x - 21  <  12x + 15

-36 < 11x

or

-36 /11 < x

or

x > -36/11

or

x is greater than -36/11.

Therefore , if we solve for the value of x we find that x is any value which is greater than -36/11.

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For the given opens down parabola, ordered pair of the vertex (h, k) = (1, -4)  , the maximum value of the parabola is y = -4.

As given,

Graph of parabola shows it open down parabola.

Vertex is the highest point on the graph of parabola.

it is known as the maximum value.

Let (h, k) be the vertex of the given parabola.

From the graph value of the vertex is equal to :

(h ,k)=(1, -4)

h represents the x-coordinate.

k represents the y-coordinate.

y-coordinate represents the maximum value of the parabola.

y =-4 is the maximum value.

Therefore, for the given opens down parabola, ordered pair of the vertex (h, k) = (1, -4)  , the maximum value of the parabola is y = -4.

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The jumbo cans of frosting would she need to frost 280 cupcakes is 8 cans.

Addition simply means the sum of the numbers that are given.

In this case, Bette used 3 jumbo cans of frosting to frost 105 cupcakes for the cupcake challenge at her school and 5 jumbo cans of frosting to frost an additional 175 cupcakes. This implies that the total cupcakes will be:

= 105 + 175 = 280

In this case, the cans used will be the addition of the cans above. This will be:

= 3 + 5

= 8 cans

This shows the concept of addition.

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Answer:

- 164/4+50y/3+ify=0

Step-by-step explanation:

hope it helps

The description of the error in finding the slope and y-intercept, of the graph of the equation is given by the option:

To be in slope-intercept form, the equation needs to be solved for y, not x

The equation in slope-intercept form is,  [tex]\displaystyle{y = -\frac{1}{4} \cdot x[/tex]

The slope-intercept form of the equation of a straight line is an equation of the form, y = m·x + c

The slope-intercept form of a straight-line equation is of the form, y = m·x + c, where:

m = The slope of the equation

c = The y-intercept

The given equation is x = -4·y

The given equation is not in the slope and intercept form given that the subject of the equation is x, rather than y

The error is therefore, in making x, the subject of the equation rather than y, that is the equation needs to be solved for y, not x

The correction of the error is performed as follows:

x = -4·y

-4·y = x

[tex]\displaystyle{y = \frac{x}{-4} = -\frac{1}{4} \cdot x[/tex]

Which gives: [tex]\displaystyle{y = -\frac{1}{4} \cdot x[/tex]

The slope of the graph of the equation is [tex]-\frac{1}{4}[/tex], the y-intercept, c, is 0

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Here is the completed table:

x           /AM/

14          16

3            13

11           33

10           40

/AM/ + /AC/ = /AC/

(x + 2) + (3x - 9) = 6x - 21

4x - 7 = 6x - 21

6x - 4x = 21 - 7

2x = 28

x = 28 / 2

x = 14

/AM/ = 14 + 2 = 16

/AM/ + /MW/ = /AW/

(2X + 7) + (3x - 4) = 18

5x + 3 = 18

5x = 18 - 3

5x = 15

x = 15/5

x = 3

/AM/ = (2 X 3) + 7 =

= 6 + 7 = 13

x + x + x + x = 44

4x = 44

x = 44 / 4

x = 11

/AM/ = 11 x 3 = 33

/AG/ + /GM/ = /AM/

2(x + 10) = 3x + 10

2x + 20 = 3x + 10

20 - 10 = 3x - 2x

10 = x

/AM/ = (3 x 10) + 10

= 30 + 10

= 40

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Answer:

I need more information to solve this.

Step-by-step explanation:

Answers ↓

angle 1 → 90°

angle 2→ 44°

angle 3 → 90°

angle 4 → 46°

I hope this helps u

The customer can select the meal in 2016 ways.

There are four different methods to choose an appetizer, eight different ways to choose a salad, nine different ways to choose an entree, and seven different ways to choose a dessert. Customers can choose a meal in the range of 4*8*7*9 if, according to the multiplication rule, a meal includes an appetizer, a salad, an entree, and a dessert.

x = 4 * 8 * 7 * 9 =  2016 ways.

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Answer:

The average speed of the puck is 110 ft per second.

Step-by-step explanation:

Using the d = st formula to find distance when given the speed and time, you can rewrite it to be s = d/t.

When you substitute the values in, you get s = 66/0.6, which is 110.

Hope this helps.

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The number of ounces of fruit and number of ounces of nuts that will meet the requirement with the least amount of calories is

The least number of calorie is 250 calories

given data

1. each ounce of fruit will supply zero units of protein, 3 units of carbohydrates, 2 units of fat and will contain 20 calories

2. each ounce of nuts will supply 3 units of protein, 2 units of carbohydrates and 4 units of fat, and will contain 50 calories

3. Every package must provide at least 9 units of protein, at least 18 carbohydrates, and no more than 22 units of fat

To get at least 9 units of protein, we take at least 3 ounces of nut

3 ounces of nut will give 3 times each unit, and they are as follows

Another restriction is no more than 22 units of fat and we have 12 already remaining 10 units of fat

fruits has lesser calories hence we use it to get the required fats

10 units of fat ÷  2 units of fat in fruit = 5

5 ounces of fruit will give 5 times each unit, and they are as follows

Combining 3 ounces of nut and 5 ounces of fruit will give

Above maintains the requirements stated in the question with the minimal calorie

the required calorie  is 250

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Answer:  ad bc is the answer

Step-by-step explanation:

Answer:

a) C(m) = flat rate + rate per mile

b) $42

Step-by-step explanation:

a) C(m) = flat rate + rate per mile*No. of miles => 30+.15x

b) 30+.15*80 = 42

Answer:

KML and LMK

Step-by-step explanation:

To calculate the surface area of a sphere, you have to use the following formula:

Where "r" is the radius of the sphere.

We know that the diameter of the sphere is d = 60 inches and that the radius is half the diameter, then the radius can be determined as follows:

Once the radius is calculated, you can determine the surface area of the sphere:

The surface area of the sphere is 3600π in², expressed as a decimal value, the surface area is equal to 11309.73 in²

The next step after drawing an arc with the compass from the first point of the construction will be, to pick a point on the arc that will be the second endpoint of the new segment. (a)

To copy a line we have to follow a few steps of the procedure.

The steps are;

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Step-by-step explanation:

+6,+10,+14,+18

+4+4+4

therefore quadratic 4/period function=2

[tex]y = 2{x}^{2} + bx + c[/tex]

y=2 x=1

[tex] 0 = b + c[/tex]

y=8 x=2

8=8+2b+c

0=2b+c

y=18 x=3

0=3b+c

therefore

the equation is 2x^2=y

Answer:

blank = - 3

Step-by-step explanation:

let x represent the blanks , then

[tex]\frac{2}{3}[/tex] ([tex]\frac{9}{5}[/tex] + x) = [tex]\frac{2}{5}[/tex] x + [tex]\frac{2}{5}[/tex]

multiply through by 15 ( the LCM of 3 and 5 ) to clear the fractions

10([tex]\frac{9}{5}[/tex] + x) = 6x + 6 ← distribute parenthesis on left side

[tex]\frac{90}{5}[/tex] + 10x = 6x + 6

18 + 10x = 6x + 6 ( subtract 6x from both sides )

18 + 4x = 6 ( subtract 18 from both sides )

4x = - 12 ( divide both sides by 4 )

x = - 3

A linear equation is a mathematical form of a line segment the point (6,5) satisfies the equation y = 2/3x + 1 so it is the solution of the equation but (9,8) is not the solution.

A straight line on the coordinate plane is represented by a linear function.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

As per the given linear equation, y = 2/3x + 1

To be a point of its solution the point must satisfy the given equation.

Substitute (6,5)

5 = (2/3)6 + 1

5 = 2(2) + 1 = 5

Therefore, the (6,5) is the solution of the equation.

Substitute,(9,8)

(2/3)9 + 1 = 7

8 ≠ 7

So,(9,8) is not the solution of the equation.

Hence "A linear equation is a mathematical form of a line segment the point (6,5) satisfies the equation y = 2/3x + 1 so it is the solution of the equation but (9,8) is not the solution".

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If p and q vary inversely and p is 5 when q is 4, the value of q when p is equal to 10 is 2.

An inverse variation can be defined as a type of proportionality which shows the relationship that exist between two (2) distinct variables, wherein, as the value of one variable increases, the value of the other variable decreases and vice-versa.

Mathematically, an inverse variation can be modeled or represented by this expression:

p ∝ 1/q

p = k/q

Where:

Next, we would determine the constant of proportionality (k) by substituting the value of the given variable as follows:

k = pq

k = 5(4)

k = 20

Now, we can determine the value of q:

q = k/p

q = 20/10

q = 2.

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Answer:

To convert the degrees to radians

we know that,

Radian is equivalent to the angle subtended at the centre of a circle by an arc equal in length to the radius.

we get that,

That is,

we get that,

Answer is: 0.8

Answer:

63

Step-by-step explanation:

12:36

36/12=3

21(3)=63