How do you find a unit rate?

Solve the example:

4/5 to 5/9

The correct answer is C. (x+4)(x+2)(x+5)=0

To find the factored form of the equation, we can use synthetic division to divide the polynomial by (x - 4). The quotient will give us the factored form of the equation: (x - 4)(x^2 + 7x - 2).

To find the factored form of the equation x^3 + 3x^2 -18x - 40 = 0 when four is a zero, we can use synthetic division. Synthetic division can be used to divide the polynomial by (x - 4). The quotient will give us the factored form of the equation.

Set up the synthetic division:

  4 | 1 3 -18 -40

Perform the synthetic division:

   •                              4                    

       ------------------------------------

     1     7    -2

Step 3:

Write the quotient as the factored form:

x^3 + 3x^2 -18x - 40 = (x - 4)(x^2 + 7x - 2)

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Your equation is just to multiply 480 by 3/4.

Easy way to do these quick.

480 (3/4) is the same as (480 * 3) / 4

480 / 4 = 120

By simplifying, you are left with just 120 * 3 in the numerator

120 * 3 = 360

There are 360 people on the plane.

If you need to check your answer:

360 / 480

Take away the zeros at the end by dividing both by 10

36 / 48

Divide both by 6

6 / 8

Now divide by 2

3 / 4

We are given

A cell phone company charges $45 a month for phone service and

$0.25 for each text message

(a)

Let's assume

total number of messages sent on each month is x

total monthly bill is $ y

so, we can set up  equation

[tex]y=45+0.25x[/tex]

now, we can solve for x

Subtract both sides by 45

[tex]y-45=45+0.25x-45[/tex]

[tex]y-45=0.25x[/tex]

[tex]x=\frac{y-45}{0.25}[/tex]

[tex]x=4y-180[/tex]...........Answer

(b)

we can plug y=75

and then we can solve for x

[tex]x=4*75-180[/tex]

[tex]x=300-180[/tex]

[tex]x=120[/tex]

so, total number messages sent were 120...........Answer

The answer is b. k=64 t=52.

For this case we have an expression of the form:

[tex]a + b (x-c)\\[/tex]

We then define the following variables:

a: represents the base salary

b: is the percentage of sales commissions

c: It is a cutoff point to obtain or not commission.

If x> c: you get commission

If x ≤ c: you do not get commission

Thus, x represents the amount of sales made above $ 300.

Answer:

option 1

To find the total fraction of food eaten by George and Silvia, convert each of their portions to have a common denominator and then add the fractions together, resulting in them eating 13/15 of the container.

The question asks us to find the total fraction of the container of Chinese food that George and Silvia ate together. George ate 2/3 of the container, while Silvia ate 1/5 of it. To find the total amount they ate, you need to add these two fractions together.

Calculating the sum of the fractions:

First, find a common denominator, which in this case is 15 (because 3 and 5 both divide evenly into 15).

Convert each fraction to an equivalent fraction with a denominator of 15:

George's portion becomes (2/3) x (5/5) = 10/15

Silvia's portion becomes (1/5) x (3/3) = 3/15

Add the two fractions: 10/15 + 3/15 = 13/15

Therefore, together, George and Silvia ate 13/15 of the container of Chinese food.

Here is your inequality:

[tex]z + \frac{1}{8} > \frac{1}{5}[/tex]

You're looking for z. To do that, you need to remove everything on the same side of z. The only thing with z is positive [tex]\frac{1}{8}[/tex] . To remove it, you need to do the opposite of it, which is negative [tex]\frac{1}{8}[/tex], which is the same as subtracting [tex]\frac{1}{8}[/tex]. Subtract:

[tex]z+\frac{1}{8} - \frac{1}{8} > \frac{1}{5} - \frac{1}{8} \\ \\z = \frac{1}{5} - \frac{1}{8}[/tex]

Subtract [tex]\frac{1}{8}[/tex] from [tex]\frac{1}{5}[/tex]. Since they have a different denominator(bottom number in a fraction), change them into fractions with common denominator. To find a common denominator, list the multiples of both numbers and see what is common.

[tex]5 - 5, 10, 15, 20, 25, 30, 35, 40, 45 \\8- 8, 16, 24, 32, 40, 48[/tex]

In the numbers listed above ↑, the only common multiples is 40. That means you need to change both fractions so that they both have a denominator of 40.

[tex]\frac{1 \times 8}{5 \times 8} = \frac{8}{40}[/tex]

[tex]\frac{1 \times 5}{8 \times 5} = \frac{5}{40}[/tex]

Here is your new equation:

[tex]z> \frac{8}{40} - \frac{5}{40}[/tex]

Subtract:

[tex]\frac{8}{40} - \frac{5}{40} = \frac{3}{40} \\\\z> \frac{3}{40}[/tex]

Your answer is z > [tex]\bf \frac{3}{40}[/tex]

If you have any questions, feel free to ask in the comments! :)

To solve the inequality z + 1/8 > 1/5, subtract 1/8 from both sides to isolate z. The solution to the inequality is z > 3/40. Graphically, represent the solution set by shading all values greater than 3/40 on a number line.

To solve the inequality z + 1/8 > 1/5, we need to isolate z. First, we subtract 1/8 from both sides of the inequality: z + 1/8 - 1/8 > 1/5 - 1/8. This simplifies to z > 3/40. Therefore, the correct solution for the inequality is z > 3/40.

To graph this inequality on a number line, we draw an open circle at 3/40 and shade all the values greater than 3/40 to the right. This represents the solution set of the inequality.

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Answer:

Line AB.

Step-by-step explanation:

Since we know that a line is a set of continuous points and it extends in both directions infinitely.

We can name a line either by a single small case letter or by labeling endpoints.

We can see that point A and point B lies on line m. We can name line m as line AB.

Therefore, another name for line m is line AB.

Answer:

X multiplied by 25 subtract 3

(Sorry this is put in words)

Step-by-step explanation:

ANSWER TO PART A

The mapping for the reflection in the line [tex]y=x[/tex], is given by

[tex](x,y)\rightarrow (y,x)[/tex].

That is the coordinates swap position .

The only way we can construct a function [tex]f(x)[/tex], such that;

[tex](x, f(x))\rightarrow (f(x),x)[/tex] are equal is when

[tex]f(x)=x[/tex].

So that when [tex]x=a, f(a)=a[/tex] .

The mapping then becomes

[tex](a,a)\rightarrow (a,a)[/tex].

Therefore the function, [tex]f(x)=x[/tex] is the function whose reflection in the line

[tex]y=x[/tex] is itself.

ANSWER TO PART B

The function is symmetrical with respect to the origin. That is to say the function is an odd function.

A function is symmetric with respect to the origin, if it satisfies the condition,

[tex]f(-x)=-f(x)[/tex]

For instance,

[tex]f(a)=a[/tex]

[tex]f(-a)=-a[/tex]

Since

[tex]f(-a)=-a=-f(a)[/tex]

We say the function is symmetric with respect to the origin.

Final answer:

The total number of different options for the car model, considering all combinations of features such as color, transmission type, four-wheel drive, air conditioning, and number of speakers, is 240.

Explanation:

To calculate the total number of different options available for a car model, we need to consider all the possible combinations of features. In the given scenario, there are 10 choices for the color, 2 choices for the transmission (automatic or not), 2 choices for four-wheel drive (with or without), 2 choices for air conditioning (with or without), and 3 choices for the number of radio CD speakers (2, 3, or 4).

To find the total number of different combinations, we multiply the number of options for each feature:

Colors: 10 options

Transmission: 2 options (with or without automatic)

Four-wheel drive: 2 options (with or without)

Air conditioning: 2 options (with or without)

Radio CD speakers: 3 options (2, 3, or 4 speakers)

By multiplying these together, we get the total number of configurations:

Total options = 10 (colors) × 2 (transmission) × 2 (four-wheel drive) × 2 (air conditioning) × 3 (speakers)

Total options = 240 different configurations are available for this model of the car.

Remark

They all have (0,0) as a point on the proportional relationship, so the general equation for this is

y = kx

Now all we have to do is find k

Method

If any two points (besides (0,0) ) give the same k as an answer then that is the proportional relationship.

Solution

(1/4) ÷(1/3)     Change to a decimal

0.25 ÷ 0.3333333 = 0.75

(4/4) ÷ (2/3) = 1 ÷ 0.666666 = 1.5 Rounded

A is not the answer

B

1 ÷ 2/7 = 1 ÷ 0.28571 = 3.5

2 ÷ 5/7 = 2÷ 7142857 = 2.8 Not the same

B is not the answer

C

(2/5) ÷  3 = 0.4 ÷ 3 = 0.13333333

(1/5) ÷ (3/2) = 0.2 / (1.5) = 0.13333333

Answer C

Comment

The answer is C or y = 0.133333 x

Notice that whenever possible, change these into decimals. Decminals are easier to handle.

Answer: A) It will have the same measure as the original angle

Step-by-step explanation:

When reflected, the angle will be the same. Essentially, reflecting is just like using a mirror. When you reflect something, or look in the mirror, it is the same only flipped. For this problem here, that would be the case. You are simply flipping the angle over the y-axis, therefore everything stays the same except the direction it faces.

Answer:

3/5 and 60%

Step-by-step explanation:

x = 2 is the answer.

Answer:  The required value of x in the given equation is 2.

Step-by-step explanation:  We are given to find the value of x in the following equation :

[tex]2.5(6x-4)=10+4(1.5+0.5x)~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To find the value of x, we need to solve the given equation (i).

The solution of equation (i) is as follows :

[tex]2.5(6x-4)=10+4(1.5+0.5x)\\\\\Rightarrow 15x-10=10+6+2x\\\\\Rightarrow 15x-10=16+2x\\\\\Rightarrow 15x-2x=16+10\\\\\Rightarrow 13x=26\\\\\Rightarrow x=\dfrac{26}{13}\\\\\Rightarrow x=2.[/tex]

Thus, the required value of x in the given equation is 2.

do you mean how do you write it? If so, 2/3x-12

Multiply the cost of the game by the sales tax:

7% tax = 0.07

50 x 0.07 = 3.5

The tax would be $3.50

Hey there!!

Given :

The total cost for 2 pairs of pants and 5 shirts is $61.

The total cost for 3 pairs of paints and 4 shirts is $67.

Let's take the cost for each pair of paints as 'p' and the cost for each shirt as 's'.

Now, let's get these into an equation.

Peter's equation :

... 2p + 5s = 61

Jessica's equation :

...3p + 4s = 67

......................................................................................................

2p + 5s = 61 --- (1)

3p + 4s = 67 --- (2)

Multiply the first equation with 3 and the second equation with 2.

6p + 15s = 183

6p + 8s = 134

Subtract both the equations -

... 7s = 49

Divide both sides with 7.

... s = 7

Hence, the cost of each shirt is $7.

Hope my answer helps!!

because of the shape it is molded as, some balloons are made to be hearts so when they are blown up they are shaped like hearts

2 3/5 - 1 1/3 = 2 6/15 - 1 5/15 = 1 1/5

The amount of snowfall in January was 2 and 3/5 feet while in February it was 1 and 1/3 feet. Upon converting these mixed numbers to improper fractions and subtracting, we find that January had 1 and 7/15 feet more snowfall than February.

The student needs to determine how much more snow fell in January compared to February. The amount of snowfall in January was 2 and 3/5 feet and the amount of snowfall in February was 1 and 1/3 feet.

To do that, first, we need to subtract the snowfall of February from that of January. Before doing so, we should convert the mixed numbers to improper fractions. 2 and 3/5 feet can be converted to 13/5 feet. 1 and 1/3 feet can be converted to 4/3 feet.

So, we subtract 4/3 feet from 13/5 feet: (13/5) - (4/3). For subtacting fractions, we need the denominators to match. Once we equalize the denominators and subtract, we get 1 and 7/15 feet. Therefore, January had 1 and 7/15 feet more snowfall than February.

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The answer is 29.

The equation is 2x - 6 = 52

Reverse the operation;

52 x 2 = 104

104 - 6 = 98

So, there 98 alternative schools in the county.

If you are looking to write an inequality equation that models this situation, then the answer would be: [tex]5+2x\leq 27[/tex].  The "at most" signals to use the less than or equal to sign.

The number is 11 if the sum of 5 and twice a number is at most 27 the answer is 11.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The question is incomplete.

The complete question is:

The sum of 5 and the twice a number is at most 27.

What is the number?

Let the number is x

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

We can frame a linear equation in one variable.

2x + 5 = 27

2x = 27 - 5

2x = 22

x = 22/2

x = 11

Thus, the number is 11 if the sum of 5 and twice a number is at most 27 the answer is 11.

Learn more about the linear equation here:

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For this case we have the following rule of three:

288 cars -------------------> 6days

x cars -------------------> 1dia

Resolving you have that the value of the variable x is given by:

[tex]x =\frac{(1)(288)}{6}\\\\x = 48\\[/tex]

Thus, the constant of proportion per day is 48 cars.

Answer:

Option B

The square root of a number can be estimated by locating which two perfect squares it falls between. This provides the two consecutive integers between which the square root lies. For example, the square root of 12 falls between the perfect squares of 9 (3^2) and 16 (4^2), thus it lies between the integers 3 and 4.

To determine between which two integers a square root lies without using a calculator, you can use the method of perfect squares. Perfect squares are numbers that result from squaring integers. For instance, the perfect squares for the integers 1, 2, 3, 4, and 5 are 1, 4, 9, 16, and 25, respectively.

Let's say you wish to locate the square root of 12. You can list the perfect squares until you find two such that 12 falls between them. In this case, we can see that 12 is between the perfect squares 9 (3^2) and 16 (4^2). Therefore, the square root of 12 is between the integers 3 and 4.

This is a straightforward method for roughly determining the value of a square root without using a calculator. Exact values can unfortunately only be determined with the help of a calculator or mathematical tools beyond middle school level.

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The given side dishes are rice potatoes and vegetables = 2

The given main dishes are chicken, fish and beef = 3

As there are 2 side dishes. With rice potatoes we can order any of the three main dish, so it is 3 combination. Similarly with vegetables also, we can order any of the three main dish, so it is 3 combination.

So, combined combination is 3+3 = 6

Hence, the correct answer is option A.

Answer:9 combinations

Step-by-step explanation:

3+3+3=9

They both flow into the Gulf of Mexico

Gulf of Mexico is where they both flow into