Solve this 2 system equations 2x - y = 7 and 6x - 3y = 14

Answer:

Option A is correct.

Change in the y-values is 40 and the change in x-values is 1.

Step-by-step explanation:

Let x represents the time in minutes and y represents the temperature(in Fahrenheit).

Given two points on the line graph i.e,

[tex]A(x_1, y_1)= (2 , 150)[/tex]  and  [tex]B (x_2, y_2)= (3, 190)[/tex]

we have to find the change in the y-value and x-value on the graph:

Change in the x-values for the given points is;

[tex](x_2 - x_1)[/tex] = 3 - 2 = 1

Similarly,

Change in the y-values for the given points is;

[tex](y_2 - y_1)[/tex] = 190-150 =40.

Since, the slope or the rate of change of the given line graph is the ratio of the change in the y-value over the change in the x-value i.e, slope = 40.

Therefore, change in the y-values is 40 and the change in x-values is 1.

Answer:

Option A

Step-by-step explanation:

edge 2021

Solution

f(x) = -20[tex]x^{2}[/tex] +14x + 12 and g(x) = 5x - 6.

(f/g)(x) = [tex]\frac{f(x)}{g(y)}[/tex]

(f/g)(x) = [tex]\frac{-20x^{2}+14x +12 }{5x - 6}[/tex]

Step 1: Now we have to factorize the numerator.

f(x) = -20x^2 + 14x + 12

Factor out -2, we get

= -2 (10x^2 - 7x - 6)

Now we can factorize 10x^2 - 7x - 6                  

f(x) = -2(2x + 1) (5x - 6)

Step 2: Plug in the factors

(f/g)(x) = [tex]\frac{-2 (2x +1)(5x - 6)}{(5x - 6)}[/tex]

Step 3: Cancel out the common factor (5x - 6) from the numerator and the denominator, we get

(f/g)(x) = -2(2x +1) = -4x -2

Since -4x -2 is linear expression, the domain is all the real numbers.

Therefore, the answer is –4x – 2; all real numbers

Thank you :)

1 inch = 400 miles The scale gives the relationship between the measurements of the model and the measurements of the real object. Hope this helps.

It's a linear function. We need only two points to draw a graph.

We choose any values of x and calculate the value of y.

[tex]6x-2y=2\qquad|-6x\\\\-2y=-6x+2\qquad|:(-2)\\\\y=3x-1[/tex]

for x= 0 → y = 3(0) - 1 = 0 - 1 = -1 → (0, -1)

for x = 2 → y = 3(2) - 1 = 6 - 1 = 5 → (2, 5)

[tex]9x-3y=1\qquad|-9x\\\\-3y=-9x+1\qquad|:(-3)\\\\t=3x-\dfrac{1}{3}[/tex]

for x = 0 → y = 3(0) - 1/3 = 0 - 1/3 = -1/3 → (0, -1/3)

for x = 2 → y = 3(2) - 1/3 = 6 - 1/3 = 5 2/3 → (2, 5 2/3)

Answer:

1)Find all the like terms=3x3x/6>1/3x+2

2)Multiply both sides by six=9x>2x+12

3)Move the variables to the left side and change the sign=9x-2x>12

4)Find the like terms=7x>12

5)Divide by sides by seven=x>12/7

6)Your answer is x>12/7

I hope this helps! :)

28° and 152°

let the angle be x then supplementary angle = 3x + 68

Supplementary angles sum to 180° , hence

x + 3x + 68 = 180

4x + 68 = 180 ( subtract 68 from both sides )

4x = 112 ( divide both sides by 4 )

x = [tex]\frac{112}{4}[/tex] = 28

the angles are 28° and ( 3 × 28) + 68 = 84 + 68 = 152°

Multiply 36.50 by 8 and then multiply that answer by 5 to get your answer

$1,460 a week

36.50 by 8 multiply the answer by 5 to get your answer $1,460 a week

[tex]180:2=90\\90:2=45\\45:3=15\\15:3=5\\5:5=1\\\\180=\boxed{2}\cdot2\cdot\boxed{3}\cdot\boxed{3}\cdot5\\\\594:2=297\\297:3=99\\99:3=3\\33:3=11\\11:11=1\\\\594=\boxed{2}\cdot\boxed{3}\cdot\boxed{3}\cdot3\cdot11[/tex]

[tex]LCM(180,\ 594)=\boxed{2}\cdot\boxed{3}\cdot\boxed{3}\cdot2\cdot3\cdot5\cdot11=5940\\\\GCF(180,\ 594)=\boxed{2}\cdot\boxed{3}\cdot\boxed{3}=18[/tex]

So, the ratio between the LCM of 180 and 594 and the GCF of 180 and 594 is [tex]\(990:1\)[/tex].

To find the ratio between the least common multiple (LCM) and the greatest common factor (GCF) of two numbers, we need to calculate both the LCM and the GCF first.

1. Calculate the LCM of 180 and 594:

  The prime factorization of 180 is [tex]\(2^2 \times 3^2 \times 5\)[/tex].

  The prime factorization of 594 is [tex]\(2 \times 3^3 \times 11\)[/tex].

  The LCM is the product of the highest power of each prime factor:

  LCM [tex]\(= 2^2 \times 3^3 \times 5 \times 11 = 5940\)[/tex].

2. Calculate the GCF of 180 and 594:

  The common factors of 180 and 594 are [tex]\(2 \times 3 = 6\)[/tex]  

  So, GCF [tex]\(= 6\)[/tex].

Now, let's find the ratio between the LCM and the GCF:

[tex]\[ \text{Ratio} = \frac{\text{LCM}}{\text{GCF}} = \frac{5940}{6} = 990 \][/tex]

Answer:

Answer 4

Step-by-step explanation:

There are 8 sitcoms that can be recorded on the remaining tape.

To find out how many 30-minute sitcoms can be recorded on the remaining tape, we need to subtract the duration of the existing movie from the maximum capacity of the VHS tape. So, 360 minutes - 120 minutes = 240 minutes remaining. Since each sitcom is 30 minutes long, we can divide the remaining time by 30 to find out the number of sitcoms: 240 minutes ÷ 30 minutes = 8 sitcoms can be recorded on the remaining tape.

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Set up  a proportion:

$288/$48000 = x/$59000

Cross multiply

16992000 = 48000x

x = 354

The tax on the $59000 house was $354

To find the tax on a house assessed at $59,000 using the same tax rate, we can set up a proportion and solve for the unknown tax value.

To find the tax on a house assessed at $59,000 using the same tax rate, we can set up a proportion. The tax paid by Serena is $288 and the house assessed value is $48,000. Let's call the tax on the house assessed at $59,000 as 'x'. The proportion will be:

$$\frac{288}{48000} = \frac{x}{59000}$$

Cross multiplying, we get:

$$288 \times 59000 = 48000 \times x$$

Simplifying, we find:

$$x = \frac{288 \times 59000}{48000}$$

Using a calculator, we can evaluate this to find the tax on a house assessed at $59,000.

Learn more about Finding tax on a house here:

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Another -150 was added to her score

The answer is -150.................................

-425-(-275)=-150

118 book on each shelf 9440 divided by 80=118

Answer: There are 118 books on each shelf.

Step-by-step explanation:

Since we have given that

Number of non fiction books a library has = 9440

Number of shelves = 80

So, Number of books on each shelf would be

[tex]\dfrac{\text{Number of non fiction books}}{\text{Number of books on each shelf}}[/tex]

[tex]\dfrac{9440}{80}\\\\=118[/tex]

Hence, there are 118 books on each shelf.

In 4 days it will be 10 and 2/3

To find out how many inches elephant grass will grow in 4 days, multiply the daily growth rate by the number of days. The elephant grass will grow approximately 10 2/3 inches in 4 days.

To find out how many inches of elephant grass will grow in 4 days, we need to multiply the daily growth rate by the number of days. The daily growth rate is 2 2/3 inches. To convert this mixed number to an improper fraction, we multiply the whole number (2) by the denominator (3), which gives us 6. Adding the result to the numerator (2), we get 8. So the daily growth rate is 8/3 inches.

Next, we multiply the daily growth rate by the number of days: 8/3 * 4 = 32/3 inches. To simplify this fraction, we divide the numerator (32) by the denominator (3), which equals 10 with a remainder of 2. So the elephant grass will grow approximately 10 2/3 inches in 4 days.

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tan(6.5) * 4 = .9 or .88110880134

Answer:

h≈0.5 mi.  (to nearest tenth of a mile)

Step-by-step explanation:

tan6.5=h/4

h=4tan6.5 mi

h≈0.5 mi.  (to nearest tenth of a mile)

The number that, when raised to the 10th power and divided by the same number to the 7th power equals 27, is 3. This is resolved by simplifying the initial equation to realize that we are looking for the cube root of 27.

The question is asking for a number which, when raised to the 10th power and divided by the same number raised to the 7th power, equals 27. Let's denote the number as 'x'. The mathematical representation of this would be x10 / x7 = 27. Since x10 / x7 simplifies to x3, our equation becomes x3 = 27. Now if we solve this, the number 'x' equals the cube root of 27, which is 3.

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Answer:  One

Why?  In math a function is something that works and is paired with exactly one input value and one output value.

Opposite rays form at 1:38 because the minute hand and the hour hand go towards the opposite direction from the center of the clock.

In the context of an analog clock, opposite rays form when the hour and minute hands point in exactly opposite directions. This doesn't occur at either 1:35 or 1:38. The closest approximation of this situation on a clock is at 6 o'clock.

If we use the analogy of a typical analog clock face, opposite rays would form when the minute and hour hands are directly across from each other. For instance, at exactly 6 o'clock the minute and the hour hands on the clock are opposite rays, because they start from the same point (the center of the clock) and extend in opposite directions.

Looking at the times 1:35 and 1:38, neither time is an exact representation of opposite rays. At 1:35, the minute hand is pointing at 7 and the hour hand is somewhere between 1 and 2, which is not directly opposite. At 1:38, the situation is similar, but the minute hand is now pointing at around 8.

So the fact is, opposite rays do not form at either 1:35 or 1:38 in the analog clock representation. Opposite rays are formed when the hour hand is on the six and the minute hand is on the twelve.

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-140

Max has -140 points

To find the answer you divide the whole amount of 1456 by 7 since there is the 1 regular priced group and the remaining 6  discounted priced ticked. When you divide the 1456 by 7 it comes out to be 208 and to find the amount of the group of 6 you would multiply the 208 times the 6 and that will give you the amount of the dicount tickets sold. which is 1248.

Answer:

Is it the subset of 1, or other numbers.

Step-by-step explanation:

please be more specific with the question so I can actually answer please, I would try to help but I don't know the question. If you update it It would be more helpful.

To list all subsets of a set, use binary representation to generate all possible combinations by including or excluding each element.

A subset is a collection of elements from a set. To list all subsets of a set, we can use the concept of binary representation. Each element in the set can be either included or excluded in a subset. By representing each element as a binary digit, we can generate all possible subsets.

For example, if we have a set {1, 2, 3}, we can represent it as 000, 001, 010, 011, 100, 101, 110, 111, where each digit represents whether the element should be included or not. The subsets are: { }, {1}, {2}, {1, 2}, {3}, {1, 3}, {2, 3}, {1, 2, 3}.

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[tex]-\dfrac{r}{3} \leq6\qquad|\text{change the signs}\\\\\dfrac{r}{3}\geq-6\qquad|\cdot3\\\\r\geq-18[/tex]

13.

y - the amount from the sale

x - a number of tickets

y = 5x + 40

Domain: x ∈ {0, 1, 2, 3, 4, 5}

Range = {40, 45, 50, 55, 60, 65}

15.

y - the cost of renting a law firm

x - a number of hour

y = 100x + 300

Domain: x ∈ {1, 2, 3}

Range = {400, 500, 600}

Since, Jesse is building a spice rack.

The total length of wood = 90 centimeters

He cuts the board into three parts.

The length of the first part = 23.5 cm

So, remaining length of the board = [tex]90 - 23.5[/tex] = 66.5 cm

Now, he cuts the second part.

The length of the second part = 33.3 cm

So, now remaining part of the board = [tex]66.5 -33.3[/tex] = 33.2 cm

Now, he cuts the third part of the board.

The length of the third part = 19.45 cm

Now, the remaining part of the board = [tex]33.2-19.45[/tex] = 13.75 cm

So, the length of the original board after cutting the three parts = 13.75 cm

So, Option A is the correct answer.

Answer:

Step-by-step explanation:

So, the length of the original board after cutting the three parts = 13.75 cm

So, Option A is the correct answer.

For this case we have:

By definition, a mathematical function is the correspondence or relation f of the elements of a set A with the elements of a set B. A function fulfills the condition of existence (all the elements of A are related to the elements of B) and with the condition of uniqueness (Each element of A is related to a single element of B).

That said, we can conclude that the relationship shown in the table defines a function of the form [tex]y = f (x)[/tex]

By definition, the domain of a function is represented by the input elements of it.

Thus, the domain is given by Domain: (m, n, p, q)

Answer:

Yes, Domain: (m, n, p, q)

Option A

Answer: x = 120°

angles: 60°, 60°, 120°, 120°

Step-by-step explanation:

x + x + [tex]\frac{1}{2}x[/tex] + [tex]\frac{1}{2}x[/tex] = 360°

3x = 360°

x = 120°

[tex]\frac{1}{2}x = \frac{1}{2}(120)[/tex] = 60°