solve the system of equations using the substitution method. state the solution as an ordered pair, (x,y). x+y=2 y=5x-4

Question 1

[tex](f \circ g)(-2)=f(-2) \cdot g(-2)=10 \cdot 3=\boxed{30}[/tex]

Question 2

[tex](g \circ h)(1)=g(1) \cdot h(1)=2(1^2 -9)=\boxed{-16}[/tex]

Question 3

[tex](g/f)(0)=\frac{g(0)}{f(0)}=\frac{0^2 -9}{6}=\boxed{-3/2}[/tex]

Question 4

[tex](h/f)(-3)=\frac{h(-3)}{f(-3)}=\frac{3^2 -9}{12}=\boxed{0}[/tex]

Answer:

PLEASE ADD A DANG PICTURE

Step-by-step explanation:

Answer:

is 2(x minus 1)(5x + 1)

Step-by-step explanation:

Answer:

B) 10

Step-by-step explanation:

The triangles are congruent by HL. Thus, by CPCTC, [tex]x=10[/tex].

The earnings for both Cynthia and Javier are same for x hours.

What is commission?

When an employee completes a task, typically selling a certain volume of goods or services, they are compensated financially. Sales commissions are occasionally used by employers as incentives to boost employee productivity. It is possible to receive a commission in place of or in addition to a salary.

Given:

Cynthia earns $680 in commissions and is paid $10.25 per hour.

Javier earns $410 in commissions and is paid $12.50 per hour.

So, the equation is

10.25x + 680 = 12.5x + 410

To simplify this equation for x.

10.25x+ 680 =12.5x +410

    680 ‐ 410 = 12.5x ‐ 10.25x

             270 = 2.25x

                  x = 270/2.25

                  x = 120

If we plug x = 120 in both the values 10.25x + 680 and 12.5x + 410 then we will get the same values.

Hence, the earnings for both Cynthia and Javier are same for x hours.

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Last option: The height and weight distributions, respectively, show positive and negative skews.

Graphs are used to represent information in bar charts. To depict values, it makes use of bars that reach various heights. Vertical bars, horizontal bars, clustered bars (multiple bars that compare values within a category), and stacked bars are all possible options for bar charts.

There isn't a lot of data, but it shows that the weights have a negative skew and the heights have a positive skew, with the long tails pointing in opposite directions.

[tex]\frac{change}{strating point } X 100%[/tex]

2.5 millions of books were sold in 1991.

Millions of books sold in 1992 equaled 3.4.

Change = 0.9 (in millions).

[tex]\frac{0.9}{2.5} X 100 = 36[/tex]%

The height and weight distributions, respectively, show positive and negative skews.

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The equation in the form of y=mx+b will be y= -3/4x+2

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.

It is given that the inequality is y< -3/4x+2,

We have to write the inequality in the form of y=mx+b

A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Thus, the equation in the form of y=mx+b will be y= -3/4x+2

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Answer:

Yes, they are parallel.

Step-by-step explanation:

61 + 119 = 180

One line is 180 degrees.

Answer:

h(6) = 180

Step-by-step explanation:

h(a)=5a²

for a=6

h(6) = 5(6)²

h(6) = 5*36

h(6) = 180

Answer: 2 2/3 or 8/3

Step-by-step explanation:

3 5/6 = 23/6

-1 1/6 = -7/6

23/6-7/6

16/6

simplify

8/3

Answer:

2 [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

3 [tex]\frac{5}{6}[/tex] can be written [tex]\frac{6}{6}[/tex] + [tex]\frac{6}{6}[/tex] + [tex]\frac{6}{6}[/tex] + [tex]\frac{5}{6}[/tex]  = [tex]\frac{23}{6}[/tex]   ( [tex]\frac{6}{6}[/tex] is the same one)

1 [tex]\frac{1}{6}[/tex] can be written [tex]\frac{6}{6}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{7}{6}[/tex]

Adding a negative number is like subtracting a positive number.

[tex]\frac{23}{6}[/tex] -  [tex]\frac{7 }{6}[/tex]  =   [tex]\frac{16}{6}[/tex]  6 goes into 16 2 times with 4 left over

2 [tex]\frac{4}{6}[/tex]  Divide the top and bottom by 2 to get

2 [tex]\frac{2}{3}[/tex]

The quadratic equation that models the company's costs is y = 25(x - 16)² + 1000

From the question, we have the following parameters that can be used in our computation:

Minimum cost of $1000 at 16 hours

Operating cost of $2600 at 8 hours

A quadratic equation is represented as

y = a(x - h)² + k

The minimum point is the vertex

So, we have

(h, k) = (16, 1000)

Substitute (h, k) = (16, 1000) in y = a(x - h)² + k

y = a(x - 16)² + 1000

The cost of $2600 at 8 hours means

(x, y)  = (8, 2600)

So, we have

2600 = a(8 - 16)² + 1000

Evaluate the difference

1600 = a(8 - 16)²

So, we have

64a = 1600

Divide by 64

a = 25

Substitute a = 25 in y = a(x - 16)² + 1000

y = 25(x - 16)² + 1000

Hence, the equation is y = 25(x - 16)² + 1000

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For the given statement about hundredth digit of the given decimal z the following statement is true:

Option E. statement (1) and (2) together are not sufficient.

As given in the question,

Let us consider decimal z is represented by k.lmn

Here hundredth digit of z is equal to m

Now,

(1) The tenths digit of 100z is 2.

100z

= 100(k.lmn)

=klm.n

This implies n = 2

(2) The units digit of 1,000z is 2.

1,000z

= 1,000(k.lmn)

= klmn

This implies n =2

From both the statements we are getting the value of n which is not sufficient to get the value of required 'm'.

Therefore, Option E is the correct answer which shows both the statements are not sufficient to get the value required hundredth digit of decimal z.

The complete question is:

What is the hundredths digit of the decimal z ? (1) the tenths digit of 100z is 2. (2) the units digit of 1,000z is 2.

A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

C. Both statements together are sufficient, but neither statement alone is sufficient.

D. Each statement alone is sufficient.

E. Statements (1) and (2) together are not sufficient.

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Answer: y = 0x + 8

Step-by-step explanation:

The slope-intercept form is y=mx + b

The slope is 0, and y-intercept is at (0,8)

So our equation is

y = 0x + 8

The linear equation of the following graph in slope-intercept form will be; y=1/2x

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

The slope of the line is calculated as follows:

m = Δy/Δx

To find the linear equation of the following graph in slope-intercept form.

Therefore, the slope of the line is;

m = Δy/Δx

m = 1/2

When we simplify it, then we get the equation as;

y=1/2x

Hence, The linear equation of the following graph in slope-intercept form will be; y=1/2x

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Use the picture equation

Answer:31

Step-by-step explanation: solve it

Answer:

should be the first one, x > 360

Step-by-step explanation:

im sorry if its wrong :*(

The situation could be modeled by a linear function is

(2) A gym charges a $50 initial fee and then $30 monthly.

A linear function in mathematics is one that has either one or two variables and no exponents.

2) Let y be the total amount charged by the gym to a person for x months.

as the initial amount for every person is $30.

The gym charges [tex]50+30x[/tex] $ after x months.

Hence this is a linear equation.

The remaining situations cannot be expressed as a linear equation because they include percentages in them.

Every situation that has a percentage is an exponential function.

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Answer:

2/9 = approximately 0.22.

Step-by-step explanation:

There are a total of 12 possible outcomes when the spinner is spun once, so the probability of getting a result that is not green is 8/12, or 2/3. Similarly, the probability of getting green on the second spin is 4/12, or 1/3.

To find the probability of getting a result that is not green on the first spin and green on the second spin, you can multiply the probabilities of each individual event. Therefore, the probability of getting not green then green is (2/3) * (1/3) = 2/9 = approximately 0.22.

Alternatively, you could also use the principle of complementary probabilities to calculate the probability of getting not green on the first spin and green on the second spin. The probability of getting not green on the first spin is 1 - (4/12) = 8/12 = 2/3, and the probability of getting green on the second spin is still 4/12 = 1/3. Multiplying these probabilities gives a result of (2/3) * (1/3) = 2/9 = approximately 0.22.

Answer:

D

Step-by-step explanation:

area of triangle  = 1/2*B*H

Assuming its one leg we write

24 = 1/2*6*h

h= 8

With this info we can use Pythagoras Theorum

[tex]a^{2} = b^{2} + c^{2}[/tex]

[tex]x^{2} = 8^{2} + 6^{2}[/tex]

[tex]x^{2} = 100[/tex]

[tex]\sqrt{100}[/tex]

[tex]x = 10[/tex]

Answer: 6,3

Step-by-step explanation:

Answer:

6,3

Step-by-step explanation:

The probability that the next report will weigh less than 45 grams = 0.106

In this question, we have been given the weight of written reports produced in a certain department has a normal distribution with mean 60 grams and standard deviation 12 grams.

We need to find the probability that the next report will weigh less than 45 grams.

We have mean= 60 grams

Standard Deviation = 12 grams

First we convert 45 to z score.

45 converted to z score for given mean and standard deviation will be:

z = (45 - 60)/12

z = -1.25

So, from standard normal table a P-value:

P(x<45) = 0.10565

Therefore, the probability would be 0.10565

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Answer:

36

Step-by-step explanation:

4/9 x = 16

9/4 * 4/9 x = 16 * 9/4

x = 36

The thing that 47.3 mean in the context of the problem is D. If no rain fell, 47.3 bushels of wheat would be produced.

It is important to note that an equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this situation, Margot is studying the yield of bushels of wheat in comparison to the amount of rainfall, in inches, that occurs. She finds the linear regression equation to be y = 47.3 +0.78x.

It should be noted that when no rain fell, 47.3 bushels of wheat would be produced. This is the constant value.

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Answer: 6 divided by 2/3

Step-by-step explanation:

The division equation which represents the situation is 6 ÷ 2/3 = 9.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

Division equation is the equation involving the operation of division.

The model shows there are 9 pieces that are each 2/3 feet long.

We can calculate the total length of the pieces using the multiplication equation.

9 × 2/3 = 6

Total length = 6 feet

Length of each piece = 2/3 feet

Number of pieces can be found using the division equation,

6 ÷ 2/3 = 9

Hence the division equation for the given situation is 6 ÷ 2/3 = 9.

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Answer:

Using substitution method for to solve, X = -4 and Y = 6

Step-by-step explanation:

1)  x+2y = 8

2) x+y = 2

solve 2)

x = 2-y

Then replaced it in 1)

(2-y) + 2y = 8

2 + y = 8

y = 6

then

x = 2 - 6

X = -4