Write an equation of a line in slope intercept form going through the points (1,6) and (3,0)

The following equation represents the function g in function notation,

g(x) = 3x - 14 [Option (A)]

Definition of a Function

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. A function, in general, represents the idealized relationship between two changing quantities.

Given equation is,

y -3x = -14

⇒ y = -14 + 3x

or y = 3x - 14

Here, y stands for or represents the function g(x) which is a function of independent variable x.

Thus, the correct function notation is as follows,

g(x) = 3x - 14

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Based on the test by result, Alex did better in the test by scoring 66.67%

Percentage scored by Alex = 40/60 × 100

= 0.66666666666666 × 100

= 66.6666666666666

= 66.67%

Therefore, Alex did better in the test

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Answer: [tex]x=11, y=9[/tex]

Step-by-step explanation:

Corresponding sides of similar figures are proportional, so:

[tex]\frac{x-2}{6}=\frac{15}{10}\\\\\frac{x-2}{6}=\frac{3}{2}\\\\x-2=9\\\\x=11[/tex]

[tex]\frac{y+3}{8}=\frac{15}{10}\\\\\frac{y+3}{8}=\frac{3}{2}\\\\y+3=12\\\\y=9[/tex]

Answer:

Right option is B.

Step-by-step explanation:

[tex] \sf \longrightarrow \frac{ \sec x \sin( - x) + \tan( - x) }{1 + \sec( - x) } \\ \\ \sf \longrightarrow \frac{ \sec x( - \sin x) - \tan x}{1 + \sec x} \\ \\ \sf \longrightarrow \frac{ - \frac{1}{ \cos x } \times \sin x - \tan x }{1 + \sec x} \\ \\ \sf \longrightarrow \frac{ - \tan x - \tan x}{1 + \sec x} \\ \\ \sf \longrightarrow \frac{ - 2 \tan x}{1 + \sec x} \\ \\ \sf \longrightarrow \frac{ \frac{ - 2 \sin x}{ \cos x} }{1 + \frac{1}{ \cos x} } \\ \\ \sf \longrightarrow \frac{ \frac{ - 2 \sin x}{ \cos x} }{ \frac{ \cos x + 1}{ \cos x} } \\ \\ \boxed{ \sf{\longrightarrow \frac{ - 2 \sin x}{ \cos x + 1} }}[/tex]

The number of chickens she had was 352

From the question, we are to determine the number of chicken she has

Let c represent chicken

and d represent ducks

From the given information,

Mrs. Anderson had twice as many chickens as ducks

c = 2d ---------- (1)

She sold 272 chickens and 16 ducks and then had half as many chickens as ducks

(c-272) = 1/2(d -16) ---------- (2)

Put equation (1) into (2)

2d - 272 = 1/2(d - 16)

2(2d - 272) = d- 16

4d - 544 = d - 16

4d - d = 544 - 16

3d = 528

d = 528/3

d = 176

Substitute the value of d into equation (1)

c = 2d

c = 2(176)

c = 352

Hence, the number of chickens she had was 352

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Answer:

a₅ = 80 , [tex]a_{n}[/tex] = 5[tex](2)^{n-1}[/tex]

Step-by-step explanation:

to find a term in the geometric sequence multiply the previous term by r

a₁ = 5

a₂ = a₁ × 2 = 5 × 2 = 10

a₃ = a₂ × 2 = 10 × 2 = 20

a₄ = a₃ × 2 = 20 × 2 = 40

a₅ = a₄ × 2 = 40 × 2 = 80

the nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

here a₁ = 5 and r = 2 , then

[tex]a_{n}[/tex] = 5 [tex](2)^{n-1}[/tex]

Answer:

502.5

Step-by-step explanation:

C = 24(12) + 5.50(39)

C = 288 + 214.5

C = $502.5

Answer: B

Step-by-step explanation:

There is a hole at x=2, so the numerator and denominator should both have a factor of x-2.

This eliminates everything except for B.

The population standard deviation of the data set is 1.414.

Standard deviation is used to determine how the values in a group differs from the mean of the values in the group. It is a measure of variation.

Mean = (8 + 9 + 10 + 11 + 12) / 5 = 10

Sum of squared differences: (8 - 10)² + (9 - 10)² + (10 - 10)² + (11 - 10)² + (12 - 10)² = 10

√10/5 = 1.414

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Answer: D. the y-intercept is (0,1)

Step-by-step explanation:

For all exponential functions without a vertical shift, the y-intercept is (0,1).

Answer: 9 triangles.

Step-by-step explanation:

Just make a dot in the middle and make lines and connect each line to an edge or bend.

Answer:

z = 5

Step-by-step explanation:

To solve for z, means to get z all by itself on one side of the equation. In your equation z has had two things done to it. First, z has been times by 4, then 10 is subtracted. So, you "un-do" that in reverse order.

FIRST, add 10. To reverse or "un-do" subtracting.

4z - 10 = 10

4z -10+10 = 10+10

4z = 20

Then, divide by 4 to reverse the multiplying.

4z/4 = 20/4

z = 5

see image.

Also, you can check you answer.

put in 5 in place of z and be sure that you get a true statement.

4(5) - 10 = 10

20 - 10 = 10

10 = 10 Checked!

Answer:

[tex]z=5[/tex]

Step-by-step explanation:

First, substitute in 5 for z: [tex]4(5) -10=10[/tex]

Since [tex]4*5=20[/tex], we can now simplify the equation to [tex]20-10=10[/tex].

Now, check the equation to make sure that the value of z is correct. Do this by subtracting [tex]20-10[/tex] to see if it results in a solution of 10.

Since the equation [tex]20-10=10[/tex] is equal/true, we can conclude that [tex]z=5[/tex].

Answer:

Each Person:

-In tips: $2

-Food Bill: $7.50

Step-by-step explanation:

Let's find the tip amount for each person. $16 for the whole group. Each person will give in $2 for the tips, for a total of $16 in tips.

Now that tips are done, we must subtract the amount of tips from the food bill, to see how much each person pays. $76 - $16 = $60.

Divide 60 by 8 to get.. 60/8= 7.5.

With 7.5 as an answer, we can conclude that each person paid $7.50 for the food bill.

I see you need to select solutions, may I see them to help you out? The description is pretty vague..

The true mean expenditure per student is different from $10,337.

What is hypothesis in math?

Sample size is greater than 30 and the population standard deviation is given. Thus, in order to test

H0: µ =$10,337

H1: µ≠$10,337

The appropriate test is one sample z test.

The formula for one sample z test:

Z=   x−μ / σ √ n

x−μ

​x=10798

μ=10337

σ=1560

n=150

[tex]Z = \frac{10798 - 10337}{1560 / \sqrt{150} } = 3.62[/tex]

Computation of p-value:

The EXCEL formula to find the p-value for a two-tailed z-test is

“=2*(1-NORM.S.DIST(3.62, TRUE))”

Thus, the p-value obtained is 0.00029

Conclusion using α = 0.05:

Rejection rule using p-value:

If p-value ≤ α, then reject the null hypothesis.

Since, 0.00029 < 0.05, there is sufficient evidence to reject the null hypothesis.

Therefore, the true mean expenditure per student is different from $10,337.

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Thus, distribution is a function that shows the possible values for a variable and how often they occur and categorical values are summarized by counts and/or percents

In statistics, the distribution is a function that shows the possible values for a variable and how often they occur.

The distribution of a data set is the shape of the graph when all possible values are plotted on a frequency graph. Usually, we are not able to collect all the data for our variable of interest. Therefore we take a sample. This sample is used to make conclusions about the whole data set.

The categorical variable is a data in which individuals are placed into groups or categories.

One way to summarize categorical data is to simply count (frequency), or tally up, the number of individuals that fall into each category. Another way is to show the percentage of individuals who fall into each category, thereby creating a relative frequency.

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The slope of y = 3x - 4 on the interval [2, 5] is 3 and the slope of y = 2x^2-4x - 2 on the interval [2, 5] is 10

The interval is given as:

x = 2 to x = 5

The slope is calculated as:

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

16. y = 3x - 4

Substitute 2 and 5 for x

y = 3*2 - 4 = 2

y = 3*5 - 4 = 11

So, we have:

[tex]m = \frac{11 - 2}{5 - 2}[/tex]

[tex]m = \frac{9}{3}[/tex]

Divide

m = 3

Hence, the slope of y = 3x - 4 on the interval [2, 5] is 3

17. y = 2x^2-4x - 2

Substitute 2 and 5 for x

y = 2 * 2^2 - 4 * 2 - 2 = -2

y = 2 * 5^2 - 4 * 5 - 2 = 28

So, we have:

[tex]m = \frac{28 + 2}{5 - 2}[/tex]

[tex]m = \frac{30}{3}[/tex]

Divide

m = 10

Hence, the slope of y = 2x^2-4x - 2 on the interval [2, 5] is 10

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If two squares have different perimeters, the one with the larger perimeter will have a larger area. If two polygons have the same perimeter, then they must have the same shape. If two polygons have the same shape but are different sizes, then they must have different perimeters.

If two squares have equal areas, they will also have sides of the same length. But although "equal areas mean equal sides" is true for squares, it is not true for most geometric figures.

In order to find the perimeter or distance around the rectangle, we need to add up all four side lengths. This can be done efficiently by simply adding the length and the width, and then multiplying this sum by two since there are two of each side length.

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The solution graphed below represents the y>2 and [tex]y\leq x[/tex] system of linear inequalities.

When a polynomial of degree 1 is compared to another algebraic expression of degree less than or equal to 1, this is an example of a linear inequality, which is an inequality involving at least one linear algebraic expression.

Expressions that compare two linear expressions using inequality symbols are referred to as linear inequalities.

Addition, subtraction, multiplication, and division are the four types of operations that can be performed on linear inequalities.

Equivalent inequality refers to linear inequalities with the same solution.

From the given graph, it can be seen that the line parallel to the x-axis represents y>2 and the other inclined line represents [tex]y\leq x[/tex] .

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By assuming that 1 + 1 = 3, we will reach an absurd.

To do this, we need to reach an absurd.

Let's assume that we are working with integer numbers, and let's assume that 1 + 1 is equal to 3.

Then we can write:

1 + 1 = 3

Now, if we subtract 1 in both sides, we get:

(1 + 1) - 1 = 3 - 1

1  = 2

Now we can subtract 1 again so we get:

1 - 1 = 2 - 1

0 = 1

This is an absurd, then the statement:

1 + 1 = 3

is false.

So we conclude that:

1 + 1 isn't 3.

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Step-by-step explanation:

hello : here is an solution

Answer:

C

Step-by-step explanation:

The average is the total of the scores divided by 5.  

128 x 5 Gives us the total scores of 640.  I know that one bowler had a score of 160.  I will subtract that from the total of 640.  640-160 = 480.  Since the 4 bowlers left, all had the same score, I will divide 480 by 4 to get 120

Answer:

Triangles MNP and QRS

Step-by-step explanation:

This is due to each corresponding line follows the same ratio of 1.5:1

e.g.

NP=6

RS=4

6:4

1.5:1

You can verify this by dividing 6 by 4 (6/4) which is 1.5

Step-by-step explanation:

pythogoras theorem = Q²=P²+R²

P=P

Q= 57.6

R=33.8 =

(57.8)²=(P)²+(33.8)²

=3,340.84=(P)²+1142.44

=3340.84-1142.44=P²

=2,198.4=P²

[tex] = \sqrt{2198.4} = p \\ = 46.8 = p[/tex]

Using proportions, it is found that the seismic activity density for this state is of 0.0059 earthquakes per square mile.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

In this problem, the density is the proportion given by the number of earthquakes divided by the area, hence:

424/71,300 = 0.0059 earthquakes per square mile.

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Answer:  Using proportions, it is found that the seismic activity density for this state is of 0.0059 earthquakes per square mile.

Step-by-step explanation:

Using the surface area formula for rectangular and triangular prism, the surface area of the composite figure is: 444 m².

Total surface area = surface area of the top triangular prism + surface area of the bottom rectangular prism - area of the surface both share together.

Surface area of the top triangular prism = (S1 + S2+ S3)L + bh = (10 + 10 + 16)5 + (16)(6) = 276 m².

Surface area of the bottom rectangular prism = 2(wl + hl + hw) = 2·(5·16+4·16+4·5) = 328 m²

Area of the surface both share together = 2(16)(5) = 160 m²

Total surface area = 276 + 328 - 160 = 444 m².

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The simplified form of the expression [1/5 (-16-9) + 4² ÷ 8] is -3.

Option A) is the correct answer.

Given the expression;  1/5 (-16-9) + 4² ÷ 8

First we remove the parentheses and perform the operations using the guidelines of BODMAS

1/5 (-16-9) + 4² ÷ 8

1/5 × -25 + 4² ÷ 8

1/5 × -25 + 16 ÷ 8

-25/5 + 16/8

-5 + 2

-3

The simplified form of the expression [1/5 (-16-9) + 4² ÷ 8] is -3.

Option A) is the correct answer.

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Answer:

Hector makes a tent shaped like a rectangular pyramid the volume is 56 cubic feet and the area is 24 square feet how tall is the tent

Step-by-step explanation: