Write the equation in slope intercept form:2x+y=2

Surface area of a rectangular prism formula

where w is width, l is length, and h is height.

Substituting with w = 4 ft, l = 6 ft, and h = 10 ft, we get:

Answer:

x = 8 + 4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

computation just means to calculate

x(2[tex]\sqrt{3}[/tex] - 3 ) = 4[tex]\sqrt{3}[/tex] ( divide both sides by (2[tex]\sqrt{3}[/tex] - 3 ) )

x = [tex]\frac{4\sqrt{3} }{2\sqrt{3-3} }[/tex]

rationalise the denominator by multiplying the numerator/ denominator by the conjugate of the denominator.

the conjugate of 2[tex]\sqrt{3}[/tex] - 3 , is 2[tex]\sqrt{3}[/tex] + 3

= [tex]\frac{4\sqrt{3}(2\sqrt{3}+3) }{(2\sqrt{3}-3)(2\sqrt{3}+3) }[/tex] ← expand denominator using FOIL

= [tex]\frac{24+12\sqrt{3} }{12-9}[/tex]

= [tex]\frac{24+12\sqrt{3} }{3}[/tex]

= [tex]\frac{24}{3}[/tex] + [tex]\frac{12\sqrt{3} }{3}[/tex]

= 8 + 4[tex]\sqrt{3}[/tex]

The linear equation that passes through the points (14, 15) and (20, 24) crosses the y-axis at y = -6.

A general linear equation can be written as:

y = m*x + b

Where m is the slope and b is the y-intercept.

If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope can be written as:

m = (y₂ - y₁)/(x₂ - x₁).

In this case the line passes through (14, 15) and (20, 24) so the slope is:

m = (24 - 15)/(20 - 14) = 9/6 = 3/2

y = (3/2)*x + b

To find the y-intercept we can replace the values of one of the points, like (14, 15)

15 = (3/2)*14 + b

15 = 3*7 + b

15 = 21 + b

15 - 21 = b

-6 = b

The y-intercept is -6.

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All of the rational numbers that we have in the question that we have here are:

This is the term that is used to refer to the ratio of two numbers that when they are expressed as a ratio of two different numbers, the denominator does not have to be 0.

The rational numbers when they are solved would not give us terminating decimals. That is they would be able to be expressed as fractions.

-√25 = -5

√0.0144 = 0.12

√0.36 = 0.6

√100 = 10

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-√25, √100, √0.36, and √0.0144n are the rational number. Options B, D, E, and F are correct.

As of the given data, numbers are given we have to determine which of the number are rational numbers.

Rational numbers are numbers that can be structured in the form of the fraction of integers. Eg- 5/6, 2/3 etc.

Here,
All the numbers are irrational numbers except -√25, √100, √0.36, and √0.0144 because the number picked out is required rational number.

Thus, -√25, √100, √0.36, and √0.0144n are the rational number. Options B, D, E, and F are correct.

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Answer:

y axis-(0,6) x axis-(5,0) quad 1-(8.7,2.3) quad 2-(-1,10)  quad 3-(-1/4,-6 1/2) quad 4-(5,-2)

Step-by-step explanation:

The equivalent expression of the given expression is [tex]\frac{g^1^5}{8h^6}[/tex].

What is inequality?

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Consider the given expression, [tex]\frac{(2g^5)^3}{(4h^2)^3}[/tex]

Using the rule, [tex](a^m)^n = a^m^n[/tex]

So, [tex]\frac{(2g^5)^3}{(4h^2)^3} = \frac{8g^1^5}{64h^6}[/tex]

After simplifying  we get,  [tex]\frac{g^1^5}{8h^6}[/tex]

Therefore, the equivalent expression of the given expression is [tex]\frac{g^1^5}{8h^6}[/tex].

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Answer:

1) y = 3x + 5

2) y = -12x + 2

3) y = 5/4 - 5

4) y = -6x + 3

Step-by-step explanation:

Answer:

4th option

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - [tex]\frac{2}{3}[/tex] x + 8 ← is in slope- intercept form

with slope m = - [tex]\frac{2}{3}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{2}{3} }[/tex] = [tex]\frac{3}{2}[/tex] , then

y = [tex]\frac{3}{2}[/tex] x + c ← is the partial equation

to find c substitute (- 6, 2 ) into the partial equation

2 = - 9 + c ⇒ c = 2 + 9 = 11

y = [tex]\frac{3}{2}[/tex] x + 11 ← equation of perpendicular line

Answer:

I miss you

Step-by-step explanation:

Answer:

g = 5

Step-by-step explanation:

8g - 7 = 18 + 3g

add 7 to both sides:

8g - 7 + 7 = 18 + 3g + 7

8g = 25 + 3g

subtract 3g from both sides:

8g - 3g = 25 + 3g - 3g

5g = 25

divide both sides by 5:

5g/5 = 25/5

g = 5

From the ellipse equation

the length of the major axis is equal to 2a. By comparing this equation with the given one, we can note that

Then, the length of the major axis is 2x7 = 14

Answer:

Step-by-step explanation:

0 mixed berry smoothies and 70 milkshakes

Jane decides to randomly interview 10 freshmen from each of the dorms, these people are her Sample.

What is Sample?

Sampling is the process of choosing a portion of a statistical population to estimate attributes of the entire population in statistics, quality control, and survey methods. Statisticians try to get samples that are typical of the population under consideration.

A little sample or amount of someone or something that is inspected, analyzed, or otherwise investigated to learn more about the rest.

Given: Jane wants to know what percentage of freshmen at her college purchase clothing with college logos. She decides to randomly interview 10 freshmen from each of the dorms.

Therefore, by the above information, these people are her Sample.

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Answer:

Step-by-step explanation:

x y

2 12

6 8

10 4

14 0

18 -4

The slope is the Rise/Run, or change in y over the change in x.  Pick any two points.  I'll choose (2,12) and (18,-4),

Rise = (-4 - 12) = -16

Run = (18 - 2) = 16

Slope = Rise/Run = -16/15, or -1

The equation becomes y = -1x + b

To find b, use any of the points in the equation and solve for b.  I'll use (14,0):

y = -1x + b

0 = -1(14) + b

b = 14

The equation is y = -x + 14

See the attached graph.

The ascending order of the set of numbers is √3 - 1, 2√10 ÷ 5, √14, 3√2, √19 + 1, 6

Given,

A set of numbers;

3√2, √3 - 1, √19 + 1, 6, 2√10 ÷ 5, √14

We have to arrange this numbers from least to greatest. That is, in ascending order.

Ascending order;

Numbers can be arranged in ascending order, from least value to highest value. The arrangement is left to right. Increasing order is another name for ascending order.

Here,

First we have to find the values of the square roots in the numbers.

3√2 = 4.24

√3 - 1 = 0.73

√19 + 1 = 5.36

6

2√10 ÷ 5 = 1.26

√14 = 3.74

Then,

6 is the greatest number and √3 - 1 is the least number.

That is,

The ascending order of the set of numbers is √3 - 1, 2√10 ÷ 5, √14, 3√2, √19 + 1, 6

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The equation of the line in slope-intercept form would be; y = -12x + 18

If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:

y = MX +c

To find the slope of a line, we the rate at which the value of 'y' is increasing as we increase the value of 'x' by one unit.

We have been given the point (1,6) and (2,-6)

y-y₁ = m(x-x₁)

m = (-6-6)/(2 -1)

m = -12/1

Now substitute;

y-y₁ = m(x-x₁)

y- 6 = -12(x- 1)

y- 6 = -12x + 12

y = -12x + 18

Hence, the equation of the line in slope-intercept form would be; y = -12x + 18

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1) We need to consider that whenever we have a variable its exponent is raised to the 1st power, even when we don't write it as a superscript.

2) So we can write out the following steps to get that product as x²:

That's why we can write that, applying the property of exponents.

In the given figure, m∠2 and m∠7 are "Alternate Exterior Angles" and they are always congruent (equal).

So we can equate them and solve for x.

So, m∠2 is

According to the straight-line angle property, the sum of m∠1 and m∠2 must be equal to 180°

Therefore, the measure of m∠1 is 147°

Answer:

Step-by-step explanation:

The cutoff score so that only 5% of the population has a higher score is 124.7.

If 5% of the population has a higher score, then the probability of selecting these is 0.05.

Find the z-score that corresponds to the probability in the z-table. (see attached images)

probability = 1 - 0.05 = 0.95

z-score = 1.647

Using the formula for the z-score below, determine the cutoff score.

z-score = (x – μ) / σ

where x = individual data value = cutoff score

μ = mean = 100

σ = standard deviation = 15

1.647 = (x - 100) / 15

1.647(15) = x - 100

x = 24.705 + 100

x = 124.705

cutoff score = 125

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The solution of the inequality is b ≥ -17.

Given inequality:-

b + 5 ≥ -12

We have to find the solution of the inequality.

Subtracting 5 from the given inequality, we get

b + 5 - 5 ≥ -12 - 5

b + (5 - 5) ≥ -17

b + 0 ≥ -17

b ≥ -17

Hence, b can be equal to or greater than -17.

Inequality

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

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ANSWER:

STEP-BY-STEP EXPLANATION:

We have the following function:

We calculate the inverse function as follows:

The perimeter of the rectangle is 6.89

Perimeter of the rectangle:

The perimeter (P) of a rectangle is the total length of all the sides of the rectangle.

The formula for the perimeter of the rectangle is

P = 2(l + w)

The letter ‘P’ denotes the perimeter of a rectangle. Let l denote the length and w denote the width of the rectangle.

Given,

Here we have the graph with the following points:

(-3/2, -1 7/9), (7/2, -1 7/9), (7/2, 3 2/9), and (-3/2 3 2/9)

Now we need to find the perimeter of the rectangle.

To calculate the perimeter, first we have to find the length and width of the rectangle.

To calculate the length, we have to use the values of x axis,

That is,

=> -3/2 + 7/2

=> (-3+7)/2

=> 4/2

=> 2

Therefore, the length of the rectangle is 2.

Now, we have to find the width of the rectangle using the y axis coordinates,

=> -1 7/9 + 3 2/9

Convert the mixed fraction into normal form, then we get,

=> -16/9 + 29/9

=> (-16 + 29)/9

=> 13/9

Therefore, the width of the rectangle is 13/9

Now, we have to use this to calculate the perimeter of the triangle,

P = 2 (2 + 13/9)

P = 2 ((18+13)/9)

P = 2 (31/9)

P = 62/9

P = 6.89

Therefore, the perimeter of the rectangle is 6.89.

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Answer:

Step-by-step explanation:

triangle area formula: A = 1/2 × b × h

7 +3 = 10 ft

1/2 10 × 4 =

5 × 4 =

20 feet²

Answer:

1.25 hours.

68.75 miles from the city

Step-by-step explanation:

Eltan's train (E) is travelling 65mph west.

Dmitri's train (D) is travelling 55mph west.

In terms of vectors, we can write E as 65E and D as 55W

The miles travelled by each is a function of time, T, in hours.

Each train's distance is:

 E:  T*65E

 D:  T*55W

They are 150 miles apart.  They will meet with the combined miles travelled is 150 miles.

 150 miles = T*65E + T*55W

150 miles = T(120 miles/hour)

T = (150 miles/120 miles/hour)

T = 1.25 hours

Make Demitri's train mile 0 and Eitan's train at mile 150 at the start.

They will have travelled the following miles in 1.25 hours:

Demitri:  (1.25hr)(55 m/hr) = 68.75 miles

Eitan:      (1.25hr)(65 m/hr) = 81.25 miles

Total = 150 miles

Dimitri is headed away from the city.  After 1.25 hours, his train will have travelled 68.75 miles when he sees Eitan passing him on the adjacent track (hopefull) headed into the city.  They meet 68.75 miles from the city.

Answer:

question one is B and question 2 is C

Step-by-step explanation:

The question asks us to solve the following system of equations by elimination:

Solution

Answer

The solution to the system of equation is:

x = -8

y = 9

The associated number of degrees of freedom for reading the t-value is 58.

The aim is to determine an interval for the mean of a population.

The standard deviation is unknown to us. The sample consists of 59 items. The mean of the sample is determined to be 32. We need to calculate the associated number of degrees of freedom for reading the t value.

We know that the degree of freedom is one less than the number of items in the sample space.

The associated number of degrees of freedom for reading the t-value is 59-1.

The associated number of degrees of freedom for reading the t-value is 58.

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The solution set for the given inequality (2q/5 + 4 < 2q/-9) is q∈(-∞, - 45/7).

So, 2q/5 + 4 < 2q/ - 9:

Now, solve for the solution set as follows:

Therefore, the solution set for the given inequality is q ∈ ( -∞, - 45/7).

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Answer:

[tex]\dfrac{x-7}{9}[/tex]

which corresponds to choice
C :   [tex]f^{\small -1}(x)\ =\ \frac{1}{9}x\ -\ \frac{7}{9}[/tex]

Step-by-step explanation:

The inverse of a function y = f(x) can be found by interchanging x and y and solving for y

Let y = f(x)

y = 9x + 7

Interchange x and y:

x = 9y + 7

9y + 7 = x  (switch sides)

subtract 7 both sides
→  9y + 7 - 7 = x - 9

→ 9y = x - 9

Divide both sides by 9

→ [tex]y = \dfrac{x - 7}{9} = \dfrac{x}{9} - \dfrac{7}{9}[/tex]

which corresponds to choice C

PLUG IN THE VALUES OF THE VARIABLES IN THE RIGHT POSITIONS AND SIMPLIFY.

[tex] \frac{1}{2} (12 - 4) \times \frac{1}{4} \\ = \frac{1}{2} (8) \times \frac{1}{4} \\ = \frac{8}{2} \times \frac{1}{4} \\ = \frac{8}{8} \\ = 1[/tex]

THE ANSWER IS OPTION B.