Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression.

Answer:

y = - 4x - 7

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 )

Here m = - 4, thus

y = - 4x + c ← is the partial equation

To find c substitute M(- 2, 1) into the partial equation

1 = 8 + c ⇒ c = 1 - 8 = - 7

y = - 4x - 7 ← equation of line

Answer:

height = 10 inches

base = 6 inches

The height and base width of the triangle will be 4 inches and 10 inches, respectively.

Assume 'h' is the height of the triangle and 'b' be the base of the triangle. Then the area of the triangle is given as,

A = (1/2) × h·b

The base of a triangle measures 6 inches less than its height. If the area of the triangle is 20 square inches. Then the equations are given as,

b = h - 6             ...1

20 = (1/2)bh

40 = bh             ...2

From equations 1 and 2, then we have

40 = (h - 6)h

40 = h² - 6h

h² - 6h - 40 = 0

h² - 10h + 4h - 40 = 0

h(h - 10) + 4(h - 10) = 0

(h - 10)(h + 4) = 0

h = 10, -4

The height can be negative, so neglect -4. Then the width of the triangle is given as,

b = 10 - 6

h = 4

The height and base width of the triangle will be 4 inches and 10 inches, respectively.

More about the area of the triangle link is given below.

https://brainly.com/question/19305981

#SPJ2

Answer:

17.1 kg

Step-by-step explanation:

One stack of rice = 26.3 kg

Two stacks of rice = 2 *26.3  = 52.6 kg

Remaining rice at end of day = Total weight of two stacks - quantity of rice sold in day

= 52.6 - 35.5

= 17.1 kg

Answer:

Step-by-step explanation:

Alternate angles:When two lines are crossed by another line the pair of angles on opposite sides of the transversal is called alternate angles.  

Theorem 1:If a transversal intersects two Parallel Lines then each pair of alternate interior angles is equal.

Theorem 2 :If a transversal intersects two lines such that a pair alternate interior angle is equal then the two lines are parallel.  

SOLUTION:

Given:  ∠AGE=126°

∠AGE=∠GED=126∘ [alternate interior angles]

 (ii) ∠GED=∠GEF+∠FED=126∘

∠GEF + 90° =126°

(GIVEN that EF⊥CD)  

∠GEF=126°−90°=36°

∠GEF=36°

(iii) ∠CEG+∠GED=180°

(GIVEN ∠GED=126∘)

∠CEG+126° =180°

∠CEG=180° −126°

∠CEG=54°

∠FGE=∠CEG= 54°     (alternate angles)

Answer:

[tex] 2\sqrt{34} + 6 units [/tex]

Step-by-step explanation:

The perimeter of the polygon shown = AC + BC + AB

Using distance formula, calculate the distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex], calculate AC, BC, and AB.

The coordinates of the points are as follows,

A(3, 5),

B(0, 0)

C(6, 0)

Find AB:

[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

Where,

A(3, 5) => (x1, y1)

B(0, 0) => (x2, y2)

[tex] AB = \sqrt{(0 - 3)^2 + (0 - 5)^2} [/tex]

[tex] AB = \sqrt{(-3)^2 + (-5)^2} = \sqrt{9 + 25} = \sqrt{34} [/tex]

[tex] AB = \sqrt{34} units [/tex]

Find BC:

BC is easy to determine from the graph directly. The distance from point B to C, is 6 units.

Find AC:

[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

Where,

A(3, 5) => (x1, y1)

C(6, 0) => (x2, y2)

[tex] AC = \sqrt{(6 - 3)^2 + (0 - 5)^2} [/tex]

[tex] AB = \sqrt{(3)^2 + (-5)^2} = \sqrt{9 + 25} = \sqrt{34} [/tex]

[tex] AC = \sqrt{34} units [/tex]

Perimeter of the polygon = [tex] \sqrt{34} + 6 + \sqrt{34} [/tex]

[tex] = (\sqrt{34} + \sqrt{34}) + 6 [/tex]

[tex] = 2\sqrt{34} + 6 [/tex]

Answer:

2√34 +6 units

Step-by-step explanation: I took the test

Answer:

B

Step-by-step explanation:

3.005 x 10 = 30.05

30.05 x 30.05 x 30.05 x 30.05 x 30.05 x 30.05 x 30.05 x 30.05 or 30.05 to the 8th power = 300,500,000

B = 300,500,000

Answer:

B

Step-by-step explanation:

● 3.005 × 10^8

10^8 is 100000000

● 3.005 × 100000000

● 300500000

Answer:

[tex]9m^2 + 17m- 9[/tex]

Step-by-step explanation:

Given

[tex]7m^2 + (2m - 1)(m + 9)[/tex]

Required:

Simplify

We start by opening the bracket

[tex]7m^2 + (2m(m + 9) - 1(m + 9))[/tex]

[tex]7m^2 + 2m^2 + 18m - m - 9[/tex]

Collect Like Terms

[tex]9m^2 + 17m- 9[/tex]

Hence, the equivalent expression is [tex]9m^2 + 17m- 9[/tex]

Step-by-step explanation:

[tex] \frac{x}{8} = \frac{9}{24} [/tex]

Cross multiply

We have

24x = 72

Divide both sides by 24

That's

[tex] \frac{24x}{24} = \frac{72}{24} [/tex]

We have the answer as

3x² + 2x - 10

when x = - 1

Substitute the value of x into the expression

That's

3(-1)² + 2(-1) - 10

= 3 - 2 - 10

We have the answer as

When x = 0

That's

3(0) + 2(0) - 10

When x = 1

That's

3(1)² + 2(1) - 10

= 3 + 2 - 10

= 5 - 10

[tex] \sqrt{( - 9)} [/tex]

First of all apply the radical rule

That's

[tex] \sqrt{ - a} = \sqrt{ - 1} \times \sqrt{a} [/tex]

So we have

[tex] \sqrt{ - 9} = \sqrt{ - 1} \times \sqrt{9} [/tex]

Using the imaginary rule

That's

[tex] \sqrt{ - 1} = i[/tex]

We have

[tex] \sqrt{9} \times i[/tex]

We have the final answer as

[tex] \frac{1}{x} [/tex]

when x = 0

We have

[tex] \frac{1}{0} = 0[/tex]

when x = 1

[tex] \frac{1}{1} = 1[/tex]

when x = 2

We have

[tex] \frac{1}{2} [/tex]

Hope this helps you

Answer:

y = 12

Step-by-step explanation:

The first step is to determine the perimeter of triangle TUV. We know side UV has a length of 20 cm and that the triangle is equilateral, so all sides have the same length. Thus the perimeter of the triangle must be 20 cm * 3 = 60 cm

The perimeter of PQRS is the sum of the lengths of sides PQ, QR, RS, and SP in cm.

PQ = y + 6

QR = 9 (given in diagram)

RS = 2y

SP = 9 (the diagram shows that it has the same length as QR)

Together they must add up to 60 cm to match the perimeter of the triangle, so:

PQ + QR + RS + SP = 60

(y + 6) + 9 + 2y + 9 = 60

3y + 24 = 60

3y = 36

y = 12

Answer:

17 = x/18 and 23 = .84/n

Step-by-step explanation:

Answer:

17. x =18

23. n =0.84

Step-by-step explanation:

17.

[tex]\frac{6}{5} = \frac{x}{15} \\\\\frac{x}{15}=\frac{6}{5}\\\\\mathrm{Multiply\:both\:sides\:by\:}15\\\\\frac{15x}{15}=\frac{6\cdot \:15}{5}\\\mathrm{Simplify\:}\frac{15x}{15}:\quad x\\\\\mathrm{Simplify\:}\frac{6\cdot \:15}{5}:\quad 18\\\\x=18\\[/tex]

23.

[tex]\frac{2}{0.21}=\frac{8}{n}\\\\ \mathrm{Apply\:fraction\:cross\:multiply:\:if\:}\\\frac{a}{b}=\frac{c}{d}\mathrm{\:then\:}a\times \:d=b\times \:c\\\\2n=0.21\times \:8\\\\\mathrm{Simplify\:}0.21\times \:8:\quad 1.68\\\\2n=1.68\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\\\frac{2n}{2}=\frac{1.68}{2}\\\\Simplify\\\\n=0.84[/tex]

Answer:

b) $640

Step-by-step explanation:

Competitor's price  = $800

Price, 20% below of competitor's:

Correct answer choice is b) $640

Answer:

26

Step-by-step explanation:

5x³ - 21 + 7

x = 2

then:

5x³ - 14

5*2³ -14

5*8 - 14

40 - 14

26

Answer:

The simplified answer to the given equation is -54.

Step-by-step explanation:

For this problem, we are given the value of x.

x = -2

So, let's plug in this value into our expression soit can be easier to solve.

5(-2)³ - 21 + 7

First, simplify the exponents.

5(-8) - 21 + 7

Now, multiply 5 by -8.

-40 - 21 + 7

Subtract -40 from 21.

-61 + 7

Add 7 to -61.

-54

Answer:

h= -5.8

Step-by-step explanation:

Answer:

[tex] x = 3 [/tex]

Step-by-step explanation:

From the figure given, we have points A,B, and C, that are collinear. Therefore, according to the segment addition postulate, [tex] AB + BC = AC [/tex].

We are given that:

AB = 9x + 7

BC = -5x + 20

AC = 39

An equation that can be used to solve for x would be:

[tex] (9x + 7) + (-5x + 20) = 39 [/tex]

Solve for x

[tex] 9x + 7 - 5x + 20 = 39 [/tex]

[tex] 9x - 5x + 7 + 20 = 39 [/tex]

[tex] 4x + 27 = 39 [/tex]

Subtract 27 from both sides

[tex] 4x + 27 -27 = 39 - 27 [/tex]

[tex] 4x = 12 [/tex]

Divide both sides by 4

[tex] \frac{4x}{4} = \frac{12}{4} [/tex]

[tex] x = 3 [/tex]

Answer:

37

Step-by-step explanation:

4x - 6 + x + 3 can be simplified to 5x - 3 by combining like terms.

substituting 8 for x, you get 5*8 - 3

evaluating, 40 - 3 = 37

Answer:

Interval Ratio

Step-by-step explanation:

In statistics, the level of measurement used for a variable determines the what summary statistics and analysis are possible. There are three types of level of measurement.

Nominal

Ordinal

Interval/ Ratio

The nominal is the most basic level of measurement. It is known as categorical or qualitative. Examples includes, numbers,color, sex.  Nominal can be stored as a word or text  or given a numerical code.However, the number do not imply order. They are usually expressed in percentage

Ordinal  are variables based on ranks, they are usually have a meaningful order but the intervals between the variables may not be equal. They are usually expressed in frequencies.

The interval/ratio level of measurement  is the most precise level of measurement. Data can be measured and ordered. Examples include, number of customers, age, weight or size. Interval / Ratio data is also known as scale, parametric or quantitative. Interval / Ratio can be discrete  with whole numbers or continuous with fractional numbers.

Answer:

Domain (0, ∞)

Range (-∞, ∞)

Step-by-step explanation:

The domain is the input values

The input is from 0 to infinity

Domain (0, ∞)

The range is the output values

The input is from negative infinity to infinity

Range (-∞, ∞)

Answer:

Step-by-step explanation:

Given expression

7.50h + 0.20s + 40

A)

Coefficients are 7.50 and 0.20

Variables are h and s

Constant=40

B) if Corinne works for 25 hours and selling $300 in magazine

Weekly earnings = 7.50h + 0.20s + 40

=7.50(25) + 0.20(300) + 40

= 187.5 + 60 + 40

=$287.5

C)

If Corinne starts earning $9 per hour.

Original expression

7.50h + 0.20s + 40

New expression

9h + 0.20s + 40

The coefficient of h will change because of the increase in earnings per hour

Coefficients are 9 and 0.20

Answer:

(-2, 8) and (5, -1)

slope: (y² - y¹) / (x² - x¹)

(-1 - 8) / (5 + 2) = -9/7

y = -9/7x + b

8 = -9/7(-2) + b

8 = 18/7 + b

8 = (2.57) + b

b = 5.43

y = -9/7x + 5.43

parallel = same slope

y = -9/7x

perpendicular = reciprocated slope

y = 7/9x

Step-by-step explanation:

(a + b)(5a – 3b) + (a – 3b)(a – b)

Expand each of the terms separately

That's

(a + b)(5a – 3b) = 5a² - 3ab + 5ab - 3b²

= 5a² + 2ab - 3b²

(a – 3b)(a – b) = a² - ab - 3ab + 3b²

= a² - 4ab + 3b²

Add the terms

That's

5a² + 2ab - 3b² + a² - 4ab + 3b²

Group like terms

5a² + a² + 2ab - 4ab - 3b² + 3b²

We have the answer as

(a – b) (a² + b² + ab) – (a + b) (a² + b²– ab)

Expand the terms separately

For (a – b) (a² + b² + ab)

Using the rule

x³ - y³ = (x - y)( x² + xy + y²) expand the expression

So we have

(a – b) (a² + b² + ab) = a³ - b³

For (a + b) (a² + b²– ab)

Using the rule

x³ + y³ = (x + y)( x² - xy + y²) expand the expression

We have

(a + b) (a² + b²– ab) = a³ + b³

Subtract the terms

That's

a³ - b³ - (a³ + b³)

Remove the parenthesis

a³ - b³ - a³ - b³

Group like terms

a³ - a³ - b³ - b³

We have the final answer as

(b² – 49) (b + 7) + 343

Expand the terms

That's

b³ + 7b² - 49b - 343 + 343

We have the final answer as

Hope this helps you

Answer: Margo does 48 activities in 4 weeks.

Step-by-step explanation:

In the calendar,

Red dots represent homework, yellow dots represent work, and green dots represent practice.

On a typical week , she uses 5 red dots, 3 yellow dots, and 4 green dots.

That means , total activity he does in a week = 5+3+4=12

Then, total activities in 4 weeks = 4 x 12 = 48

Hence, Margo does 48 activities in 4 weeks.

Answer:

12

Step-by-step explanation:

12         48........(2)

6           24........(2)

3           12.........(3)

1            4...........4

             4

Multiplication in the parentheses is our greatest common factor of 12 and 48

2 x 2 x 3 = 12

Answer:

12

Step-by-step explanation:

The greatest factor of 12 is 12

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Sample mean(x) = 23500

Sample standard deviation (sd) = 3900

Sample size (n) = 20

Population mean (m) = 20,000

Null hypothesis : m = 20000

H1: m > 20000

To obtain the z-score :

(population mean - sample mean) / (sample standard deviation /√sample size)

(x - m) / (sd/√n)

(23500 - 20000) / (3900 / √20)

3500 / (3900 /4.4721359)

3500 / 872.06651

= 4.0134

Get the P value to know if to reject or accept the null:

P(z > 4.0134) = 1 - P(z < 4.0134)

P(z < 4.0134) = 1

1 - P(z < 4.0134) = 1 - 1 =0

Since P value is < alpha, we reject the null.

Hence average is > 20000

Answer:

sinA = 35/37 & cosA = 12/37

Step-by-step explanation:

Answer: The written expression for this equation is one - fourth multiplied by nine minus a number. The variable is "a number" and you use the pronunciation of the other numbers.

Answer:

The entire class is done in 80 minutes

Step-by-step explanation:

20 % = 20/100 = 1/5

1/5  of the class in 16 minutes

Multiply each by 5

1/5 *5  of the class in 16*5 minutes

1 of the class in 80 minutes

The entire class is done in 80 minutes

Answer:

see below

Step-by-step explanation:

4c + 5 = 27

1.  5 is the calories that come from something else besides carbohydrates in the one bite.

2.

Test the values 8 and 3

4*8 +5 = 32+5 = 37  this does not equal 27

4*3+5 = 12+5 = 17   this does not equal 27

neither 8 nor 3 are solutions

3.  

4c + 5 = 27

Subtract 5 from each side

4c + 5-5 = 27-5

4c = 22

Divide each side by 4

4c/4 = 22/4

c =5.5

Answer:

A. The 5 would stand for the other ingredients.

B. She is correct since if you plug in those numbers for c they would be wrong

C. 5.5

Step-by-step explanation:

A. The 5 would stand for the other ingredients.

    The reason that it is the other ingredients since it is the only other possible answer

B. She is correct since if you plug in those numbers for c they would be wrong

C. 5.5

To do this you would just subtract 5 from both sides leaving you with 4c=22 then you would divide 4 from both sides so you get c= 22/4 and when you simplify you get 11/2 which as a number is 5.5

Answer:

63 inches

Step-by-step explanation:

the formula for the area of a triangle is

a = 1/2 bh

plug in the numbers

a = 1/2(9)(14)

9 times 14 is 126

a = 1/2(126)

half of 126 (or 126 divided by 2)

area = 63 inches