please help 8th grade math!

The solution of the equation 2.54-x+12= 21-42.5x+7 is x = 0.324

The equation is

2.54-x+12 = 21-42.5x+7

Rearrange the terms are do the suitable arithmetic operation in the equation

2.54-x+12= 21-42.5x+7

-x+12+2.54 = -42.5x+7+21

Add the like terms together

-x+14.54 = -42.5x+28

Here we have to rearrange the term and make the all the like terms in each sides

Move 14.54 to the right hand side and move -42.5x to the left hand side

Then the equation will become

-x+42.5x = 28-14.54

41.5x = 13.46

x = 13.46/41.5

x = 0.324

Hence, the solution of the equation 2.54-x+12= 21-42.5x+7 is x = 0.324

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Answer:

–37

Step-by-step explanation:

–42 – 19 – (–24)

–42 – 19 + 24

–61 + 24

= –37

The given equations (5b - 2)² + 4 = 25b²– 20b and (2x² + y²)(2x² - y²) = 4x² – y have been found not to be true identities

A) We want to check if (5b - 2)² + 4 = 25b²– 20b is a true identity.

A true identity is an equality that holds true regardless of the values chosen for its variables. They are used in simplifying or rearranging algebra expressions. By definition, the two sides of an identity are interchangeable, so we can replace one with the other at any time.

(5b - 2)² + 4 when expanded gives;

25b² - 20b + 4 + 4 = 25b² - 20b + 8

That is not equal to the right hand side and as such, we can say that both equations are not true identities

B) (2x² + y²)(2x² - y²) = 4x² – y

Expand the left side to get;

4x⁴ - y⁴

This result is not equal to the right hand side and as such, we can say that both equations are not true identities.

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Correct question is;

Which of the equations are true identities?

A. (5b - 2)² + 4 = 25b²– 20b

B. (2x² + y²)(2x² - y²) = 4x² – y

Answer: a) $171          b) $729

Step-by-step explanation:

a) 0.19 * $900 = $171

b) net pay = the money one earns after all deductions

$900 (what she earned) - $171 (taxes she had to pay) = $729

In my opinion, Report 1 is more persuasive than Report 2 due to the fact that the margin of error in Report 1 is narrower than in Report 2.

This is further explained below.

Generally,  we consider report one and report two

For Report

at 98% confidence interval = $64.35 to $83.59

Therefore, the Margin of error

M.E= $83.59 - $64.35

M.E = $19.24

For Report 2:

95% confidence interval = $58.37 to $71.93

Margin of error

M.E= $71.93 - $58.37

M.E= $13.56

Since Report 1 has a smaller margin of error than Report 2, I find Report 1 to be more convincing.

In conclusion, A report with a lower margin of error, in my opinion, is often more credible than one with a bigger one.

This is because more exact data indicates a report with a reduced margin of error.

To put it another way, information in a report with a lower margin of error is more likely to be correct than information in a report with a higher margin of error.

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The two column proof to justify the complementary angles are;

Statement 1. ∠1 and ∠2 are complementary

∠2 and ∠3 are complementary

Reason 1: Given

Statement 2: m∠1 + m∠2 = 90°

Reason 2: Definition of Complementary Angles

Statement 3. m∠2 + m∠3 = 90°

Reason 3: Definition of Complementary Angles

Statement 4: m∠1 + m∠2 = m∠2 + m∠3

Reason 4: Transitive property of equality

Statement 5: m∠1 = m∠3

Reason 5: Substitution Property of Equality

Complementary angles are defined as angles that sum up to 90 degrees.

Now, from the question, we are given that;

∠1 and ∠2 are complementary, and ∠2 and ∠3 are complementary.

From the image attached, we can get a two column proof based on the given questions as;

Statement 1. ∠1 and ∠2 are complementary

∠2 and ∠3 are complementary

Reason 1: Given

Statement 2: m∠1 + m∠2 = 90°

Reason 2: Definition of Complementary Angles

Statement 3. m∠2 + m∠3 = 90°

Reason 3: Definition of Complementary Angles

Statement 4: m∠1 + m∠2 = m∠2 + m∠3

Reason 4: Transitive property of equality

Statement 5: m∠1 = m∠3

Reason 5: Substitution Property of Equality

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Complete Question is;

Identify the correct justification for each step, given that ∠1 and ∠2 are complementary, and ∠2 and ∠3 are complementary.

1. ∠1 and ∠2 are complementary

∠2 and ∠3 are complementary

2. m∠1 + m∠2 = 90°

3. m∠2 + m∠3 = 90°

4. m∠1 + m∠2 = m∠2 + m∠3

5. m∠1 = m∠3

One package weighs 6.75 pounds.

In this question, we have been given Jack mails 10 packages that each weigh the same amount.

We need to find the weight of one packet.

Let each package weighs m pounds.

The combined weigh of all 10 package is 67 1/2 pounds.

So, we get an equation,

10m = 67.5

We solve above equation.

m = 67.5 / 10

m = 6.75 pounds

Therefore, one package weighs 6.75 pounds.

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The table of values indicates a proportional relationship between the number of gallons of gas and the number of miles driven, therefore;

A proportional relationship is one in which one variable, y, can be obtained from another variable, x, by multiplying x by a factor.

Please find attached a table showing the number of gallons of gas and the miles driven obtained from a similar question online

Let x represent the number of gallons of gas and let f(x) represent the number of miles driven

The difference between the consecutive terms of the first three values in the number of gallons and miles driven are each equal to 2 and 62 respectively

4 - 2 = 2 - 0 = 2

124 - 62 = 62 - 0 = 62

Therefore, given that the first difference is constant, the first three points have a linear relation, which gives;

Slope of the line = 62/2 = 31

Intercept = 0

Therefore;

f(x) = 31•x

Checking the fourth point, gives;

x = 10

f(10) = 31 × 10 = 310

The relationship between the miles driven, f(x), and the number of gallons is therefore a proportional relationship, which is presented as follows;

f(x) = 31•x

Therefore, if the number of gallons of gas, x, is known, the number of miles driven, f(x), can be found using the equation;

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The side of the triangle is 15 inches.

The perimeter of an equilateral triangle is 17 inches more than the perimeter of a square, and the side of the triangle is 8 inches longer than the side of the square.

Hence,

let

perimeter of the square = x inches

perimeter of an equilateral triangle = x + 17

Let

side of the square = y

side of the triangle = 8 + y

Therefore,

Perimeter of the square

x = y + y + y + y

x = 4y

Perimeter of the triangle

x + 17 = 8 + y + 8 + y + 8 + y

x + 17 = 24 + 3y

x - 3y = 7

Combine the equation,

x = 4y

x - 3y = 7

Therefore,

4y - 3y = 7

y = 7

x = 4(7)

x = 28

Therefore,

side of the triangle = 8 + y = 8 + 7 = 15 inches

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The expressions related to the roots of each quadratic equation are listed below:

Case 1 - x² + 3 · x - 9 = 0

Roots: α = - 3 / 2 - 3√5 / 2, β = - 3 / 2 + 3√5 / 2

a) α + β = - 3

b) α² + β² = 27

c) α³ + β³ = - 108

Case 2 - x² + 4 · x - 2 = 0

Roots: α = - 2 - √6, β = - 2 + √6

a) α + β = - 4

b) α² + β² = 20

c) α³ + β³ = - 88

This question consists in two parts, find the roots by factoring the quadratic equations by algebra properties and determine the expressions based on the two roots of each expression. A root is a value of x such that the polynomial is equal to zero.

Case 1

x² + 3 · x - 9 = 0

x² + 3 · x = 9

x² + 3 · x + 9 / 4 = 9 + 9 / 4

(x + 3 / 2)² = 45 / 4

x + 3 / 2 = ± 3√5 / 2

x = - 3 / 2 ± 3√5 / 2

The roots are α = - 3 / 2 - 3√5 / 2 and β = - 3 / 2 + 3√5 / 2 and the following expressions are evaluated:

a) α + β = - 3

b) α² + β² = (- 3 / 2 - 3√5 / 2)² + (- 3 / 2 + 3√5 / 2)² = 27

c) α³ + β³ = (- 3 / 2 - 3√5 / 2)³ + (- 3 / 2 + 3√5 / 2)³ = - 108

Case 2

x² + 4 · x - 2 = 0

x² + 4 · x + 4 = 6

(x + 2)² = 6

x + 2 = ± √6

x = - 2 ± √6

The roots are α = - 2 - √6 and β = - 2 + √6 and the following expressions are evaluated:

a) α + β = - 4

b) α² + β² = (- 2 - √6)² + (- 2 + √6)² = 20

c) α³ + β³ = (- 2 - √6)³ + (- 2 + √6)³ = - 88

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Answer:

it would be 150 more, so 1650

Step-by-step explanation:

divide 1500 by 10 to get 10%

Answer:

-52

Step-by-step explanation:

I hope this helps!

Answer: -52

Step-by-step explanation: Using PEMDAS

(2x3)+4-62

6+4-62

10-62

= -52

The number of sodas that can fit in inside each cooler is 8

From the question, the given parameters are:

Number of packs = 6

Kinds of soda = 4

Number of cooler = 3

The number of sodas in each cooler is calculated as

Sodas = Number of packs x Kinds of soda/Number of cooler

Substitute the known values in the above equation

So, we have

Sodas = 6 x 4/3

Evaluate

Sodas = 8

Hence, there are 8 sodas in each cooler

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56 small cubes can be placed in the given cuboid that has the given dimensions.

A cuboid's volume can be calculated using the formula below:

Volume of a cuboid = (length)(width)(height).

A cube has equal height, length, and width. Therefore, the volume of a cube is calculated as:

Volume of a cube = (side length)³.

The number of small cubes that can be placed in the given cuboid = volume of the cuboid/volume of one small cube.

Find the volume of the cuboid:

Length = 60 cm

Height = 54 cm

Width = 30 cm

Volume of the cuboid = (60)(54)(30)

Volume of the cuboid = 97,200 cm³

Find the volume of one cube:

Side length of one small cube = 12 cm

Volume of one small cube = (12)³

Volume of one small cube = 1,728 cm³.

Number of small cubes that will be placed in the cuboid = 97,200/1,728 ≈ 56 cubes.

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The graph of the function after transformation is attached below.

The connection between several systems is defined by coordinate transformations, which offer formulas for the coordinates in one system in terms of the coordinates in another system.

The graph of the transformed function is attached below. The red graph indicates the parent function f(x) = x² and the blue graph indicated the graph of transformation g(x) = x² - 2

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Answer:

(a - b)/(a + b).

Step-by-step explanation:

a²-ab-ac+bc / a² +ab-ac-bc

= a(a - b) - c(a - b) / a(a + b) - c(a + b)

= (a - c)(a - b) / (a - c)(a + b)

The (a - c) is common to top and bottom, so

= (a - b)/(a + b).

Answer: A is not equivalent to the other 2

Step-by-step explanation:

A. 15j+30

B. 5(3j-6) = 15j-30

C 3(5j-10) = 15j-30

multiply the stuff inside paranthesis for the last 2

So a is the outsider

The surface area of a cylinder is equal to 208π square units.How to calculate the surface area of right cylinder?The surface area is the sum of the areas of all faces of the solid. In the case of a right cylinder, the surface area is the sum of the two areas of the circular base and the lateral area (A), in square units, whose formula is described below:A = 2π · r² + 2π · r · h           (1)Where:r - Base radiush - HeightIf we know that r = 8 and h = 5, then the surface area of the right cylinder is:A = 2π · 8² + 2π · 8 · 5A = 208πThe surface area of a cylinder is equal to 208π square units.

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{(-4)}}} \implies \cfrac{-6}{8 +4}\implies {\Large \begin{array}{llll} -\cfrac{1}{2} \end{array}}[/tex]

Thus cost per person c as a function of the number of people n is

c(n) = 43 + (n-1)(43-(n-1)2) and amount she makes is  $229

In the problem it is given that Elizabeth gives a walking tour of a popular tourist city to one person for 43 to increase her​ business, she would lower the price by​ $2 per person for each additional person. we have to find the cost per person c as a function of the number of people n on the tour. Also the amount she makes for a tour with 7 people.

So we can write it as

c(1) = 43

c(2) = 43 + 41

c(3) = 43 + 2(43-2*2)

c(4) = 43 + 3(43-3*2)

c(n) = 43 + (n-1)(43-(n-1)2)

To find the amount she makes we write c as a function of n where n=7

c(7) = 43 + 6(43-6^2) = 43 + 6*31 = 43 + 186 = $229

Thus cost per person c as a function of the number of people n is c(n) = 43 + (n-1)(43-(n-1)2) and amount she makes is  $229.

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Answer:6+2w=h

The height of the tree will be 32 inches on week 13

Step-by-step explanation:

ok

The Radical Form is [tex]185x^3y^4[/tex].

What is the Radical Form?

If n is a positive integer that is greater than 1 and 'a' is a real number then,

 [tex]n\sqrt{a} = a1n[/tex]   where n is called the index, a is called the radicand, and the symbol [tex]\sqrt{}[/tex] is called the radical. The left side of this equation is often called  The radical form and the right side is often called the exponent form.

Now, The question is :

The Expression is : (5x3y4)37

Convert to Radical form by using the formula :

[tex]a^\frac{x}{n} = \sqrt[n]{a^x}[/tex]

(5x3y4)37 = [tex]185x^3y^4[/tex]

Therefore, The Radical Form is [tex]185x^3y^4[/tex]

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The standard deviation of the distribution of sample means (that is, the standard error, sigma_m) is; 2.9698

From the complete question written below, we are given that;

Mean Number; M = 103.4

Standard deviation; σ = 21

Sample size; n = 50

Now, in statistics, the formula for the standard error of mean is;

σM = σ/√n

Plugging in the relevant values gives us;

σM = 21/√50

σM = 2.9698

The z score typical average difference between the mean number of seats is;

z = (103.4 - 99.2)/( 2.9698 )

z = 1.41

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Complete Question is;

There are 559 full-service restaurants in Delaware. The mean number of seats per restaurant is 99.2. [Source: Data based on the 2002 Economic Census from U.S. Census Bureau.]

Suppose that the true population mean mu = 99.2 and standard deviation sigma = 21 are unknown to the Delaware tourism board. They select a simple random sample of 50 full-service restaurants located within the state to estimate mu. The mean number of seats per restaurant in the sample is M = 103.4, with a sample standard deviation of s = 18.2. The standard deviation of the distribution of sample means (that is, the standard error, sigma_m) is_.

Step-by-step explanation:

22. 7 + x

24. 5x

26. f/10

28. 3x + 16

30. k² - 11

32. x + 10

34. 18q

23. x - 35

25. x/3

27. 45/r

29. 18 - 3d

31. 20/t⁵

(although, if being superficial, it could mean (20/t)⁵)

33. (k + 2) - 15

35. 2m + 6

If x= -12 and y=8 then the value of 2/x-3/ - /2y/ over /x+y/ is: 7/2. See the explanation below.

First, recall that the numbers enclosed in |   | are absolute values. That is they remain in the positive domain regardless of their polarity. Recall that the absolute value is the distance between a number and Zero.

Since we know:

x = -12; and

y = 8

Hence,

[2|x-3| - |2y|] / |x+y|

= [2|-12-3| - |2 * 8| ]/ (|-12+8|)
= [2|-15| - | 16|] / |-4|

= ((2*15) - (16))/4    [Using the absolute values]

= (30 -16)/4

= 14/4

= 7/2

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Answer:

9. 160/2

10. 270/9

Step-by-step explanation:

To find unit rates, divide the top number (numerator) by the bottom number (denominator).

9.

160/2 = 80 mph

210/3 = 70 mph

10.

270/9 = 30 ft/min

180/9 = 20 ft/min

The result of the Nested absolute inequality  when resolved gives:
x = -10, 0. See the solution below.

It is to be noted that when one absolute-value expression is inside another one, this is called a "nested" expression. Absolute expressions are expressions that values that can NEVER be negative.

The solution hence is given as follows:

Given: ||x-5|4|≤1

One absolute-value expression is stacked inside another in this equation. I'll work from the outside in, sorting items into their respective cases. Assume the argument of the outer bars is negative (do the "minus" case):

Step 1 - first splitting:

|x-5| -4 ≤ -1
|x-5|  ≤ 3

I have to stop here since the last statement above states that an absolute value equals a negative number. Absolute values, on the other hand, are never negative! As a result, this step is invalid; it yields no viable solutions to the original problem.

Now I'll look at the scenario where the argument of the outside bars is positive (the "plus" case):

|x-5| -4 ≤ 1

|x-5|  ≤ 1 + 4

Recall that absolute values are never negative. This equation is correct, and I've isolated the leftover absolute value, so I'll go over the two situations again.

Step 2 - First, consider the "minus" case:

x+5  ≤ -5

x ≤ -5-5
x≤ -10

The variable can have a "minus" value; the sole constraint is that an absolute-value expression cannot have a "minus" value. Now consider the "plus" case:

⇒ x + 5 ≤ 5 again recall that this is an absolute expression hence the laws of polarity while cross the inequality sign is suspended.

x ≤ 5-5

x≤0

Hence the answer which is complete is:

x = -10, 0

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Step-by-step explanation:

[tex]sa = 2\pi \: r {}^{2} + 2\pi \: rh \\ = 2 \times 3.14 \times 3 { }^{2} + 2 \times 3.14 \times 11[/tex]