Part C Rewrite the expression from Part B to get the variable b alone on one side of the equation. (This is also called isolating b.)​

Answer:

15. -3 1/4

16. -4 1/2 OR -4 2/4

17. 1 1/4

18. -5 3/4

19. 1/2 OR 2/4

20. -2 1/2 OR -2 2/4

Step-by-step explanation:

Answer:

15) -3.25

16) -4.5

17)1.25

18)-5.75

19).5

20)-2.5

Case 2

The quadratic equation x² - 14 · x + 48 = 0 have the following roots: x₁ = 6 and x₂ = 8. (Correct choice: B)

Case 3

We need to add + 64 to both sides. (Correct choice: B)

Case 4

We need to add + 16 to both sides. (Correct choice: C)

In this problem we find three cases of quadratic equation that are not perfect square trinomials, these equations can be rewritten partially in that form by algebra properties. Completing the square offers a quick method to determine the roots of quadratic equations with integer coefficients. Now we proceed to determine the solutions corresponding to each case:

Case 2

x² - 14 · x + 48 = 0

x² - 14 · x + 49 = 1

(x - 7)² = 1

x - 7 = ± 1

x = 7 ± 1

The roots of the quadratic equation x² - 14 · x + 48 = 0 are x₁ = 6 and x₂ = 8, respectively.

Case 3

x² - 16 · x = - 21

x² - 16 · x + 64 = 64 - 21

(x + 8)² = 43

The first step consists in adding both sides by + 64.

Case 4

x² - 8 · x = 0

x² - 8 · x + 16 = 16

(x - 4)² = 16

The first step consists in adding both sides by + 16.

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Answer:

  (a)  0.0062

Step-by-step explanation:

You want the probability P(X > 14.5) given that X has a normal distribution with mean 2 and variance 25.

This probability can be found using a suitable calculator or spreadsheet. The calculator in the attachment specifies the normal distribution using mean and standard deviation, so we need to find the square root of the variance.

  P(X > 14.4) ≈ 0.0062

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Answer:

72 ounces

Step-by-step explanation:

1 pint = 16 ounces

4.5 pints* 16 ounces = 72 ounces

*4.5=4 1/2

Answer:

  18086.4 yd³

Step-by-step explanation:

You want the volume of an oblique cylinder with a radius of 12 yd and a height of 40 yd.

The volume is given by the formula ...

  V = πr²h

  V = 3.14·(12 yd)²(40 yd) = 18086.4 yd³

The volume of the cylinder is about 18086.4 cubic yards.

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Answer:

m/n

Step-by-step explanation:

if you have same variable on denominator AND numerator, you can cancel them

Since p is on both sides, cancel.

You are left with m/n

Combine like terms , we get \(g^3+3g^2+2g\).

In Algebra, the like terms are defined as the terms that contain the same variable which is raised to the same power. In algebraic like terms, only the numerical coefficients can vary. We can combine the like terms to simplify the algebraic expressions so that the result of the expression can be obtained very easily.

For example, 4x + 10x is an algebraic expression with like terms. In order to simplify this algebraic expression, we can add the like terms. Thus, the simplification of the given expression is 14x. In the same way, you can perform all the arithmetic operations on the like terms.

Collect like terms:

\(g^3+g^2+g+2g^2+g\)

Combine like terms:

\(g^3+3g^2+2g\)

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Answer: the answer is C

Well if you follow PEMDAS you would have to do the parentheses first but you can’t subtract 18 from a variable (Z) so then you move on to the 2 and you have to do the opposite so you don’t multiply both sides by 2 you have to divide both sides by 2. And that’s how u get C

Answer

The total rainfall last year is 12.75 inches.

Step-by-step explanation:

The total rainfall this year is 10.2 inches.

Let the total rainfall last year be x inches.

It is given that the total rain this year 20% less than last year's total rainfall

Therefore total rainfall last year is 12.75 inches.

Check the picture below.

\(\textit{Sum and Difference Identities} \\\\ cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\[-0.35em] ~\dotfill\\\\ cos(105^o)\implies cos(60^o+45^o)\implies cos(60^o)\cdot cos(45^o)-sin(60^o)\cdot sin(45^o) \\\\\\ \cfrac{1}{2}\cdot \cfrac{\sqrt{2}}{2}~~ - ~~\cfrac{\sqrt{3}}{2}\cdot \cfrac{\sqrt{2}}{2}\implies \cfrac{\sqrt{2}}{4}~~ - ~~\cfrac{\sqrt{6}}{4}\implies {\Large \begin{array}{llll} \cfrac{\sqrt{2}-\sqrt{6}}{4} \end{array}}\)

Answer: The second and last one

Step-by-step explanation:

Answer:

let x = the number of nickels

the number of pennies can be represented by (56 - x)

.05x + .01(56 - x) = 1.52

5x + (56 - x) = 152    if in the above line we multiply both sides of the equation by 100

4x + 56 = 152

4x = 96

x = 24

There are 24 nickels and 56 - 24 = 32 pennies

24 nickels are worth 24 * 5 = $1.20 and 32 pennies are obviously worth 32 cents, so the total is 1.20 + 0.32 = $1.52

Step-by-step explanation:

Answer:

you download the App your all solution is defined

When the consumption schedule lies below the 45-degree reference line, it means that at every level of income, people are consuming less than their income.

The consumption schedule represents the relationship between income and consumption in an economy, while the 45-degree reference line represents the line where income and consumption are equal.

In this scenario, saving occurs because people are not spending all of their income. The difference between their income and consumption is their savings. Thus, the amount of saving in the economy will increase as the consumption schedule moves further below the 45-degree reference line.

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When the consumption schedule lies below the 45-degree reference line, saving what does it means?

Answer:Let x be the cost of a hard-cover book and y be the cost of a paperback book.

We know that Steve spent 2 hard-cover books and 3 paperback books. So we can write the equation as:

2x + 3y = 50 - 15.5

2x + 3y = 34.5

We also know that he was planning to buy 3 hard-cover books and 4 paperbacks, so we can write another equation as:

3x + 4y = 50

Now we have a system of two equations with two unknowns:

2x + 3y = 34.5

3x + 4y = 50

We can use the first equation to eliminate one variable by multiplying both sides by 2 and then subtracting 3y:

4x + 6y = 69

3x + 4y = 50

x = 19.5

Now we can substitute this value of x into the second equation and find the value of y:

3(19.5) + 4y = 50

58.5 + 4y = 50

4y = -8.5

y = -2.125

Therefore, the cost of a hard-cover book is $19.5 and the cost of a paperback book is $-2.125.

Note that the cost of a paperback book is a negative value which is not possible in this case. It means that the given information does not have a solution.

Step-by-step explanation:

The number of years for 500g of radium to decay to 5g will be 0.6 years.

Let b is the base and n is the power of the exponent function and a is the leading coefficient. The exponent is given as

y = a(b)ⁿ

The quantity (Q) remaining after t years and k is the decay constant 0.00043.

Then the exponent function will be

\(\rm Q = 500 * (0.00043)^t\)

Then the number of years for 500g of radium to decay to 5g will be

\(\rm 5 \ \ \ \ = 500 * (0.00043)^t\\\\0.01 = 0.00043^t\)

Taking log on both sides, then we have

t × log 0.00043 = log 0.01

                     t = 0.594 ≈ 0.6 years

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Answer:

Rotation

Step-by-step explanation:

Reflection can also be done to map Triangle  DEF onto Triangle D'EF'

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Triangle DEF was rotated about point E to form triangle D'E'F'. Reflection can also be done to map Triangle  DEF onto Triangle D'EF'

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Answer:

\(x=-2\) ⇒ \(y=2\)

\(x=-1\) ⇒ \(y=-4\)

\(x=0\) ⇒ \(y=-6\)

\(x=1\) ⇒ \(y=-4\)

Step-by-step explanation:

Formula: \(y=2x^{2} -6\)

To find the value of \(y\) add the value of \(x\) given:

Now solve for each:-

For:

\(x=-2\)

\(y=2(-2)^{2} -6\)

\(y=2\)

For:

\(x=-1\)

\(y=2(-1)^{2} -6\)

\(y=-4\)

For:

\(x=0\)

\(y=2(0)^{2} -6\)

\(y=-6\)

For:

\(x=1\)

\(y=2(1)^{2}-6\)

\(y=-4\)

hope this helps.....

Answer:

the answer will be d=130

Step-by-step explanation:

substruct 110 minus 50 we get 60

A sample statistic is is any quantity from the sample of a population.

We can see in the last option, that from the population (total of subjects of study) Kaisa, selected 84 of the total students. This fits in to the definition of sample statistic.

Thus, the correct option is the last one.

To solve this question, you have to look for the answers in the table.

Let's analise each part of the question to solve it:

(a) f(1) =

f(1) means the output of the function [f(x)] when x = 1.

Looking for x =1 in the table, you can see that f(x) = 0.

f(1) = 0.

(b) f(x) = 3, x =

Now, you have to find the input (x) when the outpout [f(x)] is 3.

Looking for f(x) = 3, you can see that x = 7.

f(x) = 3, x = 7.

(c) f⁻¹(0) =

Now, you have to evaluate the inverse function.

To look for the values of the inverse function, x will be the output and f⁻¹ will be the input.

To look for f⁻¹(0), look for f(x) = 0 (input) and the output will be 1

f⁻¹(0) = 1.

(d) f⁻¹(x) = 7; x =

Again, you have an inverse function. So, 7 will be the input in the table (x). x is 7 (output).

f⁻¹(x) = 7; x = 3.

Step-by-step explanation:

2x-1/y=w+2/2z

2x-1x2z=w+2xy

4xz-1=wy+2

4xz-1-2=wy

4xz/y-2=w

w=4xz/y-2

The solution of the expression is w = (4xz - 2z)/y - 2 which is the correct answer would be option (B)

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

Arithmetic operations can also be specified by the addition, subtracting, dividing, and multiplying built-in functions.

Given expression (2x-1)/y = (w+2)/2z

To determine the solution of (2x-1)/y = (w+2)/2z for w

⇒ (2x-1)/y = (w+2)/2z

Apply cross multiplication in the expression

⇒ (2x-1)×2z = (w+2)×y

We have to open the bracket above

⇒ 4xz - 2z = (w+2)×y

Divided by y both the side

⇒ (4xz - 2z)/y = w + 2

⇒ (4xz - 2z)/y - 2 = w

⇒ w = (4xz - 2z)/y - 2

Hence, the solution of the expression is w = (4xz - 2z)/y - 2

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Given the expression: (3.2+0.2)2+12​

To get the value of the expression, do the following:

1. add 3.2 and 0.2

2. multiply 3.4 by 2

3. add 6.8 and 12

So, the value of the expression = 18.8

Answer:

8x^3+8x^2-12x+7

Answer:

8x³ + 8x² - 12x + 7

Step-by-step explanation:

(8x² - 7x + 7) + (8x³ - 5x)

8x² - 7x + 7 + 8x³ - 5x

8x³ + 8x² - 12x + 7

I hope this helps!

The given value \(\frac{9}{10} * \frac{5}{6}\) as a fraction will be \(\frac{3}{4}\) .

Fraction is a numerical number represented in form of numerator and denominator.

We have,

\(\frac{9}{10} * \frac{5}{6}\)

Now,

First multiply numerator and then denominator of both numbers ;

i.e.

\(=\frac{9*5}{10*6}\)

\(=\frac{45}{60}\)

Now,

Simplify the above fraction,

We get,

\(=\frac{3}{4}\)

So, the the given numbers in fraction from is \(\frac{3}{4}\) .

Hence we can say that the given value \(\frac{9}{10} * \frac{5}{6}\) as a fraction will be \(\frac{3}{4}\) .

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A local deli makes turkey sandwiches and salami sandwiches at a weekly ratio of 2 salami sandwiches for every 5 turkey sandwiches. If the deli makes 60 turkey sandwiches this week, how many salami sandwiches did they make?

5 salami sandwiches

16 salami sandwiches

30 salami sandwiches

24 salami sandwiches

2 to 5 = x to 60

60/5 = 12

2 * 12 = 24