Evaluate f(x)=3x-9, when x=-2
A. -18
B. -33
C. -3
D. -15

Answer:

[tex]x = 9[/tex]

Step-by-step explanation:

1 ) Cross-multiply...

[tex]\frac{3}{x}[/tex] ÷ [tex]\frac{15}{45}[/tex]

[tex]3[/tex] × [tex]45 = 15[/tex] × [tex]x[/tex]

[tex]135=15x[/tex]

2 ) Flip the equation...

[tex]15x=135[/tex]

3 ) Divide both sides by 15...

[tex]\frac{15x}{15}[/tex] = [tex]\frac{135}{15}[/tex]

[tex]x = 9[/tex]

Hope this helps! :)

Answer:

  D.  2x -y = 2

Step-by-step explanation:

You want to know the standard-form equation of the line through points (-1, 4) and (2, 2) as shown on the graph.

The graph shows the x-intercept of the line is a=1, and the y-intercept of the line is b=-2. This means the intercept form of the equation is ...

  x/a +y/b = 1

  x/1 +y/(-2) = 1

Multiplying this equation by 2 gives ...

  2x -y = 2 . . . . the standard form equation for the line

__

Additional comment

The standard form equation can also be developed from the coordinates of points on the line:

  (y2 -y1)x -(x2 -x1)y = (y2 -y1)x1 -(x2 -x1)y1

  (2 -(-4))x -(2 -(-1))y = (2 -(-4))(-1) -(2 -(-1))(-4)

  6x -3y = -6 +12

Dividing by 3 gives the standard form equation ...

  2x -y = 2

The image point of (-8, 1) after the transformation D₂ о R180° is equal to (16, -1).

Given that,

The point is (-8,1)

We must locate the point's picture. ​

In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has the coordinates (-x, -y).

We have the following for a 2 scale factor dilation: ​

Point A (-8, 1)  

= (-8 × 2, 1 × 2)  

= Point A'  is (-16, 2)

By applying a rotation of 180° to the given point, the coordinates of its image is given by:

(x, y)→(-x, -y)

Points A' = (-16, 2)

Points A' = (-(-16), -(1)) = (16, -1).

Therefore, The image point of (-8, 1) after the transformation D₂ о R180° is equal to (16, -1).

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The pairs of events, A and B, that are disjoint include option A and B.

It should be noted that disjoint events simony means the events that are mutually exclusive as they can't occur at the same time.

For option A, because a person can be either male or female but not both, events A and B are disjoint.

For B, because the person already earns more than $100,000, events A and B are not disjoint.

For C, because the sum of two dice cannot be three when one die is three, events A and B are disjoint.

Therefore, A and C are disjoint.

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Complete question

Which of the following pairs of events, A and B, are disjoint?

(a) A person is selected at random. A is the event "sex of the person selected is male" and B is the event "sex of the person selected is female."

disjoint / not disjoint

(b) A person is selected at random. A is the event "the person selected earns more than $100,000 per year" and B is the event "the person selected earns more than $250,000 per year."

disjoint / not disjoint

(c) A pair of dice are tossed. A is the event "one of the dice is a 3" and B is the event "the sum of the two dice is 3."

disjoint / not disjoint

Answer:

Step-by-step explanation:

Abigail Henderson's budget of $1,360 and the $1.30 and $1.60 trading price of the currency of country A and country B gives;

The number of each currency Abigail plans to buy are;

A budget provides an estimation of a person, business, or country's income and expenditure over a specified period or duration.

The amount Abigail Henderson budgeted = $1,360

The per currency exchange rate for country A = $1.30

The per currency exchange rate for country B = $1.60

The number of currency A Abigail wants = 4 × The number of currency B

Which gives; x = 4·y

The equation that represents Abigail's total cost of buying currencies is presented as follows;

1.3·x + 1.6·y = 1,360

Plugging in the value of x gives;

1.3 × (4·y) + 1.6·y = 1,360

6.8·y = 1,360

y = 1,360 ÷ 6.8 = 200

The number of currency of country B, Abigail purchases, y = 200

The number of currency of country A Abigail plans to buy, x = 4 × 200 = 800

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For x = -3 the relation will be a function.

We know that a relation is a function when for each input there is exactly one output.

In this question, we need to find the value of x for which the relation will be a function.

We need to select the value of x such that x ≠ 1, 3, 4, -4

This means x must be -3

Therefore, For x = -3 the relation will be a function.

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Answer:

19 liters

Step-by-step explanation:

The value of the function f(x) = 4 ( 7x ) for x = -2 is equal to f( -2 ) = -56.

As given in the question,

Given expression is equal to :

f(x) = 4 ( 7x )

Calculate the value of the given function for x = -2 is given by :

Substitute value of x = -2 we get.

f(-2)

= 4 ( 7 ( -2) )

Seven is positive and 2 is negative , multiplication of positive to negative is always negative.

So, 7 ( -2 ) is -14 Substitute in above equation we get,

= 4 ( -14 )

= -56

Therefore, the value of the function f(x) = 4 ( 7x ) for x = -2 is equal to

f( -2 ) = -56.

The complete question is  :

If f(x) = 4 (7x) , what is the value of f(-2)?

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Answer:

82.96-22% = 67.83

Step-by-step explanation:

82.96-22% = 67.83

The graph and factor to the given equation are x= 50 or x=0.

What is equation?

An equation may be a formula in arithmetic that expresses the equality of 2 expressions by connecting them with the sign =.

Main body:

I am assuming the equation as : -0.01[tex]x^{2}[/tex] + 0.5x =0

Now first removing the decimal from the equation ,

-[tex]x^{2}[/tex]/100 + 5x/10 = 0

-[tex]x^{2}[/tex] + 50 x = 0

switching signs , we get

[tex]x^{2}[/tex] - 50x= 0

taking x as common

x(x-50) =0

so either x = 0

or

x- 50 = 0

x =50

Hence the value of x are 0 or 50.

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A recording of $0 for the family simply means that they have not saved anything or have spent all the savings.

Savings simply means keeping of miney for a period of time in order to cater for future expenses. Saving is defined as income that is not spent or deferred consumption. Saving methods include putting money aside in a deposit account, a pension account, an investment fund, or as cash. Saving also entails lowering expenses, such as recurring costs.

Here, the family wants to save $100 each month and they record their progress toward this goal at the end of each month.

A recording of $0 simply means no savings.

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The classification and the output rule for each function in this problem is given as follows:

1. Output rule: y = 5x + 11. Classification: Linear.

2. Output rule: y = 2^x. Classification: Exponential.

3. Output rule: y = 3 if |x| is even, y = 1 if |x| is odd. Classification: Neither.

A linear function is defined when the increase of 1 in x result in the addition of a constant to y, hence the rule is:

y = mx + b.

In which:

Hence, for the first table, as 5 is added to x when x increases by one, the rule is:

y = f(x) = 5x + 16.

An exponential function is defined when the increase of 1 in x result in the multiplication of a constant to y, hence the rule is:

y = a(b)^x.

In which:

Hence, for the second table, the rule is:

y = 2^x.

For the third table, none of the definitions for linear and for exponential functions are true, hence the function is neither, as it is a piece-wise function that assumes one value for odd numbers and another for even numbers.

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Answer:

0.150985

Step-by-step explanation:

You add the two decimals together which gives you 120788.

Then, you move the decimal 4 places which is 12.0788.

Then you divide 12.0788 by 2 which gives you 6.0394.

Finally, you divide 6.0394 by 40 which gives you 0.150985.

The solutions to the financial ratio requirements based on the supplied facts are:

A. Current ratio is 1.125.

B. Acid test is 1.

C. Average days' collection is 26.7 days.

D. Asset turnover is 1.4x.

E. Profit margin on sales is 14.63%.

Financial ratios are ratios that show the relative magnitude of one financial account to another.

Financial ratios are used to compare or represent an entity's financial performance or position in relative terms.

Current Ratio = Current Assets ÷ Current Liabilities

= $18,000 ÷ $16,000

= 1.125

Acid Test Ratio = (Current Assets - Inventory) ÷ Current Liabilities

= ($18,000 - 2,000) ÷ $16,000

= $16,000 ÷ $16,000

= 1

Average Days' Collection = Accounts Receivable ÷ Net Sales x 365 days

= $3,000 ÷ $41,000 x 365

= 26.7 days

Asset Turnover = Net Sales ÷ Total Assets

= $41,000 ÷ $29,000

= 1.4x

Profit Margin on Sales = Net Income ÷ Net Sales x 100

= $6,000 ÷ $41,000 x 100

= 14.63%

Current Assets = $18,000

Accounts Receivable = $3,000

Current Liabilities = $16,000

Inventory = $2,000

Net Sales = $41,000

Total Assets = $29,000

Net Income = $6,000

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Answer:

2nd

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

the numbers from -10 to 10 cancel out, so all that is left is 11+12=23

The equation of the parallel line t is y = -4x  - 9

The equation of line s given as

y = -4x - 5/3

Also, from the question

The point on line t is given as

Point = (-3, 3)

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = -4

This means that the slope of y = -4x - 5/3 is -4

The slopes of parallel lines are equal

This means that the slope of the line t is -4

The equation of the parallel line is then calculated as

y = m(x - x₁) +y₁

Where

m = -4

(x₁, y₁) = (-3, 3)

Substitute the known values in the above equation

y = -4(x + 3) + 3

Evaluate

y = -4x - 12 + 3

Evaluate the sum

y = -4x  - 9

Hence, the parallel line has an equation of y = -4x  - 9

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Answer:

0

Step-by-step explanation:

subtracting same numbers give you zero

The solution to the system of equations, in terms of x, considering the augmented matrix, is of:

The augmented matrix of a system of equations is built as follows:

In this problem, there are three columns before the |, the there are three variables given as follows:

x,y and z.

The expression from the first row is:

x -0.05z = 2.

The expression from the second row is:

y + 2z = 1.

The third row is all zero, meaning that there is a free variable, hence the solution to the system is written as a function of x as follows:

x - 0.05z = 2

0.05z = x - 2.

z = (x - 2)/0.05

z = 20x - 40.

Hence the solution for y is:

y = 1 - 2z

y = 1 - 40x + 80

y = -40x + 81.

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Answer:

supplementary angles

Step-by-step explanation:

1.) angle 1& angle 2 is supple. angle 2 & and angle 3 is supple.; given

2.) measure of angle 1+ measure of angle 2= 180, measure of angle 2+ measure of angle 3=180; Def. of Supple.

3.) measure of angle 1+ measure of angle 2 = measure of angle 2+measure of angle 3; Transitive

4.) measure of angle 1= measure of angle 3; Subtraction prop. of equality

5.) measure of angle 1 is congruent to measure of angle 3; Def. of Congruence

Tan of  arc tan x is equal to x when the angle x is 0 degrees

Tangent is the ratio of the side opposite the angle we know or want to know over the side adjacent to that angle, and is sometimes abbreviated as tan.

In a right angle triangle, the formula for tan is as below

Tangent (tan) = opposite / adjacent

Arc tan (tan^(-1)) is the inverse of tan = adjacent / opposite

Arc tan is equal to tan when the angel is zero degree

therefore, tan (tan^(-1) x) = x

when x = 0

tan^(-1) 0 = 0

tan 0 = 0

tan (tan^(-1) 0)

tan (0)

0

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complete question

At what point does tan(tan^-1(x))=x

The total number of cattle Frank currently owned could be C)350

The problem is asking multiples of 7.

Multiples of 7 come into play after working the the percentage as follows

Frank sold 30%, the percentage left is

= 100% - 30%

= 70%

= 0.7

The multiple of 7 that is a number 7 will divide without remainder here is 350 and this is the correct answer.

= 350 / 0.7

= 500

This means Frank had 500 cattle sold

0.3 * 500 = 150

currently having

= 500 * 0.7 = 350

= 500 - 150 = 350

Remember that a cattle will always be in whole number

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Answer:

y = 3x + 12

Step-by-step explanation:

y = mx + b  
The m is the slope and the b is the y intercept.

Slope:

Change in y over the change in x.  The ordered pair is written in the form (x,y)

[tex]\frac{12-3}{8-5}[/tex] = [tex]\frac{9}{3}[/tex] = 3

The slope is 3.

Use the slope of the 3 and the x and y from one of the ordered pairs given.  I am going to use the point (5,3), but either point will work

slope 3

x = 5

y=3  Plug these all in and solve for b

y = mx + b

3 = (3)5 + b

3 = 15 + b  Subtract 15 from both sides

-12 = b

This is the y intercept

y = 3x - 12

Answer:

Slope-intercept form,

→ y = 3x - 12

Step-by-step explanation:

Formula we use,

→ y = mx + b

The value of slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (12 - 3)/(8 - 5)

→ m = 9/3

→ [ m = 3 ]

Then the value of b will be,

→ y = mx + b

→ 12 = (3)8 + b

→ b + 24 = 12

→ b = 12 - 24

→ [ b = -12 ]

Now the slope-intercept form is,

→ y = mx + b

→ [ y = 3x - 12 ]

Hence, the answer is y = 3x - 12.

Emi will need to locate the whole in this case because she already has the part and the percentage.

In mathematics, the total number of items being analyzed, in this case, the total number of dogs, is represented by a whole.

The term "part" refers to a quantity that is typically smaller than the total and describes particular qualities. For instance, 20 of the 30 students in a classroom enjoy playing basketball. The part is 20 then.

The relationship between the part and the whole is represented by the percentage, which is a number followed by the symbol%. In this instance, the proportion of boxers and overall dogs are related.

Emi already knows the percentage (50%), the part (16), and the total number of dogs, which in this case is 32, as a result of this.

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Answer:

Step-by-step explanation:

Given:

2[tex]x^{3}[/tex]+7[tex]x^{2}[/tex]+x-10

factor it

I used MatLab   roots(x)  to find these so I kinda cheated :P

-2.5,  -2 ,  1

so we know  -2 is a factor and,  then

x+2=0    is a factor

so the "x+2"  answer C)

The order of reasons that best justifies each step of the equation's solution is as follows;

It follows from the task content that the reasons which best justify each step of the solution be identified.

Therefore; Given the equation; -2(x - 5) = 4x; we have;

Ultimately, the reasons which best justifies each of the steps as required are as provided above.

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Answer:  Justification for each step is provided below.

Step-by-step explanation:

Original Equation: -2(x - 5) = 4x

-2x + 10 = 4x  -->  Distributive property - simplify the left side

-2x + 10 + 2x = 4x + 2x  -->  Addition property of Equality - add 2x to both sides

10 = 6x  -->  Simplifying

10/6 = 6x/6   -->   Division Property of Equality - divide each side by 6

5/3 = x   -->  Simplifying

The probability that the proportion of defective bottles in a sample of 546 bottles would differ from the population proportion by greater than 4% is: 10.9069.

To obtain the correct value, we need to use the formula for the Z score. This formula requires that we subtract the average or mean value from the data point provided and divide the remaining value by the standard deviation.

Here is the formula:

z = (x-μ)/σ

First population proportion = 0.24

The sample proportion, hat p = 0.04

​Z score =

[tex]0.04 - 0.24 / \sqrt 0.24 (1 - 0.24) / 546[/tex]

So, the Z score will

= -10.9469

So, when the z score = - 10.9469, the probability that Z is greater than - 10.9469,  is = 10.9069

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Answer:

below

Step-by-step explanation:

0.1

0.15

0.175

0.00125

1.13

2.02125

Answer:

  B

Step-by-step explanation:

You want to know the 15% down payment, the mortgage amount, the value of 1 point, and the total interest cost for a 6.5% 30 year loan on a $210,000 home.

The answer choices all have the down payment as $31,500 and the loan value as $178,500. A "point" is one percent of the loan value (not the home value), so ...

  1 point = 0.01 × $178,500 = $1785 . . . . . . eliminates choices A and C

The difference between choices B and D is in the value of the interest paid. Your experience with 30-year loans in this interest rate range tells you that the interest paid is between 1 and 2 times the loan value. That is, the chice $227,667 is more likely correct than the choice $406,167.

Comparing these two numbers, we see they differ by 178,500, which is the value of the loan. That is, we can guess that 406,167 is the total amount repaid, not just the interest.

Answer choice B is the only one that makes sense.

If you like, you can work the problem.

  down payment = 15% × $210,000 = $31,500

  loan amount = $210,000 -31,500 = $178,500

  one point = 0.01 × $178,500 = $1785

The monthly payment is found using the amortization formula:

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

  A = 178500(0.065/12)/(1 -(1 +0.065/12)^(-12·30)) ≈ 1128.24

The monthly payment amount is about $1128.

So, the total repaid is 360 payments of $1128.24, or $406,167.

The interest paid is this amount less the principal:

  interest paid = $406,167 -178,500 = $227,667