Rewrite the function by completing the square. f(x) = x2 - 8x + 7

Answer:

The second option.
y > x^2 + 4x -2

y < 3x +4

Step-by-step explanation:

First off, we can eliminate the last option because the graph shows that both inequalities are greater than or less than, but not equal to. We come to this conclusion because both lines on the graph are dashed meaning not equal to. Look at the attached image below (1).

Next, we can input the point (0,0) and test to see if the inequality works. If we input the point (0,0) into the second equation in the second option, we end up with 0 < 4. This is factual meaning that this is your answer.
Hope this helps! If I wasn’t clear enough or you need more information, please let me know in the comments. Have an amazing day!

Answer:

Your answer is 7^2.

Step-by-step explanation:

-------------------------

Have a great day,

Nish

The equivalent expression is [tex]7^{2}[/tex].

We have the following expression -

[tex]\frac{7^{-3} }{7^{-5} }[/tex]

We have to find its equivalent value.

[tex]f(x, y) =\frac{A^{x} }{A^{y} }[/tex]

In order to divide two exponents with same base, we use the 'Quotient property of exponents.

The equivalent expression can be written as -

f(x, y) = [tex]A^{x} A^{-y} = A^{x-y}[/tex]

In the question given we have -

[tex]\frac{7^{-3} }{7^{-5} }[/tex]

Using the property discussed above -

[tex]7^{-3}\;7^{5}[/tex] = [tex]7^{-3+5}[/tex] = [tex]7^{2}[/tex]

Hence, the equivalent expression is [tex]7^{2}[/tex].

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Answer:

A

Step-by-step explanation:

Based on the given table:

(x, y )  values  are

(-1, 0)

(0, 3)

(1, 6)

A.

y = 3x+3, substitute each x and y pair in the equation to see if it checks

(x= -1, y= 0)              (x= 0, y= 3)          (x= 1, y= 6)

0 = -1·3+3                 3 = 0·3 +3          6 = 1·3 + 3

0 = 0✅                    3 = 3✅               6 = 6✅

The company is considering the purchase of a new machine for $75,660 (based on the available data), and the payback period is 24 years.

The payback period is the time the company requires to recoup its investment for the new machine.

The payback period can be computed by dividing the investment cash outflows by the annual net cash inflows.

Initial investment in new machine = $75,660

Annual depreciation expense = $4,600

Investment period = 10 years

Annual sales revenue = $20,000

Annual expenses = $16,800

Ne annual cash inflow = $3,200 ($20,000 - $16,800)

Payback period = 24 years ($75,660/$3,200)

Thus, since the payback period is 24 years, while the investment period is 10 years, it sounds unwise for the company to continue the investment.

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The system of the linear systems of equation using substitution is;

3x-y=4

x+2y=6

from (2)

x = 6 - 2y

substitute into (1)

3x-y=4

3(6 - 2y) - y = 4

18 - 6y - y = 4

- 6y - y = 4 - 18

-7y = -14

y = 2

Substitute into

x+2y=6

x + 2(2) = 6

x + 4 = 6

x = 6 - 4

x = 2

2. 2x-y= -39

x+y= -21

From (2)

x = -21 - y

substitute into

2x-y= -39

2(-21 - y) - y = -39

-42 - 2y - y = -39

- 2y - y = -39 + 42

- 3y = 3

y = 3/-3

y = -1

substitute into

x+y= -21

x + (-1) = -21

x - 1 = -21

x = -21 + 1

x = -20

3. 2x+y =11

6x-5y =9

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1. Independent Variable (x) is the number of toys.

Dependent Variable (y) is the amount.

2. Graph A - Income Graph.

Graph B - Expense Graph.

3. Zandi won't make a profit while selling 5 toys.

4. Zandi must sell 10 toys to reach break-even.

5. Zandi's variable cost per toy is $15.

6. The total cost function is, total cost = 100 + 15x.

1. The independent variable will be the number number of toys marked on the x-axis, whereas the dependent variable will be the amount on the y-axis, as the cost and revenue both depend on the units.

2. Graph A will be Zandi's income as when the unit is 0, the income is 0, whereas graph B is the expense graph as when the unit is 0, still some fixed expenses are generated for example rent.

3. Zandi will make a loss while making and selling 5 toys as the amount on graph B corresponding to 5 toys, that is, the expenses, are greater than the amount on graph A corresponding to 5 toys, that is, the income.

4. The break-even is the point where the income = expense, which on the graph is at the point where the number of toys is 10.

Thus, Zandi must sell 10 boys to reach break even.

5. The variable cost per toy can be found as the slope of the expense graph, m = (400 - 100)/(20 - 0) = 300/20 = 15.

Thus, Zandi's variable cost is $15.

6. Total cost = Fixed cost + a number of units*variable costs.

Thus, the total cost = 100 + 15x.

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There are 66 ways Kim can put the 10 identical lamps on the 3 identical tables

The given parameters are:

The combination involving identical objects is calculated using:

(n + r - 1)C(r - 1)

So, we have:

n + r - 1 = 10 + 3 - 1

Evaluate the sum

n + r - 1 = 13 - 1

Evaluate the difference

n + r - 1 = 12

Also, we have:

r - 1 = 3 - 1

Evaluate the difference

r - 1 = 2

So, we have:

(n + r - 1)C(r - 1) = 12C2

Apply the following combination formula:

nCr = n!/((n - r)!r!)

So, we have:

12C2 = 12!/((12 - 2)! * 2!)

Evaluate the difference

12C2 = 12!/(10! * 2!)

Expand the numerator

12C2 = 12 * 11 * 10!/(10! * 2!)

Evaluate the quotient

12C2 = 12 * 11/2!

Expand the denominator

12C2 = 12 * 11/2 * 1

Evaluate the product

12C2 = 132/2

Evaluate the quotient

12C2 = 66

Hence, there are 66 ways Kim can put the 10 identical lamps on the 3 identical tables

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Answer:

2√(133)

Step-by-step explanation:

Triangle 1 = 8, 12, ?

triangle 2 = 18, x, ?

we have to find value of x which is a hypotenuse

a² + b² = c²

8² + 12² = 64 + 144 = √208 = 14.4222051019

x = 14.4222051019² + 18²

= 208 + 324

= 532

x = √532 = 2√(133)

the ratio of the area of the triangle to the area of the rectangle is 1: 2

The formula for calculating the area of a triangle is;

Area of triangle = 1/ 2 base × height

The formula for area of a rectangle is;

Area of a rectangle = length ×  width

From the information given, we have;

Now, let's substitute the values;

Area of a triangle = 1/ 2 × 11 × 4

Area of a triangle = 44/ 2 = 22m²

Area of a rectangle = 11 × 4

Area of a rectangle = 44m²

The ratio of the area of the triangle to the area of the rectangle is

= 22: 44

= 1 : 2

Thus, the ratio of the area of the triangle to the area of the rectangle is 1: 2

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Z = 1.555 should be used

If we seek an 88% confidence interval, that means we only want a 12% chance that our interval does not contain the true value.

Assuming a two-sided test, that means we want a 6% chance attributed to each tail of the Z-distribution.

the zα/2 value of z0.06.

This z value at α/2=0.06 is the coordinate of the Z-curve that has 6% of the distribution's area to its right, and thus 94% of the area to its left. We find this z-value by reverse-lookup in a z-table.

The standard normal distribution, also called the z-distribution, is a special normal distribution where the mean is 0 and the standard deviation is 1.

Any normal distribution can be standardized by converting its values into z-scores. Z-scores tell you how many standard deviations from the mean each value lies.

The standard score (more commonly referred to as a z-score) is a very useful statistic because it

(a) allows us to calculate the probability of a score occurring within our normal distribution and

(b) enables us to compare two scores that are from different normal distributions.

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Answer: 6/23  mph

Step-by-step explanation: We change the 1/3 of an hour to 1 hour by multiplying 1/3 and 2/23 by 3. 1/3 times 3 is 1(hour) and 2/23 x 3 is 6/23(miles). So the unit rate the turtle is traveling at is 6/23 mph.

Given the point U and point V, the midpoint between of the line segment UV is ( 0, -5/2 ).

The midpoint formula is used to find the midpoint of a line segment.

It is expressed as;

[ (x₁ + x₂ )/2 , (y₁ + y₂ )/2 ]

Given the data in the graph,

Point U = ( 3, -1 ) and Point V = ( -3, -4 )

We substitute into the formular above.

[ (x₁ + x₂ )/2 , (y₁ + y₂ )/2 ]

[ (3 + (-3) )/2 , ( (-1) + (-4) )/2 ]

[ 0/2, (-1-4)/2 ]

[ 0/2, -5 /2 ]

( 0, -5/2 )

Given the point U and point V, the midpoint between of the line segment UV is ( 0, -5/2 ).

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Answer:

  (b)  x = 10.5

Step-by-step explanation:

The angle bisector divides the triangle line segments proportionally.

The proportion between corresponding line segments can be written several ways. One of them is ...

  long side/long side = short side/short side

  x/19.3 = 3.9/7.2

Multiplying by 19.3, we get ...

  x = 19.3×3.9/7.2 ≈ 10.5 . . . units

__

Additional comment

You can eliminate the incorrect answer choices simply by looking at the possible side lengths of x.

  19.3 -(3.9+7.2) < x < 19.3 +(3.9+7.2) . . . . . from triangle inequality

  8.2 < x < 30.4 . . . . . . . simplify

There is only one answer choice in this range: the correct one.

Answer:

Step-by-step explanation:

A chord is a straight line that connects two points on a curve. An arrangement of three or more notes that blend harmoniously when played together.

A section of a circle has both endpoints on the circle. Chords are the sections of a circle.

Therefore, the final answer is "chords".

I hope this helps, let me know if you have any questions.

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Answer:

$613.04

Step-by-step explanation:

Compound Interest Formula:

   [tex]A = P(1+\frac{r}{n})^{nt}[/tex]

   n = number of compounds

   t = time

   r = interest rate

   P = principle amount (original amount)

   A = final amount

Since it's compounded quarterly, that means there will be 4 compounds per year, so n=4. The interest rate has to be converted to the decimal value, and this is done by simply dividing it by 100 to get r=0.06.

Plug Values into equation:

[tex]A = 300(1+\frac{0.06}{4})^{12*4}[/tex]

Simplify inside parenthesis

[tex]A = 300(1.015)^{48}[/tex]

Calculate exponent

[tex]A \approx 300(2.043478)[/tex]

Multiply values

[tex]A \approx 613.04348[/tex]

Round

[tex]A = 613.04[/tex]

The solution of the equation is (2, 1).

x=2 and y=1

A mathematical assertion that two expressions are equal is known as equating. It can be expressed as either an identity, in which case the variables can take on any value, or a conditional equation, in which case the variables can only have specific values (roots).

We have two options for finding the answer. The first is to solve the equations via term elimination:

x + 3y = 5  ..............1

x - 3y = -1  ...............2

2x = 4 ..............3

With the equation, we can determine x. (3)

x = 4/2

x = 2

To determine y, we may now swap out x=2 in equation (1).

x + 3y = 5

2 + 3y = 5

3y = 3

y = 1

We've discovered x and y now.

x=2

y=1

The second method involves removing x from equation 1.

x + 3y = 5

x = 5 - 3y

In the equation right now, we may substitute x = 5 - 3y.........  (2)

x - 3y = -1

(5 - 3y) - 3y = -1

5 - 6y = -1

6y = -6

y = 1

Currently, we can change y=1 in equations (1), (2), or (4) to find x.

We'll apply the equation (1)

x + 3y = 5

x + 3(1) = 5

x + 3 = 5

x = 2

The two variants x = 2 and y = 1 have allowed us to confirm this.

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Lynn wants to wait because (D) she would likely have to pay more than $55 at the time of purchase for the convenience of using her credit card.

The answer to why Lynn wants to wait would be:

Therefore, Lynn wants to wait because (D) she would likely have to pay more than $55 at the time of purchase for the convenience of using her credit card.

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The complete question is shown below:

Lynn is at a store and wants to buy a new backpack that costs $55. she only has $35 with her, but she has the rest at home. Lynn also has a credit card that does not charge her any interest if she pays the balance in full by the end of the month. why might Lynn want to wait until she has $55 in cash at the store to purchase the backpack, instead of using her credit card?

a. Using a credit would cause the store to lose money because even if she pays back her bill in full, she will still need to pay the credit card company additional dollars for the convenience of borrowing money.

b. Using cash would cause the store to lose a large amount of money because credit card companies offer incentives to stores based on the number of people who use their cards.

c. She might forget to pay the credit card bill, which would make her purchase more expensive due to interest payments and late charges.

d. She would likely have to pay more than $55 at the time of purchase for the convenience of using her credit card.

Answer:

c

Step-by-step explanation:

In geometry, an equilateral triangle is a triangle in which all three sides have the same length.

Step-by-step explanation:

4 pictures correlate to 1/3 page.

how many 1/3 pages do we need to get 1 full page ?

3, as 3 × 1/3 = 3/3 = 1.

so, to keep the ratio, we need to multiply also the pictures by 3 and get

4×3 = 12 pictures per page

The interpretation of f(30) is the distance travelled after 30 minutes

The function is given as:

A function representing distance (feet) as a function of time (minutes),

This means that, the dependent variable is the distance and the time is the independent variable

This in other words means that:

x = time

f(x) = distance

So, the interpretation of f(30) is:

The distance travelled after 30 minutes

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Rounded to the nearest square units, the surface area of the cone, is: 524 square units.

The surface area of a cone = πr(r + l), where:

r is the radius of the cone

l is the length of the cone.

Given the following:

Radius of the cone (r) = 12/2 = 6 units

Slant height of the cone (l) = √(21² + 6²) [Pythagorean theorem]

Slant height of the cone (l) = 21.8 units.

Plug in the values into πr(r + l):

Surface area of the cone = π × 6(6 + 21.8)

Surface area of the cone = 3.14 × 6(27.8)

Surface area of the cone ≈ 525 square units

The surface area of the cone, approximated to the nearest square units, we have: 524 square units.

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Answer: Line D

Step-by-step explanation:

The points in the scatterplot are closest to line D.

Answer:

g = 4

Step-by-step explanation:

if 2 tangent segments are drawn to a circle from the same external point then they are congruent , that is

RJ = RW and MJ = MB and KB = KW

given MR = 6 , then

MJ = 6 - g = MB

given KM = 5 , then

KB = 5 - MB = 5 - (6 - g) = g - 1 = KW

given KR = 7 , then

RW = 7 - KW = 7 - (g - 1) = 8 - g

Then

RJ = RW , that is

g = 8 - g ( add g to both sides )

2g = 8 ( divide both sides by 2 )

g = 4

Answer:

I don't understand the format of the questions and choices.  I simply made a few observation.

Step-by-step explanation:

The fraction - (2) can be described as the opposite of a positive number divided by a positive number.

-(2/1)?

A positive number divided by a positive number results in a Choose...     Negative Number

quotient, and its opposite is always Choose...    Opposite?  Still a negative number.

I don't understand the following:

The fraction can be described as a positive number divided by a negative number, which

-12

always results in a Choose...

quotient.

value, so Liam Choose...

The fractions have

Choose...

Y

correct.

Answer:

D. 70,244 and 70,632

Step-by-step explanation:

Got it right on PLATO/EDMENTUM

70,244 and 70,632 is the approximate 90% confidence interval for this situation.

A confidence interval, in statistics, refers to the probability that a population parameter will fall between a set of values for a certain proportion of times.

Confidence intervals measure the degree of uncertainty or certainty in a sampling method. They can take any number of probability limits, with the most common being a 95% or 99% confidence level. Confidence intervals are conducted using statistical methods.

Statisticians use confidence intervals to measure uncertainty in a sample variable. For example, a researcher selects different samples randomly from the same population and computes a confidence interval for each sample to see how it may represent the true value of the population variable. The resulting datasets are all different; some intervals include the true population parameter and others do not.

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Answer:

I think it's A (parallel)

Answer:

A. its parallel

Step-by-step explanation:

all angles are equal... two sides are perpendicular and two are parallel

[tex]1.2 \: degrees \: drop \: a \: day \\ 14 \: days \: in \: two \: weeks \\ net \: change = 14 \times 1.2 = 16.8 \: deg[/tex]

Complexes with a coordination number 4 mostly adopt tetrahedral and squar planar geometries.

Complexes with a coordination number 4 mostly adopt tetrahedral and squar planar geometries.

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