Which is the graph of f(x) = x2 - 2x + 3?

1. The best equation for circle A is (x + 4)² + (y + 2)² = 9. Option D

2. The equation of the circle with coordinates (1, 1) (1, 11) is (x - 1)² + (y - 6)² = 25. Option A

1. For the equation of circle A, we can pick out the coordinates we see.

Circle A has its midpoint at (-4, -2) and its edges at (-4, 1) and (-4, -5).

The equation of a circle in a plane is (x - h)² + (y - k)² = r²

the circle has a radius of 3 units (from -2 to 1 or from -2 to -5)

(x - (-4))² + (y - (-2))² = 3²

when we simplify, it becomes (x + 4)² + (y + 2)² = 9

2. The equation of a circle with diameter AB. A (1, 1), B(1, 11) is

h = (x₁ + x₂)/2 ⇒(1 + 1)/2 = 1

k = (y₁ + y₂)/2⇒ (1 + 11)/2 = 6

the center of the circle is at (1, 6).

A and B which are (1, 1) and (1, 11), it's clear that the diameter is 10 units (11 - 1). Thus, the radius is 5 units.

(x - h)² + (y - k)² = r²

Substituting the obtained values we get

(x - 1)² + (y - 6)² = 5²

which becomes

(x - 1)² + (y - 6)² = 25

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Answer:

4/5

Step-by-step explanation:

There are so many points on the graph whose coordinates are impossible to estimate. Look for two "nice" points--points with integer coordinates. The line passes through (-2, 0) and (3, 4).

Slope = rise / run. It's the ratio of vertical change to horizontal change as you move from one point on the line to another.

Moving from (-2, 0) to (3, 4), the vertical change is 4 - 0 = 4.

The horizontal change is 3 - (-2) = 5.

The slope is 4/5

Answer:

A) explanatory variable is "The extra support given by faculties"

B) the response variable is;

"How successful students who were placed directly into college - level statistics were able to outperform both elementary algebra treatment groups."

C) Confounding Variable is "ability of students to be successful or pass"

D) Experiment

Step-by-step explanation:

A) An explanatory variable is simply a type of independent variable used to explain the changes that occur in another variable. Furthermore, it can be manipulated by the researcher and is also used to predict differences in the response variable.

Now, from the question, we see that the variable "extra support by the faculties" is used to determine how successful community college students who were placed directly into college - level statistics were in outperforming both elementary algebra treatment groups.

Thus, the explanatory variable is "The extra support given by faculties"

B) In answer A above, we saw that the explanatory variable is used to predict the response variable.

We saw that the explanatory variable predicted how successful community college students who were placed directly into college - level statistics were in outperforming both elementary algebra treatment groups.

Thus, the response variable is;

"How successful students who were placed directly into college - level statistics were able to outperform both elementary algebra treatment groups."

C) A confounding variable is one that influences or changes the effect of the dependent & independent variable. It is therefore used to influence the result/outcome of an experiment/research.

From the question, it's clear that the ability of the students to pass or be successful is what influences the effect of the support by the faculties.

Thus, the Confounding Variable is "ability of students to be successful or pass"

D) The question portrays an experiment because it is being used to check if an hypothesis statement is true or false.

Answer:

he spent $18.57 and he can spend $7.43 more

The solution is, he can still spend no more than $6.43.

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

given that,

Wyatt wants to spend no more than $25 at the grocery store.

He bought a pizza for $7.55 and a cake for $11.02 (including tax).

now, we have to find the inequality that he can use to find how much money he can still spend.

let, we would spend = x

now, we have,

He bought a pizza for $7.55 and a cake for $11.02

so, he had = $ x - ( 7.55 + 11.02)

we have,

x ≥ 25

so, he can still spend ≥ 25 -  ( 7.55 + 11.02)

or, he can still spend ≥ 6.43

i.e.  he can still spend no more than $6.43

Hence, The solution is, he can still spend no more than $6.43.

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Answer:

Step-by-step explanation:

Find the surface area of a cylinder with a height of 7in and a bass radius of 2in. Use the value 3.14 for π, , and do not do any rounding.

A=2πrh+2πr2=2·π·2·7+2·π·2²=

not rounded 113.09734  

Rounded 113.1

The method is: Find the increase and find the ratio of the increase and the old price.

The percentage increase is 20%

A percentage is defined as the ratio that can be expressed as a fraction of 100.

The method below shows how you would calculate the % increase.

First step: Find the increase:

increase = 480 - 400 = $80

Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:

80/400 * 100 = 20%

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Answer: The equation that represents the road is y= - 1/3x +1/3

Step-by-step explanation:

The perpendicular equation that represents the road that passes through the point is \(\mathbf{y = -\frac 13x + \frac 13 }\)

The points of the red line (see attachment) are given as:

\(\mathbf{(x,y) = (0,2), (2,8)}\)

Start by calculating the slope (m) of the line using:

\(\mathbf{m = \frac{y_2 - y_1}{x_2 -x_1}}\)

So, we have:

\(\mathbf{m = \frac{8 - 2}{2 -0}}\)

\(\mathbf{m = \frac{6}{2}}\)

\(\mathbf{m = 3}\)

Next, calculate the slope (m2) of the perpendicular line using:

\(\mathbf{m_2 = -\frac 1m}\)

So, we have:

\(\mathbf{m_2 = -\frac 13}\)

The perpendicular line passes through point (1,0).

So, the line equation is calculated using:

\(\mathbf{y = m_2(x - x_1) + y_1}\)

This gives

\(\mathbf{y = -\frac 13(x - 1) + 0}\)

\(\mathbf{y = -\frac 13(x - 1) }\)

Open bracket

\(\mathbf{y = -\frac 13x + \frac 13 }\)

Hence, the line equation is \(\mathbf{y = -\frac 13x + \frac 13 }\)

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Answer:

we'll be using Pythagorean theorem to solve this question...the answer as stated above is 8

Answer:

8

Step-by-step explanation:

you would be using A^2+B^2=C^2. sense you dont have a B value you would do C^2-A^2=B^2. so 10^2(100)-A^2(36)=B^2(64). once you have what B equales you sqarer root it so it is now 8.

Answer:

me too (help)

Step-by-step explanation:

Rollaway Skates is cheaper when the number of people is less than or equal to 4. For example, the cost for 2 people at Rollaway Skates is $10, while the cost for 2 people at Wheelie's Skates and Stuff is $106.

Wheelie's Skates and Stuff is cheaper when the number of people is greater than or equal to 5. For example, the cost for 6 people at Rollaway Skates is $30, while the cost for 6 people at Wheelie's Skates and Stuff is $118.

I hope this helps! Do you have any other questions?

Explanation:

To identify the pairs of congruent angles we have to follow the order in which they are written in the similatity statement.

For two similar triangles, the proportions between corresponding sides must be constant.

Answers:

Congruent angles:

• ∠Q ≅∠X

• ∠R≅∠Y

• ∠S≅∠Z

Proportions:

(k is the scale factor)

To find f(g(x)), we need to substitute g(x) into the function f(x). Given that g(x) = x - 4, we substitute it into f(x) as follows:

\(f(g(x)) = f(x - 4) = (x - 4)^2 + 4\)

To simplify this expression, we can expand the square:

\(f(g(x)) = (x - 4)(x - 4) + 4\\ = x^2 - 8x + 16 + 4\\ = x^2 - 8x + 20\)

Therefore, f(g(x)) simplifies to\(x^2 - 8x + 20.\)

Next, let's find g(f(x)). We substitute f(x) into the function g(x):

\(g(f(x)) = g(1/x^2 + 4) = 1/x^2 + 4 - 4\\ = 1/x^2\)

Hence, g(f(x)) simplifies to 1/x^2.

In summary, f(g(x)) simplifies to\(x^2 - 8x + 20\), and g(f(x)) simplifies to 1/x^2.

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The statement is False. The entire group of individuals we want information about is called the population, not sample.

In statistics, a sample is a subset of individuals or observations taken from a larger population, which is used to estimate characteristics or parameters of the population.

The goal of statistical analysis is often to make inferences about a population based on information gathered from a representative sample. Therefore, it is important to carefully select a sample that is truly representative of the population of interest.

The sample is a subset of the population that is selected for analysis in order to make inferences about the population.

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The complete question is : The entire group of individuals we want information about is called the sample.

a. True

b. False

Answer:

The product of 19 and 32 is 608 and their sum adds up to 51.

The two numbers are: 19 and 32

the ancient Greek used the golden ratio

Answer:

An important proportion that the Ancient Greeks used was the Golden Mean, the a0

Step-by-step explanation:

Also known as Golden Ratio, Divine Proportion, or Golden Section

Answer:

1) B. at 0 and 3 only

2) D. 2eˣcosx

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

Derivative Property [Addition/Subtraction]:                                                          \(\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]\)

Derivative Rule [Product Rule]:                                                                              \(\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)\)

Trig Derivative: \(\displaystyle \frac{d}{dx}[sinu] = u'cosu\)

Trig Derivative: \(\displaystyle \frac{d}{dx}[cosu] = -u'sinu\)

eˣ Derivative: \(\displaystyle \frac{d}{dx} [e^u]=e^u \cdot u'\)

Step-by-step explanation:

*Note:

Velocity is the derivative of position.

Acceleration is the derivative of velocity.

Question 1

Step 1: Define

s(t) = t⁴ - 6t³ - 2t - 1

Step 2: Differentiate

Step 3: Solve

Question 2

Step 1: Define

f(x) = eˣ(sinx + cosx)

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Derivatives

Book: College Calculus 10e

Answer:

4.60

Step-by-step explanation:

multiply 5.75 and 0.80 to get 4.60

Answer:

460

Step-by-step explanation:

x/80 = 5 3/4 or 23/4

23*80= 1,840

1,840/4 = 460

The number of minutes that the players spend running bases during each hour of practice is the constant of proportionality of the proportional relationship.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

In the context of this problem, the variables x and y are given as follows:

The equation for the constant is given as follows:

k = y/x.

Representing the hourly time spent running times, you can calculate it taking any point (x,y) on the graph of the function.

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Answer:

  58.0 units

Step-by-step explanation:

In order to use the law of sines, we need to know angle C. It will be the angle that brings the total of all angles to 180°.

  C = 180° -A -B = 180° -72° -16°

  C = 92°

The law of sines tells us ...

  a/sin(A) = c/sin(C)

  a = c·sin(A)/sin(C) = 61·sin(72°)/sin(92°)

  a ≈ 58.0 . . . . units

The equation that represents the total price of Michigan State University per semester is determined by the number of classes taken (c) and the total cost for the semester, which includes a one-time fee for room and board (t).

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The answer should match the image below.

Answer:

b

Step-by-step explanation:

Answer:

the probability that the two committees have at least one member in common is approximately 0.3622.

Step-by-step explanation:

To find the probability that two committees have at least one member in common, we can use the complement rule, which states that the probability of an event happening is 1 minus the probability of the event not happening.

Let A be the event that the two committees have no members in common. To calculate the probability of A, we can first find the number of ways to choose three people out of 20 without any overlap, and then use this to find the total number of ways to choose two committees of three people each without any overlap:

Number of ways to choose 3 people out of 20 without overlap:

C(20,3) = (201918)/(321) = 1140

Number of ways to choose 3 people out of 20 with overlap:

C(20,3) - C(2,1)C(17,2) = 1140 - 2(2*136) = 680

The first term is the total number of ways to choose 3 people out of 20, and the second term is the number of ways to choose 3 people out of 20 such that one particular person is included. We multiply by 2 because there are two committees.

The total number of ways to choose two committees of three people each without any overlap is:

C(20,3) * C(17,3) = (1140*680) = 775200

Therefore, the probability that the two committees have no members in common is:

P(A) = 775200 / (C(20,3)*C(17,3)) = 0.6378

So the probability that the two committees have at least one member in common is:

P(at least one member in common) = 1 - P(A) = 1 - 0.6378 = 0.3622

Therefore, the probability that the two committees have at least one member in common is approximately 0.3622.

The requried center and radius of the given circle are (2, -4) and 5.

The standard equation of a circle is given as,
(x - h)² + (y - k)² = r²

Where, (h, k) is the center of the circles and r is the radius of the circle,

The equation of the given circle is,
(x - 2)² + (y + 4)² = 25

Comparing the above equation with the standard equation we have,
(h, k) = (2, -4)

r² = 5²; r =5

Thus, the requried center and radius of the given circle is (2, -4) and 5.

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Answer:

<2 and <6 are complementary angles

Step-by-step explanation:

<2 and <3 are complementary angles since they add to 90

<3 and <6 are vertical angles so they are equal

<3 = <6

Replace <3 with <6

<2 and <6 are complementary angles

Answer:

the answer should be C please give brainliest

Step-by-step explanation:

Five equal monthly installments make up the remaining balance. $ 154.25, the customer paid using a credit card for $ 127.98, the remaining money was split among 4 persons for $ 58.87, and the remaining 15 months must be paid in full to complete the repayment.

Payment is the exchange of money, products, or services for goods and services that are provided in acceptable quantities and that have been previously agreed upon by all parties. A payment can be paid using the traded services, cash, a check, a wire transfer, a credit card, a debit card, crypto currency, or any of these methods.

a) A costumer buys a laptop, which costs $1254.73 and costumer makes a down payment of $483.48 so the rest money to pay back

=  $1254.73 -   $483.48

= $ 771.25

so

the rest is paid in five equal monthly installments =  $ 771.25 / 5

= $ 154.25

b) costumer buys a sweater + a jacket + a jean = $63.99 + $71.99 + $55.99

= $ 191.97

third of the total with cash = $ 191.97 / 3

= $63 .99

so the rest is total - paid with cash = $ 191.97 - $ 63.99

=$ 127.98

c) total dinner costs - gift card paid= $ 310 ,48 - $ 75

= $ 235.48

remaining amount divided with 4 people = $ 235.48 / 4

= $ 58.87

so each person will pay = $ 58.87

d) A student requests a loan for = $1178.80

already paid = $1178.80 - $547.30

= $ 631.5

in one month = $42.10

remaining month =  $ 631.5 /  $42.10

= 15 months

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Answer:

Lo siento

Step-by-step explanation:

Step-by-step explanation:

those are 4 and 5s I swear