Consider the functions f(x) and g(x). The function f(x)=2x-5 and g(x)= -f(x+1)+3. A. Describe the three transformations that are performed on f(x) to create g(x).1.2.3.B. Sketch a graph of g(x):

The total finance charge is $3452 and the APR will be 6.45%.

The total finance charge will be:

Price = $20999

Down payment = $1000

Loan amount = $20999 - $1000 = $19999

Total repayment = $390.85 × 60 = $23451

Total finance charge = $23451 - $19999 = $3452

It should be noted that the APR will be:

= Rate(nper, pmt, -pv) × 12

where nper = 60

PMT = $390.85.

pv = 19999

APR = 6.45%

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The probability that it takes at least 6 minutes to find a parking space is given as: 0.1587. See the explanation below.

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

The working of the above solution is given as follows:

Given:

Mean = 4 minutes

Standard deviation = 3 minutes

P(X < A) = P(Z < (A - mean) /standard deviation)

P(at least 6 minutes) = P(X≥6)

= 1 - P(X < 6)

= 1 - P(Z < (6 - 4)/2)

= 1 - P(Z < 1)

= 1 - 0.8413

P = 0.1587

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The most appropriate choice for factorization will be given by-

(x +2)(x  + 3)(2x - 1) is the factorization of f(x) = 2x³+9x²+7x-6

x = -2, -3, [tex]\frac{1}{2}[/tex] are the solutions of f(x) = 0

What is factorization?

Factorization is the process of breaking down of an algebraic expression into product of algebraic expressions of smaller degree.

Each algebraic expression of smaller degree are called factors

Here,

Vanishing method will be used

f(x) =  2x³+9x²+7x-6

[tex]f(-2) = 2(-2)^3 + 9(-2)^2 + 7(-2) -6\\= -16 + 36 -14 -6\\ = 0[/tex]

(x + 2) is a factor of f(x)

[tex]f(x)[/tex] [tex]= 2x^2(x + 2) + 5x(x + 2) - 3(x + 2)[/tex]

     [tex]= (x + 2)(2x^2 + 5x - 3) \\ = (x + 2)(2x^2 + 6x - x - 3) \\ = (x + 2)[2x(x + 3) - 1(x + 3)] \\ = (x + 2)(x + 3)(2x - 1)[/tex]

For solving f(x) = 0

x +2 = 0 or x + 3 = 0 or 2x - 1 = 0

x = -2 or x = -3 or x = [tex]\frac{1}{2}[/tex] are the solutions of f(x) = 0

This is the required factorization of f(x)

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Let's write the equation system first. We have two angles, let's call the, A and B, wich are complementary. This is:

Also their difference is 40º:

The system is;

Now, if we add the two equations, since we have a "B" and a "-B", they will eliminate:

The value of one of the angles is 65º. To find the other angle, we can go back to the first equation, A + B = 90º:

And solve:

The larger angle is 65º and the smaller angle is 25º

Given function is

correct option is D 6, 4.5, 1.

Answer: I think it is -5, but im not very sure srry

Step-by-step explanation:

Given:

The equation of a parabola is given as,

The objective is to find the axis of symmetry of the parabola.

Explanation:

The general formula to find the axis of symmetry of a parabolic equation is,

From the given equation,

On plugging the obtained values in equation (1),

Hence, the axis of symmetry of the parabola is at x = 0.

to round to the nearest thousand, we have to look at the hundreds place. In this case, there is a 2 in the hundreds place, which is less than 5. Then, the 3 in the thousands place must be kept. In conclusion, 3,204 rounded to the nearest thousand is 3,000

Answer:

3,000

Step-by-step explanation:

the thousands place is where the 3 is and we look at the number next to it if it is 5 or over we round up or if it’s under 5 we round down and since 2 is under 5 we round down to 3,000

She need 1/12 cup of oil. A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters.

To find how much need to obtain 1/3 of cup

we need to subtract what we have from what we need.

so , we have 1/4 and need 1/3

 = 1/3 - 1/4

 = [tex]\frac{1 * 4}{3 * 4} - \frac{1 * 3}{4 * 3}[/tex]

 = 1/12

she need 1/12 cup of oil more to make cake.

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Given:

Customers return 14% of their gifts during the holiday season.

The total number of gifts = 500

So, the returned gifts = 14% of 500 = 0.14 x 500 = 70 gifts

So, the number of gifts were returned during the holiday season = 70 gifts

Answer:

Because it is one of the given pieces of information.

because perpendicular lines form right angles, and all right angles are congruent.

PS and PS are adjacent sides next to the two pairs of congruent angles.

By the Reflexive Property of Congruence

by ASA triangle congruence rule

Explanation:

Given the figure of the triangle in the attached image.

Given that;

Because it is one of the given pieces of information.

Then we can observe that;

because perpendicular lines form right angles, and all right angles are congruent.

Also,

PS and PS are adjacent sides next to the two pairs of congruent angles.

And;

By the Reflexive Property of Congruence

Thus,

by ASA triangle congruence rule

[tex] = \frac{2}{3} \div - \frac{5}{7} \\ = \frac{2}{3} \times - \frac{7}{5} \\ = - \frac{14}{15} [/tex]

ATTACHED IS THE SOLUTION.

NOTE WHEN WE ARE DIVIDING WE CHANGE THE DIVISION SIGN TO A MULTIPLICATION SIGN TO AND SWAP THE FOLLOWING FRACTION .

Answer:

-0.019047619

That’s the Answer Hope this helps:)

we have that

The equation of the given line is

y=1

this equation represents a horizontal line

so

the slope is zero (m=0)

Remember that, if two lines are parallel, then their slopes are equal

that means

the slope of the parallel line is m=0 too

step 2

Find out the equation in slope-intercept form

y=mx+b

we have

m=0

point (-1,3)

the equation is

Given:

To Determine: All expressions that are less than 10 2/3

Verify for each of the options

OPTION A

OPTION B

OPTION C

After simplification of the given monomial 2a²+6²-8a² + x²y - 3x + 9xy², the result is -6a²- 3x + x²y + 9xy² + 12.

So, 2a²+6²-8a² + x²y - 3x + 9xy²:

Now, simplify as follows:

Therefore, after simplification of the given monomial 2a²+6²-8a² + x²y - 3x + 9xy², the result is -6a²- 3x + x²y + 9xy² + 12.

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We need to calculate the three trigonometrics relations on the right triangle. They are as follow:

We need to use this values on each option. The "sin^-1" is the inverse of the sine, the "cos^-1" is the inverse of the cosine and the "tan^-1" is the inverse of the tangent. If we use these values on the functions we will find the value of theta.

The angle is equal to 66.93 degrees

1) Given that rule, we can write out the following for this case:

2) So let's plug into that the data:

Note that we have cross multiplied and then divided both sides by 8. So the dosage of an adult, according to this rule would be 15 ml

QUESTION:

you want to buy some beans a 6 oz package cost $2.10 a 14 oz package cost $5.04 a 20 oz package cost $6.60​. Which package is the best to buy?

ANSWER

We will first find the unit price.

6 0z = $2.10

1 oz = $2.10/6 = $0.35

a 14 oz package that cost $5.04

14 0z = $5.04

1 oz = $5.04 / 10 = $0.504

a 20 oz package that cost $6.60

20 oz = $6.60

1 oz = $6.60 / 2 =$3.30

Comparing the three prices, the 6 oz package that cost $2.30 has the lowest price. This implies that it is the best to buy.

Given:

The diameter of a circle is 20 inches.

So, d = 20 inches

We will find the radius of the circle (r)

The diameter is two times the radius

Or, we can say, the radius is half of the diameter

so, r = d/2 = 20/2 = 10 inches

so, the answer will be The radius = 10 inches

675  is product by using multiplication's commutative property.

What does multiplication's commutative property mean ?

Examples of Commutative Multiplication Property

1 × 2 = 2 × 1 = 2.

3 × 8 = 8 × 3 = 24.

12 × 5 = 5 × 12 = 60.

45 X 15

= 675

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The probabilities in the context of this problem are given as follows:

a) Negative blood test: 0.543 = 54.3%.

b) Do not have lockjaw, given that the test is positive: 0.1682 = 16.82%.

Conditional probability is the probability of one event happening, considering a previous event. The formula is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which the parameters of the formula are described as follows:

For item a, the percentages associated with negative blood tests are given as follows:

Hence the probability is:

p = 0.84 x 0.49 + 0.24 x 0.51 = 0.534 = 53.4%.

For item b, the probabilities associated with positive blood tests and not having lockjaw are given as follows:

Hence the conditional probability is:

P(B|A) = 0.49 x 0.16/0.466 = 0.1682 = 16.82%.

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5x + 2 + 5x - 2 = 180

5x = 180

x = 36

Using proportions, it is found that Micah caught up to Taylor at 11:06 AM.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using relations in the context of the problem.

For this problem, the relation between velocity, distance and time is used, that is, velocity equals distance divided by time, hence:

v = d/t.

Then the distance is:

d = vt.

For Taylor, his trail is divided in these following intervals:

For Micah, the time that he took to complete the trail is:

t = d/v = 8/7 = 1.14 hours.

Hence he completed his trial around 11:40 AM, as he left at 10:30 A.M.

He caught up to Taylor during the first interval of his trip, when the motion functions are as follows:

Then:

7t = 2t + 3.

5t = 3.

t = 3/5.

t = 0.6 hours = 36 minutes after Micah left = 11:06 A.M.

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Q.29 Variance is S² = 17.33

Q.30 Variance is S² = 46.67

Variance is the expectation of the squared deviation of a random variable from its population mean or sample mean.

S² = ∑(x - x(bar) )² / (n - 1 )

S² = sample Variance

x = the value of the one observation

x(bar) = the mean value of all observation

n = the number of observation

Q.29   |  x  |  (x -x(bar)) | (x - x(bar) )²  |

          |   -------------------------------------- |

          |    2 |        -5     |     25             |  

          |    6 |        -1      |      1               |

          |    8 |       1        |      1               |

          |   12 |       5       |      25            |

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

         |  28  |      0        |    52              |            

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

x(bar) means, x mean = ∑x

       ∑x = (2  + 6 + 8 + 12) / 4

            = 28/4

            = 7

       Now, put the values in variance formula,

        S² = ∑(x - x(bar) )² / (n - 1 )

             = 52 / (4 -1)

             =  52/ 3

             = 17.33

Q.30   |  x  |  (x -x(bar)) | (x - x(bar) )²   |

          |   --------------------------------------  |

          |  10   |        -7     |     49             |  

          |   14  |        -3      |      9             |

          |   18  |       1        |      1               |

          |   26 |       9       |      81             |

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

         |  68  |      0        |    140             |            

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

x(bar) means, x mean = ∑x

       ∑x = (10 + 14 + 18 + 26)/4

            = 68/4

            = 17

       Now, put the values in variance formula,

        S² = ∑(x - x(bar) )² / (n - 1 )

             = 140 / (4 -1)

             =  140 / 3

             = 46.67

Therefore, the Variance of Q.29 is S² = 17.33

                 and, for Q.30 Variance is S² = 46.67

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Let's call x the age of the first president bush, then:

Taking into account the sentence, "if you divide the age of the first President Bush when he was inaugurated by 2 and add 14 years you get the age of president Clinton when he was first inaugurated", we can write the following equation:

x/2 + 14 = 46

So, solving for x, we get:

x/2 = 46 - 14

x/2 = 32

x = 32*2

x = 64

Answer: The first president Bush was 64 years old when he was inaugurated.

Answer:

15

Step-by-step explanation:

from the equation 50+40h=650

solving for h which is the number of hours worked.

40h=650-50

40h=600

h=600÷40

h=15

First, if we draw the lines of the equations x-y = -3 and 3x+2y = 0, we get the following:

the red line represents the first equation and the blue line represents the second equation. But since we are working with inequalities, the intersection between these two inequalities will be the intersection of the semiplanes that they form.

To check the region that will be the intersection, we can check two opposite points and see if both inequalities are true. In this case, if we take the points (-2,-2) and (2,2), we get the following:

notice that the second inequality is not true. Now, with the point (2,2), we get:

which are true, therefore, the region that represents both inequalities is the following:

Given:

Equation of line with the points (-3,24) and (4,-4)

Answer

a) Angle L = 36.9°

Angle N = 53.1°

b) For the relationship between them, we can see that

Angle L + Angle N = 36.9° + 53.1° = 90°

Hence, they both sum up to give 90° and are thus complementary angles.

Explanation

In a right-angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.

For this question, we first use Angle L as the non-right-angle angle

Hypotenuse = LN = 5

Opposite = NM = ?

Adjacent = LM = 4

Angle = L

Trignometric ratios allow us to interprete CAH as

Cos L = (Adj/Hyp)

Cos L = (4/5)

Cos L = 0.8

L = Cos⁻¹ (0.8)

L = 36.9°

Now, using Angle N as the non-right-angle angle,

Hypotenuse = LN = 5

Opposite = LM = 4

Adjacent = NM = ?

Angle = N

Trignometric ratios allow us to interprete SOH as

Sin N = (Opp/Hyp)

Sin N = (4/5)

Sin N = 0.8

N = Sin⁻¹ (0.8)

N = 53.1°

b) For the relationship between them, we can see that

Angle L + Angle N = 36.9° + 53.1° = 90°

Hence, they both sum up to give 90° and are thus complementary angles.

Hope this Helps!!!