What is the range of the function f(x) = -3x + 1 when the domain is {-2, 0, 3}?
A. {7, 1, -8}
B. {-5, 1, -8}
C. {-31, -29, -32}
D. all real numbers

The values of a and b using the factor theorem for the polynomial f(x), we set f(1) and f(-1) equal to zero. Solving the resulting system of equations, we find that a = 12 and b = -1.

To find the values of a and b using the factor theorem, we need to use the given factors (x - 1) and (x + 1) and the fact that they are roots of the polynomial f(x).
The factor theorem states that if (x - c) is a factor of a polynomial, then f(c) = 0. Therefore, we can set x = 1 and x = -1 in the polynomial f(x) to get two equations.
First, let's substitute x = 1 into f(x):
f(1) = (1)^3 + a(1)^2 + b(1) - 12
f(1) = 1 + a + b - 12
Next, let's substitute x = -1 into f(x):
f(-1) = (-1)^3 + a(-1)^2 + b(-1) - 12
f(-1) = -1 + a - b - 12
Since (x - 1) and (x + 1) are factors, f(1) and f(-1) must equal zero. Therefore, we can set the two equations equal to zero and solve for a and b:
1 + a + b - 12 = 0
-1 + a - b - 12 = 0
Rearraning the equations, we have:
a + b = 11
a - b = 13
Now, we can solve this system of equations. Adding the two equations, we get:
2a = 24
a = 12
Substituting the value of a into one of the equations, we find:
12 - b = 13
b = -1
Therefore, the values of a and b are 12 and -1 respectively.

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The cardinal number of the set is 5.

The cardinal number of the given set A = {13, 19, 25, 31, 39} is 5.

Cardinal number is the number of elements present in a set, so counting the number of elements of the set will give us the cardinal number of the set.

In this case, we have the set A with 5 elements: 13, 19, 25, 31, and 39.

Thus, the cardinal number of the set is 5.

Hence, the answer is 5.

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Answer:

We use thales theorem

Therfore the answer is 34

To find the total in the retirement account after 38 years of investing with monthly contributions and an interest rate of 4.99%, we can use the compound interest formula.

The formula for the future value of an investment with regular monthly contributions is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value or the total in the retirement account.

P is the monthly contribution amount.

r is the monthly interest rate (annual interest rate divided by 12).

n is the number of monthly contributions (years invested multiplied by 12).

Let's calculate the total:

P = $225

r = 4.99% / 100 / 12 = 0.0041583 (monthly interest rate)

n = 38 * 12 = 456 (number of monthly contributions)

FV = $225 * [(1 + 0.0041583)^456 - 1] / 0.0041583

Using a financial calculator or spreadsheet, we can evaluate this expression to find the future value or total in the retirement account.

The calculated total may vary depending on the compounding frequency and rounding used.

Answer:

No solution

Step-by-step explanation:

Assume x - 4 ≠ 0 and x + 5 ≠ 0,

note (x - 4)(x + 5) = x² + x - 20, so x² + x - 20 ≠ 0

Multiply by (x - 4)(x + 5) both sides and

get

x(x + 5) - 4(x - 4) = 36

x² + 5x - 4x + 16 = 36

x² + x - 20 = 0

But we have assumed x² + x - 20 ≠ 0

So the equation has no solution

Answer:

1.81 inches

Step-by-step explanation:

Given that,

The circumference of the largest orange in a bag is \(9\dfrac{5}{8}\ \text{inches}\) and that of smallest orange is \(7\dfrac{13}{16}\ \text{inches}\).

Difference = largest orange - smallest orange

= \(9\dfrac{5}{8}-7\dfrac{13}{16}\\\\=\dfrac{77}{8}-\dfrac{125}{16}\\\\=\dfrac{29}{16}\\\\=1.81\ \text{inches}\)

So,  difference of the circumferences of the smallest orange and the largest orange is 1.81 inches

Combining like terms yields 7x⁵ - x³ - x² + 4x.

The total volume of the air space of spherical ball is A = 12.265625 inches³

Given data ,

Since each tennis ball has a diameter of 2.5 inches, the radius of each ball is 1.25 inches.

The air space around the balls can be thought of as a cylinder with a height equal to the diameter of one ball and a radius equal to the radius of one ball.

The height of the cylinder is 2.5 inches, and the radius is 1.25 inches.

The formula for the volume of a cylinder is:

V = πr²h

V = ( 3.14 ) ( 1.25 )² ( 7.5 )

V = 36.796875 inches³

where V is the volume, r is the radius, and h is the height.

So, the volume of the one ball is:

V₁ = ( 4/3 )π(1.25)³

V₁ = 8.177083 inches³

The total volume of three balls is = volume of 3 spherical balls

V₂ = 3V₁ = 3(8.177083) ≈ 24.53125 cubic inches

Therefore, the total volume of the air space around the three tennis balls is approximately A = 36.796875 inches³ - 24.53125 inches³

A = 12.265625 inches³

Hence , the volume of air space is A = 12.265625 inches³

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Answer:

a number is correct watch it clearly

$37,500 should be invested in B-rated bonds and $22,500 should be invested in a certificate of deposit in order to realize exactly $6,000 in interest per year.

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Answer:  4.25

Step-by-step explanation:

:)

Answer:

2(x-3)² = 5

2(x-3)(x-3) = 5

2(x²-6x+9) = 5

2x²-12x+18-5=0

2x²-12x+13=0

Use Quadratic Formula to Solve

x = 15.16 = 15.2

or

x = 8.837 = 8.8

A contradiction in the given clues and it is not possible to find a valid code with the given information.

The code to open the treasure chest can be determined using a few simple steps.
Firstly, we know that the last digit is half of 18, which is 9.

This means that the code ends with the number 9.
Next, we are given the information that the sum of the two middle digits is 10.

This tells us that the two middle digits must be 4 and 6, as they add up to 10.
Thirdly, we know that the third and fourth digits are the same.

Since we already know that the last digit is 9, this means that the third digit must also be 9.
Finally, we are told that the first digit is double the second digit.

Since we know that the second digit is 4, we can determine that the first digit must be 8.
Therefore, the code to open the treasure chest is 8469.

Mr Brainiac can now use this code to unlock the chest and discover the treasures inside.
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The monthly cell phone bill when shared data equals zero is given as follows:

$26.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The intercept of the line in this problem is given as follows:

b = 26.

Hence $26 is the monthly cell phone bill when shared data equals zero.

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Answer:

  45 minutes

Step-by-step explanation:

At 30 mph for 1/4 hour, Peter has a 7.5 mile head start. After he leaves, Mitchell closes that gap at the rate of 40-30 = 10 miles per hour. It will take him ...

  t = d/s

  t = (7.5 mi)/(10 mi/h) = 0.75 h

to catch Peter.

Mitchell will catch Peter in 45 minutes.

__

Alternate Solution

Another way to look at it is that Mitchell's 10 mph advantage is 1/3 of Peter's speed, so it will take 1/(1/3) = 3 times the period of Peter's head start:

  3 × 15 minutes = 45 minutes . . . for Mitchell to catch Peter

_____

You can write equations involving time and distance and see where the distances traveled become the same. You need to be careful choosing the time reference, since you're concerned with Mitchell's travel time. I personally prefer to work "head start" problems by considering the differences in time and speed, as above. This is where you end up using the equations approach, anyway.

The maximum number of guests she can invite is 9.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Given that If Sasha invites three guests, the cost of her retirement party will be $15.

If she can afford to spend $45 the maximum number of the guest will be calculated as:-

3 guests = $15

1 guest = $5

Calculate the maximum guest,

Number of guests = $45 / $5

Number of guests = 9

Therefore, the most visitors she may invite is 9.

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The congruent reason for the triangles is (b) HL theorem

From the question, we have the following parameters that can be used in our computation:

Triangles = FGH and JHK

The SSS similarity theorem implies that the corresponding sides of the two triangles in question are not just similar, but they are also congruent

From the question, we can see that the following corresponding sides on the triangles:

Sides GH and HK

Sides FH and JK

These parameters are given in reasons (2) and (3) and it implies that these sides are congruent sides

For the triangle to be congruent by SSS, the following sides must also be congruent

GH must be congruent to HK

The above statement is true because point H is the midpoint of line GK

This is indicated in reason (2)

Hence, the congruent statement is SSS.

However, we can also make use of the HL theorem in (B)

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Answer:

BY using the formula of h square= p square +beautiful square hole root

Answer:

300x.03 all divided by 4

Step-by-step explanation:

Marty invested $3,000 in mutual funds and the remaining $9,000 in stocks

What is ratio?

Ratio means the number of times a value is contained in other value, in this case, there are 3 times as much money invested in stocks than mutual funds, which means that the invested amounts are in ratio 3:1,such that 3 is stock investment and 1 for mutual funds amount.

On that basis, we can determine the amount invested in each investment option is the value of that investment divided by the sum of the 2 numbers(4=3+1)

The amount invested in stocks is determined 3 divided 4 multiplied by the total inheritance

amount invested in stocks=3/4*$12,000

amount invested in stocks=9,000

amount invested in mutual funds=1/4*$12,000

amount invested in mutual funds=$3,000

$3,000 would be invested in the mutual funds where $9,000 invested in stocks

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Answer:

≈ 11.66 units

Step-by-step explanation:

Given points:

To find:

The distance between two points is calculated by formula:

Answer is ≈ 11.66 units

The linear equation in standard form is g + s + b=104, the relationship between silver to bronze medals is g = s  and the solution is g=46, s=29, b=29

(a) Since the United States won 104 gold (g), silver s, and bronze (b) medals in the 2012 Summer Olympics.

This means the sum of gold (g), silver s, and bronze (b) medals is equal to 104. Thus, the linear equation in standard form is:

g + s + b = 104

(b) Since the United States won 46 gold medals and the same number each of silver and bronze medals. This implies:

g = 46

s = b

Thus, the relationship between the number of silver to bronze medals is s = b

(c) To solve the linear equation, substitute g = 46 and s = b into the equation g + s + b = 104:

g + s + b = 104

46 + b + b = 104

46 + 2b = 104

2b = 104 -46

2b = 58

b = 58/2

b = 29

Also, s = 29        (Remember: s = b)

Thus, g = 46, s =29, b = 29

Therefore, the United States won 46 gold (g), 29 silver (s), and 29 bronze (b) medals in the 2012 Summer Olympics. Select options a., d. and e. for a., b., and c. respectively

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9514 1404 393

Answer:

  (b)  y/6 = 7/5.25

Step-by-step explanation:

Clockwise from the obtuse angle, the side ratios are ...

  Fig I : Fig II

  4.2 : 3.15

  y : 6

  7 : 5.25

  6 : x

  4 : 3

__

A true proportion will have corresponding parts of these ratios in corresponding places. The only true proportion listed is ...

  \(\dfrac{y}{6}=\dfrac{7}{5.25}\)

Answer:

3. -3,0,|3|, (-3)^2

Step-by-step explanation:

Answer:

answer would be option 3

Step-by-step explanation:

help this helps

The volume of the given triangular prism is 384 cm³.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Here, the area of the base is

Area of a rectangle = 1/2 ×Base×Height

= 1/2 ×12×4

= 24 cm²

Now the volume is 24×16

= 384 cm³

Therefore, the volume of the given triangular prism is 384 cm³.

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Answer:

-6.5

Step-by-step explanation:

Answer:

B) False.

Step-by-step explanation:

Really

Answer:

False

Step-by-step explanation:

The nth term of 11,13,15,17 is,

⇒ T (n) = 9 + 2n

Given that;

The sequence is,

11, 13, 15, 17, ....

Here, Common difference is,

13 - 11 = 2

15 - 13 = 2

Hence, Sequence is in Arithmetic sequence.

So, the nth term of 11,13,15,17 is,

⇒ T (n) = a + (n - 1)d

⇒ T (n) = 11 + (n - 1) 2

⇒ T (n) = 11 + 2n - 2

⇒ T (n) = 9 + 2n

Thus, The nth term of 11,13,15,17 is,

⇒ T (n) = 9 + 2n

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C(X,Y) is a statement that means a student X from the school is enrolled in class Y which is one of the classes offered by the school.

C(X,Y) is a statement that means a student X from the school is enrolled in class Y which is one of the classes offered by the school. The domain for X consists of all students in the school and the domain for Y consists of all classes being offered. To explain this statement further, firstly it should be noted that the statement is saying that a student (X) is enrolled in a class (Y). Secondly, the term “domain” refers to the set of all possible values that can be used for a given variable. In this case, the domain for X consists of all students in the school, while the domain for Y consists of all classes being offered at the school. Therefore, the statement C(X,y) is saying that a student from the school is enrolled in one of the classes offered by the school.

The complete question: Let C(X,Y) mean that student x is enrolled in class y, where the domain for x consists of all students in your school and the domain for y consists of all classes being

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