What is the polynomial function of least degree whose only zeros are -3, ,-2, and 4 ?

Answer:

$12,162.68

Step-by-step explanation:

It's compounded monthly.  3 years is 36 months.

A = P (1 + r)^n

A = 5000 (1 + 0.025)^36

A ≈ 12162.68

Rounded to the nearest cent, her exact account balance would be $12,162.68.

Answer:

Step-by-step explanation:

1. The appropriate "dimensional analysis" is ...

[tex]\dfrac{2.9\,ft}{1\,day}\cdot\dfrac{12\,in}{1\,ft}\cdot\dfrac{1\,day}{24\,h}=\dfrac{2.9\cdot 12\cdot 1\,day\cdot ft\cdot in}{1\cdot 1\cdot 24\,day\cdot ft\cdot h}=1.45\dfrac{in}{h}[/tex]

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2. Aaron used the inverse of the correct days to hours conversion factor. The units he ends up with are in·h/day², not in/h. And the calculation he did does not match the expression he wrote.

Good evening ,

______

Answer:

A. x=all real numbers.

D. x = [tex]\frac{2-np}{2}[/tex]

___________________

Step-by-step explanation:

25-5x=5(-x+5)

25-5x=-5x+25

25-5x=25-5x

Then this equation is valid for all real number x

Note : If you replace x by any number you will get 0 = 0 and that always true.

:)

Answer:

a

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

We can express 5 × 23 as

5(20 + 3) ← distribute terms in parenthesis by 5

= 5 × 20 + 5 × 3

= 100 + 15

= 115

By distributive property , the number 5 x 23 = 115

What is Distributive Property?

The distributive property states that multiplying the sum of two or more addends by a number produces the same result as multiplying each addend individually by the number and adding the products together.

For a product of two numbers , a and d , d = b + c

By distributive property ,

a x ( b + c ) = a x b + a x c

Given data ,

Let the number be 5 x 23

Now , the number 23 can be split into ( 20 + 3 )

By opening the parentheses ,

5 x ( 20 + 3 )

The number 5 is first multiplied by 20 and then multiplied by 3 , and the sum of both the products will be taken

So ,

5 x 23 = 5 ( 20 + 3 )

5 x 23 = 5 ( 20 ) + 5 ( 3 )

5 x 23 = 100 + 15

5 x 23 = 115

Hence , by distributive property the product 5 x 23 is 115

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Answer:

Step-by-step explanation:

He would be 87 years old right now

To determine Carl's age, we subtract his birth year, 1931, from the current year, 2022, resulting in Carl being 91 years old.

To calculate how old Carl is now, you need to determine the current year and subtract Carl's birth year from it. Since Carl was born in January 1931, we would use 2022 as the current year (assuming it's the present year).

So, the calculation is simple: 2022 - 1931 = 91. Therefore, Carl would be 91 years old.

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Answer:

E and F

Step-by-step explanation:

They are the only ones which use the appropriate triangle angles and points.

Have a nice day!!!!!!!! :-)

KA

E. ΔDMR & F. ΔMRD are valid names of the triangle.

We know that, a triangle has 3 vertices.

Name of a triangle is always with the name of the vertices together in a clock or anticlockwise manner.

Example : If vertices of a triangle are A, B & C, then name of the triangle are like ΔABC, ΔBCA, ΔCAB, ΔBAC, ΔACB, ΔCBA.

Here, in the given diagram, vertices of the triangle are D, M, R

So, the names ΔDMR & ΔMRD are correct in all the options, others are not names of vertices, so they are not taken.

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First, it is important to know that there are 180 degrees in a triangle. The equation for this is 90+3x=180, since the small square means 90 degrees. From there on, you should be able to figure it out yourself.

Answer:

Azeneth needs to buy 4x² + 2x + 24 feet

Step-by-step explanation:

* Lets explain how to solve the problem

- Azeneth is putting a fence around her rectangular garden

- The width of the garden is 4x + 5 feet

- The  length is 2x² – 3x + 7 feet

- We need to find how much total fencing  Azeneth needs to buy in

  terms of x

∵ The fence will put around the four sides of the rectangular garden

∴ The length of the fence is equal to the perimeter of the garden

- The perimeter of any rectangle = 2l + 2w, where l and w are its

  dimensions

∵ The perimeter of the garden = 2 × its width + 2 × its length

∵ Width = 4x + 5

∴ 2 × width = 2(4x + 5) = 8x + 10

∵ Length = 2x² - 3x + 7

∴ 2 × length = 2(2x² - 3x + 7) = 4x² - 6x + 14

∴ The perimeter of the garden = 8x + 10 + 4x² - 6x + 14

- Add like terms

∴ The perimeter of the garden = 4x² + (8x - 6x) + (10 + 14)

∴ The perimeter of the garden = 4x² + 2x + 24

∵ The length of the fence = the perimeter of the garden

∴ The length of the fence = 4x² + 2x + 24 feet

* Azeneth needs to buy 4x² + 2x + 24 feet

the  answer is f (-3x - 22) = -6x - 33

Answer:

According to the 180°-rotation rule, you take the OPPOSITE of both the x-coordinate and y-coordinate:

180°: [x, y] → [-x, -y]

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Answer:

150(0.4),2,500(0.11)

Step-by-step explanation:The first question says 150 participants and 40%of the participants are eliminated. so it's 150(0.4)n

same goes for the second 2,500 bacteria in a colony the colony grows at a rate of 11% every hour so the answer to the question is 2,500(0.11)n

The student is tasked to match situations with their corresponding mathematical expressions, identifying key mathematical operations and formulating accurate representation for these operations

The question is asking you to match given situations with their corresponding mathematical expressions. An example might be the situation 'Tom has twice as many apples as Tim' being matched to the expression '2T', where 'T' denotes the number of apples Tim has. To solve this, read each situation carefully and identify the key mathematical operations (addition, subtraction, multiplication, division) or relationships (equal to, greater than, less than) embedded within them. Then, formulate a mathematical expression that accurately represents these operations or relationships.

For example, if the situation is 'Sally has five more books than John,' the corresponding mathematical expression might be 'J+5' with 'J' representing the number of books John has.

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Answer:

5/6

Step-by-step explanation:

Hey!

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

Steps To Solve:

~Find common denominators

2/3 = 4/6

1/6

~Add

4/6 + 1/6

~Simplify

5/6

This cannot be simplified.

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

Answer:

5/6

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Hope This Helped! Good Luck!

Answer:

-1/2

Step-by-step explanation:

For a line to be parallel, they must be equal, for it to be prependicular, the slope must have an opposite value and be over the value.

Answer:

[tex]\frac{-1}{2}[/tex]

Step-by-step explanation:

General form of equation of line = [tex]y= mx+c[/tex]

Where m is the slope of line

We are given a line [tex]y=2x + 5[/tex]

On comparing with general form

m = 2

Let n be the slope of line perpendicular to the line  [tex]y=2x + 5[/tex]

The product of the slopes of perpendicular lines is -1

So,[tex]m \times n = -1[/tex]

[tex]2 \times n = -1[/tex]

[tex]n = \frac{-1}{2}[/tex]

So, Option B is correct

Hence the slope of a line perpendicular to the line whose equation is y=2x + 5 is [tex]\frac{-1}{2}[/tex]

Answer:

63

Step-by-step explanation:

51 - ( - 12)        (-)(-)=(+)

51  +  12

  63

Answer:

63

Step-by-step explanation:

The question says 51 +12 becase two negatives make a positive.

Answer:

The answer is D. 12x - 3.

Step-by-step explanation:

To add these functions, we just add the terms.

f(x) + g(x) = (7x - 4) + (5x + 1)

7x - 4 + 5x + 1 | Simplify

7x + 5x - 3

12x - 3.

Answer:

Option D. (12x - 3)

Step-by-step explanation:

Madden's total cups of coffee made is represented by the function f(x).

f(x) = 7x - 4

Jenn's total cups of coffee made is represented by the function g(x).

g(x) = 5x + 1

Now we have to write a function that represents the total cup of coffee that represents they made.

That will be represented by f(x) + g(x) = (7x - 4) + (5x + 1)

f(x) + g(x) = 12x - 3

Therefore, option D. will be the answer.

Answer:

Given the expression -3 - 4(2x- 3) the correct solution is -8x + 9.

Step-by-step explanation:

Andy wrote -14x + 21, so his error was to do de substraction (-3 -4) and then distribute -7(2x-3) = -14x+ 21.

Sylvie wrote -8x -6. Her error was to multiplied -4 only for 2x,

then -3 - 4(2x -3) = -3 -8x -3 = -8x -6.

Andy incorrectly distributed the negative sign and Sylvie made an error in simplifying the expression. The correct answer is -8x + 9.

Andy's error: He incorrectly distributed the negative sign to both terms inside the parentheses. When distributing a negative sign to each term, the sign of each term should change. So, -4(2x - 3) becomes -8x + 12. However, Andy erroneously distributed the negative sign to only the first term, resulting in -14x + 21.

Sylvie's error: She incorrectly simplified the expression -8 - 6, which is equal to -14. However, this is not the correct result for the entire expression -3 - 4(2x - 3).

The correct answer is obtained by applying the distributive property and combining like terms. First, simplify the expression inside the parentheses: -4(2x - 3) = -8x + 12. Then, combine the terms outside the parentheses with the simplified expression: -3 - 8x + 12 = -8x + 9.

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The statement 2 + (3 + 4) = 2 + (4 + 3) is the one that uses the commutative property of addition, which states that changing the order of numbers being added does not affect the sum. So correct answer is first option.

The statement that uses the commutative property of addition is 2 + (3 + 4) = 2 + (4 + 3). The commutative property of addition states that the order in which two numbers are added does not change the sum.

This is represented by the equation A+B=B+A. In our specific example, changing the order of 3 and 4 does not affect the sum when added to 2.

This demonstrates the commutative property in a clear manner.

Answer:

$22.20

Step-by-step explanation:

We are told that $13.32 only covered 3/5 of the cost. Does this mean it covered the whole cost? No. The 5 in the denominator represents the whole cost, and the 3 represents the fraction of the cost. In this case, 13.32 represents the 3, as it did not cover the whole cost.

Let's set up our equation by making 13.32 into a fraction.

13.32/x

We will represent the present's actual cost with the letter x.

13.32/x = 3/5

We want to make sure the 13.32 is in the numerator, equal to the 3 in the numerator in the 3/5 number, because we know that $13.32 only covered for a fraction of the present's cost, not the whole cost.

We solve this by doing cross multiplication. Multiply the 13.32 by the 5.

13.32 x 5 = 66.6

Next we divide 66.6 by 3 to get 22.2

66.6/3 = 22.2

This gives us our final answer of $22.20. This means that the cost of the original present was $22.20

The question involves setting up a proportion to find the total cost of the present. This was done step-by-step by dividing $13.32 by 3 to find 1/5 of the cost, and then multiplying by 5 to find the full cost. The present cost approximately $22.20

The subject of your question is mathematics, particularly a topic in proportion. The information given is that $13.32 represents 3/5 of the cost of the present. We could set up a proportion to help calculate the full cost. If 3/5 is equal to $13.32, then 1 (or 5/5) would be equal to the full price of the present. We can solve for the full price by dividing $13.32 by 3 and then multiplying by 5 (since 5/5 represents the whole or full cost).

Step-by-step:

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Answer:

Ø

Step-by-step explanation:

Anything that is set to equal x is what is known as an undefined rate of change [slope] because it is a vertical line.

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Answer:

y = 3x² + 54x + 240

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

here (h, k) = (- 9, - 3), thus

y = a(x + 9)² - 3

To find a substitute either of the roots into the equation

Using (- 8, 0), then

0 = a(- 8 + 9)² - 3

0 = a - 3 ( add 3 to both sides )

a = 3

y = 3(x + 9)² - 3 ← in vertex form

Expand factor and simplify

y = 3(x² + 18x + 81) - 3

  = 3x² + 54x + 243 - 3

  = 3x² + 54x + 240 ← in standard form

Final answer:

Tonka can load a maximum of 29 boxes on the elevator.

Explanation:

To calculate the number of boxes Tonka can load on the elevator, we need to divide the maximum weight capacity of the elevator by the weight of each box. The weight capacity of the elevator is 2000 lb, and each box weighs 67 lb. Therefore, the number of boxes Tonka can load is found by dividing 2000 lb by 67 lb:

Number of boxes = 2000 lb ÷ 67 lb = 29.85

Since we can't have a fraction of a box, Tonka can load a maximum of 29 boxes on the elevator.

The equivalent value for (s \\circ f) (-7), given s(x) = 2 - x and f(x) = 3x, is 23.

The question asks which value is equivalent to (s \\circ f) (-7), where s(x) = 2 - x and f(x) = 3x.

To solve for (s \\circ f) (-7), we first need to find f(-7). Since f(x) = 3x, we substitute x with -7:
f(-7) = 3(-7) = -21.
Next, we calculate s(f(-7)), which means we substitute x in s(x) with the value of f(-7):
s(-21) = 2 - (-21) = 2 + 21 = 23.

Therefore, the equivalent value  is 23.

Answer:

  6^8 = 1,679,616

Step-by-step explanation:

The applicable rule of exponents is ...

  (a^b)^c = a^(bc)

__

Applied to this problem, the rule tells you ...

  (6^2)^4 = 6^(2·4) = 6^8 = 1,679,616

__

Or, you can evaluate the expression according to the Order of Operations:

  (6^2)^4 = 36^4 = 1,679,616

Answer:

6^8 = 1,679,616

Step-by-step explanation:

i looked it up and i did it on my own

Answer:

It would be Meters, .50cm = 0.005 M

Answer:

133

Step-by-step explanation:

127 + 16 = 133

Answer:

12

Step-by-step explanation:

in geometry, the hexagonal prism is a prism with hexagonal base. This polyhedron has 8 faces, 18 edges, and 12 vertices. Since it has 8 faces, it is an octahedron. However, the term octahedron is primarily used to refer to the regular octahedron, which has eight triangular faces.

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Final answer:

The algebraic expression for the phrase 'the sum of b and 11' is 'b + 11'. This expression represents adding 'b' to '11', and addition is commutative, which means it could also be written as '11 + b'. So the correct option is c.

Explanation:

The phrase 'the sum of b and 11' represents an algebraic expression where sum refers to the addition of two terms. When we talk about the sum of two algebraic expressions, we use the plus sign (+) to denote the operation. Therefore, for the given phrase 'the sum of b and 11a', the algebraic expression is b + 11.

It’s important to keep in mind that in algebra when we want to indicate that one term is multiplied by another, we often place them next to each other without any symbol, which is known as concatenation. And because addition is commutative, we could also write this expression as 11 + b, and it would mean the same thing.

Also worth mentioning is the distinction between the expression 'b - 11' (which means 'b' subtracted by '11') and 'b/11' (which means 'b' divided by '11'). These are different operations and would not correctly represent the phrase we were given to translate into an algebraic expression.

Answer:

[tex]\frac{13}{8}=1\frac{5}{8}[/tex] gallons

Step-by-step explanation:

We have been given that Jackie brought 3/4 of a gallon of iced tea to the party. Bill brought 7/8 of a gallon of iced tea to the same party.

To find the total amount of iced tea, we will add both quantities as:

[tex]\text{Amount of ice tea brought to party by Jackie and Bill}=\frac{3}{4}+\frac{7}{8}[/tex]

Make a common denominator:

[tex]\text{Amount of ice tea brought to party by Jackie and Bill}=\frac{3*2}{4*2}+\frac{7}{8}[/tex]

[tex]\text{Amount of ice tea brought to party by Jackie and Bill}=\frac{6}{8}+\frac{7}{8}[/tex]

Add numerators:

[tex]\text{Amount of ice tea brought to party by Jackie and Bill}=\frac{6+7}{8}[/tex]

[tex]\text{Amount of ice tea brought to party by Jackie and Bill}=\frac{13}{8}[/tex]

[tex]\text{Amount of ice tea brought to party by Jackie and Bill}=1\frac{5}{8}[/tex]

Therefore, Jackie and Bill brought [tex]\frac{13}{8}=1\frac{5}{8}[/tex] gallons of ice tea to the party.