Factor the polynominal. t^2+8t

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:

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 final amount of money was $50, they spent half of what they collected on canned foods, so 50 x 2 = 100.

They collected a total of $100.

Let the amount Eric collected = X

Charlotte collected 3 times as much minus $20, writing this as an equation you get 3x-20.

Now you have Eric plus Charlotte = $100:

x + 3x-20 = 100

Combine like terms:

4x-20 = 100

Add 20 to both sides:

4x = 120

Divide both sides by 4:

x = 120/4

x = 30

Eric = X = $30

Charlotte = 3x-20 = 3(30) - 20 = 90 -20 = $70

Answer:

40

Step-by-step explanation:

the the answer is 40 because if you do 40 * 3 to get 120 and if you minus 20 then you get a hundred in a hundred divided by 2 equals 50

what you do is you do 50 * 2 but you got to 100 then you add 20 which gives 220 then you ÷ by 3

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:

$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:

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:

it would 3,000

Step-by-step explanation:

the nearest rounded off to thousand for this number is 3000

Answer:

$2.33

Step-by-step explanation:

$0.89 × 3 = $2.67

$5 - $2.67 = $2.33

Answer:

$2.33

Step-by-step explanation:

$0.89 × 3 = $2.67

$5 - $2.67 = $2.33

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:

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:

The area of the polygon is 64 units²

Step-by-step explanation:

* Lets explain how to solve the problem

- The polygon has 5 sides and 5 vertices

- To find its area by easy way split it into two trapezoid by a horizontal

  line y = 1

- The vertices of trapezoid (1) are (-5 , 1) , (4 , 1) , (-5 , 5) , (0 , 5)

- The vertices of one of the parallel bases are (-5 , 1) , (4 , 1)

- The length of this base = 4 - (-5) = 4 + 5 = 9 units

- The vertices of the other parallel bases are (-5 , 5) , (0 , 5)

- The length of this base = 0 - (-5) = 0 + 5 = 5 units

- The length of its height = 5 - 1 = 4 units

- The area of the trapezoid = 1/2 (b1 + b2) × h

∴ Area of trapezoid 1 = 1/2 (9 + 5) × 4 = 28 units²

- The vertices of trapezoid (2) are (4 , 1) , (-5 , 1) , (-5 , -5) , (-2 , -5)

- The vertices of one of the parallel bases are (4 , 1) , (-5 , 1)

- The length of this base = 4 - (-5) = 4 + 5 = 9 units

- The vertices of the other parallel bases are (-5 , -5) , (-2 , -5)

- The length of this base = (-2) - (-5) = -2 + 5 = 3 units

- The length of its height = 1 - (-5) = 1 + 5 = 6 units

∴ Area of trapezoid 1 = 1/2 (9 + 3) × 6 = 36 units²

∵ Area of the polygon = Area trapezoid (1) + Area trapezoid (2)

∵ Area trapezoid (1) = 28 units²

∵ Area trapezoid (2) = 36 units²

∴ Area of polygon = 28 + 36 = 64 units²

∴ The area of the polygon is 64 units²

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:

18x²-45x

Step-by-step explanation:

Final answer:

To find the product of negative 9 and (5 minus 2x), use the distributive property, resulting in -45 + 18x.

Explanation:

The product of negative 9 and (5 minus 2x) can be found by applying the distributive property. This property states that a number multiplied by a sum or difference in parentheses is equivalent to the number multiplied by each term inside the parentheses separately, and then summing the results. So, the product will be:

Negative 9 multiplied by 5, which gives -45.

Negative 9 multiplied by -2x (note the two negatives make a positive), which gives 18x.

Combining these two products, we get the final answer, which is -45 + 18x.

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.

Step-by-step explanation:

square of 15 = 225

The Number must be between 14 and 16

Answer:

The number will lie between 14 and 16.

Step-by-step explanation:

If the square of a whole number is between 200 and 250 then the inequality formed will be

200 < x² < 250

where x is a whole number.

Now we will simplify this inequality.

[tex]\sqrt{200}<\sqrt{x^{2} } <\sqrt{250}[/tex]

14.14 < x < 15.81

By approximation, 14 < x < 16

Therefore, the number must lie between 14 and 16.

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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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.

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.

Answer:

It would be Meters, .50cm = 0.005 M

Answer:

1 - 2x + 5x^4

Explanation:

A trinomial is an equation with three terms. 6 - 2x^3 - 4x^2 + x^5 has four terms so it is a polynomial, 2p^3 - p has two terms, so it is a binomial, 1 - x has two terms and is also a binomial, 1 - 2x + 5x^4 has three terms, so it is a trinomial.

The digit 6 in January represents 60,000 due to its position in the 'ten thousands' place, whereas in February's count, the digit 6 represents 600, due to its place in the 'hundreds' place.

The value of a digit in a number depends on its position within that number, otherwise known as its place value. In the number 160,341 (representing the number of boxes of paper in January), the 6 is in the 'ten thousands' place, making it worth 60,000. In contrast, the 6 in the number 32,698 (representing the number of boxes in February) is in the 'hundreds' place, making it worth 600. Therefore, the digit 6 in January has a larger value than the digit 6 in February.

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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.

I am joyous to assist you anytime.

Answer:

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

180°: [x, y] → [-x, -y]

I am joyous to assist you anytime.

The area of the regular hexagon is approximately 2.598 cm².

Finding the Area of a Regular Hexagon

To find the area of a regular hexagon with a side length of 1 cm, we can use the formula for the area of a regular polygon:

Area = (3√3 / 2) × s², where s is the side length.

Given that the side length ( extbf{s}) is 1 cm:

Square the side length: 1² = 1 cm²

Multiply by (3√3 / 2): (3√3 / 2) × 1 cm² ≈ 2.598 cm²

Thus, the area of the regular hexagon is approximately 2.598 cm².

Answer:

y=11 x=-10

Step-by-step explanation:

Y:

Add 3 to both sides. Then divide by 9 on both sides.

X:

Subtract 11 from both sides. then divide by -3 on both sides.

Hope this helped

Answer:

[tex]7000\times 50 = 3,50,000 = 35\times 10^4[/tex]

Step-by-step explanation:

We have to find the product of 7,000 and 50 and express it in the form of product of a whole number and power of 10.

First, we will find the product.

[tex]7000\times 50 = 3,50,000[/tex]

Now, we have to express this product as a sum of whole number and power of 10.

3,50,000 can be written as:

[tex]3,50,000 = 35\times 10^4[/tex]

Here, 35 is our whole number and [tex]10^4[/tex] is required power of 10.

We used the rule of exponents to express the product in such manner.