Given the function f(x)=x2+2x+1, find:
f( 2a−3/5 )

Answer:

1 3/5

Step-by-step explanation:

10 = 10/1

4*10=40

25*1=25

40/25

now simplify:

40/5=8

25/5=5

8/5 = 1 6/10 = 1 3/5

hope this helps

The given expression in its simplest form is [tex]1\frac{3}{5}[/tex]

From the question,

We are to write the given expression in its simplest form

The given expression is 4/25 x 10

First, we will write the expression properly.

The expression can be written as

[tex]\frac{4}{25} \times 10[/tex]

The expression can be simplified as shown below

[tex]\frac{4}{25} \times 10[/tex]

This becomes

[tex]\frac{40}{25}[/tex]

Then,

[tex]1\frac{15}{25}[/tex]

In the simplest form, we get

[tex]1\frac{3}{5}[/tex]

Hence, the given expression in its simplest form is [tex]1\frac{3}{5}[/tex]

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we know he deposited 41.67, we also know that's the 60% of his paycheck, the total paycheck will be the 100%.

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 41.67&60\\ x&100 \end{array}\implies \cfrac{41.67}{x}=\cfrac{60}{100}\implies \cfrac{41.67}{x}=\cfrac{3}{5}\implies 208.35=3x \\\\\\ \cfrac{208.35}{3}=x\implies 69.45=x[/tex]

Answer:

No solution/ Not possible

Step-by-step explanation:

Let's write out the equation

4x-2+x= 2x+8+3x

First thing we should do is look and see if there are any like terms that we can combine

4x+x-2=2x+3x+8

5x-2=5x+8

Then we want to get x on one side

By adding 2 to both sides

5x=5x+10

0=10

This is false, so the answer to this is No solution

If a teacher is buying supplies for an upcoming art project. She buys x bottles of paint for $1.29 each. She is buying 7 bottles of paint and  15 canvases.

Let's represent the number of bottles of paint she buys as x and the number of canvases she buys as x + 8.

The cost of the paint would be:

Cost of paint = Number of bottles of paint * Price per bottle of paint = x * $1.29

The cost of the canvases would be:

Cost of canvases = Number of canvases * Price per canvas = (x + 8) * $1.89

The total cost is the sum of the costs of paint and canvases:

Total cost = Cost of paint + Cost of canvases

we can write the equation:

Total cost = x * $1.29 + (x + 8) * $1.89 = $37.38

solve for x:

1.29x + 1.89(x + 8) = 37.38

1.29x + 1.89x + 15.12 = 37.38

3.18x + 15.12 = 37.38

3.18x = 22.26

x = 22.26 / 3.18

x ≈ 7

Therefore , she is buying approximately 7 bottles of paint and 7 + 8 = 15 canvases.

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Answer:

Step-by-step explanation:

Answer:

Option B.

Step-by-step explanation:

The given equation is

[tex]49y-8=89[/tex]

We need to find a word problem that can represented by the given equation.

The required problem is : A water filter filters 49 ounces of water per day. The first 8 ounces of water cannot be consumed and must be dumped out. How many days will it take the water filter to produce 89 ounces of consumable water?

Let y be the number number of days it take the water filter to produce 89 ounces of consumable water.

Total water filtered in y days = 49y

The first 8 ounces of water cannot be consumed and must be dumped out.

Total consumable water filtered in y days = 49y - 8

We need to produce 89 ounces of consumable water.

[tex]49y-8=89[/tex]

Therefore, the correct option is B.

Answer:

Yes, it would be all real numbers. If a negative was more than the absolute vaule, it would be false

Step-by-step explanation:

|x-6|>-2

pos. neg.

The the absolute vaule is ALWAYS positive so like I said before if the sign was facing towards the -2 it would be false

4 |x-6| (greater than or equal to)> -8

First you have to divide 4 on both sides since its outside the absolute vaule

then you will be left with

|x-6|>-2

since the 2 is a negative, you may think that this is automatically no solution, but sadly it isn't.

since the sign says the pos. sign is greater the equation is true and "all real numbers"

hope that helps!!

Answer: x=20

y= 17/4

Step-by-step explanation:

x=37-4y

111-16y=43

y=17/4

x=20

Answer:

1000 to the 10 th power

Step-by-step explanation:

Just put it into power form

Since Alisa wrote a comparison for set b using the ten thousands place. The strategy that she could have used is 1000¹⁰

So, Alisa's strategy for comparing numbers in Set B using the ten thousand place involves focusing on a specific digit position to simplify the comparison process.

In Set B, the numbers are 492,111 and 409,867. By looking at the ten thousand place, which is the fourth digit from the right, Alisa can break down the comparison to:

Since 2 is greater than 0, Alisa can quickly deduce that 492,111 is larger than 409,867. This strategy is based on the idea that when numbers are similar in size, comparing them digit by digit can help us easily figure out which one is bigger.

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See full text below

Alisa says it is easier to compare the numbers in set a (45,000, 1,025,680) instead of set b (492,111, 409,867). Alisa wrote a comparison for Set B using ten thousand place. Explain what strategy she could have used.

The correct fraction is [tex]\(\frac{456}{1000}\)[/tex].

To convert the decimal 0.456 to a fraction, one can follow these steps:

1. Write the decimal as a fraction with a denominator of 1000, since there are three digits after the decimal point. This gives us [tex]\(\frac{456}{1000}\)[/tex].

2. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 456 and 1000 is 8.

3. Divide both the numerator and the denominator by 8 to get the simplified fraction:

[tex]\(\frac{456 \div 8}{1000 \div 8} = \frac{57}{125}\)[/tex].

Therefore, the decimal 0.456 expressed as a simplified fraction is [tex]\(\frac{57}{125}\)[/tex].

Answer:

I think that the dependent variable would be the academic performance because she hypothesizes that the performance depends on how many hours of sleep you get. And the amount of sleep would be the independent variable. I'm not too too sure.

Answer:

Independent Variable = Effect of Sleep

Dependent Variable = Academic Performance

Step-by-step explanation:

As we know that dependent variable depends on independent variable and on changing the value of independent variable, value of dependent variable also get changed.

Here in the given scenario academic performance is depend on the effect of sleep. Thus,

Independent Variable = Effect of Sleep ( Number of hours of sleep)

Dependent Variable = Academic Performance.

Answer:

39

Step-by-step explanation:

This weird notation just means we are going to put one equation inside the other, and then solve.

Makes more sense when you write it like this:

g ( f ( x ) )

To solve, we are going to take the 3, plug it into the f ( x )

g ( f ( 3 ) )

^ This makes it a lot easier to understand what we have to do.

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

Ok, so now we evaluate f ( x ) at 3.

4 ( 3 ) - 2

f( x ) = 10

Then we plug it into g ( x )

4 ( 10 ) - 1

= 39

Here's how it looks in total:

4 ( 4 ( 3 ) - 2 ) - 1 = 39

Slightly more complicated, but that's why i broke it down step by step.

Answer:

c= -1.12

Step-by-step explanation:

Answer:

Colleen

Step-by-step explanation:

Gabby spent less than Mark

Mark>Gabby

Mark spent less than Layla

Layla>Mark>Gabby

Layla spent less than Colleen

Colleen>Layla>Mark>Gabby

Answer:

Colleen

Step-by-step explanation:

It says that:

Gabby spent less than Mark. Therefore Gabby<Mark

Mark spent less money than Layla. Therefore Mark<Layla and Gabby<Mark<Layla

Layla spent less money than Colleen, so Layla<Colleen and Gabby<Mark<Layla<Colleen.

Colleen spent the most money.

Answer:

B

Step-by-step explanation:

since the domain makes up the x values so the x values are -1,1,-2,and 0

The domain of the relation is {-1, 1, -2, 0}

The domain of a relation refers to the set of all possible input values. In this relation, the x-values or inputs are -1, 1, -2, and 0. Therefore, the set of numbers that make up the domain in this relation is {-1, 1, -2, 0}.

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Answer: [tex]\dfrac{5}{7}[/tex] of an hour

Step-by-step explanation:

Given : It takes [tex]\dfrac{3}{7}[/tex] of an hour to paint [tex]\dfrac{3}{5}[/tex] of a room.

i.e. Time taken to paint [tex]\dfrac{3}{5}[/tex] of a room.= [tex]\dfrac{3}{7}[/tex] of an hour.

Using Unitary Method, we have

Time taken to paint one room.= [tex]\dfrac{3}{7}\times\dfrac{5}{3}[/tex] of an hour.

⇒Time taken to paint one room=[tex]\dfrac{5}{7}[/tex] of an hour.

Hence, it will take [tex]\dfrac{5}{7}[/tex] of an hour to paint one room.

To paint one full room, it takes approximately 5/7 of an hour based on the given information that it takes 3/7 of an hour to paint 3/5 of a room.

Given that,

It takes 3/7 of an hour to paint 3/5 of a room.

The task is to determine how long it takes to paint one full room.

To find out how long it takes to paint one full room,

First, calculate the amount of time required to paint one-fifth of a room. Since it takes 3/7 of an hour to paint 3/5 of a room,

Set up a proportion:

(3/7 hour) / (3/5 room) = (x hour) / (1 room)

By cross-multiplying, we get:

(3/7) (1 room) = (3/5) (x hour)

Simplifying further, we have:

3/7 = (3/5) * (x hour)

To isolate x, we divide both sides of the equation by (3/5):

(3/7) / (3/5) = x hour

This simplifies to:

(3/7) * (5/3) = x hour

15/21 = x hour

x = 5/7 hour

Therefore, it takes 5/7 of an hour to paint one full room.

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Answer:

The GCF of 32 and 56 are 8.

Step-by-step explanation:

Answer above! Enjoy! :)

Answer:

B. -4

Step-by-step explanation:

What you do is PEMDAS

12/3 x (-3) + |-8|=

4 x (-3) + |-8|=

-12 + 8=

-4 is your answer.

Final answer:

To evaluate the expression, divide 12 by 3, multiply by -3, find the absolute value of -8, and sum the results, obtaining -4 as the correct answer.

Explanation:

The student asked to evaluate the expression 12 ÷ 3 × (-3) + |-8|. To solve this, we follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

First, we perform the division: 12 ÷ 3 = 4.

Next, we multiply the result by -3: 4 × (-3) = -12.

Then, we evaluate the absolute value: |-8| = 8.

Lastly, we add the results of the multiplication and the absolute value: -12 + 8 = -4.

Therefore, the correct answer is b: -4.

Answer:

Step-by-step explanation:

1.25 ÷ 3.58 = 0.34916201117

i don;t know if this is right sorry

Answer:

300000

Step-by-step explanation:

you go to the thousands place and see if it is greater than 5. yes it is. it would tell you that it would round up. then you go to the hundreds thousands place and go one number up.

Answer: The correct answer is 2378. Though,maybe the answer that was given to you is wrong.

Step-by-step explanation: 82 x 29 =2378

The inequality representing the number of people who can fill their mugs before the carafe needs to be refilled is p ≥ 14.67. The number of people who can fill their mugs is at least 15.

To determine the inequality that represents the number of people who can fill their mugs before the carafe needs to be refilled, we need to understand the given information. The carafe holds 12 cups of coffee, and the waiter refills it when there is 1 cup or less left. Each coffee mug holds 0.75 cups of coffee. Let's represent the number of people who can fill their mugs as 'p'.

So, the inequality representing the number of people who can fill their mugs before the carafe needs to be refilled is p ≥ 14.67. Since you can't have a fraction of a person, the number of people who can fill their mugs before the carafe needs to be refilled is at least 15.

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Answer: the answer is D

Step-by-step explanation:

The length of third side of the triangle ABC cannot be D) 35.

A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.

Sum of the interior angles of a triangle is 180 degrees.

Given that,

For a triangle ABC,

Length of side AB = 8 units

Length of side BC = 25 units

We have that,

The third side of the triangle will be in the range of the sum and the difference of the other two side lengths.

So side AC can be in the range,

25 - 8 < AC < 25 + 8

17 < AC < 33

Hence the length 35 cannot be possible since it does not contain in the range.

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Answer:

x= 3

Step-by-step explanation:

5x-2=13 - Add 2 to both sides which cancels out the -2 and turns 13 into 15

5x=15 - Divide 5 on both sides which cancels the 5 and leaves x=3

x=3 - Is the final answer or the solution to the problem

Final answer:

The solution to the equation 5x - 2 = 13 is x = 3. To plot this on the number line, mark a point above the horizontal line at the position corresponding to 3.

Explanation:

The solution to the equation 5x - 2 = 13 is found by first adding 2 to both sides of the equation, giving us 5x = 15. We then divide both sides by 5 to isolate x, which gives us x = 3. Therefore, the solution to the equation is x = 3.

To plot the solution on the number line, we draw a horizontal line and mark off points at equal distances. We locate the point corresponding to 3 and draw a dot or vertical line at that point, above the horizontal line because it is a positive number.

Answer:

right angel obtuse angle and i cant remember the other angle

Answer:

See explanation

Step-by-step explanation:

Enzo’s profit over the last few months:

Find the difference between given data

Dec - Jan [tex]\$900-\$500=\$400[/tex]

Jan - Feb [tex]\$500-\$x[/tex]

Feb - Mar [tex]\$x-(-\$300)=\$x+\$300[/tex]

If this sequence is arithmetic, then

[tex]\$500-\$x=\$x+\$300=\$400\\ \\\$x=\$100[/tex]

So, if the profit in February was $100, then this sequence is arithmetic sequence. In this case,

[tex]a_1=900\\ \\a_2=500\\ \\a_3=100\\ \\a_4=-300\\ \\...\\ \\d=-400[/tex]

The recursive formula is

[tex]a_n=a_{n-1}-400[/tex]

Answer:

yes

Step-by-step explanation:

There are 10 4-seated cars at the carnival.

We are given that there are two types of cars at the carnival, one with 2 seats and one with 4 seats. We also know that there are a total of 25 cars and they can seat 70 children in total.

Let's assume the number of 2-seated cars is x and the number of 4-seated cars is y. We can set up a system of equations to represent the given information:

We can solve this system of equations using substitution or elimination method. Let's solve it using elimination method:

So, there are 10 4-seated cars at the carnival.

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The carnival ride question can be solved using a system of equations with two variables representing the number of 2-seated and 4-seated cars. After setting up and solving the equations, we find there are 10 4-seated cars and 15 2-seated cars.

To tackle this problem, we need to set up two equations based on the seats and cars information given. Let's define x as the number of 2-seated cars and y as the number of 4-seated cars. The problem states that there are a total of 25 cars, which gives us the equation:

x + y = 25

Furthermore, we know that the total number of seats across all cars is 70. Since 2-seated cars contribute 2x to the total number of seats and 4-seated cars contribute 4y, we have the second equation:

2x + 4y = 70

To solve for y, we can manipulate these equations using substitution or elimination. For this example, let's use elimination. Divide the second equation by 2 to simplify it:

x + 2y = 35

Now subtract the first equation from this simplified second equation:

y = 35 - 25

y = 10

So, there are 10 4-seated cars. To find the number of 2-seated cars (x), substitute y back into the first equation:

x + 10 = 25

x = 25 - 10

x = 15

Thus, there are 15 2-seated cars.

Answer:

(A)

Step-by-step explanation:

I good way to solve this is to test out each answer. We can do this by setting it equal to the expression given in the question.

Let start with (A). If [tex]x + 2y + x + 2[/tex] is equivalent to (A) then we can say

[tex]x + 2y + x + 2 = 2(x+y+1)[/tex]

And we can combine the two [tex]x[/tex]'s on the left side to make.

[tex]2x + 2y + 2 = 2(x+y +1)[/tex]

Now by expanding the right side we get

[tex]2x + 2y + 2 = 2x + 2y + 2[/tex]

which is the same thing so there are both equal!

Now lets test (B). We start off by doing the same thing as (A) except with the equation for (B)

[tex]2x + 2y + 2 = 2x + 4y + 4[/tex]

Now this doesn't look quite right, on the left side we have two [tex]y[/tex]'s but on the right we have four. This means our equation is unbalanced which means they are unequal! So it can't be (B)

So the only correct answer is (A)!

Hope this helps!

Answer:

a) 0.05m

b) 5 cm

Step-by-step explanation:

See it in the pic

Thought I already answered this.  I must have forgotten to click "add your answer."

We have similar triangle trianges ABC ~ ADE so

BC:AB = DE:AD

BC:2  = 10 : (2+3) = 10:5 = 2:1

So BC=4 because 4:2 = 2:1

Choice C.