For the function f (x) = 3x2 - 2x+1, evaluate the function. Simplify your answer. f(t) =

Answer:

25 quarters and 4 dimes. Louisa used 21 more quarters than she did dimes.

Step-by-step explanation:

q=number of quarters

d=number of dimes

6.65=.25q+.10d   6.65 (the total) is equivalent to the amount of quarters times .25 (the value of a quarter) plus the amount of dimes times .10 (the value of a dime)

Now divide 6.65 by .25.

26 quarters can be used.

26 times .25 = 6.50

26 quarters is $6.50

29-26=3

3 times .10 = .30

.30+6.50=6.80

This is too much. Let's try taking off one quarter.

Now we have 25 quarters. .25 times 25 = 6.25

29-25=4 (This means there will be 4 dimes if she used 25 quarters, but let's see)

4 times .10 = .40

.40 + 6.25=6.65

6.65 is the total amount she had to pay, so we did it. Solving this showed us that she used 25 quarters and 4 dimes. This equals $6.65, the amount she paid, uses only quarters and dimes, and uses a total of 29 coins.

I hope this helps you! Please mark as Brainliest answer! I worked really hard to type all of this out for you.

We are given a table for input and output values and the relation between them.

Consider the table,

Input           Output = Input × itself + (-5)           Output

0                                        

1

6    

                                                                              95

                                                                              59

                                                                              76

For Input = 0 :

Output = Input × itself + (-5)

Output = 0 × 0 - 5

Output = -5

Now, for Input = 1,

Output = Input x Itself + (-5)

Output = (1) × 1 + (-5)

Output = 1 - 5

Output = - 4

For Input = 6,

Output = Input x Itself + (-5)

Output = (6) × 6 + (-5)

Output = 36 - 5

Output = 31

For Output = 95,

Output = Input x Itself + (-5)

95 = (Input)²+ (-5)

95 + 5 = (Input)²

(Input)² = 100

Input = √100

Input = 10

For Output = 59,

Output = Input x Itself + (-5)

59 = (Input)²+ (-5)

59 + 5 = (Input)²

(Input)² = 64

Input = √64

Input = 8

For Output = 76,

Output = Input x Itself + (-5)

76 = (Input)²+ (-5)

76 + 5 = (Input)²

(Input)² = 81

Input = √81

Input = 9

Therefore the complete table will be:

Input           Output = Input × itself + (-5)              Output

0                     Output = 0 × 0 + (-5)                          -5

1                      Output = 1 × 1 + (-5)                             -4

6                     Output = 6 × 6 + (-5)                          31

10                  95 = Input × itself + (-5)                      95

8                    59 = Input x Itself + (-5)                      59

9                    76 = Input x Itself + (-5)                      76

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Scientific e Notation: 2.2222222e+57

Scientific Notation: 2.2222222 x 10^57

Answer:

I am pretty sure the answer is 2.2222222e+57.

Answer:

[tex]\frac{12}{4} = \frac{3}{1}[/tex]

Step-by-step explanation:

[tex]\frac{12\div4}{4\div4}=\frac{3}{1}[/tex]

Hope this helps!

Answer:

12 = 3

4      1

Step-by-step explanation:

hope the helps

Answer:

40 yellow marbles

Step-by-step explanation:

1. Divide 64 by 8 (Determine how many sets there are)

64/8 = 8

2. Multiply 8 by 5 (Because for every 8 purple marbles there are 5 yellow ones)

8*5 = 40

Answer:

-22 I arrived as fast as I could

[tex]\stackrel{\textit{\LARGE sides}}{\cfrac{x}{2}+(x-5)+(x-2)~}~ = ~~13\implies \cfrac{x}{2}+2x-7=13 \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2\left( \cfrac{x}{2}+2x-7 \right)=2(13)}\implies x+4x-14=26\implies 5x-14=26 \\\\\\ 5x=40\implies x=\cfrac{40}{5}\implies \boxed{x=8} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(8)}{2}\implies 4\hspace{5em}(8)-5\implies 3\hspace{5em}\underset{Longest}{(8)-2\implies 6}[/tex]

Step-by-step explanation:

first we need the mean value. this is the sum of all data points divided by the number of data points :

(3×9 + 5 - 3×13)/7 = -7/7 = -1

next, for the standard deviation, we need to sum the squares of the differences of the data points to the mean value, divide that by the number of data points again, and then pull the square root :

(3(-13 - -1)² + 3(9 - -1)² + (5 - -1)²)/7 =

= (3×196 + 3×100 + 36)/7 = (588 + 300 + 36)/7 =

= 924/7 = 132

the standard deviation is now the square root of 132 :

sqrt(132) = 11.48912529... ≈ 11.5

so, yes, as we can see, the numbers vary/deviate rather strongly from the mean value.

Answer:

There were 132 children admitted.

There were 165 adults admitted.

Step-by-step explanation:

Given information:

Define the variables:

Create two equations from the given information and defined variables:

[tex]\textsf{Equation 1}: \quad x+y=297[/tex]

[tex]\textsf{Equation 2}: \quad 3x+7y=1551[/tex]

Solve the first equation for y:

[tex]\implies x+y=297[/tex]

[tex]\implies x+y-x=297-x[/tex]

[tex]\implies y=297-x[/tex]

Substitute the found expression for x into the second equation and solve for y:

[tex]\implies 3x+7y=1551[/tex]

[tex]\implies 3x+7(297-x)=1551[/tex]

[tex]\implies 3x+2079-7x=1551[/tex]

[tex]\implies 2079-4x=1551[/tex]

[tex]\implies 2079-1551-4x=1551-1551[/tex]

[tex]\implies 528-4x=0[/tex]

[tex]\implies 528-4x+4x=0 + 4x[/tex]

[tex]\implies 528= 4x[/tex]

[tex]\implies \dfrac{528}{4}= \dfrac{4x}{4}[/tex]

[tex]\implies x=132[/tex]

Substitute the found value of x into the expression for y and solve for y:

[tex]\implies y=297-x[/tex]

[tex]\implies y=297-132[/tex]

[tex]\implies y=165[/tex]

Therefore:

Answer:

i would choose investment A

Step-by-step explanation:

A is simply the best anwser choice

Answer:

If I were Sam, I would buy the bond with a 3% interest rate since selling at any time is not a priority. The bond would provide a steady income from the investment, which is what he his needing.If I were Julia, I would invest in the stock, which has long-term growth potential. This would allow her to sell the investment at any time in the future.

Step-by-step explanation:

SAMPLE ANSWER!!!

Answer:

If just combining like terms: 3x^2 + 12

If solving for x: 2i, -2i

Step-by-step explanation: Combine like terms, so 3x^2 + 12 = 0; move the 12 to the other side by subtracting (3x^2 = -12), then divide both sides by 3, which gives x^2 = -4. Then get the square root of both sides to cancel out the power on the x. Since -4 is negative, use imaginary numbers, which makes x = 2i and x = -2i

Answer:

89.14%

Step-by-step explanation:

279 Out of 313 is 89.14%. Follow the below steps to calculate what percent is 279 out of 313 or how to write 279/313 as a percentage.

Step 1: Percentage Formula = Number 1/Number 2 x 100

Step 2: plugin the 279 and 313 to the percentage formula and we get 279/313 x 100 = 89.14%

Applying the law of sines, the length of ZY to the nearest hundredth is: 3.30 units.

sin X/x = sin W/w = sin Z/z [according to the law of sines].

Given:

Measure of angle X = 60°

Measure of angle Z (∠XZW) = 180 - 60 - (180 - 83) = 23°

x = WZ = ?

z = XW = 1.5

Plug in the values into sin X/x = sin Z/z

sin 60/WZ = sin 23/1.5

WZ = (sin 60 × 1.5)/sin 23

WZ = 3.32

Find ZY using the sine ratio;

sin ∅ = opp/hyp = ZY/WZ

sin 83 = ZY/3.32

ZY = (sin 83)(3.32)

ZY = 3.30

Therefore, applying the law of sines, the length of ZY to the nearest hundredth is: 3.30 units.

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Answer: 54

Step-by-step explanation:

3x=72-x       ==> 3x and 72-x are both congruent angles, so they're equal

3x+x=72-x+x

4x=72

x=18

3x=

3(18)=54 degrees

Based on the current price of gas per gallon, and the fact that it was cheaper the year before, the percent decrease in price is 31%

First, find the price of gas last year:

=Current price of gas + Decrease in price

= 3.20 + 1.43

= $4.63

The percent of decrease in price can be found by the formula:

= Change in gas price / Price of gas last year x 100%

= 1.43 / 4.63 x 100%

= 0.30885529157667386609071274298056 x 100%

= 31%

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Answer: Yes

Step-by-step explanation:

All you had/have to do is 19-11 and get 8

Answer:

Yes, you're correct.

Step-by-step explanation:

Because since the bases are the same you can set the exponents equal. Then move the constant to the right hand side and it changes the sign. Then you calculate the difference. Finally you change the signs on both sides of the equation. x = 8

The number is 5.67

Let the number be 'x'

The difference of four times a number and seven = 4x - 7

Ten more than the number = 10 + x

According to the condition given in the question,

The difference between four times a number and seven is equal to ten more than the number.

4x - 7 = 10 + x

4x - x = 10 + 7

3x = 17

x = 17/3 = 5.67

We can verify the answer,

Consider the LHS,

=> 4x - 7 = 4(5.67) - 7 = 22.68 - 7 = 15.68

Consider the RHS,

=> 10 + x = 5.67 + 10 = 15.67

Both LHS and RHS are equal.

Therefore the number that satisfies the given condition is 5.67

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Answer:

$611.17 per acre

Step-by-step explanation:

11001 ÷ 18 = 611.16666...

So, the answer is an infinite decimal, so we round it to the nearest hundredth.

Answer:1/1850

Step-by-step explanation: Davide 10% from 18500

Answer:

Step-by-step explanation:

Let Matt's age be x.

Then Pat is x + 2, Dave is x + 4 and Dan is x + 6.

Dan's age is 36 years less than twice Pat's age:

Solve it for x:

So Matt is 38, Pat is 40, Dave is 42 and Dan is 44.

Answer:

[tex] \: \: \: \: \: { \rm{2 \: \: \: 3 \: \: \: 4}} \\ { \underline{ \times \: \: 0. \: \: 3 \: \: 5}} \\ { \rm{ 1 \: \: 1 \: \: 7\: \: 0}} \\ { \underline{ + 7\: \: 0\: \: 2 \: \: 0 }} \\ { \underline{ \: \boxed{ 8\: \: 1 \: .\: \: 9 \: \: 0}}}[/tex]

Answer: 81.9

the linear equation tangent at x = -2 is:

y = 123.33*x + 226.74

To get the slope of the line we need to evaluate the first derivative in x = -2, we get:

f'(x) = 3√(2 - 4x) + (-12/2)*3x*(2 - 4x)^(-1/2)

Evaluating in x = -2 we get:

f'(-2) = 3√(2 - 4*-2) + (-12/2)*3*-2*(2 - 4*-2)^(-1/2) = 123.33

Then the line is something like:

y = 123.33*x + b

And the line must pass through:

f(-2) = 3*(-2)*√(2 - 4*(-2)) = -18.97

So the line must pass through the point (-2,  -18.97)

Replacing that in the linear equation:

-18.97 = 123.33*2 + b

-19.92 + 123.33*2 = b = 226.74

Then we conclude that the linear equation tangent at x = -2 is:

y = 123.33*x + 226.74

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The length of EC will be 154 units.

We have the data that:

BD is the bisector of AC at point E.

This means that AE = EC

Also, AE + EC = AC

AE + AE = AC

2 AE = AC

Now,

AE = 2x² - 8 and AC is 5x² - 25

Substituting the values, we get that:

2 (2x² - 8) = 5x² - 25

4x² - 16 = 5x² - 25

5 x² - 4 x² = 25 - 16

x² = 9

x = 3 ( as length cannot be negative)

AE = EC = 2x² - 8

EC = 2 (9)² - 8

EC = 162 - 8

EC = 154 units.

Therefore, we get that, the length of EC will be 154 units.

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An equivalent expression for 4d⁻³/22d⁹ is: B. 2d⁻³/11d⁻⁹

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

An exponent can be defined as a mathematical operation that is used to raise a quantity to the power of another and it is generally written as bⁿ.

Next, we would write the equation as a quotient:

Expression = 4d⁻³/22d⁹

Expression = 2d⁻³/11d⁹

By applying the law of indices, we have:

Expression = 2 × 1/11d(⁹ ⁻ ⁽⁻³⁾)

Expression = 2/11d¹²

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The value of the x in the given geometry figure is  108° .

The labelled diagram of the figure is given below.

From the figure , we can see that ∠OEA = ∠BOF as they are vertically opposite angles .

Hence ∠BOF = x

∠OFT and ∠BOF are linear pair , so on adding them , we will get sum 180°

∠OFT + ∠BOF = 180°

 72° + x = 180°

        x = 108°

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Answer:

  x° = 22°

Step-by-step explanation:

You want the measure of the angle marked x° in the figure with two parallel lines and a "bent" transversal.

Extending the upward-sloping line in the figure as shown in the attachment results in a triangle against the top horizontal line.

The angle on the right side of that triangle corresponds to the one marked 50°, so has the same measure. It is one of two "remote interior angles" whose sum is the measure of the exterior angle marked 72°. The other "remote interior angle" making up that sum is the vertical angle to the one marked x°.

So, we have ...

  x° +50° = 72°

  x° = 22° . . . . . . . . subtract 50°

__

Additional comment

You can do a "sanity check" on this answer by considering some extreme cases. If the 72° angle is reduced to 50°, the top leg of the "72°" angle would be horizontal. That would effectively reduce x to 0. Similarly, if the 72° angle were made to be 180°, then the value of x would be supplementary to the 50° angle. In other words, x is the difference between the one marked 72° and 50°, or 22°.

The domain of this function is all the real numbers except - 7 / 3 and 23 / 3.

In accordance with function theory, the domain of a function is a set of x-values such that y-values exist. Herein we find that the given function is a rational function whose denominator includes an absolute value function. The numerator is a linear equation.

Therefore, the domain of the function is all real numbers except those x-values such that denominator is equal to zero. We need to solve the following expression in two cases:

|3 · x - 15| = 8

For x ≥ 5:

3 · x - 15 = 8

3 · x = 23

x = 23 / 3

For x < 5:

- 3 · x + 15 = 8

- 3 · x = - 7

x = - 7 / 3

Then, the domain of this function is all the real numbers except - 7 / 3 and 23 / 3.

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Based on the balances in Reese Corp's trial balance, the current assets total can be found to be B. $5,555,000

The total of the current assets can be found by the formula:

= Inventory + Accounts Receivable + Cash

Solving then gives:

= 775,000 + 2,695,000 + 2,085,000

= $5,555,000

In conclusion, the current assets for Reese Corp is $5,555,000 .

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The dimensions of the rectangular field with area 120 square meters is 10 meters by 12 meters.

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Given perimeter of the rectangular plot is 44 meters.

let the length is x , and width = y

Therefore perimeter = 2 (x + y)

or, 2 (x + y) = 44

or, x + y = 22

or, y = 22 - x

Now the area of the field is given as 120 square meters.

Area of the fields in terms of x is given by:

x ( 22 - x ) = 22 x - x²

Therefore  22 x - x² = 120

or,   x² -22x +120 = 0

or,  x² - 10x - 12x + 120 = 0

or, x (x -10) -12(x-10)=0

or, (x-10)(x-12) = 0

Now either the value of x is 10m or the value of x is 12m

Therefore the dimensions of the rectangular field is 10 meters by 12 meters.

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Step-by-step explanation:

(-4,0)

(0, -4)

(1, -5)

(6, 0)