Sales tax in Pennsylvania is 6%. Carlos bought a mountain bike that costs $125.50 before tax. What was the cost of the new bike including sales tax?

Answers

Answer 1
I’m pretty sure the answer is 113.03
Answer 2

Answer:

$878.50

Step-by-step explanation:

it's asking about new bike  cost including sales tax.


Related Questions

The shortest leg of a right triangle is 27 units. The other leg is 36 units. What is the length of the hypotenuse?

Answers

Answer:

Length of Hypotenuse: 45

Step-by-step explanation:

To solve this we need to use the pythagorean theorem.

a^2 + b^2 = c^2

In this case: a = 27

b = 36

27^2 + 36^2 = c^2

729 + 1296 =  2025

then we need to find the square root of 2025

45^2 = 2025

41 divided by 836 I don’t understand this every time i ask google it uses decimal points but I just need the answer to the question without using decimals

Answers

Answer:

[tex]\frac{41}{836}[/tex] Is just that.

Any other question?

brainliest please ;)

Answer:

41/836

Step-by-step explanation:

try using mathaway.com or tiger algebra solver

Dividing Polynomials with Tables Isiah is dividing 2x3 - x2 + 2x + 5 by x + 1 using a division table. His work is shown here. What is the value of A?

Answers

Answer:

5

Step-by-step explanation:

We are asked to find the value of A. We know from the question that we need to have the sum of -3x and (A)x equal the third term of the original polynomial, which is 2x. written out in an equation, it looks like this.

[tex]-3x+(A)x=2x[/tex]

We can simplify the equation if we add 3x to both sides, which then leaves us with this.

[tex](A)x=5x[/tex]

We can further simplify the equation by dividing both sides by x. This leaves us with our last equation for this problem.

[tex]A=5[/tex]

Finally, we have our answer. We can also verify that this is a valid integer by multiplying our, now completed, quotient by the divisor and adding the remainder, which in this case, our remainder is 0, so we will not be including it in our operation.

[tex](x+1)(2x^{2}-3x+5)[/tex]

If our calculations were all correct, the product of these polynomials should equal our dividend, verifying our integer is valid; lo' and behold, it is.

[tex]2x^{3}-x^{2}+2x+5[/tex]

Figure the 7% sales tax on $2.19 bottle of window cleaning solution and a gel pen which costs $2.75.

PLZ HELP I WILL GIVE OUT TONS OF POINTS!

Answers

Answer:

sales tax on a bottle of window cleaning solution = $0.1533

sales tax on a gel pen=$0.1925

Step-by-step explanation:

The price of bottle of window cleaning solution = $2.19

Sales tax =7%

Applying the tax, 7/100 * 2.19 = $0.1533

The price of a gel pen = $2.75

Applying the sales tax;

7/100 * 2.75 = $0.1925

Final answer:

The 7% sales tax on a $2.19 bottle of window cleaning solution and a $2.75 gel pen is around $0.35.

Explanation:

To calculate the 7% sales tax on a $2.19 bottle of window cleaning solution and a $2.75 gel pen, you first need to find the total cost of the items. Add $2.19 and $2.75 which equals $4.94. This is your base amount on which you will calculate the sales tax.

To get the tax amount, multiply the total cost by the tax rate as a decimal (7% = 0.07). So, $4.94 * 0.07 = $0.35 approximately. This will be the sales tax charged on these items.

Therefore, if you buy a window cleaning solution and gel pen, you would pay around $0.35 in taxes assuming a 7% sales tax.

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What is the perimeter of rhombus ABCD?
10 units
20 units
units
units

Answers

Answer:
20 units
Step-by-step explanation:
We are given that
On a coordinate plane , rhombus ABCD in which point A is at (1,1) and point B is at (-2,-3), point C is at (-5,1) and D is at (-2,5).
We have to find the perimeter of rhombus ABCD.
Distance formula :
Using the distance formula
Side AB=
We know that sides of rhombus are equal
Therefore, AB=BC=CD=AD=5 units
Perimeter of rhombus=
Perimeter of rhombus=
Answer: 20 units


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Answer:

20

Step-by-step explanation:

what’s the mean of 14,9,20,5,17,13

Answers

Answer:

13

Step-by-step explanation:

14+9+20+5+17+13 = 78

78/6= 13

To find the mean you always add all the data and then divide it by the amount of data.

The answer would be 13

HELP ME PLEASE I BEG YOU

Answers

Answer:

∠ K = 35° and ∠ L = 105°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

let ∠ K = x then ∠ L = 3x

Sum the angles and equate to 180

3x + x + 40 = 180, that is

4x + 40 = 180 ( subtract 40 from both sides )

4x = 140 ( divide both sides by 4 )

x = 35

Thus

∠ K = 35° and ∠ K = 3x = 3 × 35 = 105°

Write an expression meaning 4 less than 5 times a number

Answers

Answer:

Expression: 5 x n - 4

Answer:

5n - 4

Step-by-step explanation:

Let the number be n.  Then we get the expression 5n - 4.

True or False: Order of Operation says to simpliy within parenteheses

Answers

true because PEMDAS means parentheses, exponent, multiply, divide, add, subtract

Answer:

True.

Step-by-step explanation:

It says to work out what is in parentheses first, (PEMDAS).

For example:

2(5 - 3) - 1    

5 - 3 = 2 so we have:

2 * 2 - 1

= 4 - 1

= 3.

5x−9y≥8

7x−4y<10

​ Is (2,2) a solution of the system?

Answers

Answer:

(2,2) is not a solution of the system.

Step-by-step explanation:

Given : Equations [tex]5x-9y\geq 8[/tex] and [tex]7x-4y<10[/tex].

To find : Is (2,2) a solution of the system?

Solution :

To know that the given point is the solution or not we have to put the values in equation if inequality is true then the point is the solution.

Substitute (2,2) in [tex]5x-9y\geq 8[/tex] ,

[tex]5(2)-9(2)\geq 8[/tex]

[tex]10-18\geq 8[/tex]

[tex]-8\geq 8[/tex]

It is not true.

Substitute (2,2) in [tex]7x-4y<10[/tex] ,

[tex]7(2)-4(2)<10[/tex]

[tex]14-8<10[/tex]

[tex]6<10[/tex]

It is true.

So, (2,2) is not a solution of the system.


On Monday, Zach sends an e-mail message
to 4 friends. On Tuesday, each of these
friends forwards the message to 4 people. On
Wednesday, each of these people forwards
the message to 4 other people.
1. How many people were sent the
message on Wednesday? Explain
how you know.​

Answers

Written out numerically, it is 4x4x4. To work this out you multiply 4x4= 16 and then you have one more 4 to multiply by, so you multiply 16x4=64
Final answer:

On Wednesday, 64 people were sent the message as each of the 16 recipients forwarded the message to 4 other people.

Explanation:

To determine the number of people sent the message on Wednesday, we need to consider the number of people who received the message on each day. On Monday, Zach sent the message to 4 friends, so there were 4 recipients. On Tuesday, each of the 4 friends forwarded the message to 4 other people, resulting in a total of 4 friends x 4 recipients = 16 recipients. On Wednesday, each of these 16 recipients forwarded the message to 4 other people, resulting in a total of 16 recipients x 4 recipients = 64 people sent the message on Wednesday.

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Which equation is equivalent y= 3x^2-15x+18

Answers

Answer:

Two solutions were found :

x = 6

x = -1

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (3x2 -  15x) -  18  = 0  

Step  2  :

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :

  3x2 - 15x - 18  =   3 • (x2 - 5x - 6)  

Trying to factor by splitting the middle term

3.2     Factoring  x2 - 5x - 6  

The first term is,  x2  its coefficient is  1 .

The middle term is,  -5x  its coefficient is  -5 .

The last term, "the constant", is  -6  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -6 = -6  

Step-2 : Find two factors of  -6  whose sum equals the coefficient of the middle term, which is   -5 .

     -6    +    1    =    -5    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -6  and  1  

                    x2 - 6x + 1x - 6

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-6)

             Add up the last 2 terms, pulling out common factors :

                    1 • (x-6)

Step-5 : Add up the four terms of step 4 :

                   (x+1)  •  (x-6)

            Which is the desired factorization

Equation at the end of step  3  :

 3 • (x + 1) • (x - 6)  = 0

In Conclusion, the answer would be 0.

In the figure below, \overline{AD} AD start overline, A, D, end overline and \overline{BE} BE start overline, B, E, end overline are diameters of circle PPP. What is the arc measure of \stackrel{\LARGE{\frown}}{CD} CD ⌢ C, D, start superscript, \frown, end superscript in degrees? ^\circ ∘ degrees

Answers

Answer:

The measure of the arc CD = 64°

Step-by-step explanation:

It is required to find the measure of the arc CD in degrees.

So, as shown at the graph

BE and AD are are diameters of circle P

And ∠APE is a right angle ⇒ ∠APE = 90°

So, BE⊥AD

And so, ∠BPE = 90° ⇒(1)

But it is given: ∠BPE = (33k-9)° ⇒(2)

From (1) and (2)

∴ 33k - 9 = 90

∴ 33k = 90 + 9 = 99

∴ k = 99/33 = 3

The measure of the arc CD = ∠CPD = 20k + 4

By substitution with k

∴ The measure of the arc CD = 20*3 + 4 = 60 + 4 = 64°

Which of the following expressions represents the distance between 4.354.354, point, 35 and -2\dfrac{1}{5}−2
5
1

minus, 2, start fraction, 1, divided by, 5, end fraction on a number line?
Choose 1 answer:
Choose 1 answer:

(Choice A)
A
\left\lvert -2\dfrac15 -4.35\right\rvert






−2
5
1

−4.35






open vertical bar, minus, 2, start fraction, 1, divided by, 5, end fraction, minus, 4, point, 35, close vertical bar

(Choice B)
B
\left\lvert 4.35+ \left(-2\dfrac15\right)\right\rvert






4.35+(−2
5
1

)






open vertical bar, 4, point, 35, plus, left parenthesis, minus, 2, start fraction, 1, divided by, 5, end fraction, right parenthesis, close vertical bar

(Choice C)
C
None of the above

Answers

The expression that represents the distance is [tex]|-2\dfrac{1}{5}-4.35|[/tex]

How to determine the expression?

The points are given as:

4.35 and [tex]-2\dfrac{1}{5}[/tex]

The distance between points a and b is calculated using the following absolute value expression

Distance = |b - a|

This means that:

[tex]Distance = |-2\dfrac{1}{5}-4.35|[/tex]

Hence, the expression that represents the distance is [tex]|-2\dfrac{1}{5}-4.35|[/tex]

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Complete question

Which of the following expressions represents the distance between 4.35 and -2 1/5 on a number line?

A: | -2 1/5-4.35|

B: | 4.35+(-2 1/5)|

C: None of the above.

30% of the tickets sold at the Sweet Tarrant School carnival were early-admission tickets. If the school sold 200 tickets in all, how many early-admission tickets did it sell?

Answers

Answer: they sold 60 admission tickets
the answer to 30% of 200 is 60

Help plz ~_~
Which number can be added to the data so that the range of the data will be 55?
56, 81, 54, 47, 45, 94

Answers

Answer:

39 or 100

Step-by-step explanation:

45 47 54 56 81 94

Range is 94 - 45 = 49

Either add 100 or 39 to the set.

94+6 = 100

45-6 = 39

What are the end behaviors of f(x) = -2(x - 2)5?
O
A. Both ends go down.
O
B. The left end goes down; the right end goes up.
O'C. Both ends go up.
O
D. The left end goes up; the right end goes down.

Answers

Answer:

Step-by-step explanation:

D.The left end goes up and the right end goes down because this is a first order function

Final answer:

The end behavior of the function f(x) = -2(x - 2)^5 is that the left end goes up and the right end goes down. This is determined by the odd degree and negative leading coefficient of the function.

Explanation:

The end behaviors of a function can be determined by looking at the highest degree term, also known as the leading term. In this case, for the function f(x) = -2(x - 2)^5, the highest degree is odd (5), and the coefficient, -2, is negative.

Odd degree with a negative leading coefficient means that the end behaviors of this function will be: as x approaches negative infinity (moves left), the function values will go toward positive infinity (up), and as x approaches positive infinity (moves right), the function values will go toward negative infinity (down).

So the correct option here is: D. The left end goes up; the right end goes down.

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A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi.

(The cone has a radius of 8 inches and a height of 12 inches.)

Answers

Answer:

1875.6 in³

Step-by-step explanation:

(⅓×3.14×8²×12) + (⅔×3.14×8³)

1875.626667 in³

Please help! Help would be appreciated! I am having a brain fart, or maybe I'm just dumb.

What are the factors of 49?

Idk if there is any, but idk.

Thanks!

Answers

Answer:

1,7,49

Step-by-step explanation:

Answer: 7 squared

Step-by-step explanation:

49 = 1 x 49 or 7 x 7.

Factors of 49: 1, 7, 49.

Prime factorization: 49 = 7 x 7

which can also be written 49 = 7².

anyone got the answer Simplify 2x + x.

Answers

The Simplification of the expression of 2x + x  can be written as 3x

What is Simplification of expression ?

A mathematical expression is simplified when it is expressed in the simplest way possible. The expression is usually reduced to its simplest form by using fundamental features of numbers, exponents, algebraic principles, etc. to eliminate any repetitions or redundancies.

Given that 2x + x

Then we can factorize as

x(2+1)

=(x*3)

=3x

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5(9 + p) = 125 find a

Answers

do you mean find “a” or find “p” ?

Answer: p = 16

Step-by-step explanation: 125 divided by 5 is 25

then subtract 25 by 9 to get 16 so p = 16

hope this helps please mark brainliest

Find the volume of a rectangular prism that has base 6 inches long and 9 inches wide. The height
of the prism is 4 inches.

Answers

Answer:

The answer is 216 I got It wrong at first but the other answer has it right so I changed mine so no one gets confused.

Step-by-step explanation:

Answer:

216 inches is the volume

Step-by-step explanation:

multiply length times width times height

Karen earns $62.25 for working 9 hours. if the amount she earns varies with the number of hours she works how much will she earn for working 15 hours? round to the nearest hundredth

Answers

Answer:

$103.75

Step-by-step explanation:

we know that

Karen earns $62.25 for working 9 hour

so

using proportion

Find out  how much she will  earn for working 15 hours

[tex]\frac{62.25}{9}\ \frac{\$}{h}=\frac{x}{15}\ \frac{\$}{h}\\\\x=62.25(15)/9\\\\x=\$103.75[/tex]

Please simplify: (-2b^3)^4-3(-2b^4)^3

Answers

16b^12-3(-8b^12)=16b^12-(-24b^12)=40b^12

I need a bit of help. Evaluate the expression: -11²

Answers

Answer:

-121

Step-by-step explanation:

-11² = -1 × 11² = -1 × 121 = -121

Answer:

If the negative is included in the square, that makes the number positive.

(-11)^2 = 121

If the negative is not included in the square, that makes the number negative.

-(11^2) = -121

Factor each expression by factoring put the GCF.
(3n + 1)(4n + 1) + (n + 2)(4n + 1)​

Answers

Answer: 16n^2+16n+3

Steps:

I used the foil method:

(3n+1)(4n+1) = 12n^2+3n+4n+1
(n+2)(4n+1) = 4n^2+n+8n+2

Now combine like terms:

12n^2 + 4n^2 = 16n^2
3n + 4n + n + 8n = 16n
1 + 2 = 3

Put them together:

16n^2 + 16n + 3

Since there's nothing each variable has in common, that's the simplest answer you can get.

Find an equation of the line that passes through the points (-5, -3) and (3, 1)

Answers

[tex]\bf (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-3})\quad (\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-5)}}}\implies \cfrac{1+3}{3+5}\implies \cfrac{4}{8}\implies \cfrac{1}{2}[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{\cfrac{1}{2}}[x-\stackrel{x_1}{(-5)}]\implies y+3=\cfrac{1}{2}(x+5) \\\\\\ y+3=\cfrac{1}{2}x+\cfrac{5}{2}\implies y=\cfrac{1}{2}x+\cfrac{5}{2}-3\implies y = \cfrac{1}{2}x-\cfrac{1}{2}[/tex]

Answer:

x - 2y - 7 = 0

Step-by-step explanation:

To find the equation of a line that passes through (-5, -3) and (3,1)

All we need to do is to use the find the slope and then plug it into the straight line equation

straight line equation :   y -  [tex]y_{1}[/tex]   =   m (x  -  [tex]x_{1}[/tex])

[tex]x_{1}[/tex] = -5     [tex]y_{1}[/tex] = -3   [tex]x_{2}[/tex] = 3   [tex]y_{2}[/tex] = 1

 

m = slope =  [tex]y_{2}[/tex]  -  [tex]y_{1}[/tex]   /  [tex]x_{2}[/tex]  -  [tex]x_{1}[/tex]

                =   1 -(-3)  /   3 -(-5)

                 =4/8

                  =1/2

m=1/2

So, we can now plug in our value into  the equation;

y  -  [tex]y_{1}[/tex]   =   m (x -  [tex]x_{1}[/tex])

y - (-5) = [tex]\frac{1}{2}[/tex] [x - (-3)]

y + 5 = [tex]\frac{1}{2}[/tex](x+3)

y +  5  =  [tex]\frac{x + 3}{2}[/tex]

cross-multiply

2(y + 5) =   x + 3

2y + 10  =  x + 3

take 2y and 10 to the right-hand side of the equation;

x + 3 - 2y - 10  = 0

x - 2y - 7 = 0

Therefore the equation of the line is x - 2y - 7 = 0

After being rearranged and simplified, which two of the following equations
could be solved using the quadratic formula?
A. 5x + 2x - 4 = 2x2
B. x2 - 6x - 7 = 2x
C. 5x2 – 3x+ 10 = 2x2
D. 2x2 – 3x+ 10 = 2x2 + 21

Answers

Answer:

A. 5x + 2x - 4 = 2x2  <- Yes

x = 7/4 + sqrt(17)/4 or x = 7/4 - sqrt(17)/4

B. x^2 - 6x - 7 = 2x    <- Yes

x = 4 + sqrt(23) or x = 4 - sqrt(23)

C: 5x^2 – 3x+ 10 = 2x2    <- Yes

x = 1/2 + 1/2 i sqrt(37/3) or x = 1/2 - 1/2 i sqrt(37/3)  

D . 2x^2 – 3x+ 10 = 2x^2 + 21x = -11/3     <- No

Step-by-step explanation:

Solve for x over the real numbers:

5 x + 2 x - 4 = 2 x^2

5 x + 2 x - 4 = 7 x - 4:

7 x - 4 = 2 x^2

Subtract 2 x^2 from both sides:

-2 x^2 + 7 x - 4 = 0

Divide both sides by -2:

x^2 - (7 x)/2 + 2 = 0

Subtract 2 from both sides:

x^2 - (7 x)/2 = -2

Add 49/16 to both sides:

x^2 - (7 x)/2 + 49/16 = 17/16

Write the left hand side as a square:

(x - 7/4)^2 = 17/16

Take the square root of both sides:

x - 7/4 = sqrt(17)/4 or x - 7/4 = -sqrt(17)/4

Add 7/4 to both sides:

x = 7/4 + sqrt(17)/4 or x - 7/4 = -sqrt(17)/4

Add 7/4 to both sides:

Answer: x = 7/4 + sqrt(17)/4 or x = 7/4 - sqrt(17)/4

______________________________________________

Solve for x over the real numbers:

x^2 - 6 x - 7 = 2 x

Subtract 2 x from both sides:

x^2 - 8 x - 7 = 0

Add 7 to both sides:

x^2 - 8 x = 7

Add 16 to both sides:

x^2 - 8 x + 16 = 23

Write the left hand side as a square:

(x - 4)^2 = 23

Take the square root of both sides:

x - 4 = sqrt(23) or x - 4 = -sqrt(23)

Add 4 to both sides:

x = 4 + sqrt(23) or x - 4 = -sqrt(23)

Add 4 to both sides:

Answer: x = 4 + sqrt(23) or x = 4 - sqrt(23)

_________________________________________________

Solve for x:

5 x^2 - 3 x + 10 = 2 x^2

Subtract 2 x^2 from both sides:

3 x^2 - 3 x + 10 = 0

Divide both sides by 3:

x^2 - x + 10/3 = 0

Subtract 10/3 from both sides:

x^2 - x = -10/3

Add 1/4 to both sides:

x^2 - x + 1/4 = -37/12

Write the left hand side as a square:

(x - 1/2)^2 = -37/12

Take the square root of both sides:

x - 1/2 = 1/2 i sqrt(37/3) or x - 1/2 = -1/2 i sqrt(37/3)

Add 1/2 to both sides:

x = 1/2 + 1/2 i sqrt(37/3) or x - 1/2 = -1/2 i sqrt(37/3)

Add 1/2 to both sides:

Answer: x = 1/2 + 1/2 i sqrt(37/3) or x = 1/2 - 1/2 i sqrt(37/3)

________________________________________________

Solve for x over the real numbers:

2 x^2 - 3 x + 10 = 2 x^2 + 21

Subtract 2 x^2 + 21 from both sides:

-3 x - 11 = 0

Multiply both sides by -1:

3 x + 11 = 0

Subtract 11 from both sides:

3 x = -11

Divide both sides by 3:

Answer: x = -11/3

Answer: A. 5x + 2x - 4 = 2x2  <- Yes

x = 7/4 + sqrt(17)/4 or x = 7/4 - sqrt(17)/4

B. x^2 - 6x - 7 = 2x    <- Yes

x = 4 + sqrt(23) or x = 4 - sqrt(23)

C: 5x^2 – 3x+ 10 = 2x2    <- Yes

x = 1/2 + 1/2 i sqrt(37/3) or x = 1/2 - 1/2 i sqrt(37/3)  

D . 2x^2 – 3x+ 10 = 2x^2 + 21x = -11/3     <- No

Step-by-step explanation:

Solve for x over the real numbers:

5 x + 2 x - 4 = 2 x^2

5 x + 2 x - 4 = 7 x - 4:

7 x - 4 = 2 x^2

Subtract 2 x^2 from both sides:

-2 x^2 + 7 x - 4 = 0

Divide both sides by -2:

x^2 - (7 x)/2 + 2 = 0

Subtract 2 from both sides:

x^2 - (7 x)/2 = -2

Add 49/16 to both sides:

x^2 - (7 x)/2 + 49/16 = 17/16

Write the left-hand side as a square:

(x - 7/4)^2 = 17/16

Take the square root of both sides:

x - 7/4 = sqrt(17)/4 or x - 7/4 = -sqrt(17)/4

Add 7/4 to both sides:

x = 7/4 + sqrt(17)/4 or x - 7/4 = -sqrt(17)/4

Add 7/4 to both sides:

Answer: x = 7/4 + sqrt(17)/4 or x = 7/4 - sqrt(17)/4

______________________________________________

Solve for x over the real numbers:

x^2 - 6 x - 7 = 2 x

Subtract 2 x from both sides:

x^2 - 8 x - 7 = 0

Add 7 to both sides:

x^2 - 8 x = 7

Add 16 to both sides:

x^2 - 8 x + 16 = 23

Write the left-hand side as a square:

(x - 4)^2 = 23

Take the square root of both sides:

x - 4 = sqrt(23) or x - 4 = -sqrt(23)

Add 4 to both sides:

x = 4 + sqrt(23) or x - 4 = -sqrt(23)

Add 4 to both sides:

Answer: x = 4 + sqrt(23) or x = 4 - sqrt(23)

_________________________________________________

Solve for x:

5 x^2 - 3 x + 10 = 2 x^2

Subtract 2 x^2 from both sides:

3 x^2 - 3 x + 10 = 0

Divide both sides by 3:

x^2 - x + 10/3 = 0

Subtract 10/3 from both sides:

x^2 - x = -10/3

Add 1/4 to both sides:

x^2 - x + 1/4 = -37/12

Write the left-hand side as a square:

(x - 1/2)^2 = -37/12

Take the square root of both sides:

x - 1/2 = 1/2 i sqrt(37/3) or x - 1/2 = -1/2 i sqrt(37/3)

Add 1/2 to both sides:

x = 1/2 + 1/2 i sqrt(37/3) or x - 1/2 = -1/2 i sqrt(37/3)

Add 1/2 to both sides:

Answer: x = 1/2 + 1/2 i sqrt(37/3) or x = 1/2 - 1/2 i sqrt(37/3)

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Solve for x over the real numbers:

2 x^2 - 3 x + 10 = 2 x^2 + 21

Subtract 2 x^2 + 21 from both sides:

-3 x - 11 = 0

Multiply both sides by -1:

3 x + 11 = 0

Subtract 11 from both sides:

3 x = -11

Divide both sides by 3:

Answer: x = -11/3

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When Justin goes to work, he drives at an average speed of 60 miles per hour. It takes about 1 hour and 30
minutes for Justin to get to work. His car travels about 25 miles per gallon of gas. If gas costs $3.65 per
gallon, how much money does Justin spend on gas to get to work?

Answers

Answer:

$13.14

Step-by-step explanation:

60 mi/1 hour = x mi/1.5 hours

x = 90 mi to drive to work

25 mi/1 gallon = 90 mi/y gallons

y = 3.6 gallons to get to work

$3.65/1 gallon = $z/3.6 gallons

z = $13.14

Justin spends $13.14 on gas to get to work.

What is an Equation?

An equation is a mathematical statement formed when two expressions are equated using an equal sign.

The equations are useful in determination of unknown parameters.

The average speed of Justin when he goes to work is 60 miles/hour.

The time taken to reach to work is 1 hour 30 minutes.

Justin's car travels 25 miles for 1 gallon of gas.

The cost for one gallon of gas is $3.65 per gallon.

The total miles travelled is 60 miles/ hour * 1 hour 30 minutes.

Total miles travelled = 60 * (1.5)

Total miles travelled = 90 miles

The gas used for 25 miles is 1 gallon

The gas used for 90 miles is 90/25 = 3.6 gallon.

The cost of gas is $3.65 per gallon

The cost of 3.6 gallon is 3.65 *3.65

The cost of the gas used to get to work is $13.14.

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There are 350 calories in 1 1/2 cups of spaghetti. Two cups of spaghetti have

Answers

Answer: 466.67 calories in 2 cups of spaghetti

Step-by-step explanation: if there are 350 calories in 1 1/2 cups of spaghetti you only need have a cup to make 2 cups then 1/3 of 350 calories is 116.67

so 350 + 116.67= 466.67

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Final answer:

This question pertains to Health in Middle School.

Explanation:

The subject of this question is Health and the grade level is Middle School.

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