Write an expression for the sentence: Kelly has $120 to spend at the fair and spent $15 on food and wants to play games that cost 4$ each


Smart people can answer

Answer:

[tex]\left\{\begin{matrix}3x+4y+8z=36.65\\ 5x+3y+10z=37.50\\ 4x+5y+6z=43.35\end{matrix}\right.[/tex]

Step-by-step explanation:

System of equations

Let's set the following variables:

x=Price of chocolate pumpkins

y=Price of masks

z=Price of candy witches

We'll establish the system of equations needed to know the prices of all the Halloween treats.

Cory bought 3 chocolate pumpkins, 4 masks, and 8 candy witches and he spent $36.65. This leads to the following equation:

[tex]3x+4y+8z=36.65\qquad\qquad [1][/tex]

Josh bought 5 chocolate pumpkins, 3 masks, and 10 candy witches and he spent $37.50. This leads to the following equation:

[tex]5x+3y+10z=37.50\qquad\qquad [2][/tex]

Dan bought 4 chocolate pumpkins, 5 masks, and 6 candy witches and he spent $43.45. This leads to the following equation:

[tex]4x+5y+6z=43.35\qquad\qquad [3][/tex]

Collecting the equations [1] [2] [3], we form the system of equations to represent this problem:

[tex]\left\{\begin{matrix}3x+4y+8z=36.65\\ 5x+3y+10z=37.50\\ 4x+5y+6z=43.35\end{matrix}\right.[/tex]

Answer:

1. 16=v    top left

2. n=5.8   bottom left

3. n= -31.9   top right

4. b= 6 .   bottom right

If I am wrong I am sorry

Step-by-step explanation:

1 result(s) found

x  

2

−x−3

Step by Step Solution:

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STEP

1

:

Equation at the end of step 1

STEP

2

:

           x3 + 3x2 - 7x - 12

Simplify   ——————————————————

                 x + 4        

Checking for a perfect cube :

2.1    x3 + 3x2 - 7x - 12  is not a perfect cube

Trying to factor by pulling out :

2.2      Factoring:  x3 + 3x2 - 7x - 12  

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  -7x - 12  

Group 2:  x3 + 3x2  

Pull out from each group separately :

Group 1:   (7x + 12) • (-1)

Group 2:   (x + 3) • (x2)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

2.3    Find roots (zeroes) of :       F(x) = x3 + 3x2 - 7x - 12

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  -12.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,3 ,4 ,6 ,12

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -3.00      

     -2       1        -2.00        6.00      

     -3       1        -3.00        9.00      

     -4       1        -4.00        0.00      x + 4  

     -6       1        -6.00        -78.00      

     -12       1       -12.00       -1224.00      

     1       1        1.00        -15.00      

     2       1        2.00        -6.00      

     3       1        3.00        21.00      

     4       1        4.00        72.00      

     6       1        6.00        270.00      

     12       1        12.00        2064.00      

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms

In our case this means that

  x3 + 3x2 - 7x - 12  

can be divided with  x + 4  

Polynomial Long Division :

2.4    Polynomial Long Division

Dividing :  x3 + 3x2 - 7x - 12  

                             ("Dividend")

By         :    x + 4    ("Divisor")

dividend     x3  +  3x2  -  7x  -  12  

- divisor  * x2     x3  +  4x2          

remainder      -  x2  -  7x  -  12  

- divisor  * -x1      -  x2  -  4x      

remainder          -  3x  -  12  

- divisor  * -3x0          -  3x  -  12  

remainder                0

Quotient :  x2-x-3  Remainder:  0  

Trying to factor by splitting the middle term

2.5     Factoring  x2-x-3  

The first term is,  x2  its coefficient is  1 .

The middle term is,  -x  its coefficient is  -1 .

The last term, "the constant", is  -3  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -3 = -3  

Step-2 : Find two factors of  -3  whose sum equals the coefficient of the middle term, which is   -1 .

     -3    +    1    =    -2  

     -1    +    3    =    2  

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Canceling Out :

2.6    Cancel out  (x+4)  which appears on both sides of the fraction line.

Final result :

 x2 - x - 3

Terms and topics

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Polynomial root calculator

Polynomial long division

Related links

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Root Finder -- Polynomials Calculator

How to factor five term polynomial - Yahoo Answers

Long Polynomial Division

Polynomial long division - Wikipedia

Polynomial Long Division

Polynomials - Long Division

Answer:

-4x^12y^11z^4

Step-by-step explanation:

Answer:

1) The information required in order to describe a translation of triangle ABC to A'B'C', are;

a) The coordinates of the vertices of the triangle ABC

b) The amount by which the triangle ABC is translated along the x-axis

c)  The amount by which the triangle ABC is translated along the yx-axis

2) The information required in order to describe a rotation of triangle ABC to A'B'C', are;

a) The coordinates of the vertices of the triangle ABC

b) The coordinates of the point about which the triangle ABC is to be rotated

c) The amount in degrees, the triangle ABC is to be rotated

2) The information required in order to describe a reflection of triangle ABC to A'B'C', are;

a) The coordinates of the vertices of the triangle ABC

b) The equation of the line about which the triangle ABC is to be reflected

Step-by-step explanation:

Answer:

make a line going through points (2,0) and (0,-2) I put a picture.

Step-by-step explanation:

Answer:

the product of the two integers is -80

Answer:

-80

Explanation:

it was on a mathcounts competition

Answer :pls delete my answer.

Answer: 3x(x-5) (x+5)

Step-by-step explanation Step 1: Factor out comon coeffecient factor. 3x3 (exponent) - 75x.- 3(x3 (exponent)-25x)

Step 2: Find One factor. 3x(x2(exponent)-25)

Step 3 an final step: Find One factor again. Factor by grouping, Factor by grouping again, Factor by grouping a third time. Edit: I hope this was helpful and I wish the best of luck to the person that asked this question and people that want to know this question.

Answer:

A

Step-by-step explanation:

Answer:

im confused lol

Step-by-step explanation:

Answer:

6ft

Step-by-step explanation:

Answer:

Did you try looking it up

Step-by-step explanation:

sorry If I am wrong and don't forget to make me brainliest

Answer:

5

Step-by-step explanation:

Answer:

y= −2/3x+2

Step-by-step explanation:

2x+3y=6

Add -2x to both sides.

2x+3y+−2x=6+−2x

3y=−2x+6

Divide both sides by 3.

3y/3=−2x+6/3

Answer:it’s D

Step-by-step explanation: put the equation into standard form and plugged it into my graphing calculator.

20 + 9 is the first answer

4(20)+4(9)+4( 6) is the second answer

80+36+24=140 is the third answer :)

Answer:

1: 20 + 9

2: 4(20) + 4(9) + 4(6)

3: 140

Step-by-step explanation:

look at the picture

Answer:

[tex]m=\frac{-1}{3}[/tex]

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Simply plug in the 2 coordinates into the slope formula to find slope m:

Points (0, -1) and (-3, 0)

[tex]m=\frac{0-(-1)}{-3-0}[/tex]

[tex]m=\frac{0+1}{-3}[/tex]

[tex]m=\frac{1}{-3}[/tex]

[tex]m=\frac{-1}{3}[/tex]

Answer: n = 28/4

Step-by-step explanation:

Number of leaves uses to feed each caterpillar = 4.

If Oscar has 28 leaves, the number of caterpillars n he'll be able to feed in a day will be represented by the equation below:

n = 28/4

This implies that 7 caterpillars can be fed in a day.

Answer:

The rate of the second car is 30 miles/hour

Step-by-step explanation:

The Given formula is:

4(r + 15) + 4r = 300, where r is the rate for the second car

Let us solve the equation to find r

→ Multiply 4 by (r + 15) first

∵ 4(r + 15) = 4(r) + 4(15) = 4r + 60

→ Substitute it in the equation above

∴ 4r + 60 + 4r = 300

→ Add the like terms in the left side

∵ (4r + 4r) + 60 = 300

∴ 8r + 60 = 300

→ Subtract 60 from both sides

∴ 8r + 60 - 60 = 300 - 60

∴ 8r = 240

→ Divide both sides by 8

∴ [tex]\frac{8r}{8}=\frac{240}{8}[/tex]

∴ r = 30

∴ The rate of the second car is 30 miles/hour

Answer:

6x-12-3x+2

Step-by-step explanation:

8x-12-3x-6

5x-18 this is the answer

Answer:

A.380160 B. 240

Step-by-step explanation:

1 Square foot (sq ft) is equal to 144 square inches (sq in). To convert square feet to square inches, multiply the square foot value by 144.

Answer:

y = -3/4x -7

Step-by-step explanation:

hope this helps!

Answer:

it moves down

Step-by-step explanation:

for the graph originally f(x)=x and subtract 6 from it, it will move 6 units down, and to find the new coordinate you subtract 6 in y so (x , y-6)→for the new coordinate.

NOTE: if the graph added to 6 it will move up 6 units.

Answer:

y = 2x + 4

Step-by-step explanation:

the line intersects the y axis at 4. so, b = 4

For the slope, to make it really easy, you can find a point where the line is on a point purfectly and just count how many times you went up or down and then left or right. Or, you can pick  2points and use the slope formula (y2-y1)/(x2-x1). the slope is 2.

Answer: 498,173.26.

Step-by-step explanation:

Place value of the 9 in 329,513 = 9,000

9 is 10 times the value of the 9 in 329,513.

Then, place value of 9 in required number = 10x 9,000 = 90,000

from options only  95,826 and 498,173.26 has 9 at ten thousands place. (cancel all other options)

Also,  2 is [tex]\dfrac1{10}[/tex] the value of the 2 in 7,562.

place value of 2 in required number =[tex]\dfrac1{10}\times2=0.2[/tex]

i.e. place value of 2 in required number 2 tenths

which is in  498,173.26   [place value of 6 is  [tex]\dfrac1{10}[/tex] the value of the 6 in 4.68]

Hence, th required number is 498,173.26.

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

First we have to line them up by the decimal points...

         -12.4

       +  9.2

           -3.2

That's all after you solved it you get -3.2

Answer:

The sum of the internal ángles = 360°

(3y+40)°  and  (3x-70°) are suplementary angles = 180°

then:

(3x-70) + (3y+40) + 120 + x = 360     ⇒ first eq.

(3y+40) + (3x-70) = 180      ⇒  second eq

development:

from the first eq.

3x + x + 3y  =  360  + 70 - 40 - 120

4x + 3y = 430 - 160

4x + 3y = 270       ⇒  third eq.

3y = 270 - 4x

y = (270 - 4x) / 3    ⇒  fourth eq.

from the secon eq.:

3y + 3x = 180 + 70 - 40

3y + 3x = 250 - 40

3y + 3x = 210    ⇒  fifth eq.

multiply by -1  the fifth eq and sum with the third eq.

  -3y  - 3x = -210    ⇒   (fifth eq. *-1)

   3y  + 4x = 270

⇒  0   +  x  = 60

x = 60°

from the fourth eq.

y = (270-4x)/3

y = (270-(4*60)) / 3

y = (270 - 240) / 3

y = 30/3

y = 10°

Probe:

from the first eq.

(3x-70) + (3y+40) + 120 + x = 360

3*60 - 70 + 3*10 + 40 + 120 + 60 = 360

180 - 70 + 30 + 40 + 120 + 60 = 360

180 + 30 + 40 + 120 + 60 - 70 = 360

430 - 70 = 360

Answer:

y = 10

Answer:

Sorry and where is your questions..