Jay needs 19 quarts more paint for the outside of his barn than for the inside.If he uses 107 quarts in all,how many gallons of paint will be used to paint the inside of the barn?

we are given

system of equations

First equation is

[tex]3x-2y=31[/tex]

Second equation is

[tex]3x+2y=-1[/tex]

now, we can find augmented matrix

[tex]A=\begin{pmatrix}3&-2&31\\ 3&2&-1\end{pmatrix}[/tex]

now, we can change it into reduced row echelon form

step-1: multiply the 1st row by 1/3

[tex]A=\begin{pmatrix}1&-2/3&31/3\\ 3&2&-1\end{pmatrix}[/tex]

step-2:add -3 times the 1st row to the 2nd row

[tex]A=\begin{pmatrix}1&-2/3&31/3\\ 0&4&-32\end{pmatrix}[/tex]

step-3:multiply the 2nd row by 1/4

[tex]A=\begin{pmatrix}1&-2/3&31/3\\ 0&1&-8\end{pmatrix}[/tex]

step-4: add 2/3 times the 2nd row to the 1st row

[tex]A=\begin{pmatrix}1&0&5\\ 0&1&-8\end{pmatrix}[/tex]

so, we get

[tex]x=5,y=-8[/tex]

Answer is (5,-8)

Solution is (5,-8)

3x – 2y = 31

3x + 2y = -1

first we write it in matrix form

3  -2   | 31   -------------> Row 1

3   2   | -1  -------------> Row 2

We use row operations and get matrix in 1   0    and 0  1  form

Subtract Row 2 by row 1.  R2 -> R2 - R1. So R1 remains the same

3  -2   | 31   -------------> Row 1

0   4   | -32  -------------> Row 2

Divide row 1 by 3, R1-> R1/3. So R2 remains the same

1   [tex]\frac{-2}{3}[/tex]   | [tex]\frac{31}{3}[/tex]    -------------> Row 1

0   4   | -32  -------------> Row 2

Divide row 2 by 4. R2 -> R2/4

1   [tex]\frac{-2}{3}[/tex]   | [tex]\frac{31}{3}[/tex]    -------------> Row 1

0   1   | -8  -------------> Row 2

Now we need to get 0 in the place of -2/3

Multiply Row 2 by 2/3  and add it with Row 1. R1 --> 2/3 times R2 + R1

1   [tex]1*\frac{2}{3}+\frac{-2}{3}[/tex]   | [tex]-8*\frac{-2}{3}\frac{31}{3}[/tex]    -------------> Row 1

0   1   | -8  -------------> Row 2

Now simplify the fraction

1   0   | 5    -------------> Row 1

0   1   | -8  -------------> Row 2

So from this we can see that x=5  and y = -8

Solution is (5,-8)

This is a more difficult one to explain. Let's start with the line to the right.  It has a slope (m) of [tex]\frac{-2}{2}[/tex] = -1 and a y-intercept of +3 (continue the line to see where it crosses the y-axis). So, the equation of that line is: y = -x + 3 when x ≥ 2. This can also be written as y = 3 - x when x ≥ 2.  The only option that has that equation is A.

Answer: A

First of all, you can see that this is a piecewise polynomial, since it is shaped like a parabola before [tex] x = 2 [/tex], and is a line after [tex] x = 2 [/tex] So, option C is surely wrong, because it uses [tex] x = 3 [/tex] as splitting point.

Moreover, the way the parabola "bounces" on the x axis, avoiding its negative part, tells us that there is an absolute value. This excludes options B and D, and the answer is thus A.

10 units up means to add 10 to the y-coordinate of the vertex (h, k).

p(x) = 0.005(x - 40)² + 60

p(x) shifted up 10 units = 0.005(x - 40)² + (60 + 10)

                                q(x) =  0.005(x - 40)² + 70  

the answer is 39.9 %

To arrange numbers from least to greatest:

First write them down in decimal form. Now it will be easy to determine which value is greater than the other.

Arrange the decimal numbers from least to greatest.

Finally revert the decimal values to their fraction form having arranged them from one with least value to one with greatest value.

Answer:

Y = 10

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

Find all of the factor pairs of 120, then look for the ones that are even-odd

         120

           ∧

      120   1     even-odd

        60   2    even-even

        40   3    even-odd

         30   4    even-even

         24   5    even-odd

         20   6    even-even

          8    15    even-odd

           10  12    even-even

There are 4 even-odd factors pairs for 120.

Let's find out how much tax was paid. Subtract the amounts: 1800 - 1683 = 117

So $117 was paid in tax. Divide this over the initial amount 1800 and we get 117/1800 = 0.065

To convert from decimal form to percent form, you multiply by 100. This is basically moving the decimal point 2 spots to the right. So we go from 0.065 to 6.5%

Therefore the answer is 6.5%

Answer:

The measure of angle ABC = The measure of angle A prime B prime C prime

Step-by-step explanation:

we know that

The transformation of the figure is a reflection, so after the transformation  the shape still has the same size, area, angles and line lengths.

the triangles ABC and A'B'C' are congruent

therefore

the corresponding sides and corresponding angles are equal

so

The relationship between the measures of the angles of the two triangles is

[tex]m<ABC=m<A'B'C'[/tex]

[tex]m<BCA=m<B'C'A'[/tex]

[tex]m<BAC=m<B'A'C'[/tex]

Dan will earn £59.40 for 6 hours of work.

To calculate Dan's earnings for 6 hours of work, we can multiply his hourly rate (£9.90) by the number of hours (6).

So, Dan will earn £9.90 x 6 = £59.40 for 6 hours of work.

Therefore, Dan will earn £59.40 for 6 hours of work.

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Answer:

45mins ÷ 15pages = 3

so she reads 3pages per minute

3pages × 60minutes = 180

she read 180pages in 60minutes

hope this helps

Step-by-step explanation:

Answer:

Anything that does not cost more than $2,560.00

Step-by-step explanation:

Provided that Nikita is spending money that she had invested and the amount  she collected over the period of 7 years. She can buy any item that costs no more than $2,560.00 but how?

It is a problem of simple interest:

Here the principal amount (P) = $2,000.00

Interest rate (r) = 4%

Time period (t) = 7 years

So, total amount that she would get by the end of 7 years is:

[tex]A=P+SI[/tex]

[tex]SI=\frac{P\times r\times t}{100}[/tex]

Plugging the values we get:

[tex]SI=\frac{2000\times 4\times 7}{100}=560.00[/tex]

So the interest collected over 7 years is $560.00

Therefore, the total amount after 7 years is:

[tex]\$2000.00+\$560.00=\$2,560.00[/tex]

If Nikita is using this money then the most expensive item that she could buy will cost no more than $2,560.00.

Answer:

The answer is B (a mountain bike priced at $2,500) in Plato

Step-by-step explanation:

In order to answer this question, you must do some multiplication!

So, in order to have a pair of shoes, you must have 2 shoes. There are 42 PAIRS of shoes. So if you wanna find the number of ALL of the shoes, you have to multiply da numbers.

42 × 2 = 84

There are 84 shoes altogether.

If you need anymore help, just let me know!

The number of shoes in one pair is two thus there will be 84 in the office.

Multiplication is the general procedure in mathematics in which we multiply two or more numbers by each other to find a new multiplied number.

Multiplication gives us a resultant number that will be very big compared to the number which is going to be multiplied if and only if the number which is going to be multiplied is more than one.

As per the given,

Number of pairs of shoes = 42

Number of shoes in one pair of shoes = 2

Total number of individual shoes = 42 x 2 = 84

Hence "The number of shoes in one pair is two thus there will be 84 in the office".

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you said times and sum, sum is addition and times is multiplication so im confused. can you copy the exact question so i can help?

So the Rational Zeros Theorem states that the potential zeros are ± P/Q, with P = factors of the constant and Q = factors of the leading coefficient.

In this case, the constant is -3 and the leading coefficient is 2.

With P and Q established, divide them all as such:

[tex]\pm \frac{1}{1}, \pm \frac{3}{1}, \pm \frac{1}{2}, \pm \frac{3}{2}\\\\\pm 1,\pm 3, \pm \frac{1}{2}, \pm \frac{3}{2}[/tex]

In short, your potential zeros are ± 1/2, ± 3/2, ± 1, and ± 2.

−24−(−19) =

- 24 + 19 =

-5

Final answer:

To calculate 3 to the 7th power times 3 to the power of negative 4, you add the exponents since the base is the same. This results in 3 cubed (33), which equals 27.

Explanation:

The question asks to calculate 3 to the 7th power times 3 to the power of negative 4. This can be simplified using the rules of exponents. When multiplying powers with the same base, you add the exponents. So for this problem, you would do the following:

3⁷ *3⁻⁴ = 3⁷⁺⁽⁻⁴⁾

3³ because 7 + (-4) equals 3

Therefore, the answer is 33 which is 3*3*3, equaling 27.

Moreover, a negative exponent like 3 to the power of negative 4 indicates that the number 3 is on the denominator, yielding 1 over 3 raised to the 4th power or 1/34.

The answer to this question is A

Answer:

-1075

Step-by-step explanation:

The other person was right they forgot to make it a negative

There are two sequence in mathematics, one is arithmetic and other is geometric sequence. Therefore, the 64th term of the arithmetic sequence is -1075.

In an arithmetic sequence, the difference between consecutive terms, called common difference, is always the same. Another sequence is the geometric sequence.

The nth term of an arithmetic sequence is given by:

[tex]a_{n}[/tex]=a₁+(n-1)d

In which  is the first term from−4,−21,−38 is a₁  -4

Common difference between two consecutive terms is d=-38-(-21)=-17

substituting in the above equation an=a1+(n-1)d

[tex]a_{n}[/tex]=-4+(n-1)(-17)

Since we have to find the 64th term of the arithmetic sequence we have to put n=64

[tex]a_{n}[/tex]=-4+(64-1)(-17)

 [tex]a_{n}[/tex]   =-4+(63)(-17)

[tex]a_{n}[/tex] =-1075

Therefore, the  64th term in the arithmetic sequence -4, -21, -38 is -1075.

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(2.99×c)+(50×s) this is the equation for the word problem

Its not correct because the answer would be 1,440 (rounded) this is no where near as close as 222.3.

117 * 19

= 120 * 20  to the nearest 10

=  2400   which indicates that 2223 is a reasonable answer.

The standard form of the number 5.871x10⁻⁷ is 0.0000005871 after using the properties of the integer exponent.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

It is given that:

The number is:

= 5.871x10⁻⁷

After using the properties of the integer exponent:

= 5.871x(1/10⁷)

= 5.871x(1/10000000)

= 5.871x0.0000001

= 0.0000005871

Thus, the standard form of the number 5.871x10⁻⁷ is 0.0000005871 after using the properties of the integer exponent.

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