A home has a living room that is 14 ft. wide, 22 ft. long, and a height of 9ft. Bob needs to paint
the room. He has to paint the walls and the ceiling. There are two 3.0 ft. by 5.0 ft. windows and
a 4.0 ft. by 7.0 ft. opening into the room. A gallon of paint covers 320 ft? How many gallons of
paint are needed? Explain how you reached your answer. (All data are accurate to two
significant figures.)

Answer:

x-int = 18

y-int = -9/2

Step-by-step explanation:

Use slope-intercept form y=mx + b

To find the slope, substitute the two points into the slope formula and solve.

[tex]m  = \frac{y2 - y1}{x1 - x1} \\m  = \frac{-4 - (-6)}{2 - (-6)} \\m = \frac{2}{8}\\m= \frac{1}{4}[/tex]

Substitute a random point (2,-4) and m=1/4 into slope-intercept form

y = mx+b

-4 = 1/4 (2) + b

-4 = 2/4 + b

-4 = 1/2 + b

Isolate b to solve

b = -4 - 1/2

b = -8/2 - 1/2

b = -9/2    <= this is the y-intercept

b is the y-intercept in slope-intercept form

Substitute b= -9/2 and m=1/4 to get the equation of the line.

y = 1/4 x - 9/2

Substitute y for 0 to find the x intercept

y = 1/4 x - 9/2

0 = 1/4 x - 9/2

9/2 = 1/4 x

x = (9/2) / (1/4)

x = (9/2) X (4/1)

x = 36/2

x = 18

Answer:

$14.4

Step-by-step explanation:

I don't really understand the question, but this is what I think it is

Eric needs to have $60 in savings if he wants to spend only 40% of it on a $24 video game.

To determine how much Eric must have in savings to spend only 40% on a $24 video game, we set up a simple equation where 40% of his total savings (S) equals the price of the game ($24). The equation is 0.40 × S = $24. Solving this equation for S (total savings), we divide both sides by 0.40:

× S = $24
÷ 0.40 ÷ 0.40

S = $24 ÷ 0.40
S = $60

Therefore, Eric must have a total of $60 in savings to spend only 40% on the video game.

Answer:

x=-6

Step-by-step explanation:

Use Substitution

so 5-2x=-4x-7

I'ma move that -4x to the other side by making it a positive

5+2x=-7

than I'ma move that 5 to the other side by making it a negative

2x=-12

to isolate the x you dived by both sides by the 2

x=-6

I doubled checked and it's -6

Answer:

Pull out like terms: 12 + 2x = 2 • (x + 6)

Solve: x+6 = 0

Then you get; X=-6

I hope this is right and hopefully it helped you

Rewriting the expression 15x+9 as 9+ 15x is an example of the commutative property of addition

The commutative property of addition states that when two numbers are being added, their order can be changed without affecting the sum.

To “commute” means to move around or travel.  

According to the commutative property of addition, changing the order of the numbers we are adding, does not change the sum

When two numbers are added, the sum is the same regardless of the order of the addends. For example 4 + 2 = 2 + 4

For addition, the rule is a + b = b + a

Here in the problem 15x + 9 is equivalent to 9 + 15x

Hence, rewriting the expression 15x+9 as 9+ 15x is an example of the commutative property of addition

The process of rewriting 15x + 9 as 9 + 15x uses the Commutative property of addition. This asserts that changing the order of addition doesn't affect the sum.

Rewriting the expression 15x+9 as 9+15x is an example of the Commutative property of addition. The Commutative property states that the order in which you add or multiply numbers does not affect the sum or product. So in your case, 15x + 9 =  9 + 15x because of the Commutative property of addition. This is true for addition of ordinary numbers as well, for instance 2 + 3 will yield the same result as 3 + 2.

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The equation of the line that passes through the point (3 , 5) and is

perpendicular to the line x = 4 is y = 5 ⇒ answer 1

Step-by-step explanation:

Let us revise some notes about the horizontal and vertical lines

∵ The equation of the given line is x = 4

- From the 4th note above the given line is a vertical line

∴ The given line is a vertical line

- The perpendicular line to a vertical line is a horizontal line

∴ The perpendicular line to the given line is horizontal

∵ The perpendicular line passes through the point (3 , 5)

∵ The equation of the horizontal line is y = b, where b the

   y-coordinate of any point lies on the line

∵ The point (3 , 5) lies on the line

- The y-coordinate of the point is 5

∴ b = 5

∴ The equation of the perpendicular line is y = 5

The equation of the line that passes through the point (3 , 5) and is

perpendicular to the line x = 4 is y = 5

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Answer:

$15.40

Step-by-step explanation:

first, let's find the 3/4. to find this, just multiply the decimal form, .75 by the price per pound because then we get the amount for 3/4 pound. that number is $4.20. next, we need to find the 2 pounds by multiplying the price per pound by the 2 pounds, which gets us $11.20. add those together and you get $15.40.

Jason hit 11 homeruns.

Step-by-step explanation:

Homeruns hit by Nathan = 19

Let,

Homeruns hit by Nathan = x

Homerun hit by Jason = y

According to given statement;

x = 2y - 3   Eqn 1

We know that Nathan hit 19 homeruns, therefore, putting x=19 in Eqn 1

[tex]19=2y-3\\19+3=2y\\22=2y\\2y=22[/tex]

Dividing both sides by 2;

[tex]\frac{2y}{2}=\frac{22}{2}\\y=11[/tex]

Jason hit 11 homeruns.

Keywords: linear equations, addition

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Answer:

-15

Step-by-step explanation:

x-1/2(x+5)=-10

x-1/2x-5/2=-10

2/2x-1/2x-5/2=-10

1/2x-5/2=-10

1/2x=-10+5/2

1/2x=-20/2+5/2

1/2x=-15/2

x=(-15/2)/(1/2)

x=(-15/2)(2/1)

x=-15/1

x=-15

Answer:

The earning to James per year is $ 39,440

The earning of Lin per year is $ 42,540  .

Step-by-step explanation:

Given as :

The total earning of James and Lin together = $ 81,980 per year

The earning of Lin is $ 3100 more per year than James

Let The earning of James = $ J

And The earning of Lin = $ J + $ 3100

So, According to question

The total earning of James and Lin together = $ 81,980 per year

Or, The earning of Lin +  The earning of James  = $ 81,980 per year

Or,  $ J + $ 3100 + $ J  = $ 81,980 per year

or, 2 $ J = $ 81,980 - $ 3100

Or,  2 $ J = $ 78880

∴ J = [tex]\frac{78880}{2}[/tex]

I.e The earning to James per year = $ 39,440

And  The earning of Lin per year = $ 34,440 + $ 3100 = $ 42,540

Hence, The earning to James per year is $ 39,440

And The earning of Lin per year is $ 42,540  . answer

Bella can cut 24 pieces of ribbon from this long strip

Solution:

Given that Bella has 85 feet of ribbons in total

She needs identical strips of ribbon measuring 3.5 feet each

To find: Number of peices of ribbon can she cut from long strip

Number of peices of ribbon can she cut from long strip can be calculated by dividing the total feet of ribbon she has by length of identical strips she needs

Mathematically written as:

[tex]\text { Number of Strip that can be cut }=\frac{\text { Total length of ribbon }}{\text { Length of each piece }}[/tex]

[tex]\begin{array}{l}{\text { Number of Strip that can be cut }=\frac{85}{3.5}} \\\\ {\text { Number of Strip that can be cut }=24.28 \approx 24}\end{array}[/tex]

Hence , the number of strip can be 24 each of size 3.5 feet

Answer:

a) Mr. Sanchez's class sold 28 fruit pies and Mr. Kelly's class sold 32 bottles of fruit juice.

b) Mr. Kelly's class

c) Mr. Kelly's classs earned  $1.40 more than Mr. Sanchez's class.

Step-by-step explanation:

Let x be the number of fruit pies sold and y be the number of bottles of fruit juice sold.

Together, the classes sold 60 items, so

x + y = 60

Mr. Sanchez’s class sold fruit pies for $1.55 each, so x fruit pies cost $1.55x.

Mr. Kelly’s class sold bottles of fruit juice for $1.40 each, so y bottles of fruit juice cost $1.40y.

Together, the classes  earned $88.20 for their school, so

1.55x + 1.40y = 88.20.

a) You get the system of two equations:

[tex]\left\{\begin{array}{l}x+y=60\\ \\1.55x+1.40y=88.20\end{array}\right.[/tex]

From the first equation:

[tex]x=60-y[/tex]

Substitute it into the second equation:

[tex]1.55(60-y)+1.4y=88.2\\ \\155(60-y)+140y=8,820\\ \\9,300-155y+140y=8,820\\ \\-15y=8,820-9,300\\ \\-15y=-480\\ \\15y=480\\ \\y=32\\ \\x=60-32=28[/tex]

Mr. Sanchez's class sold 28 fruit pies and Mr. Kelly's class sold 32 bottles of fruit juice.

b) Mr. Sanchez's calss earned:

[tex]\$1.55\cdot 28=\$43.40[/tex]

Mr. Kellyz's calss earned:

[tex]\$1.40\cdot 32=\$44.80[/tex]

Since [tex]\$44.80>\$43.40,[/tex] Mr. Kelly's class earned more.

c) Mr. Kelly's classs earned  [tex]\$44.80-\$43.40=\$1.40[/tex] more than Mr. Sanchez's class.

Answer:

C) Profit f(x) of the yogurt company after selling x units is given as :

    f(x)   = 1.03 x - 1850

Step-by-step explanation:

Here, the fixed cost spend by the company  = $1850

Also,cost per yogurt per unit = $0.22

Now, let us assume the total yogurt units sold  = x

So, the total cost for m units  = x ( cost per unit) = x ($0.22) = 0.22 x

SO, the total COST PRICE of company  = Cost of m units +  Fixed cost

                                                                    = $1850 + 0.22 x

Also,selling price of each unit = $1.25

So, the selling price of m units =  x ( per unit selling price) = x ($1.25)

                                                    =  1.25 x

PROFIT = SELLING PRICE - COST PRICE

or f(x)  = 1.25 x  -  $1850 + 0.22 x  

or, f(x)   = 1.03 x - 1850

Hence, the profit f(x) of the yogurt company after selling x units is given as :      f(x)   = 1.03 x - 1850

The value of b is 14

The value of c is 65

Step-by-step explanation:

The quadratic equation ax² - bx + c = 0, where a = 1 has two roots

∵ The quadratic function is g(x) = ax² + bx + c

∵ a = 1

∴ g(x) = x² + bx + c

∵ g(x) has two complex roots (-7 + 4i) and (-7 - 4i)

∴ g(x) = 0

∴ x² + bx + c = 0

∵ The general form of the quadratic equation is x² - bx + c = 0,

   with sum of roots b and product of roots c

- Compare them

∴ x² - (-b) + c = 0

∵ -b = the sum of the two roots

∴ -b = (-7 + 4i) + (-7 - 4i)

- Add like terms

∴ -b = (-7 + -7) + (4i + -4i)

∴ -b = -14 + 0

∴ -b = -14

- Multiply both sides by -1

∴ b = 14

The value of b is 14

∵ c is the product of the two roots

∴ c = (-7 + 4i)(-7 - 4i)

- Remember (a + b)(a - b) = a² - b²

∵ (-7 + 4i)(-7 - 4i) = (-7)² - (4i)²

∵ (-7)² = 49

∵ (4i)² = 16i²

∵ i² = -1

∴ (4i)² = -16

∴ (-7)² - (4i)² = 49 - (-16) = 49 + 16 = 65

∴ (-7 + 4i)(-7 - 4i) = 65

∴ c = 65

The value of c is 65

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Answer:

5×4=20

Step-by-step explanation:

5 blocks across multiplied by the 4 blocks down equals 20 blocks all together

Answer:

Negative

Step-by-step explanation:

The lines are:  B) Perpendicular

Step-by-step explanation:

we have to convert both lines in slope-intercept form to find slopes

So,

[tex]3x - 6y = -13\\-6y = -3x-13\\\frac{-6y}{-6} = \frac{-3x-13}{-6}\\\frac{-6y}{-6} = \frac{-3x}{-6}+\frac{-13}{-6}\\y = \frac{1}{2} +\frac{13}{6}[/tex]

Let m1 be the slope of first line

[tex]m_1 = \frac{1}{2}[/tex]

For the second line:

[tex]18x + 9y = 5\\9y = -18x+5\\\frac{9y}{9} = \frac{-18x+5}{9}\\\frac{9y}{9} = \frac{-18}{9}x+\frac{5}{9}\\y = -2x+\frac{5}{9}[/tex]

Let m2 be the slope of line 2

So,

If the lines are parallel, their slopes are equal

If the lines are perpendicular, product of their slopes is -1

We can see that

[tex]\frac{1}{2} * -2 = -1[/tex]

Hence,

The lines are:  B) Perpendicular

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The lines given by the equations 3x - 6y = -13 and 18x + 9y = 5 are neither parallel nor perpendicular because their slopes, 1/2 and -2 respectively, are neither equal nor negative reciprocals of each other.

To decide whether the pair of lines given by the equations 3x - 6y = -13 and 18x + 9y = 5 is parallel, perpendicular, or neither, we need to find the slope of each line. First, we convert the equations into the slope-intercept form, which is y = mx + b where m is the slope.

For the first equation, 3x - 6y = -13, we solve for y:

The slope of this line is 1/2.

For the second equation, 18x + 9y = 5, we also solve for y:

The slope of this line is -2.

Since the slopes of the two lines are neither equal (which would make them parallel) nor negative reciprocals of each other (which would make them perpendicular), the lines are neither parallel nor perpendicular.

Answer:

12+4y

Step-by-step explanation:

12+3y+y=12+4y

Answer:

2 should be your answer

Step-by-step explanation:

There is 2 horizontal and 2 vertical in total there are 2 lines of symmetry.

Answer:

55 degrees

Step-by-step explanation:

So to figure this out, you need to know what a complementary angle is. A complementary angle is a 90 degree angle.

Now you know what a complementary angle is, all you have to do is 90-35 to find the remaining angle.

90-35=55

The answer is 55 degrees

Answer:

Ashley should have added 4.5 to both sides.

Step-by-step explanation:

Given expression:

[tex]-4.5+m=17[/tex]

Ashley's solution:

Subtracted 4.5 to both sides and got,

[tex]m=12.5[/tex]

Correct solution:

Adding 4.5 to both sides.

[tex]-4.5+m=17[/tex]

 [tex]+4.5[/tex]          [tex]+4.5[/tex]

∴ [tex]m=21.5[/tex]

Error made by Ashley was subtracting 4.5 both sides. Instead he should have added 4.5 both sides.

Answer: 30.5

Step-by-step explanation:

30.5 times 4 equals 122

Answer:

X=-15

Step-by-step explanation:

Multiply both sides by 11

5x-2=-77

add 2 to both sides

5x=-75

Divide both sides by 5

x=-15

The value of x equal to -15 will make the given equation a true statement.

It is a mathematical statement that shows that two mathematical expressions are equal.

The given equation is

(5x-2) / 11 = -7

Multiply both sides by 11

i.e. 5x-2 = -77

Then add 2 to both sides

i.e. 5x = -75

Divide both sides by 5

i.e x = -15

Hence, the value of x that will make the equation 5x-2/11 = -7 a true statement is -15.

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Answer:

The percent of down payment of the cost $2500 is 16% .

Step-by-step explanation:

Given:

Down payment = $400.

Cost = $2500.

Now, to find the percent of down payment of the cost.

According to question:

$400 / $2500 × 100.

⇒[tex]\frac{400}{2500} \times 100[/tex]

⇒[tex]0.16\times 100[/tex]

⇒[tex]16[/tex].

Therefore, the percent of down payment of the cost $2500 is 16%.

16% is the answer to your question.

Answer:

The  number of original students desk were there before the purchase is 980 .  

Step-by-step explanation:

Given as :

The total number of students and teachers new desks to be purchased = 295

The number of teacher's new desk to be purchased = 50

So , The number of student's new desk to be purchased = 295 - 50 = 245

The number of student's new desk to be replaced this year = [tex]\frac{1}{4}[/tex] of the original students desk

Let The number of original students desk were there before the purchase = x

Or, According to question

[tex]\frac{1}{4}[/tex] of x = 245

Or, x = 245 × 4

∴   x = 980

Hence The  number of original students desk were there before the purchase is 980 .  Answer

Answer:

D

Step-by-step explanation:

Straight line (straight angle) is always 180 degrees.

The angle adjacent to 115 and 115 degree angle would sum up to 180 (straight line).

So, that angle would be:

180 - 115 = 65

Now, we know the triangle's 2 angles: 85 (given) and 65 (found), thus we can find the third angle (leftmost):

85 + 65 + third angle = 180 [sum of 3 angles in a triangle is 180]

150 + third angle = 180

third angle = 180 - 150

third angle = 30

This third angle is adjacent to w and forms a straight line, so we can write:

third angle + w  = 180

30 + w = 180

w = 180 - 30

w = 150

Correct answer is D

Answer:

6. [tex]\displaystyle y - 1 = 2(x + 5)[/tex]

5. [tex]\displaystyle y + 4 = -3(x - 2)[/tex]

4. [tex]\displaystyle y - 5 = -2(x + 1)[/tex]

3. [tex]\displaystyle y - 2 = 3(x - 4)[/tex]

2. [tex]\displaystyle y - 4 = -3(x + 2)[/tex]

1. [tex]\displaystyle y - 5 = 2(x - 1)[/tex]

Step-by-step explanation:

In the Point-Slope Formula [y - y₁ = m(x - x₁)], all the negative symbols give the OPPOSITE terms of what they really are, so be EXTREMELY CAREFUL inserting the coordinates into the formula with their CORRECT SIGNS.

I am joyous to assist you anytime.

Answer:

the answer is 1/4 ^10

Step-by-step explanation: