A painter leans a 25-foot ladder against the wall. The bottom of the ladder is 20 feet from the base of the wall. The painter then moves the bottom of the ladder 13 feet closer to the wall. How much higher is the top of the ladder on the wall?

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Work Shown:

a = 3 is the first term

r = 2 is the common ratio

Sn = a*(1-r^n)/(1-r) ... sum of the first n terms

S8 = 3*(1-2^8)/(1-2) ... sum of the first 8 terms

S8 = 3*(-255)/(-1)

S8 = 765

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We can generate the first 8 terms to get 3, 6, 12, 24, 48, 96, 192, 384. Each new term is found by multiplying the previous one by 2.

Then add them up to get 3+6+12+24+48+96+192+384 = 765. We get the same result.

Answer: Answer: 765

Work Shown:

a = 3 is the first term

r = 2 is the common ratio

Sn = a*(1-r^n)/(1-r) ... sum of the first n terms

S8 = 3*(1-2^8)/(1-2) ... sum of the first 8 terms

S8 = 3*(-255)/(-1)

S8 = 765

Answer:

30 gallons of 6% milk, and 45 gallons of 1% milk.

Step-by-step explanation:

x=quarts of 6% butterfat

0.06x+0.01(75-x)=0.03*75

0.06x*100+0.01*100(75-x)=100*0.03*75

6x+75-x=3*75

6x+75-x=225

5x=225-75=150

5x=150

x=30

75-30=45

So, we need 30 gallons of 6% milk, and 45 gallons of 1% milk.

So, the mixture contains 60 quarts of 6% milk and 15 quarts of 1% milk

The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1

Let [tex]x[/tex] quats and [tex]y[/tex] quats of 6% and 1%  butterfat milk then,

[tex]x+y=75...(1)[/tex]

And

[tex]\frac{6x}{100} +\frac{y}{100} =375\\6x+y=375...(2)[/tex]

Now, solving equations (1) and (2) we get,

[tex]x=60\\y=15[/tex]

Learn more about the topic linear equations:

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Answer:

$11095.45

Step-by-step explanation:

This is a problem in continuous compounding, for which the formula is

P = Ae^rt, r being the annual interest rate as a decimal fraction and t being the time in years.  Here we have:  

P = $9900e^(0.019)(6) = $11095.45

Answer:

11095

Step-by-step explanation:

Rounding to the nearest dollar

Answer:

5 cans

Step-by-step explanation:

$2/1 can = $10/x cans

x = 5

Answer:

5

Step-by-step explanation:

10 divided by 2 equalls 5

plan B would share less

because, 20% of 1700 is 340 and 30% of 1450 is 435

I hope this helps!!

Answer:

plan A

Step-by-step explanation:

Plan A

1700-8450=6750*.20=1350+1700=3050

Plan B

1450-8450=7000*.30=2100+1450=3550

Answer=Plan A

Answer:

(-1,-1)

Step-by-step explanation:

Go across the X axis first then the y axis

Step-by-step explanation:

Do you mean (5-4)*(25) or 5-4(25)

(5-4) * (25)

= 5^2

Or

5-4(25)

=5 - 100

=-95

?

Answer:

13

Step-by-step explanation:

volume of pad : 8x8x1=64

64/5=12.8

so you would need 13 bags

Answer:

Step-by-step explanation:

Since the pad frame is a square frame measuring 8 feet long and 1 foot high, we would determine its volume by applying the formula for determining the area of a cuboid which is expressed as

Volume = length × width × height

Volume of pad frame = 8 × 8 × 1 = 64 cubic feet

Since each bag of cement will fill 5 cubic feet, then the number of bags that you will need to buy to ensure enough to fill the entire frame is

64/5 = 16.8

Approximately 17 bags

Answer:

y = (-1/2)x - 3

Step-by-step explanation:

Please present the equation symbolically instead of in words:

m = -1/2, passing through (4, -5):

Using the slope-intercept formula y = mx + b, and using m = -1/2, x = 4 and y = -5, we get:

-5 = (-1/2)(4) + b, or -5 = -2 + b.  Then b = -3 and the desired equation is:

y = (-1/2)x - 3

y = -x/2 - 3 equation represents a line that has a slope of -1/2 and passes through point (4, –5)

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Given that a line has slope -1/2 and passes through point (4, -5)

The standard equation of a line is y = mx + c where m is the slope of the line.

Solving for c,

-5 = -1/2*4 + c

c = -3

Hence, y = -x/2 - 3 equation represents a line that has a slope of -1/2 and passes through point (4, –5)

For more references on the equation, click;

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Answer:

The answer is C:2 and 23

Step-by-step explanation:

Answer:

U have told the answer in the ques. then why r u asking question.

U know the answer already...

Answer:

D) f(x)=(1/2)^x, g(x)=(1/8)^x, h(x)=(2/3)^x.

Step-by-step explanation:

Answer:

1 and 3.

Step-by-step explanation:

The given system of equations

[tex]2x-7y=-13[/tex]     ...(1)

[tex]-2x+11y=1[/tex]     ... (2)

Here, coefficients of x have same values with opposite signs.

The x-variable will be eliminated when adding the system of equations.

Add (1) and (2), we get

[tex]2x-7y-2x+11y=-13+1[/tex]

[tex]4y=-12[/tex]

Divide both sides by 4.

[tex]y=-3[/tex]

Put y=-3 in (1).

[tex]2x-7(-3)=-13[/tex]

[tex]2x+21=-13[/tex]

[tex]2x=-13-21[/tex]

[tex]2x=-34[/tex]

Divide both sides by 2.

[tex]x=-17[/tex]

So, the given system of equations have unique solution, i.e., (-17,-3).

Therefore, the correct options are 1 and 3.

Answer:

$10.10

Step-by-step explanation:

We are told that she bought 3 CDs of the same price. Her total was $34.20 with $3.90 tax. We want to find the price of a CD before tax.

Since we are finding the price before tax, we need to subtract the tax from the total.

total - tax

We know she paid $34.20 with the tax of $3.90

$34.20 - $3.90

Subtract

$30.30

The total before tax was $30.30

Now we must find the price of a CD. Each CD is the exact same price, and she bought 3. Therefore, we can divide the total before tax ($30.30) by 3.

$30.30 / 3

Divide

$10.10

Each CD costs $10.10 before tax.

Answer:

10.1 $

Step-by-step explanation:

The total price Lella paid was 34.20 $ wich includes the Cd's price and the taxes

The taxes value is 3.9 $

So we need to substract 3.9 $ from 34.20 $ to get the price of the Cds

34.20 -3.9 = 30.3

The total price of the cds is 30.3 $

There are 3 cds with the same price

To get the price of each Cd divife the total of cds by 3

30.3÷3 = 10.1

The price of 1 cd is 10.1$

Answer:

phone c :)

Step-by-step explanation:

Answer:

x = 12

Step-by-step explanation:

multiply both sides by the reciprocal of [tex]\frac{1}{6}[/tex], which is 6

x = 12

Answer: x is 12

Step-by-step explanation:

Answer:

1) 3 marbles

2) The number of people born every hour is 9000 people

The number of people born every day is 216,000 people

The number of people born every year = 78,840,000 people

Step-by-step explanation:

1) The given information are;

The number of students =  3 or 6

Amount of marbles remaining after sharing = None

Least amount of marbles that can be shared equally among the students = Condition each student gets one marble = 1 × 3 = 3 marbles

The least amount of marbles that can be shared equally among the students = 3 marbles

2) The number of people born int eh world every minute = 150 people

The number of minute in one hour = 60 minutes

∴ The number of people born every hour = 150 × 60 = 9000 people

Given that the number of hours in one day = 24 hours

∴ The number of people born every day = 9000 × 24= 216,000 people

Given that the number of days in one year = 365 days

∴ The number of people born every year = 216,000 × 365= 78,840,000 people

Answer:

we need picture

Step-by-step explanation:

probaby d tho

Answer:

95

Step-by-step explanation:

GH = SR

SR = 30

FG =TS

TS = 39

104-39 =65

30+65 =95

Answer:

The answer is

None of the above

Hope this helps you

Answer:

None of the above

Step-by-step explanation:

Answer:

3244.5

Step-by-step explanation:

LxW=A

Answer:

1,110,000

Step-by-step explanation:

1,112,433

  ↑ this is the digit in the ten thousand place

We look at the digit below to determine if we need to round up

2 is less than 5 so we leave the digit in the ten thousands place alone

1,110,000

Answer:

1110000

Step-by-step explanation:

2 is smaller than 5 so it will round to 0 and so will everything under it.

Answer:

1,2 and 4 are correct.

Step-by-step explanation:

A mineral cannot be a liquid or a gas.

Answer:

|, ||, |V

Step-by-step explanation:

Only I, II, and IV are true. Minerals are solid, naturally occurring inorganic substances, each having a specific chemical makeup. Each mineral also has a particular type of ordered internal structure. Rocks are made of two or more minerals.

x = 9

y = 0

y = -2x + 18

4y - x + 9 = 0

4(-2x + 18) - x + 9 = 0

- 8x + 72 - x + 9 = 0

- 9x + 81 = 0

81 = 9x

x = 81 : 9

x = 9

y = - 2×9 + 18

y = - 18 + 18

y = 0

Answer:

The answer is B.

Step-by-step explanation:

First you have to find the angle of ATB. Given that ∠TAB and ∠TBA have the same angle and the total angle in a triangle is 180°. So you have to subtract :

∠TAB + ∠TBA + ∠ATB = 180°

∠ATB + 62° + 62° = 180°

∠ATB + 124° = 180°

∠ATB = 180° - 124°

∠ATB = 56°

A tangent to a circle will always be 90°, so ∠TAO and ∠TBO are 90°. In a quadrilateral, total angles is 360°. So the angle of AOB is :

∠ATB + ∠TAO + ∠TBO + ∠AOB = 360°

56° + 90° + 90° + ∠AOB = 360°

236° + ∠AOB = 360°

∠AOB = 360° - 236°

∠AOB = 124°

Answer:

x = 29

Step-by-step explanation:

If the lines are parallel

< CBA = < DAB due to the fact that they are alternate interior angles

42 = DAB

We also know that

DAB + BAC + CAE = 180 since they form a straight line

Substituting the given values

42+ 109 + x = 180

Combine like terms

151 + x = 180

151+x-151 = 180-151

x = 29

Answer:

y =  -[tex]\frac{1}{2}[/tex]x + 10

Step-by-step explanation:

To find the equation of a line that passes through the point (8,6) and perpendicular to the equation 2x - y = 4, we will follow the steps below:

first write the equation 2x - y = 4 in a standard form

we will find the slope of our equation using this equation

2x - y = 4

y = 2x -4

comparing the above with

y = mx  + c

m = 2

[tex]m_{1}[/tex][tex]m_{2}[/tex] = -1  ( slope of perpendicular equations)

2[tex]m_{2}[/tex] = -1

[tex]m_{2}[/tex]  = -1/2

our slope m = -1/2

We can now go ahead and form our equation

[tex]x_{1}[/tex] =8   [tex]y_{1}[/tex] =6

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

y-6 = -[tex]\frac{1}{2}[/tex](x-8)

y-6 =  -[tex]\frac{1}{2}[/tex]x + 4

y=  -[tex]\frac{1}{2}[/tex]x+4+6

y =  -[tex]\frac{1}{2}[/tex]x + 10

Answer:

Step-by-step explanation:

Sum of interior angle of any polygon = 180* (n- 2 )

Here, n= number of sides

Sum of interior angles of regular octagon = 180 * ( 8-2) = 180 * 6 = 1080°

In regular octagon, all the angles are congruent,

So, measure of an interior angle of regular octagon = 1080/8 =  135°

Sum of interior angles of regular hexagon = 180 * ( 6-2) = 180*4 = 720°

In regular hexagon, all the angles are congruent,

So, measure of an interior angle of regular hexagon = 720/6 =  120°

The measure of an interior angle of a regular octagon is  greater than the measure of an interior angle of a regular hexagon by 15°

Answer:

15

Step-by-step explanation:

The sum of the angle measures in a polygon with n sides is 180(n-2) degrees. So, the sum of the octagon's angles is 180(8-2) = 1080 degrees. The polygon is regular, so all the angles have the same measure, which means each is 1080/8 = 135. Similarly, the sum of the angles of a hexagon is 180(6-2) = 720 degrees, which means each angle in a regular hexagon has measure 720/6 = 120.

Therefore, the desired difference is 135 - 120 = 15

Answer: 3/5

Step-by-step explanation:

This spinner has 5 sections, 3 of which are pink.  Thus, you have a 3/5 chance to get pink.

Total outcomes: 5

Favored outcomes: 3

Hope it helps <3

Answer:

P = [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

Total Parts = 5

Pink Parts = 3

Probability = [tex]\frac{No. OfPossible Outcomes}{No.OfFavourable Outcomes}[/tex]

P = [tex]\frac{3}{5}[/tex]

Answer:

A

Step-by-step explanation:

Answer:

1 Employee gets = Rs 13,020

Step-by-step explanation:

25% profit = Rs 26,04,000

Bonus is always 20% of the profit

So, Bonus:

=> 26,04,000/5

=> Rs 520,800

50% bonus  from the profit = 520,800/2

=> Rs 260,400

This was divided equally among 20 employees.

So, Each Employ gets:

=> 1 Employee = 260,400/20

=> 1 Employee gets = Rs 13,020