A 24 foot ladder leans against the wall of a building. The foot of the ladder is 5 feet from the base of the wall. How many feet above the ground is the point where the ladder touches the wall?

Answer:

The answer is C: 35°

Step-by-step explanation:

The sum of all angles in a triangle is 180°

So, 180°-(60°+85°)

= 180°-145°

= 35°

m∠L = 35°

Hope it helps!

Answer:

The equation of the line would be y = -4x - 3

Step-by-step explanation:

To find any equation when you have the slope and a point, start with point-slope form and then solve for y.

y - y1 = m(x - x1)

y - 5 = -4(x + 2)

y - 5 = -4x - 8

y = -4x - 3

Answer:

The statement that most accurately represents the data given is the 'The mean and median age are more likely to be the same for the students in Math 1.'

Step-by-step explanation:

The box and whisker plots given for the two sets of data show a few different things.  Box and whisker plots first show us the median in a given set of data, which is the line in the middle of the box.  For both Math 1 and Math 2, this line occurs at 19.  The whiskers that extend from the box on either side represent the range, or lowest and highest numbers, in the data.  For Math 1, the range is 17-21 and for Math 2, the range is 17-23.  Since the range is more evenly distributed in Math 1, we can conclude that the mean, or average of the data, is most likely the same as the median of the data, which is 19.  

Answer:

its d

Step-by-step explanation:

its d

The two angles are corresponding angles, so they are congruent (due to the horizontal lines being parallel)

x+15 = 102

x+15-15 = 102-15 .... subtract 15 from both sides

x = 87

Answer:

False

Step-by-step explanation:

(-2,0)  x is equal to -2 and y = 0

y=x  

Substitute the values in.

-2 =0

False

Answer:

the answer is $8.29

Step-by-step explanation:

1.60 marked up by 60% in decimal form is .60

multiply that .60 by 1.60 and you get .64

you add .64 to 1.60 and you get 2.56

you multiply 2.56 by 3 and you get 7.68

you have a 8% sales tax so you multiply 0.08 by 7.68

you will get .61 you add that to 7.68 to get $8.29

Answer:

$6.64

Step-by-step explanation:

When the price of an item is marked up by a percentage, the new price (after markup) is result when the product of the percentage and the original price added  to the original price.

The price after markdown is similar to the mark up except that the product of the percentage and the original price is subtracted from the original price.

Hence when a box of spaghetti at the grocery store is purchased for $1.60 wholesale and is marked up by 60 percent, the new price

=60% * $1.60 + $1.60

$2.56

If the store marks down the item by 20 percent, then the new price becomes

= $2.56 - 20% * $2.56

= $2.048

If a customer wants to buy 3, the price

= $2.048 * 3

= $6.144

Including 8% tax, the price becomes

=$6.144 + 8% * $6.144

= $6.63552

To the nearest cent

= $6.64

Answer:

0.163

Step-by-step explanation:

The mass difference between Darragh's Golden Eagle coin and an uncirculated one is 0.163g. This difference could be from various factors including wear and tear, oxidation, or minor variations in the minting process.

The question relates to the difference in mass of an uncirculated Golden Eagle coin and one that is in Darragh's collection. First, we need to calculate the difference in mass. The mass of the uncirculated Golden Eagle coin is 13.714g and the mass of Darragh's Golden Eagle coin is 13.551g. By subtracting Darragh's coin mass from the uncirculated coin mass, we get a difference of 0.163g.

This means that Darragh's Golden Eagle coin is 0.163g lighter than an uncirculated one. This difference could be due to factors like wear and tear from handling the coin over time, oxidation, or even from slight variations within the minting process itself. As with any other measurement, there will be a minor uncertainty that should be considered in scientific contexts.

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Answer:

There are 8 cans on each of the equal shelves

Step-by-step explanation:

Total number of cans put in display = 35

Shelves with equal no of cans =  4 Shelves

And one shelf displays only 3 cans

Therefore, 4 shelves with equal no of cans + 1 shelf with 3 cans = 35 cans

Let us assume equal no. of cans be x

We get, 4x + 3 = 35

             4x = 35 - 3

             4x = 32

              x  = 32 ÷ 4

              x = 8

Thus, 4 shelves with equal no of cans contains 8 cans each.

The slope-intercept form: y= mx + b

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (6, 2) and (5, 5). Substitute:

[tex]m=\dfrac{5-2}{5-6}=\dfrac{3}{-1}=-3[/tex]

Therefore we have y = -3x + b.

Put the coordinates of the point (5, 5) to the equation:

5 = -3(5) + b

5 = -15 + b     add 15 to both sides

20 = b

Answer:

y = -3x + 20

Step-by-step explanation:

(a) Slope

The point-slope formula for a straight line is

y₂ - y₁ = m(x₂ - x₁)     Insert the points  

2 - 5 = m(6 - 5)

    -3 = m×1

    m = -3

=====

(b) y-intercept

y₂ - y₁ = m(x₂ - x₁)

y₂ - 5 = -3(x₂ - 5)     Remove parentheses

y₂ - 5 = -3x₂ - 15       Add 5 to each side

      y = -3x + 20

To find the length of the wall represented by a line that is 3 7/8 inches long on the blueprint, we can use the scale conversion. The length of the wall is 15 1/2 feet.

To find the length of the wall represented by a line that is 3 7/8 inches long on the blueprint, we need to use the scale conversion.

The given scale is 1 inch corresponds to 4 feet.

So, we can set up a proportion:

1 inch − 4 feet

3 7/8 inches − x feet

To solve for x, we can cross-multiply:

1 × x = 4 × 3 7/8

Multiply 4 by the whole number 3 and then add the product to the result of 4 multiplied by the fractional part 7/8.

x = 12 + 28/8

x = 12 + 3 1/2

x = 15 1/2 feet

Therefore, the length of the wall represented by a line that is 3 7/8 inches long on the blueprint is 15 1/2 feet.

Answer:

y = 30

Step-by-step explanation:

We can use ratio's to solve this

40        20

-----  = -----------

100       20 + y

Using cross products

40 * (20+y) = 20*100

Distribute

800 + 40y = 2000

Subtract 800 from each side

40y = 2000-800

40y = 1200

Divide by 40

y = 1200/40

y =30

Answer:

c = 0.6d + 1.2

Step-by-step explanation:

Use distance as the independent variable and cost as the dependent variable. Each point (x, y) is (distance, cost).

The 3 mile ride for $3.00 gives you point (3, 3).

The 6 mile ride that cost $4.80 gives you point (6, 4.8).

Now you need to find the equation of the line that passes through points

(3, 3) and (6, 4.8).

y = mx + b

m = slope = (y2 - y1)/(x2 - x1) = (4.8 - 3)/(6 - 3) = 1.8/3 = 0.6

Use point (3, 3).

y = 0.6x + b

3 = 0.6(3) + b

3 = 1.8 + b

b = 1.2

The equation is

y = 0.6x + 1.2

Use c for cost and d for distance to get

c = 0.6d + 1.2

Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

rearrange 13x + 8y = 12 into this form

subtract 13x from both sides

8y = - 13x + 12 ( divide all terms by 8 )

y = - [tex]\frac{13}{8}[/tex] + [tex]\frac{3}{2}[/tex] ← in slope-intercept form

with slope m = - [tex]\frac{13}{8}[/tex] and y-intercept c = [tex]\frac{3}{2}[/tex]

x^2 + x(x - y) + 10xy

Distributive property.

x^2 + x^2 - xy + 10xy

Combine like terms.

2x^2 + 9xy

Factor x out of each term.

Answer:

Anna

Step-by-step explanation:

Compare the answers, and when you do that then you can see that anna had more money come in then the others.

Answer:

1.) There are 16 juniors and 8 seniors in the Chess Club. If the club  members decide to send 9 juniors to a tournament, how many different  possibilities are there?  

(16 over 9) = 16!/(9!*7!) = 11440

2.) How many different ways can 3 cards be drawn from a deck of 52  cards without replacement?  

52*51*50 = 132600

3.) How many different ways can 3 cards be drawn from a deck of 52  cards with replacement?  

52^3 = 140608

4.) A corporation has 5 officers to choose from which 3 are selected  to comprise the board of directors. How many combinations are there?

(5 over 3) = 5!/(3! * 2!) = 10

5.) A combination lock has the numbers 1 to 40 on each of three  consecutive tumblers. What is the probability of opening the lock in  ten tries?

10/40^3 = 1/6400

The questions deal with computing combinatorial possibilities such as selecting members for a Chess Club tournament, drawing cards from a deck with and without replacement, determining the number of combinations for a board of directors, and calculating the probability of opening a combination lock within a limited number of tries.

1. Chess Club tournament possibilities: This can be calculated using the combination formula. The number of ways to select 9 juniors from 16 is given by the formula C(n, k) = n! / (k!(n-k)!) where n is the total number of items, and k is the number of items to choose. In this case, it is C(16, 9).

2. Ways to draw 3 cards without replacement: This also uses the combination formula because the order of drawing doesn't matter. It is C(52, 3).

3. Ways to draw 3 cards with replacement: Since each draw is independent and the card is replaced each time, it's simply 52 x 52 x 52 = 1,40,608.

4. Combinations for a board of directors: Choosing 3 officers from 5 to form a board is C(5, 3).

5. Probability of opening a combination lock: The total number of combinations is 40 x 40 x 40. With ten tries, the probability of opening the lock on each try is 1/64000.

Thus the probability of opening within ten tries is 10/64000.

A(1, 1), B(7, 1), C(1, 9)

AB = 7 - 1 = 6

AC = 9 - 1 = 8

Use the Pythagorean theorem:

AB² + AC² = BC²

Substitute:

BC² = 6² + 8²

BC² = 36 + 64

BC² = 100 → BC = √100 → BC = 10

The perimeter of ΔABC:

P = 6 + 8 + 10 = 24

To calculate SUTA and FUTA for the first 12 weeks, calculate the taxable wages for each employee. Multiply the taxable wages by the respective tax rates to find the amount owed. Roger owes $371 for SUTA and $56 for FUTA for the first 12 weeks.

To calculate the amount that Roger owes for SUTA (State Unemployment Tax Act) and FUTA (Federal Unemployment Tax Act) for the first 12 weeks, we need to calculate the taxable wages for each employee. The taxable wages for SUTA is the first $7,000 and for FUTA is the first $7,000 as well.

Since the three employees earn $500, $550, and $700 respectively, their total wages for the first 12 weeks would be $17,100 (12 weeks x ($500 + $550 + $700)). However, since SUTA and FUTA only consider the first $7,000 of wages, we can calculate the amount for each tax.

For SUTA, the total taxable wages would be $7,000. Using the SUTA rate of 5.3%, we can calculate the amount owed: $7,000 x 0.053 = $371.

For FUTA, the total taxable wages would also be $7,000. Using the FUTA rate of 0.8%, we can calculate the amount owed: $7,000 x 0.008 = $56.

Therefore, Roger owes $371 for SUTA and $56 for FUTA for the first 12 weeks for his three employees.

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Answer:

The expression equal to 2x^(2)+8 is:

First option (2x-4i)(x+2i)

Step-by-step explanation:

If we multiply

(2x-4i)(x+2i)=(2x)(x)+(2x)(2i)-(4i)(x)-4i(2i)

(2x-4i)(x+2i)=2x^(1+1)+4xi-4xi-8i^(1+1)

Simplifying:

(2x-4i)(x+2i)=2x^2-8i^2

and i^2=-1, then:

(2x-4i)(x+2i)=2x^2-8(-1)

Multiplying:

(2x-4i)(x+2i)=2x^2+8

Answer: (2x-4i)(x+2i)

Step-by-step explanation:

Answer:

[tex]6^{18}[/tex]

Step-by-step explanation:

if the base is same we can add the exponential terms

her base is same which is 6. so we can add exponential terms

therefore

[tex]6^{9+9}[/tex]

[tex]6^{18}[/tex]

Hi! See the image attached

Answer:

D

Step-by-step explanation:

f(x) - g(x) = -9x^2 - 7x + 12 - (3x^2 - 4x - 15)  Remove the brackets

f(x) - g(x) = -9x^2 - 7x  + 12 - 3x^2 + 4x + 15

f(x) - g(x) = -9x^2 - 3x^2 - 7x + 4x + 12 + 15

f(x) - g(x) = -12x^2- 3x + 27

Answer D

Answer:

Option D. -12x² - 3x + 27

Step-by-step explanation:

The given functions are f(x) = -9x² - 7x + 12 and g(x) = 3x² - 4x - 15

We have to find the value of f(x) - g(x)

f(x) - g(x) = (-9x² - 7x + 12) - (3x² - 4x - 15)

              = -9x² - 7x + 12 - 3x² + 4x + 15

              = (-9x² - 3x²) - (7x - 4x) + 12 + 15

              = -12x² - 3x + 27

This value of f(x) - g(x) matches with option D.

Therefore, Option D. is the correct option.

Answer:

[tex]\frac{(L x M)}{6}[/tex]

Step-by-step explanation:

The greatest common factor is the greatest number that will divide two values. We have two values L and M. Each has numbers which multiply together to give the number. The highest value or most in common they share is 6. This is the GCF.

The least common multiple is the smallest positive number which is a multiple of the two. This means both L and M divide into it evenly.

We know L x M is a multiple because L and M will be factors of it. But we don't know its the least.

As an example if L= 42 and M = 60, they have GCF 6. We can multiply them to find a multiple 42 x 60 = 2520 but we don't know this is the smallest or least multiple we can find. If we divide by the GCF, 2520/6=420. Interestingly, 42 x 10 =420 and 60 x 7 =420. This means 420 is the least common multiple.

We can multiply (L x M) and then divide by the GCF of L & M to find the least common multiple.

[tex]\frac{(L x M)}{6}[/tex]

The number of cubes needed with an edge length of  [tex]\bold{\dfrac{1}{3}}[/tex] inches is needed to build a cube with an edge length of 1 inch is 27.

the edge length of smaller cube, a = [tex]\bold{\dfrac{1}{3}}[/tex] inches

the edge length of the cube to be built, S = [tex]\bold{\dfrac{1}{3}}[/tex] inches

we know that volume of a cube is given by (side)³.

[tex]\bold{Volume\ of\ cube = (side)^3}[/tex]

Volume of the smaller cube =  (edge length of the smaller cube)³

                                              =   a³

                                              =   [tex]\bold{(\dfrac{1}{3})^3}[/tex]

                                              =   [tex]\bold{\dfrac{1}{27}}[/tex] in.³

Volume of the cube to be build =  (edge length of the cube to be built)³

                                                    =   S³

                                                    =   1³

                                                    =   1 in.³

solving,

Cubes of smaller length are needed for the larger cube

                                                         [tex]\bold{=\dfrac{Volume\ of\ the\ Larger\ cube}{Volume\ of\ the\ Smaller\ cube}}[/tex]

                                                         [tex]\bold{=\dfrac{1}{\dfrac{1}{27}}}[/tex]

                                                         [tex]\bold{=27}[/tex]

Hence, the number of cubes needed with an edge length of  [tex]\bold{\dfrac{1}{3}}[/tex] inches is needed to build a cube with an edge length of 1 inch is 27.

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The surface area of the cylinder is approximately 191.9 square inches.

The surface area of a cylinder is the sum of the areas of its curved surface and its two circular bases. The formula for the surface area of a cylinder is:

SA = 2πr² + 2πrh

where SA is the surface area, r is the radius of the circular base, h is the height of the cylinder, and π is the mathematical constant pi (approximately equal to 3.14159).

The first term on the right-hand side of the equation (2πr²) represents the area of the two circular bases of the cylinder. The second term (2πrh) represents the area of the curved surface of the cylinder.

The area of the square embedded in the circular base of the cylinder is 18 in², which means each side of the square has a length of √18 in = 3√2 in. Since the square is embedded in the circular base, the diameter of the base of the cylinder is equal to the diagonal of the square, which is 2 times the length of one side, or 6√2 in.

The radius of the circular base is half the diameter, or 3√2 in. The surface area of the cylinder consists of the area of the top circular base, the area of the bottom circular base, and the lateral area (the curved surface area) of the cylinder.

The area of each circular base is πr² = π(3√2)² = 18π in².

The lateral area of the cylinder can be found by multiplying the height (which is given as 10 inches) by the perimeter of the circular base (which is 2πr). The perimeter of the circular base is 2π(3√2) = 6π√2 in. Therefore, the lateral area is 10(6π√2) = 60π√2 in².

The total surface area of the cylinder is the sum of the areas of the two circular bases and the lateral area:

Surface area = 2(18π) + 60π√2

= 36π + 60π√2

≈ 191.9 in² (rounded to one decimal place)

Therefore, the surface area of the cylinder is approximately 191.9 square inches.

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Answer:

1

Step-by-step explanation:

Slope = change in y / change in x

Y-values: 9 and 2

x-values: 3 and -4

Change is the difference

9-2)/(3- (-4)) = 7/7 = 1

Answer:

The slope is 1

Step-by-step explanation:

To find the slope, we use the formula

m = (y2-y1)/(x2-x1)

where (x1,y1) and (x2,y2) are the points on the line

m = (9-2)/(3--4)

 = (9-2) /(3+4)

 = 7/7

 =1

The slope is 1

Answer:

slope = - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

y = - 2x is in this form

with slope m = - 2 and c = 0

Answer: 198 students

Step-by-step explanation:

220-22=198students

Final answer:

After subtracting Mr. Thompson's class size of 22 students from the school cafeteria's capacity of 200, 178 students can still eat in the cafeteria.

Explanation:

The student's question pertains to the capacity of the school cafeteria and how many more students can be accommodated when a specific class is having lunch. If the cafeteria holds 200 students and Mr. Thompson's class has 22 students, we can calculate the number of additional students that can still eat in the cafeteria by subtracting Mr. Thompson's class size from the total capacity of the cafeteria.

To solve this, we perform the following subtraction:

Capacity of cafeteria - Number of students in Mr. Thompson's class = Number of remaining spots

200 - 22 = 178

Therefore, 178 students can still eat in the cafeteria when Mr. Thompson's class is having lunch.