If you place a 89-foot ladder against the top of a 80-foot building, how many feet will
the bottom of the ladder be from the bottom of the building?

Answer:

D

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (8, - 1), thus

y = a(x - 8)² - 1

To find a substitute (0, - 17), the coordinates of the y- intercept into the equation.

- 17 = a(0 - 8)² - 1

- 17 = 64a - 1 ( add 1 to both sides )

- 16 = 64a ( divide both sides by 64 )

a = [tex]\frac{-16}{64}[/tex] = - [tex]\frac{1}{4}[/tex]

y = - [tex]\frac{1}{4}[/tex](x - 8)² - 1 → D

Answer:

Option C) 144 centimeters squared.

Step-by-step explanation:

The picture of the question in the attached figure

we know that

The surface area of a prism is equal to

[tex]SA=2B+PL[/tex]

where

B is the area of the base of the prism

P is the perimeter of the  base

L is the length or height of the prism

Find the area of the base B

[tex]B=\frac{1}{2}(3)(4)=6\ cm^2[/tex] ---> the base is a right triangle

Find the perimeter of the base P

[tex]P=3+4+5=12\ cm[/tex] ---> is the perimeter of a triangle

we have

[tex]L=11\ cm[/tex]

Find the surface area SA

[tex]SA=2(6)+12(11)=144\ cm^2[/tex]

Answer:

144

Step-by-step explanation:

Answer:

Step-by-step explanation:

in order to be like terms, they have to have the same variable (and exponent, if there is any).....or be just a constant with no variables (just a number)

like terms in 12a - 7 + 7a + 12b are :

12a and 7a....because they have the exact same variable (a)

12b....no like terms

-7...no like terms

so ur answer is : 12a and 7a

Answer:

The total area of the shape = 4 + 4 + 2 = 10 square units

Step-by-step explanation:

This shape consists of three shape parts.

So, the total area of this shape is the sum of the areas of these shape parts.

1st Part) Finding the area of Right Triangle with base 4 units and perpendicular 2 units

A right triangle with base 4 units and perpendicular 2 units.

Let

'a' be perpendicular side = 2 units

'b' be the base side = 4 units

As

The area of right triangle

[tex]A=\frac{ab}{2}[/tex] ⇒ [tex]\frac{(4)(2)}{(2)}[/tex] = 4 square units

2nd Part) Finding the area of Square with the equal length and width i.e. 2 units

Let  a be the length of any side = 2 units

As the area of square

[tex]A=a^{2} }[/tex]

[tex]A = (2)^{2}=4[/tex] square units

3rd Part) Finding the area of Right Triangle with base 2 units and perpendicular 2 units

A right triangle with base 2 units and perpendicular 2 units.

Let

'a' be perpendicular side = 2 units

'b' be the base side = 2 units

As

The area of right triangle

[tex]A=\frac{ab}{2}[/tex] ⇒ [tex]\frac{(2)(2)}{(2)}[/tex]= 2 square units

Therefore the total area of the shape will be the sum of area of Right Triangle with base 4 units and perpendicular 2 units, area of Square with the equal length and width i.e. 2 and area of Right Triangle with base 2 units and perpendicular 2 units

So,

The total area of the shape = 4 + 4 + 2 = 10 square units

Keywords: area of a shape, area of triangle, area of square

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If Justin saves $8 every week, and x represents the number of weeks, this can be set up as 8x. We are trying to find the amount of money Justin has after x weeks, so y = 8x.

The expression x+2x+(x-4) represents the number of candles Julio sold in three weeks.

Step-by-step explanation:

Let,

x be the number of candles sold by Julio in first week.

According to given statement;

Candles sold in first week = x

He sold twice the number of candles the second week as he did the first week.

Candles sold in second week = 2x

In the third week, Julio sold 4 less than the number he sold the first week.

Candles sold in third week = x-4

Total candles sold = First week + Second week + Third week

Total candles sold = x+2x+(x-4)

The expression x+2x+(x-4) represents the number of candles Julio sold in three weeks.

Keywords: addition, variable

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The average speed is 135.26 miles per hour

Solution:

Given that, woman traveled 2445.9 miles in 18 hours five minutes

To find: Average speed of her flight in miles per hour

Let us first convert 18 hours 5 minutes to hours

We know that,

[tex]1 \text{ minute } = \frac{1}{60} \text{ hour }[/tex]

Therefore,

[tex]5 \text{ minute } = \frac{5}{60} \text{ hour } = 0.083 \text{ hour }[/tex]

Thus we get,

18 hours five minutes = 18 hour + 0.083 hour = 18.083 hour

Given that, distance = 2445.9 miles

Average speed is given by formula:

[tex]Average\ speed = \frac{distance}{time}\\\\Average\ speed = \frac{2445.9}{18.083}\\\\Average\ speed = 135.26[/tex]

Thus average speed is 135.26 miles per hour

Answer: 90

Step-by-step explanation:

The formula for calculating the nth term of a sequence is given as :

[tex]t_{n}[/tex] = a + ( n - d )

Where a is the first term

d is the common difference and

n is the number of terms

This means that the 4th term of an arithmetic sequence will have the formula :

[tex]t_{4}[/tex] = a + 3d

And the 4th term has been given to be , 12 ,substituting into the formula we have

12 = a + 3d .............................. equation 1

Also substituting for the 8th term , we have

36 = a + 7d .............................. equation 2

Combining the two equations , we have

a + 3d = 12  ................... equation 1

a + 7d = 36 ------------ equation 2

Solving the system of linear equation by substitution method , make a the subject of formula from equation 1 , that is

a = 12 - 3d ................... equation 3

substitute a = 12 - 3d into equation  2 , equation 2 then becomes

12 - 3d + 7d = 36

12 + 4d = 36

subtract 12 from both sides

4d = 36 - 12

4d = 24

divide through by 4

d = 6

substitute d = 6 into equation 3 to find the value of a, we have

a = 12 - 3d

a = 12 - 3 ( 6)

a = 12 - 18

a = -6

Therefore , the 17th term of the sequence will be :

[tex]t_{17}[/tex] = a + 16d

[tex]t_{17}[/tex] = -6 + 16 (6)

[tex]t_{17}[/tex] = -6 + 96

[tex]t_{17}[/tex] = 90

Therefore : the 17th term of the sequence is 90

The premiums indicated in the chart below on $30,000 policies are $240.00, $122.40, $62.40, $21.60, $652.50, $332.775, $169.50, $58.725 , $945.00, $482.475, $245.70, $85.05, $1,346.10, $686.761, $350.286  and $121.15.

To calculate the premiums for a $30,000 policy, first, we need to find the appropriate premium amount based on the given percentages for different payment frequencies (annual, semiannual, quarterly, and monthly).

**10-year Term Policy:**

- Annual premium: $240.00

- Semiannual premium (51% of annual): $240.00 * 51% = $122.40

- Quarterly premium (26% of annual): $240.00 * 26% = $62.40

- Monthly premium (9% of annual): $240.00 * 9% = $21.60

**Whole Life Policy:**

- Annual premium: $652.50

- Semiannual premium (51% of annual): $652.50 * 51% = $332.775 (approximately $332.78)

- Quarterly premium (26% of annual): $652.50 * 26% = $169.50

- Monthly premium (9% of annual): $652.50 * 9% = $58.725 (approximately $58.73)

**20-Payment Life Policy:**

- Annual premium: $945.00

- Semiannual premium (51% of annual): $945.00 * 51% = $482.475 (approximately $482.48)

- Quarterly premium (26% of annual): $945.00 * 26% = $245.70

- Monthly premium (9% of annual): $945.00 * 9% = $85.05

**20-year Endowment Policy:**

- Annual premium: $1,346.10

- Semiannual premium (51% of annual): $1,346.10 * 51% = $686.761 (approximately $686.76)

- Quarterly premium (26% of annual): $1,346.10 * 26% = $350.286 (approximately $350.29)

- Monthly premium (9% of annual): $1,346.10 * 9% = $121.15

Please note that the semiannual, quarterly, and monthly premiums are rounded to the nearest cent.

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The medication reach half of its highest concentration in the patient's bloodstream in 3 hours 45 minutes, the correct option is D.

Concentration of a solution is the milligrams of the solvent dissolved in a liter of solution.

The graph shows the variation of the concentration of the solution with time.

The highest concentration of the medicine is 2.5 mg/L.

The half of the highest concentration is 1.25 mg/L.

The graph can be seen for the time corresponding to the concentration 1.25 mg/ L.

The time taken is 3.75 hours = 3 hours 45 minutes.

The missing diagram is attached with the answer.

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Answer:

D on Edge

Step-by-step explanation:

Just got it right.

Answer:

Step-by-step explanation:

5x - y = 3.......(1)

2y = 10x+2.....(2)

Rearranging (2)

-10x + 2y = 2......(3)

Multiply equation (1) by 2

10x - 2y = 6..........(4)

Adding (3) and (4)

-10x + 10x + 2y - 2y = 2 + 6

No solution since both x and y are eliminated.

Answer:

When solving equations you goal is to get x by itself so

18-6.3x=49.5 (first step would be to minus 18 from each side)

-6.3x=31.5 (18-18=0, 49.5-18=31.5) (now you want to divide each side by -6.3)

x=-5 (-6.3/-6.3=1, 31.5/-6.3=-5)

Your final answer is

x=-5

Hope this helps ;)

Answer:

  3.25

Step-by-step explanation:

The slope of the line is ∆y/∆x = (-2-1)/(7-3) = -3/4.

The point-slope form of the line with slope m through (h, k) is ...

  y -k = m(x -h) . . . . . . . . . . we have m=-3/4, (h, k) = (3, 1)

  y -1 = -3/4(x -3)

The y-intercept is the point on the line where x=0. For x=0, the value of y is ...

  y = -3/4(-3) +1 = 9/4 +4/4

  y = 13/4 = 3 1/4

The y-intercept is 3 1/4.

Answer:

d^2 - π(d/2)^2

Step-by-step explanation:

Since the diameter of the circle is equal to the side of a square (d), that means that we have a circle inscribed in square.

If we draw a square and inscribe a circle in it, all parts of the square outside the circle will be waste, in this particular case.

If we want to find the area of the wasted material we need to subtract the area of the circle from the area of the square.

Area of the circle is:

P1 = πr^2, r being the radius

Since radius is half the diameter, that means that:

P1 = π • (d/2)^2

Area of the square whose side is d is:

P2 = d^2

So, the area of wasted material is:

P = P2 - P1

P = d^2 - π(d/2)^2

Answer:

g (x) = 2 ^ (x + 2)

Step-by-step explanation:

For this case the transformation of f (x) is given by

g (x) = 2 ^ (x + 2)

To prove it, we must verify that equality is met by replacing the ordered pairs shown in the function g (x)

For (-2,1)

g (-2) = 2 ^ ( -2 + 2)

g(-2)=1

For (-1,2)

g (-1) = 2 ^ ( -1+ 2)

g(-1)=2

For (0,4)

g (0) = 2 ^ ( 0+ 2)

g(0)=4

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Answer: Should Be 0.01

Step-by-step explanation: It’s Asking How Thick it is and never asked when So it would automatically mean from the start therefore it’s 0.01 cm thick

Answer:

-1(7x-9)(x-2)

Step-by-step explanation:

Because I'm right you're wrong, I'm big, you're small, and there's nothing you can do about it!!!

Answer:

  ≈ 58

Step-by-step explanation:

Estimation usually means you want an answer good to one or maybe two significant figures. That usually means you want to round the numbers involved to one or two significant figures.

Doing that here transforms the problem to 180/3 = 60, an answer with one significant figure.

You can improve the estimate a bit by recognizing that it is a little high (the numerator is higher than 175.32, but the denominator is the same). Since the numerator is high by about 5, the estimate is high by about 5/3 or a little less than 2. A closer estimate will be 60 - 2 = 58.

_____

The degree to which you refine the estimate will depend on the error requirements you have. Certainly an estimate of 60 is within 10% of the true value, so is "close enough" for many purposes.

To estimate 175.32 by 3, round 175.32 to 175, and divide by 3 to get 58. Since 175 is just under 180, which divides evenly by 3 to give 60, an estimate of 58 is reasonable.

To estimate the division of 175.32 by 3, we can round the numbers to make the calculation easier. First, we round 175.32 to 175 which is very close in value, and 3 remains as it is because it is already a whole number. So, our estimation becomes 175 / 3.

Dividing 175 by 3 gives us 58 as 3 times 58 is 174. We can see that this approximation is just 1 less than our rounded number, so it is a reasonable estimate. Therefore, 175.32 / 3 is approximately 58 when we estimate it without a calculator.

To check our estimation, we can compare it to similar, simple calculations. For example, if we divide 180 by 3, we get 60. Since 175 is slightly less than 180, our estimation of 58 is likely a good approximation for the division of 175.32 by 3.

Answer:

Students= 6

Teachers= 2

Step-by-step explanation:

Given: Art museum trip:

           Cost of ticket= $5.5 per teacher and $3 per student.

           Total amount paid= $29.

           Science trip:

           Cost of ticket= $22 per teacher and $11.5 per student.

           Total amount paid= $113.

Lets assume number of teacher be "x" and number of students be "y".

Now, forming an equation for cost of each trip.

we know, total cost= [tex]cost\ of \ each\ ticket \times numbers\ of\ tickets[/tex]

∴Art museum trip, [tex]5.5x+3y= 29[/tex] ---- 1st equation

Science museum trip, [tex]22x+11.5y= 113[/tex] ---- 2nd equation

Next using elimination method to find number teacher and students

[tex]5.5x+3y= 29\\22x+11.5y= 113[/tex]

Multiplying both side of 1st equation by 4

∴ [tex]22x+12y= 116\\22x+11.5y= 113[/tex]

changing sign of 2nd equation on both side and solving it.

∴ [tex]0.5y= 3[/tex]

Dividing both side by 0.5

[tex]y= \frac{3}{0.5}= 6[/tex]

Hence, number of students on field trip was 6.

Subtituting the value of y in 1st equation to find the number of teachers in field trip.

[tex]5.5x+3y= 29[/tex]

⇒ [tex]5.5x+3\times 6= 29[/tex]

⇒ [tex]5.5x+18= 29[/tex]

Subtracting both side by 18

⇒ [tex]5.5x= 11[/tex]

Dividing both side by 5.5

⇒ [tex]x= \frac{11}{5.5}= 2[/tex]

Hence, there were 2 teachers on field trips.

Answer:

No Solution

Step-by-step explanation:

4x-2y=8

y=2x+1

Make the first equation into where it says y=.

-2y=-4x+8

y=2x-4

Substitute either equation into the other as y=.

2x+1=2x-4   or    2x-4=2x+1

Switch terms around so they're with their like terms. Make sure it becomes the opposite when switching.

2x-2x=-1-4    or    2x-2x=4+1

0=-5                     0=5

Since x did not come back to equal an answer, this problem is not workable. There is no solution to it. If you were to do it a different way, there still would not be a solution to it.

Answer:

4<5<6

4<5<7

4<6<7

5<6<7

since there are 4 pieces of wood, you will have 4 combinations.  since the sum of the 2 shortest sides need to be more than the longest side the inequalities above are valid.

Hope this helps!!

Final answer:

Out of the four lengths of wood provided, there are three valid combinations that can form triangles: 4 cm, 5 cm, 6 cm; 4 cm, 6 cm, 7 cm; and 5 cm, 6 cm, 7 cm. These combinations satisfy the Triangle Inequality Theorem, which is necessary for forming triangles.

Explanation:

To determine how many different combinations of 3 pieces of balsa wood can be used to make triangles, we must recall the Triangle Inequality Theorem which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. For the pieces of lengths 4 cm, 5 cm, 6 cm, and 7 cm, we can form the following combinations that satisfy the Triangle Inequality Theorem:

4 cm, 5 cm, 6 cm

4 cm, 6 cm, 7 cm

5 cm, 6 cm, 7 cm

The inequalities for these combinations are as follows:

4 cm + 5 cm > 6 cm

4 cm + 6 cm > 5 cm

5 cm + 6 cm > 4 cm

4 cm + 7 cm > 6 cm

6 cm + 7 cm > 4 cm

5 cm + 7 cm > 6 cm

Each of these combinations is valid as the sum of the lengths of any two pieces is greater than the length of the third piece.

Answer:

B. Tuesday

Step-by-step explanation:

It is the only decrease in price going by the graph

Answer:

Tuesday

Step-by-step explanation:

It went down by the most that day, i.e. from $3.25 to $3.00.

Other days, it did not decrease by as much.

Answer:

3000 inches cubed

Step-by-step explanation:

I hope this help sorry if I'm wrong

Answer:

it's 1480

Step-by-step explanation:

I just did it on imagine math :)

Answer:

a

Step-by-step explanation:

if f(x)=y then when x is 1 2(3)^X= 6

Answer:

first graph

Step-by-step explanation:

given: [tex]f(x) = 2(3)^{x}[/tex]

substitute some values for x and see which curves accurately reflect the corresponding y-values:

when x = 0, f(0) = 2(3)^0 = 2(1) = 2

hence the graph must pass through the point (0,2)

We can see from the choices that the 2nd and 4th graphs do not pass through (0,2), so we can eliminate these 2 from consideration

when x = 1, f(1) = 2(3)^1= 2(3) = 6

hence the graph must pass through the point (1,6)

We can see that the 3rd graph does not pass through this point so we can eliminate the 3rd graph also.

Only the 1st graph gives points consistent with the 2 cases above.

Answer:

25 2/15

Step-by-step explanation:

A = length x width

width is 4 1/6

35 = 4 1/6 x length

solve for length

divide both sides by 4 1/6

35 divided by 4 1/6  or multiply 35 x 6/25 (reciprocal)

210/25

8 10/25 = 8 2/5 is the length

to find perimeter 2xlength + 2xwidth

2 x 4 1/6 + 2 x 8 2/5 = 2 x 25/6 + 2 x 42/5 = 50/6 + 84/5

convert to common denominator and add

use 30 as common denominator

250/30 + 504/30= 754/30

25 4/30 or 25 2/15

Final answer:

To find the perimeter of the rectangle, calculate the length using the given area and width. Then, apply the perimeter formula P = 2l + 2w. The perimeter is approximately 25.1 feet.

Explanation:

Calculating the Perimeter of a Rectangle

To find the perimeter of a rectangle, you need to know both the width and the length of the rectangle. The perimeter is the total distance around the rectangle, which is the sum of twice the width and twice the length: P = 2l + 2w.

The width of the rectangle is given as 4 1/6 feet. To find the length, we can use the provided area of the rectangle which is 35 square feet. The area of a rectangle is found by multiplying the length by the width: A = l × w. Let's call the length 'l'.

First, convert the width to an improper fraction: 4 1/6 = (4 × 6 + 1)/6 = 25/6 feet. Now set up the equation using the area: 35 = (25/6) × l. Solving for 'l' gives us l = (35 × 6)/25 = 210/25 = 8.4 feet.

Now that we have the length, calculate the perimeter using the equation P = 2l + 2w:

P = 2 × 8.4 + 2 × 4 1/6

P = 16.8 + 2 × 25/6

P = 16.8 + 50/6

P = 16.8 + 8.333...

P = 25.133... feet

Therefore, the perimeter of the rectangle is approximately 25.1 feet when rounded to one decimal place.

Question:

Which scenario best matches the linear relationship expressed in the equation y = –14x + 1,700?

1) Kent has $1,700 in his bank account and spends $14 each week.

2) Kent has $1,700 in his bank account and deposits $14 each week.

3) Kent had $1,700 in his bank account and deposited another $14.

4) Kent has $14 in his bank account and spent $1,700.

Answer:

Option  1) Kent has $1,700 in his bank account and spends $14 each week.

Step-by-step explanation:

Let x denote the number of weeks.

Option 1: Kent has $1,700 in his bank account and -14x as the negative sign denotes how much amount he spend each week.

Thus, Option 1 is the correct answer.

Option 2: Kent has $1,700 in his bank account and deposits $14 each week.

Writing it as equation, we have, [tex]y=14x+1700[/tex] which is not the expressed linear equation.

Hence,  Option 2 is not the correct answer.

Option 3: Kent had $1,700 in his bank account and deposited another $14.

Writing it as equation, we have, [tex]y=14+1700[/tex] which is not the expressed linear equation.

Hence,  Option 3 is not the correct answer.

Option 4: Kent has $14 in his bank account and spent $1,700.

Writing it as equation, we have, [tex]y=14-1700[/tex] which is not the expressed linear equation.

Hence,  Option 4 is not the correct answer.

Thus, the scenario that matches the linear equation relationship expressed in the equation is Option 1.

The answer is Kent has $1,700 in his bank account and spends $14 each week.

Answer:

A

Step-by-step explanation:

Answer:

The number is 40

Step-by-step explanation:

Step 1:  To find the number, multiply all of the numbers together

2 * 2 * 2 * 5

40

Answer:  The number is 40

Answer:

40

Step-by-step explanation:

2×2×2×5 = 40

Answers:

These are the three major and pure mathematical problems that are unsolved when it comes to large numbers.

The Kissing Number Problem: It is a sphere packing problem that includes spheres. Group spheres are packed in space or region has kissing numbers. The kissing numbers are the number of spheres touched by a sphere.  

The Unknotting Problem: It the algorithmic recognition of the unknot that can be achieved from a knot. It defined the algorithm that can be used between the unknot and knot representation of a closely looped rope.

The Large Cardinal Project: it says that infinite sets come in different sizes and they are represented with Hebrew letter aleph. Also, these sets are named based on their sizes. Naming starts from small-0 and further, prefixed aleph before them. eg: aleph-zero.

Answer: 1/4 ( 12x + 24 ) -9x=−6x+6