What are the next three terms of 50,150,450,1350,...

Answer: C

Step-by-step explanation:

 x² + 25

= x² - (-25)

This can now be factored using the sum & difference formula:

√x² = x

√-25 = 5i

So, x² - (-25) = (x - 5i)(x + 5i)

If a, b and c are the lengths of the sides of a triangle then

if a ≤ b ≤ c, then a + b > c.

5, 7, 11

5 + 7 = 12 > 11   CORRECT

7, 10, 11

7 + 10 = 17 > 11   CORRECT

7, 11, 12

7 + 11 = 18 > 12   CORRECT

7, 11, 19

7 + 11 = 18 < 19   INCORRECT

Using the Triangle Inequality Theorem, the third side of the triangle must be less than the sum of other two sides and more than the absolute difference of the two sides. With the sides 7 and 11 given, the third side must be more than 4 but less than 18. Therefore, 19 cannot be the length of the third side.

In mathematics, particularly in geometry, the length of the third side of a triangle when the lengths of two sides are known, can be determined by using the Triangle Inequality Theorem. This theorem states that the length of any side of a triangle must be less than the sum of the lengths of the other two sides. In this case, the lengths of the two sides are given as 7 and 11. The sum of these two lengths is 18.

So the possible length of the third side must be less than 18 but more than the absolute difference of 7 and 11 (which is 4). Hence, the third side can be more than 4 and less than 18. Therefore out of the options provided, the value 19 could not be the length of the third side of the triangle.

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If the shape shown is rotated about the axis, a solid cylinder would be formed.

A cylinder is a three dimensional shape (has length, width and height) which has two parallel bases joined by a curved surface, at a fixed distance.

If the shape shown is rotated about the axis, a solid cylinder would be formed.

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When a rectangle is rotated about an axis, it forms a solid cylinder.

The shape that best describes the object generated when a rectangle is rotated about an axis is a solid cylinder. When a rectangle is rotated around an axis, it forms a three-dimensional shape that is similar to a cylinder. The base of the shape is a rectangle, and the height is equal to the length of the original rectangle. The shape has a curved surface and two circular faces at the top and bottom, just like a cylinder.

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Answer:

Step-by-step explanation:

Step 1: Calculate the change by subtracting old cost ($52) from the new cost ($64)

Step 2: Divide that change by the old cost ($52).  You will get a decimal number

Step 3: Convert the decimal number to a percentage by multiplying by 100%

Part A:

The range is the difference between the highest and lowest values:

Highest value = 78

Lowest value = 40

Range = 78-40 = 38

Part B:

The interquartile range is the difference between Q1 and Q3.

Q1 is the middle value of the lower half and Q3 is the middle value of the upper half.

There are 11 total numbers,  40 , 64, 66, 67,67,68,69,70, 71, 72, 78

The median would be the middle value, 68, so the lower half would be the 5 numbers below 68:  40 , 64, 66, 67,67.

The middle value of those numbers would be 66

The upper half are the 5 numbers above 68: 69,70, 71, 72, 78.

The middle value of those numbers is 71

The interquartile range would be 71 - 66 = 5

Part C:

The interquartile range is the better measure.

The correct Answer is option (A).10,800 [tex]cm^3[/tex] oil can the small container carry.

To determine how much oil the small container can carry, given the scale factor and the capacity of the large container, follow these steps:

1. Identify the given values:

  - Capacity of the large container: [tex]\( 144,000 \, \text{cm}^3 \)[/tex]

  - Scale factor from large to small container: [tex]\( 0.075 \)[/tex]

2. Calculate the capacity of the small container:

  - Use the formula: [tex]\[ \text{Capacity of small container} = \text{Capacity of large container} \times \text{Scale factor} \][/tex]

  - Substitute the given values: [tex]\[ \text{Capacity of small container} = 144,000 \, \text{cm}^3 \times 0.075 \][/tex]

3. Perform the multiplication:

[tex]\[ 144,000 \times 0.075 = 10,800 \, \text{cm}^3 \][/tex]

Therefore, the capacity of the small container is:

[tex]\[ \boxed{10,800 \, \text{cm}^3} \][/tex]

x = 3

"Standard form" is the form ...

... ax + by = c

where a, b, c are mutually prime integers. The coefficients a and b cannot both be zero. The leading coefficient must be positive. If "a" is zero, then the leading coefficient is "b".

So ...

... x = 3

is in standard form already. (a=1, b=0, c=3)

_____

Further comments on Standard Form

Of course, if the line has irrational slope or intercept, the coefficients cannot all be integers.

The order of the variables may be swapped, in which case the coefficient of y is the leading coefficient and must be positive.

This is the only way a vertical line can be written, as slope-intercept form is undefined for a vertical line.

Answer:

6 miles all together in them 8 days

Step-by-step explanation:

3/4 times 8

Answer:

6 miles in all

Step-by-step explanation:

3/4 *8 duh

Answer:

2 hours

Step-by-step explanation:

using the relationship

distance = speed × time, then

time = [tex]\frac{distance}{speed}[/tex] = [tex]\frac{30}{15}[/tex] = 2 hours

It will take 2 hours to cover 30 miles so option (C) is correct.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Given that,

A cyclist rode at an average speed of 15 mph for 30 miles.

So,

15 miles ⇒ hour

Multiply by 2

2 hours ⇒ 30 miles.

Hence "It will take 2 hours to cover 30 miles".

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Answer:

Associative property.

Step-by-step explanation:

Associative property implies that, for instance; no matter how the numbers are grouped in the sum involving (-5, x and 4), the result is the same.

Answer:

5x

Step-by-step explanation:

Answer:

Part 1. [tex]\dfrac{x+1}{2x}=\dfrac{x^2-7x+10}{4x}.[/tex]

Part 2. Solutions: [tex]x_1=1,\ x_2=8.[/tex]

Extraneous solution: [tex]x=0.[/tex]

Step-by-step explanation:

Part 1. You are given the equation

[tex]\dfrac{1}{2}+\dfrac{1}{2x}=\dfrac{x^2-7x+10}{4x}.[/tex]

Note that

[tex]\dfrac{1}{2}+\dfrac{1}{2x}=\dfrac{x+1}{2x},[/tex]

then the equation  rewritten as proportion is

[tex]\dfrac{x+1}{2x}=\dfrac{x^2-7x+10}{4x}.[/tex]

Part 2. Solve this equation using the main property of proportion:

[tex]4x\cdot (x+1)=2x\cdot (x^2-7x+10),\\ \\2x(2x+2-x^2+7x-10)=0,\\ \\2x(-x^2+9x-8)=0.[/tex]

x cannot be equal 0 (it is placed in the denominator of the initial equation and denominator cannot be 0), so [tex]x=0[/tex] is  extraneous solution to the equation.

Thus,

[tex]-x^2+9x-8=0,\\ \\x^2-9x+8=0,\\ \\x_{1,2}=\dfrac{9\pm\sqrt{(-9)^2-4\cdot 8}}{2}=\dfrac{9\pm7}{2}=1,\ 8.[/tex]

Part A: i forgot the question but i know its the third option (c)

Part B:

Solve the original equation by solving the proportion.

The solutions are: (1,6)

Part c:

Name the extraneous solution(s) to the equation

answer: Neither

These are for edu2020

Answer:

10

Step-by-step explanation:

7 2/9 + 2 7/9  common denominators already the same so add

7+2=9 first start with the whole number

2/9 + 7/9= 9/9 = 1 then add the fractions

9+1=10 then add the whole number and fraction

Answer:

10

Step-by-step explanation:

She drove 2 hours at 35 miles per hour for a total of 35 * 2 = 70 miles.

She drove 3 hours at 48 miles per hour for a total of 48 * 3 = 144 miles.

Her total miles were: 70 + 144 = 214.

Her total driving time was 3 + 2 = 5 hours.

Divide her total miles by total time for her average speed:

214 / 5 = 42.8 miles per hour average speed.

Not sure if you need to round the answer or not.

Mrs. Padre's average speed for the entire trip is 42.8 miles per hour, which is calculated by dividing the total distance (214 miles) by the total time (5 hours).

To determine Mrs. Padre's average speed for the whole trip, we need to use the formula for average speed:

Average speed = Total distance / Total time

First, we calculate the distance traveled during each part of the trip:

Next, we sum up the total distance and total time:

Now we can calculate the average speed:

Average speed = 214 miles / 5 hours = 42.8 miles per hour

Answer:

1 cubic foot

Step-by-step explanation:

Volume = length * width * height

= 1*1*1 = 1 ft^3

The volume of the given box shaped like a cube is 1 cubic foot.

We have given that,

The box has a length of 1 foot, a width of 1 foot, and a height of 1 foot.

Volume = length * width * height

Volume= 1*1*1

Volume= 1 ft^3

Therefore the volume of the given box shaped like a cube is 1 cubic foot.

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Answer:

(f+g)(x) = 13x + 3

Step-by-step explanation:

Rewrite  f(x)=2x+7 and g(x)=11x-4 in columns, as follows:

f(x)=2x+7

+g(x)=11x-4

----------------

Now add each column separately.

f(x)+g(x) = (f+g)(x) ("the sum of functions f and g")

2x + 11x = 13x, and, finally, 7-4 = 3.

Therefore,

 f(x)=2x+7

+g(x)=11x-4

----------------

(f+g)(x) = 13x + 3

Answer:

21 child tickets

Step-by-step explanation:

For this problem, you'd use a system of equations.

First, define your variables.

x = # of child tickets sold

y = # of adult tickets sold

There were 4 times as many adult tickets (y) as child tickets (x) sold, so:

4 x = y

4 x - y = 0

93 (4 x - y = 0)

372 x - 93 y = 0

The total revenue was $909.30, adult tickets were $9.30 each, child tickets were $6.10 each, so:

6.10 x + 9.30 y = 909.30

10 (6.10 x + 9.30 y = 909.30)

61 x + 93 y = 9093

372 x - 93 y = 0

433 x = 9093

433 x / 433 = 9093 / 433

x = 21

There are 750 spectators in the stadium. 420 of these spectators are women and the rest are men. What percent of the spectators are men.

The fraction [tex]\frac{420}{750}[/tex] represents the number of women in the stadium out of all the 750 people in the stadium. We can subtract 420 from 750 and we will get a difference of 330. Now we know that there are 330 men in the stadium.

The fraction [tex]\frac{330}{750}[/tex] represents the number of men at the stadium out of everyone. To find the percent of men at the stadium, we need to turn [tex]\frac{330}{750}[/tex] into a percent. [tex]\frac{330}{750}[/tex] reduced is [tex]\frac{11}{25}[/tex] because we are dividing both the numerator and denominator by the Greatest Common Factor of 330 and 750 using 30.

11 ÷ 25 = 0.44

0.44 × 100 = 44%

Therefore, 44% of the spectators in the stadium are men.

Answer:

1.5

Step-by-step explanation:

The real rate of return is calculated as the difference between rate of interest and the inflation.

so,Interest=2.5%

Inflation=1%

=2.5-1

=1.5%

Answer:

1.485 % ( approx )

Step-by-step explanation:

We know that,

[tex]\text{Real rate of return}=\frac{1+\text{Nominal rate}}{1+\text{Inflation rate}}-1[/tex]

Given,

Nominal rate = 2.5 % = 0.025

Inflation rate = 1 % = 0.01,

[tex]\implies \text{Real rate of return}=\frac{1+0.025}{1+0.01}-1[/tex]

[tex]=\frac{1.025}{1.01}-1[/tex]

[tex]=1.01485149-1=0.01485149\approx 0.01485[/tex]

Thus, the real rate of return is 0.01485 or 1.485 %.

Answer:

50+2p=C

Step-by-step explanation:

Answer: Our required equation to find the total cost of his monthly membership to the gym  would be [tex]C=50+2p[/tex]

Step-by-step explanation:

Let C be the total cost for your monthly membership.

Let p be the number of times you used the pool in one month.

Cost of every time he want to use the pool = $2

Monthly fee = $50

According to question, it becomes,

[tex]C=50+2p[/tex]

Hence, our required equation to find the total cost of his monthly membership to the gym  would be [tex]C=50+2p[/tex]

Answer:

The answer would be 24

Step-by-step explanation:

7 pies= 1/4 so 7 times four (to equal whole) = 24

Answer:

$1.02

Step-by-step explanation:

We are told that Clark buys 2 gallons of paint for $ 16.39.

To find the cost per pint of paint let us convert amount of paint in gallons.

1 gallon = 8 pints.          

2 gallons= 8*2 pints= 16 pints.

Now let us find cost per pint of paint by dividing the total cost of paint by number of pints in 2 gallons.

[tex]\text{The cost per pint of paint}=\frac{16.39}{16}[/tex]

[tex]\text{The cost per pint of paint}=1.024375[/tex]

Upon rounding our answer to nearest cent we will get,

[tex]\text{The cost per pint of paint}=1.02[/tex]

Therefore, the cost per pint of paint is $1.02.

Answer:

Option B is correct

The maximum revenue that the company can make from the treadmill sales is, $81,000

Step-by-step explanation:

Let x represent the number of treadmill x sold and y represents the number of treadmill y sold

As per the statement: Three times the number of treadmill y sold must be less than or equal to twice the number of treadmill x sold.

⇒[tex]3y\leq 2x[/tex]                    ......[1]

Also, it is given that the company has at most 100 treadmills to sell.

⇒[tex]x+y\leq 100[/tex]

using a graph tool for equation [1] and [2] as shown in figure given below;

⇒ the solution is the shaded area

The maximum revenue that the company can make is for the point, (60, 40)

⇒ x = 60 treadmills

and y = 40 treadmills

Maximum Revenue = [tex]60 \times 750 + 40 \times 900 = 45000+36000 = \$81,000[/tex]

Therefore, the maximum revenue that the company can make from the treadmill sales is, $81,000

Answer:

8 minutes

Step-by-step explanation:

time = distance/speed

A decrease of 15 mph from 45 mph means the speed on the second segment is 30 mph. Filling in the given values in the above equation, we have ...

... time = (4 mi)/(30 mi/h) = 4/30 h = 8/60 h × (60 min/h) = 8 min

Answer:2 times

Step-by-step explanation:

i did the assinment

The answer is 2,240 + 170n

2,240 in savings

210n

3

Henry saves each week

100n parents put in savings each week

thus,

2,240 + 210n

3

+ 100n

2,240 + 70n + 100n

2,240 + 170n

Answer:

185.39 m

Step-by-step explanation:

Central angle = 8π/5 radians

Let's convert radians to degrees.

Answer:

The length of arc is 185.39 m      

Step-by-step explanation:

Given that in a circle with a radius of 36.9 m, an arc is intercepted by a central angle of [tex]\frac{8\pi}{5}[/tex] radians.

we have to find the arc length.

[tex]Radius=36.9 m[/tex]

[tex]\text{Central angle=}\frac{8\pi}{5}[/tex]

The arc length can be calculated by the formula

[tex]L=r\theta[/tex]

[tex]\text{where r is radius and }\theta \text{ is central angle in radians. }[/tex]

[tex]L=36.9 \times \frac{8\pi}{5}[/tex]

[tex]L=36.9 \times \frac{8\times 3.14}{5}[/tex]

[tex]L=\frac{926.928}{5}=185.3856\sim 185.39 m[/tex]

hence, the length of arc is 185.39 m

Answer:

See attached diagram

Step-by-step explanation:

Given quadrilateral has vertices at points A(-8,4), B(4,-4), C(0,-8) and D(-4,-4).

A dilation with a scale factor of [tex]\dfrac{3}{4}[/tex] and a center of dilation (0,0) has a rule

[tex](x,y)\mapsto \left(\dfrac{3}{4}x,\dfrac{3}{4}y\right).[/tex]

Then

See attached diagram for details.

Remark: If a scale factor is 34, then the rule is (x,y)→(34x,34y) and image vertices have coordinates (-272,136), (136,-136), (0,-272), (-136,-136).

A line that intersects a circle at exactly one point is called a tangent.

A line segment that touches a circle specified to only one point is called a tangent to that circle.

The point where it touches the circle is called the point of tangency.

We can see that point line segment PT is the tangent of our circle and point P is the point of tangency.  

Therefore, A line that intersects a circle at exactly one point is called a tangent.

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