In the diagram below, JK is similar to MNO. If segment Mn is 8 cm, segment Bo is 18 cm, segment OM is 20 cm, and segment JK is 22 cm, how long is segment LJ?

Answer:

The volume is increasing at a rate of 25,133 mm/s.

Step-by-step explanation:

Diameter is 40mm

Radius is half the diameter, so [tex]r = \frac{40}{2} = 20[/tex]

How fast is the volume increasing when the diameter is 40mm?

We have to apply implicit differentiation, of V and r in function of t. So

[tex]V = \frac{4}{3} \pi r^3[/tex]

[tex]\frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}[/tex]

The radius of a sphere is increasing at a rate of 5 mm/s.

This means that [tex]\frac{dr}{dt} = 5[/tex]

Then

[tex]\frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}[/tex]

[tex]\frac{dV}{dt} = 4\pi (20)^2(5)[/tex]

[tex]\frac{dV}{dt} = 25133[/tex]

The volume is increasing at a rate of 25,133 mm/s.

Answer:

f(x) = 12x = 10

Step-by-step explanation:

We need a linear equation in the slope-intercept form.

y = mx + b

where y = total pay, m = hourly salary, x = number of hours worked, and b = y-intercept, or initial value

Let's look in the table.

1 hour: $22

2 hours: $34

The difference in pay between 1 hour and 2 hours is $34 - $22 = $12.

The difference in time between 1 hour and 2 hours is 1 hour.

In 1 hour he earns $12. That means the slope is 12.

We know he earns $22 for working a total of 1 hour.

Start at 1 hour and $22 on the table.

Subtract 1 hour from 1 hour to get 0 hours.

Subtract $12 form $22 to get $10.

That means for 0 hours he gets $10. b = 10

The equation is

y = 12x + 10

In function form, we have:

f(x) = 12x = 10

Here we want to find a linear relation with only using the data in a table, we will find that the line is:

[tex]y = 12\cdot x + 12[/tex]

We know that Damian's earns a set amount plus an hourly wage, then this can be modeled with a linear equation:

[tex]y = a\cdot x + b[/tex]

Where a is the slope, which in this case is the hourly wage, and b is the y-intercept, which in this case is the set amount.

Such that x is the number of hours and y is the pay.

We know that if the line passes through two points (x₁, y₁) and (x₂, y₂) the slope can be given as:

[tex]a = \frac{x_2 - x_1}{y_2 - y_1}[/tex]

By looking at the table we can find two points of our line, for example, if we use the first and third points:

(1, 22) and (2, 34) then the slope will be:

[tex]a = \frac{34 - 22}{2 - 1} = 12[/tex]

Then the line is something like:

[tex]y = 12\cdot x + b[/tex]

To find the value of b, we can use one of the points, for example, the point (1, 22) means that when x = 1, we must have y = 22.

Replacing that in the above equation we have:

[tex]22 = 12\cdot1 + b\\\\22 = 12 + b\\\\22 - 12 = b = 12[/tex]

Then the equation of the line is:

[tex]y = 12\cdot x + 12[/tex]

If you want to learn more, you can read:

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Answer: Since he had fourteen, and he gave away six of them, he has eight left.

Step-by-step explanation:

The number sentence shows the number of apples Austin has left is 14 - 6 and equal to 8.

A way to express or represent numbers is through the number system.

The Number System includes any of the several sets of symbols and the rules for using them to represent numbers.

As per the given,

Total number of apples = 14

Number of apples that make a pie = 6

Left = 14 - 6 = 8

Hence "The number sentence shows the number of apples Austin has left is 14 - 6 and equal to 8".

For more about the number system,

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Answer:

{4, 4, 8, 13, 16}

Step-by-step explanation:

If we have a set of N numbers in order:

{x₁, x₂, ..., xₙ}

The median is the middle number of the set.

The mode is the value that is repeated more times in the set

The mean is computed as:

[tex]M = \frac{x_1 + x_2 + ... + x_n}{N}[/tex]

And the range is the difference between the largest value and the smallest value.

Here we want 5 positive integers, so we have something like:

{x₁, x₂, x₃, x₄, x₅}

We know that the median is 8.

Then the middle value, x₃, is equal to 8.

We also know that the mode is 4, then we can have the number 4 repeated two times, and because 4 is smaller than 8 and this must be in order, then we can have:

x₁ = x₂ = 4

Replacing these in the set we have:

{4, 4, 8, x₄, x₅}

Now we know that the range is 12, and this was the difference between the largest and smallest value.

We know that the smallest value is 4, and the largest value is x₅, then we will have:

x₅ - 4 = 12

x₅ = 12 + 4 = 16

Then our set is:

{4, 4, 8, x₄, 16}

Finally, we know that the mean is 9.

Remember that the equation for the mean is:

[tex]M = \frac{4 + 4 + 8 + x_4 + 16}{5}[/tex]

Then we need to solve:

[tex]9 = \frac{4 + 4 + 8 + x_4 + 16}{5}[/tex]

[tex]9*5 = 4 + 4 + 8 + x_4 + 16}[/tex]

[tex]45 = 32 + x_4[/tex]

[tex]45 - 32 = x_4 = 13[/tex]

Then the set of five positive integers is:

{4, 4, 8, 13, 16}

Answer:

(-0.5, -1)

Step-by-step explanation:

A turning point is a point of the graph where the graph changes from increasing to decreasing (rising to falling) or decreasing to increasing (falling to rising)

Answer:

2.56

Step-by-step explanation:

Divide 20.48/8

I hope this helped!

Step-by-step explanation:   6 4 12 00

V = a²(h/3)    where a is the length of a side s    and  since h = (2/3)s

V = s²(2s/3)/3

V = s³(2/9)    I'll go the D

Answer:

-3, -4, -5

Step-by-step explanation:

x = 1st integer

x+1 = 2nd integer

x+2 = 3rd integer

x+x+1 = 3(x+2)

2x + 1 = 3x + 6

1 = x + 6

-5 = x

-4 = x+1

-3 = x+2

Answer:

FE = 3

Step-by-step explanation:

FE + ED = 11.

(2x - 17) + (x-2) = 11

Combine like terms, and you'll get:

3x -19 = 11

3x = 11+19 = 30

x = 10

FE = 2x - 17

= 2(10) - 17

= 20 - 17

= 3

Answer:

Aids

Step-by-step explanation:

AIDS is what ur mom has

Answer:

[tex]x=53\\[/tex]

Step-by-step explanation:

Together they make 90 degrees,

Now, form an equation to solve:

[tex]x+37=90[/tex]

[tex]x=90-37[/tex]

[tex]x=53[/tex]

{CHECK: [tex]53+37=90[/tex]}

hope this helps.....

Answer:  AREA OF H IS S= R4

Step-by-step explanation:

Answer: Choice A) [tex]14^3[/tex]

This is the same as writing 14^3

===================================================

Explanation:

Since all the sides are 14 feet long, we can basically say length = width = height = 14.

Or put another way:

The volume of the cube is length*width*height = 14*14*14 = 14^3 = 2744 cubic feet.

-----------

The term 14^3 has a base of 14 and exponent of 3.

The base is what we multiply out while the exponent tells us how many copies of the base to multiply. In this problem, we have 3 copies of 14 being multiplied. So that's why 14^3 = 14*14*14

If you were to say something like 3^14, then you would have 14 copies of 3 multiplied out, which is a much larger value. So we'll cross choice B off the list.

Choice C isn't correct either since again we're using exponents and not multiplication to tie together the 14 and 3.

Choice D would be correct if your teacher wanted it in expanded form, instead of exponent form.

Answer:A is the answer

Step-by-step explanation:

Answer:

Maybe 24 ft.......................????

Answer:

24 feet.

Step-by-step explanation:

We can solve this with a proportion.

[tex]\frac{Height}{Shadow}=\frac{Height}{Shadow}\\\frac{Height}{12}=\frac{2}{1}\\Height=\frac{2}{1}(12)\\Height = 24[/tex]

Therefore, the height of the sailboat is 24 feet.

Answer: A

Step-by-step explanation:

Answer: 70 mph

Step-by-step explanation:

======================================================

Explanation:

Vector u has magnitude 8 and direction 150 degrees.

So r = 8 and theta = 150

The polar form

r*(cos(theta)+i*sin(theta))

updates to

8*(cos(150)+i*sin(150))

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

Use your calculator to evaluate that last expression to get it into a+bi form

8*(cos(150)+i*sin(150))

8*(-0.866025 + i*0.5)

-6.9282 + 4i

So this is the a+bi form of vector u. It's a rough approximation of it.

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

Repeat those steps for vector v

v = r*(cos(theta)+i*sin(theta))

v = 3*(cos(115)+i*sin(115))

v = 3*(-0.422618 + i*0.906308)

v = -1.267854 + 2.718924i

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

We're converting each vector to a+bi form so that we can add the vectors.

The general idea is that if you want to add v = a+bi and w = c+di, then

v+w = (a+c)+(b+d)i

we simply add the corresponding real components together, and the imaginary components are added together as well.

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

Add up u and v

u+v = (-6.9282 + 4i) + (-1.267854 + 2.718924i)

u+v = (-6.9282 + -1.267854) + (4i + 2.718924i)

u+v = -8.196054 + 6.718924i

When rounding to four decimal places, the real and imaginary components are -8.1961 and 6.7189 respectively. These represent the x and y components of the vector.

So we can say vector u+v is approximately < -8.1961, 6.7189 >

Answer:

The answer is A, the CPI is 25.50, and the rate of inflation is 2%.

Step-by-step explanation:

I took the test and I know the correct answer. :)

Answer:

E) 102 and 2%

Step-by-step explanation:

Answer:

[tex]a=-\frac{2}{3}[/tex]

Step-by-step explanation:

We are given the lines, [tex]y=3x+8[/tex] and [tex]2y=ax-5[/tex]. For the latter equation, we can isolate the variable y to have the same format as the first. We want to create a y=mx+b equation where m represents the slope of the line. We now have the equations:

[tex]y=3x+8[/tex] and

[tex]y=\frac{a}{2}x-2.5[/tex]

The definition of perpendicular lines is that their slopes must be the negative reciprocal of each other. Thus:

[tex]-\frac{1}{3}=\frac{a}{2} \\\\a=-\frac{2}{3}[/tex]

I hope this helps! Let me know if you have any questions :)

Answer:

33

Step-by-step explanation:

x(14 - x)

Step One: Substitute

3(14 - 3)

Step Two: Brackets/Parenthesis

3(11)

Step Three: Multiply

33

Answer:

33

Step-by-step explanation:

1. Subtract the numbers

(14-3)

2. Multiply the numbers

3*11= 33

Answer:

Rule:-15

Step-by-step explanation:

36,21,6,-9,-24,-39,-54,-69...

Answer:

73,63

Step-by-step explanation:

it just goes down by 2 everytime

Answer:

5/15

Step-by-step explanation:

Out of 15, 5 are yellow. Converted to a fraction this will be 5/15. Hope this helps!! :)

Answer:

1/3

Step-by-step explanation:

Take the total number of socks and compare it to the number of yellow socks. 15 and 5. Now divide the total by the specified group (yellow socks), by doing so, you get 3.

Every 1 in 3 socks is yellow, meaning the chance of picking a yellow sock at random is 1/3.

Answer:

4670

Step-by-step explanation:

that is the workings above

If the third term is 8 and eighth term is 143 then the sum of first 20 terms is 4210.

Arithmetic progression is a sequence in which all the terms have equal differences. Nth term will be a+(n-1)d in which a is first term, d is difference and n is number of term.

We have been given that third term is 8 and eight term is 143 and we have to calculate the sum of first 20 terms.

[tex]A_{3}[/tex]=a+(3-1)d

8=a+2d-----1

[tex]A_{8}[/tex]=a+(8-1)d

143=a+7d---2

Subtract equation 1 from equation 2.

a+7d-a-2d=143-8

5d=135

d=27

Put the value of d in equation 1.

a+2d=8

a+2*27=8

a+54=8

a=-46

We know that,

[tex]S_{n}[/tex]=n/2[2a+(n-1)d]

=20/2[2*(-46)+(20-1)*27]

=10(-92+19*27)

=10(-92+513)

=10*421

=4210

Hence if the third term is 8 and eighth term is 143 then the sum of first 20 terms is 4210.

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Answer:

x = 1, x = -5

[tex]x/5 = 1/x+4\\Apply Fraction and Multiply : \\\\x(x+4)=5 x 1\\Simplify :\\x(x+4) = 5\\Solve.[/tex]

I hope this is what you were looking for !

Answer:

x = 81°

Step-by-step explanation:

Refer to the attachment for the steps.~

Answer: it’s 70 years

Step-by-step explanation:

Answer:

[tex]A(2,4)<-3,-2)A'(-1,2)>A''(-4,8)[/tex]

[tex]B)(5,2)-> B'(2,0)->B''(8,0)[/tex]

[tex]C(3,1)->C'(0,-1)->C''(0,-4)[/tex]

[tex](x,y)->(x-3,y-2)->([(x-3)*4],[(y-2)*4])[/tex]

Answer:

0.2

Step-by-step explanation: