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Thank you so much!

"Kelvin is 3 years older than Daniel" Let Kelvin be K and Daniel be D 

K=D+3 (1) (Well K>D so in order for D to be equal to K we have to add 3 since K Is more than D by 3)

"Two years ago, K was 4 times as old as daniel"

K=4D (2)

Solve the equation by substituting (2) into (1)

\(4D=D+3\) Subtract D 

\(3D=3\) Divide by 3

\(D=1\) Notice that is 2 years ago thus now D+2= 1+2=3 

So Daniel = 3 years old now

Kelvin is 6 years old now.

We see that the rectangle with side lengths 5 and 10 have an area of 50 and another rectangle with the same sides on the opposite side. 

The two bottom rectangles have side lengths 3.6 and 10 have a combined area of 3.6*2*10 = 72.

The two front triangles have bases of 6 and heights 2 and 4 which have a combined area of \(\dfrac{6\cdot2}{2}\cdot \dfrac{6\cdot4}{2} = 6\cdot 12= 72\)

There are also the two triangles on the back which have the same area. 

Thus the total surface area is 72+72+72=216.

We can see that \(DG = 12\) and \(DF = 5\).

By Pythagorean theorem we get:

\(a^2+b^2= c^2\)  \(\rightarrow\) \(12^2+5^2=13^2\)\(\).

Thus FG  = 13.

I found a similar thread.

https://web2.0calc.com/questions/cos-3-4-where-3-2-tan-3-4-where-0-2-what-is-the-exact_2

Since the diameter of the smaller circle is 2 units the radius is 1 unit.
We know that the radius of the larger circle is 4 times the radius of the smaller circle the radius of the larger circle is 4 units.
Notice that the area of the gray region is equal to the larger circle minus the smaller one.
Since the area of a circle is  \(\pi \cdot r^2\) we can find the area of the gray area by substituting.
\(\pi \cdot 4^2 - \pi \cdot 1^2 = 16\pi - \pi = 15\pi\).

Okay I followed those steps and got 236.3 seconds as my answer, is that correct? Thanks so much for your help:)

Step 1:  Since the point moves at the rate of 32pi/9 radians per minute, divide this number by 60 to find the 

              rate per second.

Step 2:  Since there are 2pi radians in one revolution, multiply this number by 7 to find the number of radians

              in 7 revolutions.

Step 3:  Divide the answer of step 2 by the answer of step 1 to find how may seconds that it will take.

The bottom block is 12*9*2 = 216 \(cm^3\).

The top bock is 10*9*8 = 720 \(cm^3\).

Thus the total volume is 720+216 = 936 \(cm^3\)

1/4 is equivalent to 3/12 

1/3 is equivalent to 4/12 

So if we conclude that this arithmetic sequence is the addition of 1/12 to each term, then: 

–5/12   –4/12   –3/12   –2/12   –1/12   0/12   1/12   2/12   3/12   4/12 

  1st       2nd      3rd       4th        5th     6th     7th     8th     9th    10th 

second term –4/12  =  –1/3 

_.

It says in the question that no two are equal

The answer depends if there are paranthesis around -c or not. Just to clarify

The block that is the base:  12 cm x 9 cm x 2 cm 

The block that is on top:  8 cm x 9 cm x 10 cm 

Find the two volumes and add them together.

I believe that it is a cardiod. (heart shaped)

It has 8 petals.

This will be true if x = y = z.

thank u so much!!

you helped me a lot!

I really appreciate it! 

The numbers with a digit of 9 in the one's place are:  9, 19, 29, 39, 49, 59, 69, 79, 89, and 99.

The probability of getting the first number with a 9 in the one's place is 10/100.

The probability of getting the second number (without replacement) with a 9 in the one's place is 9/99.

To find the final probability, multiply these numbers together:  10/100 x 9/99  =  ...

a)  The graph on the right does not have a complete y-axis; it skips a region.

b)  Actually, the opposite is true; because of the incomplete y-axis, the graph makes it appear that the Mountain Clear water company is cheaper.

c)  Again, the opposite is true; the slope of the graph of the H2O water company appears to be steeper.

d)  The Mountain Clear water company.

There is a total of 5 + 7 + 9 = 21 coins.

The probability of selecting 2 pennies (no replacement)  =  5/21 x 4/20

The probability of selecting 2 pennies (with replacement)  =  5/21 x 5/21

The probability of selecting the same coin twice (without replacement)  =  0  (once he coin has been selected, it can't be selected again, if there is no replacement)

Draw a line segment parallel to the base that continus the 7.5 cm segment.

This will divide the segment into a bottom rectangle:  18 cm x 11.5 cm

and a bottom rectangle:  10.5 cm x 4 cm.

Find the area of each rectangle and add them together.

Ohhh, ok thanks

If you understand the answer to solving the problem given the 16^th and 17^th terms, work this problem in a similar fashion.

The equation of the parabola is:  y  =  -2x² + 12x - 8

a = -2     b = 12     c = -8

The formula is:  -b/(2a)  =  -12 / (2·-2)  =  -12 / -4  =  3

To find the value of y, substitute 3 into the equation of the parabola