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Let her average speed for the first 1/3 of her drive==S

Let the distance between her house and her mother's house==D

D / S ==180 / 60

1/3D / S  +  2/3D / (S - 20) ==276 / 60

S==45 mph - Her average speed.

D ==135 miles - distance between her house and her mother's house.

Can anyone see an easy way to do this?

Since b is positive, the common ratio \(\dfrac b{12}\) is also positive. Then all the numbers in the sequence are positive.

Using geometric mean, \(a = \sqrt{16 \cdot 12} = 8\sqrt3\).

We can find the common ratio by calculating the second term divided by the first term, so the common ratio is \(\dfrac{8\sqrt 3}{16} = \dfrac{\sqrt 3}2\).

Therefore, \(\dfrac b{12} = \dfrac{\sqrt 3}2\). Multiply both sides by 12 to get \(b = 6\sqrt 3\).

\(m + n \equiv 4 + 10 = 14 \equiv 0 \pmod {14} \)

The remainder is 0.

Dividing by 2 on both sides gives x^2 + y^2 + 2x + 6y + 3 = 0.

Complete the square to get (x + 1)^2 + (y + 3)^2 = 7. This is now in center-radius form. Can you proceed from here?

If you reflect (0, -5) across x = 5, you get another point on the graph. Can you proceed from here?

Also, sometimes it incorrectly determines that a nonexistent limit exists.​

The step-by-step solution is not correct for some functions. For example, check this case: ​

Generally, for piecewise functions, you break the integral at the boundary points of the cases. In this problem, you break the integral at x = 3.

\(\newcommand{\dint}{\displaystyle\int} \dint_0^5 f(x)\,dx = \left(\dint_0^3 + \dint_3^5\right)f(x)\,dx = \dint_0^3 f(x) \,dx + \dint_3^5 f(x)\,dx\)

Now, you can use the fact that f(x) = 3 for 0 < x < 3 and f(x) = x for 3 < x < 5 to continue. Use the power rule of integration.

Moving r to the other side gives \(\left\lfloor\dfrac r4\right\rfloor = 15.5 -r \).

Then 15.5 - r is an integer. Then r = k + 0.5 for some integer k.

Then \(\left\lfloor\dfrac {k + \frac12}4\right\rfloor = 15 - k\).

That means \(15-k\leq \dfrac{k + \frac12}4 < 16 - k\) by definition of floor function. Now it becomes a compound inequality. To proceed, solve the compound inequality and list its integer solutions.

Consider the term in x.

\(7(tx) + (-6x)(10) = -39x\\ (7t - 60)x = 39x\\ 7t - 60 = 39\)

Please continue to solve for the value of t on your own.

\(\begin{array}{cc} &A + 2 = C + 2\\ \implies & A = C \end{array}\)

\(\begin{array}{cc} &B - 2 = D - 2\\ \implies & B = D \end{array}\)

\(\begin{array}{cc} &A + 2 = B - 2\\ \implies & B = A + 4 \end{array}\)

\(\begin{cases} A = C\\ B = D = A + 4 \end{cases}\)

Since A + B + C + D = 36 and with the above system of equation,

\(A + (A + 4) + A + (A + 4) = 36\)

Now you can solve for the value of A. If you know the value of A, you know the values of B, C, D. Then you will be able to find the product ABCD.

Sorry about that, hopefully, this will make it easier for you!!

Let x be the first term and a be a common difference.

We have the arithmetic sequence: \(x, x+a, x+ 2a, x+ 3a\) and the geometric sequence is: \(x, x+a, x+ 3a\)

From the geometric sequence, we can derive the equation: \(\large{{{x +a} \over x} ={ {x+3a} \over {x+a}}}\). 

Basically, this equation states that the common difference between the first 2 terms (x+a and x) is the same as the common difference between the next 2 terms (x+3a and x+a). 

 From the geometric series, we know that \({{x+3a}\over x} = 2a\) (value of 3rd term divided by 1st term is 2 times the common difference)

When we solve this system, we find that \(x = a = 2\), meaning the series is 2,4,6,8. 

thank you so very much!!

the answer would be 20-28i

*how sad but i understand your reasoning

You have asked 22 questions and you have not even once responded to an answer.

Why should people help you?

Since it is a geometric sequence, ask yourself "What number times 1 will give you 2?"   --->  2

Again:  "What number times 2 will give you 4?"   --->   again, the answer is 2.

So, this is your common ratio; you can find all the rest of the terms by multiplying each preceding term by 2.

A stack contains 7 green marbles and 3 red marbles. 2 marbles are taken from the sack w/out replacement. What is the probability of taking one green marble and one red marble (in any order)?

P(Green followed by Red)  =  \(\frac{7}{10}*\frac{3}{9}=\frac{21}{90}\)

Now do something very similar to get the prob of a red followed by a green.

Then add the answers together and simplify.

The common ratio is  sqrt(2).

The  sqrt(2)  can be written as  2^1/2.

A formula for the n^th term of a geometic sequence is:  a_n  =  a₁ · r^{n - 1}.

Filling in the known values:                                          192  =  3 · (2^1/2)^{n - 1}

Dividing by 3:                                                                 64  =   (2^1/2)^{n - 1}

Rewriting 64:                                                                  2⁶  =  (2^1/2)^{n - 1}

Looking at only the exponents:                                        6  =  (1/2)(n - 1)

                                                                                       12  =  n - 1

                                                                                         n  =  13

I kind of understandbut could you please deeply elaborate on how to get the answer since I have multiple question like that so if you ahve a method I could find it useful.

With a bit of trial and error, we can find the sequence to be 2,4,6,8.

Can you take it from here?

you use the formula     Tn=a+(n-1)d

\(a+22d=\frac{2}{3}\qquad (1)\\ a+52d=\frac{3}{2}\qquad (2)\\~\\ (2)-(1)\\ 30d=\frac{3}{2}-\frac{2}{3}\\ 30d=\frac{5}{6}\\ d=\frac{1}{36}\\ \)

Check what i have done, then sub d in to find a

Then find  a₃₅

_{Any questions? , then i am happy to discuss further.}

Each of the digits​ 0-9 is written on a slip of​ paper, and the slips are placed in a hat. If 5 slips of paper are selected at​ random, determine the probability that the 5 numbers selected are greater than 3.

4,5,6,7,8,9    there are 6 favourable numbers out of 10

6C5  /  10C5   =  6 / 252 =      1/42

You can set n = 13k + 5, and solve for k.  This will give you an answer of 26.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

The probability is: 6/10  x  5/9  x  4/8  x  3/7  x  2 /6=6! /  30,240 =1/42