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Let his speed for the remaining distance=S
1 mile / 12 + 1 mile /S =15 / 60 [1/4 of an hour]

Solve for S
S = 6 mph - his speed for the remaining distance
2 miles / (1/4) of an hour=2 x 4 =8 mph - his average speed.

Ling lives 2 miles from school. It took him 15 minutes to bike from school to home. The first half of the distance he biked at a speed of 12 mph. What was his speed for the remaining distance? What was his average speed?

Thanks Dragan,

I expect yours is better because I let Geogebra do half the work for me.

I have not worked out how to do it without Geogebra helping.

Would you like to put up your logic?

Yours too, Melody!  

A midpoint of 2 points is the (average value of the x's, average value of the y's)

T is on the x axis (y=0)

U and V are both on the line y=6, 

So R, W and S must be on the line  y=12

And P must have a y value of 24.

Mmm

Here is a graphical solution.  (It is not the logic solution that you need though.)

It appears that Dragan has beaten me to it.   Nice work Dragan.  

But neither of us has provided an answer with explained logic.

Maybe Dragan does have one.  Do you Dragan?

Q  (16, 0)

T   (8, 0)

W  (10, 12)

P   (12, 24)       ( P is 'somewhere over the rainbow' )  

R   (6, 12)

S   (14, 12)

Devi and Dave had the same amount of money x initially. After Devi donated $258 and Dave donated $196 to charity, Dave had 3 times as much as Devi. How much had Dave in the end?

Devi und Dave hatten anfangs den gleichen Geldbetrag x. Nachdem Devi 258 Dollar und Dave 196 Dollar für wohltätige Zwecke gespendet hatte, hatte Dave dreimal so viel wie Devi. Wie viel hatte Dave am Ende?

Hello Guest!

\(x-258+x-196=x-258+3(x-258)\)

   Devi            Dave           Devi           Dave

\(2x-454=x-258+3x-774\\ -2x=-578 \)      

\(x=289\)  

Dave ended up with $289 - $196 = $ 93

  !

Mauro has 140ft of rope. He will cut it into two pieces so that the length of the longer piece is 3 times the length of the shorter piece. What will the length of the longer piece be ?

Mauro hat 140ft Seil. Er wird es in zwei Stücke schneiden, so dass die Länge des längeren Stücks das Dreifache der Länge des kürzeren Stücks beträgt. Wie lang wird das längere Stück sein?

Hello Guest!

The longer piece of rope is x.

\(\frac{x}{3}+x=140\ |form\ the\ same\ divisor\\ \frac{x+3x}{3}=140\ | * 3 \\ x+3x=140\cdot 3\ |calculate \\ 4x=420\ | : 4 \\ \color{blue}x=105\)

The length of the longer piece is 105ft.

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Hi Juriemagic,  it is good to see you 

firstly it is not right because if you substitute in x=10 into the original equation you get 6=0 which is obviously incorrect.

      Read on if you want to dispute this 

Also note that we are both only talking about real numbers. x is in the set of real.

When there is a square root in a question the square root value MUST be positive.

so

\(\sqrt{x-1}\)    is positive

-3 is negative.

They cannot be equal.  Hence there is no solution.

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

Here are two important facts.

\(\sqrt{9}=+3\)

The square root was in the question so the answer must be positive.

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

BUT IF

\(x^2=9\\ then\\ x=\pm\sqrt{9}=\pm3\)

The second one is different from the first one because in the second one the square root was introduced as a part of the solution.

It was not there to start with.   Do you get the difference?

In  △CDE ,  CD=10 ,  DE=7 , and  m∠E=62∘ What is  m∠D to the nearest tenth of a degree?

∠D ≈ 79.825°

Nya selects a tile for her shower that is in the shape of a rhombus. Each side of the rhombus measures 6 inches. The diagonal opposite the smaller angle is 4.6 inches.What is the measure of the larger angle in the rhombus?

Larger angle θ ≈ 134.9°  

\(\text{let the distance to the truck be L}\\ h = L \tan(10^\circ)\\ h = (L-800)\tan(24^\circ)\\ (L-800)\tan(24^\circ)=L \tan(10^\circ)\\ L = \dfrac{800 \tan(24^\circ)}{\tan(24^\circ)-\tan(10^\circ)}\\ h = \dfrac{800 \tan(24^\circ)}{\tan(24^\circ)-\tan(10^\circ)}\tan(10^\circ)\)

In △CDE , DE=c=14 , CE=d=9 , and ∠\(\epsilon =71^o\) .
What is the length of CD=e?

Hello Guest!

\(e^2=c^2+d^2-2cd\cdot cos(\epsilon)\)        cosine

\(e=\sqrt{14^2+9^2-2\cdot 14\cdot 9\cdot cos(71^o)}\)

\(e=13.96269...\)

The length of CD is 13.96269...

  !

What is the area of a triangle whose sides have length a=√70, b=√70, and c=√28?

Hello Guest!

\(A=\sqrt{s(s-a)(s-b)(s-c)}\)     Heron's formula

\(s=\frac{a+b+c}{2}=\frac{2\cdot \sqrt{70}+\sqrt{28}}{2}=11.0123515764\\ A=\sqrt{s(s-\sqrt{70})(s-\sqrt{70})(s-\sqrt{28})}\\ \)

\(A=21\)

  !

5 x 15 = 75 

8 x 10 = 80 

Attn: Valva2205,

I notice you have asked a lot of questions.

You have not responded in any way to any of your answerers.

No thank you, no comments, nothing.

I see no evidence that you have even given a single one of them a point.

The answerers here are not your personal slaves, to ignore as you please.

I will not be answering any more of your questions unless I see a very marked improvement in your attitude.

Draw it and then use trigonometry to solve it.

Alyssa and her brother luke are racing cars around a track. it takes alyssas car 15 seconds to go one complete run and around the track. it takes lukes car 12 seonds to go around the track one time. how many seconds will it takes for both cars to return to the starting point at the same time?​ 

I think it will have taken 60 seconds. 

In 60 seconds, Alyssa will have gone all the way around 4 times, and Luke will have gone all the way around 5 times. 

_.

Ah these are AOPS questions.

Hint for nr. 3.

We know that the 4 sides are equilateral triangles, and then we can find slant height. Using pythag, we can then find the height of the pyramid.

First spin = 3 possible outcomes

Second spin = 3 possible outcomes

Third spin = 3 possible outcomes

so there will be 3*3*3 = 27 possible outcomes.

Answer D.

And please help with these problems....I need help badly!

4) The perimeter of the cross-sectional triangle of a prism is $45 \text{ cm}$, the radius of the incircle of the triangle is $8 \text{ cm}$ and the volume of the prism is $900 \text{ cm}^3$. What is the length of the prism?

5) A rectangular prism with length $l$, width $w$, and height $h$ has the property that $l + w + h = 11$ and $l^2 + w^2 + h^2 = 59$  What is the surface area of the prism?

6) A square-based pyramid of height $3$ cm and base length $2$ cm is set on its square base. Water is poured through an infinitesimally small hole in the top of the pyramid to a height of $1$ cm measured from the base, and then the hole is sealed. If the pyramid is turned upside-down, what will be the new height of the water?

Find the sum of all values of a such that the point (a,21) is 10 sqare root 2 from the point (4,7).

Finden Sie die Summe aller Werte von a so, dass der Punkt (a, 21)  ( \(10\cdot \sqrt{2}\) )  vom Punkt (4,7) entfernt ist.

\(x_1=a\\ x_2=4\\ y_1=21\\ y_2=7\)

\(y=\frac{y_2-y_1}{x_2-x_1}(x-x_1)+y_1 \)

\((x_2-a)^2+(y_2-y_1)^2=(10\cdot \sqrt{2})^2\\ (4-a)^2+(7-21)^2=(10\cdot \sqrt{2})^2\\ 16-8a+a^2+196=200\)

\(a^2-8a+12=0\\ a=4\pm\sqrt{16-12}=4\pm 2 \)

\(a_1=6\\a_2=2\\ \sum{(a_{values})}=8\)

  !

4, i keep on deleting my answer so i'm just going to say the answer