Straight

Hello Guest,

8(x+15)=12x

im confused on how to start it.

8(x + 15) = 12x

(8x + 8 * 15) = 12x

8x + 120 = 12x

(8x - 12x) + 120 = 12x -12x

-4x + 120 = 0

(120 - 120) -4x = -120

-4x = -120

\(\frac{-4x}{-4}=\frac{-120}{-4}\)

\(x = \frac{-120}{-4}\)

\(x = \frac{-30}{-1}\)

\(x = 30\)

So x = 30 is the right answer. 

Hope that was helpful. ^^

Straight

Hello Guest,

han says that the value of the 7 in 735,208 is 10 times the value of the 7 in 137,342 is this correct??

Multiply 7 by 735,208 and that's equal to 5,416,456 and I do know that this isn't correct because 5,416,456 is not ending with 0 - a whole number multiplied by a whole number is a whole number and the solution 5,416,456 divided by 10 is equal to 541,645.6 and that is not a whole number.

Hope that was helpful. ^^

Edit: Grammatical errors have been corrected.

Straight

Hello Guest,

If a, b, and c are positive integers satisfying ab + c = bc + a = 13  and ac + b = 41, what is the value of a + b + c?

There are 2 solutions for \(a , b , c \in \mathbb{Z}\) , namely:

S1: a = 5 ; b = 1 ; c = 8 and

S2: a = 8 ; b = 1 ; c = 5 .

The value (a + b + c) for S1 and btw. S2 is (5 + 1 + 8 =) 14.

The answer is 14.

Hope that was helpful. ^^

Straight

Hello Guest,

Speed: \(\frac{Distance}{Time}\)

Now put in: \(\frac{1.4}{2.8}\)

So his speed is 0.5 miles per minute.

Straight

Hello Guest,

Determine all numbers in the number range up to 1000, whose divisor are all natural digits, whereby here the 0 is nonsense.

That is a good question, find the smallest common multiple of 2, 4, 6, 8 and that would be 24.

All multiples of 24 up to 1000 are divisible by these divisors.

These would be 41 numbers that fulfil these properties/conditions. 

Hope this was helpful

 !

Hello Guest,

Can anyone use the p-q formula to solve this equation?

\(x^2+2x=8\)

Thanks in advance

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

the p-q formula: \(x_1 \mbox { and } x _2 = -\frac{p}{2} \pm \sqrt{\Big(\frac{p}{2}\Big)^2-q}\) .

\(x^2 + 2x = 8 \ |\ -8\)

. . . let \((p, \mbox { } q) = (2, \mbox { } -8)\) .

\(x_1 \mbox { and } x_2 = \frac{-2}{2} \pm \mbox {} \sqrt{\Big(\frac{2}{2}\Big)^2-(-8)}\)

\(x_1 \mbox { and } x_2 = -1 \pm \mbox {} \sqrt{ 1 + 8 }\)

\(x_1 = -1 + 3\)

\(x _1 = 2\)

\(x_2 = -1 - 3\)

\(x_2 = -4\)

This equation has two solutions, namely \(x_1 = 2\) and \(x_2 = -4\) .

Hope this was helpful. ^^

 !

Hello Guest,

Solve for x and y such that \(x^2-y=xy\) . 

There are 2 pairs for (x, y), namely:

\((x, \mbox { } y) = ( 0, \mbox { } 0)\) and

\((x, \mbox { } y) = (-2, \mbox { } -4)\)

Hope this was helpful.

Straight

Hello Guest,

Jeff was on his way to visit his mother in Königshausen.

In doing so, he had to cross the river "Benk" by boat, so he did.

It took 1h and 40 min to cross it with an average speed of 48 km/h. During the trip he said that the river is only 90 km long.

    a) Is his statement true, give reasons.

    After he crossed the river and was finally with his mother, she baked him a cake, saying that it would only take \(\frac{3}{4} \cdot 32\) min.

    After it was ready, she cut it into 3 equal parts. 

    b) Show if this is possible (you may be able to show a picture here).

    c) "I s*ck at math!", Jeff says. 

        Explain to Jeff how to proceed here with the corresponding solution.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    a) His statement is not true, because if we take the remaining 40 min, that corresponds to \(\frac{2}{3}h\) .

        So it took \(48 \mbox { } km + (\frac{2}{3} \cdot 48 \mbox { } km)\) and that is equal to 80 km.

    b) I can show you a picture here:

       I do not think, I must write something here. (The picture is from Google.)

    c) I think that the duration of the baked cake is meant here.

       \(\frac{3}{4} \cdot 32 = \frac{3 \cdot 32}{4} = \frac{96}{4} \mbox { } min = 24 \mbox { } min\) , so it takes 24 min until the cake is ready.

I hope that was helpful. 

Straight

Hello Guest,

calculate this on our home page 👤Web 2.0 scientific calculator (0calc.com) {https://web2.0calc.com/} .

Straight

Hello Guest,

In Fizic school there was a math competition, with 5/7 of the students in the whole high school participating.

There were 3 rounds to master in order to win the tournament.

From the first to the 2nd round only 1/6 of the whole students who participated made it, from the 2nd round to the 3rd round only 16/400.

This tournament was won by 5 students in total.

Find out the number of students who participated and the number of students in Fizic High School.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Students in Fizic High School \(\Rightarrow\) 1050 students

Students that participated \(\Rightarrow\) 750 students

Shorten the fraction \(\frac{16}{400}\) into \(\frac{1}{25}\) .

At the end 5 students won the tournament.

\(\mbox {Multiply 5 by 25 and divide 1. }\)

\(5 \cdot 25 = 125\)

\(125 : 1 = 125 \mbox { (Any number divided by 1 is the same.) }\)

\(\mbox {Multiply 125 by 6 and divide 1. }\)

\(125 \cdot 6 = 750\)

\(750 : 1 = 750 \mbox { (Any number divided by 1 is the same.) }\)

Thus, 750 students from Fizic High School participated.

\((750 : 5) \cdot 7 = 1050\)

Thus, there are a total of 1050 students at Fizic High School.

Straight