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3 years ago

If aſc and a +b = C, prove that a|b.

Mathematics

1 answer:

mars1129 [50]3 years ago

7 0

Answer with Step-by-step explanation:

Since we have given that

a + b = c

and a|c

i.e. a divides c.

We need to prove that a|b.

⇒ a = mb for some integer m

Since a|c,

So, mathematically, it is expressed as

c= ka

Now, we put the above value in a + b = c.

So, it becomes,

$a+b=c\\\\a+b=ka\\\\b=ka-a\\\\b=a(k-1)\\\\\implies a|b$

a=mb, here, m = k-1

Hence, proved.

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Find coordinates for x+5y=10 and 3x+5y=0. I need to know how to do this plz explain.

maks197457 [2]

Answer:

(-5,3)

Step-by-step explanation:

Method

There are several ways you can do this, but one of the best ways is to use a graphing coordinate calendar. The most popular one is Desmos Graphing Calculator. I've attached an image of my work below using the system.

Answer

As you can see, both equations intersect at a certain coordinate point. This coordinate point is the point you need for the answer. The intersection is (-5,3).

I hope this helps. If you have any more questions, please feel free to post them and someone will be able to help you, whether it's myself or others. Please leave a like, rating, and if possible, Brainliest. Have a great day!

4 0

3 years ago

Read 2 more answers

If BC = 5, DE = 9, and AB = 4, what is the length of AD? 7 8 7.2 7.5

steposvetlana [31]

There are two triangles here: ABC and ADF. These triangles are similar, and thus proportional. So, we can set up a proportion between the left side of each triangle and the base of each triangle.

AB / AD = BC / DE

4 / (4 + BD) = 5 / 9

---AD is made up of AB and DB. We know AB, but not BD, so we need to find its value to find the length of AD.

5(4 + BD) = 9 x 4

20 + 5BD = 36

5BD = 16

BD = 3.2

AD = AB + BD

AD = 4 + 3.2

AD = 7.2

Hope this helps!

8 0

3 years ago

Water boils at 100LaTeX: ^\circ∘ Celsius or 212LaTeX: ^\circ∘ Fahrenheit. Water freezes at 0LaTeX: ^\circ∘ Celsius or 32LaTeX: ^

Lubov Fominskaja [6]

Answer:

$F = 1.8C +32$

$F = 86^{\circ}F$

Step-by-step explanation:

Represent Celsius with C and Fahrenheit with F.

So, we have:

$(C_1,F_1) = (100,212)$

$(C_2,F_2) = (0,32)$

Solving (a): Represent as a linear equation

First, we calculate the slope:

$m = \frac{F_2 - F_1}{C_2 - C_1}$

This gives:

$m = \frac{32 - 212}{0 - 100}$

$m = \frac{-180}{- 100}$

$m = 1.8$

The linear equation is then calculated using:

$F - F_1 = m(C -C_1)$

Where

$(C_1,F_1) = (100,212)$

$m = 1.8$

$F - 212 = 1.8(C -100)$

$F - 212 = 1.8C -180$

Make F the subject

$F = 1.8C -180+212$

$F = 1.8C +32$

Solving (b): The value of F when C = 30

Substitute 30 for C in $F = 1.8C +32$

$F = 1.8 * 30 + 32$

$F = 54 + 32$

$F = 86$

8 0

3 years ago

Read 2 more answers

A restaurant cook earns $8 per hour for the first 40 hours worked and $12 per hour for over time (hours worked in addition to th

Likurg_2 [28]

Answer:the answer is 560

Step-by-step explanation:

The reason is because you multiply to get 8 and 40 to get the amount for regular time which is 320.Then you subtract 60 from 40 which is 20.You multiply that amounnt by 12 because that is the overtime which will equal 240.Add them together and you get 560. ☺

6 0

3 years ago

7- square root of 3i

r-ruslan [8.4K]

Step-by-step explanation:

Any complex number is of the form: $a + bi$ where a is real part and B is imaginary part.