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4 years ago

Find two integers whose difference is -6. ( There are many!)

Mathematics

1 answer:

olga nikolaevna [1]4 years ago

5 0

Step-by-step explanation:

There are infinitely many such integers.

x - y = -6 add y to both sides

x = -6 + y → x = y - 6

1. Choose any y value.

2. Substitute for the equation.

3. Calculate the value of x.

Examples:

for y = 0 → x = 0 - 6 = -6

check: -6 - 0 = -6

for y = 10 → x = 10 - 6 = 4

check: 4 - 10 = -6

for y = -9 → x = -9 - 6 = -15

check: -15 - (-9) = -15 + 9 = -6

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The sum of four siblings ages is 71. The second child’s age is twice the youngest, the third child’s age is twelve more than the

user100 [1]

Answer: 9, 18, 21, and 23 respectively

Step-by-step explanation:

To solve any problem like this, you want to assign a variable to each child because you dont know their age. So lets write an equation and assign variables to these children.

r = first child (youngest)

x = second child

y = third child

z = fourth child (oldest)

We know that r + x + y + z = 71

We also are given info on the comparisons of their ages.

r = r

x = 2r (2 times the youngest)

y = 12 + r (12 more than the youngest)

z = 3r - 4 (4 less than 3 times the youngest)

That was the easy part tbh, now we have to solve for 'r'. We can see that all the ages are a function of the same variable (r), and we know the sum of them is equal to 71. So lets solve for r and then plug that r value into each equation we just derived.

Child #1 (youngest)

$r+2r+(12+r)+(3r-4)=71\\3r+12+r+3r-4=71\\7r+12-4=71\\7r+8=71\\7r=63\\r=9yrs$

Child #2

$x=2*9=18yrs$

Child #3

$y=12+r=12+9=21yrs$

Child #4 (oldest)

$z=3r-4=(3*9)-4=27-4=23yrs$

Fact Check:

$9+18+21+23=71$

8 0

3 years ago

Please help.................

Svetradugi [14.3K]

Answer:

The equation you need for 3 is the volume of a sphere.

Then divide 12 by 2 to get the radius, which gives you 6, then insert this into the equation, and the answer you get for 3 is 904.78cm cubed. 904.8 (4 Significant figures) cm cubed.

5 0

4 years ago

What lines have a slope of -2?

umka2103 [35]

Both a and b.
Hope this helps!!!

3 0

4 years ago

A quadratic equation is shown below: x2 − 8x + 13 = 0 Which of the following is the first correct step to write the above equati

Andreyy89

Answer:

Add 3 to both sides of the equation

Solution:

The first step is to basically realize that all it's asking you to do is to find a way to make the expression on the left ( $x^2 - 8x + 13$ ) into an expression that is a perfect square. So what number should you add to both sides such that $x^2 - 8x + (13 + j)$ can be factored into $(x-p)^2$ ? Well, we can approach it like this:

Since $(x-p)^2$ can be turned into $x^2 -2px + p^2$ , and our original form was $x^2 - 8x + (13 + j)$ , we quickly realize that $-2px = -8x$ . From there, we can easily tell that $p = 4$

Plug this into our last value $p^2$ to get 16. Therefore, if we compare this with our original equation again $x^2 - 8x + (13 + j)$ , we notice that 13 + j = 16.

Thus, j = 3 for the last answer.

Add 3 to both sides of the equation.

Note: With more practice, you will quickly gain enough intuition to notice that $x^2 - 8x + 13$ is very close to $x^2 - 8x + 16$ which can be factored into $(x-4)^2$ . But for now, the solution above will suffice. I hope this helps :))