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3 years ago

Mary is comparing fractions whose denominators are 6 and 8. which number is the least common multiple that she can use?

Mathematics

1 answer:

Nuetrik [128]3 years ago

3 0

Answer:

Step-by-step explanation:

It says she need the least common number that can divide 6 and 8 which is 2

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The sum of the squares of two numbers is 8 . The product of the two numbers is 4 . Find the numbers.

fenix001 [56]

Hello there.

First, assume the numbers $x,~y$ such that they satisties both affirmations:

The sum of the squares of two numbers is $8$ .
The product of the two numbers is $4$ .

With these informations, we can set the following equations:

$\begin{center}\align x^2+y^2=8\\ x\cdot y=4\\\end{center}$

Multiply both sides of the second equation by a factor of $2$ :

$2\cdot x\cdot y = 2\cdot 4\\\\\\ 2xy=8~~~~~(2)^{\ast}$

Make $(1)-(2)^{\ast}$

$x^2+y^2-2xy=8-8\\\\\\ x^2-2xy+y^2=0$

We can rewrite the expression on the left hand side using the binomial expansion in reverse: $(a-b)^2=a^2-2ab+b^2$ , such that:

$(x-y)^2=0$

The square of a number is equal to $0$ if and only if such number is equal to $0$ , thus:

$x-y=0\\\\\\ x=y~~~~~~(3)$

Substituting that information from $(3)$ in $(2)$ , we get:

$x\cdot x = 4\\\\\\ x^2=4$

Calculate the square root on both sides of the equation:

$\sqrt{x^2}=\sqrt{4}\\\\\\ |x|=2\\\\\\ x=\pm~2$

Once again with the information in $(3)$ , we have that:

$y=\pm~2$

The set of solutions of that satisfies both affirmations is:

$S=\{(x,~y)\in\mathbb{R}^2~|~(x,~y)=(-2,\,-2),~(2,~2)\}$

This is the set we were looking for.

7 0

3 years ago

The linear scale factor of two similar solids is given. Then the surface area and volume of the smaller figure are also given. F

gogolik [260]

Answer:

Surface area: 250

Volume: 1375

Step-by-step explanation:

Scale factor: 4:5

This means that the dimensions of the larger figure are 5/4 of those in the smaller figure.

Surface area:

The surface area is found multiplying the square of the change(5/4) by the original surface area(160). So

$S = (\frac{5}{4})^2 \times 160 = \frac{25}{16} \times 160 = 25 \times 10 = 250$

Volume:

The volume is found multiplying the cube of the change(5/4) by the original volume(704). So

$S = (\frac{5}{4})^3 \times 704 = \frac{125}{64} \times 704 = 125 \times 11 = 1375$

6 0

3 years ago

What is the domain of the function represented by the graph?

il63 [147K]

Answer:

Step-by-step explanation:

‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌

7 0

3 years ago

Given that two terms of an arithmetic sequence are u5 = -3.7 and u15 = -52.3, find the value of the 19th term.

Mazyrski [523]

Answer:

a19 = -71.74

Step-by-step explanation:

The general term of an arithmetic sequence with first term a1 and common difference d is ...

an = a1 +d(n -1)

The given 5th and 15th terms tell us ...

-3.7 = a1 +d(5 -1)

-52.3 = a1 +d(15 -1)

Subtracting the first of these equations from the second, we find ...

10d = -48.6

d = -4.86 . . . . . . divide by 10

The 19th term will be ...

a19 = a1 +d(19 -1)

Subtracting the 15th term from this, we find ...

a19 -a15 = 4d

a19 = 4d +a15 = 4(-4.86) +(-52.3)

a19 = -71.74

4 0

2 years ago

What is the slope of a line that passes through the origin and the point (-2,1)?

Mazyrski [523]

Answer:

The slope would be -1/2.

Step-by-step explanation:

Since, the midpoint of the segment joining the points P (0, -4) and B (8, 0),

= ( 4, -2 ),

Now, the slope of the line passes through the origin and the point ( 4, -2) is,

= -1/2

<h3>i think thats the answer</h3><h2> HOPE IT HELPS YOU THOUGH</h2>

8 0

3 years ago

Mary is comparing fractions whose denominators are 6 and 8. which number is the least common multiple that she can use?​

Mary is comparing fractions whose denominators are 6 and 8. which number is the least common multiple that she can use?