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3 years ago

8 5x=-2 whats the value of the variable?

1 answer:

8 0

In order to get the value of x you have to set x by itself subtract from both sides because the only way to get rid of a positve its with a negative now you have 5x=6, now divide 5 from both sides because the only way to get rid of a multiplication is with a division, this will give you the final answer of x=6/5

Hope this helps

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There are some Nichols dimes and quarters in a large piggy bank for every two nickels there a sweetheart forever to Diane’s ther

grigory [225]

Answer:

There are 80 nickels, 120 dimes and 300 quarters in the piggy bank.

All coins in the piggy bank worth $91.

Step-by-step explanation:

Please consider the complete question:

There are some nickels, dimes, and quarters in a large piggy bank. For every 2 nickels there are 3 dimes. For every 2 dimes there are 5 quarters. There are 500 coins total. How many nickels, dimes, and quarters are in the piggy bank? Explain your reasoning. How much are the coins in the piggy bank worth?

Let n, d, q represent number of nickles, dimes and quarters respectively.

For every 2 nickels there are 3 dimes. We can represent this information in an equation as:

$\frac{2}{n}=\frac{3}{d}...(1)$ or

$n=\frac{2d}{3}...(1)$

For every 2 dimes there are 5 quarters. We can represent this information in an equation as:

$\frac{2}{d}=\frac{5}{q}...(2)$ or

$q=\frac{5d}{2}...(2)$

There are 500 coins total. We can represent this information in an equation as:

$n+d+q=500...(3)$

We will use substitution method to solve our given system.

Upon substituting equation (1) and equation (2) in equation (3), we will get:

$\frac{2d}{3}+d+\frac{5d}{2}=500$

Multiply the equation by 6:

$\frac{2d}{3}*6+d*6+\frac{5d}{2}*6=500*6$

$2d*2+6d+5d*3=3000$

$4d+6d+15d=3000$

$25d=3000$

$\frac{25d}{25}=\frac{3000}{25}$

$d=120$

Therefore, there are 120 dimes in the piggy bank.

Upon substituting $d=120$ in equation (1), we will get:

$n=\frac{2(120)}{3}$

$n=2(40)$

$n=80$

Therefore, there are 80 nickels in the piggy bank.

Upon substituting $d=120$ in equation (2), we will get:

$q=\frac{5d}{2}$

$q=\frac{5(120)}{2}$

$q=5(60)$

$q=300$

Therefore, there are 300 quarters in the piggy bank.

Now, we need to find the value of all coins.

We know 1 quarter is worth $0.25, so 300 quarters will be worth $\$0.25\times 300=\$75$ .

We know 1 dime is worth $0.10, so 120 dimes will be worth $\$0.10\times 120=\$12$ .

We know 1 nickel is worth $0.05, so 80 nickels will be worth $\$0.05\times 80=\$4$ .

$\text{All coins worth}=\$75+\$12+\$4$

$\text{All coins worth}=\$91$

Therefore, all coins in the piggy bank worth $91.

7 0

4 years ago

CONVERGENT AND DIVERGENT SERIES PLEASE HELP

drek231 [11]

Answer:

Step-by-step explanation:

We are given a series

We can see that numerators are same

and denominators are

49 , 64 , 81 , .....

so,

7^2 , 8^2 , 9^2

We can write nth term

$a_n=(n+7)^2$

so, we can write as

$\sum _{n=0}^{\infty }\:\frac{1}{\left(n+7\right)^2}$

We can use p-series test

$\frac{1}{n^p}$

we can compare

and we get

$p=2>1$

So, this series is convergent

this is FALSE

5 0

3 years ago

QUESTION IS STATED IN PICTURE DONT FORGET TO ROUND TO THE NEAREST HUNDRETH. USE 3.14 pi IF NEEDED

Anna007 [38]

The area of a circle is given by:

$A=\pi\cdot r^2$

Where r is the circle's radius. In this case we have a diameter of 8cm so the radius 4cm. Using pi=3.14 we have that the area of the circle is:

$A=3.14\cdot4^2=50.24$

So the area is 50.24 cm^2.

5 0

1 year ago

Please help. Thank you. (30 points included) (Shown work)

Georgia [21]

Answer:

True

Step-by-step explanation:

Supplementary angles are angles that add up to 180 degrees (straight line). *5 degrees + x create a straight line.

3 0

3 years ago

What is the slant height of a square pyramid that has a surface area of 336 square meters and a side length of 12

Artist 52 [7]

Check the picture below.

the surface area of the pyramid is simply the area of the four triangular faces plus the squarish base, and the triangular faces have a base of 12 and an altitude or height of "s", and we know that's 336.

$336~~ = ~~\stackrel{\textit{\LARGE Areas}}{\stackrel{square}{(12)(12)}~~ + ~~\stackrel{\textit{four triangles}}{4\left[ \cfrac{1}{2}(\underset{b}{12})(\underset{h}{s}) \right]}}\implies 336~~ = ~~144~~ + ~~24s \\\\\\ 192=24s\implies \cfrac{192}{24}=s\implies 8~m=s$

6 0

2 years ago