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The sum of three numbers $x$ ,$y$, $z$ is 165. When the smallest number $x$ is multiplied by 7, the result is $n$. The value $n$

babymother [125]

You're given

x + y + z = 165

7x = n

n = y - 9

n = 9 + z

and you want to find xyz.

Solve the last three equations for x, y, and z :

7x = n → x = n/7

n = y - 9 → y = n + 9

n = 9 + z → z = n - 9

Substitute x, y, and z into the first equation and solve for n :

n/7 + (n + 9) + (n - 9) = 165

n/7 + 2n = 165

n + 14n = 1155

15n = 1155

n = 77

Now solve for x, y, and z :

x = 77/7 = 11

y = 77 + 9 = 86

z = 77 - 9 = 68

Then the product is

xyz = 11 • 86 • 68 = 64,328

6 0

3 years ago

X = – 2y – 1 x = – 5y + 5

motikmotik

Answer:

x = -5

y = 2

Step-by-step explanation:

x = – 2y – 1

= -x - 2y - 1

-x - 2y = 1

x = – 5y + 5

= -x - 5y + 5

-x - 5y = -5

-x - 2y = 1

-x - 5y = -5

___________--

3y = 6

y = 6/3

y = 2

-x - 2y = 1

-x - 2(2) = 1

-x - 4 = 1

-x = 1 + 4

-x = 5

x = -5

6 0

3 years ago

Please, help thanks! I would like an explanation how to do it too, IF you dont mind.

Aneli [31]

Answer:

Phoebe has £180, Andy has £60, and Polly has £30.

Step-by-step explanation:

Ok, to start of let's establish some variables! We'll give Phoebe the variable "p", Andy the variable "a", and Polly the variable "o". By giving each person a variable we can create an equation and solve for it!

So, what do we know?

Well we know the following information...

p + a + o = 270

(Phoebe + Andy + Polly = £270)

p = 3a

(Phoebe = 3 times more than Andy)

a = 2o

(Andy = 2 times more than Polly)

To be able to solve this equation we have to solve for just one variable first.The only one we can use is "o" for Polly!

3(2o) + 2o + o = 270

6o + 2o + o = 270 (Distribute 3 to get like terms)

9o = 270 (Combine like terms [6+2+1])

o = 30 (Divide by 9 on both sides to get "o" by itself)

Now that we have how much Polly has, we have to solve for Andy and Phoebe. (To do this we will input our value, 30, where our variable is "o")

Andy

a = 2(30) (Input term)

a = 60 (Multiply by 2 to get final answer)

(Since we now know what Andy has we can input 60 into our "a" variable to solve for Phoebe)

Phoebe

p = 3(60) (Input term)

p = 180 (Multiply by 3 to get final answer)

Now! Just to check we are going to input our variables into our original equation to be sure we have the right variables.

p + a + o = 270

180 + 60 + 30 = 270!!

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

4 0

3 years ago

The temperature in Minneapolis was -9°F. The next day, the temperature was warmer than -9°F.

Dimas [21]

Answer:

The temperature in Minneapolis was -9°F. The next day, the temperature was warmer than -9°F.

let increased temperature be x

temperature of next day = -9°f +x

4 0

3 years ago

PLEASE HELP!

Wittaler [7]

Answer:

See below

Step-by-step explanation:

Use the formulae directly

For a cone, with base radius = r and height = h, here are the related formula

$\textrm{Slant height l} = \sqrt{r^2 + h^2}$ (1)

$\textrm{Lateral surface area} = \pi r l$

$\textrm {Base area} = \pi r^2$

$\textrm { Total Surface Area SA} = \textrm{Base Area + Lateral Area} = \pi r^2 + \pi rl = \pi r(r + l)$ (2)

$\textrm{Volume V = } (1/3) \pi r^2h$ (3)

Therefore directly plugging in the numbers in the above equations:

Note:

l = slant height in cm
SA = total surface area in sqcm
V = Volume in cubic cm

Figure(a)

r = 4, h = 8

$\textrm{l} = \sqrt{4^2 + 8^2} =\sqrt{80} = 8.944 \\\textrm{SA} = 4\pi(4 + 8.944) = 4\pi(12.944) = 162.66\\\textrm{V} = (1/3)\pi(4^2)(8) = 134.04$

Figure(b)

r = 7, h =15

$\textrm{l} = \sqrt{7^2 + 15^2} =\sqrt{274} = 16.55$

$\textrm{SA} = 7\pi(7 + 16.55) = 517.89$

Figure (c)

r = 5, l = 8

$h = \sqrt{l^2 - r^2} = \sqrt{8^2 - 5^2} = \sqrt{39} = 6.245\\SA = \textrm{SA} = 5\pi(5 + 8) = 204.2\\V = (1/3)\pi(5^2)(6.245) = 163.5$

6 0

2 years ago