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Alex17521 [72]
3 years ago
5

The sum of three numbers is 85. The second is 7 more than the first. The third is 2 more than four times the second. Find the nu

mbers.
Mathematics
2 answers:
horsena [70]3 years ago
6 0

"The sum of three numbers is 85"

x+y+z = 85

"The second number is 7 more than the first."

y = x+7

"The third is 2 more than four times the second."

z = 4y+2

z = 4(x+7) + 2 = 4x+30


x + (x+7) + (4x+30) = 85

6x = 48

x = 8

y = x+7 = 15

z = 4x+30 = 62

Hope this helps!

9966 [12]3 years ago
4 0
Let x=the first number
Then x+7=second number
And 4(x+7)+2=third number (2 more than 4 times the second)
Now we are told that:
x+(x+7)+(4(x+7)+2)=85 get rid of parentheses
x+x+7+4x+28+2=85 simplify
6x+37=85 subtract 37 from each side
6x+37-37=85-37
6x=48
x=8---first number
x+7=8+7=15 second number
4(x+7)+2=4*15+2=62 third number
CK
8+15+62=85
85=85
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Assignment: Translating Functions Investigation
Leto [7]

Answer:

Part A)

1) The graph in the attached figure N 1

2) The coordinate rule is (x,y) -----> (x,y+10)

3) The translation of the function up 10 units means that the initial deposit is $60 instead of $50

Part B)

1) The graph in the attached figure N2

2) The coordinate rule is (x,y) -----> (x-10,y)

3) The translation of the function right 10 units means that the initial deposit is equal to $10

Part C)

1) In each translation, the slope is the same (m=5) are parallel lines

2) The vertical translation would be up 40 units

Step-by-step explanation:

we have

f(x)=5x+50

where

f(x) --> represents Jeremy's account balance

x ---> the time in years

Part A)

The translation of the function is up 10 units.

The rule of the translation is equal to

(x,y) -----> (x,y+10)

so

The new function will be

f(x)=5x+50+10

f(x)=5x+60

The graph in the attached figure N 1

The translation of the function up 10 units means that the initial deposit is $60 instead of $50

Part B)

The translation of the function is right 10 units.

The rule of the translation is equal to

(x,y) -----> (x-10,y)

so

we have

f(x)=5x+60 ----> function Part A

The new function will be

f(x)=5(x-10)+60

f(x)=5x+10

The graph in the attached figure N 2

The translation of the function right 10 units means that the initial deposit is equal to $10

Part C)

1. Look at the translations, what characteristic of the graph stayed the same in each translation?

In each translation, the slope is the same

The slope m is equal to m=5  

Are parallel lines

2. Look at the original graph and the graph of the translation right 10 units. What vertical translation of the graph in Part B would put the graph back to its original position?

we have

f(x)=5x+10

The vertical translation would be up 40 units

The rule of the translation is equal to

(x,y) -----> (x,y+40)

so

The new function will be

f(x)=5x+10+40

f(x)=5x+50

3 0
3 years ago
The measure of one acute angle is 3 times the sum of the measure of the other acute angle and 8
Anettt [7]
Let x be the unknown angle. 

Make an equation using the formula.

<span>"measure of one acute angle is 3 times" Since we know that x is the one acute angle, we can multiply that by 3 to get 3x.

"</span><span>the sum of" when ever you see the word 'sum' it means that there will be an addition process involved and in this case it also means that 3x will equal to the rest of the equation. (3x=)
</span>
<span>"measure of the other acute angle and 8" We already know that the other angle is x . Since there is no other indicator of the 8 being subtracted, multiplied, and divided and that we know this is an addition problem, we can conclude that 8 will be added to the other angle. (x+8)
</span>
So, now we have the equation and all we have to do is simplify it. 

3x= x+8
-x   -x             *Move constants and variables to opposite sides*
------------
2x=8
---  ---             *Divide by 2 to isolate the variable* 
2    2

x=4

So, I'm assuming you want to know the measure of both angles. All you have to do is plug in the x in the 3x and x+8 depending on which angle you want.

3x
3(4)=12
The measure of the first angle is 12.

x+8
4+8= 12
The measure of the second angle is also 12.
8 0
2 years ago
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