The average of two numbers is 5x. If one of the numbers is 2x + 3, find the other number.

Answers

Question (1):
The constant in an expression will be the term having no variable in it.
The given expression is:
−3x+4y+1.8−3x+4y+1.8
The variables in this expression are x and y. Therefore, the constant would be the term having no x or y in it.
1.8

Question (2):
We know that 1 hour has 60 minutes and that one minute has 60 seconds.
Therefore, 1 hour has 60*60 = 3600 seconds.
Using cross multiplication, we can find the seconds in 4.2 hours as follows:
4.2 hours = (4.2*3600) / 1
4.2 hours has 15120 seconds

Question (3):
To solve for x, we would isolate the x on side of the equation as follows:
−5x−4(x−6)=−3
-5x - 4x + 24 = -3
-9x = -3-24 = -27
x = -27/-9 
x = 3

Question (4):
To solve for a, we would need to isolate the a on one side of the equation as follows:
m = (a+b) / 2
2m = a + b
a = 2m - b

Question (5):
5(x−2) < −3x+6
5x - 10 < -3x + 6
5x + 3x < 6 + 10
8x < 16
x < 16/2
x < 2

Question (6):
Part (a): 
To get the x-intercept, substitute with y = 0 in the equation as follows:
y−3=3(x+5)
0 - 3 = 3x + 15
3x = -3-15 = -18
x = -18/3
x-intercept is -6
Part (b):
To get the y-intercept, substitute with x = 0 in the equation as follows:
y−3=3(x+5)
y - 3 = 3 (0+5)
y - 3 = 15
y = 15+3
y-intercept is 18

Question 7:
To get the order pair that belongs to the line, we will substitute with the x-value of the given pair in the equation and solve for y. Then compare the calculated value with the given one as follows:
For x = 4:
y+3.5=0.75(x−2)
y + 3.5 = 0.75(4-2) = 0.75(2) = 1.5
y = 1.5 - 3.5 = -2 > This choice is wrong
For x = -4:
y+3.5=0.75(x−2)
y + 3.5 = 0.75(-4-2) = 0.75(-6) = -4.5
y = -4.5 - 3.5 = -8 > This choice is correct
For x = 7:
y+3.5=0.75(x−2)
y + 3.5 = 0.75(7-2) = 0.75(5) = 3.75
y = 3.75 - 3.5 = 0.25 > This choice is wrong
For x = 1:
y+3.5=0.75(x−2)
y + 3.5 = 0.75(1-2) = 0.75(-1) = -0.75
y = -0.75 - 3.5 = -4.25 > This choice is wrong
 (−4, −8)

Question (9):
The posters (x) cost $14.65 each while the frames (y) cost $11.75 each. The total amount spent should not exceed $85. This means that the total amount spent should be less than or equal to $85
 14.65 x + 11.75 y ≤ 85

Question (13):
g(x) is equal to f(x) after translation of 2 units to the units.
This means that:
g(x) = f(x+2)
So, we will substitute the value of x in the given function with x+2 as follows:
g(x) = f(x+2)
g(x) = −4(x+2) + 3
g(x) = -4x - 8 + 3
g(x) = -4x - 5

Question (14):
The given function is:
f(x)=−85x+3145
Let's substitute with x = 37:
f (37) = −85(37)+3145 = 0
Substitute with x = 0:
f(0) = -85(0) + 3145 = 3145
This means that your range (the values for f(x)) would be all the numbers (starting zero) less than 37 (at 37, the function is zero meaning that all pages have been printed). They have to be whole numbers and not real numbers as real numbers include irrational numbers as well
 all whole numbers from 0 to 37

Hope this helps :)
Alright, let's do all of these (though this is a bit long).
1.
The constant is 1.8. All other values are coefficients to variables, which as the name implies will change.
2.
1 hour is 60 minutes, 1 minute is 60 seconds.
So, 4.2 *60 *60 = 15120 seconds.
3.
−5x−4(x−6)=−3-5x-4(x-6)=-3
Let's move all x to one side, and all other numbers to another.
-5x-4(x-6)=-3-5x-4(x-6)=-3
x can be any value you want, if you actually solve this you'll only end up with -3 = -3, which is correct, of course.
Let me show you:
−5x−4(x−6)=−3-5x-4(x-6)=-3
+5x +4(x-6)        +5x +4(x-6)
-3 = -3
The value of x is irrelevant, then. X can be any real number.
4.
I'm going to assume it was an error in printing with this? If not please correct me.
m=a+2b(or b2)
subtract 2b from each
a=m-2b
(This question seems kind of odd. We should probably address this in the comments.)
5.
5(x−2)<−3x+6
Move all x to one side, numbers to other.
5x-10<-3x+6
+3x     +3x
    +10      +10
8x<16
/8
x < 2
6.
y-3=3(x-5)
alright, to find zeros set one variable to zero and solve
x first
-3=3x-15
+15    +15
3x=12
/3
x=4
x-int is (4,0)
now y
y-3=3(0-5)
y-3=-15
+3     +3
y=-12
so y-int is (0,-12)
i've got to sleep now so i'll do the rest tomorrow. Sorry for the incomplete answer.

is taekwondo correct, and yes, the taekwondo martial art is very much dead

1. B

2. A (n ≤ 13)

3. A (2m - 7)

4. B (8x+8y)

5. School C

6. C (6.08 pounds)

7. A (5 + 3p ≥ 30)

8. A (95 + 25x + 25y)

9. D (29)

10. A (Add 3 to both sides)

11. C (Malia)

12. C (n ≤ 48)

13. TRUE



Step-by-step explanation:

1.

We need to find 8.45% of each of them so that the answer is 2.1 hours.

For 20 hours: 8.45% of 20 = 0.0845 * 20 = 1.69 hours (this is not the answer)

For 25 hours: 8.45% of 25 = 0.0845 * 25 = 2.11 hours (this is the answer)

For 10 hours: 8.45% of 10 = 0.0845 * 10 = 0.85 hours (this isn't it)

For 18 hours: 8.45% of 18 = 0.0845 * 18 = 1.52 hours (this is not it)

We see that option B is right.

2.

Macy has $95.

She buys $12.99 worth of stationery. She now was 95 - 12.99 = $82.01

She needs to keep $42 intact for skateboard, so she can spend remaining on ice-cream bars.

She can spend  82.01-42=40.01 for ice cream bars each worth 3.07.

Number of ice-cream bars, n, she can buy for 40.01 is  \frac{40.01}{3.07}=13.03. SHE CAN'T BUY 0.03 (the fractional amount) ice-cream bars, so the maximum is 13.

Answer choice A is right (n ≤ 13)

3.

We need to use the distributive property (a(b+c)=ab+ac) to expand and them add like terms. The steps are shown below:

2(m-4)+1\\=2m-8+1\\=2m-7

Answer choice A is right (2m - 7)

4.

Total number roses is = total red roses and total white roses

total red roses = x groups of 8 in each group = 8x

total white roses = y groups of 8 in each group = 8y

Hence, total = 8x + 8y

Answer choice B is right.

5.

We divide "number of students who like sandwiches" by "total number of students" , then multiply by 100 to get the percentage. Which ever is the greatest, is the answer. Let's do for each:

School A: \frac{12}{38}*100=31.58%

School B: \frac{9}{48}*100=18.75%

School C: \frac{10}{26}*100=38.46%

School D: \frac{8}{24}*100=33.33%

School C has the greatest percentage.

6.

Subtracting 25.2 from 86 will give us the amount of flour Sam used in last 10 days.

Amount used = 86 - 25.2 = 60.8 pounds

Since he used same amount for each day, we can divide 60.8 by 10 to get how much he used each day.

So, \frac{60.8}{10}=6.08 pounds used each day

Answer is C, 6.08 pounds

7.

"Score" needs to be atleast 30. Let first round score be 5 (given) and each of the three remaining rounds's score be p. So,

Score = 5 + 3p

This SCORE NEEDS to be ATLEAST 30, which means "5 + 3p should be greater than or equal to 30"

First answer choice is right (5 + 3p ≥ 30)

8.

First day printed = 95 (given)

Second day printed = 25 barcodes per minute for x minutes = 25x AND 25 barcodes per minute for y minutes = 25y

Subtotal is 25x+25y


Total in 2 days = 95 + 25x + 25y

Answer choice A is right.

9.

Let first number be x, so next consecutive number is x + 1 and the next one is x + 2. We take the sum and equate to 84 and solve:

x+(x+1)+(x+2)=84\\3x+3=84\\3x=84-3\\3x=81\\x=\frac{81}{3}=27

Hence, the 3 numbers are 27, 28, and 29. The largest is 29, answer choice D is right.

10.

The question is

\frac{3}{4x}-3=-18

The first step would be to "isolate" the terms with x's and constant terms. So we sould take 3 to the right hand side.

Adding 3 to both sides "eliminates" 3 from left and takes it to the right.

Answer choice A is right (Add 3 to both sides)

11.

Finding the respective PERCENTAGES will give us the answers. The greatest amount is what we are looking for. Let's find it.

Zak = 15% of 56 = 0.15 * 56 = 8.4 pages

Karen = 12% of 64 = 0.12 * 64 = 7.68 pages

Malia = 14% of 68 = 0.14 * 68 = 9.52 pages

Ali = 10% of 72 = 0.10 * 72 = 7.2 pages

We see that Malia reads the most. Answer choice C is right (Malia)

12.

Subtracting John's weight (100) from maximum the elevator can carry (340) will give us the amount alloted for the packages.

Amount alloted for packages = 340 - 100 = 240

Since each package weights 5, the MAXIMUM is  \frac{240}{5}=48

It means "the number of packages, n, can be LESS THAN or EQUAL to 48"

Answer choice C is right (n ≤ 48)

13.

We can simplify the expression  by using distributive property (a(b+c)=ab+ac) and collecting like terms to fully simplify the expression. let's do it:

3x-4(2x-5)\\=3x-8x+20\\=-5x+20

Indeed the expression is equal to "20 - 5x" (the two terms are just placed differently)

Answer is TRUE



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