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kupik [55]
3 years ago
5

John bought 3 pencils for $0.75 each and a notebook for $4.25. If the tax rate is 5%, what is the total amount of John's purchas

e including the tax?
Mathematics
1 answer:
SIZIF [17.4K]3 years ago
7 0

Answer:

$6.83

Step-by-step explanation:

First calculate the before-tax total amount:

$0.75 + $0.75 + $0.75 + $4.25, or

3($0.75) + $4.25 = $2.25 + $4.25 = $6.50    (total before tax)

The before-tax total PLUS the 5% tax comes to:

$6.50 + 0.05($6.50) = $6.50 + $0.33  =  $6.83

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4. Divide, using synthetic division: 16x^3 +80x^2+x+5/x+5
fgiga [73]

Answer:

Step-by-step explanation:

x+5=0

x=-5

-5) 16   80   1    5

  |       -80   0  -5

 ____________

  | 16    0    1  | 0

quotient=16x²+1

Remainder=0

8 0
3 years ago
The sum of two numbers is 12. The first number,x, is twice the second number ,y,
vlada-n [284]
Judging by the question at hand I generated this equation.
x+y=12
x=2y

I begin this question by plugging in the x=2y into the equation for x. 
So the new equation should be 3y=12. I then divide the entire equation by 3 to get y=4.

Next I plug y=4 into the equation, the new equation should be x+4=12. I then subtract 4 from both sides to get x=8.

The two numbers are :
x=8 y=4
3 0
3 years ago
Estephany has a box that is filled with toys. The box has a length of 3.5 feet, a width of 6 feet, and a height of 3 feet. What
Zigmanuir [339]

Answer:

63

Step-by-step explanation:

The formula for volume of a box is length×width×height = volume

So you would multiply  3.5×6×3=63

6 0
3 years ago
Please explain with working!!! Find the set of values of x that satisfy the inequality 9x^2-15x<6
Oksi-84 [34.3K]

Answer:

-1/3

Step-by-step explanation:

When solving a quadratic inequality, first solve it normally like you would for a normal quadratic equation. We have:

9x^2-15x

Ignore the less than sign and replace it with an equal sign and solve the quadratic for its zeros:

9x^2-15x=6

Subtract 6 from both sides:

9x^2-15x-6=0

Divide everything by 3:

3x^2-5x-2=0

Factor. Find two numbers that equal (3)(-2)=-6 that add up to -5.

-6 and 1 works. Thus:

3x^2-6x+x-2=0\\3x(x-2)+1(x-2)=0\\(3x+1)(x-2)=0

Find the x using the Zero Product Property:

3x+1=0 \text{ or }x-2=0\\x=-1/3\text{ or }x=2

Now, we need to replace the equal signs with symbols again. To do so, we need to test which symbol to place. Let's do the first zero first.

So, the first zero is:

x=-1/3

Assume that the correct symbol is >. Thus,

x>-1/3

Now, pick any number that is greater than -1/3. I'll pick 0 since it's the easiest. Now, plug 0 back into the very original inequality. If it works, then the sign is correct, if it doesn't, then simply use the opposite one. Therefore:

9x^2-15x

0 is indeed less than six, so our first correct solution is:

x>-1/3

For the second one, do the same thing. We have:

x=2

Assume that the correct symbol is <. Thus:

x

Again, pick any number less than 2. I'm going to use 0. Plug 0 back into the original equation

9x^2-15x

Again, this is correct. Therefore, x<2 is also the correct inequality.

So together, we have:

x>-1/3 \text{ and } x

Together, we can write them as:

-1/3

(Note that we don't need to worry about the "or equal to" part since the original inequality didn't have it.)

6 0
3 years ago
Write a sentence representing the equation x+56/7=11
Anastasy [175]
Hey there! :D

x+56/7=11

A number plus fifty-six sevenths is equal to eleven. 

I hope this helps!
~kaikers
8 0
3 years ago
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