Answer:
6/12
Step-by-step explanation:
Note the shaded amount of "parts". You are supposed to put the shaded amount of parts over the <em>total</em> amount of parts.
In the first rectangle, it shows 2 of 3 parts as shaded, and so the fraction is: 2/3
In the second rectangle, it shows 3 of 4 parts shaded, and so the fraction is: 3/4
Finally, the 3rd rectangle shows 6 of 12 parts shaded, and so the fraction is:
6/12
Check by multiplying the fractions across:
(2/3) x (3/4) = (2 x 3)/(3 x 4) = 6/12
6/12 is your answer.
If you need to simplify, divide common factors from both the numerator and denominator, in this case being 6.
(6/12)/(6/6) = 1/2
1/2 is your reduced answer.
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Answer:
consistent, independent
Step-by-step explanation:
Systems of equations are most easily classified these ways if the equations are in the same form. If we solve the second equation for y, we have ...
y = x - 1
The x-coefficients of this and the first equation are different, so the system is <em>consistent</em> and <em>independent</em>.
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A system is independent if the equations describe different lines.
A system is inconsistent if the equations describe parallel lines.
Here, the different lines are not parallel, so the system is independent and consistent.
Answer:
Part A. the x-intercepts are: x=4 and x= -1/4
Part B. The vertex of the graph is going to be a maximum
Part C. y-intercept is y=8
Step-by-step explanation:
We have the following function:
f(x) = −8x^2 + 30x + 8
Part A: What are the x-intercepts (zeros) of the graph of the f(x)?
To find the x-intercepts we have to make y=0 and solve for x. Then:
y = −8x^2 + 30x + 8
0 = −8x^2 + 30x + 8
8x^2 - 30x - 8 = 0
Dividing the whole expression by 8:
x^2 - 15/4x - 1 = 0
Using the quadratic formula we have that:
(x−4)(4x+1)
So the x-intercepts are: x=4 and x= -1/4
Part B. Is the vertex of the graph of f(x) going to be a maximum or minimum?
The vertex of the graph is going to be a maximum, given that the quadratic term is multiplied by a negative sign.
PArt C. What is the y intercept of the graph?
To calculate the y-intercept we need to make x=0, so:
y = −8(0)^2 + 30(0) + 8 = 8
So the y-intercept is y=8
Answer:
Selling Price of the Book - $7.70
I believe that this is the answer
Step-by-step explanation:
We need to find what is 40% of 5.50.
40/100 x 5.50
After solving this, we will get 2.20
Now, the question is asking what is the selling price of the book will be after it is marked up. Marked up means an increase in price, and the increase in price is 40% of 5.50 which we have already found. All there is left for us to do is add 5.50 and 2.2. This will give us $7.70.
Answer:
1.2195
Step-by-step explanation:
For each month, he is given (on avg) $100 (CAD).
If on avg he can spend $82 (USD) each month,
then the USD: CAD ratio is
100:82, meaning $1 (USD) is equivalent to $.82(CAD)
and the exchange rate is calculated by equating 1 = .82x
thus, x= 1/.82 = 1.2195