11. 4x-3=14
add 3 to both sides
4x=17
17 divided by 4 = 4.25
x=4.25
if you want to check if thats correct you put
4(4.25)-3=14
4 times 4.25 = 17
17-3 = 14
Discussion
1. Put brackets around the first two terms
y = (-x^2 + 6x) + 5
2. Take out the common factor of -1
y = -(x^2 - 6x) + 5
3. Inside the brackets, take 1/2 of - 6 and square it
y = -(x^2 - 6x + ( - 6 / 2)^2 ) + 5
y = -(x^2 - 6x + (- 3)^2 ) ) + 5
y = -(x^2 - 6x + 9 ) + 5
Note: Step 3 is very long. Make sure you work your way through it
4. You have added 9 inside the brackets. <em><u>It is actually - 9. So add 9 outside to balance the equation out. </u></em> This is the key step. Make sure you understand it.
y = - (x^2 - 6x + 9) + 5 + 9
5. Express the brackets as a square.
y = - (x + 3)^2 + 14
Discussion
The equation is now in vertex form. The minus tells you that the equation is a maximum. The maximum is located at ( - 3, 14 )
A graph follows to show the results.
9514 1404 393
Answer:
- pancake: $0.50
- waffle: $1.20
Step-by-step explanation:
You can model the bills using w and p for the price of a waffle and pancake, respectively.
10w + 4p = 14
5w +8p = 10
Subtract half the first equation from the second:
(5w +8p) -(1/2)(10w +4p) = (10) -(1/2)(14)
6p = 3 . . . . . . . simplify
p = 0.50 . . . . . divide by 6
10w + 4(0.50) = 14 . . . . substitute into the first equation
10w = 12 . . . . . . . . . . . . subtract 2
w = 1.20 . . . . . . . . . . . . .divide by 10
A waffle costs $1.20; a pancake costs $0.50.
2.5x1.30=3.25
4x4.50=18
2x3.75=7.5
3.25+18+7.5=$28.75 total price
2.5+4+2=8.5lb. total weight
28.75/8.5= 3.38 dollars per pound.
Answer:
7 × 10 + 3 × 1 + 3 × 0.1 + 8 × 0.01 + 5 × 0.001 > 73.293
Step-by-step explanation:
Given: Numbers are 7 × 10 + 3 × 1 + 3 × 0.1 + 8 × 0.01 + 5 × 0.001 and 73.293
To compare: the two given numbers
Solution:
7 × 10 + 3 × 1 + 3 × 0.1 + 8 × 0.01 + 5 × 0.001 is equal to
Compare the numbers and 73.293
Digits at the ones pace and tens place in both the numbers are same.
Observe the digit at the tenth place in both the numbers.
Digit at the tenth place in 73.385 is 3
Digit at the tenth place in 73.293 is 2
As ,
73.385 > 73.293
So,
7 × 10 + 3 × 1 + 3 × 0.1 + 8 × 0.01 + 5 × 0.001 > 73.293