Answer:
The market sold 18 6-ounce cans of soup on Tuesday
Step-by-step explanation:
Let us solve the question
- The number of the 6-ounce cans is x
- The number of 12-ounce cans is y
- 6x + 12y = 420
→ Divide each term by 6 to simplify the equation
- x + 2y = 70 ⇒ (1)
- x + y = 44 ⇒ (2)
→ Subtract equation (2) from equation (1)
- (x - x) + (2y - y) = (70 - 44)
- 0 + y = 26
- y = 26
Substitute the value of y in equation (2) to find the value of x
-x + 26 = 44
→ Subtract 26 from both sides
- x + 26 - 26 = 44 - 26
- x = 18
- x represents the number of the 6-ounce cans
- The market sold 18 6-ounce cans of soup on Tuesday
Answer:
Step-by-step explanation:
1. 2x - 1 < x + 3
Subtract x and add 1 to both sides
2x - 1 - x + 1 < x + 3 - x + 1
x < 4
2. 5x - 1 > 6 - 2x
Add 1 and 2x to both sides
5x - 1 + 1 + 2x > 6 - 2x + 1 + 2x
7x > 7
Divide both sides by 7
7x/7 > 7/7
x > 1
3. x - 5 < 0
Add 5 to both sides
x-5 + 5 < 0 + 5
x < 5
Answer b: the system of equations does not have a solution
Suppose the systems consits of two first grade equations with two varaibles. If the two equations are parallel you would obtaing a result like Vinnet.
This is an example:
x = y + 1
7x = 7y + 9
substitue to get:
7(y+1) = 7y +9
7y + 7 = 7y + 9
7=9
There is not mistake, the system has no solutions, because the two equations represent parallel lines, which do no intercept one to each other.
<h2>Answer</h2>
Which simplifies to:
<h2>Explanation</h2>
Let 
the number of feet they are going to expand the width and length of the patio. So the new width of the patio will be 
and the new length 
.
Remember that the area of a rectangle is <u>width times length</u>, so the length of our expanded patio will be 
. But, we also know form our problem that they want to increase the total area of the patio by 160 ft2. The actual area of the patio is 
, so the expanded area of the patio will be 
.
Now we can equate the expanded area of the patio and simplify:
To apply the changes to the equation of a vertical stretch of 4 and a translation of 3 units to the right, as well as the correct answer would be choice B.
The reason for this is when you apply a vertical stretch, because it changes the y-values (which causes it to vertically stretch or appear skinnier when graphed), you would multiply 4 to f(x) which would look like 4x^2.
Then, since you have a reflection over the x-axis, you must multiply a -1 to f(x) to reflect it over the x-axis which would result in -4x^2.
Finally, it also asks to shift the graph right 3 which by moving it right, you change the x values meaning you will perform f(x-3) to achieve this (subtract the value from x when you move right, and add the value to x when you move left).
This therefore results in your answer, the new graph would be
g(x)= -4(x-3)^2 or choice B.
