Each question would be worth about 2.22 points.
Answer:
The line of reflection is 1
Answer:
17 quarters, 37 nickels
Step-by-step explanation:
We just have to set up a system of equations
quarters are x
and nickels are y
x+y=54
0.25x+0.05y=6.10
now we can get ready to substitute
x=54-y
substitute it in
0.25(54-y)+0.05y=6.10
simplify/evaluate
13.5-0.25y+0.05y=6.10
-0.2y=-7.4
y=37
plug it back in
x+37=54
x=17
Multiply each term by
b
and simplify.
a = cb
Rewrite the equation as
cb = a
Divide each term by
c
and simplify.
b = a/ c
Answer:
Step-by-step explanation:
A product is formed by multiplying the factors. Here, you want the product of -2 and x, so that is indicated as ...
-2x
You want that product greater than 30. The symbol for "greater than" is >, so you have ...
-2x > 30 . . . . the desired inequality
__
The most straightforward way to solve this is to divide by the coefficient of x. Because that is negative, you must reverse the inequality symbol from "greater than" to "less than."
x < 30/(-2)
x < -15 . . . . . . the desired solution
_____
<em>Additional comment</em>
It may not be clear why multiplying or dividing an inequality causes the symbol to be reversed. You can think of it as reflecting the inequality over the point x=0 on the number line. Where larger numbers were on the right, they get reflected to points farther left, so as negative numbers, they are smaller numbers.
Consider ...
1 < 2
-1 > -2
