Answer:
70 = 10x + 35 is your equation (10x + 35 is your expression).
3 1/2 hr is the time needed.
Step-by-step explanation:
Let hours = x.
You need 70 bookmarks, you have 35 (constant number), and you make 10 bookmarks an hour (varys).
Set the equation:
70 = 10x + 35
Solve for x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. First subtract, then divide.
Subtract 35 from both sides:
70 (-35) = 10x + 35 (-35)
70 - 35 = 10x
35 = 10x
Isolate the variable (x). Divide 10 from both sides:
(35)/10 = (10x)/10
x = 35/10
x = 3.5
3 1/2 hours is your answer.
~
Answer:
The height of the tower = 24 units.
Explanation:
In the question above, we are given the following variables.
The total number of blocks used = 312 blocks
The bottom layer( base of the tower) = 13 blocks
We are to find how tall the tower is = height of the tower = unknown.
The total number of blocks used = Volume of the tower = 312 cubic units(blocks)
Area of the base = number of the blocks used in the bottoms layer = 13 square units( block).
Because blocks are used, we assume that this is a Rectangular based prism
The Volume of a Rectangular based prism = Area of the base × h
312 = 13 × h
h = 312 cubic units ÷ 13 square units.
h = 24 units.
There fore, the height of the tower = 24 units
Step-by-step explanation:
given that y=4+2x
for x=5
y=4+2(5)
y=14
for x=7
y=4+2(7)
=18
for x=9
f(9)=4+2(9)
Y=22
for x=10
y=4+2(10)
=y=24
Answer:
x > -1
Step-by-step explanation:
Simplify the inequality using the distributive property (multiply the term outside the bracket with each number inside the bracket). Then, isolate 'x' by performing the reverse operations for every number that's on the same side as 'x'. (Reverse operations 'cancel out' a number.)
18 < -3(4x - 2) Expand this to simplify
18 < (-3)(4x) - (-3)(2) Multiply -3 with 4x and -2
18 < -12x + 6 Start isolating 'x'
18 - 6 < -12x + 6 - 6 Subtract 6 from both sides
18 - 6 < -12x '+ 6' is cancelled out on the right side
12 < -12x Subtracted 6 from 18 on the left side
12/-12 < -12x/-12 Divide both sides by -12
12/-12 < x 'x' is isolated. Simplify left side
-1 < x Answer
x > -1 Standard formatting puts variable on the left side
Factor by grouping. Group up the terms into pairs, factor each pair, then factor out the overall GCF.
x^3 + 2x^2 - 16x - 32
(x^3 + 2x^2) + (-16x-32) ... pair up terms
x^2(x + 2) + (-16x - 32) ... factor x^2 from the first group
x^2(x + 2) - 16(x + 2) ... factor -16 from the second group
(x^2 - 16)(x + 2) .... factor out (x+2)
(x - 4)(x + 4)(x + 2) .... Use the difference of squares to factor x^2-16
---------------------------
The original expression completely factors to (x - 4)(x + 4)(x + 2)
The three factors are x - 4 and x + 4 and x + 2