Answer:
X=10
X=-8
Step-by-step explanation:
(x+1)*(x-3)=77
x²-3x+x-3=77
x²-2x-3=77
x²-2x-3-77=0
x²-2x-80=0
(x-10)*(x+8)=0
x-10 = 0
x=10
x+8=0
X=-8
X= cost per cherry pie
y= cost per pumpkin pie
NICOLE
1x + 9y= $60
LISA
11x + 4y= $90
STEP 1
multiply Nicole's equation by -11
-11(1x + 9y)= -11($60)
multiply -11 by all terms
(-11 * x) + (-11 * 9y)= (-11 * 60)
-11x - 99y= -660
STEP 2
add Nicole's new equation from step 1 to Lisa's equation to solve for y (using the elimination method)
-11x - 99y= -660
11x + 4y= 90
the x terms "cancel out"
-95y= -570
divide both sides by -95
y= $6 per pumpkin pie
STEP 3
substitute y value into either original equation to solve for x
x + 9y= $60
x + 9(6)= 60
x + 54= 60
subtract 54 from both sides
x= $6 per cherry pie
CHECK
11x + 4y= $90
11(6) + 4(6)= 90
66 + 24= 90
90= 90
ANSWER: Each cherry pie costs $6 and each pumpkin pie costs $6.
Hope this helps! :)
Answer:
Step-by-step explanation:
(96 minutes)/(32 sculptures) = (96/32 minutes)/sculpture = (3 minutes)/sculpture
It takes 3 minutes to make one sculpture.
(160 balloons)/(32 sculptures) = (160/32 balloons)/sculpture = (5 balloons)/sculpture
It takes 5 balloons to make one sculpture.
(160 balloons)/(96 minutes) ≈ 1.7 balloons used per minute.
Given that the volume of a cell is 50 cubic micrometers. It says to find the number of cells present in 1 cubic centimeter.
So we need to first convert the units of volume of a cell, then we can find the total number of cells in 1 cubic centimeter.
We know 1 meter = 100 centimeters = 1000000 micrometers
So 1 centimeter = 10000 micrometers
Taking Cubic powers on both sides :-
1 cubic centimeters = 10¹² cubic micrometers
1 cubic micrometers = 10⁻¹² cubic centimeters
50 cubic micrometers = 50 × 10⁻¹² = 5 × 10⁻¹¹ cubic centimeters
So volume of one cell = 5 × 10⁻¹¹ cubic centimeters
Number of cells =
= 2 × 10¹⁰ cells.
So, total number of cells = 2 × 10¹⁰ cells.
There are 19 people total, and groups of four are being asked of us. We can use the formula for permutations or combinations.
Permutations:

Combinations:

Where in both scenarios, there are <em>n</em> objects being chosen at <em>r</em> times.
19 P 4 is 93024
19 C 4 is 3876
It all depends on whether order matters with group placement; if it does, your answer is
93024, if not, then your answer is
3876.:)