It looks like we have two unknowns here and two possible equations so to solve this we will need to utilize our systems of equations, I will be using the substitution method.
We know that all of the parts multiplied together is equal to the volume.
We know that the volume is 126 square inches
The height is seven inches
The width is unknown, let w be the width
The length is unknown, let l be the length
We know that the length is three inches more than the width (l=w+3)
We know that the height times the length times the width is equal to the volume (7lw=126)
Since we know that l=w+3, we can substitute w+3 in for l,
7(w+3)(w)=126
Now we can solve our equation
7(w+3)(w)=126
(7w+21)(w)
7w^2+21w=126
Now we will complete the square to solve for w
7w^2+21w=126
w^2+3w=18
w^2+3w+2.25=20.25
(w+1.5)^2=20.25
w+1.5=4.5
w=3
We have now found out using our knowledge of systems of equations that the width of this prism is 3 inches.
Answer:
Step-by-step explanation:
Set up two equations with the information given-- and things you know from experience: a penny is worth 1 cent and a nickel is worth 5 cents. $ 2.38 is 238 cents (so you can eliminate decimals for now)
Put those values into an equation about the total value:
p + 5n = 238
and you know the total number of coins is 66.
p + n = 66
get a value for p by "solving" (subtract n from both sides)
p = 66-n
Substitute that value for p in the first equation. Then solve.
(66 -n) + 5n = 238
4n = 238-66 Then isolate n by dividing both sides by 4
n = 172/4
n = 43 Substitute that in the second equation, then solve for p
p + 43 = 66 p = 66 - 43
p = 23
So Chuck has 23 pennies and 43 nickels
For the given set of equations, the values of x = -8 and x = -2.
We have, f(x) = x² + 7x- 24 and g(x) = -3x - 40
An Equation is an algebraic statement that shows that two quantities are equal.
For one x-value of a solution,
We equate both the given functions,
Thus, f(x) = g(x)
x² + 7x- 24 = -3x - 40
+7x + 3x -24 + 40 = 0
+10x + 16 =0
+ 8x + 2x +16 =0
x(x+8) + 2(x +8) =0
(x+8) (x+2) = 0
x = -8 and x = -2
Hence, Concluding, we have x = -8 and x = -2
To read more about equations, visit brainly.com/question/14686792
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Answer:
b
Step-by-step explanation:
150+128+X=450
(a) 95 = (x+7)*(x-7)
(b) 95 = (x+7)*(x-7)
Expand the brackets:
95 = x² -7x + 7x -49 = x² - 49
Subtract x² from both sides:
95-x² = -49
Subtract 95 from both sides:
-x²=-49-95
-x²= -144
Divide both sides by -1 to get rid of the negative numbers:
-x²/-1=-144/-1
x²=144
Take the square root of 144:
x = ± squareroot of 144
x = 12 or -12
x = 12 because you cannot have a negative age so Trina is 12 years old.
