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A ball bounces to a height of 6.7 feet on the first bounce. Each subsequent bounce reaches a height that is 81% of the previous bounce. What is the height, in feet, of the sixth bounce
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After solving, the height in feet of the sixth bounce is 1.892 feet.
In the given question, we ave to find the height, in feet, of the sixth bounce.
From the given question,
Height on the first bounce = 6.7
Subsequent bounce reaches a height of the previous bounce = 81%
Suppose the height is h.
So according to the question:
h(6) = height on the first bounce*(subsequent bounce reaches a height of the previous bounce)^6
h(6) = 6.7*(81%)^6
h(6) = 1.892 feet
So the height of sixth bounce is 1.892 feet.
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A chef that manages two restaurants buys seven bags of rice and six bags of flour.
Restaurant A receives four bags of rice and two bags of flour for a total cost of
$78. Restaurant B receives three bags of rice and four bags of flour for a total
cost of $71.50. What is the cost of each bag of rice and each bag of flour?
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Answer:
- A bag of rice is $16.9
- A bag of flour is $5.20
Step-by-step explanation:
Let R and F stand for the price of a bag of Rice and Flour, respectively.
We can use the information provided to set an equation that will predict the total cost for that restaurant, given the quantities of rice and flour received (Restaurants A and B)
A) 4R + 2F = 78 [4 bags of rice and 2 bags of flour, when multiplied by the prices per bag, R and F, will result in a total cost of $78.
B) 3R + 4F = 71.5 [Now it is 3 bags of rice and 4 of flour, for a total cost of $71.50
We have 2 equations and 2 unknowns. We can use substitution to find the answers. Take one of the equations and reorganize it to isolate one of the variables (R or F). We'll take the equation for A and isolate F
---
A) 4R + 2F = 78
2F = 78-4R [subtract 4R from both sides]
F = 39-2R [divide both sides by 2]
We've isolated F, and we can use this definition of F in the second equation:
===
B) 3R + 4F = 71.5
3R + 4(39 - 2R) = 71.5 [Use the definition of F derived above. In this manner, we have legally eliminated one of the two variables. (Sneaky, effective, and fun)]
3R + 156 - 8R = 71.5 [Multiply, combine like terms, and simplify]
-5R = -84.5 [Isolate R]
R = $16.9 A bag of rice costs $16.9
Now use the price of rice (R=$16.9) in one of the equations. Since the rearranged equation we used above is already conveniently written for F, we'll use it:
F = 39 - 2R
F = 39 - 2(16.9)
F = 39 - 33.8
F = $5.20 A bag of flour costs $5.20
===
CHECK:
Do these two prices satisfy both equations we first formulated?
Restaurant A: 4R + 2F = 78?
4(16.9) + 2(5.20) = 78 YES
Restaurant B: 3R + 4F = 71.5?
3(16.9) + 4(5.20) = 71.5 YES
These are the correct answers.
If 14 more than the product of -3 and a number x
is less than 56, which values could represent x?
Check all that apply. Write and solve the inequality.
-17
-14
■
-21
-2
-9
-15
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bring the variable to the left side and bring all the remaining values to the right side.
How do you write a step-by-step inequality?Image search results for Write the inequality and solve it. -17 -14 ■ -21 -2 -9 -15
To fix an inequality, use these steps:
Step 1: Remove fractions by multiplying all terms by the fractions’ least common denominator.
Step 2 Simplify the inequality by merging like words on either side.
Step 3 Subtract or add amounts to get the unknown on one side and the digits on the other.
In algebra, the letter “x” is frequently used to represent an unknown value. It is referred to as a “variable” or “unknown” at times. X is a variable in x + 2 = 7, but we can deal with it.
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ALGEBRA 2 NEED HELP ASAP
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The rule for g(x) = f(x-1)-3 is g(x) = (x-1)⁶-3(x-1)³ - 1
How to write the rule for g(x) = f(x-1)-3?A function is an expression, rule, or law that defines a relationship between an independent variable and a dependent variable. Based on the information given, we can see that the variables that are illustrated in the question are f and g.
In order to write the rule for g(x) = f(x-1)-3 when f(x) = x⁶ - 3x³ + 2, replace x with x-1 in f(x) and subtract 3. That is:
g(x) = f(x - 1) - 3
g(x) = (x-1)⁶ - 3(x - 1)³ + 2 - 3
g(x) = (x-1)⁶ - 3(x - 1)³- 1
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Mamas bakery just opened and is currently selling only two types of pastry. Each month mamas bakery will add two more types of pastry to their menu. Suppose this pattern continues. What algebraic expression can be used to find the number of pastries offered after any given number of months? How many pastries will be offered in one year?
Answers
The number of pastries will be offered in one year could be 26 and the algebraic expression could be x = 2 + 2y
What is Arithmetic progression ?
Arithmetic progression could be defined as the sequence of number where the difference between two consecutive number is same.
Given,
Mamas bakery just opened and is currently selling only two types of pastry.
Each month mamas bakery will add two more types of pastry to their menu.
let the number of pastries be x.
let y be the given number of pastries.
Hence the algebraic expression could be
x = 2 + 2y
Number of pastries will be offered in one year could be
x = 2 + 2 * 12
x = 26
Hence, the number of pastries will be offered in one year could be 26 .
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