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Vladimir [108]
3 years ago
9

Jake’s measures the height of a tree to be 74 3/8

Mathematics
1 answer:
goblinko [34]3 years ago
7 0

I'm assuming the question is asking how tall the tree is if it has grown 2 3/4 inches.

The initial height of the tree is 74 3/8 inches and it grows 2 3/4 inches after six months. We can add these two numbers together to calculate the height of the tree now.

74\frac{3}{8} + 2\frac{3}{4}

Since these are both mixed numbers, we must find a common denominator to add our fractions. 8 is the lowest common denominator for 4 and 8. So:

74\frac{3}{8} + 2\frac{6}{8}

We can now add our whole numbers up (74 + 2) and add the numerators of the fractions together to get a single fraction (\frac{3}{8} + \frac{6}{8}).

74 + 2 = 76

\frac{3}{8} + \frac{6}{8} = \frac{9}{8}

Putting these two together, we get 76 \frac{9}{8}, which is equal to 77\frac{1}{8}.

We can also turn this answer into an improper fraction. This is done by multiplying the whole number by the denominator and adding the numerator. So in this case:

77 x 8 = 616

616 + 1 = 617

The denominator stays the same, so our answer as an improper fraction would be \frac{617}{8}.

So the tree is 77\frac{1}{8} inches tall, or \frac{617}{8} inches tall.

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Answer:

all x intercepts [-4, 0] [4, 0]

Step-by-step explanation:

x-intercept, i.e. y=0

f(x) = x^3 - 4x^2 - 16x + 64 = 0

(x^3 + 4^3) - 4x^2 - 16x = 0         [FYI, x^3 + y^3 = (x + y)(x^2 - xy + y^2)]

(x + 4)(x^2 - 4x + 16) - 4x^2 - 16x = 0

(x + 4)(x^2 - 4x + 16) - 4x(x + 4) = 0

(x + 4)(x^2 - 4x + 16 - 4x) = 0

(x + 4)(x^2 - 8x + 16) = 0

(x + 4)(x - 4)^2 = 0

x = -4 or 4

all x intercepts [-4, 0] [4, 0]

4 0
2 years ago
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3 years ago
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a_sh-v [17]

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5 0
3 years ago
A music store sold a total of 27 used trumpets and clarinets in one month. Trumpets cost $149 and clarinets cost $99. If total s
vodomira [7]
Answer: 16

Solution:

1) Use letters to identify the variables:

Number of trumpets: t
Number of clarinets: c

2) Translate each statement into algebraic (mathematical) language.

2.1) Sold a total of 27 used trumpets and clarinets

=> t + c = 27

2.2) Trumpets cost $149 and clarinets cost $99

Total cost of the trumpets: 149t
Total cost of clarinets: 99c

Total cost = 149t + 99c

2.3) Total sales were $3223

=> 149t + 99c = 3223.

3) State the system of equations:

Equation (1) t + c = 27
Equation (2) 149t + 99c = 3223

4) Solve the system of equations:

4.1) Multiply equation 1 by 149:

=> 149t + 149c = 4023

4.2) Subtract the equation (2) from the equation obtained in 4.1

=> 149c - 99c = 4023 - 3223

=> 50c = 800

=> c = 800 / 50 = 16

5) Verify the solution:

From equation (1) t = 27 - 16 = 11

Total cost = 149*11 + 99*16 = 3223

Now you have a verified answer: they sold 16 clarinets
7 0
3 years ago
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