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forsale [732]
3 years ago
12

James wants to compete in the international speed texting competition next year where participants compete on text speed and acc

uracy. James’s current text speed is 2 characters per second. James has found that his texting speed increases at a rate of 1⁄2 a character per second for each month that he practices.
1. a. What is James’s new texting speed if he practices for only 1 month? __________
b. What is James’s new texting speed if he practices for 2 months? ____________
c. What is his new texting speed if he practices for 3 months? _____________
d. Write an algebraic equation that gives James’s texting speed s for m months of
practice.

2. a. Solve the equation from question 1d to determine how many months of practice it will
take before James’s texting speed reaches 8 characters per second.
b. Explain the steps to solve your equation from question 2a.

3. a. If Lydia wants to text at least 8 characters per second, like James, then the equation
10r + 4 = 8 could be used to model this situation. Solve this equation for r.
b. Explain what the variable r represents in the equation given in question 3.

4. Consider the equation 8x + 5 = 37. Write a real-life scenario that this equation could model.
Mathematics
1 answer:
makkiz [27]3 years ago
3 0

1a 2.5 characters per second

1b 3 characters per second

1c 3.5 characters per second

1d s = 2 + 0.5m

2a 8 = 2 +0.5m

6=0.5 m

m=12

2b the final speed James wants is 8 cps. sub that in for s. we want to know m. first, subtract 2 from both sides to get 6. then, divide by 0.5, which is 1/2 as a fraction. In order to divide a number by a fraction, you need to invert the fraction and switch operations from division to multiplication. It becomes 2/1 * 6 = 12.

3a 10 r +4 = 8

10r =4

r =4/10=2/5

3b. In this equation, r could be the increase in amount of characters that Lydia can type per second.

4. John buys a small tree that is 5 inches tall. Each month, this tree grows 8 inches. How long will it take for the tree to reach 37 inches in height?

If this helps, please consider giving me brainliest.  

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3 years ago
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A cone has a slant length of 10 and a diameter of 8. Height is unknown.
patriot [66]

Answer: 153.56

Step-by-step explanation:

Hi, to answer this question we have to apply the next formulas:

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Where r is the radius and h is the height (unknown)

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8/2 =r

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Before calculating the volume we have to apply the Pythagorean Theorem to find h. (where the slant is the hypotenuse and h and r are the sides of the triangle)

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Solving for h

100 = h² + 16

100-16 = h²

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Back on the volume formula:

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3 years ago
Four-fifths of a spinach casserole is leftover after Sam has lunch. Jackie and Alicia each take 1/2 of the leftover casserole. J
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3 years ago
What are the exact solutions of x^2 = 5x + 2?
aleksandrvk [35]
Move everybody to one side
minus 5x+2 both sides
x^2-5x-2=0
use quadratic formula where
if you have
ax^2+bx+c=0
x=\frac{-b+/- \sqrt{b^{2}-4ac} }{2a}

1x^2-5x-2=0
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x=\frac{-(-5)+/- \sqrt{(-5)^{2}-4(1)(-2)} }{2(1)}
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aprox
x=5.372281323 or -0.3722813233
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