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4 years ago

Use the above graph to answer the following:

Mathematics

1 answer:

igor_vitrenko [27]4 years ago

6 0

Slope of the line is -4/5, y-intercept is 3, equation in slope-intercept form is y = -4/5 x + 3 and the x-intercept is 15/4

Step-by-step explanation:

Step 1: Find slope, m.

Slope = (y2 - y1)/(x2 - x1)

Here, x1 = 0, y1 = 3, x2 = 5, y2 = -1 (based on the plotted points)

⇒ m = (-1 - 3)/(5 - 0) = -4/5

Step 2: Find the y-intercept

y-intercept is the point where the line intersects the y-axis.

Here, the y-intercept, b = 3

Step 3: Write the equation of the line in slope-intercept form

y = mx + b ⇒ y = -4/5 x + 3

Step 4: Find the x-intercept using the equation.

x-intercept is the point where the line intersects the x-axis. Then y = 0

⇒ 0 = -4/5 × x + 3

⇒ -4/5 × x = -3

⇒4x = 15

∴ x = 15/4

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Loren drove 200 miles at a certain rate, and his wife, Lois, drove 100 miles at a rate 10 mph slower. If Loren had driven for th

NeX [460]

As long as Loren drove, the law of motion was

$200 = st_1 \implies t_1 = \dfrac{200}{s}$

As long as Loid drove, the law of motion was

$100 = (s-10)t_2 \implies t_2 = \dfrac{100}{s-10}$

So, the total time they took is

$t_1+t_2=\dfrac{200}{s}+\dfrac{100}{s-10}$

Had Loren driven the whole time, the law of motion would have been

$300=st_3 \implies t_3 = \dfrac{300}{s}$

And we know that this time would have been 30 minutes (i.e. 0.5 hours) faster. So, we have

$t_3 = t_1+t_2-0.5$

This translates into

$\dfrac{300}{s}=\dfrac{200}{s}+\dfrac{100}{s-10}-\dfrac{1}{2}$

If we subtract 200/s from both sides, we have

$\dfrac{100}{s}=\dfrac{100}{s-10}-\dfrac{1}{2}$

We can simplify the right hand side by summing the two fractions:

$\dfrac{100}{s-10}-\dfrac{1}{2} = \dfrac{200-(s-10)}{2(s-10)}=\dfrac{210-s}{2(s-10)}$

So, we have to solve

$\dfrac{100}{s}=\dfrac{210-s}{2(s-10)}$

If we cross multiply the denominators, we have

$200(s-10)=s(210-s) \iff 200s-2000=210s-s^2 \iff s^2-10s-2000=0$

Which yields the solutions

$s=-40,\quad s=50$

We accept the positive solution, because the negative would mean to travel backwards, so Loren's rate was 50mph

5 0

3 years ago

Read 2 more answers

−2/3(3x−4)+3x=5/6 whoever gets right gets brainlyest

REY [17]

−2/3(3x−4)+3x=5/6

= -11/6

7 0

4 years ago

Read 2 more answers

You bought a car for $50,000. Each year it depreciates in value by 7.5%.

sweet-ann [11.9K]

Answer:

y= 50,000(1-.075)^x

Step-by-step explanation:

The first year of depreciation is calculated by:

50,000 - (0.075)*(50,000) = 46,250

This can also be written as:

(50,000)*(1 - 0.075) [Pull out the 50,000]

The second year will depreciate starting with the $46,250 value at the end of the first year:

46,250 - (0.075)*(46,250) = 42,781

This may be written as:

(46,250)(1 - 0.075) = 42,781

The 46,250 was derived from the first year depreciation calculation, so we can substitute that instead of the 46,250:

((50,000)*(1 - 0.075))(1 - 0.075) = 42,781

This reduces to:

(50,000)*(1 - 0.075)^2 = 42,781. Note that the term (1-0.075) is now raised to the 2nd power. This power represents the 2nd year. Each succeeding year would be raised by one additional power, so that we can write a depreciated value after x years will be:

(50,000)*(1 - 0.075)^x

3 0

2 years ago

The weights of the apples grown on an orchard are normally distributed. The mean weight has been m0 = 9.500 ounces. Because of t

diamong [38]

Answer:

t(s) is in rejection zone then we reject H₀.

Bad weather indeed make apples weight decrease

Step-by-step explanation:

Normal Distribution

population mean μ₀ = 9.5 ou

sample size = n = 16 then we should apply t-student table

degree of fredom df = n - 1 df = 16 - 1 df = 15

1.-Test hypothesis

H₀ null hypothesis μ₀ = 9.5

Hₐ alternative hypothesis μ₀ < 9.5

One left tail-test

2.-Confidence level 95 %

α = 0,05 and df = 15 from t-student table we get t(c) = - 1.761

3.-Compute t(s)

t(s) = [ μ - μ₀ ] /√s/n t(s) = (9.32 - 9.5 )* √16 / 0.18

t(s) = - 0.18*√16 / 0.18

t(s) = - 4

4.-Compare t(s) and t(c)

t(s) < t(c) -4 < - 1.761

Then t(s) is in the rejection zone.

5.- Decision

t(s) is in rejection zone then we reject H₀.

Farmer conclude that bad weather make apples weight decrease

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4 years ago

PLz help!!! Look at the picture below for the question.

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speed of plane flying east = x

speed of plane flying west = x+75

total speed = 2x+75

distance after 4 hours ( 7-3) = 8x+300

8x+300 = 5460

8x = 5160

x = 5160/8 = 645

speed of plane flying east = 645 km/h

7 0

3 years ago