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3 years ago

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Consider this system of equations. Which shows the first equation written in slope-intercept form?

1 answer:

eimsori [14]3 years ago

8 0

Question:

Consider this system of equations. Which shows the first equation written in slope-intercept form?

½(2y + 10) = 7x.

y = 8.

A. y = 7x - 10

B. y = 7x/2 - 5

C. y = 7x - 5

D. y = 7x/4 - 5

Answer:

C. y = 7x - 5

Step-by-step explanation:

Given

½(2y + 10) = 7x.

Required

Convert to slope intercept form.

To do this, we simply make y the subject of formula from the given equation

We start by writing out the equation

½(2y + 10) = 7x.

Then, we open the bracket

½ * 2y + ½ * 10 = 7x

2y/2 + 10/2 = 7x

y + 5 = 7x

Then, subtract 5 from both sides of the equation

y + 5 - 5 = 7x - 5

y = 7x - 5

The equation can't be simplified any further. So, we've arrived at a solution

Hence, the slope intercept form of ½(2y + 10) = 7x is y = 7x - 5

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Jose earned 5h + 5 dollars for h hours and Alex earned 8h – 10 for h hours mowing lawns. If they earned the same amount

AlekseyPX

Answer:

5 hours

Step-by-step explanation:

This is a classic pre-algebra question.

$5h+5=8h-10\\5=3h-10\\15=3h\\h=5$

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3 years ago

Your brother is 1/5 your age. Your sister is 9 years older than your brother. Your sister is 11 years old. Write and solve an eq

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3 years ago

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3 years ago

Charlie runs a book rental business. He currently charges $3 per book and rents out an average of 38 books a day.

liberstina [14]

Answer:

b(x) = (3+0.5x) (38-4x)

Step-by-step explanation:

Let the generated revenue per day be b(x)

Let x be the number for every 50cents($0.5) price increase

Formula to be used to generate the revenue generated is expressed using the formula:

b(x) = Price × Quantity

Next is to derive the price and quantity function in terms of x.

For the price:

If he currently charges $3 per book

Let derive the price function for the model and x number of price increase for every 50 cents, then

Price = ($0.5 of x)+$3

Price = $3+$0.5x

Price = $(3+0.5x)

For the quantity:

Number of books rent out per day = 38

If for every 50cents increase in rental price x, the average business can expect to lose 4 rentals a day, then the total lost per quantity = 4x

Quantity per time = Number of books rent out daily - loss on each book

Quantity = $(38-4x)

Next is to substitute the price and quantity function into the revenue formula above:

Revenue = Price × Quantity

Revenue = (3+0.5x)(38-4x)

Hence the equation that models this scenario, where b(x) is the revenue generated and x is the number of 50 price increases is b(x) = (3+0.5x)(38-4x)

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4 years ago

The pesticide diazinon is in common use to treat infestations of the German cockroach, Blattella germanica. A study investigated

cluponka [151]

Answer:

We conclude that there is no difference in the proportion of cockroaches that died on each surface.

Step-by-step explanation:

We are given that a study investigated the persistence of this pesticide on various types of surfaces.

After 14 days, they randomly assigned 72 cockroaches to two groups of 36, placed one group on each surface, and recorded the number that died within 48 hours. On the glass, 18 cockroaches died, while on plasterboard, 25 died.

<em>Let </em> $p_1$ <em> = proportion of cockroaches that died on glass surface.</em>

<em /> $p_2$ <em> = proportion of cockroaches that died on plasterboard surface.</em>

So, Null Hypothesis, $H_0$ : $p_1-p_2$ = 0 {means that there is no difference in the proportion of cockroaches that died on each surface}

Alternate Hypothesis, $H_A$ : $p_1-p_2\neq$ 0 {means that there is a significant difference in the proportion of cockroaches that died on each surface}

The test statistics that would be used here <u>Two-sample z proportion</u> <u>statistics</u>;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of cockroaches that died on glass surface = $\frac{18}{36}$ = 0.50

$\hat p_2$ = sample proportion of cockroaches that died on plasterboard surface = $\frac{25}{36}$ = 0.694

$n_1$ = sample of cockroaches on glass surface = 36

$n_2$ = sample of cockroaches on plasterboard surface = 36

So, <u><em>test statistics</em></u> = $\frac{(0.50-0.694)-(0)}{\sqrt{\frac{0.50(1-0.50)}{36}+\frac{0.694(1-0.694)}{36} } }$

= -1.712

The value of z test statistics is -1.712.

Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis</u>.

Therefore, we conclude that there is no difference in the proportion of cockroaches that died on each surface.

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3 years ago