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3 years ago

Danielle plans to graph the linear equation 5x-2y=10 by plotting the x-intercept and y-intercept.

Mathematics

1 answer:

lesya692 [45]3 years ago

4 0

x-intercept is (2,0)

y-intercept is (0,-5)

Step-by-step explanation:

Danielle plans to graph the linear equation 5x-2y=10 by plotting the x-intercept and y-intercept.

Finding x-intercept

X-intercept: Substitute 0 for y and then solve for x. Write your answer in the form (__, 0)

Putting y=0

$5x-2y=10\\5x-2(0)=10\\5x=10\\x=10/5\\x=2$

So, x-intercept is (2,0)

Finding y-intercept

Y-intercept: Substitute 0 for x and then solve for y. Write your answer in the form (0, __)

Putting x=0

$5x-2y=10\\5(0)-2y=10\\-2y=10\\y=10/-2\\y=-5$

So, y-intercept is (0,-5)

Keywords: Solving Equations

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find the smallest number of terms of the AP "-54,-52.5,-51,-49.5" ....that must be taken for the sum of the terms to be positive

wel

The smallest number of terms of the AP that will make the sum of terms positive is 73.

Since we need to know the number for the sum of terms, we find the sum of terms of the AP

<h3>Sum of terms of an AP</h3>

The sum of terms of an AP is given by S = n/2[2a + (n - 1)d] where

n = number of terms,
a = first term and
d = common difference

Since we have the AP "-54,-52.5,-51,-49.5" ....", the first term, a = -54 and the second term, a₂ = -52.5.

The common difference, d = a₂ - a

= -52.5 - (-54)

= -52.5 + 54

= 1.5

<h3>Number of terms for the Sum of terms to be positive</h3>

Since we require the sum of terms , S to be positive for a given number of terms, n.

So, S ≥ 0

n/2[2a + (n - 1)d] ≥ 0

So, substituting the values of the variables into the equation, we have

n/2[2(-54) + (n - 1) × 1.5] ≥ 0

n/2[-108 + 1.5n - 1.5] ≥ 0

n/2[1.5n - 109.5] ≥ 0

n[1.5n - 109.5] ≥ 0

So, n ≥ 0 or 1.5n - 109.5 ≥ 0

n ≥ 0 or 1.5n ≥ 109.5

n ≥ 0 or n ≥ 109.5/1.5

n ≥ 0 or n ≥ 73

Since n > 0, the minimum value of n is 73.

So, the smallest number of terms of the AP that will make the sum of terms positive is 73.

Learn more about sum of terms of an AP here:

brainly.com/question/24579279

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1 year ago

A sweater that cost $63 and are sold for $54

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Answer:

not sure what the question is but here are some possible answers

Step-by-step explanation:

cost 63 - sell price 54 = 9 dollars lost per sweater sold

percentage of lose per sweater would be 14%

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The answer is 6
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Suppose that the probability of a baseball player getting a hit in an at-bat is 0.3089. If the player has 25 at-bats during a we

klio [65]

Answer:

$P(X>9) = 0.3593$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=25, p=0.3089)$