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lara31 [8.8K]
3 years ago
8

What happens to a line when the y-intercept is changed? Check all that apply. A. As the y-intercept increases, the graph of the

line shifts up. B. as the y-intercept decreases, the graph of the line shifts left. C. As the y-intercept increases, the graph of the line gets steeper. D. As the y-intercept decreases, the graph of the line shifts down. E. as the y-intercept increases, the graph of the line shifts right.
Mathematics
2 answers:
olga nikolaevna [1]3 years ago
5 0
<span>Answer: two options apply: A and D.
</span>
<span /><span /><span>A. As the y-intercept increases, the graph of the line shifts up.

D. As the y-intercept decreases, the graph of the line shifts down.
</span><span />

<span>Justification:


</span><span>1) Take the slope-intercept equation of the line: y = f(x) = mx + b</span>
<span /><span>
</span><span>2) The y-intercept is b
</span>
<span /><span /><span>
3) When b is increased, f(x) will increases too, that is f(x) will be higher or its graph will be shifted up, which is what the option A. states.
</span><span />

<span>4) When b is decreased, f(x) will decreases too, that is f(x) will be lower or its graph will be shifted dOwn, which is what the option D states.
</span><span />

<span>5) Regarding the options B and E, which deal with motions in the horizontal direction (left or righT), nothing can be said, as the effect of a change in the y -intercept on the horizontal direction will depend on the slope.
</span><span />

<span>6) Regarding the option C, a change in the y-intercept does not change the slope (the steep of the line).
</span><span />

USPshnik [31]3 years ago
3 0

Answer:

A. As the y-intercept increases, the graph of the line shifts up.

D. As the y-intercept decreases, the graph of the line shifts down.

Step-by-step explanation:

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Two altitudes of a triangle have lengths $12$ and $14$. What is the longest possible integer length of the third altitude
nataly862011 [7]

The longest possible altitude of the third altitude (if it is a positive integer) is 83.

According to statement

Let h is the length of third altitude

Let a, b, and c be the sides corresponding to the altitudes of length 12, 14, and h.

From Area of triangle

A = 1/2*B*H

Substitute the values in it

A = 1/2*a*12

a = 2A / 12 -(1)

Then

A = 1/2*b*14

b = 2A / 14 -(2)

Then

A = 1/2*c*h

c = 2A / h -(3)

Now, we will use the triangle inequalities:

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2A/12 < 2A/14 + 2A/h

Solve it and get

h<84

  • b < a+c

2A/14 < 2A/12 + 2A/h

Solve it and get

h > -84

  • c < a+b

2A/h < 2A/12 + 2A/14

Solve it and get

h > 6.46

From all the three inequalities we get:

6.46<h<84

So, the longest possible altitude of the third altitude (if it is a positive integer) is 83.

Learn more about TRIANGLE here brainly.com/question/2217700

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The sum of the first n odd numbers is n squared! So, the short answer is that the sum of the first 70 odd numbers is 70 squared, i.e. 4900.

Allow me to prove the result: odd numbers come in the form 2n-1, because 2n is always even, and the number immediately before an even number is always odd.

So, if we sum the first N odd numbers, we have

\displaystyle \sum_{i=1}^N 2i-1 = 2\sum_{i=1}^N i - \sum_{i=1}^N 1

The first sum is the sum of all integers from 1 to N, which is N(N+1)/2. We want twice this sum, so we have

\displaystyle 2\sum_{i=1}^N i = 2\cdot\dfrac{N(N+1)}{2}=N(N+1)

The second sum is simply the sum of N ones:

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\displaystyle \sum_{i=1}^N 2i-1 = 2\sum_{i=1}^N i - \sum_{i=1}^N 1 = N(N+1)-N = N^2+N-N = N^2

which ends the proof.

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