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3 years ago

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Which equation is NOT true? A. 55 + 27 + 45 =100 + 27 C. 14(126)= 14(100) + 14(26) B. 5⦁ 7⦁ 2 = 2⦁7 D. 31(152) = 30(150) + 1(2)

5

1 answer:

stiv31 [10]3 years ago

8 0

Answer:

5⦁ 7⦁ 2 = 2⦁7 is not true

Step-by-step explanation:

70 ≠ 14

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The equation -x = y + 7 written in slope-intercept form is

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I think that it's B, y = -x - 7 because first you'd subtract y to get it on the other side then add x and then you'd need to make the y positive so you would divide x + 7 by -1 and that would make it y = -x - 7.

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Write a real word problem that can be represented by the equation a - 6 = 15

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Step-by-step explanation:

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Determine the intervals on which the function f(x)=−7x2−7x+6f(x)=−7x2−7x+6 is concave up or down and find the points of inflecti

vazorg [7]

Answer:

Point of Inflection: Does not Exist
f(x) is concave up when x∈(-∞,-6)
f(x) is concave down when x∈(-6, ∞)

Step-by-Step Explanation

We are to determine the intervals on which the function $f(x)=\frac{-7x^2-7}{x+6}$ is concave up or down and find the points of inflection.

A function f(x) is concave up in the intervals for which the second derivative of the function $\frac{d^{2}}{dx^{2}} > 0$ .

A function f(x) is concave down in the intervals for which the second derivative of the function $\frac{d^{2}}{dx^{2}} < 0$ .

Given $f(x)=\frac{-7x^2-7}{x+6}$

We need to solve for the second derivative of the function.

The first derivative:

Using Quotient Rule:

$f^{'}(x)=\frac{14x(x+6)-(7x^2-7)}{(x+6)^{2}}$ .

$f^{'}(x)=\frac{7x^2+84x+7}{(x+6)^{2}}$ .

The Second derivative:

Similarly applying quotient rule:

$f^{''}(x )=\frac{(x+6)^{2}(14x+84)-( 7x^2+84x+7)(2x+12)}{(x+6)^{4}}$

$f^{''}(x)=\frac{14(x+6) (x+6) (x+6) -14(x+6)(x^2+12x+1) }{(x+6)^{4}}$

$f^{''}(x )=\frac{14(x+6) [(x+6) (x+6) -x^2+12x+1)] }{(x+6)^{4}}$

$f^{''}(x)=\frac{490 }{(x+6)^{3}}$

Now $f^{''}(x)=\frac{490 }{(x+6)^{3}} =0$ is 490, thus $f^{''}(x) =0$ does not have a solution,

However, we determine the point where $f^{''}(x)$ is undefined. This point is x=-6.

In the Interval, (-∞,-6), f(x) is concave Up and in the Interval (-6, ∞), f(x) is concave down. It has no Inflection point.

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Find the sum of all numbers from 150 to 200 which are divisible by7

podryga [215]

Step-by-step explanation:

The sum is 1225

Solution :

The numbers from 150 to 200 divisible by 7 are 154,161 ,168,…., 196

Here, a=154,d=7a=154,d=7 and tn=196tn=196

tn=a+(n−1)dtn=a+(n-1)d …(Formula )

∴196=154+(n−1)×7∴196=154+(n-1)×7 …(Substituting the values )

∴196−154=(n−1)×7∴196-154=(n-1)×7

∴427=n−1∴427=n-1 ∴n−1=6∴n-1=6 ∴n=7∴n=7

Now, we find the sum of 7 numbers.

Sn=n2[t1+tn]Sn=n2[t1+tn] ...(Formula )

=72[154+196)=72[154+196)

=72×350=72×350

=7×175=7×175

=1225

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