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2 years ago

For two real values of $n$, the equation $9x^2+nx+36=0$ has exactly one solution in $x$. What is the positive value of $n$?

Mathematics

2 answers:

BabaBlast [244]2 years ago

7 0

Completing the square, you get n = 24.

statuscvo [17]2 years ago

3 0

Answer:

Step-by-step explanation:

If the quadratic expression on the LHS has exactly one root in $x$, then it must be a perfect square. Dividing 9 from both sides, we have $x^2+\frac{n}{9}x+4=0$. In order for the LHS to be a perfect square, it must factor to either $(x+2)^2=x^2+4x+4$ or $(x-2)^2=x^2-4x+4$ (since the leading coefficient and the constant term are already defined). Only the first case gives a positive value of $n$, which is $n=4\cdot9=\boxed{36}$.

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Angie and Becky each completed a separate proof to show that the measures of vertical angles AKG and HKB are equal. Who complete

kykrilka [37]

Answer:

Becky, because her reason I'm step 2 does not justify her 2ndbstatement.

Step-by-step explanation:

Two angles which add up to give 180° are said to be defined as supplementary angles.

The Definition of Supplementary Angles is the most appropriate statement to justify the second statement in the proof, as written by Angie, compared to the Angle Addition Postulate stated by Becky.

The Angle Addition Postulate does not justify why the two of angles both equal 180°. According to the Angle Anldditiin Postulate, sum of 2 angles that share the same side can does not necessarily have to be 180°. It could be less than or greater than 180°.

Therefore, Becky completed her proof incorrectly.

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2 years ago

Which graph represents the function f(x) = (x – 5)2 + 3?

goblinko [34]

The function
$f(x)=(x-5)^2+3$
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The graph of the function is attached.

4 0

2 years ago

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A garden supply store sells two types of lawn mowers. Total ales of mowers for the year were $8379.70. The total number of mower

Anestetic [448]

Answer:

The number of small mowers are 19 and the large mowers are 11.

Step-by-step explanation:

Given:

A garden supply store sells two types of lawn mowers. Total sales of mowers for the year were $8379.70. The total number of mowers sold the 30. The small mower cost $249.99 and the large mower costs $329.99.

Now, to find the number of each type of mower sold.

Let the number of small mower be $x.$

And the number of large mower be $y.$

So, total number of mowers are:

$x+y=30$

$x=30-y\ \ \ ....(1)$

Now, the total sales of mowers are:

$249.99(x)+329.99(y)=8379.70$

Substituting the value of $x$ from equation (1) we get:

$249.99(30-y)+329.99y=8379.70$

$7499.7-249.99y+329.99y=8379.70$

$7499.7+80y=8379.70$

<em>Subtracting both sides by 7499.7 we get:</em>

$80y=880$

<em>Dividing both sides by 80 we get:</em>

$y=11.$

The number of large mower = 11.

Now, to get the number of small mowers we substitute the value of $y$ in equation ( 1 ):

$x=30-y\\x=30-11\\x=19.$

The number of small mower = 19.

Therefore, the number of small mowers are 19 and the large mowers are 11.

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2 years ago

The weight, w, of a spring in pounds is given by 0.9 times the square root of the energy, E, stored by the spring in joules. If

frutty [35]

For this case we have the following equation:
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E: the energy stored by the spring in joules.
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$w = 0.9* \sqrt{12}$
Making the corresponding calculation:
$w=3.12$
Answer:
the approximate weight of the spring in pounds is:
$w=3.12$

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vlada-n [284]

Answer:

Step-by-step explanation:

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