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2 years ago

9

Complete the equation so that it has the indicated number of solutions.

1 answer:

MatroZZZ [7]2 years ago

3 0

6 Winston I got the addy and

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What is the maximum number of turns for the graph of f(x)=x^4+3x^2?

Stels [109]

Answer:

The turns of a graph is represented by the number of maximum or minimum that the function has.

If we differenciate f(x) we get:

f'(x)=4x^3+6x

f'(x)=2x(2x^2 + 3)

Therefore f'(x) =0, when x=0. Given that negative roots are not defined.

Therefore, the number of turns will be given by the number of solutions of f'(x) which is 1.

Attached you find the graph of the function which confirms the number of turns.

If the function had other solutions, the maximum number of turns it could have is 3! because f'(x) is a third degree polynomial, therefore it can't have more than 3 solutions!

6 0

3 years ago

When the sum of \, 528 \, and three times a positive number is subtracted from the square of the number, the result is \, 120. F

aleksandr82 [10.1K]

Let $x$ be the unknown number. So, three times that number means $3x$ , and the square of the number is $x^2$

We have to sum 528 and three times the number, so we have $528+3x$

Then, we have to subtract this number from $x^2$ , so we have

$x^2-(3x+528)$

The result is 120, so the equation is

$x^2 - 3x - 528 = 120 \iff x^2 - 3x - 648 = 0$

This is a quadratic equation, i.e. an equation like $ax^2+bx+c=0$ . These equation can be solved - assuming they have a solution - with the following formula

$x_{1,2} = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

If you plug the values from your equation, you have

$x_{1,2} = \dfrac{3\pm\sqrt{9-4\cdot(-648)}}{2} = \dfrac{3\pm\sqrt{9+2592}}{2} = \dfrac{3\pm\sqrt{2601}}{2} = \dfrac{3\pm51}{2}$

So, the two solutions would be

$x = \dfrac{3+51}{2} = \dfrac{54}{2} = 27$

$x = \dfrac{3-51}{2} = \dfrac{-48}{2} = -24$

But we know that x is positive, so we only accept the solution $x = 27$

6 0

3 years ago

There is a parallelogram ABCD with diagonals AC and BD. The diagonals AC and BD intersects each other at point E. Side AB is con

grandymaker [24]

Answer:

SAS theorem

Step-by-step explanation:

Given

$\square ABCD$

$\[ \lvert \[ \lvert AB =\[ \lvert \[ \lvert CD$

$\angle BAC = \angle DCA$

Required

Which theorem shows △ABE ≅ △CDE.

From the question, we understand that:

AC and BD intersects at E.

This implies that:

$\[ \lvert \[ \lvert AE = \[ \lvert \[ \lvert EC$

and

$\[ \lvert \[ \lvert BE = \[ \lvert \[ \lvert ED$

So, the congruent sides and angles of △ABE and △CDE are:

$\[ \lvert \[ \lvert AB =\[ \lvert \[ \lvert CD$ ---- S

$\angle BAC = \angle DCA$ ---- A

$\[ \lvert \[ \lvert BE = \[ \lvert \[ \lvert ED$ or $\[ \lvert \[ \lvert AE = \[ \lvert \[ \lvert EC$ --- S

<em>Hence, the theorem that compares both triangles is the SAS theorem</em>

4 0

2 years ago

2 more than 919 998??

Pepsi [2]

2 More than 919 998 is equal to 920 000...I.e Nine hundred and twenty thousand.. It is simply the sum of 2 and 919 998.

8 0

3 years ago

In Nebraska on I-80, the speed limit is 75 mph. How long would it take you to travel 525 miles in Nebraska on I-80 if you went t

julia-pushkina [17]

the answer to your question is 7 hours just keep adding 75 together

3 0

3 years ago