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3 years ago

Which values of n degree polynomials must there definitely exist an x-intercept. Please explain all the reasoning

Mathematics

2 answers:

disa [49]3 years ago

7 0

Answer:

There will definitely exist an x-intercept for all n degree polynomials (a·xⁿ + c) that have real roots where n>0 or c = -a

Step-by-step explanation:

The x=intercept of a polynomial is the coordinates of the point on the polynomial where the equation of the polynomial f(x) = 0

Therefore, the coordinates of the x-intercept = (k, 0)

Where x = k is the solution of the f(x) = 0

Hence, there will definitely exist an x-intercept for all n degree polynomials (a·xⁿ + c) that have real roots where n>0 or c = -a.

AveGali [126]3 years ago

5 0

Answer: There must be definitely at most n value of x - intercept

Step-by-step explanation: If a polynomial has a value of n degree, then, there must be definitely at most n value of x - intercept.

For instance, The polynomial has a degree of 8, so there are at most 8 x-intercepts and at most 8–1 = 7 turning points.

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Log10 (2x + 1) - logio(3x - 2) = 1

Pavlova-9 [17]

Answer: x=3/4

Step-by-step explanation:

To solve, first express the left side as one logarithm. To do so, apply the quotient rule which is log_bM/N=log_bM-log_bN .

log((2x+1)/(3x-2))=1

Then, express the equation to its equivalent exponential form to eliminate the logarithm.

Note that the exponential form of log_b M=a is M=b^a .

Since the base of the logarithm in the given equation is not written, it indicates that its base is 10.

So re-writing the equation, it becomes:

log_10((2x+1)/(3x-2))=1

And its exponential form is:

(2x+1)/(3x-2)=10^1

(2x+1)/(3x-2)=10

Now that the equation has no more logarithm, the next step is to remove the x in the denominator.

To do so, multiply both sides by 3x-2.

(3x-2)*(2x+1)/(3x-2)=10*(3x-2)

2x+1=30x-20

Next, combine like terms.

To combine 30x and 2x, bring them together on one side of the equation. So, move 2x to the right side by subtracting both sides by 2x.

2x-2x+1=30x-2x-20

1=28x-20

To combine 20 and 1, bring them together on the side opposite the term with x. So, add both sides by 20.

1+20=28x-20+20

21=28x

And, divide both sides by 28 to have x only at the right side.

21/28=(28x)/28

3/4=x

Hence, the solution to the given equation is x=3/4 .

3 0

3 years ago

Of the pets in the pet show,

Kay [80]

Answer:

45/58 it is already in simplest form

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Jane Martin-Smith and her husband deposited $500 in an account on their wedding day and each subsequent anniversary. The money w

PolarNik [594]

Answer:

On their 25th anniversary, their account will have $850

Step-by-step explanation:

7% per year for 25 years is 170%

170% of 500 is 850

I hope this helps!

8 0

3 years ago

Read 2 more answers

Find the area of the following figure.

Zigmanuir [339]

Answer:

312

Step-by-step explanation:

Triangles

1/2 12 *10 = 6*10 = 60

there are two triangles meaning we have to multiply 60 by 2 = 120

Rectangle

12*16 = 192

Add the two and you have the area 120+192=312

5 0

3 years ago

A lighthouse operator sights a sailboat at an angle of depression of 12 degrees. If the sailboat is 80m away, how tall is the li

mart [117]

Check out the attached image for the drawing of how this would look. The drawing isn't 100% needed but it helps I think.

Based on the figure shown in the attachment, we have a right triangle with the adjacent leg of 80 (this leg is closest to the bottom 12 degree angle) and an opposite leg of h

In short,
adjacent = 80
opposite = h

We'll use the tangent rule
tan(angle) = opposite/adjacent
tan(12) = h/80
80*tan(12) = h
h = 80*tan(12)
h = 17.0045249336018 <<-- see note below

So the lighthouse is roughly 17.0045249336018 meters tall

Answer: 17.0045249336018

Note: Make sure you are in degree mode. The value is approximate. Round this answer however you need to

4 0

3 years ago