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2 years ago

Which statements are true about the graphs of all nth degree polynomials?

Mathematics

2 answers:

vova2212 [387]2 years ago

6 0

The statements are true about the graphs of all nth degree polynomials are B and D.

B. It goes up and down at most a total of n times.

D. The number of x-intercepts is at most n.

vagabundo [1.1K]2 years ago

5 0

<h2>Answer:</h2>

The statement that is true about the graphs of all nth degree polynomials is:

B.) It goes up and down at most a total of n times.

D.) The number of x-intercepts is at most n.

<h2>Step-by-step explanation:</h2>

We know that the number of times the graph goes up and down depends on the number of distinct zeros of a polynomial and as we know that a polynomial of nth degree may have repetitive zero.

Hence, the graph of nth degree polynomial goes up and down at most a total of n times.

Also, the number of x-intercept is the x-value of the point where the function is zero i.e. it depends on the number of zeros of polynomial.

Hence, The number of x-intercepts is at most n.

Also, the end behavior of graph depends on degree as well as sign of the leading coefficient.

Hence, correct options are:

Option B and option: D

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Shayna enlarged a square photo by adding 10 inches to each side so it could be seen on a large poster. The area of the enlarged

Over [174]

The area of a square is expressed as the length of the side to the power of two, A = s^2. We were given the area of the enlarged photo which is 256 in^2. Also, it was stated that the length of the enlarged photo is the length of the original photo plus ten inches. So, from these statements we can make an equation to solve for x which represents the length of the original photo.

A = s^2
where s = (x+10)
A = (x+10)^2 = 256
Solving for x,
x= 6 in.

The dimensions of the original photo is 6 x 6.

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2 years ago

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The formula uppercase S = StartFraction n (a Subscript 1 Baseline plus a Subscript n Baseline) Over 2 EndFraction gives the part

yanalaym [24]

Answer:

Step-by-step explanation

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2 years ago

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A rectangular portrait measures 50cm by 70cm. It is surrounded by a rectangular frame of uniform width. If the area of the frame

snow_tiger [21]

Let us assume uniform width = x cm wide.

Length of rectangular portrait = 50cm and width of rectangular portrait = 70cm.

Therefore, length of rectangle made by frame = 50 + x+x = (2x+50) cm.

And width of rectangle made by frame = 70+x+x = (2x+70) cm.

We know, the area of rectangular portrait = 50 × 70 = 3500 cm^2.

Total area of the rectangle made by frame would be = (2x+50) * (2x+70)

We know,

Actual area of frame = Area of rectangle made by frame - area of rectangular portrait.

We also given "the area of the frame is the same as the area of the portrait."

We can setup an equation now,

3500 = (2x+50) * (2x+70) - 3500.

Subtracting 3500 from both sides, we get

3500-3500 = (2x+50) * (2x+70) - 3500-3500.

0 = (2x+50) * (2x+70) -7000.

FOIL (2x+50) * (2x+70), we get

0 = 2x*2x +2x*70 + 50*2x +50*70 - 7000.

0 = 4x^2 +140x +100x +3500 -7000.

4x^2 +240x -3500 = 0.

Dividing whole equation by 4, we get

x^2 +60x - 875 =0

Applying quadratic formula $=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ , we get

$=\frac{-60\pm \sqrt{60^2-4\cdot \:1\left(-875\right)}}{2\cdot \:1}$

$x=\frac{-60+\sqrt{60^2-4\cdot \:1\left(-875\right)}}{2\cdot \:1}=5\left(\sqrt{71}-6\right)$

$x=\frac{-60-\sqrt{60^2-4\cdot \:1\left(-875\right)}}{2\cdot \:1}:\quad -5\left(6+\sqrt{71}\right)$

We cant take negative value.

So, $x=5\left(\sqrt{71}-6\right)=12.13$

We could take approximately 12 cm.

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2 years ago

Which solution is the best estimate to the system of equations? {y=14x−2y=−2x+3 (2.2, −1.4) (0, 3) (0, −2) (1.5, 0) A system of

sertanlavr [38]

Answer:

The best estimate solution to the system of equations is (0, 3)

Step-by-step explanation:

we have

y=14x-2 ------> equation A

y=-2x+3 -----> equation B

Solve the system by elimination

Multiply the equation B by 7 both sides

(7)y=(7)(-2x+3)

7y=-14x+21 -------> equation C

Adds equation A and equation C

y=14x-2

7y=-14x+21

-----------------

y+7y=-2+21

8y=19

y=19/8

Find the value of x

y=14x-2

19/8=14x-2

19=112x-16

112x=19+16

112x=35

x=35/112

The solution is the point (35/112,19/8)

Convert to decimal number

(0.3125,2.375)

therefore

The best estimate solution to the system of equations is (0, 3)

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2 years ago

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Answer:

No you can't because just like multiplication, you cant divide anything by zero.

Step-by-step explanation:

You must evaluate the function f first. Division by 0 is undefined.

Therefore, The composition cannot be evaluated.

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