How can polynomial functions be written when given the zeros?

Answer:

Width of rectangle = 5 cm

Length of rectangle =  17 cm

Step-by-step explanation:

Let the dimensions of rectangle:

Width of rectangle = x

Length of rectangle = 3x+2

Area of rectangle = 85 cm

We need to find dimensions of rectangle i.e length and width.

The formula used is: [tex]Area\:of\:rectangle=Length\times Width[/tex]

Putting values and finding dimensions

[tex]Area\:of\:rectangle=Length\times Width\\85=3x+2 \times x\\85=3x^2+2x\\The\;equation\:will\:be:\\3x^2+2x-85=0[/tex]

Now, finding value of x using quadratic formula:

[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

We have, a =3, b =2 and c=-85

[tex]x=\frac{-2\pm \sqrt{(2)^2-4(3)(-85)}}{2(3)}\\x=\frac{-2\pm \sqrt{4+1020}}{6}\\x=\frac{-2\pm \sqrt{1024}}{6}\\x=\frac{-2\pm 32}{6}\\x=\frac{-2+ 32}{6}\:or\:x=\frac{-2- 32}{6}\\x=5\:or\:x=-5.6[/tex]

So, we get x = 5 and x = -5.6

But since the width of rectangle cannot be negative so, we would consider x = 5

Now, the dimensions of rectangle will be:

Width of rectangle = x = 5 cm

Length of rectangle = 3x+2 = 3(5) + 2 = 15+2 = 17 cm

Answer:

65

Step-by-step explanation:

8(5) + 25 = 65

We plugged in 5 for c since we know its value.

Answer:

65

Step-by-step explanation:

8x5=40 25+40=65

I hope this helps, and have a nice day!

Answer:

Option 3

Step-by-step explanation:

The number on the inside is the dividend and the number on the outside is the divisor. So we just have to place the dividend on the top and the divisor on the bottom.

Answer:

x = 5

Step-by-step explanation:

add positive one to both -1 and 14

divide each side by 3

Answer:

[tex]\sin \alpha = \frac{5}{13}[/tex], [tex]\cos \alpha = \frac{12}{13}[/tex], [tex]\tan \alpha = \frac{5}{12}[/tex], [tex]\cot \alpha = \frac{12}{5}[/tex], [tex]\sec \alpha = \frac{13}{12}[/tex], [tex]\csc \alpha = \frac{13}{5}[/tex]

Step-by-step explanation:

The angle [tex]\alpha[/tex] is the angle opposite to the side of length 5 and adjacent to the side of length 12. From Trigonometry we remember the following relationships:

[tex]\sin \alpha = \frac{5}{\sqrt{5^{2}+12^{2}}}[/tex]

[tex]\sin \alpha = \frac{5}{13}[/tex]

[tex]\cos \alpha = \frac{12}{\sqrt{5^{2}+12^{2}}}[/tex]

[tex]\cos \alpha = \frac{12}{13}[/tex]

[tex]\tan \alpha = \frac{5}{12}[/tex]

[tex]\cot \alpha = \frac{12}{5}[/tex]

[tex]\sec \alpha = \frac{\sqrt{5^{2}+12^{2}}}{12}[/tex]

[tex]\sec \alpha = \frac{13}{12}[/tex]

[tex]\csc \alpha = \frac{\sqrt{5^{2}+12^{2}}}{5}[/tex]

[tex]\csc \alpha = \frac{13}{5}[/tex]

Answer:

X>5

Step-by-step explanation:

So first distribut the numbers

6x-12>2x+8

now subtrct 2x on both sides

4x-12>8

Now add 12 on both sides

4x>20

x>5

Answer: > 5

Step-by-step explanation: I just know

Answer:

c. m

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

It is wise to remember Slope-Intercept Form as it tell us how to graph a linear equation and tells us specific things about the line itself.

Answer:

the slope of the line is m

Step-by-step explanation:

why m?

because as you see in the equation

y=mx+b this means y-b/x = m

as you know slope is ∆y/∆x =m

it is the same as the first one .

Answer:

2 is the correct answer you know it also

Answer: This file i added shows the graph. If it doesnt help, then you can use M.a.th w.a.y to find the graph

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

So, we see that both Francie and Jake lives miles from the school. Hence, they both live the same distance from the school.

Answer:

hjskkdoododkdkdndndndndndndndnsn sorry I needed points to ask a question

Step-by-step explanation:

Cost of each golf ball = $9.31 / 18

≈ $9 / 18 = $0.5.

Answer: 0.5172222222222222

Step-by-step explanation: divide 18 by 9.31

Answer:

C = {-5,2,5} answer

Step-by-step explanation:

ccccccc

Answer: a. The sales price $568.40

b.the price for the club members is $511.56

Step-by-step explanation: I have no idea I got it wrong on porpoise to get the correct answer for u

Answer:

A and C are the correct answer

Step-by-step explanation:

Answer:

in the explanation

Step-by-step explanation:

According to the triangle midsegment theorem (if these points are midpoints),

2x + 3 is two times longer than 7, meaning it's 14.

2x+3=14

2x=11

x = 11/2

If there is an option for not enough info given, that should be right as it doesn't actually say that they are midpoints

Answer:

No.

Step-by-step explanation:

We can set this proportion up as:

[tex]\frac{4.2}{1.5}=\frac{12}{5}[/tex]

For this to be true, cross-products need to be equal:

[tex]4.2(5)=12(1.5)[/tex],

However, we can see that this is not the case:

[tex]4.2\cdot 5 \neq 12 \cdot 1.5[/tex]

Therefore, these ratios are not proportional.

Answer:

The angle the aero plane makes with the horizontal is approximately 20.925°

Step-by-step explanation:

The given parameters are;

The distance the aero plane flies = 5.6 km

The elevation to which the aero plane flies = 2 km

The angle the path of the aero plane as it takes off makes with the horizontal, θ, is the angle opposite the altitude of the right triangle formed by the aero plane's path (the hypotenuse), the horizontal, and the line drawn from the final position of the aero plane, representing the altitude (the opposite leg to angle θ)

By the trigonometric ratio for the sin of the angle, θ, we have;

[tex]sin(\theta) = \dfrac{Opposite \ leg \ length}{Hypotenuse \ length} = \dfrac{2 \ km}{5.6 \ km} = \dfrac{2}{5.6}[/tex]

Therefore, the angle θ the aero plane makes with the horizontal is given as follows;

[tex]\theta = arcsin \left (\dfrac{2}{5.6} \right ) \approx 20.925 ^{\circ}[/tex]

The angle the aero plane makes with the horizontal ≈ 20.925°.

Answer:

x = 4

Step-by-step explanation:

2 x 4 = 8

24 - 8 = 16

Answer:

x=4

Step-by-step explanation:

Answer:

Unknown number = 36

Step-by-step explanation:

Equivalent ratio means,

[tex]\frac{x_1}{y_1}=\frac{x_2}{y_2}[/tex]

If [tex]x_1=2, y_1=9[/tex] and [tex]x_2=8[/tex],

[tex]\frac{2}{9}=\frac{8}{y_2}[/tex]

By cross multiplication,

2 × y₂ = 8 × 9

2y₂ = 72

[tex]\frac{2y_2}{2}=\frac{72}{2}[/tex]

y₂ = 36

Therefore, missing number in the denominator of the fraction will be 36.

Answer:

$400

Step-by-step explanation:

140 ÷ 35% = 400

Answer:

domain=-6,5,0,-2

range=4,-1,3,4

Step-by-step explanation:

u gotta ask function to someone else sry

Answer:

The train traveled 60 kilometers per hour.

Step-by-step explanation:

300/5=60

Answer:

60 km/hours

Step-by-step explanation:

in the picture above.

Answer:

36:1

Step-by-step explanation:

Divide 504 by 14 to get the ratio

Answer:

angle side angle

Step-by-step explanation:

Answer:

[tex](x+1)(5x-4)(x-2)[/tex]

Step-by-step explanation:

We know that (x+1) is a factor, so we can use synthetic division to factor it out of [tex]5x^3-9x^2-6x+8[/tex].

Once factored, we get [tex](x+1)(5x^2-14x+8)[/tex]

Now all we need to do is factor[tex](5x^2-14x+8)[/tex]

[tex](5x^2-14x+8)=(5x-4)(x-2)[/tex]

This gives us the answer [tex](x+1)(5x-4)(x-2)[/tex].

p(x) as a product of its linear factors is:

[tex]p(x) = (x+1)(x-2)(5x-4)[/tex]

The given polynomial is:

[tex]p(x) = 5x^3-9x^2-6x+8[/tex]

The divisor = x + 1

The division expression can be written as:

[tex]\frac{5x^3 - 9x^2 -6x + 8 }{x+1} \\\\= 5x^2-14x+8[/tex]

Factorize [tex]5x^2-14x+8[/tex]

[tex]5x^2-14x+8\\\\5x^2-10x-4x+8\\\\5x(x-2)-4(x-2)\\\\(5x-4)(x-2)[/tex]

Therefore, p(x) as a product of its linear factors is written as:

[tex]p(x) = (x+1)(x-2)(5x-4)[/tex]

Learn more here: https://brainly.com/question/18818577