MATHEMATICS HIGH SCHOOL

Which of the number(s) below are potential roots of the function?p(x) = x4 + 22x2 – 16x – 12

Answers

Answer 1
Answer: Potential\ roots\ of\ the\ function:\n\np(x)=x^4+22x^2-16x-12\ are:\n\n\{\pm1;\pm2;\pm3;\pm4;\pm6;\pm12\}
Answer 2
Answer:

Answer:

6,1,3

Step-by-step explanation:

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Someone Please Help!!! A barrel of tomato sauce has spilled on a tile floor. The sauce flow can be expressed with the function r(t) = 2t, where t represents time in minutes and r represents how far the sauce is spreading.

The spilled sauce is creating a circular pattern on the tile. The area of the pattern can be expressed as A(r) = πr2.

Part A: Find the area of the circle of spilled sauce as a function of time, or A[r(t)]. Show your work. (6 points)

Part B: How large is the area of spilled sauce after 5 minutes? You may use 3.14 to approximate π in this problem. (4 points)

Answers

basically, r=2t
A(r)=pir^2
sub 2t for r
A(2t)=pi(2t)^2
A(2t)=4pit²


A. A=4pit²

B. t=5
A=4pi5²
A=4pi25
A=100pi
A=314 square units

Answer:

A: π(2t)^2 =   4πt^2

B: 4π5^2 5^2= 25x4= 100x3.14=314.

answer to B: 314(.159)

Step-by-step explanation:

Please Help!!!a. Write in words, a two-step sequence of transformations, that maps ΔABC to ΔA’B’C’.




b. Write a two-step ordered-pair rule, for the transformation sequence.

Answers

Answer:

a) Δ ABC is rotated around the origin by angle 180° and then translated 1

unite to the right and 3 units up

b) R (O , 180°) and T (x + 1 , y + 3)

Step-by-step explanation:

* Lets revise some transformation

- If point (x , y) rotated about the origin by angle 180° then its image

 is (-x , -y)

- If the point (x , y) translated horizontally to the right by h units

 then its image is  (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

 then its image is  (x - h , y)

- If the point (x , y) translated vertically up by k units

 then its image is  = (x , y + k)

- If the point (x , y) translated vertically down by k units

 then its image is  (x , y - k)

* Lets solve the problem

∵ Δ ABC change its place from 2nd quadrant to the 4th quadrant

  and reverse its direction Point A up and its image A" down

∵ No change in its size

∴ Triangle ABC rotates 180° clockwise around the origin

# Remember : There is no difference between rotating 180° clockwise

  or  anti-clockwise around the origin

∵ The vertices of Δ ABC are:

# A = (-3 , 5)

# B = (-3 , 2)

# C = (-1 , 2)

∵ If point (x , y) rotated about the origin by angle 180° then its image

 is (-x , -y)

∴ A'' = (3 , -5)

∴ B'' = (3 , -2)

∴ C'' = (1 , -2)

∴ Triangle ABC rotates 180° around the origin to form ΔA"B"C"

∵ The vertices of Δ A'B'C are:

# A' = (4 , -2)

# B' = (4 , 1)

# C' = (2 , 1)

- By comparing the x-coordinates and y-coordinates of points of

 Δ A''B''C'' and Δ A'B'C' we will find that every x-coordinate add by 1

 and every y-coordinate add by 3

∵ 4 - 3 = 1 and 2 - 1 = 1 ⇒ x- coordinates

∵ -2 - (-5) = -2 + 5 = 3 and 1 - (-2) = 1 + 2 = 3 ⇒ y-coordinates

∴ ΔA''B''C'' translates to the right 1 unite and up 3 units to form

  Δ A'B'C'

a) Δ ABC is rotated around the origin by angle 180° and then

   translated 1 unite to the right and 3 units up

b) R (O , 180°) and T (x + 1 , y + 3)

What is the value of the function when x = −2? y =

A graph of a function. The function graph goes through point negative 2, negative 3 and point negative 3, 0.

Answers

(x,y)
if the point (-2,-3) is on there
x=-2
y=-3

y=-3

Which represents a quadratic function?f(x) = −8x3 − 16x2 − 4x

f (x) = x 2 + 2x − 5

f(x) = + 1

f(x) = 0x2 − 9x + 7

Answers

A quadratic function is one of the form f(x) = ax^2 + bx + c, where a, b, and c are numbers with a not equal to zero. In the given question, the only function that satisfies the condition of a quadratic function is f(x) = x^2 + 2x - 5 and thus is the correct answer to the question.

Answer:

f (x) = 3/4 x ^2 + 2x − 5

Step-by-step explanation:

Mairé is thinking of two numbers. The first number is 14 less than the second number. When she adds them, she gets 40. Help her younger sister, Enya, figure out the numbers.

Answers

Using equations, the two numbers are 27 and 13, with the first number being 14 less than the second number, and their sum is 40.

How to use equations to find the two numbers?

Let's represent the two numbers as x (the second number) and y (the first number).

According to the given information:

The first number is 14 less than the second number: y = x - 14

When she adds them, she gets 40: x + y = 40

Now, we can use these two equations to find the values of x and y.

Substitute the value of y from the first equation into the second equation:

x + (x - 14) = 40

Now, solve for x:

2x - 14 = 40

2x = 54

x = 27

Now that we have the value of x, we can find y using the first equation:

y = x - 14

y = 27 - 14

y = 13

So, the two numbers are 27 and 13.

Learn more about equations on:

brainly.com/question/25678139

#SPJ3

Answer:

34 and 6 =40

Step-by-step explanation:

40 divided by 2=20 20-14=6 14+20=34

The diameter of a Frisbee is 12 in. What is the area of the Frisbee?a. 37.68 sq. in.
b. 452.16 sq. in.
c. 18.84 sq. in.
d. 113.04 sq. in.

Answers

we know that

Area of the circle is equal to

A=\pi r^(2)

where

r is the radius

in this problem

diameter=12\ in \n radius=diameter/2\n radius=12/2\n radius=6\ in

A=3.14* 6^(2)

A=113.04 in^(2)

therefore

the answer is the option

d. 113.04 sq. in.

The area of the Frisbee is about 113 in.² ( Option D )

Further explanation

The basic formula that need to be recalled is:

Circular Area = π x R²

Circle Circumference = 2 x π x R

where:

R = radius of circle

The area of sector:

\text{Area of Sector} = \frac{\text{Central Angle}}{2 \pi} * \text{Area of Circle}

The length of arc:

\text{Length of Arc} = \frac{\text{Central Angle}}{2 \pi} * \text{Circumference of Circle}

Let us now tackle the problem!

Given:

Diameter of Frisbee = d = 12 in

Unknown:

Area of Frisbee = A = ?

Solution:

Area of the Frisbee could be calculated using the area of circle as follows:

A = (1)/(4) \pi d^2

A = (1)/(4) * \pi * 12^2

A = 36 \pi ~ in.^2

A \approx \boxed {113.10 ~ in.^2}

The closest option available will be option D. 113 in.²

Learn more

Answer details

Grade: College

Subject: Mathematics

Chapter: Trigonometry

Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse, Circle , Arc , Sector , Area, Inches , Frisbee , Diameter , Radius , Trigonometry ,
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