Work out the equation of a line which has a gradient of 3 and passes through the point (-1,3)

Answer:A) -16

Step-by-step explanation:

The roots of the polynomial function f(x) = x³ - 3x² + 2 are [tex]\frac{2-\sqrt{12} }{2}, \frac{2+\sqrt{12} }{2}, \ and \ 1[/tex].

Given the polynomial function in the question:

f(x) = x³ - 3x² + 2

To find the roots of the polynomial function f(x) = x³ - 3x² + 2, we need to solve for values of x that make the function equal to zero.

f(x) = x³ - 3x² + 2

x³ - 3x² + 2 = 0

Factor the equation using the rational root test:
( x - 1 )( x² - 2x - 2 ) = 0

Equate each factor zero and solve for x:

( x - 1 ) = 0

x - 1 = 0

x = 1

( x² - 2x - 2 ) = 0

x² - 2x - 2 = 0

Using the quadratic formula:

[tex]x = \frac{-b\±\sqrt{b^2 - 4(ac)} }{2a} \\\\x = \frac{-(-2)\±\sqrt{(-2)^2 - 4(1*-2)} }{2*1} \\\\x = \frac{2\±\sqrt{4 + 8} }{2} \\\\x = \frac{2\±\sqrt{12} }{2}\\\\Hence:\\\\x = \frac{2-\sqrt{12} }{2}, \frac{2+\sqrt{12} }{2}[/tex]

Therefore, the roots are [tex]x = \frac{2-\sqrt{12} }{2}, \frac{2+\sqrt{12} }{2}, 1[/tex].

Options A, B and D are the correct answers.

Learn more about quadratic equations here: brainly.com/question/1863222

#SPJ1

compare the line y=8x-9 to y=mx+b where m is a slope and b is y-intercept

so, the line y=8x-9 has a slope m=8

by definition, the slope of a line parallel to this line will be same, m=8

by definition, the slopes of perpendicular lines are negative reciprocals to each other; so, m = -1/8

Answer: 128/15 min or 8.5 min

i

am

right

so

trust

me

i

swear

on

my

mama

this

is

correct

my

g

Answer:

m=-1/2 or m=-2/4

Step-by-step explanation:

The rate of change or slope of the given line is [tex]m=-\frac{1}{2} or m=-\frac{2}{4}[/tex]

Given :

The graph of a line . To find out the slope or rate of change , we pick two points on the line.

Two points are (-8,2) and (4,-4)

Lets apply slope formula

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

(-8,2) is (x1,y1)  

(4,-4) is (x2,y2)

Substitute all the values inside the formula

[tex]Slope = \frac{y_2-y_1}{x_2-x_1}\\slope =\frac{-4-2}{4+8} =\frac{-6}{12} =-\frac{-2}{4} =-\frac{1}{2}[/tex]

The rate of change or slope of the given line is [tex]m=-\frac{1}{2} or m=-\frac{2}{4}[/tex]

Learn more : brainly.com/question/17572076

Let us consider,

A special [tex]8-[/tex]sided die is marked with the numbers [tex]1[/tex] to [tex]8[/tex].

The odd numbers on the die are [tex]1,3,5,7.[/tex]

The even numbers are [tex]2,4,6.[/tex]

For the experimental sequence of [tex]15[/tex] rolls.

There are [tex]9[/tex] odd number  out of 15, which is [tex](3,5,7,1)[/tex].

So the experimental  probability is,

       [tex]\frac{9}{15} =\frac{3}{5} \\\\=0.60\\[/tex]

[tex]\implies0.60=60[/tex] %

The theoretical probability given that there are odd numbers [tex](1,3,5,7)[/tex] out of [tex]8[/tex] on the dice should be [tex]50[/tex] %  because [tex]\frac{1}{2}[/tex] of the numbers are prime.

Thus,

The theoretical probability is [tex]50[/tex] % .

Then,

         [tex]60[/tex]%[tex]-50[/tex]%[tex]=10[/tex]%

Hence, the experimental probability of rolling an odd number is [tex]60[/tex]%, which is [tex]10[/tex] % more than the theoretical probability [tex]50[/tex]%.

For more information,

https://brainly.com/question/537526

Answer:

60%,  10%

Step-by-step explanation:

Plato/Edmentum

Answer:

Step-by-step explanation:

1 is the answer

Answer:

1) 2,6,18,54,162,468 (multiply by 3 each time)

2) 2, -4, 8, -16, 32, -64 (i'm not sure what this is but i'm pretty confident i'm right lol)

3) 1,3,5,7,9,11 (add 2 each time)

4) 1, 2/3 , 4/6  , 8/9 ,  _ _ (i'm sorry i tried my hardest but i don't know this one)

Step-by-step explanation:

hope this helped! so sorry about 4...

Answer:

x= 1.5

y= 4.125

Step-by-step explanation:

Step one:

given the two equations

[tex]-2x - 8y = -30-------1\\\\2x + 8y = 36--------2[/tex]

Step two:

let us subtract the equations

[tex]-2x - 8y = -30-------1\\\\ -(2x + 8y = 36)--------2\\\\0x-16y=-66[/tex]

[tex]-16y=-66\\\\16y=66[/tex]

divide both sides by 16

[tex]y=66/16\\\\y=4.125[/tex]

put y= 4.125 in equation 2

[tex]2x + 8(4.125)= 36\\\\2x+33=36\\\\2x=36-33\\\\2x=3\\\\x= 3/2\\\\x= 1.5[/tex]

The third degree - polynomial can be factored into a linear factor of x+2 and a quadratic factor of 2x²+x+5.

A third degree polynomial is a collection of algebraic expressions such that the highest degree of the variable is 3 and there are no fractional degrees and exponential variable.

To factor a polynomial we will use the factor theorem to find the linear factor. Then by dividing the polynomial by the linear factor we will calculate the quadratic factor.

Given polynomial P(x) = 2x³ + 5x² + 7x + 10

Now by using the trial and error method factor theorem we see that

g(x) = (x+2) is a factor of P(x) .

Now let us find the quadratic factor as:

P(x) ÷ g(x) = ( 2x³ + 5x² + 7x + 10) ÷ (x+2) = 2x²+x+5

Hence the third degree - polynomial can be factored into a linear factor of x+2 and a quadratic factor of 2x²+x+5.

To learn more about polynomial visit:

https://brainly.com/question/20121808

Disclaimer: The correct polynomial is  P(x) = 2x³ + 5x² + 7x + 10 .

#SPJ1

Answer:

The volume of cylinder is 58.2 cm³.

Step-by-step explanation:

The formula of volume of cylinder is :

[tex]v = \pi \times {r}^{2} \times h[/tex]

So, you have to substitute the values into the expressions :

[tex]let \: r = 2.1,h = 4.2[/tex]

[tex]v = \pi \times {2.1}^{2} \times 4.2[/tex]

[tex]v = 58.2 \: {cm}^{3} \: (3sf)[/tex]

Answer:

132 km :)))))))))))))))

Step-by-step explanation:

The Hint said to find the two things in comparison

they are:

cross multiply the two equations

=99km*12lit=9lit*Xkm

=1188lit/km=9Xlit

note;

liters will annul liters

hence,

X=1188km/9

X = 132km

is the final answer

Answer:

FG = 3

Step-by-step explanation:

let me know if you are still confused!

Answer:

38.24

Step-by-step explanation:

You need to do 45.3-7.06 and you get x

Answer:

-10

Step-by-step explanation:

20-34=-14, 8/2 is just 4, so add 4 to -14 which = -10

Answer:

6.5

Step-by-step explanation:

Answer:

6.5

Step-by-step explanation:

The value of absolute value expression is equal to 133. The correct option is B.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The absolute value or modulus of a real number x abbreviated |x| in mathematics, is the non-negative value of x regardless of its sign.

The absolute value of the function will be calculated as,

E =  |−152| + |5| − |−24|

E = 152 + 5 - 24

E = 133

To know more about expression follow

https://brainly.com/question/28505282

#SPJ1

Answer:

r = 14

Step-by-step explanation:

r = -5 + 19

Simplify the right side by subtracting 5 from 19

r = 14

Answer:

9 months

Step-by-step explanation:

Given

Fabulous fitness charges a one-time fee of $90 and an additional $25 per month

let the number of months be x

and the total charges be y

y= 25x+90---------1

Wonder weights charges a one-time fee of only $ 27 dollars but charge an additional $32 each month

let the number of months be x

and the total charges be y

y= 32x+27------------2

Required

The value of x, that is the number of months

Step two:

Equating both equations we have

25x+90=32x+27

collect like terms

25x-32x=27-90

-7x=-63

7x=63

divide both sides by  7

x= 63/7

x= 9 months

Answer:

Answer is TS ≅ HG.

Step-by-step explanation:

When a triangle is rotated the corresponding parts are congruent.

Here we get image triangle S T R when we rotate the triangle G H J. So, the corresponding parts of congruent triangles are congruent.

So, ST = GH

RT= HJ

SR= GJ

<S= <G

<T = <H

<R=<J

According to them, the option TS= HG is correct.

Answer:

C. TS ≅ HG

Step-by-step explanation:

Credits to the person above!!!

Answer:The answer is 1/6

Step-by-step explanation:1/8 miles in 3/4 minutes

then, that means in 1 minute ( 1 min = 3/4 * 4/3) Emma will ride a distance of (1/8)*(4/3)= (1*4)/(8*3)= 1/6.

The answer is 1/6 (in 1 min she will ride 1/6 miles).

[tex]2(i+3)>4(1-i)[/tex]

Distribute 2 in (i+3) and 4 in (1-i)

[tex]2i+6>4-4i[/tex]

Move -4i to another side and 6 to another side. When moving to another side, you'll have to change the sign/operator to opposite (Plus -> Minus, Multiply -> Divide)

[tex]2i+4i>4-6\\6i>-2\\[/tex]

For this part, move 6 to divide -2.

[tex]i>\frac{-2}{6} \\i>\frac{-1}{3}\\i>-\frac{1}{3}[/tex]

Whenever either a numerator or a denominator is in negative, we can pull out the negative in the middle of fraction.

Note that i is the symbol of imaginary number - as defined -  i = √-1 But for this one, It's just a variable if I assume.

Thus, the answer is i > -1/3

Answer:

The answer is below

Step-by-step explanation:

The distance between two points on a coordinate plane is given by:

[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Given the location of the apartment (AP) is at A(0,0), the Chicken Shack's (CS) location is at C(3, 4) and Baskin Robbins (BR) is at the location B(- 4, 4). Hence the following distance are:

[tex]|AB|=\sqrt{(-4-0)^2+(4-0)^2} =4\sqrt{2}\ units\\\\|AC|=\sqrt{(3-0)^2+(4-0)^2}=5\ units \\\\|BC|=\sqrt{(3-(-4))^2+(4-4)^2}=7\ units[/tex]

Hence the total distance travelled = distance between the apartment and chicken shack +distance between apartment and Baskin Robbins + distance between Baskin Robbins and chicken shack

total distance travelled = AB + BC + AC = 4√2 + 7 + 5

total distance travelled = 17.66 units

Answer:

lol ok

Step-by-step explanation:

Answer:

ok Y?

Step-by-step explanation:

Given:

The three points are (-7,134), (-3,10) and (5,50).

To find:

The equation of parabola using quadratic regression.

Solution:

The general equation of quadratic regression is

[tex]y=ax^2+bx+c[/tex] ...(i)

The three points are (-7,134), (-3,10) and (5,50).

Using the graphing calculator, we get a=3, b=-1 and c=-20. Putting these values in (i), we get

[tex]y=3x^2+(-1)x+(-2)[/tex]

[tex]y=3x^2-x-2[/tex]

Therefore, the equation of parabola is [tex]y=3x^2-x-2[/tex] and the missing values in the given equation are 3, -1 and -20.