If a polynomial function f(x) has roots -9 and 7-i, what must be a factor of f(x)
(x-(7+i))
(x-(-7-i))
(x+(7+i))
(x+(7-i))

Answer;

x² = 42 - 2

3

Step-by-step explanation:

#carryonlearning

Answer:

Step-by-step explanation:

y² - 3x² = 6

Subtract y² from both sides

-3x² = 6 - y²

Divide by -3

[tex]\frac{-3x^{2}}{-3}=\frac{6-y^{2}}{-3}\\\\x^{2}=\frac{y^{2}-6}{3}[/tex]

Answer:

x = –1

Step-by-step explanation:

From the question given above, the following data were obtained:

y = √(–2x + 7)

y = 3

x =?

The value of x can be obtained as follow:

y = √(–2x + 7)

3 = √(–2x + 7)

Take the square of both side

3² = –2x + 7

9 = –2x + 7

Collect like terms

9 – 7 = –2x

2 = –2x

Divide both side by –2

x = 2 / –2

x = –1

Answer:

See Below.

Step-by-step explanation:

Problem 1)

We want to simplify:

[tex]\displaystyle \frac{a+2}{a^2+a-2}+\frac{3}{a^2-1}[/tex]

First, let's factor the denominators of each term. For the second term, we can use the difference of two squares. Hence:

[tex]\displaystyle =\frac{a+2}{(a+2)(a-1)}+\frac{3}{(a+1)(a-1)}[/tex]

Now, create a common denominator. To do this, we can multiply the first term by (a + 1) and the second term by (a + 2). Hence:

[tex]\displaystyle =\frac{(a+2)(a+1)}{(a+2)(a-1)(a+1)}+\frac{3(a+2)}{(a+2)(a-1)(a+1)}[/tex]

Add the fractions:

[tex]\displaystyle =\frac{(a+2)(a+1)+3(a+2)}{(a+2)(a-1)(a+1)}[/tex]

Factor:

[tex]\displaystyle =\frac{(a+2)((a+1)+3)}{(a+2)(a-1)(a+1)}[/tex]

Simplify:

[tex]\displaystyle =\frac{a+4}{(a-1)(a+1)}[/tex]

We can expand. Therefore:

[tex]\displaystyle =\frac{a+4}{a^2-1}[/tex]

Problem 2)

We want to simplify:

[tex]\displaystyle \frac{1}{(a-b)(b-c)}+\frac{1}{(c-b)(a-c)}[/tex]

Again, let's create a common denominator. First, let's factor out a negative from the second term:

[tex]\displaystyle \begin{aligned} \displaystyle &= \frac{1}{(a-b)(b-c)}+\frac{1}{(-(b-c))(a-c)}\\\\&=\displaystyle \frac{1}{(a-b)(b-c)}-\frac{1}{(b-c)(a-c)}\\\end{aligned}[/tex]

Now to create a common denominator, we can multiply the first term by (a - c) and the second term by (a - b). Hence:

[tex]\displaystyle =\frac{(a-c)}{(a-b)(b-c)(a-c)}-\frac{(a-b)}{(a-b)(b-c)(a-c)}[/tex]

Subtract the fractions:

[tex]\displaystyle =\frac{(a-c)-(a-b)}{(a-b)(b-c)(a-c)}[/tex]

Distribute and simplify:

[tex]\displaystyle =\frac{a-c-a+b}{(a-b)(b-c)(a-c)}=\frac{b-c}{(a-b)(b-c)(a-c)}[/tex]

Cancel. Hence:

[tex]\displaystyle =\frac{1}{(a-b)(a-c)}[/tex]

Please find attached photograph for your answer.

Hope it helps

Do comment if you have any query

Step-by-step explanation:

hope it helps

Answer:

Step-by-step explanation:

Multiply the numbers. For multiplying variables, if they have same variables, add the exponents.

(3a²b⁷)*(5a³b⁸) = 3*5* a²⁺³ *b⁷⁺⁸

                         = 15a⁵b¹⁵

Answer:

0.84 kg

Step-by-step explanation:

Given that :

Weight per liter = 1.12kg per liter

That is 1 Litre weighs 1.12 kilogram

The weight of saline solution of 0.75 Litre will be :

1 Litre = 1.12 kg

0.75 Litre = x

Cross multiply :

1 * x = 1.12 * 0.75

x = 0.84 kg

Hence, 0.75 Litre weighs 0.84 kg

Answer: y = 25 - 2x

Step-by-step explanation:

y = mx + b

y = -2x + 25

Step-by-step explanation:

First find h(10)

h(10)=2(10)-8

h(10)=12

Now plug in 12 as the value of x in g(x) ie.g(12)

So g(12)=√12-4=√8=2√2

Answer:

3/4=176

Step-by-step explanation:

Answer:

3/4 = b/176

Step-by-step explanation:

pls give me brainliest

Answer:its Graph C

(According to the law of Nicoloas Sadi Carnot)

Answer:

2a+15 = 125(being alternate angle)

or,2a = 125-15

or,2a = 110

or,a = 110÷2

,a = 55

again,2a+15+b+30=180(Being co-interior angle)

or,2×55+15+b+30=180

or,110+15+30+b=180

or,155+b=180

or,b=180-155

Therfore,b=25

Answer:

AG = 18

Step-by-step explanation:

The relationship of the segments created is one is 1/3 (shorter) and the other (longer) is 2/3 of the total length.

Lets make x represent AG.

So, 2/3 of x is 12

or

[tex]\frac{2}{3}[/tex]x = 12

Multiply both sides by the reciprocal of [tex]\frac{2}{3}[/tex] , which is [tex]\frac{3}{2}[/tex].

( [tex]\frac{3}{2}[/tex]) [tex]\frac{2}{3}[/tex]x = 12 ([tex]\frac{3}{2}[/tex])  (x is left alone, the fractions = 1 when multiplied)

x = 12 ([tex]\frac{3}{2}[/tex])         ( 12 times 3 = 36, divided by 2 = 18)    

x = 18

Hello,

[tex]f^{-1}(-3)=-1\\[/tex]

You have just to read the arrows un reversed order:

in f we find (-1,-3)  so in f^{-1} we find (-1,-3)^{-1}=(-3,-1)

Answer:

23

Step-by-step explanation:

-18+(18+5) = 5,

so adding any integer that is greater than (18+5)=23 will give a sum that is greater than 5.

Answered by GAUTHMATH

Answer:

Augusto vivió durante 75 años cumplidos, muriendo casi un mes antes de cumplir 76 años.

Step-by-step explanation:

Dado que Augusto nació en Roma el 23 de septiembre del año 63 a. C y fue el primer emperador romano que gobernó entre el año 27 a. C y 14 d. C considerándose como el emperador con el reinado más prolongado de la historia, y después de su muerte el 19 de agosto del año 14 d. C el senado romano lo inmortalizó glorificando su legado, por esta razón, varios de los emperadores que lo siguieron adoptaron sus nombres, para determinar cuántos años cumplidos vivió Augusto se debe realizar el siguiente cálculo:

Nacimiento: 23/09/63 AC

Primer año: 23/09/62 AC

Tercer año: 23/09/60 AC

Sesenta y dos años: 23/09/01 AC

Sesenta y tres años: 23/09/01 DC

Setenta y tres años: 23/09/11 DC

Setenta y cinco años: 23/09/13 DC

Así, Augusto vivió durante 75 años cumplidos, muriendo casi un mes antes de cumplir 76 años.

Answer:

x = 4

Step-by-step explanation:

steps are in the pic above.

Answer:

D

Step-by-step explanation:

First find h(3)

2(3)-2= 4

then find g(4)

4³-5= 59

Answer:

I think it would be 4 apples for each of them !

Step-by-step explanation:

its division. you had to do 12 ÷ 3

Answer:

The answer is 4 apples per child.

Step-by-step explanation:

If we have 12 apples and 3 children we write as a ratio like this:

12:3

So we have to figure out how many apples each child gets to have.

Next, we cancel out 3 from 12 and 3 which becomes:

4:1

So each child gets 4 apples.

I hope this helps!

Answer:

Values of y in order: 0, 2, 4, 6

Step-by-step explanation:

Hi there!

In the table, the first value of x is -2. To find the value of y for this row of the table, we can use the given equation [tex]y=2x+4[/tex].

[tex]y=2x+4[/tex]

Plug in -2 as the value of x

[tex]y=2(-2)+4\\y=-4+4\\y=0[/tex]

Therefore, y is 0 when x is -2. (In the table, in the row where x is -2, y would be 0.)

We repeat this process for the rest of the values in the table.

When x=-1:

[tex]y=2(-1)+4\\y=-2+4\\y=2[/tex]

When x=0:

[tex]y=2(0)+4\\y=0+4\\y=4[/tex]

When x=1:

[tex]y=2(1)+4\\y=2+4\\y=6[/tex]

I hope this helps!

Answer:

option c

Step-by-step explanation:

Quadratic function f(x) = ax² + bx  +c

Here the the co-efficient of x,  that is a tells if the graph is wider or narrower.

1) a < 1  that is if a is decimal less than 1, then the graph is wider.

2) a > 1, then the graph is narrow.

Hello,

the line passing through (5,2) and (1,0) has for equation:

y-0=(x-1)*(-2)/(-4) or y=x/2-0.5

if y= 5 then 5=x/2-0.5 ==> 5.5=x/2 ==> x=11

Answer C

Answer:

C

Step-by-step explanation:

Since the points lie on the same line then the slope between consecutive points will be the same.

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (5, 2) and (x₂, y₂ ) = (1, 0)

m = [tex]\frac{0-2}{1-5}[/tex] = [tex]\frac{-2}{-4}[/tex] = [tex]\frac{1}{2}[/tex]

Calculate the slope again and equate to [tex]\frac{1}{2}[/tex]

with (x₁, y₁ ) = (1, 0) and (x₂, y₂ ) = (a, 5)

m = [tex]\frac{5-0}{a-1}[/tex] = [tex]\frac{1}{2}[/tex] , so

[tex]\frac{5}{a-1}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

a - 1 = 10 ( add 1 to both sides )

a = 11

Answer:

Meena has twelve (12) ₹20 notes and thirty six (36) ₹10 notes

Step-by-step explanation:

The amount Meena has as notes in ₹10 and ₹20 denominations = ₹600

The number of ₹10 notes = 3 × The number of ₹20 notes

Let 'x' represent the number of ₹20 notes Meena has, we get;

The number of ₹10 notes = 3 × x

The total number of notes = x × 20 + 3·x × 10 = 50·x = ₹600

∴ 600/50 = 12

The number of the ₹20 notes, x = 12

The number of the ₹10 = 3 × x

∴ The number of the ₹10 = 3 × 12 = 36

Answer:

Third option:

Ax + By < 0

Step-by-step explanation:

The general form of an inequality is:

(something)  (symbol)  (another thing).

Where the symbols can be:

> = "larger than"

< = "smaller than"

≤ = "smaller than or equal to"

≥ = "larger than or equal to"

So, a given inequality can be:

K > M

This means that K is larger than M.

From the given options, the only one that has this general form is the third option:

Ax + By < 0

This can be read as:

"A times x, plus B times y, is smaller than zero"

Therefore, f(c) = 3c+5

OPTION B is the correct answer

Answer:

(B) f(c) = 3c + 5

Step-by-step explanation:

Since variable "c" is the independent variable, that means in terms of y = mx + b, c would be the variable "x".

So that means to rewrite 6c = 2p - 10, you would solve for p, because p would equal y in the formula.

Use basic algebra to solve for p:

6c = 2p - 10

6c + 10 = 2p

3c + 5 = p

p = 3c + 5 or f(c) = 3c + 5

Hope it helps (●'◡'●)

Answer:

x+y-5=0

Step-by-step explanation:

let eqn Perpendicular to eqn 5y-5x=-20 be -5x-5y+k=0------(1)

eqn (1) passes through (-3,8)

-5×-3-5×8+k=0

15-40+k=0

K=25

since required eqn perpendicular to 5y-5x=-20 is -5x-5y+25=0

x+y-5=0ans.

Answer:

Estimating the economic impact of climate change from weather variation

Step-by-step explanation:

Estimating the economic impact of climate change from weather variation:If economists are going to be able to offer clear guidance about the appropriate ambition of climate change policy, we need firmer damage estimates.This column introduces a new model that prices farmers’ ex-post and ex-ante adaptations to weather changes and forecasts. #accelerationism

Answer:

A

Step-by-step explanation:

6/3 = 2

Answer:

$2 each

Step-by-step explanation:

3 pounds of apples for $6

$6÷3 lbs= $2 each pound

Answer:

2/5

Step-by-step explanation:

18x+12x=-4+16

30x=12

x=2/5

Answer:

18x-16=-12x-4

18x+12x=-4+16

30x=12

x=12/30

x=2/5

Answer:

t > 28

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

1,2 are both supplementary

Answer:

Tom earns $7.00 per hour