The graph below represents the function f(x) and the translated function g(x).
AVA
2x
/g(x)
a
If f(x) = x, which of the following functions could be an algebraic representation of g(x)?

a. We have GCD(34, 89) = 1; using the Euclidean algorithm,

89 = 2•34 + 21

34 = 1•21 + 13

21 = 1•13 + 8

13 = 1•8 + 5

8 = 1•5 + 3

5 = 1•3 + 2

3 = 1•2 + 1

b. Working backwards,

1 = 3 - 2

1 = 3 - (5 - 3) = 2•3 - 5

1 = 2•(8 - 5) - 5 = 2•8 - 3•5

1 = 2•8 - 3•(13 - 8) = 5•8 - 3•13

1 = 5•(21 - 13) - 3•13 = 5•21 - 8•13

1 = 5•21 - 8•(34 - 21) = 13•21 - 8•34

1 = 13•(89 - 2•34) - 8•34 = 13•89 - 34•34

c. Using the linear combination find in part b,

1 ≡ 13•89 - 34•34 (mod 89)

1 ≡ (-34)•34 (mod 89)

and

-34 ≡ -34 + 89 ≡ 55 (mod 89)

So, the inverse of 34 modulo 89 is 55.

d. Multiply both sides of the congruence by the inverse of 34:

55•34x ≡ 55•53 (mod 89)

x ≡ 2915 ≡ 32•89 + 67 ≡ 67 (mod 89)

Answer:

Option B is correct answer

Answer:

1

Step-by-step explanation:

Perpendicular lines always have the opposite slope (meaning that you have to switch the numerator and denominator) and sign when comparing to the given equation.

To start off, convert the equation to be formatted into y=. You do this by first subtracting the 3x from both sides of the equation so that it now reads 3y=-3x-273y=−3x−27 . Now, divide the whole equation by three in order to get rid of the value attached to the y. The equation should now read to be: y=-x-9y=−x−9 . Now, just switch the the slope into its opposite (which is the reciprocal) and switch the negative sign into a positive.

Answer:

Mary - 14

Mary's sister - 21

Step-by-step explanation:

Let x be the age of Mary = x

age of Mary's sister = x + 7

Add up to 35

x + x + 7 = 35

2x = 35 - 7

2x = 28

2x/2 = 28/2

x = 14

Now substitute the value of x

Mary = 14

Mary's sister = 14 + 7 = 21

21 + 14 = 35

It will take 3.3 years to accumulate $28,500  on this account

According to the compound amount formula expressed as:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

P is the principal = $25,000

A is the amount = $28,500

r is the rate in decimal = 4% = 0.04

n = 2 (semi annualy)

Substitute the given parameters into the formula as shown:

[tex]28,500=25,000(1+\frac{0.04}{2} )^{2t}\\1.14=(1+0.02)^{2t}\\1.14 = (1.02)^{2t}\\ln1.14 = 2tln1.02\\2t=\frac{ln1.14}{ln1.02}\\2t= \frac{0.13103}{0.01980}\\2t= 6.6177\\t = 3.30yrs[/tex]

Hence it will take 3.3 years to accumulate $28,500  on this account

learn more on compound interest here: https://brainly.com/question/18456266

Answer:

11 1/2

Step-by-step explanation:

So we fist should add 9 and 2 which is 11 then we should add 3/8 and 1/8 which is 4/8, which is equal to 1/2. So the answer is 11 1/2

Answer

x Is less than 4

Step-by-step explanation:

It will be an open circle and the arrow is going the left direction on the number 4

Answer:

3?

Step-by-step explanation:

is this a trick question..

24/8=3 cm

So a rat is 3 cm times as long as a mouse

Answer:

Step-by-step explanation:

The investment was

20(£15.98) = £319.60

After the sale, they want to have

£319.60 + £135.00 = £454.60

Which means each suit sells for

£454.60/20 = £22.73

The markup was

£22.73 - £20.00 = £2.73

which as a fraction of the purchase price is

£2.73/£20.00 = 0.1365

0.1365(100) = 13.65%

Answer:

7 inches

Step-by-step explanation:

5 square + 5 square=50

the square root of 50 is 7.07

7.07 to the nearest whole number is 7

Answer:

7 Inches

Step-by-step explanation:

Pythagorean Theorem: a² + b² = c²

5² + 5² = c²

50 = c²

[tex]\sqrt{50}[/tex] = c

c = 7.07

ROUND

c = 7 inches

I think any of these would work

10;18

15;28

20;35

Answer:

5:9

Step-by-step explanation:

To Find:

ratio of yellow paint to blue paint to make a particular shade of green.

Solution:

The ratio can be written as 5 to 9, or 5:9

We know that if we mix 5 gallons of blue paint with 9 gallons of yellow paint we get the particular shade of green that we want.

Then the ratio of gallons of blue paint to gallons of yellow paint is 5 to 9, or 5:9

Meaning that for every 5 gallons of blue paint we need 9 of yellow paint.

Answer:

$105

Step-by-step explanation:

Turn 25% to decimal

25% = 0.25

Now multiply it to 140

140 x .25

= $35

The discount price is 35$

Now subtract it to 140

140 - 35

= $105

Answer:

See below:

Step-by-step explanation:

Hello! I hope you are having a nice day!

We can solve this problem in two steps; Comprehending and Solving.

I'll start off with Comprehending.

Comprehending

We can start solving the problem by setting up an equation to help us solve the problem.

We know the original price is $140 and we get a 25% off.

We also know that 25% is equal to [tex]\frac{1}{4}[/tex].

Hence we can solve for this by multiplying [tex]140*\frac{1}{4}[/tex].

Solving

We can solve the problem by using the equation that we found out above.

We can use algebra to find out and simplify it!

[tex]140*\frac{1}{4}= x\\70*\frac{1}{2}=x\\x= 35[/tex]

But wait! We have only found out what 25% of $140 is, we still need to subtract it from the original equation.

$140-$35=$105

We've gotten our answer of $105.

Cheers!!

Answer:

slope = 4, y- intercept = - 35

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

2y = 8x - 70 ( divide through by 2 )

y = 4x - 35 ← in slope- intercept form

with slope m = 4 and y- intercept c = - 35

Answer: Choice A

[tex]x \le 5[/tex]

========================================

Explanation:

Any point in the shaded purple region has an x coordinate that is 5 or smaller. So we go for [tex]x \le 5[/tex]. Either x = 5 or x < 5. The boundary line is solid to indicate that points on the boundary are included in the solution set.

Answer:

y = x

Step-by-step explanation:

The equation of a line passing through the origin is

y = mx ( m is the slope )

Calculate m using the slope formula

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

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (1, 1) ← 2 points on the line

m = [tex]\frac{1-0}{1-0}[/tex] = [tex]\frac{1}{1}[/tex] = 1 , then

y = x ← equation of line

Answer:

7.6m

hope this helps :)

This expression 40=4+(n-1)3 represents the correct arithmetic progression.

What is an arithmetic progression?

Every term following the first is derived by adding a constant value, known as the common difference, in an arithmetic progression.

We have,

4 + 7 + 10 + 13 + 16 + 19 + 22 + 25 + 28 +31 + 34 + 37 + 40

Arithmetic progression formula:

                             [tex]a_{n}=a_{1}+(n-1)d[/tex]

where

[tex]a_{n}[/tex] = the nᵗʰ term in the sequence

[tex]a_{1}[/tex] = the first term in the sequence

[tex]d[/tex] = the common difference between terms

By using arithmetic progression formula we can find last term of an Arithmetic series.

                    [tex]a_{n}=a_{1}+(n-1)d[/tex]

                    [tex]a_{n}[/tex]= 4 + (n-1)3

                    [tex]a_{n}[/tex] = 4 + (13-1)3

                     [tex]a_{n}[/tex]  = 40.

we have calculated the last term by using arithmetic progression formula which is 40.

Hence, This expression 40=4+(n-1)3 represents the correct arithmetic progression.

To learn more about arithmetic progression from the given link,

https://brainly.com/question/24191546

#SPJ1

Answer:

15 pairs

Step-by-step explanation:

total:$20

cat food: $8:50

two pair of socks: $1.50

$20 - $8.50= $11.50(the rest of the money)

the rest is divided by the price of the socks to obtain how may socks you can pay with $11.50.

$11.50÷$1.50≈ 7.6

Now you multiply 7.6 by two to get the exact amount of socks with the offer.

7.6×2≈15.2

15.2≈15

So with $11.50 you will buy 14 socks for 1.50 every two pairs and a pair for 0.75

Answer:

16 road trips

Step-by-step explanation:

Answer:

x = 0

Step-by-step explanation:

[tex]\frac{3}{2}(\frac{7}{3}x + 1) = \frac{3}{2}[/tex]

To start, let's multiply each side by the reciprocal of [tex]\frac{3}{2}[/tex].  Multiplying a fraction by its reciprocal gives us 1, which will make the left side of our equation simpler.

[tex]\frac{2}3} * \frac{3}{2}(\frac{7}{3}x + 1) = \frac{2}3} * \frac{3}{2}[/tex]

[tex]\frac{2}{3} * \frac{3}{2} = 1[/tex], so we have:

[tex]1(\frac{7}{3}x + 1) = 1[/tex] or [tex]\frac{7}{3}x + 1= 1[/tex]

Next, we can subtract 1 from both sides to further simplify the left side:

[tex]\frac{7}{3}x + 1 - 1= 1 - 1\\\frac{7}{3}x=0[/tex]

Finally, we can multiply by the reciprocal of [tex]\frac{7}{3}[/tex] on both sides in order to isolate x on the left.  Anything multiplied by 0 = 0, so now we have:

x = 0

7/2x + 3/2 = 3/2 <=> 7/2x = 0 <=> x=0

Answer:

5

Step-by-step explanation:

trust

Answer:

(4+6)/(2•1)

(4+6=10)/(2×1=2)

10÷2

5

Answer:

29

Step-by-step explanation:

We first need to know what 1-digit numbers add up to 11.

One digit numbers that add up to 11 are:

2 and 9

3 and 8

4 and 7

5 and 6.

The only pair here who's difference is 7 is: 2 and 9.

9 and 2 wont work because it's even, So the answer is 2 and 9 or 29.

Steps are in the attachment.

Note :-

=》2 is taken as negative & also taken out of the square root as it's the common factor.

______

⚜ Hope it helps :))

Answer:

124.409

Step-by-step explanation:

sana makatulong sa inyong lahat

It will take 3 years and 4 months to accumulate $ 28,500.

To determine, if an amount of $ 25,000 is deposited into a saving account at an interest rate 4%, compounded semi-annually, how long will it take to accumulate on this account $ 28,500, the following calculation must be performed:

Therefore, it will take 3 years and 4 months to accumulate $ 28,500.

Learn more in https://brainly.com/question/23251895

Answer:

x=9

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

You were on the right track, but 3-2 = 1, so the exponent of (x-4) is 1.

Answer:

C and B

Step-by-step explanation:

(6)

[tex]\frac{(x-4)^3(3x+6)}{(x-4)^2}[/tex]

Cancel (x - 4)³ on numerator with (x - 4)² on denominator

leaving (x - 4) on numerator and 1 on denominator

= (x - 4)(3x + 6) → C

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

Using the rule of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex] , then

4a² × 7[tex]a^{\frac{1}{2} }[/tex]

= 4 × 7 × a² × [tex]a^{\frac{1}{2} }[/tex]

= 28 × [tex]a^{\frac{4}{2} }[/tex] × [tex]a^{\frac{1}{2} }[/tex]

= 28 × [tex]a^{(\frac{4}{2}+\frac{1}{2}) }[/tex]

= 28[tex]a^{\frac{5}{2} }[/tex] → B

Answer:

Step-by-step explanation:

27x3=81

Answer:

It's 3 hope it's help....