What is the value of [tex]\frac{81^4}{3^5}[/tex]? (Express your answer in exponential form.)

Answer:

-6 is an extraneous solution.

Step-by-step explanation:

We can start by solving this problem.

First, to remove the square root, we can square both sides.

[tex](x+4)^{2} = x + 10\\x^2 + 8x + 16 = x + 10\\[/tex]

Next, we can subtract both sides by (x+10)

[tex]x^2 + 7x + 6 = 0\\[/tex]

Then, we can factor out the equation.

[tex](x+1)(x+6) = x^2 + 7x + 6 \\= 0[/tex]

Given this, it seems like -1 and -6 would be correct. Plugging this back into the original equation, though,

-1 + 4 = √(-1 + 10)

3 = 3

-6 + 4 = √(-6+10)

-2 ≠ 2

Therefore, -6 is an extraneous solution.

Answer:

135

Step-by-step explanation:

9*5=45*3=135

Answer:

f(3) = 9

Step-by-step explanation:

In the given figure,

when x=3,

f(x)=9

substituting x=3 in f(x),

=> f(3)=9

Answer:

i don't see questions but I'll go download the app on your picture:))

4.79 × 10^-6

0.0000000734

Hope this helps! :)

Answer:question AB +BD= AD

BC+CE=BE

Step-by-step explanation:

segment addition postulate

Answer:

[tex]\frac{0.00467}{100000}[/tex]

Step-by-step explanation:

Given :

0.00467

Now,

[tex]0.00467=\frac{0.00467}{100000}[/tex]

Standard form of given equation is :

[tex]\frac{0.00467}{100000}[/tex]

Answer:

this at all so yea

Step-by-step explanation:

hihkjfnkjerbfjbfr

Answer:

this means she ate an average of 30 raisins each day

so she ate 30 on the third day

so the amount she ate each day is like this

1. 16

2. 23

3. 30

4. 37

5. 44

16 + 23 +30 +37 +44=150

Answer:

a. 30 b. 16

Step-by-step explanation:

n=number of days

a1= raisins she at on 1st day

d=increase per day

n(a1+an)/2

5(a1+a1+d(n-1))/2=150

5(2a1+4d)=300

d=7, 10a1+20(7)=300

a1+14=30

a1=16

a. a1+2d 16+14=30 b. 16

Answer

The answer is y= x-3

- - - - -

5

Explanation

Replace

f(x) with y.

y =5x+3

Swap x and y.

x =5y+3

Solve for y.

x - 3=5y

x-35=y

Answer:

y = 91

Step-by-step explanation:

y = 5² + 10(5) + 16

y = 25 + 50 + 16

y = 91

Answer:

D. SSS

Step-by-step explanation:

SSS (Side-Side-Side) is a proof of congruence where two triangles share three sides.

Answer:

SSS

Step-by-step explanation:

We are given that the triangle has all congruent sides therefore we can prove that the triangles are similar by the SSS theorem ( side - side - side )

Answer:

D option

Step-by-step explanation:

Hope this helps

the volume is 1/3 * height *area of the base (the circle) in cubic units

the area of the circle is pi*r²

wich gives us

1/3 * 11 * pi * 5²

rearrange

= 5² * 11 * 1/3 * pi

= 25*11*1/3*pi

= 275*1/3*pi

= 275/3 *pi

= (91 2/3)*pi

in cubic units

so your answer is the first option

Answer:

(x+1)^2 + (y-7)^2 = 2^2

Step-by-step explanation:

The center of the circle is at (-1,7) and the radius from the center to the edge is 2, so the equation should look like (x-h)^2 + (y-k)^2 = r^2

You would flip the signs of the center so that when you solve the equation it ends up in the correct place.

Answer:

$ 181

Step-by-step explanation:

He has total savings account= $550

If he took out every month = $ 30.75 ,

= $ 369

micheal has total balance = $ 550 - $369

= $ 181

Answer:

a) csc∅ = √53/2

b) cot ∅ = 15/√514

Step-by-step explanation:

a) The value of cot ∅ = -7/2

cos ∅ < 0

We note that cos(∅) is less than 0 in Quadrant II and III, and cot(∅) is less than 0 in the Quadrant II, therefore, we have;

∅ is in the Quadrant II

csc∅ = (√((-7)² + 2²))/2 =√53/2 ≈ 3.64

csc∅ = √53/2

b) cos∅ 15/17

∅ is in Quadrant IV

∴ cot ∅ = 15/(√(15² + 17²)) = 15/√514 ≈ 0.662

cot ∅ = 15/√514

Answer:

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Answer:

6 men are ill.

Step-by-step explanation:

the work of 30 men in 40 hours is the product

30×40

an unknown number of men (x) is sick, and now the remaining workers do the same work in 50 hours

(30-x)×50

so,

30×40 = (30-x)×50

1200 = 1500 - 50x

-300 = -50x

x = 6

Answer:

Options : B & D

Step-by-step explanation:

E(x) = 10x - 30 , where x is the number of doors she knocks

Given she has to pay her own expense.

So whatever she earns $30 is reduced from it ,for her expense.

Option A: She can earn $10 even if she does not knock

any doors - False

                 That is, x = 0

                 When x = 0 , E (x) = 10 ( 0 ) - 30 = - 30

                 => she loses $30.

Option B :Her expenses are $ 30 per week - True

                E(x) = 10x  - 30

                 Expenses are reduced from her earnings.

Option C: She will lose $10 per week if she does not knock

any doors - False.

                 Already checked on option A that if she does not knock

                 on any door, means x = 0 , then loses $30.

Option D : If she does not knock on any doors at all during

the week , she will lose $30 - True

Step-by-step explanation:

tan < BCA = x/y = 3/18= 0.1667

< BCA = arc tan 0.1667 = 9.464° => 9.46°

Given:

The expression is:

[tex]18\dfrac{2}{5}-4\dfrac{1}{10}[/tex]

To find:

The difference.

Solution:

We have,

[tex]18\dfrac{2}{5}-4\dfrac{1}{10}[/tex]

It can be rewritten as:

[tex]=\dfrac{90+2}{5}-\dfrac{40+1}{10}[/tex]

[tex]=\dfrac{92}{5}-\dfrac{41}{10}[/tex]

Taking LCM, we get

[tex]=\dfrac{184-41}{10}[/tex]

[tex]=\dfrac{143}{10}[/tex]

[tex]=\dfrac{140+3}{10}[/tex]

[tex]=14\dfrac{3}{10}[/tex]

Therefore, the value of the difference is [tex]14\dfrac{3}{10}[/tex].

Answer:

[tex]f(x) = 5x -11[/tex]  and  [tex]g(x) = \frac{x + 11}{5}[/tex]

Step-by-step explanation:

Required

The inverse pairs

Solving (a):

[tex]f(x) = 5x -11[/tex]    [tex]g(x) = \frac{x + 11}{5}[/tex]

Calculate the inverse of f(x)

[tex]f(x) = 5x -11[/tex]

Replace f(x) with y

[tex]y = 5x - 11[/tex]

Swap x and y

[tex]x = 5y - 11[/tex]

Solve for y

[tex]5y = x + 11[/tex]

[tex]y = \frac{x + 11}{5}[/tex]

So, we have:

[tex]g(x) = \frac{x + 11}{5}[/tex]

Hence, f(x) and g(x) in (a) are inverse functions

Others are not

Answer:

cost of 12 bars = $3.60

cost of 1 bar = $3.60 ÷ 12

= $0.3

hope it helps

have a nice day

Answer:

$0.30

Step-by-step explanation:

12 granola bars = $3.60

1 granola bars = $3.60/12 = $0.30

Answer:

2133$

Step-by-step explanation:

5400-(5400$ *60.5/100)

Answer:

12 mph and 16 mph

Step-by-step explanation:

distance = speed * time

56 = s * 2 + (s - 4) * 2

56 = 2s + 2s - 8

56 = 4s - 8

64 = 4s

16 = s

s = 16

s - 4 = 12

Let the speed of the faster bike = X

The slower bike would be x - 4 ( 4 mph slower)

Multiply each speed by time and add to equal total distance:

2x + 2(x-4) = 56

Simplify:

2x + 2x -8 = 56

4x -8 = 56

Add 8 to each side:

4x = 64

Divide both sides by 4:

x = 64/4

x = 16

The faster bike rode at 16 miles per hour

The slower bike traveled at 16-4 = 12 miles per hour

Answer:

7

Step-by-step explanation:

70+16x-2

68+16x=180

16x=180-112

x=112/16

x=7

Answer:

x = 7

Step-by-step explanation:

70 + 16x - 2 = 180 degree (being co interior angle)

68 + 16x = 180

16x = 180 - 68

16x = 112

x = 112/16

x = 7

Answer:

1. X-intercept

Step-by-step explanation:

Answer:

quadranttwo

linear

Step-by-step explanation:

1 across

quadranttwo

14 across

linear

Answer:

$205.60

160(1.135)+ 160(.15)

Step-by-step explanation: