Which of the following is an equivalent expression to the expression a1/3 / a1/4

A. A1/12

B. A7/12

C. 1/1/1/a12

D. 1/7/a12

Answer:

[tex]y=-5x+22[/tex]

Step-by-step explanation:

If two lines are perpendicular to each other, the product of their slopes will be -1.

Therefore, the slope (m) of the line that is perpendicular to [tex]y=\dfrac{1}{5}x-3[/tex] is:

[tex]\begin{aligned}\implies m \cdot \dfrac{1}{5} & =-1\\m & =-5\end{aligned}[/tex]

Using the point-slope form of a linear equation, with the given point (4, 2) and the calculated slope of -5:

[tex]\begin{aligned}y-y_1 & =m(x-x_1)\\\implies y-2 & = -5(x-4)\\y-2 & = -5x+20\\y & = -5x+22\end{aligned}[/tex]

Therefore, the equation of a line that passes through the point (4, 2) and is perpendicular to the line [tex]y=\dfrac{1}{5}x-3[/tex] is:

[tex]\Large \boxed{y=-5x+22}[/tex]

Answer:

4.5 miles in 3/4 hours

Step-by-step explanation:

Find the amount of miles in 1 hour. 18/3=6

Now multiply 1.5x3=4.5

3/4=75

This is how i got 4.5 miles

Answer:

+5.5

Step-by-step explanation:

Lets say you have an apple and you apply -5.5 newtons of force to it, for it to be balanceds you have to push the opposite, which is +5.5 newtons.

Using the proportions in the table, is the sample proportion an unbiased estimator?

Yes, the mean of the sample proportions is 0.6, which is the same as the population proportion.

Mean of sample proportions = (0 + 0.5 + 0.5 + 0.5 + 0.5 + 0.5 + 0.5 + 1 + 1 + 1)/10 = 0.6

This is equal to the population proportion. Hence,

Option B is correct.

A sample proportion is a portion of the sample that corresponds to a predetermined confidence level or a confidence interval, where the confidence level represents the confidence or probability percentage for a given point, as opposed to a sample mean, which is calculated by taking the arithmetic mean of all the values of a given sample.

Read more about mean here:

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Answer:

They will need √161 feet, or about 12.69 feet of fencing. √161 is irrational because 161 is not a perfect square.

Step-by-step explanation:

[tex] {8}^{2} + {x}^{2} = {15}^{2} [/tex]

[tex]64 + {x}^{2} = 225[/tex]

[tex] {x}^{2} = 161[/tex]

[tex]x = \sqrt{161} = 12.69[/tex]

Answer:

Answer A is correct

Step-by-step explanation:

Formula to find the volume of a cylinder is :

Volume = π r² h

Given that,

radius ⇒ 8 units

height ⇒ 7 units

Let us find it now.

Volume =  π r² h

Volume = π × 8 × 8 × 7

Volume = π × 64 × 7

Volume = π × 448

Volume = 448 π units³

Answer:

820

Step-by-step explanation:

(2×58) = 116

(4×113) = 452

158+116+452+94= 820

Answer:

820

Step-by-step explanation:

First, I multiplied the ones in parenthesis and the I added 158 then I added 94.

How to help you know what to do first. PEMDAS!!

P: Parenthesis
E: Exponents
M: Multiplication
D: Division
A: Addition
S: Subtraction

That is the order you should do those kind of problems, so just remember PEMDAS!!!!!! I hope this helped!!

Answer:

A

Step-by-step explanation:

I had this same question on a quiz the other day

[tex]\begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array}~\hfill \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\\\ \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\log_3\left( \cfrac{18}{25} \right)\implies \log_3(18)~~ - ~~\log_3(25)\implies \log_3(2\cdot 3\cdot 3)~~ - ~~\log_3(5^2) \\\\\\\ [\log_3(2)+\log_3(3)+\log_3(3)]~~ - ~~2\log_3(5) \\\\\\\ [\log_3(2)+1+1]~~ - ~~2\log_3(5)\implies 2+\log_3(2)-2\log_3(5)[/tex]

Answer:

A

Step-by-step explanation:

Add the lengths together then multiply by 5 times

Answer:

the answer is 980 hope this helps

Answer:

c. 14.4

Step-by-step explanation:

when your divide 271.4^3 by 1000 you get 7.2 and then you multiply that by  2 and get 14.4 as your answer.

Answer:

Step-by-step explanation:

You need to find the equivalent of 54 by solving and finding the root of it.

GIVEN:

2*3³

3³=27

2*27=54

Change to square root.

[tex]\sf{\sqrt{2*3^3}}[/tex]

Use the exponent rule.

EXPONENT RULE:

[tex]\Longrightarrow: \sf{\:A^{B+C}=A^B\cdot \:A^C}}[/tex]

[tex]\Longrightarrow: \sf{\sqrt{2\cdot \:3^2\cdot \:3}}[/tex]

[tex]\sf{\sqrt{2\cdot \:3^2\cdot \:3}=\sqrt{3^2}\sqrt{2\cdot \:3}}[/tex]

[tex]\Longrightarrow: \sf{\sqrt{3^2}=3}[/tex]

[tex]\sf{3\sqrt{2*\:3}}[/tex]

Then, you multiply the numbers from left to right.

2*3=6

SOLUTIONS:

[tex]\Longrightarrow: \boxed{\sf{3\sqrt{6}}}[/tex]

I hope this helps. Let me know if you have any questions.

Answer: -1

Step-by-step explanation:

Add 35 to both sides

Divide both sides by 5

The measure of the angles are: ∠1  = 30°, ∠2  = 30°, ∠3 = 21°, ∠4 = 39°, ∠5 = 39°, ∠6 = 24°, ∠7 = 24°, ∠8 = 66°, ∠9 = 66°, ∠10 = 21°,  ∠11 = 60°, ∠12 = 120°, ∠13 = 60°, ∠14 = 120°, ∠15 = 48°, ∠16 = 105°, ∠17 = 27°, ∠18 = 129°, ∠19 = 51°, ∠20 = 129° and ∠21 = 51°

The given parameters are:

AB = 78°

FE = 105°

ED = 27°

CD = 42°

Considering the semicircle ABCD, the measure of arc BC is:

BC = 180 - AB - CD

This gives

BC = 180 - 78 - 42

Evaluate

BC = 60°

Considering the semicircle A FED, the measure of arc A F is:

A F = 180 - FE - ED

This gives

A F = 180 - 105 - 27

Evaluate

A F = 48°

The angle 16 subtends arc FE.

So, we have:

∠16 = FE

This gives

∠16 = 105°

Similarly, the angles 15 and 17 subtend arcs A F and ED respectively.

So, we have:

∠15 = 48°

∠17 = 27°

Angles at the circumference are half the angles at the arc.

This means that:

∠1 = Arc BC/2

∠3 = Arc CD/2

∠4 = Arc AB/2

∠5 = Arc AB/2

∠6 = Arc A F/2

∠10 = Arc CD/2

So, we have:

∠1 = 60/2 = 30°

∠3 = 42/2 = 21°

∠4 = 78/2 = 39°

∠5 = 78/2 = 39°

∠6 = 48/2 = 24°

∠10 = 42/2 = 21°

The angle in a semicircle is 90 degrees.

This means that:

∠2 = 90°

The sum of angles in a triangle is 180 degrees.

This means that:

∠11 = 180 - ∠1 - ∠2

∠12 = 180 - ∠3 - ∠4

So, we have:

∠11 = 180 - 30 - 90 = 60°

∠12 = 180 - 21 - 39 = 120°

Vertical angles are equal.

So, we have:

∠13 = ∠11

∠14 = ∠12

This gives

∠13 = 60°

∠14 = 120°

The sum of angles in a triangle is 180 degrees.

This means that:

∠18 = 180 - ∠17 - ∠6

So, we have:

∠18 = 180 - 27 - 24 = 129°

Vertical angles are equal.

So, we have:

∠20 = ∠18

This gives

∠20 = 129°

Angle on a straight line equals 180°.

So, we have:

∠21 = 180 - ∠18

This gives

∠21 = 180 - 129° = 51°

Vertical angles are equal.

So, we have:

∠19 = ∠21

This gives

∠19 = 51°

The sum of angles in a triangle is 180 degrees.

This means that:

∠7 = 180 - ∠21 - ∠16

So, we have:

∠7 = 180 - 51 - 105

∠7 = 24°

The angle in a semicircle is 90 degrees.

This means that:

∠7 + ∠8 = 90°

So, we have:

24 + ∠8 = 90°

Subtract 24 from both sides

∠8 = 66°

The sum of angles in a triangle is 180 degrees.

This means that:

∠8 = 180 - ∠15 - ∠9

So, we have:

∠8 = 180 - 48 - 66

So, we have:

∠8 = 66°

Hence, the measure of the angles are:

∠1  = 30°, ∠2  = 30°, ∠3 = 21°, ∠4 = 39°, ∠5 = 39°, ∠6 = 24°, ∠7 = 24°, ∠8 = 66°, ∠9 = 66°, ∠10 = 21°,  ∠11 = 60°, ∠12 = 120°, ∠13 = 60°, ∠14 = 120°, ∠15 = 48°, ∠16 = 105°, ∠17 = 27°, ∠18 = 129°, ∠19 = 51°, ∠20 = 129° and ∠21 = 51°

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Answer:£1.8Step-by-step explanation:2kg apples and 7kg pears = £12.701 kg pear costs £1.307 kg pear costs £(1.30×7)=£9.12 kg apples costs £(12.70-9.1)=£3.61kg apples cost £(3.6÷2)=£1.8

The measure of the angle ∠DEF is 85 degrees and the measure of the angle ∠CFE is 57 degrees.

It is a polygon that has four sides. The sum of the internal angle is 360 degrees.

In a cyclic quadrilateral, the sum of opposite angles is 180°.

∠DCE + ∠DEF = 180°

             ∠DEF = 180° - ∠DCF

             ∠DEF = 180° - 95°

             ∠DEF = 85°

Similarly for the other two angles, we have

∠CDE + ∠CFE = 180°

             ∠CFE = 180° - ∠CDE

             ∠CFE = 180° - 123°

             ∠CFE = 57°

More about the quadrilateral link is given below.

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Answer: C=2πr

Step-by-step explanation:

Answer:

9 cm.

Step-by-step explanation:

We are given that the area of a circle is 81π cm2. 81 π c m 2 . Hence the radius of the given circle is 9 cm.

Answer:

28 tiles in 85 minutes

1 tile in 3 minutes

Step-by-step explanation:

Figure out how long it takes Meg to lay one tile - 50 / 15 - 3.33 minutes per tile

This suggests that Jessica should take less than 3.33 mins to lay one tile for the statement to be correct.

If she lays 20 tiles in 85 minutes, it will take her 85 / 20 = 4.25 minutes per tile, so it can't be this one.

If she lays 24 tiles in 85 minutes, it will take her 85 / 24 = 3.5416 minutes per tile, so it can't be this one.

If she lays 28 tiles in 85 minutes, it will take her 85 / 28 = 3.0357 minutes per tile, so it can be this one.

If she lays 1 tile in 3 minutes, it will take her 3 / 1 = 3 minutes per tile, so it can be this one.

If she lays 1 tile in 4 minutes, it will take her 4 / 1 = 4 minutes per tile, so it can't be this one.

:)

The mathematical mistake that Riley made is that:
"She used the wrong common denominator." (Option A)

A common denominator is a factor that is similar to all the fractions in the sequence of equations.

Hence the correct answer is:

(2(2x² - 6x + 9))/((x-3) (x-2) (x+3))

See the correct sequence of steps below:

Step One - the Expression is given as:

(x/(x-3)(x-2)) + (3/(x+3))

Step 2 - Find the common denominator and rewrite the expression so that the numerators are above the common denominators.

Hence we have:  (x (x+3) + 3(x-3) (x-2))/(x-3)(x-2)(x+3)

Step 3  Apply the Law of Multiplicative Distribution:

Hence we have  (x² +3x+3x²-9x-6x+16)/(x-3)(x-2)(x+3)

Step 4 -  Collect Like Items

This gives us: (x²+3x²)+(3x-9x-6x)+18/(x-3)(x-2)(x+3)

Step 5 Sort for like coefficients

This gives us:  ((1+3)x² +(3-9-6) * x + 18)/(x-3)(x-2)(x+3)

Step 6 -  check for the sum or difference

This gives us: (4x²+(3-9-6) * x+ 18)/(x-3)(x-2)(x+3)

We simplify and factor the expression to get

(2(2x²-6x+6)/(x-3)(x-2)(x+3).

See the attached for full question.

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Answer:

She used the wrong common denominator.

Step-by-step explanation:

Answer:

AC

Step-by-step explanation:

sin C = opp/hyp

For angle C, the opposite leg is AB. The hypotenuse is AC.

sin C = AB/AC

Answer:

Step-by-step explanation:

Sin of an angle refers to the ratio between the opposing side and the hypotenuse.

Answer:

1. angle addition postulate

2. angle addition postulate

3. given

4. substitution

5. given

6. substitution

7. subtraction property of equality

4

2x +2x +1 =13 + x

4x - x = 13 - 1

3x = 12

x=12/3

x=4

Checking, 2*4+2*4+1 =17

13+4=17

Answer:

Step-by-step explanation:

2x + 2x + 1 = 13 + x

To find the value of x, isolate 'x'

Step1: Subtract x from both sides

2x + 2x - x + 1 = 13

Step 2: Subtract 1 from both sides

2x + 2x - x  = 13 - 1

Step3: Combine like terms

       3x   = 12

Step 3: Divide both sides by 3

          x = 12/3

x = 4

Answer:

400 entries (i think that's the answer)

Answer:

c

Step-by-step explanation:

Answer: 47

Step-by-step explanation:

Rate in hours /week = 705/ 15

since the powers are same, ignore 'em , and let's calculate the bases.

-16.(1/2)

-8.1 (upon cancellation)

ans = -8

hope it helps...!!!

Answer:

see in picture

Step-by-step explanation:

Answer:

see carefully see carefully see carefully see carefully see carefully see carefully and see carefully see carefully see carefully see carefully

Answer:

C

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let x be the hypotenuse , then

x² = 7² + 8² = 49 + 64 = 113 ( take square root of both sides )

x = [tex]\sqrt{113}[/tex]