Determine the period.

Acellus

find the value of n.

8 × 2^3n = 2^12

n = 3

[tex]\sf\ given \:: \: 8 \times 2 ^{3n} [/tex]

[tex]\sf\rightarrow 8 \times 2 ^{3n} \: = {2}^{12} [/tex]

[tex]\sf\rightarrow {2}^{3n} = {2}^{12} \: \: (8 = {2}^{3} )[/tex]

[tex] \sf\rightarrow {2}^{3n + 3} = {2}^{12} \: \: \: ( {a}^{m} \times {a}^{n} = {a}^{m + n} )[/tex]

Equating powers since bases are same.

[tex]\sf\rightarrow 3n \: + 3 = 12[/tex]

[tex]\sf\rightarrow 3n \: + 3 - 3 = 12 - 3[/tex]

[tex]\sf\rightarrow 3n = 9[/tex]

Divide both sides by 3.

[tex]\sf\rightarrow n = 3[/tex]

Thus the value of n is 3 .

Let's see

[tex]\\ \rm\Rrightarrow 1\dfrac{1}{5}\times2\dfrac{1}{3}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{6}{5}\times \dfrac{7}{3}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{6(7)}{5(3)}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{42}{15}[/tex]

[tex]\\ \rm\Rrightarrow2 \dfrac{12}{15}[/tex]

Answer:

b, d, e

Step-by-step explanation:

Answer:

B, D, E

Read explanation... it always helps...

Step-by-step explanation:

alrighty, we know that anything positive multiplied by anything negative results in a negative number....

with that said.... b, d, and e are the only answer choices that result in a negative number that matches the expression -5/19

i hope this helps!!!

Answer:

three four five

u welcome glam rock freddy

Answer to your question

-6x sqrt21x

Answer:

120 meters

Step-by-step explanation:

The triangle area using Heron's formula

Heron's formula gives the area of a triangle when the length of all three sides is known. There is no need to calculate angles or other distances in the triangle first. Heron's formula works equally well in all cases and types of triangles.

[tex]T=\sqrt{s(s-a)(s-b)(s-c)} \\[/tex]

[tex]T=\sqrt{25(25-17)(25-17)(25-16)}[/tex]

[tex]T=\sqrt{14400} =120[/tex]

Answer:

Step-by-step explanation:

   [tex]\boxed{Mean = \dfrac{Sum \ of \ all \ data}{number \ of data}}[/tex]

              [tex]\sf = \dfrac{234 + 247 + 236+212+248+243+176+195}{8}\\\\= \dfrac{1791}{8}\\\\= 223.875[/tex]

Arrange the numbers in ascending order.

  176 , 195 , 212 , 234 , 236 , 243 , 247, 248  

Number of data is even. So, median will be the average of 234 and 236

Median = average of the middle two terms.

            [tex]\sf = \dfrac{234+236}{2}\\\\ =\dfrac{470}{2}\\\\= 235[/tex]

Mode is the data which is occurring more number of times.

Range = maximum - minimum

           = 248 - 176

            = 72

Answer:

Y = 32 + T

Step-by-step explanation:

Given:

- temperature Y, in degree Fahrenheit (°F)

- temperature T, in degree Celsius (°C)

- Y equal to 32 more than of the temperature T

Y = 32 (more means add) + temperature T

Parallel lines are the top & bottom lines - labelled 10 & 2

A = 0.5(2+10) x 2

=12 units^2

Hope this helps!

Answer:

96 days. Divide 3072 by 32 and you get 96.

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[tex]\diamond\large\textsf{\textbf{\underline{\underline{Question:-}}}}\diamond[/tex]

       Which of the following ordered pairs are y-intercepts?

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and How to solve:-}}}}\diamond[/tex]

All y-intercepts have an x-coordinate of 0.

So a y-intercept looks like this:-

[tex]\sf{(0,b)}[/tex]

Where:-

        b - y-intercept

So we conclude that the right options are:-

[tex]\square\!\!\!\!\!\Large\checkmark[/tex] (0,0)

[tex]\square\!\!\!\!\!\Large\checkmark[/tex] (0, -7)

[tex]\square\!\!\!\!\!\Large\checkmark[/tex] (0, -0.25)

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

If the value of x will be 11 degrees. Then the measure of angle ∠AEB will be 72 degrees.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Vertically opposite angle - When two lines intersect, then their opposite angles are equal.

Two lines AC and BD are intersecting each other at point E.

The angle ∠AEB = 7x - 5 and the angle ∠CED = 2(4x - 8).

Then the measure of angle ∠AEB will be

We know the angle ∠AEB and ∠CED are the vertically opposite angle. Then they both are equal.

∠AEB = ∠CED

7x - 5 = 2 (4x - 8)

7x - 5 = 8x - 16

16 - 5 = 8x - 7x

      x = 11

Then the measure of angle ∠AEB will be

∠AEB = 7x - 5

∠AEB = 7 (11) - 5

∠AEB = 77 - 5

∠AEB = 72°

More about the angled link is given below.

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Answer:

254.34 square feet

Step-by-step explanation:

Area of a circle: πr²

Given:

Substitute the given values into the formula:

A = (3.14)(9)²

A = (3.14)(81)

A = 254.34 ft²

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Answer:

D : 66

Step-by-step explanation:

separate the composite figure into 3 different shapes then multiple then find the area of them all. after this just add them and you're good to go

also to get the area of a triangle you gotta add both sides then divide by 2.

The time at which the buses will leave at the same time is 8:40 am.

A factor is a number that divides another number, leaving no remainder

Example: 3 x 2 = 6

2 is a factor of 3.

We have,

Buses:

X leaves every 25 minutes.

Y leaves every 20 minutes.

We need to find the least common multiples of 25 and 20.

25 x 4 = 100

20 x 5 = 100

100 is our least common multiple of 25 and 20.

We see that,

4 is a factor of 24 which gives 100.

This means after 4 times, bus X will leave with bus Y at the same time.

5 is a factor of 20 which gives 100.

This means after 5 times, bus Y will leave with bus X at the same time.

The first buses to X and Y leave a bus station at 7 am.

After 100 minutes, buses X and Y will leave at the same time.

= 7am + 100 minutes

= 7 + 60 minutes + 40 minutes

= 7 + 1 hour + 40 minutes

= 8:40 am

Thus,

The time at which the buses will leave at the same time is 8:40 am.

Learn more about factors here:

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Answer:

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

The number of loaves of bread remaining can only go as low as ZERO (you can't have negative loaves) ...and can only go as high as when h = 0

     so    0 = 42-3.5 h    

             3.5 h = 42

                h = 12       and   min is  h = 0   ( when there are 42 loaves to start)

So:

0≤ h ≤ 12

The length of arc JL is 24.46 units see attachment for diagram.

An arc is a part of the circumference of a circle that meets two radii of a circle to form a sector.

Analysis:

From bigger triangle, if we bisect 144, the line meets JL at 90°.

To find AL,

sin 72 = AL/6

AL = 6 sin 72 = 5.71

To find the angle at O

∠O = 2∠K ( twice angle at circumference is equal to angle at center)

∠O = 2 (144) = 288°

For smaller right-angled triangle,

sin 144 = AL/OL

sin 144 = 5.71/OL

OL = radius of circle =  5.71/0.587 = 9.73 unit

length of arc JL = ∅/360 x 2πr

= 144/360 x 2 x 3.142 x 9.73 = 24.46 units

In conclusion, the length of arc JL is 24.46 units

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Answer:

Elena incorrectly used the slant height instead of the height.

Step-by-step explanation:

Answer:

its b

Step-by-step explanation:

i got it right

Answer:

1) 45%

2) 24%

Step-by-step explanation:

1) Total number of people surveyed = 26 + 84 + 72 + 34 = 216

    number of people who own a smartphone = 26 + 72 = 98

           ∴ relative frequency = [tex]\frac{98}{216}[/tex]   ˣ   100 = 45%

2) Total number of elementary school students = 26 + 84 = 110

               ∴ relative frequency = [tex]\frac{26}{110}[/tex]   ˣ   100 = 24%

Hope this helps!

Answer:

B

Step-by-step explanation:

We know that AB has endpoints at A(4, -3) and B(3, 7).

To find Line D, which is the perpendicular bisector of AB, we first need to find the slope of AB and its midpoint.

So, let's find the slope of AB using the slope formula:

Let (4, -3) be (x₁, y₁) and let (3, 7) be (x₂, y₂). Substitute them into the slope formula:

So, the slope of AB is -10.

Remember that the slopes of perpendicular lines are negative reciprocals of each other.

Therefore, the slope of our Line D is the negative reciprocal of -10. Which is -10 flipped and multiplied by a negative.

So, Line D has a slope of 1/10.

Now, since Line D is also the perpendicular bisector of AB, we need to find the midpoint of AB since Line D must pass through this point.

To find the midpoint, we can use the midpoint formula:

We can again let (4, -3) be (x₁, y₁) and let (3, 7) be (x₂, y₂). Substitute them into the midpoint formula to obtain:

Evaluate. So, the midpoint is:

Now, we can find the equation of our Line D. We know that its slope is 1/10, and that it must pass through (3.5, 2). So, we can use the point-slope form:

Where m is the slope. Let's let (3.5, 2) be (x₁, y₁) and substitute 1/10 for m. This yields:

This is the same as choice C. So, choice C is indeed an equation of Line D.

We can distribute the right to obtain:

Add 2 to both sides to acquire:

This is the same as choice D. So, choice D is indeed an equation of Line D.

Moreover, we can put this into standard form by multiply everything by 10, which gives:

Subtracting x from both sides yields:

This is the same as A. So, choice A is also an equation of Line D.

There is no way to acquire choice B. So, B is not an equation of Line D.

Therefore, our answer is B.

And we're done!

Answer:

s=55°

Step-by-step explanation:

sum of angles of the inside pentagon is 540°

2s+2s+1s+130°+135° =540°

5s+265°=540°

5s=540°-265°

5s=275°

5s/5=275°/5

s=55°

Answer:

AB = 12 in

Step-by-step explanation:

given a tangent and a secant from an external point to the circle, then the square of the measure of the tangent is equal to the product of the measures of the secant's external part and the entire secant, that is

AB² = BC × BD = 8 × 18 = 144 ( take square root of both sides )

AB = [tex]\sqrt{144}[/tex] = 12

Answer:

AB = 12 in

Step-by-step explanation:

Theorem

When a secant segment and a tangent segment meet at an exterior point, the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.

Secant: a straight line that intersects a circle at two points.

Tangent: a straight line that touches a circle at only one point.

Given:

[tex]\sf AB^2=BD \cdot BC[/tex]

[tex]\implies \sf AB^2=(8+10) \cdot 8[/tex]

[tex]\implies \sf AB^2=18 \cdot 8[/tex]

[tex]\implies \sf AB^2=144[/tex]

[tex]\implies \sf AB=\pm\sqrt{144}[/tex]

[tex]\implies \sf AB=\pm 12[/tex]

As distance is positive, AB = 12 in