Which logarithmic equation correctly rewrites this exponential equation? 8x = 64

Answer:

84.82 cm

Step-by-step explanation:

Volume of a cone: [tex]\frac{1}{3} \pi r^2h[/tex]

[tex]\frac{1}{3} \pi r^2h\\\\\\\\= \frac{1}{3}\pi (3)^2(9)\\\\= \frac{1}{3}\pi(9)(9)\\\\\\\= \frac{1}{3} \pi (81)\\\\= 27\pi \\[/tex]

≈ 84.82 cm

Applying the sine ratio and law of sines, the correct measurements are:

B. m∠B = 15°

E. h ≈ 31.28 ft.

Sine ratio that can be used to determine the side length of a right triangle is, sin ∅ = opposite side/hypotenuse.

Find c using the law of sines:

C = 33°

A = 180 - 48 = 132 [linear pair]

B = 180 - 33 - 132 = 15° [triangle sum theorem]

b = 20 ft

c = ?

Using the law of sines, b/sin B = c/sin C, we have:

20/sin 15 = c/sin 33

(c)(sin 15) = (20)(sin 33)

c = (20 × sin 33)/sin 15

c ≈ 42.09

Use the sine ratio to find h:

∅ = 48°

Hypotenuse = c = 42.09

Opposite = h = ?

sin 48 = h/42.09

h = (sin 48)(42.09)

h ≈ 31.28

The correct measurements are:

B. m∠B = 15°

E. h ≈ 31.28 ft

Learn more about the sine ratio on:

https://brainly.com/question/2920412

#SPJ1

Answer:

B. and E.

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

if there 2 to begin with and the bacteria dobles every hour and there were 6 hours it would be 2⁶ and when you time 2 to the power of 6 you get 64

The table represents an exponential function:

[tex]f(x) = 3^x[/tex]

Then the correct option is B.

Here we have the table:

x       y

1       3

2      9

3      27

4      81

5      243

You can see that each time that x increases by one unit, the value of is multiplied by 3. This is clearly an exponential function.

The function actually is:

[tex]f(x) = 3^x[/tex]

Evaluating it we get:

[tex]f(1) = 3^1 = 3\\\\f(2) = 3^2 = 9\\\\f(3) = 3^3 = 27\\...[/tex]

So the correct option is B, exponential.

If you want to learn more about exponential functions:

https://brainly.com/question/11464095

#SPJ1

Answer:

14n^2.

Step-by-step explanation:

This is Arithmetic with first term a =  14 and common difference d =  28.

Sum of n terms = n/2[2a + (n-1)d]

= n/2(28 +( n -1)28]

= n/2(28 + 28n - 28)

= 14n^2

Answer:

14n²

Step-by-step explanation:

14 = 14 *1

42 = 14 *3

70 = 14 *5

28n -14 = 14*2n - 14 = 14*(2n -1)

14 + 42 + 70 + ........+(28n -14) = 14*1  + 14*3  + 14*5 + ....... + 14*(2n - 1)

                                               = 14 * (1 + 3 + 5 + ......+ (2n-1) )

                                               = 14 * n²

                                               = 14n²

1 + 3 + 5 + .... +(2n -1)  ->  sum of first 'n' odd numbers.

Formula for finding sum of first 'n' odd numbers  = n²

(i) 57students liked at least one game.

(ii) 7 students who liked both the games.

(iii) 27 students liked football.

(iv) 37 students liked cricket.

(v) Below we represented the result in a Venn diagram.​

What is Venn diagram?

John Venn popularized the Venn diagram in the 1880s, which is a type of diagram that displays the logical relationship between sets. The illustrations are used in probability, logic, statistics, linguistics, and computer science to demonstrate basic set relationships and to teach rudimentary set theory.

Part (i)- We have to get number of people who like at least one game, there are total 75 students and only 18 did not like any of two games, so students who like at least one game are-

75-18 = 57

Part (ii)- There are 57 students who like at least one game, from the question statement we know that 20 students like football only and 30 liked cricket only, so student who like both games are-

57-20-30 = 7

Part (iii)- There are 7 students who liked both games and 20 who liked football only, so student who liked football are-

20+7 = 27

Part (iv)- There are 7 students who liked both games and 30 who liked cricket only, so student who liked cricket are-

30+7=37

Part (v)- Venn Diagram will look like-

To learn more about Venn diagram from below link

https://brainly.com/question/2099071

#SPJ4

Complete Question- In a group of 75 students, 20 liked football only, 30 liked cricket only and 18 did not like any of two games? (i) How many of them liked at least one game? (ii) Find the number of students who liked both the games. (iii) How many of them liked football? (iv) How many of them liked cricket? (v) Represent the result in a Venn diagram.​

Answer:

x = 19

Step-by-step explanation:

You would use vertical angles to move the 8x - 14 so that we could use the Consecutive Interior angles theorem. Which says that consecutive angles equal 180. So, you would set up your equation: 8x-14+2x+4 = 180. Add the 8 and 2 = 10. Add the -14 and 4 = -10. You get 10x-10 = 180. 180+10 = 190. 190/10 = 19. X = 19

Answer:

C

Step-by-step explanation:

Please refer to the attached photo for step by step solutions.

Note: Square roots and squares will always cancel out each other.

Answer:

Step-by-step explanation:

the third one is correct

[tex]6 \times 3 - \frac{18}{9} \\ (6 \times 3) - (18 \div 9)[/tex]

Answer:

Hello,

Step-by-step explanation:

here is the answer in a picture.

Surface area = 400 unit square

Surface area = 1100 unit square

Surface area = 1100 unit square

Surface area = 2400 unit square

The first figure is a cuboid;

Surface area of a cuboid = 2lw+2lh+2hw

L = 9

W = 11

h = 4

Surface area = 2( 9 × 11) + 2(9 × 4) + 2( 4× 11)

Surface area = 2(99) + 2(36) + 2(44)

Surface area = 198 + 72 + 88

Surface area = 400 unit square

Surface area of a triangular prism = Area of top + area of base

Area of the top = 1/ 2 b × h

Area = 1/2 × 4 × 8

Area = 16 unit square

Area of base = length × width

Area = 4× 4

Area = 16 unit square

Surface area = 16 + 16

Surface area = 1100 unit square

Surface area of a cylinder = 2πrh + 2πr² = 2 ( 3. 412 × 7. 5 × 15) + 2 ( 3. 141× 7. 5 × 7.5)

Surface area = 706. 95 + 353. 48

Surface area = 1100 unit square

Surface area of a cone =πr(r+ √h² + r2)

Surface area = [tex]3. 142 * 15 ( 15 + \sqrt{10^2 +34^2 }[/tex]

Surface area = [tex]47. 13 * 50. 44[/tex]

Surface area = 2400 unit square

Learn more about surface area here:

https://brainly.com/question/76387

#SPJ1

Answer:

Can i have the graph? THis doesn't make sense

Step-by-step explanation:

The graph of (f+g)(x) is on the coordinate plane, a straight line with a positive slope crosses the x-axis at (negative 1, 0) and crosses the y-axis at (0, 5).

The graph of a parabolic equation is a curved U-shape graph from where the domain, the range, x-intercept(s), and the y-intercept(s) can be determined.

Given that:

f(x) = -x² + 3x + 5

g(x) = x² + 2x

To find (f + g)(x), we have:

(f + g)(x) = (-x² + 3x + 5)+(x² + 2x)

(f + g)(x) = -x² + 3x + 5 +x² + 2x

(f + g)(x) = 3x + 2x + 5

(f + g)(x) = 5x + 5

Use the Slope-intercept form: We are to find the graph of y = 5x + 5

y = 5x + 5

Here:

Therefore, we can conclude that on the coordinate plane, a straight line with a positive slope crosses the x-axis at (negative 1, 0) and crosses the y-axis at (0, 5)

Learn more about parabolic equation here:

https://brainly.com/question/4061870

#SPJ1

By the definition of similar polygons, the lengths of corresponding sides are proportional.

The proportion for [tex]x=40[/tex].

As it is given in the definition, similar polygons have congruent angles and proportional sides.

Therefore, by the definition of similar polygons, the lengths of corresponding sides are proportional.

Cross multiply and solve the proportion  [tex]x[/tex] as follows:

The blank should be proportional.

[tex]\frac{12}{8} =\frac{20+x}{x}\\ 12x=160+8x\\4x=160\\x=40[/tex]

Therefore, the proportion for [tex]x=40[/tex].

Know more about similar polygons here:

https://brainly.com/question/1493409

#SPJ4

The sequence of the ball is   3, 1, 1/3, 1/9,...

The ball starts bouncing with a height of 3 feet.

Each bounce reaches a third of the height of the previous bounce.

Therefore,

a = first term = 3

r = common ratio = 1 / 3

Therefore,

nth term = arⁿ⁻¹

where

First term = 3

2nd term = 3 × (1 / 3) = 1

Third term = 3 × (1 / 3)² = 1 / 3

Fourth term = 3 × (1 / 3)³ = 1 / 9

Therefore, the sequence of the ball is   3, 1, 1/3, 1/9,...

learn more on sequence here: https://brainly.com/question/13042200

#SPJ1

The average daily balance for the month was $84.21, and the finance charge for the month was $30.13.

Given that Sally's balance on her credit card is $75.00 on the first day of August, and she makes a payment of $18.00 on August 17 and a new purchase of $41.00 on August 29, and the annual interest rate is 21.25%, to determine what is Sally's average daily balance and finance charge for the month of August, the following calculation must be made:

Therefore, the average daily balance for the month was $84.21, and the finance charge for the month was $30.13.

Learn more about averages in https://brainly.com/question/23455102

#SPJ1

The total possible number of outcomes for the season record is [tex]2^{33}[/tex].

An event that may be given a mathematical probability is known as an outcome in mathematics (an outcome of an experiment). The amount of potential outcomes for a particular experiment determines the probability assigned to each result.The result of an experiment is a number of outcomes.

According to the question,

The basketball team at a college will play 33 games next winter. There are only two possible outcomes for each game: a win or a loss.

So, the total number of possible outcomes for the season record=[tex]2^{33}[/tex].

Learn more about outcomes here:

https://brainly.com/question/25688842

#SPJ4

Answer:

26

Step-by-step explanation:

You want to know the value of x that makes y=1000. You can plug the equation in to your calculator or desmos. Look at the table for when y=1000. X is 26.

To check, plug in 26 for x. 26^2 + 20(26) - 196 = 1000.

Answer: 26 sales

Step-by-step explanation:

The expected value for the given Five possibilities is $6.

We have,

Payoffs of $2, $4, $6, $8, and $10.

Now,

We know that,

The expected value  [tex]=\Sigma (x*P(x))[/tex]

i.e. The sum of product of possible outcome and each outcome.

Here, x = Each outcome

And

P(x) = Possible outcomes

So,

Probability of x (Px) [tex]=\frac{1}{5}[/tex],

Now,

According to the above mentioned formula,

i.e.

The expected value  [tex]=\Sigma (x*P(x))[/tex]

We get,

[tex]=\Sigma\ (\frac{1}{5} * 2) + (\frac{1}{5} * 4) + (\frac{1}{5} * 6) +(\frac{1}{5} * 8) +(\frac{1}{5} * 10)[/tex]

On solving we get,

[tex]=\Sigma\ (0.4 + 0.8 + 1.2 + 1.6 + 2)[/tex]

i.e.

The expected value = $6

So,

The expected value for given possibilities is $6.

Hence we can say that the expected value for the given Five possibilities is $6.

Learn more about expected value here

https://brainly.com/question/17324165

#SPJ4

Answer:

Step-by-step explanation:

Reflection over any line is a rigid transformation that does not change angles or lengths. Dilation is a transformation that changes lengths by the same scale factor, but has no effect on angles. Dilated figures are similar to the original.

When ΔXYZ is reflected over a vertical line, no lengths or angles are changed. When the reflected triangle is dilated by half, we get ...

  Y'X' = (1/2)YX . . . . . . . makes option 3 false

  X'Z' = (1/2)XZ . . . . . . . makes option 4 true

Since no angles are changed, we have ...

  Angle XZY ≅ Angle Y'Z'X'   (another name for angle X'Z'Y')

  ... makes option 2 true

Of course, the resulting triangle is similar to the original, so ...

  △XYZ ~ △X'Y'Z' . . . . . option 1 is true

The triangle drawn on a grid is in the image attached and the complete procedure for the construction of the triangle is summarized in the explanation.

In this question we are asked to draw a triangle on a Cartesian plane. The procedure is summarized below:

Lastly, we present the result of this method in the image attached below.

To learn more on triangles: https://brainly.com/question/2773823

#SPJ1

The area as a function of the height H is:

[tex]A= 9cm*H[/tex]

We know that for a triangle of base B and height H, the area is given by:

[tex]A = \frac{B*H}{2}[/tex]

In this case, we already know that the base measures 18cm, then the formula for the area as a function of the height H is:

[tex]A= \frac{18cm*H}{2} = 9cm*H[/tex]

If you want to learn more about triangles:

https://brainly.com/question/2217700

#SPJ1

Answer:

D (the last choice)

Step-by-step explanation:

Taking the fourth root of each element individually:

49^(1/4) = sqrt(7)

(d^8)^(1/4) = d^2

(e^2)^(1/4) = sqrt(e)

Multiplying them back together:

sqrt(7) * d^2 * sqrt(e) = d^2 * sqrt(7e)

Answer:

The last bubble (that of which is cut from the screen) is simplified.

Step-by-step explanation:

The provided equation is simplified by following these steps:

[tex](49d^{8}e^2)^\frac{1}{4}[/tex]

= [tex](49)^\frac{1}{4}(d)^\frac{8}{4}(e)^\frac{2}{4}[/tex]

[tex](7)^\frac{2}{4}(d)^\frac{8}{4}(e)^\frac{2}{4}[/tex]

=[tex]\sqrt{7} (d^2)(\sqrt{e})[/tex]

Answer:

x=17

Step-by-step explanation:

Since they are intersecting lines, 3x=51

x=17

Answer:

x = 17

Step-by-step explanation:

When two lines intersect each other, the opposite angles are identical. Therefore, you can set both angles equal to each other to find the value of "x".

3x = 51

x = 17

We can identify that the missing reason in the proof is: Definition of Congruent angles.

We know that an angle measure of 90° of ∠ABC in the triangle means that it is a right angle triangle.

We also see that ∠ADB is also a right angle and is equal to 90°.

Now, since they have exactly the same measure, these angles are congruent. Then we can say that the angles are congruent and as such:

∠ABC ≅ ∠ABD

Thus, we can identify that the missing reason is: Definition of Congruent angles.

Read more about Triangle proof at; https://brainly.com/question/1248322

#SPJ1

The polynomial's maximum value is relative.

Here we have the polynomial:

[tex]V(x) = 36x^2 - 3.75x^3[/tex]

Notice that the leading coefficient is negative, so, as x tends to negative infinite, V(x) will tend to positive infinite.

So we only have a relative maximum, because is local maximum (at x = 6.4), but the function can take larger values than that.

You can also check that on the graph of V(x), which you can see below:

If you want to learn more about maximums:

https://brainly.com/question/1938915

#SPJ1

The equation of the line in slope intercept form is y = 7x - 2

The equation of the line can be solved with the following equation.

y = mx + b

where

Therefore,

m = -2  - 5 / 0 - 1 = -7 / -1

m = 7

Hence, using (1, 5)

y = 7x + b

5 = 7(1) + b

5 - 7 = b

b = -2

Therefore,

y = 7x - 2

Hence, the equation of the line in slope intercept form is y = 7x - 2

learn more on equation of a line here: https://brainly.com/question/14956513

#SPJ1