1
Enter the correct answer in the box
Rewrite this logarithmic equation as an exponential equation
log, 18 = 3

Answer:

Step-by-step explanation:

Let the width of the pool deck be x.

We have equation:

1)

2)

Correct choice is B

The width of the pool deck is 10 feet (x = 10).

So, the answer is option B: 10 ft.

Here, we have to find the width of the pool deck, we need to calculate the total area occupied by the pool and the deck and then find the value of x that makes the total area equal to 1,408 square feet.

First, let's calculate the area of the pool.

The pool is 12 feet by 24 feet:

Area of the pool = Length × Width

Area of the pool = 12 ft × 24 ft

Area of the pool = 288 ft²

Now, we want to add the deck around the pool.

The length and width of the entire area (pool + deck) will be (12 + 2x) feet and (24 + 2x) feet, respectively, because we add x feet to both sides of the pool.

Area of the entire area (pool + deck) = (12 + 2x) ft × (24 + 2x) ft

We want this area to equal 1,408 square feet:

(12 + 2x) ft × (24 + 2x) ft = 1,408 ft²

Now, we can solve for x:

(12 + 2x) × (24 + 2x) = 1,408

Expand the equation:

288 + 48x + 24x + 4x² = 1,408

Combine like terms:

4x² + 72x - 1,120 = 0

Now, let's solve this quadratic equation for x.

We can either factor it or use the quadratic formula:

Using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a

where a = 4, b = 72, and c = -1,120.

x = (-(72) ± √(72² - 4 * 4 * -1,120)) / 2 * 4

x = (-72 ± √(5,184 + 17,920)) / 8

x = (-72 ± √23,104) / 8

x = (-72 ± 152) / 8

Now, we have two possible solutions:

x = (-72 + 152) / 8

x = 80 / 8

x = 10

x = (-72 - 152) / 8

x = -224 / 8

x = -28

Since we are interested in a positive width for the deck, the width of the pool deck is 10 feet (x = 10).

So, the answer is option B: 10 ft.

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Answer:

  a) the x-coordinate changes sign

  b) the y-coordinates are unchanged

  c) this is a reflection across the y-axis

Step-by-step explanation:

Each image point is on the same horizontal line as the original. It is as far from the y-axis as the original, but in the opposite direction. Its x-coordinate has changed sign.

__

The y-coordinate is the same for each image point as for the original. The y-coordinates have not changed.

__

The line of reflection is the perpendicular bisector of the segment joining the original point and its image. In every case, that is the y-axis. The image is a reflection across the y-axis.

Answer:

A. x = 4

Step-by-step explanation:

[tex]\sqrt{4} +9=2+9=11[/tex]

Hope this helps

Answer:

     A.  [tex]x =4[/tex]

Step-by-step explanation:

Answer:

use Pythagoras theorem and a graph to be fluent in this

Step-by-step explanation:

answer is 2sqr(7)

Answer:

F(x) is greater.

Step-by-step explanation:

f(2) = 2 + 1

(2,3)

Have a good day!

Answer:

F(x) is greater.

Step-by-step explanation:

Answer:

2/5, 4/10, 6/15, 8/20, 10/25, 12/30, 14/35, 16/40, 18/45, 20/50, 22/55, 24/60, 26/65, 28/70, 30/75, 32/80, 34/85, 36/90, 38/95, 40/100 ...

Answer:

-20/3

Step-by-step explanation:

m = ∆y/∆x

∆y = -8 - 12 = -20

∆x = 8 - 5 = 3

Hence m= ∆y/∆x = -20/3

Answer:

241/20 or 24.05 0r 481/20

Step-by-step explanation:

First simply your fractions

then add 6+4 to your fractions !!

Answer:

24 1/20 meters

Step-by-step explanation:

To find perimeter, you add all the side lengths.

6 4/5 + 4 + 6 + 7 1/4 = 24 1/20

Answer:

The value of x is 20 degrees.

Step-by-step explanation:

The three angles of a triangle must equal 180 degrees.

100 + 40 + 2x = 140 + 2x

180 - 140 = 40 (goal)

2(x) = 40

2(20) = 40

A) 20 degrees

Answer:

There are 6 men in the dance recital.

Step-by-step explanation:

We have a ratio of 2:5, men to women. If there are 15 female performers we can do a cross multiplication to find the males performers:

Then it will be

[tex]\tt \frac{15}{x} =\frac{5}{2}[/tex]

[tex]\tt 5x=15*2[/tex]

[tex]\tt 5x=30[/tex]

[tex]\tt x=\frac{30}{5}[/tex]

[tex]\tt x=6[/tex]

[tex]\tt Therefore,there~are~6~Men~at~the~dance[/tex]

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Answer:

5 hours, and 30 minutes ago, which would be 7:15 AM

Step-by-step explanation:

add hours, then minutes, then subtract both times: 12:45 - 5:30 = 7:15

By iteratively substituting, we have

[tex]a_n = a_{n-1} + n[/tex]

[tex]a_{n-1} = a_{n-2} + (n - 1) \implies a_n = a_{n-2} + n + (n - 1)[/tex]

[tex]a_{n-2} = a_{n-3} + (n - 2) \implies a_n = a_{n-3} + n + (n - 1) + (n - 2)[/tex]

and the pattern continues down to the first term [tex]a_1=0[/tex],

[tex]a_n = a_{n - (n - 1)} + n + (n - 1) + (n - 2) + \cdots + (n - (n - 2))[/tex]

[tex]\implies a_n = a_1 + \displaystyle \sum_{k=0}^{n-2} (n - k)[/tex]

[tex]\implies a_n = \displaystyle n \sum_{k=0}^{n-2} 1 - \sum_{k=0}^{n-2} k[/tex]

Recall the formulas

[tex]\displaystyle \sum_{n=1}^N 1 = N[/tex]

[tex]\displaystyle \sum_{n=1}^N n = \frac{N(N+1)}2[/tex]

It follows that

[tex]a_n = n (n - 2) - \dfrac{(n-2)(n-1)}2[/tex]

[tex]\implies a_n = \dfrac12 n^2 + \dfrac12 n - 1[/tex]

[tex]\implies \boxed{a_n = \dfrac{(n+2)(n-1)}2}[/tex]

Answer:

6,16

Step-by-step explanation:

Answer:

The base is 6.69 and the height is 6.02 (these are rounded to the nearest hundredth)

Step-by-step explanation:

soh-cah-toa

cos 42 = adjacent/9

adjacent = cos 42 x 9

adjacent = 6.69

sin 42 = opposite/9

opposite = sin 42 x 9

opposite = 6.02

Answer:

(x³+2x²-2x)-(-3x³+4x²-x)

(x³+2x²-2x)+(3x³-4x²+x)

(x³+3x³)+(2x²-4x²)+(-2x+x)

4x³-2x²-x ----you may write till here.

But, if not satisfied, factorize it

x(4x²-2x-1)

please mark brainliest

Answer:

9cm

Step-by-step explanation:

a square has 4 equal sides therefore if you divide 36 by 4 you will get the length of 1 side

Answer:

[tex]V = \frac{1}{2} LBH \\ \\ \\ LH =V \div ( \frac{1}{2} B) \\ \\ LH =V \times \frac{2}{B} \\ \\ \\LH = \frac{2V}{B} [/tex]

Answer:

1+1=2

Step-by-step explanation:

as we know that one is made up of 1/2+1/2=1

so 1/2+1/2+1/2+1/2=2

hope this helps you

have a great day :)

Answer:

I think its 2nd one

HOPE IT HELPS, BE SAFE! Brainiest if possible pls! :)

The histogram for the data is given at the end of this answer.

An histogram is a graph that shows the number of times each element of x was observed.

In this problem:

Hence, the graph given at the end of this answer is the histogram.

You can learn more about histogram at https://brainly.com/question/2962546

[tex]\bold{\huge{\green{\underline{ Solution}}}}[/tex]

[tex]\bold{\underline{ Given :- }}[/tex]

[tex]\bold{\underline{ To \: Find :- }}[/tex]

[tex]\bold{\underline{ Let's \: Begin :- }}[/tex]

In the given right angled triangle, we have

Now, By using trigonometric ratios

[tex]\bold{\pink{ Sin Φ = }}{\bold{\pink{\frac{Perpendicular }{Hypotenuse}}}}[/tex]

[tex]\bold{\red{ Cos Φ = }}{\bold{\red{\frac{Base}{Hypotenuse }}}}[/tex]

[tex]\bold{\blue { tan Φ = }}{\bold{\blue{\frac{Perpendicular }{Base }}}}[/tex]

According to the question :-

[tex]\bold{ Cos \: 45° = }{\bold{\frac{2}{m}}}[/tex]

[tex]\bold{ 1/√2= }{\bold{\frac{2}{m}}}[/tex]

[tex]\bold{\red{ m = 2√2 \: units }}[/tex]

Therefore,

Let the unknown angle be x

[tex]\sf{ 45° + x + 90° = 180° }[/tex]

[tex]\sf{ x = 180° - 135 ° }[/tex]

[tex]\sf{ x = 45° }[/tex]

Now,

[tex]\bold{ Cos \: x° = }{\bold{\frac{n}{2√2}}}[/tex]

[tex]\bold{ Cos \: 45° = }{\bold{\frac{n}{2√2}}}[/tex]

[tex]\bold{ 1/√2= }{\bold{\frac{n}{2√2}}}[/tex]

[tex]\bold { n = 2√2/√2 }[/tex]

[tex]\bold{\red{ n = 2\: units }}[/tex]

Thus, The value of m = 2√2 and n = 2

[tex]\sf{\blue{ Hence, \: option \: D \: is \: Correct }}[/tex]

Answer:

[tex]\frac{4}{7}[/tex]

Step-by-step explanation:

The equation for slope is:

[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

We can plug in the given points into the equation:

[tex]Slope=\frac{-6-(-2)}{1-8}=\frac{-6+2}{-7}=\frac{-4}{-7}=\frac{4}{7}[/tex]

Answer:

B. H(w) gets very small.

Step-by-step explanation:

This should be the answer you're looking for

From the graph of H(w) and w, H(w) gets very small when w gets very large option (B) H(w) gets very small is correct.

It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x

where a is a constant and a>1

As we know, It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a graph shown in the picture.

From the graph:

H(w) represents the vertical axis or y-axis and w represents the horizontal axis or x-axis.

H(w) is decreasing as the w increasing

Thus, from the graph of H(w) and w, H(w) gets very small when w gets very large option (B) H(w) gets very small is correct.

Learn more about the exponential function here:

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Answer:

Step-by-step explanation:

1 ton = 2000 pounds

thus:

0.65T * (2000lb / 1 T) = 1300 lbs

Hope that helps!

Answer:

A = ks^2

I hope this helps :D

Percentage

8% x 75%.x = 6

0.06x = 6

x = 100

Answer:

55 feet

Step-by-step explanation:

This is a subtraction problem.

You need to find the difference between what Janice has (27feet) and what she would like to have (82feet)

82 - 27

= 55

Janice needs 55 feet of ribbon. This amount along with the 27 feet she already has will give her a total of 82 feet of ribbon.

55 + 27 = 82

Answer:

24

Step-by-step explanation:

L = library

A = animal shelter

A = 5L

20 = 5L

20 ÷ 5 = 5L ÷ 5

4 = L(L = 4)

4 + 20 = 24

10

Answer:

[tex] - 1(2)( - 5) \\ - 2 \times ( - 5) \\ = 2 \times 5 \\ 10[/tex]

Answer:

10

Step-by-step explanation:

-1(2)(-5)

-1(-10) = 10

[RevyBreeze]

The area of a shape is the amount of space on the shape

The area of the shape is 110 unit square

From the complete question, the composite shape has:

The area of the rectangle is:

Area = 10 * 9 = 90 unit square

The area of the triangle is:

Area = 0.5 *10 * 4 = 20 unit square

So, the area of the figure is:

Total = 90 + 20

Total = 110 unit square

Hence, the area of the shape is 110 unit square

Read more about areas at:-

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