9. Angeline fills one water jug with 5.8 gallons of water. She needs to fill 17 water jugs for day camp. How many gallons of water does she need?

Answer:

21.5 feet

Step-by-step explanation:

d = Distance of the bottom of the tower to the point of observation

x = Height of the top section of the tower

a = Height of bottom section

b = Total height of tower

[tex]\tan28^{\circ}=\dfrac{a}{d}\\\Rightarrow a=d\tan28^{\circ}\\\Rightarrow a=70\tan28^{\circ}[/tex]

[tex]\tan40^{\circ}=\dfrac{b}{d}\\\Rightarrow b=d\tan40^{\circ}\\\Rightarrow b=70\tan40^{\circ}[/tex]

[tex]x=b-a\\\Rightarrow x=70\tan40^{\circ}-70\tan28^{\circ}\\\Rightarrow x=70(\tan40^{\circ}-\tan28^{\circ})\\\Rightarrow x=21.5\ \text{feet}[/tex]

The height of the top section of the tower is 21.5 feet.

Answer:66

Step-by-step explanation:

66

Answer:

20

Step-by-step explanation:

The line a is an illustration of a linear function

From the complete figure, we have the following points on line a

(x,y) = (0,2) and (2,4)

The slope (m) is calculated using:

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

This gives

[tex]m = \frac{4 - 2}{2 - 0}[/tex]

Evaluate

m = 1

Hence, the slope of line a is 1

This is calculated as

y = m(x - x1) + y1

So, we have:

y = (x - 0) + 2

Evaluate the difference and the product

y = x + 2

Hence, the equation of the line a is y = x + 2

See attachment for the graph of line a

Read more about linear equations at:

https://brainly.com/question/4025726

Answer:

Step-by-step explanation:

First solve for the common ratio:

[tex]\frac{30}{180} = \frac{1}{6} 6 \\ \\\frac{5}{30} = \frac{1}{6}[/tex]

Use the geometric summation equation to solve for sum:

[tex]a(\frac{(1-r^{n} )}{(1-r)})\\180(\frac{(1-\frac{1}{6} ^{6}) }{(1-\frac{1}{6} )}) = \frac{46655}{216} = 216[/tex]

The sum of the first 6 terms of the following series is 540.

A geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms.

The sum of the terms of the geometric sequnece is given by;

[tex]\rm S_n=\dfrac{a(1-r^n)}{1-r}[/tex]

The common ratio of the sequence is;

[tex]\rm \dfrac{a_2}{a_1}=\dfrac{30}{180}=\dfrac{1}{6}\\\\ \dfrac{a_2}{a_1}=\dfrac{5}{30}=\dfrac{1}{6}\\\\[/tex]

The sum of the first 6 terms of the following series is;

[tex]\rm S_n=\dfrac{a(1-r^n)}{1-r}\\\\\rm S_6=\dfrac{180(1-1/6^6)}{1-1/6}\\\\ S_6=\dfrac{180\times 0.99}{5/6}\\\\S_6=\dfrac{180\times 0.99}{0.33}\\\\S_6=\dfrac{178.2}{0.33}\\\\S_6=540\\[/tex]

Hence, the sum of the first 6 terms of the following series is 540.

Learn more about geometric sequence here;

https://brainly.com/question/8934175

#SPJ2

Answer:

1/2(2x-6)= -6

Step-by-step explanation:

Multiply the two sides by the equation 2

2x-6=12

move the constant to the right hand side change sign

2x = -12 + 6

calculate the sum

2x= -6

Divide the 2 sides by 2

x= -3

Answer:

The total distance Remy will swim is approximately 236 meters

Step-by-step explanation:

From the given diagram, of triangle ΔCAB, we have that the path Remy is to swim are;

1) Length of segment C to A

2) Length of segment A to B

3) Length of segment B to C

The length of the perpendicular at point D on segment AB to C = 60 meters

Therefore, DC = 60 m

By trigonometric ratios, we have;

[tex]tan (\theta) = \dfrac{Opposite \ leg \ length}{Adjacent \ leg \ length}[/tex]

[tex]cos(\theta) = \dfrac{Adjacent\ leg \ length}{Hypotenuse \ length}[/tex]

We are given the values of the trigonometric ratios of the following angles;

tan(27°) = 0.51

tan(43°) = 0.93

cos(27°) = 0.89

cos(43°) = 0.73

∴ tan(43°) = AD/DC = 0.93

Where the lengths of AC, AD, DB, DC and BC

AD = DC × tan(43°)

∴ AD = 60 × 0.93 ≈ 55.8

Similarly, we have;

tan(27°) = DB/DC

∴ DB = DC × tan(27°)

DB = 60 × 0.51 ≈ 30.6

From [tex]cos(\theta) = \dfrac{Adjacent\ leg \ length}{Hypotenuse \ length}[/tex], we have;

cos(43°) = DC/AC

AC = DC/(cos(43°))

∴ AC = 60/0.73 ≈ 82.2

Similarly, we have;

cos(27°) = DC/BC

BC = DC/(cos(27°))

∴ BC = 60/0.89 ≈ 67.4

The total distance Remy will swim = AC + AD + DB + BC

∴ The total distance Remy will swim = 82.2 + 55.8 + 30.6 + 67.4 = 236

The total distance Remy will swim = 236 meters

Answer:

The population is 384 bacteria at 2pm

Step-by-step explanation:

Because u just need multiplied

Explanation is in the file

tinyurl.com/wpazsebu

Answer:

[tex]135 + 4x + 5x = 180 \\ 9x = 180 - 135 \\ 9x = 45 \\ x = \frac{45}{9} \\ x = 5[/tex]

Angle A will be

[tex]5 \times 5 = 25[/tex]

=25°

Answer:

(a) unpaid balance = $667.95

(b) Previous balance = $761.67

(c) his new balance = $683.98

Step-by-step explanation:

In the question, we are given the following:

Monthly periodic rate = 2.4%, or 0.024

Curren charges = $256.28

Total payment made = $350

Finance charge = $18.28

Therefore, we now proceed as follows:

(a) unpaid balance

This can be calculated as follows:

Unpaid balance = Previous balance + Current charges - Total payment made ................. (1)

Note that from part (b), Previous balance is equal to $761.67.

Substituting this and other values from the question into equation (1), we have:

Unpaid balance = $761.67 + $256.28 - $350 = $667.95

(b) Previous balance

This can be calculated as follows:

Previous balance = Finance charges / Monthly periodic rate = $18.28 / 2.4% = $18.28 / 0.024 = $761.67

(c) his new balance

This can be calculated as follows:

New balance = Unpaid balance * (1 + Monthly periodic rate) = $667.95 * (1 + 2.4%) = $667.95 * (1 + 0.024) = $667.95 * 1.024 = $683.98

Complete question is;

Find the dimensions or, the square or circle. Area = 64π in²

Answer:

r = 8 inches

Step-by-step explanation:

We know that formula for area of a circle is; A = πr²

Where r is radius.

We are given Area as 64π in²

Thus;

πr² = 64π

π will cancel out to give;

r² = 64

r = √64

r = 8 inches

Answer:

You need to find 84% of 4200 to get the amount of students.  First change the percent to a decimal, and multiply 0.84 x 4200.

There were 3528 total students at the theater.

Answer:

1. 12

2. 0

3. 9

Step-by-step explanation:

Answer:

The answer is -1,1

Step-by-step explanation:

if the question is asking what is X then the answer is

X - 3 >-25

X >-25+3

X >-22

Answer: 4

Step-by-Step Explanation: When written in slope-intercept form, the equation becomes y = 4x - 2; the basic structure of this formula is y=mx+b, where m is the slope and b is the y-intercept.

Knowing this information, we can also figure out the slope and y-intercept. 4, or m, is the slope of the proposed line.

Answer:

9 and -5

Step-by-step explanation:

Answer:

11:45

Step-by-step explanation:

Answer:40

Step-by-step explanation:

Answer: I believe it is the X axis. <3

Step-by-step explanation:

Answer:

A and B are equivalent to -96x + 120

Step-by-step explanation:

-96x + 120

A. 8 (-12x + 15)

8 * -12x = -96x

8 * 15 = 120

8 (-12x + 15) = -96x + 120

-96x + 120 = -96x + 120

Equivalent

B. -12 (8x - 10)

-12 * 8x = -96x

-12 * -10 = 120

-12 (8x - 10) = -96x + 120

-96x + 120 = -96x + 120

Equivalent

C. -8 (12x + 15)

-8 * 12x = -96x

-8 * 15 = -120

-8 (12x + 15) = -96x-120

-96x + 120 ≠ -96x - 120

Not Equivalent

Answer:

37.4

Step-by-step explanation:

Answer:

6.5

Step-by-step explanation:

3(x+6)2=75 | Given

6x + 36 = 75 | Distribute

6x = 39 | Subtract 36 from both sides

x = 6.5

Answer:

In 11 teaspoons, there are 53.9 milliliters.

Step-by-step explanation:

Since you know that one teaspoon is equal to 4.9 milliliters, to find the answer, you have to multiply 4.9 times the amount of teaspoons, or 11. Hence, the answer is 53.9.

Please like and mark brainliest!

Hope it helps!

Answer:

14.7, because 5x + 90 + 16.5 =180

so 180-90-16.5=5x

x= 14.7

Answer:

48 cups of sugar.

Step-by-step explanation:

12 cups of sugar for 8 cups of lemonade then I let 32 cups of lemonade corresponding with x cups of sugar, then 12/8 = x/ 32, then 8x = 32 * 12, then solve for x get 8x = 384, x =48.

Answer:

32÷8= 4 cups of sugar...........