Approximately what is the length of the rope for the kite sail, in order to pull the ship at an angle of 45° and be at a vertical height of 150 m, as shown in the diagram opposite?

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The number of seventh-graders that must join the club in order to meet the president's wishes is 10.

Since there are 45 eighth graders and 20 seventh graders in a school club and the president of this club wants 40% of the club’s members to be seventh graders, we need to find the number of seventh graders that will be added to the school club to make their percentage 40 %.

Let the number of seventh-graders to be added be x.

So, the new number of seventh-graders is 20 + x and the new number of people in the club is 45 + 20 + x = 65 + x

Thus, the percentage of seventh graders in the club is thus

[tex]\frac{20 + x}{65 + x} X 100[/tex] %

Since this percentage equals 40 %, we have that

[tex]\frac{20 + x}{65 + x} X 100[/tex]% = 40 %

[tex]\frac{20 + x}{65 + x} = \frac{40}{100} \\\frac{20 + x}{65 + x} = 0.4[/tex]

Cross-multiplying we have

[tex]20 + x = 0.4(65 + x)[/tex]

Expanding the bracket, we have

[tex]20 + x = 26 + 0.4x[/tex]

Subtracting 20 from both sides we have

[tex]x = 26 - 20 + 0.4x\\x = 6 + 0.4x[/tex]

Subtracting 0.4x from both sides, we have

[tex]x - 0.4x = 6\\0.6x = 6[/tex]

dividing both sides by 0.6, we have

x = 6/0.6

x = 10

So, the number of seventh-graders that must join the club in order to meet the president's wishes is 10.

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Answer:

Step-by-step explanation:

I'll use x  instead of theta.

So we have:

sin x / ( 1 + cos x) + (1 +cos x) / sinx

The LCM is sin x(1 + cos x) so we have

sin^2 x + (1 + cos x)^2 /  sin x(1 + cos x)

= sin^2 x + cos^2x + 2 cos x + 1 /  sin x(1 + cos x)

Now sin^2x + cos^2x = 1 so:

= 2 + 2 cos x /  sin x(1 + cos x)

= 2(1+ cos x) /  sin x(1 + cos x)

The 1 + cos x is common so we have:

2 / sin x

= 2 cosec x.

Answer:

A

Step-by-step explanation:

We can find a common denominator for all of these fractions, compute, and then compare the values to find the right answer.

Step-by-step explanation:

[tex] {9}^{ - 53} . {9}^{37} [/tex]

To solve this question we use the rules of indices

Since the bases are the same and are multiplying we add the exponents using the formula

So for the above question we have

We have the final answer as

Which is the same as

Hope this helps you

Answer:

A. 311.4 ft²

Step-by-step explanation:

Use the formula for the surface area of a square pyramid: SA = 2bs + b², where b is the length of a side of the base and s is the slant height.

Plug in the values and solve:

SA = 2(9)(12.8) + 9²

SA = 230.4 + 81

SA = 311.4 ft²

The surface area of the pyramid is 311.4 square units

The surface area of a pyramid is given by the formula:

Surface Area = 1/2 × base area × slant height + perimeter of base × slant height

The base area of the pyramid is 9 × 9 = 81 square units.

The slant height of the pyramid is the length of a line segment that connects a vertex of the pyramid to the midpoint of a side of the base.

We can find the slant height of the pyramid using the Pythagorean Theorem.

slant [tex]h^{2}[/tex] = [tex]h^{2}[/tex] + [tex](base/2)^{2}[/tex]

slant [tex]h^{2}[/tex] = [tex]12.8^{2}[/tex] + [tex]9/2^{2}[/tex] = 230.4

slant height = 15.2

Therefore, the surface area of the pyramid is:

Surface Area = 1/2 × 81 × 15.2 + 4 × × 15.2 = 311.4 square units

So the answer is A.

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Answer:

6.1 seconds

Step-by-step explanation:

set the equation equal to zero

0 = -16t² + 97.6t

factor out t

t(-16t + 97.6) = 0

-16t =- 97.6

t =  6.1

The NFL kicker's kicks remain in the air on average for approximately 3.05 seconds.

To find the average hang time of the NFL kicker's kicks, we need to determine the time at which the height (h) reaches its maximum value. The maximum height corresponds to the peak hang time.

The equation that models the hang time is given as: h = -16t^2 + 97.6t

This is a quadratic equation in the form: h = at^2 + bt + c

In our case, a = -16, b = 97.6, and c = 0 (since there is no constant term).

The time (t) at which the height (h) reaches its maximum value can be found using the formula: t = -b / 2a

Let's calculate the time (t):

t = -b / 2a

t = -97.6 / (2 * -16)

t = -97.6 / -32

t = 3.05 seconds (rounded to two decimal places)

So, the NFL kicker's kicks remain in the air on average for approximately 3.05 seconds.

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Answer:

Hey there!

The temperature started at -8 degrees.

The total rise of the temperature was 6(4) or 24 degrees.

-8+24=16

The temperature after 6 hours was 16 degrees.

Let me know if this helps :)

The temperature after 6 hour is 16°. Therefore, option B is the correct answer.

Temperature is a degree of hotness or coldness the can be measured using a thermometer. It's also a measure of how fast the atoms and molecules of a substance are moving. Temperature is measured in degrees on the Fahrenheit, Celsius, and Kelvin scales.

Given that, One January day, the low temperature in Fargo, ND was -8 degrees.

Over a period of six hours, the temperature rose 4 degrees per hour.

So, total temperature rose in 6 hours is 24 degrees

Temperature after 6 hour is -8+24

= 16°

The temperature after 6 hour is 16°. Therefore, option B is the correct answer.

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Answer:

8 ^ 20

Step-by-step explanation:

(8 ^ 10) ^2

We know that a^ b^ c = a^ ( b*c)

8 ^ (10*2)

8 ^ 20

Answer:

The correct answer is b.

Step-by-step explanation:

if you arrange the data set in ascending order you will have:

x              y

-2            [tex]\frac{1}{100}[/tex]

-1              [tex]\frac{1}{10}[/tex]

0               1

1                10

3               1000

Exponential growth is an increase in a specific way of a data set over time. here, as x increases by a +1, y increases with ×10

Answer:

Step-by-step explanation:

(a - b)² = a² - 2ab + b²

a = 0.1x

b = 0.2y

(0.1x - 0.2y)²= (0.1x)² - 2*0.1x*0.2y + (0.2y)²

                   = (0.1)²x² - 0.04xy + (0.2)²y²

                   = 0.01x² - 0.04xy + 0.04y²

Answer:

A=d-c/b

Step-by-step explanation:

Answer:

ab+c=d

Step-by-step explanation:

just took the test

Part (a)

The length is supposed to be 22.2 cm, but it could be 0.3 cm less

So 22.2 - 0.3 = 21.9 cm is the smallest value for the length. This is the lower bound of the length.

The upper bound is 22.2 + 0.3 = 22.5 cm as it is the largest the length can get.

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

Use this for the width as well

The width is supposed to be 12 cm, but it could be as small as 12-0.3 = 11.7 cm and as large as 12+0.3 = 12.3 cm

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

============================================

Part (b)

Use the smallest length and width to get the smallest possible area

smallest area = (smallest width)*(smallest length) = 11.7*21.9 = 256.23

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

Repeat the same idea but for the largest length and width to get the largest possible area

largest area = (largest width)*(largest length) = 12.3*22.5 = 276.75

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

The correct answers are Losing 12; Winning 15

Explanation:

The ratio of winning to losing is 5: 6 or 5/6. This means for every 5 winning spaces in the wheel there are 6 losing spaces. This ration should be used to complete the values of the table.

1. The first row shows there are 10 winning and you need to calculate the number of losing spaces. The process is shown below.

[tex]\frac{5}{6} = \frac{10}{x}[/tex] - Express the ratios using fractions; use x to show the missing value

[tex]5x = 60[/tex] - Cross multiply to find the value of x

[tex]x = 60 / 5[/tex] - Solve the equation to find x

[tex]x = 12[/tex] - The number of losing is 12 if there are 10 winning spaces

2. The second row shows there are 18 losing spaces, and you need to calculate the number of winning spaces. Repeat the process.

[tex]\frac{5}{6} = \frac{x}{18}[/tex]

[tex]6x = 90[/tex]

[tex]x = 90 / 6[/tex]

[tex]x =15[/tex] - The number of winning spaces is 15 if there are 18 losing spaces

Answer:

22 and 15 i know because i got it right on khan

Step-by-step explanation:

Please mark mine the brainliest !!

Answer:

4 and 5

Step-by-step explanation:

cube root of 66 is 4.041240021

Answer:

-13a

Step-by-step explanation:

Since -8 and -5 have like variables, you can subtract them. -8-5 is -13, so the answer is -13a.

Answer:

-13a

Step-by-step explanation:

These two numbers are already like terms, so you can subtract it easily.  

First, don't look at the a.

-8-5= -13 because if something is negative and gets subtracted, that means it'll still be negative.

Now that we now it equals -13, we can add the variable a back onto the answer.  We get -13a.  

Answer:

Bridget's first fish =f = 5 ounces

Bridget's dad first fish weighs 17 ounces

Step-by-step explanation:

Bridget went fishing with her dad. Bridget caught the first fish of the day, and it weighed f ounces. That day, she caught four more fish. One was 2 times the weight of the first fish, another was 2 more than 3 times the weight of the first fish, the next was 1/2 the weight of the first fish, and the last was 3/5 the weight of the first fish. Bridget’s dad caught four fish. The first fish he caught weighed 2 more than 3 times the weight of the first fish caught that day. One fish weighed 4/5 the weight of the first fish caught that day, one weighed 4 more than 2 times the weight of the first fish caught that day, and the last weighed 1/2 the weight of the first fish caught that day. If all the fish Bridget caught have the same total weight as all the fish her dad caught, then the first fish Bridget caught weighed___ ounces and the first fish her dad caught___ weighed ounces.

Solution:

Bridget's fishes:

f ounces

2f ounces

3f+2 ounces

1/2f ounces

3/5f ounces

Total= f +2f + (3f+2) + 1/2f +3/5f

=3f + 3f + 2 + 5f+6f/10

=6f + 2 + 11f/10

=60f+11f/10 +2

=71/10f +2

Bridget's dad fishes

3f+2

4/5f

2f+4

1/2f

Total =(3f+2) + (2f+4) + 4/5f +1/2f

=3f+2+2f+4 + 8f+5f/10

=5f + 6 + 13/10f

= 50f+13f/10 + 6

=63/10f +6

Equate the total weight

71/10f +2=63/10f +6

Collect like terms

71/10f - 63/10f =6-2

71f-63f/10 = 4

8f/10=4

Cross product

8f=40

Divide both sides by 8

f=5

Bridget's first fish =f = 5 ounces

Bridget's dad first fish = 3f +2

=3(5)+2

=15+2

=17 ounces

Bridget's dad first fish weighs 17 ounces

Answer:

21.7 m

Step-by-step explanation:

The question above is a right angle triangle and we would be using the trigonometric function of tangent to solve for it.

tan θ = Opposite/ Adjacent

Opposite side = Height = unknown

Adjacent = 20sqrt(3) m

θ = Angle of Elevation = 30°

Hence, we have:

tan 30° = Opposite/ 20√3

Opposite = tan 30° × 20√3m

Opposite = 20m

Height of the tower = Height of the observer + Height (Opposite side)

Height = 20m

Height of the the observer as given in the question is = 1.7m

Height of the tower = 20m + 1.7m

= 21.7m

Therefore, the height of the tower = 21.7m

Answer:

11/30

Step-by-step explanation:

Because the repeating value is a multiple of 3, first multiply the decimal representation by 3; 0.36666 · [tex]\frac{3}{3}[/tex] = 1.1/3. Since we can't have decimals in a fraction, we'll need to multiply the result above until we have all integers. 11.3 x 10/10 = 11/30. We can't simplify this, so 11/30 is our answer.

Answer:

Kameron is 50 years old.

Step-by-step explanation:

We can make equations and start filling in what we already know, assuming [tex]n[/tex] is Niko's age, [tex]L[/tex] is Lila's age, [tex]a[/tex] is Amber's age, and [tex]k[/tex] is Kamerons age.

Our first equation:

n = 3L

We know that Niko is 45, so

45 = 3L

Divide both sides by 3:

L = 15

So, Lila is 15 years old.

Another equation:

n = L + 3a

We already know Niko and Lila's age:

45 = 15 + 3a

Subtract 15 from both sides:

30 = 3a

Divide both sides by 3:

a = 10

So Amber is 10 years old.

Another equation:

k = 2(a + L)

We know Amber and Lila's age:

k = 2(10 + 15)

k = 2(25)

k = 50

So Kameron is 50 years old.

Hope this helped!

Answer:

96 sq. m

Step-by-step explanation:

If the width is x, the length is x + 4 and since perimeter = 2 * (length + width), we can write:

40 = 2(x + x + 4)

40 = 2(2x + 4)

20 = 2x + 4

16 = 2x

x = 8 so x + 4 = 12, therefore the area is 8 * 12 = 96 square meters.

Answer:

96m^2

Step-by-step explanation:

40=2(x+x+4)--> 2(2x+4).

20=2x+4

20-4=2x

16=2x

8=x

8✖️12=96m^2

Answer:

3/8 is your answer.

Step-by-step explanation:

Given:

8 kids bought a 3 cakes.

Required:

How many equal parts will need to divide it so that everyone can have it.

Solution:

3/8

Hope this helps ;) ❤❤❤

Step-by-step explanation:

A protractor is a handheld to use in measuring angles. It is most cases made up of plastic or glass materials, and can accurately measure angles of circles up to 180°.

However, when measuring straight lengths, a ruler or tape has better measuring accuracy than the protector.

Answer:

12 ^ 1/2 or [tex]\sqrt{12}[/tex]

Step-by-step explanation:

12^2

We want to do the inverse operation, which is the square root

We can write the square root as

^ 1/2  or as [tex]\sqrt{ }[/tex]

So the inverse of squaring 12 is

12 ^ 1/2 or [tex]\sqrt{12}[/tex]

=======================================================

Explanation:

Both of these represent the same idea. Square root notation is probably what you're more familiar with. It turns out that raising any positive number to the 1/2 power is the same as a square root. We can write

[tex]\sqrt{x} = x^{1/2}[/tex]

The 1/2 power notation may seem more clunky or confusing, but its helpful to extend to things like cube roots, fourth roots, etc.

The more general rule is

[tex]\sqrt[n]{x} = x^{1/n}[/tex]

which says the nth root of x is the same as x^(1/n).

Answer:

[tex]\boxed{s=3}[/tex]

Step-by-step explanation:

Use a proportion to solve for the missing side length - a/c = b/d.

4/2 = 6/s cross-multiply

4s = 12 divide by 4

[tex]\boxed{s=3}[/tex]

Answer:

Step-by-step explanation:

Because these triangles are similar, their sides exist in proportion to one another. Their angles are exactly the same. but their sides are proprtionate IF they are similar. We are told they are so setting up the proportion:

[tex]\frac{4}{2}=\frac{6}{s}[/tex] and cross multiply:

4s = 12 so

s = 3

You could also look at the fact that the height of the larger triangle is 4 and the height of the smaller is 2, so the larger is twice as big as the smaller; likewise, the smaller is half the size of the larger (that means the same thing). So if the larger side is 6, half of that is 3.

Answer:

D) 36x²-4

Step-by-step explanation:

36x²+12x-12x-4

36x²-4

[tex](6x - 2)(6x + 2) \\ = {(6x)}^{2} - {(2)}^{2} \\ = {36x}^{2} - 4[/tex]

Answer:

D.

[tex] {36x}^{2} - 4[/tex]

Hope you could understand.

If you have any query, feel free to ask.

Answer:

the first four answers are all correct

Answer:

6

Step-by-step explanation:

Doing the fourth root of something is the equivalent of doing said number to the power of 1/4. So in this case I will convert the fourth root into an exponent and simplify:

6^(4*1/4) = 6^1 = 6

Hope this helps!

Answer:

Real and unequal

Step-by-step explanation:

We are tasked with finding the nature of the roots of the given quadratic equation.

The given quadratic equation is;

x^2 -5x -7

Firstly, we should know that we cannot solve this by factorization, as we will run into problems.

Now the catch is, although we cannot solve by factorization, we can solve by using the quadratic formula.

Now let’s check if our roots are imaginary or real.

For the roots to be imaginary or real, we will work with calculating the value of the expression b^2 -4ac

The value of this would tell us the nature of the roots. While a negative value would tell us the roots are imaginary, a positive value will tell us the roots are real.

So from the question, b = -5( coefficient of x) , while c = -7 and a = 1 ( coefficient of x^2)

Plugging these values into the equation, we have;

-5^2 - 4(1)(-7) = 25 + 28 = 53

This tells us the roots are real

The last issue is to know if the roots are equal or not.

The roots cannot be equal. This is because the term b^2 - 4ac would be in the root and yield a positive and a negative value which cannot give equal answers when added to (-b)

This from the quadratic formula;

x = {-b ± √(b^2-4ac)}/2a

Answer:

$8.00

Step-by-step explanation:

You need to add 3.50 and 2.50. your answer will be 6.00. If you subtract 6.00 from 14.00 you will get your answer which is 8.00