3
Rewrite the following equation as a function of x.
21x+3y-45=0
A. f(x)= 7x-15
B. f(x)=-7x-6
C. f(x)=3x+6
D. f(x) = -7x + 15

Answer: C

Step-by-step explanation: -5,3,1 answer ;)

The simplest radical form of the sine of y/2 is:

sin(y/2) = ±√(2/5)

Here we know that:

cos(y) = 1/5.

We want to find  sin(y/2), so we can use the identity:

sin(y/2) = ±√( ( 1 - cos(y))/2)

Replacing cos(y) there we will get.

sin(y/2) = ±√( ( 1 - 1/5)/2)

sin(y/2) = ±√( ( 4/5/2)

sin(y/2) = ±√(2/5)

That is the simplest radical form.

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=The total surface area of the rectangular prism is 192 square inches.

You calculate the total surface area of the rectangular prism using the dimensions provided in the net. Since the net has 6 rectangular faces, we can find the area of each face and then sum them up to get the total surface area.

1. Top rectangle (8 inches by 3 inches): Area = length × width = 8 × 3 = 24 square inches.
Since the bottom rectangle is the same, its area is also 24 square inches.

2. Left rectangle (4 inches by 6 inches): Area = length × width = 4 × 6 = 24 square inches.
As the right rectangle is identical, its area is also 24 square inches.

3. Middle rectangle (8 inches by 6 inches): Area = length × width = 8 × 6 = 48 square inches.
The back rectangle is the same, so its area is 48 square inches as well.

Now, we'll sum up the areas of all 6 faces to get the total surface area:

Total Surface Area = (2 × 24) + (2 × 24) + (2 × 48) = 48 + 48 + 96 = 192 square inches.

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The length of the lake is equivalent to 295 meters.

We can write that -

tan(32°) = 250/{x}

{x} = 250/tan(32°)

also

tan(68°) = 250/{y}

{y} = 250/tan(68°)

We can write the length of the lake as -

L = x - y

L = 250/tan(32°) -  250/tan(68°)

L = 250{1/tan(32°) - 1/tan(68°)}

L = 250{1/(0.63) - 1/(2.48)}

L = 250{1.58 - 0.40}

L = 250 x 1.18

L = 295 meters

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Answer: 17

Step-by-step explanation:

Substitute the value of the variable into the equation and simplify.

3 ( 3 ( 2 ) - 1 ) + 2 = 17

The median of the boxplot is 420.

In a boxplot, the median is the line in the Centre of the box.

Given that;

The upper horizontal line of the box is at 490

The Lower horizontal line of the box is at 350

Therefore the median of boxplot

= (upper point + lower point)/2

= (490 + 350)/2

= 420

Hence middle point be at 420.

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The values of the variables x, y and a in the circles are calculated below

Circle 1

The measure of the angle x is calculated as

28 = 1/2(x - 61)

So, we have

x - 61 = 56

This gives

x = 117

For y, we have

y² = 4 * 18

So, we have

y = 6√2

Circle 2

The measure of the angle x is calculated as

x + 48 = 180

So, we have

x = 132

The length y is calculated as

tan(24) = 7/y

So, we have

y = 7/tan(24)

Evaluate

y = 15.7

Circle 3

This is calculated as

9 * (9 + a) = 8 * 21

So, we have

81 + 9a = 168

So, we have

a = 9.67

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Answer:

Marty has 768 pints of orange juice.

Step-by-step explanation:

To convert gallons to pints, we need to remember that 1 gallon is equal to 128 fluid ounces, and 1 fluid ounce is equal to 1/8 pint.

Given that Marty has 6 gallons of orange juice, we can calculate the total amount in pints as follows:

6 gallons x 128 fluid ounces/gallon x 1/8 pint/fluid ounce = 768 pints

So, Marty has 768 pints of orange juice.

Answer:

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The diagonals of a square bisect each other.

It makes all half-diagonals of equal length. Therefore:

Substitute and solve for x:

Hence the value of x is 4.

The calculated time of is that the baseball game was 1 7/12 hour longer than the movie

The given parametes in the question are

Movie = 1 3/4 hours

Baseball = 3 1/3 hours

To calculate how much longer was the baseball game than the movie, we subtract

So, we have

Longer = 3 1/3 - 1 3/4

Evaluate

Longer = 19/12

This gives

Longer = 1 7/12

Hence, the baseball game was 1 7/12 hour longer than the movie

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The cuboid in question has a surface area of 202 square units.

We must sum together the areas of all six faces to determine a cuboid's surface area.

The dimensions of the given cuboid are:

length (l) = 9 units

width (w) = 5 units

height (h) = 4 units

The area of each face is given by:

Top and bottom faces:[tex]lw = 9 * 5 = 45[/tex] square units each

Front and back faces: [tex]lh = 9 *4 = 36[/tex] square units each

Left and right faces: [tex]wh = 5 * 4 = 20[/tex] square units each

Therefore, the total surface area of the cuboid is:

[tex]2(lw + lh + wh) = 2(45 + 36 + 20)\\ = 2(101) \\= 202 \ square \ units[/tex]

Hence, the surface area of the given cuboid is 202 square units.

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Based on these samples, the generalization that can be made is The median weight of the professional players is greater than the median weight of the college players.

Therefore Option A is correct.

The median weight of the ordered data is found when the  number that splits the data into two equal parts.

The median weight of the college players is

(215 + 232)/2 = 223.5 pounds.

The median weight of the professional players is

(235 + 255)/2 = 245 pounds.

In conclusion,  the median weight of the professional players is greater than the median weight of the college players, so  the generalization that can be made is The median weight of the professional players is greater than the median weight of the college players.

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Answer:

29°

Step-by-step explanation:

since a right angle in 90° just subtract 61 out of 90

90°-61°=29°

The area of the new shape is 74 squared cm

The area of the new shape is solved by dividing the shape into three sections and then sum up all the areas

The area of the sections are as follows

Section 1: length x width

= 8 x 5

= 40 squared cm

Section 2: length x width

= 5 x 2

= 10 squared cm

Section 3: length x width

= 8 x 3

= 24 squared cm

Total area

= 24 + 10 + 40

= 74 squared cm

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The area of the new shape is 74cm²

The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.

The shape is a combination of two rectangles. One of the rectangles cut out.

The area of the cut out is calculated as;

A = l × w

A = 3 × 2

A = 6cm²

The area of the cut out rectangle = area of the whole rectangle - area of cut out rectangle

= 8×5 -6

= 40-6

= 34cm²

The area of the second rectangle = l×w

= 8× 5

= 40cm²

Therefore area of the new shape = 40+34

= 74cm²

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The prediction that is not supported by the data is option B: "The number of non-fiction books sold on Friday will be two-and-a-half times the number of arts and crafts books sold on Friday."

We can see from the table that on Thursday, 7 sports and trivia books and 19 arts and crafts books were sold, for a difference of 12.

On Thursday, 13 non-fiction books and 19 arts and crafts books were sold.

If we assume that the same ratio will hold on Friday, then we can predict that the number of non-fiction books sold will be (19/2)×2.5 = 23.75 Which is not a whole number.

Therefore, this prediction is not supported by the data.

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We can use the given recursive formula to find the value of each term in the sequence.

Starting with a1 = 10, we can use the recursive formula to find a2:

a2 = a1 + 4 = 10 + 4 = 14

Similarly, we can find a3, a4, and a5:

a3 = a2 + 4 = 14 + 4 = 18

a4 = a3 + 4 = 18 + 4 = 22

a5 = a4 + 4 = 22 + 4 = 26

Therefore, the value of a5 is 26.

A recursive formula is what?

A formula which explains how to move from one word in a sequence to the next is known as a recursive rule for a sequence. The variable is typically used to represent the term "number."

What does a1 in the formula represent?

The first term of the formula, a1, and the nth term of the series, an, are both expressions containing the first term (the term preceding it), an-1.

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Answer:

Your answer will be B. A town's population grows at a rate of 7.2% every year.

Step-by-step explanation:

Pls give me brainliest thx

The expression sec θ / csc θ + 2sin θ / cos θ is equal to the expression 3tan θ is proven below.

Given that:

sec θ / csc θ + 2sin θ / cos θ = 3 tan θ

The properties are given as,

tan x = sin x / cos x

sec x = 1 / cos x

sin x = 1 / csc x

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

Take the left-hand side, then

LHS = sec θ / csc θ + 2sin θ / cos θ

LHS = sin θ / cos θ + 2tan θ

LHS = tan θ + 2 tan θ

LHS = 3 tan θ

LHS = RHS

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Answer:

To factor the quadratic equation y = x^2 - 8x - 9, we need to find two numbers that multiply to give -9 and add to give -8 (the coefficient of the x term).

We can start by looking for two factors of -9 that add up to -8. The only pair of factors that works are -9 and 1. This is because (-9) + 1 = -8, and (-9) times 1 is -9.

Now we can use these factors to express the middle term of the quadratic in terms of two separate terms that can be factored by grouping. We can do this by splitting the -8x term into -9x + x:

y = x^2 - 9x + x - 9

Now we can group the first two terms together and the last two terms together:

y = (x^2 - 9x) + (x - 9)

We can factor out x from the first group, and factor out -9 from the second group:

y = x(x - 9) + (-9)(x - 9)

Finally, we can factor out the common factor of (x - 9):

y = (x - 9)(x - 1)

Therefore, the factor form of the quadratic equation y = x^2 - 8x - 9 is (x - 9)(x - 1).

Answer:

Let's assume that the number of children who used the public swimming pool is 'x' and the number of adults who used the pool is 'y'.

From the given information, we can form two equations:

x + y = 454 (equation 1) --> the total number of people who used the pool

1.5x + 2.5y = 1043 (equation 2) --> the total revenue collected from admission fees

We can use these equations to solve for 'x' and 'y'. Let's start by multiplying equation 1 by 1.5 to eliminate 'x':

1.5x + 1.5y = 681 (equation 1 multiplied by 1.5)

1.5x + 2.5y = 1043 (equation 2)

Now, we can subtract equation 1 from equation 2 to eliminate 'x' and solve for 'y':

2.5y - 1.5y = 1043 - 681

y = 224

So, there were 224 adults who used the pool. We can substitute this value into equation 1 to solve for 'x':

x + 224 = 454

x = 230

Therefore, there were 230 children who used the pool.

"If you share 7 apples equally with 3 people, then there are 2 1/3 apples for each person."The whole number 2 represents the number of apples that each person will get when sharing 7 apples equally with 3 people.

The numerator 1 represents the remaining part of an apple that is left after sharing equally among 3 people. The denominator 3 represents the number of persons with whom the apples are being shared equally.

A possible real-life application for the expression 1 ÷ 1/4 is dividing a pizza into quarters and then sharing one slice of pizza equally among a group of people.

To simplify the expression for sharing, we need to remember that dividing by a fraction is the same as multiplying by its reciprocal. So, 1 ÷ 1/4 is equivalent to 1 × 4/1, which simplifies to 4.

Thus, 1 ÷ 1/4 is equal to 4.

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Answer:

the probability of winning the bet is 4/9 or approximately 0.444 or 44.44%.

Step-by-step explanation:

To calculate the probability of winning a bet given odds in favor, we can use the following formula:

Probability of winning = Odds in favor / (Odds in favor + Odds against)

In this case, the odds in favor are given as 4 to 5. This means that for every 4 favorable outcomes, there are 5 unfavorable outcomes.

Plugging these values into the formula:

Probability of winning = 4 / (4 + 5)

Probability of winning = 4 / 9

So, the probability of winning the bet is 4/9 or approximately 0.444 or 44.44%.

Answer:

To find (g of f)(x), we need to first find f(x) and then substitute it into g(x).

f(x) = x - 4

Now we can substitute f(x) into g(x):

g(f(x)) = 9f(x) + 4

g(f(x)) = 9(x - 4) + 4

g(f(x)) = 9x - 36 + 4

g(f(x)) = 9x - 32

Therefore, the answer is (A) 9x+32.

Answer:

the answer is d- (x-5)

The probability 0.7977 that the sample mean weight of 12 adult male passengers is greater than 162 lb.

There is a 79.77% chance that the elevator is overloaded

We can use the Central Limit Theorem here, which states that the sample mean of a sufficiently large sample size (n≥30) will be approximately normally distributed with mean μ and standard deviation σ/√n, where μ is the population mean and σ is the population standard deviation.

In this case, n=12, μ=169 lb, and σ=29 lb. Therefore, the sample mean weight of 12 adult male passengers will be approximately normally distributed with mean 169 lb and standard deviation 29/√12 ≈ 8.38 lb.

Now we can standardize this distribution to find the probability that the sample mean weight is greater than 162 lb:

z = (162 - 169) / 8.38 ≈ -0.83

We determine that the probability of z being less than or equal to -0.83 is approximately 0.2023, which can be calculated using a standard normal distribution table or calculator.

Therefore, there is a probability of 1 - 0.2023 ≈ 0.7977 that the sample mean weight of 12 adult male passengers is greater than 162 lb.

This indicates that if the elevator is filled with 12 adult male passengers, there is a 79.77 percent chance that it will be overloaded. The elevator does not appear to be safe for this many passengers, and this is a very high probability

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The equation that results from each transformation is given as follows:

a) reflect in the x-axis (vertical reflection): y = -7^x.

b) stretch vertically by a factor of 3: 3(7)^x.

c) stretch horizontally by a factor of 2.4: y = (7)^(x/2.4).

d) reflect in the y-axis and stretch vertically by a factor of 7: y = 7^(1 - x).

The parent function in the context of this problem is given as follows:

y = 7^x.

The reflection over the x-axis means that the sign of the entire function is exchanged, hence:

y = -7^x.

The vertical stretch by a factor of 3 means that the entire function is multiplied by 3, thus:

y = 3(7)^x.

The horizontal stretch by a factor of 2.4 means that x -> x/2.4, hence:

y = (7)^(x/2.4).

The reflection over the y-axis means that x -> -x, while the vertical stretch by a factor of 7 means that the function is multiplied by 7, hence the function for item d is given as follows:

y = 7(7)^(-x)

y = 7^(1 - x).

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Answer:

A. 60%

B. 40%

C. Math because Math has higher chance of being chosen.

D. 0%

The value of the height of the cone is 38 units

The formula for calculating the circumference of a cone is represented as;

Circumference = 2πr

Now, substitute the value to determine the radius, we have;

24π = 2πr

Divide by the coefficient of r

r = 24π/2π

r = 12 units

The formula for the volume of a cone is;

Volume = πr²h/3

Substitute the values

1824 π = π × 144 ×h/3

Multiply the values

1824π = 144πh/3

Make h the subject

h = 38 units

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Answer:

The formula for calculating the future value of a present amount with compound interest is:

FV = PV * (1 + r)^n

where FV is the future value, PV is the present value, r is the annual interest rate (as a decimal), and n is the number of compounding periods.

In this case, Nkaiseng wants to invest some money now to retire with R500 300 in 40 years (from 25 to 65). The annual interest rate is 11.5%, which is equivalent to a monthly interest rate of 0.115/12 = 0.00958.

So we have:

FV = PV * (1 + 0.00958)^ (40*12)

500300 = PV * (1.00958)^480

Dividing both sides by (1.00958)^480, we get:

PV = 500300 / (1.00958)^480

PV = 500300 / 20.4524

PV = 24406.53

Therefore, Nkaiseng should invest R24406.53 (rounded up to the nearest rand) now to have R500 300 when she retires at 65 years with an interest rate of 11.5% per annum.

The area of the composite figure is A = 135 cm²

Given data ,

Let the figure consists of a rectangle and quarter circle

where the area of the rectangle is R and area of quarter circle is C

And , A = R + C

Area of rectangle A = 20 x 2 = 40 cm²

And , area of quarter circle C = ( 1/4 )π ( 11 )²

C = 95.033 cm²

So , A = 95 + 40

A = 135 cm²

Hence , the area of the figure is A = 135 cm²

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The complete question is attached below :

Determine the area of the composite figure to the nearest whole number.

135cm²

117cm²

173cm²

74cm²