Sin Cos Tan
Geometry

The equation that represents the number of books will be 6x - 8 = 58. And the number of books will be 11.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Melissa bought some books. She spent a total of $58 after a discount of $8 off of her total purchase. Each book cost $6.

Let 'x' be the number of books. Then the equation is given as,

6x - 8 = 58

Simplify the equation, then we have

6x - 8 = 58

6x = 66

x = 11

The equation that represents the number of books will be 6x - 8 = 58. And the number of books will be 11.

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Let's call the time you drove "x" and the time your wife drove "y". We know that the sum of the two times is 20 hours:

x + y = 20

We also know the distance traveled during each part of the trip. The first part of the trip was 55x miles, and the second part of the trip was 65y miles. The total distance of the trip was 1170 miles:

55x + 65y = 1170

We can use the first equation to solve for x in terms of y:

x = 20 - y

We can then substitute this expression for x in the second equation:

55(20 - y) + 65y = 1170

Simplifying and solving for y:

1100 - 55y + 65y = 1170

10y = 70

y = 7

So your wife drove for 7 hours. We can use the first equation to find your driving time:

x + 7 = 20

x = 13

So you drove for 13 hours.

Answer:

13 hours

Step-by-step explanation:

Answer:

7a - 4ab + 3b

Step-by-step explanation:

5a - 3ab + 6b - (ab - 2a + 3b)

=5a - 3ab + 6b - ab + 2a - 3b

=7a - 4ab + 3b

The table should be completed as follows;

Coordinate   Key feature    Does the coordinate        Justification

                                                  make sense  ___________________

(-7.565, 0)   it is a key feature          yes                     it is a zero (root).

(0, 37)          it is a key feature          yes                     it is the y-intercept.

(6, 46)          it is a key feature          yes                     it is the vertex.

A reasonable constraint for the context in set builder notation is {y|y ∈ R ≤ 46}.

In Mathematics, a quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two or more variable on a graph, with a maximum exponent of two (2).

In Mathematics, the y-intercept of any graph such as a quadratic function, generally occur at the point where the value of "x" is equal to zero (x = 0).

In this scenario, the y-intercept of this quadratic function can be calculated as follows;

G(x) = -1/4(x²) + 3x + 37

G(0) = -1/4(0²) + 3(0) + 37

G(0) = 37.

In conclusion, the vertex (maximum point) of this quadratic function is given by the ordered pair (6, 46).

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Answer: 5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

First do 18-2 which is 16
Then do 16 divided by 8 which is 2

Right now the equation is 8 - 1 - 2

Then we minus 8 by 1 which is 7
and then 7 - 2 which is 5
So then our final answer is 5

Answer:

Your answer should be: TRUE FALSE TRUE FALSE

Step-by-step explanation:

Step One→ Solve one equation for either x or y.

Step Two→ Substitute the expression from step one into the 2nd equation.

Step Three→ Solve the second equation for the given variable.

Step Four→ Plug you solution back into the first equation.

Step Five→ Write your solution as a point.

The other side lengths of the triangle will be 24 and 26 units.

How to calculate the side?

The shortest side of a triangle similar to triangle XYZ is 20 units long and the shortest side on the other. triangle is 10. This means the proportion is [tex]\frac{20}{10}[/tex]=2

The other sides will be:

⇒12 × 2 = 24

⇒13 × 2 = 26

Therefore, the sides are 24 and 26 respectively.

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Let x be the amount of money invested in the 9% fund. Then the amount invested in the stock is $32,000 - x. The profit from the 9% investment is 0.09x and the loss from the stock investment is -0.03(32000 - x).

What exactly does compounding mean?

Compounding is the method through which interest is added to both the principle balance already in place and the interest that has already been paid. Thus, compounding can be thought of as interest on interest, with the result that returns on interest are magnified over time, or the so-called "magic of compounding."

The overall net profit was $2,040, so we can set up the following equation to solve for x:

0.09x - 0.03(32000 - x) = 2040

Expanding the second term,

0.09x - 9600 + 0.03x = 2040

Combining like terms,

0.12x - 9600 = 2040

Adding 9600 to both sides,

0.12x = 1640 + 9600

Simplifying,

0.12x = 11240

Dividing both sides by 0.12,

x = 93, 666.67

So, the amount invested in the 9% fund is $93,666.67 and the amount invested in the stock is $32,000 - $93,666.67 = $-61,666.67.

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The inverse tangent function [tex]tan^{-1}[/tex] can be used to find the values of x for which tan x = 0.8645 in the interval 0 degrees < x < 360 degrees. The inverse tangent function gives us the angle that has a tangent equal to the input value.

The function can be expressed as:

[tex]x = tan^{-1 (0.8645)}[/tex]

Using a scientific calculator or trigonometry tables, we can find that the value of [tex]tan^{-1 (0.8645)}[/tex] is approximately 47.5 degrees.

So, in the interval 0 degrees < x < 360 degrees, there is one value of x that satisfies the equation tan x = 0.8645, and it is approximately 47.5 degrees. It's important to remember that the inverse tangent function is a one-to-one function and its range is restricted to the interval -90° < x < 90°, so the value found represents the smallest angle in the interval 0° < x < 360° that has a tangent equal to 0.8645.

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The expression to represent the phrase "6 times a number plus 3" is:

"6n + 3".

"n" represents an unknown number, and "6" and "3" are constants. The expression means that 6 is being multiplied by "n" to get an intermediate result, and then 3 is being added to that result to get the final answer.

For example, if n = 2, then the expression would evaluate to 6 * 2 + 3 = 12 + 3 = 15. So, the expression "6n + 3" represents the mathematical relationship between the unknown number "n" and the final result.

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Answer: The savings per movie with the pass is $3.50 - $1.00 = $2.50. For the pass to benefit Seth's father, Seth must attend enough movies such that the total savings is equal to or greater than $40.

Let's call x the number of times Seth must attend for the pass to benefit his father. Then:

$2.50x >= $40

Solving for x:

$2.50x/$2.50 >= $40/$2.50

x >= 16

So Seth must attend at least 16 movies in order for the pass to benefit his father.

Answer/Solution:

15a^5b^15

Explanation:

First, multiply the numbers, then combine the exponents until you get the answer.

The average speed for the whole journey is 72.5 km/h. The result is obtained by using the formula for the average speed.

Average speed is the overall speed of a moving object during a given amount of time. It can be expressed as

Avg speed = Total distance covered / Total time taken

The speed itself is

v = s/t

Where

Orla drove 155 km in 2 hours. Then, she drove 48 km at a speed of 60 km/h. Find the average speed for the whole journey!

We have

The time taken in the second journey is

v₂ = s₂/t₂

60 = 48/t₂

t₂ = 48/60

t₂ = 0.8 h

The average speed will be

= total distance covered / total time taken

= (s₁ + s₂)/(t₁ + t₂)

= (155 + 48)/(2 + 0.8)

= (203)/(2.8)

= 72.5 km/h

Hence, the whole journey will have the average speed of 72.5 km/h.

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The greatest possible speed that Oleg could have bicycled that day is 13 miles per hour.

Let's call the total distance that Oleg jogged z. Then z = 2x.

The total distance that Oleg bicycled was 30 - z - 2. Let's call this distance w. Then w = 30 - 2x - 2.

Since Oleg bicycled for 2 hours, the speed that he bicycled was w / 2. So, w / 2 = y.

Substituting the expressions for z and w, we have:

y = (30 - 2x - 2) / 2.

Since y must be the greatest possible speed that Oleg could have bicycled that day, x must be the smallest possible value.

Since Oleg jogged for 2 hours, the minimum value of x is 2 / 2 = 1.

Substituting x = 1 into the expression for y, we have:

y = (30 - 2 * 1 - 2) / 2 = (26) / 2 = 13.

So, the greatest possible speed that Oleg could have bicycled that day is 13 miles per hour.

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Answer:

10.8s

Step-by-step explanation:

120÷11.1= 10.8s (to 3 s.f.)

4500(1+0.055)^24

4500(1.055)^24

= 16,265.65456755

The value of the other side is 9. 7 m

Using the Pythagorean theorem stating that the square of the hypotenuse side is equal or equivalent to the sum of the squares of the other two sides.

From the information given, we have that;

This is represented as;

12² = 7² + x²

Find the value of the squares, we get;

144 = 49 + x²

collect like terms. we get;

x² = 144 - 49

subtract the values, we have;

x² = 95

Find the square root of both sides

x = 9. 7 m

Hence, the value is 9. 7 m

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The given trigonometric function Cosec 2A + cot 4A = cot A - cosec 4A​ can be proved using the properties of the trigonometric functions.

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

Given that,

Cosec 2A + cot 4A = cot A - cosec 4A​

Taking the LHS

= Cosec 2A + cot 4A

= 1 / sin 2A + cos 4A / sin 4A

To take the LCM we multiply and divide the first term by 2cos 2A:

= 2cos 2A / 2 sin 2A cos 2A + cos 4A/ sin4A

= 2cos 2A / sin 4A + cos 4A/ sin4A

= 2 cos 2A + 2 cos² A -1 / Sin 4A

= 2 cos 2A (1 + cos 2A) - 1 / sin 4A - 1/ sin 4A

=  2cos 2A 2cos² A / 2 sin 2A cos 2A - cosec 4A

= cos A / sin A - cosec 4A

= cot A - cosec 4A

Hence proved.

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In a coin flip experiment, you would see a pattern of 50/50 heads and tails if every student in the class skewed their findings to show 5 heads and 5 tails.

This is due to the fact that each participant purposefully altered their results to display an equal number of heads and tails.

It is crucial to remember that this pattern does not accurately reflect the chances of either getting heads or tails in a fair coin flip. The results cannot be taken as a representative sample of a fair coin flip because everyone purposefully slanted their findings. It is crucial to conduct experiments with appropriate controls and prevent results bias in order to acquire reliable findings.

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Y=2x+1 is an equation used in mathematics to calculate the relationship between two variables, X and Y.

An equation is a physical and mathematical statement that describing physical phenomena are describe the relationship between different physical quantities it typically consists of two or more variable which are simple representing physical quantity and then equal sign the variable may be quantity such as force velocity or energy.

This equation is a linear equation, meaning it is a straight line when graphed. It is a very basic equation and one of the most commonly used equations.

To use this equation, you will need to know the value of X. Once you have determined the value of X, you can plug it into the equation to calculate the value of Y. For example, if X=3, then the equation would look like this: Y=2(3)+1, which equals 7. Therefore, when X=3, Y=7.

The equation Y=2x+1 is often used in a variety of math problems, such as determining the slope of a line, calculating the area of a triangle, and finding the equation of a circle. It is also used in physics to calculate velocity or acceleration. As you can see, this equation is quite versatile and can be used in a variety of situations.

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Answer:

n = -3

Step-by-step explanation:

3n - 15 = 7n + n

3n - 15 = 8n

3n - 8n = 15

-5n = 15

n = -3

Answer:

x = 56°

Step-by-step explanation:

x and 124° are a linear pair and sum to 180° , that is

x + 124° = 180° ( subtract 124° from both sides )

x = 56°

Answer:

56°

Step-by-step explanation:

angle on a straight line = 180°

124° + x =180°

x = 180° - 124

x = 56°

Answer:

y-intercept: 5

slope: -1

equation: y = -x + 5

Step-by-step explanation:

The y-intercept is when x is 0, and it is shown on the table as 5.

The slope can be found by doing [tex]y_1-y_2/x_1-x_2[/tex], which is 6-5/-1-0 = 1/-1 = -1.

The equation is y = mx + b, so we can write it as y = -x + 5

Answer:

w=6, L=24

Step-by-step explanation:

let the width be x,

then, L=4x

Perimeter=2(l+w)

                =2(4x+x)

the new dimensions,

perimeter=2(l+w)

           74 =2(4x+5+x+2)

               =2(5x+7)

               =10x+14

       10x=74-14

       10x=60

          x=60/10

           x=6

Therefore, The width is 6 cm

L=4x

 =4(6)

 =24

Therefore the length is 24 cm

The equation involving an integral expression that can be used to find the value of k is π integration [(k - x²)² - (k - 4)²] dx.

We need to perform integration to find the value of k which will have same volume. Thus, tos over the question the clarity of concepts of volume of any area and integration is required.

The graph representing the mentioned situation is attached in the picture. So, now, writing the expression -

π integration [(k - x²)² - (k - 4)²] dx

Remember tha the integration limit in the mentioned equation will be -2 to 2.

On solving we will get the volume 256π/5.

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The comp question is -

The shaded region, R, is bounded by the graph of y = x² and the line y = 4, as

shown in the figure.

There exists a number k, k 4 , such that when R is revolved about the line y = k , the resulting solid has the same volume as the solid in part (b).

Write, but do not solve, an equation involving an integral expression that can be used to find the value of k.

The time it will take both of them to pick enough apples is 7.27 minutes.

The time it will take both of them to pick enough apples is calculated as follows;

Let the time = t ( minutes )

3t  + (5/2)t = 40

3t + ( 5t / 2 ) = 40

multiply through by 2

6t + 5t = 80

11t = 80

divide through by 11

t = 80 / 11

t = 7.27 minutes

Thus, the time to pick enough apples depends on the rate at which they are picking the apples.

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The table is filled as follows

x    P(x)   x P(x)   (x - μ)²

3    3       9          961

4    7      28         900

5   22    110         841

6   60    360       784

7   85    595       729

8   32    256       676

9   8      72          625

mean, μ = 34.05

variance = 919.33

standard deviation = 30.32

The mean is calculated using the information provided as follows

= summation of (x P(x) ) / summation of x

= 1430 / 42

=34

The variance is solved by the formula

= summation of (x - μ)² / (n - 1), where n = 7

= 5516 / (7 - 1)

= 5516 / 6

= 919.33

the standard deviation is solved using the formula

= √variance

= √919.33

= 30.32

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Answer:

306

Step-by-step explanation:

Let's call the number of fiction books "f" and the number of non-fiction books "n". From the given information, we know that the ratio of fiction books to non-fiction books is 5:2 and the total number of books is 1421, so we can write the following equation:

f + n = 1421

Since the ratio of fiction books to non-fiction books is 5:2, we can write:

f/n = 5/2

We can cross-multiply to solve for f:

f = (5/2) * n

Substituting this expression for f into the first equation:

(5/2) * n + n = 1421

Expanding the left side:

(5/2 + 2/2) * n = 1421

Simplifying the left side:

(5 + 2)/2 * n = 1421

(7/2) * n = 1421

Dividing both sides by (7/2):

n = 1421 * 2/7

n = 204

So there are 204 non-fiction books and 5/2 * 204 = 204 * 5/2 = 102 * 5 = 510 fiction books.

The difference between the number of fiction books and non-fiction books is 510 - 204 = 306. So there are 306 more fiction books than non-fiction books in the library.

Step-by-step explanation:

If the ratio of fiction and non-fiction books are 5:2. Therefore that means that the total books were divided into 7 parts and the fiction books took 5 parts while the non-fiction books took two parts.

To get the number of fiction and non-fiction books we first add the ratio

[tex]5 + 2 = 7[/tex]

So that means that 7 = 1421

After adding the ratio we now take

The total parts that the books took as the numerator and the total of the ratio as the denominator, and multiply the fraction by the total number of books which is 1421

[tex] \frac{5}{7} \times 1421 = number \: of \: fiction \: books[/tex]

[tex] \frac{2}{7} \times 1421 = number \: of \: non - fiction \: books[/tex]

let's work out each fraction separately

[tex] \frac{5}{7} \times 1421 = \frac{7105}{7} [/tex]

[tex] \frac{7105}{7} = 1015[/tex]

[tex] \frac{2}{7} \times 1421 = \frac{2842}{7} [/tex]

[tex] \frac{2842}{7} = 406[/tex]

To get the answer to the question we subtract the number of non-fiction books from the number of fiction books

[tex]1015 - 406 = 609[/tex]

The discount amount based on 35% discount offered on $89.95 is $31.5.

The discount amount can be calculated by the formula -

Final amount = original price - discount percentage × original price

The method of solving this formula will be to first multiply followed by subtraction according to PEMDAS rule.

Now, keep the values in formula

Final amount = 89.95 - 35/100 × 89.95

Performing multiplication and division on Right Hand Side of the equation

Final amount = 89.95 - 31.48

Now performing subtraction on Right Hand Side of the equation

Final amount = $58.47

Here we see that that the discount amount is $31.48

Round to nearest penny = $31.5

Thus, the discount amount is $31.5.

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