Find the exact value of sin

The solution for the following equation 5x+7x=60 is x=30.

A statement that affirms the equivalence of two expressions joined by the equals symbol "=" is known as an equation. For illustration, 2x - 5 = 13.  The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Given that 5x+7x=60

2x =60

x=60/2

=30

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The values on the graph of the velocity of the body, indicates that we get;

a. t = 2 seconds and t = 7 seconds

b. 3 ≤ t ≤ 6

c. Please find attached the speed of the body in the interval 0 ≤ t ≤ 10 created with MS Excel

b. Please find attached the acceleration of the body in the interval 0 ≤ t ≤ 10

Velocity is the rate of change of the position of an object with respect to a specified reference frame and time.

The figure is a velocity time graph, and the velocity of an object is the rate of change of the displacement with time, such that when graph is above the horizontal axis, the velocity is positive, and when the velocity is below the horizontal axis, the velocity is negative, therefore, we get;

a. When the velocity of the changes sign, the direction of the body reverses. The points at which the velocity changes sign, which are the x-intercepts are at t = 2, and t = 7

b. The speed is constant when the velocity remains the same, which are locations on the graph, where the graph is an horizontal line. Therefore, the interval at which the body is moving at a constant velocity is; 3 ≤ t ≤≤6

c. The speed of a body is its absolute velocity, which can be found from the graph by taking the absolute value of the velocity at each point on the graph as follows;

The points on the resulting graph will therefore be; (0, 0), (1, 4), (3, 4), (6, 4), (8, 4) and (10, 0).

Please find attached the speed of the body in the interval 0 ≤ t ≤ 10

d. The acceleration is the rate of change of the velocity of the body with time. The acceleration of the body which has a velocity graph consisting of straight lines is a piecewise constant graph, such that we get;

From t = 0 to t = 1, a = (4 - 0)/(1 - 0) = 4

From t = 1 to t = 3, a = (4 - (-4))/(1 - 3) = -4

From t = 3 to t = 6 , a = (-4 - (-4))/(6 - 3) = 0
From t = 6 to t = 8, a = (4 - (-4))/(8 - 6) = 4

From t = 6 to t = 10, a = (0 - 4)/(10 - 8) = -2

Please find attached the graph of the acceleration of the body, created with MS Excel

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Answer: 12 | Constant Function

Step-by-step explanation:

The function always produces the value 3 * 4, which is 12, regardless of the input x. Thus the answer is 12 and is a constant function.

The two lines are neither parallel nor perpendicular.

To determine whether two lines are parallel, perpendicular, or neither, we need to compare their slopes. Let's examine the given lines and analyze their slopes:

Line 1: y + 1 = -5x

We can rewrite Line 1 in slope-intercept form (y = mx + b) by isolating y:

y = -5x - 1

From this equation, we can identify that the slope of Line 1 is -5.

Line 2: y = (1/5)x - 2

Line 2 is already in slope-intercept form, and we can observe that the slope of Line 2 is 1/5.

Compare the slopes: The slopes of Line 1 and Line 2 are -5 and 1/5, respectively. Since the slopes are not equal (they are not the same value), the lines are not parallel.

Determine perpendicularity: To determine if the lines are perpendicular, we need to check if the product of their slopes is -1. Multiplying the slopes of Line 1 and Line 2, we have:

(-5) * (1/5) = -1

Since the product is -1, the lines would be perpendicular. However, in this case, the product of the slopes is -1/5, not -1. Therefore, the lines are not perpendicular either.

Hence, the two lines given by the equations y + 1 = -5x and y = (1/5)x - 2 are neither parallel nor perpendicular.

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To copy angle ABC onto ray DE to create angle FDE, the correct sequence of steps are:

1.Step 1: Draw ray DE.

2. Step 2: Place the compass at point D and set the width to any convenient width.

3. Step 3: Without changing the width, draw an arc that cuts both rays DE and DC. Label the intersection point F.4. Step 4: Place the compass at point B and set the width to the same amount.

5. Step 5: Without changing the width, draw an arc that intersects with ray BC.

6. Step 6: Without changing the width, draw an arc that intersects with the previously drawn arc at point G.

7. Step 7: Draw a line from point D to point G.

8. Step 8: Draw a line from point F to point E.
9. Step 9: The created angle FDE is the copy of angle ABC.

Thus, the correct sequence of steps needed to copy angle ABC onto ray DE to create angle FDE are:

Draw ray DE, place the compass at point D and set the width to any convenient width, without changing the width, draw an arc that cuts both rays DE and DC, label the intersection point F, place the compass at point B and set the width to the same amount, without changing the width, draw an arc that intersects with ray BC, without changing the width, draw an arc that intersects with the previously drawn arc at point G, draw a line from point D to point G, draw a line from point F to point E, the created angle FDE is the copy of angle ABC.

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The statements that are correct about the function that have been shown are;A, B, C, F

A mathematical function called an exponential function has the independent variable in the exponent. Its general form is:

f(x) = a^x

where "x" is the variable and "a" is the base, a positive constant. The exponential function's appearance and behavior depend on the base "a".

The function grows exponentially when the base "a" is greater than 1. The function expands quickly as "x" grows in value. As "x" rises, the growth rate becomes steeper.

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Answer:

-3 and 4

Step-by-step explanation:

if y=0 then just look in the x axis

a) The condition is deducible (valid). Joe having room 303 as his homeroom confirms he is a freshman.

b) The condition is deducible (valid). If angles A and B in triangle ABC are acute, then triangle ABC is acute.

c) The condition is not deducible (invalid). A vehicle stopped at a railroad crossing does not necessarily mean it is a school bus.

d) The condition is not deducible (invalid). Being depressed on Thursday does not imply that Thursday was cloudy.

a) The condition is valid. The reasoning is correct because it follows a valid logical form of "If A, then B." In this case, if a student has room 303 as their homeroom (A), then the student is a freshman (B). Joe is a student with room 303 as his homeroom, so it can be deduced that Joe is a freshman.

b) The condition is valid. The reasoning is correct because it follows a valid logical form of "If A, then B." In this case, if the three angles of a triangle are acute (A), then the triangle is acute (B). Given that angles A and B of triangle ABC are acute, it can be deduced that triangle ABC is acute.

c) The condition is not valid. The error in reasoning is called "affirming the consequent." While it is true that all school buses stop at railroad crossings, it does not necessarily mean that any vehicle stopped at the Santa Fe railroad crossing is a school bus. There could be other vehicles, such as cars or trucks, stopped at the crossing for various reasons.

d) The condition is not valid. The error in reasoning is similar to affirming the consequent. Just because all cloudy days are depressing does not mean that all instances of being depressed imply a cloudy day. There could be various reasons for feeling depressed on Thursday, unrelated to the weather conditions.

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The man would receive a commission of R3,600 on sales totaling R70,000, with a 6% commission rate excluding the first R10,000.

To calculate the commission, we first need to determine the sales amount on which the commission applies.

In this case, the first R10,000 is excluded from the commission calculation.

Therefore, the commission would be calculated on the remaining amount of R70,000 - R10,000 = R60,000.

To find the commission, we multiply the sales amount by the commission rate of 6%:

Commission = R60,000 * 6% = R3,600.

Therefore, the man would receive R3,600 in commission.

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The two points on the number line that represent numbers that can be combined to make zero are point A (-1) and point B (1).

To find two points on the number line that can be combined to make zero, we need to look for two numbers that have opposite signs.

Looking at the number line:

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

We can see that the numbers -1 and 1 are located on opposite sides of zero. When combined, they add up to zero:

-1 + 1 = 0

Therefore, the two points on the number line that represent numbers that can be combined to make zero are point A (-1) and point B (1).

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Answer:

170 boys

Step-by-step explanation:

If there are five boys to every seven girls, then one group will have a total of 12 students.

Since there are 408 total students enrolled, then there would be 408/12 = 34 groups.

Therefore, there are 5*34 = 170 boys

Yes, The series "axBx" satisfies all the rules of the language defined above

Let's analyze each rule:

1. Each series must contain one and only one prefix character:

The series "axBx" contains one prefix character, 'a'. It meets this rule by having exactly one prefix character.

2. A series must start with a prefix character:

The series "axBx" starts with the prefix character 'a'. It satisfies this rule by starting with the required prefix character.

3. A series must end with a punctuation character:

The series "axBx" ends with the punctuation character 'x'. It follows this rule by ending with the required punctuation character.

4. A series can have up to but no more than 5 characters, including prefix and punctuation characters:

The series "axBx" has a total of 5 characters, which includes the prefix character 'a', the letters 'x' and 'B', and the punctuation character 'x'. It adheres to this rule by having the maximum allowed number of characters in the series.

Therefore, the series "axBx" satisfies all the rules of the language defined above. It contains one prefix character, starts with a prefix character, ends with a punctuation character, and has the maximum allowed number of characters.

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Answer:

$2,403.02

Step-by-step explanation:

To calculate the amount of interest earned on an investment of $12,585 at 3.5% interest over 5 years if the interest is compounded monthly, we can use the compound interest formula:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ I=P\left(1+\frac{r}{n}\right)^{nt}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ interest earned. \\ \phantom{ww}$\bullet$ $P =$ principal amount. \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form). \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year. \\ \phantom{ww}$\bullet$ $t =$ time (in years). \\ \end{minipage}}[/tex]

Given values:

Substitute the values into the formula and solve for I:

[tex]I=12585\left(1+\dfrac{0.035}{12}\right)^{12 \cdot 5}-12585[/tex]

[tex]I=12585\left(1.00291666...\right)^{60}-12585[/tex]

[tex]I=12585(1.19094282...)-12585[/tex]

[tex]I=14988.015...-12585[/tex]

[tex]I=2403.01550...[/tex]

[tex]I=\$2403.02[/tex]

Therefore, the interest earned on an investment of $12,585 at 3.5% interest over 5 years if the interest is compounded monthly is $2,403.02 (to the nearest cent).

The height is  (x + 1) /x⁴ + 4x³ + 3x² + 8. Option D

From the information given, we have that the formula for calculating the volume of a rectangular prism is expressed as;

Volume = area × height

Then, we have that;

Area = x³ + 3x² + 8

Volume = x⁴ + 4x³ + 3x² + 8x + 4

Now, substitute the values, we get;

x⁴ + 4x³ + 3x² + 8x + 4 =  x³ + 3x² + 8 × height

Divide both sides by the coefficient of the height, we have;

Height =  x⁴ + 4x³ + 3x² + 8x + 4 /x³ + 3x² + 8

Factor the expression;

Height = (x + 1) /x⁴ + 4x³ + 3x² + 8

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Answer:

P(A) =  0.5

P(B) = 0.33

P(A ∩ B) = 0

P( A ∪ B) = 0.83

Step-by-step explanation:

Tot = 6 + 18 + 12 = 36

P(A) = 18/36 = 0.5

P(B) = 12/36 = 0.33

P(A ∩ B) = 0

P( A ∪ B) = P(A) + P(B) - P(A and B)

= 0.5 + 0.33 - 0

= 0.83

Since the translation moved the entire triangle ABC to the right without rotating it, the length of side AC remains the same. Therefore, side AC is congruent to side DF.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find Jonas's total score after 9 holes of golf, we add up all the individual scores:

+2 + 1 - 1 + 0 + 0 - 1 + 3 + 4 - 1 = 7

Jonas's total score after 9 holes is 7.

Since the total score is positive (above zero), Jonas's score is above par.

In the rock cycle diagram, these three processes occur in a specific order as D. Uplift, reaction with chemically active fluids, melting

Uplift: Uplift refers to the movement of rocks from deep within the Earth's crust towards the surface. This can occur due to tectonic forces, such as plate collisions or volcanic activity. Uplift exposes rocks to the Earth's surface, where they can undergo further processes.

Reaction with chemically active fluids: Once rocks are uplifted and exposed to the surface, they come into contact with chemically active fluids, such as water or magma. These fluids can infiltrate the rocks, leading to chemical reactions and alteration of their composition. This process is commonly observed in hydrothermal systems or areas of volcanic activity.

Melting: The last step in the sequence is melting. When rocks are subjected to intense heat and pressure, either due to tectonic forces or proximity to a magma source, they can undergo partial or complete melting. This molten rock, called magma, can then solidify and form igneous rocks through processes like cooling and crystallization.

Option D correctly represents the order of these processes in the rock cycle diagram. It starts with uplift, followed by the reaction with chemically active fluids, and concludes with melting. Understanding the sequence of these processes is crucial for comprehending the dynamic nature of Earth's geology and the continuous transformation of rocks throughout geological time. Therefore, Option D is correct.

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Step-by-step explanation:

arithmetic sequence :

a1 = 7

d = 3

an = an-1 + d = a1 + (n-1)×d

the formula for the sum of an arithmetic sequence is

n/2 × (2×a1 + (n-1)×d)

40 is a12 (n = 12), as 40-7 = 33, 33/3 = 11, 11 plus 1 from a1 is 12.

we have the sum of 12 terms.

12/2 × (2×7 + 11×3) = 6 × (14 + 33) = 6×47 = 282

so, we have :

the sum = 282

A = 12

B = 7 + (n-1)×3 = 7 + 3n - 3 = 4 + 3n

Answer: 287.1 billion liters

Step-by-step explanation:

Water usage per person: 30 liters/day

World population: 9.57 * 10^9

Total water needed = Water usage per person * World population

Total water needed = 30 liters/day * 9.57 * 10^9

To simplify the calculation, we can express 9.57 * 10^9 in scientific notation:

Total water needed ≈ 30 liters/day * 9.57 * 10^9

To multiply the two values, we multiply the numbers and add the exponents:

Total water needed ≈ (30 * 9.57) * 10^(0 + 9)

Total water needed ≈ 287.1 * 10^9

Now, we can convert the result back to standard notation:

Total water needed ≈ 287,100,000,000 liters

Therefore, if every person in the world used 30 liters of water a day, the total amount of water needed for one day would be approximately 287.1 billion liters.

The percentage of the books at the library are fiction books is 93%.

The percentage of the books at the library are fiction books is calculated as follows;

Total number of books = 2,790 (fiction) + 210 (non-fiction) = 3,000

Percentage of fiction books = (number of fiction books) / (total number of books) x 100%

Percentage of fiction books  =  (2,790 / 3,000) x 100

Percentage of fiction books = (0.93)  x 100

Percentage of fiction books  = 93%

Thus, the percentage of the books at the library are fiction books is determined by applying percentage formula.

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The given system of equations is represented as: 2x - 3y + z = 0-2x - y + 4z = 7x + 2y - 5z = -5

The solution of the given system of equations is x = 2, y = -1, z = 3, which can be verified by substituting these values of x, y and z in each equation of the given system of equations, respectively.

The given system of equations is a consistent system of equations, which means it has a unique solution.

The unique solution is found by solving the equations simultaneously using different methods such as substitution method, elimination method or matrix method.

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The inside of the bronchioles are covered in cilia and mucus that trap and remove dust and other foreign particles. The Option B.

The bronchioles which are small air passages in the lungs are lined with specialized structures called cilia and produce mucus. The cilia are tiny hair-like structures that constantly beat in coordinated motions, creating a wave-like movement.

The mucus which i a sticky substance is produced by goblet cells and acts as a protective layer. Together, the cilia and mucus form a defense mechanism that helps trap and remove dust, pollen, bacteria and other foreign particles that enter the airways during breathing.

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a.) The sample space for this scenario would be: Option A.

GG, GB, GR, BG, BB, BR, RG, RB, RR

b The probability distribution for X is:

X | 0 | 1 | 2 |

P(X) | 1/3 | 2/3 | 0 |

GG: There are no red crayons selected. X = 0.

GB, BG, RG: Only one red crayon is selected. X = 1.

GR, RB: One red crayon and one non-red crayon are selected. X = 1.

BB: There are no red crayons selected. X = 0.

BR, RB: One red crayon and one non-red crayon are selected. X = 1.

RR: Two red crayons are selected. X = 2.

The probability distribution for X would be as follows:

X = 0: P(X = 0) = 2/6 = 1/3

X = 1: P(X = 1) = 4/6 = 2/3

X = 2: P(X = 2) = 0/6 = 0

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The exact values of 3^-2 and 4^-3 are 1/9 and 1/64, respectively.

To find the exact values of 3^-2 and 4^-3, we must first understand the concept of exponents. Exponents are a shorthand way of representing repeated multiplication of the same number.

For example, 2^3 means 2 multiplied by itself three times: 2 × 2 × 2 = 8. Similarly, 3^4 means 3 multiplied by itself four times: 3 × 3 × 3 × 3 = 81.

3^-2 can be written as 1/3^2. Using the concept of exponents, 3^2 means 3 multiplied by itself two times: 3 × 3 = 9. Therefore, 3^-2 can be rewritten as 1/9.

4^-3 can be written as 1/4^3. Using the concept of exponents, 4^3 means 4 multiplied by itself three times: 4 × 4 × 4 = 64. Therefore, 4^-3 can be rewritten as 1/64.

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Answer: the car travels 2,870 meters with 52,700 joules of energy.

Step-by-step explanation:

The given car uses 756 joules of energy every second. So, it would use x amount of energy to travel for t seconds. We know that the car uses 52,700 joules of energy. Let's find the time first.T = E ÷ P = 52,700 ÷ 756 = 70 seconds.

Now, we can calculate the distance covered by the car with this amount of energy.

Distance = Speed × Time = 41 m/s × 70 s = 2,870 meters.

Therefore, the car travels 2,870 meters with 52,700 joules of energy.

The axiom in Euclidean geometry states that in space, there are at least four points that do not lie in the same plane.

Having at least four points that do not lie in the same plane is important in concept of Euclidean geometry because it allows for the construction of a three-dimensional coordinate system.

These non-coplanar points together with the three coordinate axes, form a basis for describing and analyzing spatial relationships and measurements. With a three-dimensional coordinate system, geometric figures and their properties are represented and enables the development of various mathematical principles and theorems in three-dimensional space.

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Answer:

d = -4.3

Step-by-step explanation:

-2d = 8.6

d is being multiplied by -2. You want d alone, so divide both sides of the equation by -2.

-2d/-2 = 8.6/-2

d = -4.3

The inequality 5m - 7 > 16 holds true for the values m = 6, 7, 8, 9, and 10, in the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

To determine the values for which the inequality 5m - 7 > 16 holds true, we can solve it algebraically and then check if each value in the given set satisfies the inequality.

Let's solve the inequality:

5m - 7 > 16

Adding 7 to both sides, we have:

5m > 23

Dividing both sides by 5, we get:

m > 23/5

Now we need to check if each number in the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} satisfies the inequality m > 23/5.

For m = 1:

1 is not greater than 23/5, so the inequality does not hold true.

For m = 2:

2 is not greater than 23/5, so the inequality does not hold true.

For m = 3:

3 is not greater than 23/5, so the inequality does not hold true.

For m = 4:

4 is not greater than 23/5, so the inequality does not hold true.

For m = 5:

5 is not greater than 23/5,  so the inequality does not hold true.

For m = 6:

6 is greater than 23/5, so the inequality holds true.

For m = 7, 8, 9, and 10:

All these values are also greater than 23/5, so the inequality holds true for them as well.visit

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