A system of equations is given. −5y = 10 − 5x −2y = 8 − 4x Solve for (x, y) using the elimination method.

The solution of the trigonometric equation sin^2(2x+3)+cos^2(2x+3)=2x+3 is x = -1.

Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles

sin²(2x+3) + cos²(2x+3) = 2x + 3

Remember, the trigonometric identity, sin²θ + cos²θ = 1.

Thus, we can say sin²(2x+3) + cos²(2x+3) = 1. We now have:

sin²(2x+3) + cos²(2x+3) = 2x + 3

1 = 2x + 3

2x = 1-3

2x = -2

x = -2/2

x = -1

Therefore, the solution of the equation is x = -1

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Note that the explicit equation and domain for an arithmetic sequence with a first term of 3 and a second term of 5 is n = 3 + 2(n − 1); all integers where n ≥ 1 (Option D)

Arithmetic progression or arithmetic sequence is a numerical series in which the difference between subsequent terms is constant. For example, the sequence 5, 7, 9, 11, 13, 15..

The first term of the arithmetic sequence is 3, followed by 5. Thus, the common difference is, 5-3  = 2. You use these values to the derived formulas for arithmetic progression. One of these formulas is

An = A1 + (n-1)d

where

An is the nth term in the sequence

A1 is the first term of the sequence

n is the total number of terms within the sequence

d is a common difference.

In this problem, A1 = 5 and d=2. Substituting to the equation,

An = 3 + (2)(n-1)

An = 3 + 2(n-1), where n should be more than 1. In order for it to become a sequence, it should contain more than one term.

Therefore, it is correct to appropriate an explicit equation and domain for an arithmetic sequence with a first term of 3 and a second term of 5 to be: n = 3 + 2(n − 1); all integers where n ≥ 1

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Step-by-step explanation:

[tex]volume \: of \: cylinder = \pi \: {r}^{2} h \\ volume = 3.14 \times {7}^{2} \times 19 \\ = 2923.34 \: millimetres[/tex]

It is not possible to construct a triangle whose sides are 5 cm 7 cm and 12 cm because the sum of two sides(5 cm and 7 cm) are equal to the third sides(12 cm). Two equal sides cannot form a triangle.

In the given question, we have to check that it is possible to construct a triangle whose sides are 5 cm 7 cm and 12 cm.

The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.

To check this we firstly add the 5 and 7.

7 + 5 = 12

12 = 12

Now we add 5 and 12

5 + 12 > 7

17 > 7

Now we add 7 and 12

7 + 12 > 5

19 > 5

It is not possible to construct a triangle whose sides are 5 cm 7 cm and 12 cm because the sum of two sides(5 cm and 7 cm) are equal to the third sides(12 cm). Two equal sides cannot form a triangle.

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The complete question is:

Can a triangle have the sides 5 cm 7 cm and 12 cm?

The value of x is equal to 9 for the two-variable equation -2x - 7y = 17 when y is equal to -5.

A two-variable equation is an equation that has 2 variables, typically x and y

For the two-variable equation;

-2x - 7y = 17

we shall evaluate for the value of x when y = -5 as follows:

-2x - 7(-5) = 17

-2x + 35 = 17

subtract 35 from both sides of the equation

-2x = 17 - 35

-2x = -18

divide through by -2

x = -18/-2

x = 9

Therefore, 9 is the value of x when y is equal to -5 for the two-variable equation -2x - 7(-5) = 17.

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Answer:

not enough info

Step-by-step explanation:

Let h = number of history books.

Let m = number of math books.

"The number of history textbooks sold was three times the number of math textbooks sold."

h = 3m

"A textbook store sold a combined total of history and math textbooks in a week."

h + m = t

t = total number of books sold.

We have a system of equations:

h = 3m

h + m = t

Since we do not have a value for t, and we have a system of 2 equations in 3 variables, we cannot find the numbers of history or math books sold.

Argument A is deductive and Argument B is inductive.

Deductive reasoning uses broad premises to arrive at specific conclusions, while inductive reasoning starts with specific premises and draws general conclusions.

If the premises are valid, deductive reasoning's conclusions cannot be false. This is so because there is nothing in the conclusion that isn't already there in the premises. Yet, an inductively drawn conclusion goes beyond the information in the premises, unlike deductive reasoning.

Argument A is deductive because from the premise it is saying that the Grand Canyon was carved out by aliens from Jupiter, which is not sure.

Argument B is inductive because from the premise it is saying that Since the United States' Declaration of Independence was signed in the year 1776, it follows that the United States is over 200 years old, which is true.

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The complete question is:

INDUCTIVE /DEDUCTIVE ARGUMENT

Argument A: The Grand Canyon could not have been made by humans, so it follows that the Grand Canyon was carved out by aliens from Jupiter.

Argument B: Since the United States' Declaration of Independence was signed in the year 1776, it follows that the United States is over 200 years old.

Answer::b.

Step-by-step explanation:

Substitution is the name of the process in algebra which is used for swapping an algebraic letter for its value.

The substitution method is the algebraic method to solve different linear equations. In this method, the value of one variable from one of the equations is substituted in the other equation.

In substitution the following steps are used to solve an equation by substitution method:

Step 1. Simplify the given equation by removing the parenthesis.

Step 2. Solve one of the equations for any unknown value.

Step 3. Substitute step 2 result in the other equation.

Step 4. Now solve the equation which gets from step 3 obtained using elementary arithmetic operations.

Step 5. Finally, solve the final equation for the second variable.

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Answer:

-3c

Step-by-step explanation:

During photosynthesis, what is the path or flow of energy among biotic and abiotic parts of an ecosystem?

Answer:

-3c

Step-by-step explanation:

c+-4c+10+-10=  c+-4c= -3c

The equation of the relationship between the price of oranges last week and this week is y = 1.2x

From the question, we have the following parameters that can be used in our computation:

Price last week = x

Rate of increment = 20%

Price this week = y

Using the above as a guide, we have the following:

Price this week = Price last week * (1 + Rate of increment)

Substitute the known values in the above equation, so, we have the following representation

y = x * (1 + 20%)

Express as decimal

y = x * (1 + 0.2)

Evaluate the sum

y = x * 1.2

So, we have

y = 1.2x

Hence, the equation is y = 1.2x

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The derivatives of the given functions are 2 - 7/x, 6x + 4 - 5/x^4 Inx, -10t + 3 - 1/t Log t, and 6/x In 5 - 4x, respectively.

5. f'(x) = 2 - 7/x;

6. f'(x) = 6x + 4 - 5/x^4 Inx;

7. y' = -10t + 3 - 1/t Log t;

8. y' = 6/x In 5 - 4x

5. To find the derivative of the given expression, apply the chain rule. The derivative of 2x is 2, and the derivative of -7Ln x is -7/x. Thus, the derivative of the function is 2 - 7/x.

6. To find the derivative of the given expression, apply the chain rule. The derivative of 3x^2 is 6x, the derivative of 4x is 4, and the derivative of -Inx^5 is -5/x^4 Inx. Thus, the derivative of the function is 6x + 4 - 5/x^4 Inx.

7. To find the derivative of the given expression, apply the chain rule. The derivative of -5t^2 is -10t, the derivative of 4 is 0, and the derivative of -3t is -3. The derivative of Logt is 1/t Log t. Thus, the derivative of the function is -10t + 3 - 1/t Log t.

8. To find the derivative of the given expression, apply the chain rule. The derivative of 6In5x is 6/x In 5, and the derivative of -2x^2 is -4x. Thus, the derivative of the function is 6/x In 5 - 4x.

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0 is not an exponential function.

We know that the general form of exponential function f with base b is defined as:

f(x) = b^x

where b > 0 and b is not equal to 1

and x is any real number.

If it is negative  b < 0, the function is undefined for -1 < x < 1.

If in an exponential function the base is less than zero, then it would make the function values complex for certain fractional values.

If the base of exponential function is 0 then function would create a graph which violates the properties / definition of exponential functions.

Also, we can not write 0 in exponential function form.

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Answer: False

Step-by-step explanation:

-3/7 roughly equals -0.428

-2/5 equals -0.4

-0.4>-0.428

-2/5>-3/7

Answer:

For the first question, To determine the probability that a student studied for exactly 1 hour, we can use the formula:

P(X=1) = (number of students who studied for 1 hour) / (total number of students)

In this case,

P(X=1) = 8/30 = 0.27 (rounded to two decimal places)

So the probability that a student studied for exactly 1 hour is 0.27

For the second question, to determine the experimental probability of drawing a heart, we can use the formula:

P(Heart) = (number of times a heart is drawn) / (total number of draws)

In this case,

P(Heart) = 7/20 = 0.35

So the experimental probability of drawing a heart is 0.35

Therefore, the option 3 is the answer.

Step-by-step explanation:

Answer:The 3 in 103 is called the exponent. The expression 103 is called the exponential expression. base → 103 ←exponent

Step-by-step explanation:

Answer:

Two possible ways Arvin can complete his training plan are:

Biking 35 miles a week, 3 days a week, biking 11.67 miles per day.

Biking 41 miles a week, 4 days a week, biking 10.25 miles per day.

In the first option, Arvin bikes 35 miles a week, 3 days a week, which means he bikes 11.67 miles per day to achieve his goal.

In the second option, Arvin bikes 41 miles a week, 4 days a week, which means he bikes 10.25 miles per day to achieve his goal.

It is important to note that these are just examples, and there could be other options that Arvin can consider, as long as it meets his requirement of biking between 35 and 41 miles a week, either 3 or 4 days a week, and the same number of miles each day.

Step-by-step explanation:

The quote mentioned in the question was given by John F. Kerry who was a famous American personality, he was born on 11 December 1943.

Professionally he was an attorney and later became a politician and, diplomat and he currently serves as the first United States special presidential envoy for climate. He is a member of the Forbes family and the Democratic Party, and that he previously served as the 68th United States secretary of state .

Some of his other popular quotes are , "I saw courage both in the Vietnam War and in the struggle to stop it. I learned that patriotism includes protest, not just military service."

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On adding three digit number 109 to 7845 we get 7954 so the number is 109.

The one -ended or all of the addends in a 3-digit addition are numbers of three digits. Three-digit numbers can be added by placing them in columns so according their place values. Following that, we start adding the numbers from of the ones and tens columns before finishing with the hundreds column.

The numbers being added are termed addends, and the outcome of the operation, or the answer we ultimately get, is referred to as the sum. It is a fundamental mathematical operation that we employ on a daily basis. We add numbers in a variety of circumstances.

7845 + 1100

= 8945 so it is wrong

7845+109=7954

109 is 3 digit

and because of that, we won't need to consider any other options. If you checked them again, you would not receive a three-digit number.

so 109 is your answer

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The magnitude of the correlation coefficient indicates the strength of the association. For example, a correlation of r = 0.9 suggests a strong, positive association between two variables, whereas a correlation of r = -0.2 suggest a weak, negative association.

How to interpret a correlation coefficient?

The statistical measure of how well changes in the value of one variable predict changes in the value of another is called a correlation coefficient. The value rises or falls together when the variables are positively linked.

Is r or r 2 the correlation coefficient?

The summary table in the Regression output contains the "R" value, which is the coefficient of correlation. The term "coefficient of determination" also applies to R square. To obtain the value of R squared, multiply R by R. In other words, the square of the coefficient of correlation is the coefficient of determination.

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Answer:

5•8-(4+2)=34

Step-by-step explanation:

because you need to change the order of operation

The original amount is (100%) if you have an increased by 30%

Percentage increase is the difference between the final value and the initial value, expressed in the form of a percentage.

In the given question, the percentage increase can be calculated with the help of the percentage increase formula,

Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100

To get the original amount,

Just add the percentage increase to 100, divide 100 by it, then multiple by the final number to get the original number.

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Answer:

CD = 27

Step-by-step explanation:

2(4x - 1) + 2(3x + 3) = 116

8x - 2 + 6x + 6 = 116

14x + 4 = 116

14x = 112

x = 8

3(8) + 3

= 24 + 3

= 27

The value of  ∛64 will be equal to 4.

In mathematics, a number r is said to be the nth root of a number x if it is raised to the power n. where n is a positive integer, also referred to as the root's degree. Degree 3 roots are referred to as cube roots, while degree 2 roots are known as square roots.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The radical expression will be solved as,

∛64 = ∛ ( 4 x  4 x 4 )

∛64 = ∛ ( 4³ )

∛64 = 4

Hence, the solution for ∛64 will be 4.

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The value of b can be -32 or +32 to ensure that the equation has only one true solution.

The discriminant is the quadratic formula section behind the square root symbol: b2-4ac. The discriminant indicates whether there are two solutions, one solution, or none at all. The "discriminant" is the argument (that is, the contents) of the square root, which is the equation b2 4ac, because by utilizing its value, you may "discriminate" between (that is, determine the difference between) the various solution types.

Here,

The discriminant of the equation is ...

d = b² -4ac

d = b² -4(2)(128)

d = b² -1024

In order for there to be one real solution, we must have d=0. So ...

0 = b² -1024

1024 = b²

±√1024 = ±32 = b

The value of b can be -32 or +32 to cause the equation to have one real solution.

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39

40-32÷8+5-2

40-4+3

40-1

39

Answer:

slope = [tex]\frac{7}{3}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (5, 2 ) and (x₂, y₂ ) = (8, 9 )

m = [tex]\frac{9-2}{8-5}[/tex] = [tex]\frac{7}{3}[/tex]

By algebra properties, the values of algebraic expression x³ - 4 · x are - 3 and 0 for x² + x = 3.

In this question we must derive the value of algebraic expression x³ - 4 · x based on the fact that x² + x = 3. First, determine the value of x by algebra properties:

x² + x = 3

x² + x - 3 = 0

x² + (2 - 1) · x + 2 · (- 1) = 0

x² + 2 · x - x - 2 = 0

x · (x + 2) - (x + 2) = 0

(x - 1) · (x + 2) = 0

x = 1 or x = - 2

The roots of x² + x = 3 are 1 and - 2.

Second, determine the values associated with the two roots found in previous step:

x = 1

y = x³ - 4 · x

y = 1³ - 4 · 1

y = 1 - 4

y = - 3

x = - 2

y = x³ - 4 · x

y = (- 2)³ - 4 · (- 2)

y = - 8 + 8

y = 0

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