Select the 2 answers that would be like terms with 10x.
2x²
3x
x²
2a
4x
10

Answer: We can start by using the trigonometric identity:

tan(A + B) = (tan A + tan B) / (1 - tan A * tan B)

To find tan A and tan B, we can use the given information:

tan A = 2/3

sin B = sqrt(5)/5

To find tan B, we can use the relationship between sin, cos and tan:

tan B = sin B / cos B

Since sin² B + cos² B = 1, we know that:

cos B = sqrt(1 - sin² B) = sqrt(1 - (5/5)²) = sqrt(1 - (5/25)) = sqrt(20/25) = 2/sqrt(5)

So,

tan B = sin B / cos B = sqrt(5)/5 / 2/sqrt(5) = sqrt(5) / (2*sqrt(5)) = sqrt(5) / 10

Now, we can substitute these values back into the original identity:

tan(A + B) = (2/3 + sqrt(5)/10) / (1 - (2/3)(sqrt(5)/10))

Simplifying this expression gives us:

tan(A + B) = (2/3 + sqrt(5)/10) / (7/15)

And that's the final answer.

Step-by-step explanation:

The x-value that corresponds to the z-score -1.28 is 59.0

z-score=(x-value - Mean)/(Standard deviation)=-1.28;

or, x-value=Mean-1.28*Standard deviation=68-1.28*7=59.04=59.0 (rounded to the nearest tenth)            

where, Mean=68, Standard deviation=7.                

The x-value that corresponds to the z-score -1.28 is 59.0          

Both the terms standard deviation and mean are used in statistics. Standard deviation is a statistic that measures the distance from the mean and is calculated as the square root of variance by determining the position of each data point in relation to the mean. In the world of finance, standard deviation is extremely important. When applied to an investment's annual rate of return, standard deviation is a statistical measurement in finance.    

To learn more about mean and standard deviation  
https://brainly.com/question/28108712
#SPJ4      

The complete question is given below

The scores on a mathematics exam have a mean of 68 and a standard deviation of 7. Find the x-value that corresponds to the z-score -1.28. Round the answer to the nearest tenth.                          

For the function f(x)=1/2sin(2x-4)+3, the Domain: (-∞, ∞) and the Range: [2.5, 3.5].

The range of values that can be plugged into a function is known as its domain. In a function like f, this range corresponds to the x values (x).

The collection of values that the function assumes is known as its range. Following the insertion of an x value, the function outputs this set of values. The values of y are those.

An assembly line's machines can be compared to functions in this way. The machine in the middle performs the function. On one end of the assembly line are a few screws and bolts, and on the other end is a car.

Given that

F(x)=1/2sin(2x-4)+3

For the given function graph is sinewave (see attachment)

For which

Range: [2.5, 3.5]

Domain: (-∞, ∞)

Thus, For the function f(x)=1/2sin(2x-4)+3, the Domain: (-∞, ∞) and the Range: [2.5, 3.5].

Learn more about Domain and Range

https://brainly.com/question/28135761

#SPJ1

The expression 4√567 can be written in simplest form as 24√7.

Expression in math is a combination of numbers, symbols, and/or variables that represent a specific quantity or value. Expressions can be simple or complex, depending on the number of components that make up the expression. Expressions are used in mathematics to represent the calculation of a value from one or more other values. Examples of expressions include algebraic equations, polynomials, and trigonometric functions. Expressions can be evaluated to determine their numerical value or to determine relationships between different components of the expression.
To simplify the expression, we can use the property of radicals, which states that when an exponent is applied to a radical, the root and the exponent can be divided. In this case, the given expression can be simplified by dividing the root (4) and the exponent (567). Dividing 4 by 567 gives us the result 0.007059. To make this result a whole number, we can multiply it by 100 to get 0.7059. This result is the new exponent for the radical. The root remains the same, so the simplified expression is 24√7.

To know more about expression click-
https://brainly.com/question/1859113
#SPJ1

Answer: 13.3 :D

Step-by-step explanation:

The sum of 2 and b is greater than or equals to -27 is expressed as 2 + b ≥ -27. Therefore, b ≥ -29

Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.

Therefore, let's convert the words expression to a mathematical expression(inequality).

The sum of 2 and b is greater than or equals to -27 can be expressed as follows:

2 + b ≥ -27

Let's solve for b

2 + b ≥ -27

subtract 2 from both sides of the inequality

2 - 2 + b ≥ -27 - 2

b ≥ - 29

learn more on inequality here: https://brainly.com/question/30231190

#SPJ1

Answer:Y=15 X=9

Step-by-step explanation:

The value of 1% of 200% is 1/50 or 0.02

A percentage is a way to express a number as a fraction of 100. It is often denoted using the symbol %. It can also be used to express a change in a value, such as a increase or decrease in percentage.

1% of 200% can be written as:

1% of 200% = (1/100) × (200/100)

1% of 200% = ( 1 × 200)/ (100 × 100)

1% of 200% = 200/10000

1% of 200% = 1/50 = 0.02

Learn more about percentage on:

brainly.com/question/843074

#SPJ1

The corresponding sides and the corresponding angles along with the figure are given below.

A trapezium is a quadrilateral with four sides where two sides are parallel to each other.

We have,

From the given information we get the figure given below.

Trapezium ABCD.

Trapezium PQRS.

Now,

The corresponding sides are:

AB = RS

BC= SP

AD = RQ

CD = QP

The corresponding angles are:

∠B = ∠S = 90

∠C = ∠P = 90

∠A = ∠R

∠D = ∠Q

Thus,

The corresponding sides and angles are given above.

Learn more about trapezium here:

https://brainly.com/question/22607187

#SPJ1

Osvoldo fell short of his objective because the condition is getting AT LEAST 30%. He fell short of the requisite 30%, just achieving 25%.

In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100. Occasionally, the acronyms "pct.," "pct," and "pc" are also used. But it is commonly indicated by the percent sign, "%." The % amount has no dimensions. Percentages are essentially fractions when the denominator is 100. Use the percent sign (%) to indicate that a number is a percentage by placing it next to it. For instance, you score a 75% if you properly answer 75 out of 100 questions on a test (75/100). Divide the money by the total and multiply the result by 100 to calculate percentages. The formula for calculating the percentage is (value/total) x 100%.

given

30% would be the base. The ratio of whole grains to carbohydrates has been multiplied by 100.

Mass percentage equals (55/220)*100.

Percent mass Equals 25%

Osvoldo fell short of his objective because the condition is getting AT LEAST 30%. He fell short of the requisite 30%, just achieving 25%.

To know more about percentage visit:

https://brainly.com/question/28269290

#SPJ1

Translating words into algebraic expressions means taking words and replacing them with mathematical symbols to create an equation. For example, the expression "five more than a number" can be written as "x + 5" where "x" represents the number.

Translating words into algebraic expressions is a useful skill when solving math problems. It involves taking words and replacing them with mathematical symbols to create an equation. For example, the expression "five more than a number" can be written as "x + 5" where "x" represents the number. By translating words into an algebraic expression, it becomes easier to solve problems using the correct equations. It is important to remember to use the correct symbols and to be mindful of the order of operations when translating words into algebraic expressions. When done correctly, translating words into algebraic expressions can help to make complex math equations easier to understand and solve.

Learn more about expression here

https://brainly.com/question/14083225

#SPJ4

The solution for the equation is,

1. x = 2 and y = 1

2. no solution

3. y = 0 and x = 11

4. x = 4/3 and y = 10/3

How do linear equations work?

Since each term in a linear equation has an exponent of 1, graphing an algebraic equation always yields a straight line. It is called a "linear equation" because of this.

There are linear equations with one variable and those with two variables.

Given sets of equations,

1. x - y = 1

x + y = 3

add both the equations we get,

x - y + x + y = 1 + 3

2x = 4 (+y and -y eliminated)

x = 4/2 = 2

substitute value of  x

x + y = 3

2 + y = 3

y = 3 - 2 = 1

x = 2 and y = 1

2.  x + y = 1

x + y = 11

The two lines that are used to symbolize the equations in this instance are parallel, hence the problem has no solution.

3. x + 4y = 11

x - 6y = 11

We may remove the equations since x is a common constant in both equations.

x + 4y -(x - 6y) = 11 - 11

4y + 6y = 0

y = 0 and x = 11

4. -3x + 3y = 6

6x + 3y = 18

subtract equation 1 from 2

6x + 3y -(-3x + 3y) = 18 - 6

6x - 3y + 3x - 3y = 12

9x = 12

x = 12/9 = 4/3

substitute value of x

-3x + 3y = 6

-3(4/3) + 3y = 6

-4 + 3y = 6

y = 10/3

Hence the solution is 1. x = 2 and y = 1

2. no solution,

3. y = 0 and x = 11

4. x = 4/3 and y = 10/3.

Learn more about linear equations;

brainly.com/question/29739212

#SPJ4

Evaluating The function

f(x) = 6x - 4 ;

f(0) = -4

f(2) = 8

f(-2) = -16

f(4) = 20

f(-3) =  -22

Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The whole set of values that the function's output can produce is referred to as the range. The collection of values that might result in a function's outputs is known as the co-domain.

The function

f(x) = 6x - 4

Evaluating

f(0) = 6* 0 - 4 = -4

f(2) = 2*6 - 4 = 8

f(-2) = -2*6 - 4 = -16

f(4) = 4*6 - 4 = 20

f(-3) = -3*6 - 4 = -22

To learn more about Function refer to  :

brainly.com/question/29131910

#SPJ1

log 7 can be approximated by using the common logarithm values of nearby integers.

log 7 = log 4 + log 2 + log (7/4)

log 2 = 0.3010

log (7/4) = 0.1403

log 7 = 0.6021 + 0.3010 + 0.1403 = 1.0434

To calculate the logarithm of 7 without a calculator, we can use the common logarithm values of nearby integers. First we determine the logarithm of 4, which is 0.6021. Then, the logarithm of 2 is 0.3010. Finally, the logarithm of the fraction 7/4 is 0.1403. We then add all of these together to get the logarithm of 7 which is 1.0434. Therefore, the logarithm of 7 is approximately 1.0434 when calculated without a calculator.

log 7 can be approximated by using the common logarithm values of nearby integers.

learn more about logarithm here

https://brainly.com/question/30085872

#SPJ4

At 7.4 ( round to nearsest tenth) meters mark will Ario be present when Miguel starts the race. So, option (c) is right choice here.

We have, Miguel and his brother Ario are both deciding to a race.

Total length of pool = 25 meters

But they are standing 3 meters from one side of a 25-meter pool when both are decide to race.

So, the length of racing area = 25 - 3 = 22 meters.

Also, Miguel said that he will start when the ratio of Ario’s completed meters to Ario’s remaining meters is 1 : 4. Let us assume, the Ario’s completed meters be "x meters" . Then, Ario’s remaining meters = 22 - x

so, x : 22- x = 1 : 4

=> x/(22 - x) = 1/4

=> 4x = 22 - x

=> 5x = 22

=> x = 22/5 = 4.4

Ario position when Miguel starts the race with respect to pool's length = 4.4 meter + 3 meters

= 7.4 meter

Hence, required length is 7.4 meters.

To learn more about ratio , refer :

https://brainly.com/question/573032

#SPJ4

Complete question:

We have to rearrange the question as

Miguel and his brother Ario are both standing 3 meters from one side of a 25-meter pool when they decide to race. Miguel offers Ario a head start. Miguel says he will start when the ratio of Ario’s completed meters to Ario’s remaining meters is 1:4. At what meter mark will Ario be when Miguel starts the race? Round to the nearest tenth.

a) 4 meters

b) 6 meters

c) 7.4 meters

d) 7 meters

Answer: x16/6

Step-by-step explanation:

Divide the first term of the dividend by the first term of the divisor to divide polynomials using long division.

Divide the dividend's first term by the divisor's first term to get the quotient's first term. Multiply the divisor by the quotient's first term and subtract the product from the dividend to get the remainder. This residual is now handled as a fresh dividend, but the divisor stays unchanged.

Polynomial division steps:

Step 1: Take the dividend's first term (x^2) and divide it by the divisor's first term to get the quotient's first term.

Step 2: In this situation, multiply the divisor(x - 2) by the answer(x), then insert the product beneath the dividend(x^2 + 2x + 3).

Step 3: Subtract to create a new polynomial.

For more questions on Polynomials

https://brainly.com/question/28119824

#SPJ4

The total cost of the framing for the painting would be $13.20.

The length of the painting is 10.25 inches and the width is 6.25 inches. To find the total length of the framing needed to go around the perimeter of the painting, we need to add the length and width of the painting and then multiply by 2. This is because the framing is needed for both the length and the width of the painting.

10.25 inches + 6.25 inches = 16.50 inches of framing needed

Since we need to go around the perimeter of the painting we need to multiply the 16.50 inches of framing by 2 = 33 inches of framing.

Finally, we multiply the total inches of framing needed (33 inches) by the cost per inch of framing ($0.40/inch) to get the total cost:

33 inches x $0.40/inch = $13.20

So the total cost of the framing for the painting would be $13.20.

Learn more about perimeter here: https://brainly.com/question/19819849

#SPJ4

The density of the land will be 0.5 Deer/foot

Density is the amount of things (people, animals, plants, or items) in a given area. To compute density, divide the number of items by the area measured. A country's population density is the number of inhabitants divided by its area in square kilometers or miles.

The amount of a quantity (typically mass) per unit of area is known as surface density. Density=Quantity/Area.

The quantity of data that can be stored on a given unit of physical space on storage medium is measured as areal density.

Total number of deer = 12

Area occupied = 6 Sq. foot

So, the value of density = (6/12) 0.5 Deer/Foot

For more questions on Density

https://brainly.com/question/26364788

#SPJ4

The person that would have to clean the higher number of rooms would be Mackenzie.

This would be gotten from the rate that the both of the persons involved are working.

On that particular day, they are both said to have cleaned equal number of rooms. The next day, they have the same shift length but Mackenzie is working for fewer hours.

This tells us that Mackenzie has a higher work rate than Lilian, hence she would have to clean more rooms.

Read more on rate of work here: https://brainly.com/question/28380981

#SPJ1

Domain = R or (-∞, ∞)

Range = R, because ∀ x ∈ R(Domain) y is also real.

How do you find the domain and range of f(x) =3x + 5

Clearly no real value of f(x) can make f(x) an imaginary value or value like ∞.

Domain = R or (-∞, ∞)

Range = R, because ∀ x ∈ R(Domain) y is also real.

As we observe, lines go off infinitely in both directions.

Therefore, the domain and range of this function are both set of reals or (-∞, ∞).

Example:

Suppose f(x) = 1/x

When x = 0, f(x) = 1/0 = infinity

Thus, the domain of f(x) cannot be R. Therefore, to define the domain the values of x which make f(x) = infinity are excluded from the set of reals.

Therefore the domain is R - {0}.

To know more about domain visit brainly.com/question/28135761

#SPJ4

The solution of y is equal to 4

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here: The equation is 6+3y=4y+2

Simplifying this expression we get 4y-3y=4

                                                                y=4

Hence, the solution of y is equal to 4

Learn more about the solution of a linear equation:

https://brainly.com/question/545403

#SPJ1

In mathematics, inequality refers to a relationship between two expressions or values that is not equal to one another.

A connection in mathematics that compares two numbers or other mathematical expressions in an unequal way is known as an inequality. It is most frequently used to compare the sizes of two numbers on the number line.

A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics. So inequality emerges from an imbalance.

Both equations and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >.

"Less than or equal to," "less than," or "not equal to" are all ways to describe an inequality, which is a mathematical relationship between two expressions.

To learn more about inequalities refer to:

https://brainly.com/question/25275758

#SPJ1

The value of {x} is equivalent to 7.

Given is a triangle ΔXYW.

The median of a triangle is a bisector of the angle. Median is found to be joining the vertex of the triangle with the opposite side of the triangle. So, we can write -

m∠1 = m∠2

(2x + 9) = (4x - 5)

2x + 9 = 4x - 5

14 = 2x

x = 7

Therefore, the value of {x} is equivalent to 7.

To solve more questions on triangles, visit the link below -

brainly.com/question/12413243

#SPJ1

The equation in the form [tex]x^{2}[/tex] + bx = c is [tex]x^{2}[/tex] - 2x = 15.

By adding to both sides the term needed to complete the square is 1.

Factors of the perfect square trinomial are 5 and - 3.

As per the given data the given equation is:

[tex]x^{2}[/tex] - 2x - 15 = 0

1. Rewrite the equation in the form [tex]x^{2}[/tex] + bx = c

Since a = 1 keep the “x-terms” (both the squared and linear terms) on the left side but move the constant to the right side.

Add 15 on both sides of the equation.

[tex]x^{2}[/tex] - 2x - 15 + 15 = 0 + 15

[tex]x^{2}[/tex] - 2x = 15

2. Add to both sides the term needed to complete the square.

Divide by 2, followed by squaring (raising to the 2 nd power).

[tex]& x^2-2 x=15 \\[/tex]

[tex]& \left(\frac{-2}{2}\right)^2=1[/tex]

The output here, which is +1, will be added to both sides of the quadratic equation.

[tex]x^{2}[/tex] - 2x + 1 = 15 + 1

[tex]x^{2}[/tex] - 2x + 1 = 16

[tex](x-1)^2=16[/tex] (Perfect square trinomial express into square of a binomial)

3. Factor the perfect square trinomial.

[tex]\sqrt{(x-1)^2} & =\pm \sqrt{16} \\[/tex]

x - 1 = ± 4

x - 1 + 1 = ± 4 + 1

x = ± 4 + 1

x = 4 + 1           x = -4 + 1

x = 5                x = - 3

For more questions on quadratic Equations

https://brainly.com/question/15645424

#SPJ4

The nearest ten of 741 is 740.

The number system or the numeral system is the system of naming or representing numbers. We know that a number is a mathematical value that helps to count or measure objects and it helps in performing various mathematical calculations.

In mathematics, there are various number systems such as the decimal number system, binary number system, octal number system, and hexadecimal number system.

Round the number to the nearest ten. 741 is between 740 and 750.

Looking at the 1 in the one's place. It's less than 5, so round down to 740.

Thus, the nearest ten of 741 is 740.

To know more about number system visit: brainly.com/question/17429689

#SPJ4

The equation of linear function f with the given values f(0) = 5 f(9) = -4 is,

⇒ f (x) = - x + 5

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The given values are,

⇒ f(0) = 5 and f(9) = -4

Now,

Let a linear equation is,

⇒ f (x) = ax + b

Here,  f(0) = 5

So, We get;

⇒ f (0) = a × 0 + b

⇒ 5 = b

⇒ b = 5

And, f(9) = -4

So, We get;

⇒ f (9) = a × 9 + 5

⇒ - 4 = 9a + 5

⇒ 9a = - 4 - 5

⇒ 9a = - 9

⇒ a = - 1

So, The linear equation is,

⇒ f (x) = ax + b

⇒ f (x) = - x + 5

⇒ y = - x + 5

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

The range of the function f(x) = |x-1| is all non-negative real numbers from 0 to infinity.

The range of a function is all the possible values that can be outputted from the function. The range of the function f(x) = |x-1| is determined by looking at the expression and analyzing its behavior for different values of x.

When x is less than 1, the expression becomes negative and the absolute value makes the result positive. Therefore, for x less than 1, the result will be a positive number greater than 0. When x is equal to 1, the result is 0. When x is greater than 1, the expression is already positive, so the absolute value does not change the result.

This means that for x greater than 1, the result will also be a positive number greater than 0. Therefore, the range of the function f(x) = |x-1| is all non-negative real numbers from 0 to infinity.

For more questions like Range click the link below:

https://brainly.com/question/24217266

#SPJ4

Answer: The area of a rectangle is given by the formula: A = L x W

Where A is the area, L is the length and W is the width.

Given that the area of the rectangle is 32a^3b^4 square units, and the length is shown in the image, we can use the formula to find the width:

32a^3b^4 = L x W

To find the width, we need to divide both sides of the equation by L.

32a^3b^4 = L x W

W = 32a^3b^4 / L

As the length of the rectangle is given as 8a^2b^2, we can substitute it in the above equation to find the width of the rectangle

W = 32a^3b^4 / 8a^2b^2

W = 4ab^2

So the width of the rectangle is 4ab^2 square units.

We used the formula of the area of the rectangle and the given information of the area and length to find the width of the rectangle by isolating the width on one side of the equation.

Step-by-step explanation: