Which facts could be applied to simplify this expression? Check all that apply. 5 x 3 y (negative x) 6 z To add like terms, add the coefficients, not the variables. First add 5x x. The simplified expression is 4 x 3 y 6 z. Only combine terms which contain the same variable. The simplified expression is 5 x 3 y 6 z.

By using the cosine rule, we will see that the distance between the golfer and the hole is 69.7 yd.

Basically, we need to find the length of the missing side of the shown triangle.

So, one side measures 300yd, other side measures 275 yd, and the angle between these sides measures 13°.

Now we can use the cosine rule, where for sides a, b, and c, and angle A (A is the opposite angle to the side a) the rule says:

a^2 = b^2 + c^2 - 2bc*cos(A).

In this case we define:

Replacing that we get:

a^2 =  (300yd)^2 + (275yd)^2 - 2*(300yd*275yd)*cos(13°) = 4,853.94 yd^2

a = √(4,853.94yd^2) = 69.7 yd

So the distance between the golfer and the hole is 69.7 yd.

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Answer:

7°C is the answer cause its the opposite value of −7°C

Step-by-step explanation:

Answer: 15.64

Step-by-step explanation:

kahn

When an object is attached to a vertical spring and bobs up and down between points A and B, the location of the object when its elastic potential energy is minimum is at either A or B. Therefore, the correct option is C.

The elastic potential energy is the potential energy stored when a material is stretched or compressed. This energy is stored when the material is stretched or compressed and is used to return the material to its original state when the stress is removed.
Elastic potential energy is given by the formula:

PE = (1/2)kx^2,

where PE is the potential energy, k is the spring constant, and x is the displacement from the equilibrium position.

The potential energy is minimum when the displacement (x) is minimum, which occurs at the endpoints of the object's motion (points A and B).

Therefore, the object's elastic potential energy is minimum at either point A or point B. Hence, option C is correct.

Note: The question is incomplete. The complete question probably is: An object is attached to vertical spring and bobs up and down between points A and B. Where is the object located when its elastic potential energy is minimum? A) one-fourth of the way between A and B. B) one-third of the way between A and B. C) at either A or B. D) midway between A and B. E) at none of the above points.

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The definite integral equal to limn→[infinity]∑k=1n10kn(1+5kn−−−−−−√)(5n) is ∫50101+x−−−−−√ⅆx.

What is integral ?

An integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data.

to find the definite integral from a given interval that is equal to the limit of a summation as n approaches infinity. The limit of the summation is expressed as the product of 10, the summation of a term k that ranges from 1 to n, and a fraction involving the square root of 1 plus 5k times n.

To determine the definite integral that is equal to this limit, we need to identify the integrand, the interval of integration, and the constant factor of 10. By comparing the integrand, interval, and constant factor to the different definite integrals listed in the answer choices,  identify the correct answer.

The definite integral equal to limn→[infinity]∑k=1n10kn(1+5kn−−−−−−√)(5n) is ∫50101+x−−−−−√ⅆx.

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The nearest whole number when rounding to the nearest metre forces us to choose 3, which is the case here as 2.51 is closer to 3 than it is to 2.

The digits in a numerical value known as significant figures, sometimes known as significant digits, are those that show how precisely the measurement was made. The degree of precision of the measuring device used to perform the measurement determines the number of significant figures in the measurement.

We must round the height restriction to the closest metre in order to show it on the sign because it is specified as 2.51 metres.

We look at the digit in the tenths place, which is 5, to round to the closest metre. We round up the number to the next one since 5 is more than or equal to 5, which is 1. Thus, 3 m should be listed as the maximum height.

This is due to the fact that picking the nearest whole number when rounding to the nearest metre forces us to choose 3, which is the case here as 2.51 is closer to 3 than it is to 2.

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The variable x is the hypotenuse, and the value of x in the right triangle is 24.8

The complete question is a right triangle, where x is the hypotenuse.

So, the equation of x is:

\(x^2 = 19^2 + 16^2\)

Evaluate the sum of exponents

\(x^2 = 617\)

Take the square root of both sides

x = 24.8

Hence, the value of x is 24.8

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Answer:

Figure D

Step-by-step explanation:

dilation by a factor of 1/2: (x,y) -> (1/2 x , 1/2 y)

rotation 180°: (1/2 x , 1/2 y) -> (-1/2 x , -1/2 y)

Step-by-step explanation:

look at the graph !

there is an explicit horizontal limit line at y = -1.

no such vertical line for a limit for x.

as usual for exponential functions, f(x) grows rapidly, but is still valid for all x of R.

so, D is the right answer.

when x gets more and more to the left, f(x) grows and grows strongly, and goes to infinity.

when x gets more and more to the right, f(x) gets closer and closer to -1 (but will never reach it, only at infinity ...).

Answer:

when you 4, your sister is 2 years old

now that you 100, your sister should be 50 years old

half equal x/2 x indicates 100

Answer:

x=7

Step-by-step explanation:

4x-8=2x-6

4x-2x=-6+8

2x=-14(divide both the sides by 2)

x=7

\(\frac{x}{3}+5=x-1\)

Whenever there's a denominator. Multiply all whole equation with the denominator. For example, the denominator here in the equation is 3. So we multiply the whole equation by 3.

\(\frac{x}{3}(3)+5(3)=x(3)-1(3)\\x+15=3x-3\)

Moving the x to the same term which goes for the same as the constant for easier in solving.

\(15+3=3x-x\)

Moving to the another side, changing the sign/operator to opposite (From plus to minus, from multiply to divide.)

\(18=2x\\2x=18\\\)

Move 2 to another side, aka to divide 18.

\(x=\frac{18}{2}\\x=9\)

Therefore, the answer is x = 9.

Answer: 255°

Step-by-step explanation:

To convert an angle in radians to degree, we've to multiply it by 180/π. In this case, converting the angle 17pi/12 radians to degrees will be:

= 17π/12 × 180/π

= 17 × 15°

= 255°

The answer is 255°.

Answer:

y= −2/3x+2

Step-by-step explanation:

2x+3y=6

Add -2x to both sides.

2x+3y+−2x=6+−2x

3y=−2x+6

Divide both sides by 3.

3y/3=−2x+6/3

To simplify the expression 5√8 + √3, we can simplify each radical term separately and then combine them.

First, let's simplify the radical terms:

√8 can be simplified as 2√2 because 8 can be factored into 4 * 2, and √4 is equal to 2.

√3 cannot be simplified further since 3 is a prime number.

Now, let's substitute the simplified radical terms back into the expression:

5√8 + √3 becomes 5(2√2) + √3.

Next, we can multiply the coefficients outside the radicals:

5(2√2) is equal to 10√2.

Putting it all together, the simplified expression is:

10√2 + √3.

So, 5√8 + √3 simplifies to 10√2 + √3.

The value of each investment scenario based on the given interest compounded will be:

Let's discuss each scenario we have.

The value of Rod's annuity after 20 years will be $30,904.95. This is calculated by using the formula A = P((1+r/n)^(nt)), where P is the payment, r is the annual interest rate (7.88%), n is the number of times compounded per year (quarterly, or 4), and t is the number of years (20).

The value of Bubba's investment after 25 years will be $41,438.55. This is calculated by using the formula A = P((1+r/n)^(nt)), where P is the payment, r is the annual interest rate (7.26%), n is the number of times compounded per year (monthly, or 12), and t is the number of years (25).

The equivalent APY for the account at Crab Key Bank with an annual interest rate of 5.15% compounded quarterly is 5.25%. This is calculated by using the formula APY = (1+r/n)^n - 1, where r is the annual interest rate (5.15%), and n is the number of times compounded per year (quarterly, or 4).

The difference between an investment earning 8.75% annual interest compounded quarterly and one earning 8.7% compounded monthly is the number of times the interest is compounded each year. An investment earning 8.75% compounded quarterly has an interest rate of 8.75% that is compounded four times per year, while an investment earning 8.7% compounded monthly has an interest rate of 8.7% that is compounded twelve times per year.

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Answer:$9

Step-by-step explanation:Here's what we know:

2 * 24 + 3s = 75 (the pants ($24 each) and shirts all together is $75)

What we need to do is isolate s

Simplify:

48 + 3s = 75

subtract 48 from both sides:

48 + 3s - 48 = 75 - 48

3s = 27

Divide by 3:

3s / 3 = 27 / 3

s = 9

Shirts are $9 each.

Answer:

2 x 24 = 48

48 - 75 = 27

27 ➗ 3 = 9

so the cost of 1 shirt is $9

Step-by-step explanation:

Answer:

6) y= -3x+3

7) y= -4x+5

Step-by-step explanation:

Answer:

Step-by-step explanation:

3/9 can be a rational number.

Let me show you:

The Answer and/or 1 : 3 or 3 : 9.

Answer:

Is y = (x+8) (x+3)

Answer:

1. y=(x+8)(x+3)

Step-by-step explanation:

Problem to solve:

The eigenvalues of the matrix [0 -3; 1 -2] with multiplicity two twice are 2, 2, and -3.

The matrix given is:

[ 0 -3 ]

[ 1 -2 ]

To find the eigenvalues of this matrix, we need to solve the characteristic equation:

det(A - λI) = 0

where A is the matrix, λ is the eigenvalue, and I is the identity matrix. Substituting the given matrix, we get:

det([0 -3; 1 -2] - λ[1 0; 0 1]) = 0

Simplifying the above expression, we get:

det([-λ -3; 1 -2 - λ]) = 0

Expanding the determinant, we get:

(-λ) * (-2 - λ) - (-3) * 1 = 0

Simplifying the above expression, we get:

λ^2 - 2λ + 3 = 0

Solving the above quadratic equation, we get:

λ = (2 ± √(-8)) / 2 = 1 ± i√2

Since the given matrix has multiplicity two for one of the eigenvalues, the correct answer is (c):

λ = 2 (multiplicity two) and λ = -3.

Therefore, the eigenvalues of the matrix [0 -3; 1 -2] with multiplicity two twice are 2, 2, and -3.

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After solving the expression (x^2+3x-5)-(4x^2+3x-6) = -3x^2+1. So the option B is correct.

In the given question, we have to find which expression is equivalent to (x^2+3x-5)-(4x^2+3x-6).

The given options are:

A. 5x^2+6x-11

B. -3x^2+1

C. 3x^2+1

D. -3x^4+6x^2+1

To find  which expression is equivalent to (x^2+3x-5)-(4x^2+3x-6). We firstly simplify the given expression.

To simplify the expression, we multiply the bracket of right hand side by minus sign. As we know that when we multiply the variable with minus sign the sign will change.

(x^2+3x-5)-(4x^2+3x-6) = x^2+3x-5-4x^2-3x+6

(x^2+3x-5)-(4x^2+3x-6) = -3x^2+1

After solving the expression (x^2+3x-5)-(4x^2+3x-6) = -3x^2+1. So the option B is correct.

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Answer:

x=1 and y= 6

Step-by-step explanation:

and for y its a positive cause their both negitives

Answer:

The greatest common factor is 4

Step-by-step explanation:

1.Find the prime factorization of 12

         a) 12 = 2 × 2 × 3

2.Find the prime factorization of 196

         a) 196 = 2 × 2 × 7 × 7

To find the GCF, multiply all the prime factors common to both numbers:

          a)GCF=2x2

Therefore, GCF = 2 × 2

GCF = 4

The greatest common factor of the numbers 196 and 12 is 4.

The largest factor of the two numbers which divides both numbers is called as greatest common factor or GCF. The greatest common factor is the largest number which can divide both the numbers.

1. Find the prime factorization of 12

12 = 2 × 2 × 3

2. Find the prime factorization of 196

196 = 2 × 2 × 7 × 7

To find the GCF, multiply all the prime factors common to both numbers:

GCF=2x2

GCF=4

Therefore, the greatest common factor of the numbers 196 and 12 is 4.

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Answer:

f(x) = x - 3

Step-by-step explanation:

note that y = f(x) , then

x - y = 3 ( add y to both sides )

x = 3 + y ( subtract 3 from both sides )

x - 3 = y , that is

f(x) = x - 3

f(x) = x - 3  is the equation written in function notation, with x as the independent variable.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

To write the equation x - y = 3 in function notation with x as the independent variable, we need to solve for y in terms of x.

x - y = 3

y = x - 3

Therefore, the function represented by the equation x - y = 3, with x as the independent variable, can be written in function notation as:

f(x) = x - 3

So the answer is O f(x) = x - 3.

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The quadratic equation x² - 9 has two real roots.

The quadratic equation x² + 3 · x - 10 has two real roots.

The cubic equation x³ - 5 · x² + 10 · x - 8 has two complex conjugate roots and a real root.

According to complex conjugate root theorem, if a quadratic equation has a root of the form a + i b, where a, b are real numbers, then the other root is  a - i b. In addition, roots of quadratic equations of the form a · x² + b · x + c, where a, b, c are real coefficients. By quadratic formula, the equation has complex conjugate roots if:

b² + 4 · a · c < 0

Now we proceed to check each quadratic equations:

Case 1: (a = 1, b = 0, c = - 9)

D = 0² - 4 · 1 · (- 9)

D = 36

The equation has no complex conjugate roots.

Case 2: (a = 1, b = 3, c = - 10)

D = 3² - 4 · 1 · (- 10)

D = 9 + 40

D = 49

The equation has no complex conjugate roots.

The latter case is represented by a cubic equation, whose standard form is a · x³ + b · x² + c · x + d, where a, b, c, d are real coefficients. The equation has a real root and two complex conjugate roots if the following condition is met:

18 · a · b · c · d - 4 · b³ · d + b² · c² - 4 · a · c³ - 27 · a² · d² < 0

Now we proceed to find the nature of the roots of the polynomial: (a = 1, b = - 5, c = 10, d = - 8)

D = 18 · 1 · (- 5) · 10 · (- 8) - 4 · (- 5)³ · (- 8) + (- 5)² · 10² - 4 · 1 · 10³ - 27 · 1² · (- 8)²

D = - 28

The equation has a real root and two complex conjugate roots.

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The relative frequencies of this data by row is

          150 cc    180 cc

Black 0.43         0.57

Blue   0.47         0.53

Red   0.55          0.45

The table of values is given as:

          150 cc    180 cc

Black 18              24

Blue   15              17

Red   26              21

Calculate the row total.

          150 cc    180 cc    Total

Black 18              24          42

Blue   15              17           32

Red   26              21           47

Divide each element by the row total

          150 cc    180 cc

Black 0.43         0.57

Blue   0.47         0.53

Red   0.55          0.45

Hence, the relative frequencies of this data by row is

          150 cc    180 cc

Black 0.43         0.57

Blue   0.47         0.53

Red   0.55          0.45

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