What is the slope of a line parallel to the line whose equation is 9x-3y=-54

b. <2 ≅ < 3; corresponding angles are equal

d. < 1 + < 2 = 180 degrees; sum of angles on a straight line

To determine the reasons, we need to know about transversals

Transversals are lines that passes through two lines at the given plane in two distinct points.

It intersects two parallel lines

It is important to note the following;

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Answer: Stephens dog weighs 60 pounds

Step-by-step explanation:

Answer:

a=m-n

(Add n to both sides)

a+n=m-n+n

(The -n and +n cancel out, on the right side of the equation)

a+n=m

(Now subtract a from both sides)

a+n-a=m+a

(The +a and -a cancel out, on the right side of the equation)

n=m+a

Answer:

\(\huge \boxed{n=-a+m}\)

Step-by-step explanation:

\(a=m-n\)

Adding \(n\) to both sides.

\(a+n=m-n+n\)

\(a+n=m\)

Subtracting \(a\) from both sides.

\(a+n-a=m-a\)

\(n=m-a\)

There is a probability of approximately 31.43% that three students selected at random from the class will all be girls.

To find the probability that all three selected students are girls, we need to calculate the probability of selecting a girl on the first draw, then a girl on the second draw, and finally a girl on the third draw.

The probability of selecting a girl on the first draw is 12/16 (since there are 12 girls out of a total of 16 students).

After one girl has been selected, there will be 11 girls left out of a total of 15 students, so the probability of selecting a girl on the second draw is 11/15.

After two girls have been selected, there will be 10 girls left out of a total of 14 students, so the probability of selecting a girl on the third draw is 10/14.

So, the overall probability of selecting three girls in a row is:

(12/16) x (11/15) x (10/14) = 0.3143 or approximately 31.43%

Therefore, there is a probability of approximately 31.43% that three students selected at random from the class will all be girls.

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Answer:

B)6^-2

Because

6^-2

1/6²

1/36

Step-by-step explanation:

Answer:

b , c , f

Step-by-step explanation:

1/36 = 0.028

a) 3^-6 = 0.0014

b)6^-2 = 0.028

c) 6^3/6^5 = 0.028

d)6^2/ 6^-1 = 216

e) 6×6^-2 = 0.1667

f) 6^-9×6^7​ = 0.028

To determine whether the set S = {-2x + x^2, 8 + x^3, -x^2 + x^3, -4 + x^2} spans P3, we need to check if every polynomial in P3 can be expressed as a linear combination of the polynomials in S.

First, let's check if S is a set of linearly independent polynomials. We can do this by setting up the matrix equation: c1(-2x + x^2) + c2(8 + x^3) + c3(-x^2 + x^3) + c4(-4 + x^2) = 0, This gives us the system of equations: -c1 + c2 - c3 + c4 = 0
c1 = 0
c3 = 0
c1 - c2 + c3 + c4 = 0
Simplifying these equations, we get: c1 = 0
c3 = 0
c2 = c1 + c4
c4 = -c1 + c2.

Since c1 and c3 are both 0, we can solve for c2 and c4 in terms of a single variable. Let's set c1 = t, where t is any real number. Then: c2 = t + c4, c4 = -t + c2, So the set S is linearly dependent. This means that not every polynomial in P3 can be expressed as a linear combination of the polynomials in S. Therefore, S does not span P3. We do not need to list the c's in this case, since S does not span P3.

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Euler's method will be more accurate if the solution to the differential equation is a lower order polynomial. As the order of the polynomial increases, the accuracy of Euler's method decreases.

Euler's method is a numerical approximation technique used to estimate the solution to a differential equation. It is not exact and introduces some error due to its approximation nature.

The accuracy of Euler's method depends on the order of the polynomial that represents the solution.

In general, Euler's method is more accurate for lower order polynomials. This means that if the solution to the differential equation is a lower order polynomial, the approximation obtained using Euler's method will be more accurate.

To understand this, let's consider an example. Suppose we have a first-order polynomial as the solution to the differential equation.

In this case, Euler's method will provide a reasonably accurate approximation. However, as the order of the polynomial increases, the accuracy of Euler's method decreases.

It's important to note that higher order polynomials have more complex behavior, and Euler's method cannot capture all the intricacies of the solution.

In such cases, other numerical approximation methods, like the Runge-Kutta method, may be more suitable.

In summary, Euler's method will be more accurate if the solution to the differential equation is a lower order polynomial. As the order of the polynomial increases, the accuracy of Euler's method decreases.

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Answer:

Inequalities may show an expression that is greater than or less than something. (You can remember this because the bigger, open end is first.) (You can remember this because the smaller, closed end is first.) (The line under the symbol means equal to.)

Step-by-step explanation:

Answer:

2. 36

3. 8

4. 64 - 32

5. 7

I hope that this helps you, I'm not sure if number 4 is correct, but I am 100% sure that the rest are correct. I did the math for all of the questions and they should all be correct. I hope you have a wonderful evening!

Given the points (2, k) and (0, -6), and the distance is √5

The distance between two points is calculated by the formula:

Hence,

Therefore, the values of k would be -5 or -7 [option A is correct]

Answer:

C. She used GF = 2BG, but the correct statement is BG = 2GF.

Step-by-step explanation:

credits to the other person!

Answer:

C.

Step-by-step explanation:

Edge 2021

Answer:

M = 36

Step-by-step explanation:

Since SAM = ZYX

We can assume that all angles on SAM will equal the same as ZYX.

There are 180° total in a triangle, so you add 60 + 84, which equals 144, then you subtract 144 from 180 to find the remaining angle.

Therefore M = 36°

The output of the function can be calculated by plugging in 2 for x and evaluating the equation:\(f(2) = 2(2^3) + 5(2^2) - 7(2) + 4 = 16 + 20 - 14 + 4 = 26.\)

The Common Core standards for Pre-Calculus focus on the study of functions and their applications, as well as the development of a deeper understanding of the algebraic and geometric principles in the mathematical field. One of the core concepts covered in Pre-Calculus is the concept of polynomial functions. A polynomial function is an expression made up of terms that involve only constants, variables, and exponents. It is represented by the equation \(f(x) = ax^n + bx^n-1 + cx^n-2 + … + z\), where a, b, c, …, z are constants and n is a non-negative integer. To find the value of a polynomial function at a given value of x, the equation can be evaluated by plugging in the x value and calculating the output. For example, if a polynomial function is represented by the equation f(x) = 2x^3 + 5x^2 - 7x + 4, and the x value is 2, then the output of the function can be calculated by plugging in 2 for x and evaluating the equation: \(f(2) = 2(2^3) + 5(2^2) - 7(2) + 4 = 16 + 20 - 14 + 4 = 26.\)

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Complete question:

What is the output of the polynomial function f(x) = 2x^3 + 5x^2 - 7x + 4 when x = 2?

Given the function is f(x) = kx² and the interval is [0, 3]. To find k such that the function is a probability density function over the given interval, follow these steps:Step 1: For a probability density function, the area under the curve should be equal to 1.

Step 2: Integrate the given function to get ∫₀³ kx² dx = k(x³/3) [0, 3] ∫₀³ kx² dx = k(3³/3 − 0³/3) ∫₀³ kx² dx = 9kStep 3: Equate the above value to 1. 9k = 1 k = 1/9Now that we have found k, we can write the probability density function.The probability density function is given as:f(x) = kx², where k = 1/9; and the interval is [0, 3].f(x) = (1/9)x²;[0,3]Hence, the probability density function is f(x) = (1/9)x², where the interval is [0, 3].

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The expression for the power delivered to a resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).

According to the given information, the power delivered to a resistance R when an alternating current of frequency f and peak current I_0 passes through it is represented by the equation P = I^2_0 R sin^2 2 pi ft.

To express this equation in terms of csc^2 2 pi ft, we can use the trigonometric identity csc^2 x = 1/sin^2 x. Substituting this identity into the equation, we get P = I^2_0 R (1/sin^2 2 pi ft).

Since csc^2 x is the reciprocal of sin^2 x, we can rewrite the equation as P = I^2_0 R (csc^2 2 pi ft). This expression represents the power delivered to the resistance in terms of csc^2 2 pi ft.

Therefore, the correct expression for the power delivered to the resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).

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Answer:

3x^2−2

Step-by-step explanation:

Given f(x)=3x−5 and g(x)=x^2+1

∴f(g(x))=f(x^2+1)

=3(x^2+1)−5

=3x^2−2

The value of the given question by using the above pattern is (i)127, (ii)397, (iii)1141, (iv)7651.

In the real world, in artificial design, or in abstract concepts, a pattern is a regularity. As a result, a pattern's components repeat in a predictable way. Any of the senses can directly witness patterns, which are types of patterns made of geometric shapes and frequently repeated like wallpaper designs. On the other hand, abstract patterns in science, math, or language might only be visible through analysis. In actuality, direct observation entails recognizing visual patterns, which are common in both nature and art. Natural visual patterns are frequently chaotic, hardly ever precisely repeat, and frequently contain fractals. Spirals, meanders, waves, foams, tilings, fissures, and patterns produced by rotational and reflective symmetries are examples of natural patterns.

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Answer:

The equation is an example of the associative property of addition.

Step-by-step explanation:

Associative property of addition: changing the grouping of addends does not change the sum.

For example: A+(B+C) = (A+B)+C.

Answer:

A. p is the independent variable, and s is the dependent variable.

Step-by-step explanation:

In this scenario, the number of people attending the potluck is the independent variable because it is the variable that is being controlled or determined before the brownies are cut. The number of squares the brownies are cut into, on the other hand, depends on the number of people attending the potluck. Therefore, the number of squares is the dependent variable in this scenario.

The pythagorean theorem establish that:

where c is the hypotenuse, a and b are the legs of the right triangle.

In this case then:

Solving for x we have:

Therefore, x=15.

Answer: 36

Step-by-step explanation:

The answer is 36 because if you multiply:

6 * 2 = 12

12 * 3 = 36

And so that equals 36 sq cm

OR:

6 * 2 * 3 = 36 sq cm

I hope this helped!

Answer:

y = x - 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 1, - 7 ) and (x₂, y₂ ) = (7, 1 )

m = \(\frac{1-(-7)}{7-(-1)}\) = \(\frac{1+7}{7+1}\) = \(\frac{8}{8}\) = 1 , then

y = x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (7, 1 ) , then

1 = 7 + c ⇒ c = 1 - 7 = - 6

y = x - 6 ← equation of line

From the 25,000 participants,

14,810 are less than 35 years old.

Answer:

a man invests his savings in two accounts, one paying 6% and the other paying 10% simple interest per year. he puts twice as much in the lower-yielding account because it is less risky. his annual interest is $2,640. how much did he invest at each rate?a man invests his savings in two accounts, one paying 6% and the other paying 10% simple interest per year. he puts twice as much in the lower-yielding account because it is less risky. his annual interest is $2,640. how much did he invest at each rate?a man invests his savings in two accounts, one paying 6% and the other paying 10% simple interest per year. he puts twice as much in the lower-yielding account because it is less risky. his annual interest is $2,640. how much did he invest at each rate?a man invests his savings in two accounts, one paying 6% and the other paying 10% simple interest per year. he puts twice as much in the lower-yielding account because it is less risky. his annual interest is $2,640. how much did he invest at each rate?a man invests his savings in two accounts, one paying 6% and the other paying 10% simple interest per year. he puts twice as much in the lower-yielding account because it is less risky. his annual interest is $2,640. how much did he invest at each rate?a man invests his savings in two accounts, one paying 6% and the other paying 10% simple interest per year. he puts twice as much in the lower-yielding account because it is less risky. his annual interest is $2,640. how much did he invest at each rate?a man invests his savings in two accounts, one paying 6% and the other paying 10% simple interest per year. he puts twice as much in the lower-yielding account because it is less risky. his annual interest is $2,640. how much did he invest at each rate?a man invests his savings in two accounts, one paying 6% and the other paying 10% simple interest per year. he puts twice as much in the lower-yielding account because it is less risky. his annual interest is $2,640. how much did he invest at each rate?a man invests his savings in two accounts, one paying 6% and the other paying 10% simple interest per year. he puts twice as much in the lower-yielding account because it is less risky. his annual interest is $2,640. how much did he invest at each rate?

To construct a 98% confidence interval for the mean of repeated measurements of the weight, we can use the formula:

Confidence interval = mean ± (t-value) x (standard error)

where the standard error is the standard deviation of the sample divided by the square root of the sample size, and the t-value is based on the degrees of freedom (n-1) and the desired level of confidence. Since we are given the sample mean, standard deviation, and sample size, we can plug in the values and solve for the confidence interval and margin of error.

First, we need to calculate the standard error:

Standard error = standard deviation / √n

Standard error = 0.020 gram / √40

Standard error = 0.00316 gram

Next, we need to find the t-value for a 98% confidence interval with 39 degrees of freedom. We can use a t-distribution table or calculator to find the t-value, which is approximately 2.423.

Substituting the values into the formula, we get:

Confidence interval = 10.230 ± (2.423)(0.00316)

Confidence interval = 10.230 ± 0.00766

Rounding to three decimal places, the 98% confidence interval for the mean weight is (10.222, 10.238) grams. The margin of error is half the width of the confidence interval, which is 0.00766/2 = 0.00383 grams

Answer:

\( \frac{1}{76543^4} \)

Step-by-step explanation:

We are given base that is raised to a negative power of 4, \( 76543^{-4} \).

Another way to rewrite this is as indicated as follows: thus, \( a^{-x} = \frac{1}{a^x} \), where, a is the base, and x is the exponent.

Therefore, an equivalent expression of \( 76543^{-4} \) = \( \frac{1}{76543^4} \)

Answer: 3/6

Step-by-step explanation:

Answer:

L = 5/4 yards

L = 1 1/4 yards

L = 1.25 yards

Step-by-step explanation:

area = Length * Width

3/4 = L * 3/5

Divide both sides by 3/5

(3/4) / (3/5) = L

When dividing by a fraction flip it over and multiply

3/4 * 5/3 = L

The 3 cancels

5/4 = L

L = 5/4 yards

as a proper fraction

L = 1 1/4 yards

As a decimal

L = 1.25 yards

Answer:

Its D.

Step-by-step explanation:

The expanded form of this number 630.052 is (6×100)+(3×10)+(5×1/100)+(2×1/1,000). Option D is correct.

Arithmetic is a branch of mathematics that studies numbers and the many operations that may be applied to them. The four basic math operations are addition, subtraction, multiplication, and division.

The expanded form of this number 630.052 is solved by the BODMAS rule ;

630.052= (6×100)+(3×10)+(5×1/100)+(2×1/1,000)

630.052=6×100+3×10+5×0.01+2×0.001

630.052=600+30+0.05+0.002

630.052=630.052

The expanded form of this number 630.052 satisfy the option D.

Hence option D is correct.

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