Solve the system of equations using elimination. {3x+5y=22.55x+3y=17.5 Enter the correct answer in the boxes.

The results are : (b^(-6))(b^(-3)) = b^(-9), k^2 / k^1 = k,(y^(-6))^(-7) = y^(42),

(y^1)(y^2) = y^3

Let's complete the operations by filling in the exponents for the results:

(b^(-6))(b^(-3)) = b^(??)

To multiply the same base with different exponents, we add the exponents:

b^(-6) * b^(-3) = b^(-6 + -3) = b^(-9)

Therefore, (b^(-6))(b^(-3)) = b^(-9).

k^2 / k^1 = k^(??)

To divide with the same base, we subtract the exponents:

k^2 / k^1 = k^(2 - 1) = k^1 = k

Therefore, k^2 / k^1 = k.

(y^(-6))^(-7) = y^(??)

To raise an exponent to another exponent, we multiply the exponents:

(y^(-6))^(-7) = y^((-6) * (-7)) = y^(42)

Therefore, (y^(-6))^(-7) = y^(42).

(y^1)(y^2) = y^(??)

To multiply the same base, we add the exponents:

(y^1)(y^2) = y^(1 + 2) = y^3

Therefore, (y^1)(y^2) = y^3.

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Answer:

The biconditional statement p <-> q is true when p and q have the same truth values and is false otherwise.

Step-by-step explanation:

This is because the biconditional is saying "p if and only if q"

A biconditional statement, written as "p if and only if q" or "p <--> q," is only true when both p and q have the same truth value. In other words, if p is true, then q must also be true for the biconditional statement to be true. Likewise, if p is false, then q must also be false.

Therefore, a biconditional statement is only true when the two statements being compared have equivalent truth values. A biconditional statement, represented as p ↔ q, is only true when both p and q have the same truth values. In other words, it is true when:

1. p is true and q is true, or
2. p is false and q is false.

A biconditional essentially means "p if and only if q." If both statements are true or both statements are false, then the biconditional is true. If one statement is true and the other is false, then the biconditional is false.

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Answer:

D

Step-by-step explanation:

The distance from the vertex to the centroid is twice as long as the distance from the centroid to the midpoint, that is

ZY = \(\frac{1}{2}\) UZ = \(\frac{1}{2}\) × 8 = 4

Then

UY = UZ + ZY = 8 + 4 = 12 → D

Answer:

7

Step-by-step explanation:

love is = 4, because love + love = 8 meaning its 4+4

heart is = 5, because heart - 4(love) = 1

bird is = 3, because bear is = 9 since 5(heart) + 4(love) is bear, and 3 birds make  a bear.

Answer:

17

8 ÷ 2 = 4. love = 4.

heart - 4 = 1. heart = 5.

love 4 + heart 5 =9. bear =9

9÷3=3. birds = 3.

   123456789000009876543212345678908765435rtgbhnmkjhgvf bjlogvoufcggg      60

The probability that the sum is 7 given that neither die showed a 6 is 4/25 or 0.16.

To find the probability that the sum is 7 given that neither die showed a 6, we need to consider the possible outcomes of rolling two dice without any 6s, and then identify the outcomes where the sum is 7.

Determine the total number of possible outcomes without rolling a 6.
Since there are 5 possible outcomes for each die (1, 2, 3, 4, and 5), there are 5 x 5 = 25 possible outcomes for rolling two dice without any 6s.

Identify the outcomes where the sum is 7.
The possible outcomes that result in a sum of 7 are: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). However, since neither die can show a 6, we can only consider the following four outcomes: (1, 6), (2, 5), (3, 4), and (4, 3).

Calculate the probability.
The probability that the sum is 7 given that neither die showed a 6 is the number of favorable outcomes divided by the total number of possible outcomes:
P(sum is 7 | no 6s) = (number of outcomes with sum 7) / (total number of outcomes without 6s) = 4 / 25

So, the probability that the sum is 7 given that neither die showed a 6 is 4/25 or 0.16.

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Answer:

32 units squared

Step-by-step explanation:

8(4) = 32

Answer:

Step-by-step explanation:

All that making a list does is creates a visible step by step instruction manual on what needs to be done in order to solve the math problem that needs to be solved. Lists are extremely helpful and can be used in every single math problem, for example....

15x - 25 = 275

See making a list isolates the problem into an easy to read instruction manual.

The limit of the ratio test for the series ∑[infinity] to n=1 10^n÷n! is infinity (∞).

The ratio test is used to determine the convergence or divergence of a series. It involves taking the limit of the absolute value of ratio of consecutive terms. If the limit is less than 1, the series converges. If the limit is greater than 1 or infinity (∞), the series diverges. If the limit is exactly 1, the test will be inconclusive.

In this case, we have f(n) = ∣(10^n+1)÷(10^n)∣ = ∣10∣ = 10. The limit of f(n) as n approaches infinity is 10.

Since the limit of f(n) is greater than 1, the series fails the ratio test. This means that the series ∑[infinity] to n=1 10^n÷n! diverges. The ratio test suggests that the series does not have a finite sum and continues indefinitely.

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Answer:

41.18987

Step-by-step explanation:

The opportunity cost is merely the expense of not making a decision.

As a result, if you chose Project P placed above a white Project Q, the opportunity cost for such a decision is 75,000 times the estimated NPV of Project Q.

The distinction between current value of money over time value of cash outflows over time is defined as net present value (NPV).

Some key features regarding the Net Present Value (NPV) are-

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The proof of expression include:

The cosine law, also known as the law of cosines, is a trigonometric formula that relates the sides and angles of a triangle. It states that for any triangle with sides a, b, and c, and angles opposite those sides A, B, and C, the following equation holds true:

c² = a² + b² - 2ab cos(C) or a² = b² + c² - 2bc cos(A) or b² = a² + c² - 2ac cos(B)

These equations can be used to find the length of a side or the measure of an angle in a triangle if the lengths of the other sides and angles are known.

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Image transcribed:

Note: Type x in place of theta for any answers where you need the angle/variable, and type pi instead of using the symbol

cos (Θ-(3π)/2)=-sin Θ

Proof:

1. cos (Θ-(3π)/2)

2. Use the sum to product identity: cos Θ ________ + sin Θ ___________

3. Replace the values that you know in the function. (i.e. replace any specific angle values)

cos Θ ________ + sin Θ ___________

4. Simplify: __________

Answer:

16. -16+7=-9

17. -11+1=-10

18. 12+13=25

19. -4+(-8)=-12

Answer:

8+2w=y

Step-by-step explanation:

Step-by-step explanation:

14x-3=4x+13+6x+2(sum of two interior angle is equal to exterior)

14x-4x-6x=13+2+13

4x=28

x=28/4

x=7

14x-13=14*7-13=85

4x+13=4*7+13=85

6x+2=6*7+2=44

Conclusion of the given statement are as follow,

Statement 1 is true.

Statement 2 is true.

Statement 3 is false.

Let's analyze each statement and determine whether they are true or false,

Statement 1,

"For all objects j, if j is a square then j has four sides."

This statement is true.

By definition, a square is a polygon with four equal sides.

Therefore, for any object j that is a square, it will always have four sides.

Statement 2,

"All squares have four sides."

This statement is also true.

Again, by the definition of a square, it is a polygon with four equal sides.

Every square will always have exactly four sides.

Statement 3,

"An object is a square if it has four sides."

This statement is false.

While it is true that squares have four sides, having four sides does not necessarily mean that an object is a square.

There are other polygons, such as rectangles and rhombuses,

that also have four sides but do not meet the specific criteria of a square

having all sides equal in length and all angles equal to 90 degrees.

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The probability that a student scores between 450 and 600 on the SAT math section is approximately 0.4147 or 41.47%.

To find the probability that a student scores between 450 and 600 on the SAT math section, we need to use the properties of the normal distribution. We know that the mean is 511 and the standard deviation is 110.

First, we need to standardize the values of 450 and 600 using the formula:

z = (x - μ) / σ

where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

For 450:

z = (450 - 511) / 110 = -0.55

For 600:

z = (600 - 511) / 110 = 0.81

Next, we need to find the area under the normal curve between these two standardized values. We can use a table or a calculator to find that the area between z = -0.55 and z = 0.81 is approximately 0.4147.

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Answer:3(6+x)(6-x)

Step-by-step explanation:

Used a math app

Neither statement (1) nor statement (2) alone is sufficient to determine whether the mean of the set x is even.

To determine whether the mean of a set containing n integers is even, we need to consider the given statements:

Statement (1): n is even.

Statement (2): All of the integers in set x are even.

Let's analyze each statement:

Statement (1): If n is even, it means that the number of integers in the set x is even. However, this does not provide any information about the individual integers or their parity (even or odd). Therefore, statement (1) alone is not sufficient to determine whether the mean of the set x is even.

Statement (2): If all the integers in set x are even, then the sum of these integers will be even since the sum of even numbers is always even. However, this does not directly imply that the mean of the set x is even. The mean is calculated by dividing the sum of the numbers by the number of elements in the set.

Without knowing the value of n (the number of elements in the set), we cannot definitively determine the parity of the mean. Therefore, statement (2) alone is not sufficient to determine whether the mean of the set x is even.

Combining both statements: Even though statement (1) tells us that the number of integers in the set x is even, and statement (2) indicates that all the integers in set x are even, we still cannot determine with certainty whether the mean of the set x is even. We need additional information about the specific values of the integers in the set x to determine the parity of the mean.

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Therefore, the antiderivative of f(x) is F(x) = 1623x - 8x^3 + 2x^2 - 5x + 7.

To find an antiderivative F(x) of the given function f(x) = 1623 – 24x2 + 4x – 5, we need to find a function whose derivative is f(x). This process is called integration, and it is the reverse of differentiation.

We can integrate the function term by term, since we know the antiderivative of each term. The antiderivative of 1623 is 1623x, the antiderivative of -24x^2 is -8x^3, and the antiderivative of 4x is 2x^2. The constant term -5 integrates to -5x.

Therefore, the antiderivative of f(x) is F(x) = 1623x - 8x^3 + 2x^2 - 5x + C, where C is the constant of integration. To find the value of C, we use the given condition F() = 7. Substituting x = 0 and F() = 7, we get 0 + 0 + 0 + 0 + C = 7, which implies that C = 7.

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Answer:

3628800 ways if the women are always required to stand together.

To solve this problem, we can consider the number of ways to arrange the women and men separately, and then multiply the results together.

First, let's consider the arrangement of the women. Since no two men can be seated next to each other, the women must be seated in between the men. We can think of the 5 men as creating 6 "gaps" where the women can be seated (one gap before the first man, one between each pair of men, and one after the last man).

Out of these 6 gaps, we need to choose 7 gaps for the 7 women to sit in. This can be done in "6 choose 7" ways, which is equal to the binomial coefficient C(6, 7) = 6!/[(7!(6-7)!)] = 6.

Next, let's consider the arrangement of the 5 men. Once the women are seated in the chosen gaps, the men can be placed in the remaining gaps. Since there are 5 men, this can be done in "5 factorial" (5!) ways.

Therefore, the total number of ways to seat the 5 men and 7 women is 6 * 5! = 6 * 120 = 720.

There are 720 ways to seat the 5 men and 7 women in a row such that no two men are next to each other.

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a) The cost of the stereo system is $4,760.

b) The total amount of interest paid is $1,760.

To find the cost of the stereo system, we need to calculate the sum of the down payment and the total of monthly payments over 4 years. The down payment is $400, and the monthly payment is $90 for 48 months (4 years). Thus, the total cost of the stereo system is $400 + ($90 × 48) = $4,760.

To calculate the total amount of interest paid, we need to subtract the initial principal amount (down payment) from the total cost of the stereo system. The initial principal amount is $400, and the total cost is $4,760. Therefore, the total interest paid is $4,760 - $400 = $1,760.

In summary, the cost of the stereo system is $4,760, and the total amount of interest paid is $1,760.

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Use trigonometry to find L.

Tangent = opposite over adjacent on any right triangle.

tan(L) = 18/23

Take the inverse on both sides.

arctan(tan(L)) = arctan(18/23)

L = 38.0470425318

L = 38.05°

Done.

Explanation:

This equation represents a line, so there are many points that are solutions to the equation. To fill in this boxes we just have to pick a x-value that's in the domain, replace it into the equation and solve for y. The domain of this function is all real numbers, so any number will work.

Using x = 1:

Answers:

A solution is (-24) = 8( 1 ) - 32

Answer:

y = -x+5

Step-by-step explanation:

m = -1, so y = -x+5

The length of PR is 12cm using the Pythagorean theorem.

So, Pythagorean formula: \(c^{2} ={a^2+b^2}\)

Now, insert the values in the formula as follows:

\(c^{2} ={a^2+b^2}\\37^{2} ={35^2+PR^2}\\37^{2} - 35^2={PR^2}\\PR^2 = 1369 - 1225\\PR^2 =144\\\\PR\sqrt{144} \\PR = 12\\\)

Therefore, using the Pythagorean theorem the length of PR is 12cm.

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Answer: y=1/2x+2

Step-by-step explanation: i just picked that one and got it correct

(a), The equation of the line that is perpendicular to this line and passes through the point (7, 6) is y = 7/8x - 1/8.

(b), The equation of the line that is parallel to this line and passes through the point (7, 6) is y = -8/7x - 1/8

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the equation is -8x - 7y = 1.

a) For perpendicular lines the slope will be inverse and opposite of the given equation.

y = mx + c

-8x - 7y = 1.

y = -8/7x - 1/7

The equation can be written as,

y = -8/7x - 1/7

6 = ( 7/8 ) x ( 7 ) + c

c = ( -1 / 8 )

The equation can be written as,

y = 7/8x  - 1/8.

b) For the parallel lines the slope will remain the same,

y = -8/7x - 1/7

y = -8/7x + c

6 = (-8/7 x 7 ) + c

c = 6 + 8

c = 14

The equation can be written as,

y = (-8/7)x + 14

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