> Next question You can retry this question below What is the slope of a line that is parallel to the line – 7x - y = 2 ? Write your answer as an integer or fraction. The slope is Check Answer Type here to search O​

A one-to-one correspondence between the set of all positive integers and the set of all rational numbers exists.

By definition, any rational number can be expressed as a fraction a/b, where a and b are integers and b is nonzero. Since any positive integer can be expressed as the fraction a/1, each positive integer can be associated with a rational number a/1.

Thus, there is a one-to-one correspondence between the set of all positive integers and the set of all rational numbers. Furthermore, since any rational number a/b can be expressed as the product of a and b, it can also be associated with the product of two positive integers a and b.

Thus, there is also a one-to-one correspondence between the set of all rational numbers and the set of all positive integers.

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Answer:

1 ¼

Step-by-step explanation:

5/8 + 5/8

= ( 5 + 5 ) / 8

= 10/8

= 5/4

= 1 ¼

Answer:

x = 90

Step-by-step explanation:

The given diagram shows a circle with intersecting chords, KM and JL.

To find the value of x, we can use the Angles of Intersecting Chords Theorem.

According to the Angles of Intersecting Chords Theorem, if two chords intersect within a circle, the angle formed at the intersection point is equal to half the sum of the measures of the arcs intercepted by the angle and its corresponding vertical angle.

Let the point of intersection of chords KM and JL be point P.

As the chords are straight lines, angle x° forms a linear pair with angle JPM.

Note: We cannot use the Angles of Intersecting Chords Theorem to find the value of x directly, since we have not been given the measures of the arcs KJ and ML. Therefore, we need to use the theorem to find m∠JPM first.

From inspection of the given diagram:

Using the Angles of Intersecting Chords Theorem, we can calculate the measure of angle JPM (shown in orange on the attached diagram):

\(\begin{aligned}m \angle JPM &=\dfrac{1}{2}\left(m\overset\frown{JM}+m\overset\frown{LK}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+(2x-30)^{\circ}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+2x^{\circ}-30^{\circ}\right)\\\\&=\dfrac{1}{2}\left(2x^{\circ}\right)\\\\&=x^{\circ}\end{aligned}\)

As angle JPM forms a linear pair with angle x°, the sum of the two angles equals 180°:

\(\begin{aligned}m \angle JPM+x^{\circ}&=180^{\circ}\\\\x^{\circ}+x^{\circ}&=180^{\circ}\\\\2x^{\circ}&=180^{\circ}\\\\\dfrac{2x^{\circ}}{2}&=\dfrac{180^{\circ}}{2}\\\\x^{\circ}&=90^{\circ}\\\\x&=90\end{aligned}\)

Therefore, the value of x is 90, which means that the two chords intersect at right angles.

Segments MS and QS are therefore congruent by the definition of bisector. Therefore, the correct answer option is: D. MS and QS.

In Mathematics and Geometry, a perpendicular bisector is a line, segment, or ray that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.

This ultimately implies that, a perpendicular bisector bisects a line segment exactly into two (2) equal halves, in order to form a right angle that has a magnitude of 90 degrees at the point of intersection.

Since line segment NS is a perpendicular bisector of isosceles triangle MNQ, we can logically deduce the following congruent relationships;

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Complete Question:

The proof that ΔMNS ≅ ΔQNS is shown. Given: ΔMNQ is isosceles with base MQ, and NR and MQ bisect each other at S. Prove: ΔMNS ≅ ΔQNS

We know that ΔMNQ is isosceles with base MQ. So, MN ≅ QN by the definition of isosceles triangle. The base angles of the isosceles triangle, ∠NMS and ∠NQS, are congruent by the isosceles triangle theorem. It is also given that NR and MQ bisect each other at S. Segments _____ are therefore congruent by the definition of bisector. Thus, ΔMNS ≅ ΔQNS by SAS.

NS and NS

NS and RS

MS and RS

MS and QS

Answer:

Step-by-step explanation:

3√2×8√17=24√(2×17)=24√(34)

it is an irrational number.

√34 can't be expressed in the form p/q where p and q are integers.

moreover

5²=25

6²=36

so √34 is between 5 and 6.

Answer:

-6 + 4 = -2

Step-by-step explanation:

Just start from -6 then go to the right four places and you'll get -2

Suppose \(f(x) =8^{3x\) and \(g(x) =8^{4x\), function operations that are correct include the following:

A. (f + g)(x) = \(8^{3x} + 8^{4x}\)

B. (f × g)(x) = \(8^{7x}\)

C. (f - g)(x) = \(8^{3x} - 8^{4x}\)

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the division and multiplication law of exponents for powers of the same base to the functions, we have the following:

(f × g)(x) = \(8^{3x+ 4x}=8^{7x}\)

(f ÷ g)(x) = \(8^{3x- 4x}=8^{-x}\)

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Answer:

Each person will get 2 pounds of candy

Step-by-step explanation:

Nicole + 3 friends = 4 total

8 pounds of candy = total

total candy / total people

8/4 = 2

Answer:

14 divided by 5

The quotient is 2, and the remainder is 4.

Let me know if this helps!

Answer:

quotient 2.8 , reminder 0

Answer:

1. James encourage Dan and Andy to work together

2. James encourage Dan and Andy to offer a solution.

3. James let's Dan and Andy express their individual opinion in an open manner

4. James discuss........

Answer: I got drip

Step-by-step explanation: drip drip drip

a) The initial height of the football at t = 0 is 2 feet.

b) The ball reaches its maximum height at approximately t = 2.05 seconds.

c) The maximum height of the ball is approximately 23.9 feet.

d) It takes approximately 4.579 seconds for the ball to hit the ground.

a) The initial height of the football at time t = 0 can be found by substituting t = 0 into the equation \(5t^2 + 20.5t + 2:h = -5(0)^2 + 20.5(0) + 2 = 0 + 0 + 2 = 2\)

Therefore, the initial height of the football is 2 feet.

b) To find the time at which the ball reaches its maximum height, we can observe the graph of the equation h = \(-5t^2 + 20.5t + 2.\) The maximum height corresponds to the vertex of the parabolic graph. The t-coordinate of the vertex can be calculated using the formula t = -b/2a, where a and b are the coefficients of the quadratic equation.

In this case, a = -5 and b = 20.5. Plugging these values into the formula, we get:

\(t = -20.5 / (2\times (-5)) = -20.5 / -10 = 2.05\)

Therefore, the ball reaches its maximum height at approximately t = 2.05 seconds.

c) The maximum height of the ball can be found by substituting the time t = 2.05 into the equation \(h = -5t^2 + 20.5t + 2:\)

h = -5(2.05)^2 + 20.5(2.05) + 2 ≈ -20.125 + 42.025 + 2 ≈ 23.9

Therefore, the maximum height of the ball is approximately 23.9 feet.

d) To find the time it takes for the ball to hit the ground, we need to determine when the height h becomes zero. We can set the equation \(-5t^2 + 20.5t + 2 = 0\) and solve for t.

This quadratic equation can be solved using factoring, the quadratic formula, or by graphing. The solutions are t ≈ -0.179 and t ≈ 4.579. Since time cannot be negative in this context, the ball takes approximately 4.579 seconds to hit the ground.

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Answer:

22,873.35

Step-by-step explanation:

A=p+I where P(principal) = 18,000

I(interest) = 4,873.35

Answer:

A = 22,775

Step-by-step explanation:

A = amount after 6 years

P = 18,000

r = 4%  (in decimal = 0.04)

t = 6 years

A = 18,000 ( 1 + 0.04)^6

A = 22,775

Answer:

484836281726261919292762

Answer:

55.8

Step-by-step explanation:

if 1 cake needs 9.3, 6 cakes would need (6*9.3)

9.3 * 6 = 55.8

Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

Let's assume that Bryan invested an amount of x dollars in the first account, which earns 11% interest, and (6500 - x) dollars in the second account, which earns 7% interest.

The interest earned from the first account can be calculated as 0.11x, and the interest earned from the second account can be calculated as 0.07(6500 - x).

According to the problem, the total interest earned after one year is $519. So we can set up the equation:

0.11x + 0.07(6500 - x) = 519

Simplifying the equation:

0.11x + 455 - 0.07x = 519

0.04x + 455 = 519

0.04x = 64

x = 64 / 0.04

x = 1600

Therefore, Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

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The value of cos(45°) is √2/2. The correct answer choice is D. √2.

In the given diagram, the angle labeled as 45° is part of a right triangle. To find the value of cos(45°), we need to determine the ratio of the adjacent side to the hypotenuse.

Since the angle is 45°, we can assume that the triangle is an isosceles right triangle, meaning the two legs are congruent. Let's assume the length of one leg is x. Then, by the Pythagorean theorem, the length of the hypotenuse would be x√2.

Now, using the definition of cosine, which is adjacent/hypotenuse, we can substitute the values:

cos(45°) = x/(x√2) = 1/√2

Simplifying further, we rationalize the denominator:

cos(45°) = 1/√2 * √2/√2 = √2/2

Therefore, the value of cos(45°) is √2/2.

The correct answer choice is D. √2.

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Answer:

To prove that none of the terms of the sequence 2, 5, 8 are perfect squares, we need to show that no integer exists such that its square equals 2, 5, or 8.

First, let's consider 2. We can start by assuming that there exists an integer n such that n^2 = 2. However, this leads to a contradiction, because the square of any integer is always non-negative, so n^2 cannot be equal to a negative number like 2. Therefore, there is no integer n such that n^2 = 2, and 2 is not a perfect square.

Similarly, let's consider 5. Again, assume that there exists an integer n such that n^2 = 5. However, this leads to another contradiction, because the square of any integer is always either a perfect square or a number that is slightly larger than a perfect square (for example, 4^2 = 16 and 6^2 = 36). Since 5 is not a perfect square, it cannot be equal to the square of any integer, and there is no integer n such that n^2 = 5.

Finally, let's consider 8. We can again assume that there exists an integer n such that n^2 = 8. However, this leads to a contradiction, because the square of any even integer is always a multiple of 4 (for example, (2n)^2 = 4n^2). Since 8 is not a multiple of 4, it cannot be equal to the square of any integer, and there is no integer n such that n^2 = 8.

Therefore, we have shown that none of the terms of the sequence 2, 5, 8 are perfect squares.

Answer:

A.

Step-by-step explanation:

Let's think of this as a clock.  We can see that the 2 lines start in the same place, around 3 o'clock.  Next, one of the line segments shifts down to around 6 o'clock.  Next, it shifts to about 9 o'clock.  Logically, the next step (in a clock) would be 12 o'clock, making A the correct choice.

We can also just use a regular circle, with one of the line segments moving 90 degrees each time.

Hope this helps! :)

Answer:

15 yards

Step-by-step explanation:

the length of fencing required for the rectangular garden is

2( 4 \(\frac{1}{2}\) + 3)

= 2 × 7 \(\frac{1}{2}\)

= 15 yards

Answer:

29-16x+10y

Step-by-step explanation:

21-14x+7y+8+3y-2x

simplify the expression

21+8=29

-14x-2x=-16x

7y+3y=10y

final answer

29-16x+10y

*** don't forget to include x with 16 and y with 10***

hope this helped :)

Answer:

29 - 16 x + 10 y

Step-by-step explanation:

21 - 14 x + 7 y + 8 + 3y - 2x

combine like terms

21 + 8 - 14x - 2x + 7y + 3y

29 - 16 x + 10 y

Answer:translation, 12^2+35^2, squre root the answer, thgen add it to 12

Step-by-step explanation:

An absolute value is the numerical value of a number without consideration of its sign. It can be represented graphically by a straight line known as a number line. Absolute value equations are equations that include absolute values of variables or unknown quantities. The following are examples of how to write an absolute value equation in the form |x-c|=d to fit the provided solution sets:

Example 1:

Solution set: {x|x≤-3 or x≥1}
Absolute value equation: |x-(-1)|=4
Explanation: -1 is the midpoint of the two ranges (-3 and 1) in the solution set. |x-(-1)|=|x+1| is the absolute value expression for the midpoint -1. The distance d from -1 to the solutions' furthest endpoints, 1 and -3, is four, hence the value of d in the absolute value equation is 4.
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By adding 3 to both sides of the equation (6+3)-3=9-3, this demonstrates the addition property of equality. This results in the equation being simplified to 6+3=9.

The properties of equality describe the relationship between two sides of an equation and state that the two sides remain equal even after the same arithmetic operation is performed on each side. a = a, according to the reflexive property of equality. For example, 5 = 5, because the number's value is equal to itself.

As per the addition property of equality, when we add the same number to both sides of an equation then the two sides remain equal. This can be written as, if a = b, then a + c = b + c.

Translated question "Draw a line from each equation to the property of equality it illustrates. (6+3)−3=9−3 Addition Property of Equality"

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Answer:

There are two ways

Step-by-step explanation:

1. Multiply 5 by the fraction, 1/3

When you multiply a whole number by a fraction, it will give the same result as you would have by dividing it.

2. Divide 5 by 3

Answer:

15

Step-by-step explanation:

Answer:

13.

Step-by-step explanation:

\(42 = a + (a+1) + (a+2) = 3a + 3 = 3(a+1)\)

Then, \(a+1 = 14\), so \(a=13.\)

Answer: first, second and fourth are primes, the third is not-prime.

Hope it helps :)

Answer:

No

Step-by-step explanation:

There is no formula

There is no formula

The tourist's investment function can be expressed as follows:

f(x) = 720 + 35x

According the question,

The tourist's investment function can be expressed as follows:

f(x) = 720 + 35x

Where x represents the quantity of additional tours that the tourist wants to add to their travel package.

The function f(x) represents the total cost of the travel package plus the additional cost of the extra tours.

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