The mapping diagram shows a functional relationship.
Domain
Range
-1
0
3
9
Intro
0349
Complete the statement.
f(3) is
חחחחחחחחחחחnחחa n
Done

Answer:Your answer would be F

Step-by-step explanation:

Answer:

A) (2,5)

Step-by-step explanation:

longest side is between points (1,4) and (3,6)

so midpoint is ((1+3)/2), ((4+6)/2), which equals (2, 5)

Answer:

3.2 x 10^20 or 320000000000000000000

Step-by-step explanation:

Thats it, i think. I might be off on a few zeroes. Hope this helps!

Answer:

3.2 x 10^20 or 320000000000000000000

Step-by-step explanation:

The height of the skyscraper is approximately 156.25 feet

First of all, let's recall some trigonometric functions that are used in the given problem:

tanθ = Perpendicular/Base

or tan θ = Opposite/Adjacent

where θ is the angle of elevation.

We have given the length of the shadow, which is the base.

We have to determine the height of the skyscraper, which is the perpendicular.

We can calculate the angle of elevation using the following formula:

θ = tan⁻¹(opposite/adjacent)

Here, opposite is the height of the skyscraper, and adjacent is the length of the shadow.

We can calculate the value of θ as:θ = tan⁻¹(h/200) .... (1)

According to the problem, θ = 38.

We can substitute the value of θ in equation (1) and find the value of h:

h = 200 tan(38°)h

= 200 × 0.78125h

= 156.25 feet.

We can check our answer using the Pythagorean theorem:

Height² + Base² = Hypotenuse²h² + 200²

= (200/tan(38°))²h² + 40000

= 29554.45²h²

= 29554.45² - 40000h²

≈ 24589.59h

≈ 156.26 approximately .

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By showing that a statement is true for a base case and proving that it is true for k+1, assuming that it is true for k, we can show that it is true for all integers in the range of interest.

To show that a formula is true for all integers 1 ≤ k ≤ n, we can use mathematical induction. The process of mathematical induction has two steps: the base case and the induction step.

Base case: Show that the formula is true for k = 1.

Induction step: Assume that the formula is true for some integer k ≥ 1, and use this assumption to prove that the formula is also true for k + 1.

If we can successfully complete both steps, then we have shown that the formula is true for all integers 1 ≤ k ≤ n.

Let's illustrate this with an example. Suppose we want to show that the formula 1 + 2 + 3 + ... + n = n(n+1)/2 is true for all integers 1 ≤ k ≤ n.

Base case: When k = 1, the formula becomes 1 = 1(1+1)/2, which is true.

Induction step: Assume that the formula is true for some integer k ≥ 1. That is,

1 + 2 + 3 + ... + k = k(k+1)/2

We need to prove that the formula is also true for k + 1. That is,

1 + 2 + 3 + ... + (k+1) = (k+1)(k+2)/2

To do this, we can add (k+1) to both sides of the equation in our assumption:

1 + 2 + 3 + ... + k + (k+1) = k(k+1)/2 + (k+1)

Simplifying the right-hand side, we get:

1 + 2 + 3 + ... + k + (k+1) = (k+1)(k/2 + 1/2)

We can rewrite k/2 + 1/2 as (k+2)/2:

1 + 2 + 3 + ... + k + (k+1) = (k+1)(k+2)/2

This is the same as the formula we wanted to prove for k + 1. Therefore, by mathematical induction, we have shown that the formula is true for all integers 1 ≤ k ≤ n.

In summary, mathematical induction is a powerful tool for proving statements about a range of integers. By showing that a statement is true for a base case and proving that it is true for k+1, assuming that it is true for k, we can show that it is true for all integers in the range of interest.

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The names of the pair of angles are:

∠3 and ∠6: alternate interior

∠7 and ∠3: supplementary

∠5 and ∠4: alternate exterior

∠5 and ∠4: corresponding

Alternate interior angles are pairs of nonadjacent angles located on opposite sides of a transversal and inside the two parallel lines, while alternate exterior angles are pairs of nonadjacent angles located on opposite sides of a transversal and outside the two parallel lines.

Therefore, the pair of angles can be named as shown below:

∠3 and ∠6 are alternate interior angles

∠7 and ∠3 are supplementary

∠5 and ∠4 are alternate exterior angles

∠5 and ∠4 are corresponding angles

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Answer: Isaac Newton and Gottfried Leibniz.

Isaac Newton and Gottfried Leibniz

Answer:

2.0625

Step-by-step explanation:

8.25%=0.0825

0.0825*25=2.0625

Answer:

2.0625

Step-by-step explain

8.25% of 25 dollar  is $2.0625

The age of Barbra is 22 years.

The algebraic method for solving simultaneous linear equations is the substitution method. A quantity of one variable through one expression is replaced in the second equation, as the name implies.

Now, according to the question.

Let 'a' be the age of Alice.

Let 'b' be the age of Barbra

Let 'c' be the age of Carol.

The sum of age of all three sisters is 68 years.

Thus,  a + b + c = 68

Now, as Alice is three years younger than Barbra.

a = b - 3

and, Barbra is 5 years younger than Carol.

b = c - 5

c = b + 5

By substitution of values of a and c in total age.

(b - 3) + b + (b + 5) = 68

3b - 3 + 5 = 68

On solving the expression.

b = 22

Therefore, the age of Barbra is 22 years.

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Answer:

no

Step-by-step explanation:

it is not strait

Hope this works!

Answer:

$30

Step-by-step explanation:

Use the formula:

Interest = Principal(rate)(time)

I = Prt

P = 300

r = 5%, change to a decimal by dividing by 100. 5/100 = .05

t = 2

Plugin in the numbers and multiply

I = 300(.05)(2)

I = 30

Answer:

Its 14

Step-by-step explanation:

8+6=14

Answer:

The answer is 16

08

+ 06

----------

16

Hope it helps ;)

Please mark as brainliest

Answer:

it is irrational

Step-by-step explanation:

hope this helps

plz give brainliest

Answer:

Pi is an irrational number.

Step-by-step explanation:

It's a never ending number.

Answer:

c

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Therefore , the solution of the given problem of integral comes out to be 8ln2 is solution for the integral expression.

The region beneath a curve among two set limits is referred to as a definite integral. The representation of the definite integral for such a function of two variables), defined to reference to the x-axis, is ∫ baf(x)dx a b f (x) d x, where an is the lower bound and b is the upper bound.

Here,

Given :

\(\int\limits \int\limitsa_R\) 3xy²/x²+ 1 dA

=> R = {(x, y) | 0 ≤ x ≤ 3, −2 ≤ y ≤ 2} ·

So,

=>  \(\int\limits^1_{x=0} \int\limits^2_{y=-2}\) 3xy²/x²+ 1  dxdy

=> \(\int\limits^1_{x=0}\) 3x / x²+ 1  \(\int\limits^2_{y=-2}\) y²

=>\(\int\limits^1_{x=0}\) 3x / x²+ 1 ( y³/2)²dx

=>   \(\int\limits^1_{x=0}\) 3x / x²+ 1 (8 + 8 /3) dx

=> \(\int\limits^1_{x=0}\) 16x/x²+ 1

=> 8 [ln(x²+ 1) ]

=>  8 [ln2 -ln1 ]

=>8ln2

Therefore , the solution of the given problem of integral comes out to be

8ln2 is solution for the integral expression.

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Answer:

3/14

Step-by-step explanation:

1 1/4 can be written as 5/4

5 5/6 can be written as 35/6

so divide (5/4)/(35/6)

= (5/4)*(6/35)

=(1/4)*(6/7)

=6/28

simplified = 3/14

Answer:

-2 3/4.

Step-by-step explanation:

8 2/3 = 26/3

26/3 / -104/33

= 26/3 * 33/-104

= 1 /3 * 33/-4

= 1/1 * 11/-4

= -11/4

= -2 3/4.

Answer:

B   -6

Step-by-step explanation:

in the function equation, simply substitute 10 for f(x) on the LHS and solve for x

\(10 = -\dfrac{1}{2}x+ 7\)

Solving for x gives x = -6

The right-hand side of the given equation is rational and can be expressed as a ratio of two integers. Specifically, it can be expressed as the ratio of the integer 2 and the integer 1 raised to the power of\(2^n\).

To determine if the right hand-side of the given equation is rational, we need to evaluate the expression on the right-hand side and see if it can be expressed as a ratio of two integers.

Using the formula given on the left-hand side, we can simplify the right-hand side as follows:

\(1 - (1/2^n+1) / 1 - (1/2)\\= [(1 - 1/2^(n+1)) * 2] / [2 - 1]\\= (2 - 1/2^(n)) / 1\\= 2 - 1/2^n\)

Since 2 and\(1/2^n\) are both rational numbers (2 can be expressed as 2/1 and \(1/2^n as 1/(2^n/1))\), their difference \(2 - 1/2^n\) is also a rational number.

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Answer:

X=10

Step-by-step explanation:

So, -2x+10+5x=40. first we subtract ten from both sides, getting us to -2x+5x=30, then we subtract 2x from 5x, because its negative, getting us to 3x=30, basically x=10.

Answer:

0.1356 g

Step-by-step explanation:

The formula for density is, \(\rho ={\frac {m}{V}}\), so we can plug in our values and solve for m, the mass.

\(\rho ={\frac {m}{V}}\)

1.2x10⁻²= \(\frac{m}{11.3} \)

m= 0.1356 g

A student says that the function represented by the rule \(y = x^{2} -1\) is ,

Then the x = 0 and y = -1 represented by rule \(y = x^{2} -1\) is correct the error.

Then the x = 1 and y = 1 represented by rule \(y = x^{2} -1\) is incorrect the error.

Then the x = 3 and y = 5 represented by rule \(y = x^{2} -1\) is incorrect the error.

Then the x = 3 and y = 5 represented by rule \(y = x^{2} -1\) is incorrect the error.

Then the x = 4 and y = 7 represented by rule \(y = x^{2} -1\) is incorrect the error.

Consider function,

\(y = x^{2} -1\)

For x = 0 and y = -1

\(y = x^{2} -1\)

We can substitute x = 0 and y = -1 values,

-1 = \(0^{2}\) - 1

-1 = 0-1

-1 = -1

Then the x = 0 and y = -1 represented by rule \(y = x^{2} -1\) is correct the error.

For x = 1 and y = 1

\(y = x^{2} -1\)

We can substitute x = 1 and y = 1 values,

\(y = x^{2} -1\)

1 = \(1^{2}\) -1

1 = 1-1

1  ≠ 0

Then the x = 1 and y = 1 represented by rule \(y = x^{2} -1\) is incorrect the error.

For x = 2 and y = 3

\(y = x^{2} -1\)

We can substitute x = 2 and y = 3 values,

\(y = x^{2} -1\)

3 = \(2^{2}\) - 1

3 = 4 -1

3 = 3

Then the x = 2 and y = 3 represented by rule \(y = x^{2} -1\) is correct .

For x = 3 and y = 5

\(y = x^{2} -1\)

We can substitute x = 3 and y = 5 values,

\(y = x^{2} -1\)

5 = \(3^{2}\) - 1

5 = 9 - 1

5 ≠ 8

Then the x = 3 and y = 5 represented by rule \(y = x^{2} -1\) is incorrect the error.

For x = 4 and y = 7

\(y = x^{2} -1\)

We can substitute x = 4 and y = 7 values,

\(y = x^{2} -1\)

7 = \(4^{2}\) - 1

7 = 16 - 1

7 ≠ 15

Then the x = 4 and y = 7 represented by rule \(y = x^{2} -1\) is incorrect the error.

Therefore,

The function represented by the rule \(y = x^{2} -1\) is ,

x = 0 and y = -1 represented by rule \(y = x^{2} -1\) is correct the error.

x = 1 and y = 1 represented by rule \(y = x^{2} -1\) is incorrect the error.

x = 3 and y = 5 represented by rule \(y = x^{2} -1\) is incorrect the error.

x = 3 and y = 5 represented by rule \(y = x^{2} -1\) is incorrect the error.

x = 4 and y = 7 represented by rule \(y = x^{2} -1\) is incorrect the error.

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The mean of the sample size of 25 would fall between 68 and 72 68% of the time.

Using the 68-95-99.7 rule, if a variable is normally distributed with mean μ and standard deviation σ, then:

Since the interval we are interested in (68 to 72) falls within the 68% of the data that falls within 1 standard deviation of the mean, it means that 100% - 32% = 68% of the data falls within this interval.

Thus, the mean of this sample size of 25 would fall between 68 and 72 68% of the time.

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For the function:

f(x) = -24

The domain and range are:

Domain: all real number.

Range:  {-24}

For a function:

y = f(x)

The domain is the set of possible inputs, this is, possible values of x.

The range is the set of possible outputs, this is, possible values of y.

Here the function is:

f(x) = -24

Notice that the input can be any value, we don't have any restrictions, and the output can only be -24, then we have:

Domain: all real number.

Range:  {-24}

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The proof by contrapositive of the theorem is "For every real number x, if x is rational, then -3x - 8 is rational."

Assume x is rational, meaning x can be expressed as a ratio of two integers a and b, where b is not equal to zero. Thus, x = a/b.

We want to prove that -3x - 8 is rational. Substituting x = a/b, we get -3(a/b) - 8 = (-3a - 8b)/b.

Since a and b are integers, -3a and 8b are also integers. Thus, the numerator (-3a - 8b) is an integer.

We know that a/b is rational, so b is not equal to zero. Therefore, (-3a - 8b)/b is a ratio of two integers and is therefore rational.

Thus, we have shown that if x is rational, then -3x - 8 is rational, which is the contrapositive of the original theorem.

Therefore, the original theorem is true since its contrapositive is true.

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Answer:

A.

Step-by-step explanation:

6*2 = 12

9*2 = 18

4*2 = 8

Answer is 12 yd. 18 ft. 8 in.

We have shown that for every whole number n, there exists a value of x in the interval (2n−1)π/2 < x < (2n+1)π/2 such that tan(x) = x.

To prove that there exists a value of x such that tan(x) = x for each whole number n, we can use the Intermediate Value Theorem.

The Intermediate Value Theorem states that if a continuous function takes on two different values at two different points in an interval, then it must also take on every value between those two points at some point within the interval.

In this case, we consider the function f(x) = tan(x) - x. We want to show that there exists a value of x in the [(2n-1)π/2, (2n+1)π/2] where f(x) = 0, which means tan(x) = x.

First, we note that f(x) is continuous within the given interval since both tan(x) and x are continuous functions.

Next, we evaluate f((2n-1)π/2) and f((2n+1)π/2):
f((2n-1)π/2) = tan((2n-1)π/2) - (2n-1)π/2 = -∞ - (2n-1)π/2 < 0
f((2n+1)π/2) = tan((2n+1)π/2) - (2n+1)π/2 = ∞ - (2n+1)π/2 > 0

Since f((2n-1)π/2) < 0 and f((2n+1)π/2) > 0, by the Intermediate Value Theorem, there must exist a value of x in the integral  [(2n-1)π/2, (2n+1)π/2] such that f(x) = 0. This means there exists an x such that tan(x) = x for each whole number n.

Therefore, we have shown that for every whole number n, there exists a value of x in the interval (2n−1)π/2 < x < (2n+1)π/2 such that tan(x) = x.

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Step-by-step explanation:

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Answer:

y=1/4x-13

Step-by-step explanation:

use y=mx+b where 0 is the x value, -13 is the y value, and 1/4 is the m value

-13=0+b

put back into y=mx+b where m is slope and b is y-intercept

Answer:

y=1/4x-13

Step-by-step explanation:

The question is wanting you to put the information in the format of y=mx+b. To create the equation you tie in the y-intercept which is -13 and the slope. You put the y-intercept in place of "b" and put the slope in place if the "m".