Explain how to use a number line to find the sum of two rational numbers,

The value of angle LAF in the intersecting chords is determined as  104⁰.

The value of angle LAF is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.

m∠LAF = ¹/₂ (arc LF + arc YS)

From the diagram, we have arc LF = 160⁰ and YS = 48⁰

m∠LAF = ¹/₂ (160 + 48)

m∠LAF = 104⁰

Thus, the value of angle LAF is calculated by applying intersecting chord theorem.

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Answer:

When \(x=0\), the value of f(x) is 1.

Each time x increases by 1, f(x) is multiplied by 4.

Equation of function: \(f(x)=1\cdot 4^x\)

Step-by-step explanation:

The detailed explanation is attached below.

The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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The solution to the nonlinear system of equations is (x, y) = (-3, -2) and (x, y) = (1, 6). These points represent the coordinates where the two equations intersect and satisfy both equations simultaneously.

To solve the nonlinear system of equations:

Equation 1: \(y = -x^2 + 7\)

Equation 2: y = 2x + 4

We can equate the right sides of both equations since they both represent y.

\(-x^2 + 7 = 2x + 4\)

To simplify the equation, we can rearrange it to be in the standard quadratic form:

\(x^2 + 2x - 3 = 0\)

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:

(x + 3)(x - 1) = 0

From this equation, we get two possible solutions:

x + 3 = 0 => x = -3

x - 1 = 0 => x = 1

Now, we substitute these x-values back into either equation to find the corresponding y-values.

For x = -3:

y = 2(-3) + 4

y = -6 + 4

y = -2

For x = 1:

y = 2(1) + 4

y = 2 + 4

y = 6

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Answer:

To simplify the expression (a÷b)³×(b÷c)×(c÷a)³ when a=3, b=a², c=a³, we can substitute the given values and perform the calculations.

Substituting the values of a, b, and c:

a = 3

b = a² = 3² = 9

c = a³ = 3³ = 27

Now let's simplify the expression:

(a÷b)³×(b÷c)×(c÷a)³

(3÷9)³×(9÷27)×(27÷3)³

Simplifying each term:

(3÷9) = 1/3

(9÷27) = 1/3

(27÷3) = 9

Now we can substitute the simplified values back into the expression:

(1/3)³×(1/3)×9

Simplifying further:

(1/27)×(1/3)×9

1/9

Therefore, the simplified expression is 1/9.

Answer:

Lower quartile = 6

Median = 8

Upper quartile = 9

Step-by-step explanation:

If you take away a number from each end of the number set one by one, you will end up with 7 and 9 in the middle. To find the median between two numbers, add them together then divide them by 2.

7 + 9 = 16

16 ÷ 2 = 8

_________________

To find the lower and upper quartiles, split the number set into two where the median is, then, find the median of those two sections.

Lower quartile: 4, 5, 6, 6, 7

Median = 6

-

Upper quartile: 9, 9, 9, 9, 9

Median = 9

So, the median of the whole set is 8, the lower quartile is 6, and the upper quartile is 9.

hope this helps!

Answer:

300

Step-by-step explanation:

For every 1 of the base, there's 4 of the area.

30-25 = 5

The stock has dropped $5 total.

$5 / $0.50 per hour = 10 hours

1) The three main trigonometric ratios of the given triangle are:

sin B = 5/9.43

cos B = 8/9.43

tan B = 5/8

2) The measure of angle A is: ∠A = 39.6°

3) The length of side x is: x = 39.5 mm

The six trigonometric ratios of a right angle triangle are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

cot x = 1/tan x

sec x = 1/cos x

cosec x = 1/sin x

1) The three main trigonometric ratios of the given triangle are:

sin B = 5/9.43

cos B = 8/9.43

tan B = 5/8

2) The measure of angle A is gotten from:

∠A = cos⁻¹ (47/61)

∠A = 39.6°

3) The length of side x using trigonometric ratios is:

21/x = tan 28

x = 21/tan 28

x = 39.5 mm

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Answer:

10 miles

Step-by-step explanation:

3 mi/1 hr  x (h hours + 2/3 hr) = 5 mi/1 hr  x  h hours

3h + 2 = 5h

2 = 2h

h = 1 hour

3mi/hr  x 1 2/3 hr = 5 miles

5 mi/hr x  1 hr = 5 miles

He hiked 10 miles. (

Answer:

$50

Step-by-step explanation:

Answer:

$50 I think lol I hope you get it right

Answer: 97/125

Step-by-step explanation:

Answer:

Brand A

Step-by-step explanation:

Brand A has a box of 25 forks for 1.99

Take the price per fork

1.99 /25 = .0796

              .08 per fork

Brand B has a box of 42 totals for 3.89

3.89 / 42

.092319048

.09 per fork

Answer:

the answer is your welcome

$33.52

As per the error function, \(\int e^{-5t^2} dt\) is a erf(bx) | = 0

To illustrate this concept, let us consider the integral ∫ e^(-5t²) dt with limits of integration from 0 to x. We can rewrite this integral in terms of the error function by making the substitution u = √5t, which gives us du/dt = √5 and dt = du/√5. Thus, the integral becomes ∫ (e^-u²) (du/√5), with limits of integration from 0 to √(5x²).

Next, we can express the integrand as e^(-u²) = (2/√π) ∫ e^(-v²) dv, which follows from the standard result that ∫ e^(-x²) dx = √π/2. Substituting this expression into our integral, we obtain:

∫ (e^-u²) (du/√5) = (2/√(5π)) ∫ ∫ e^(-v²) du dv,

with limits of integration from 0 to √5x and 0 to u, respectively. Interchanging the order of integration, we get:

∫ (e^-u²) (du/√5) = (2/√(5π)) ∫ ∫ e^(-v²) dv du

= (2/√(5π)) ∫ e^(-v²) (u=0 to u=√5x) dv

= (2/√π) ∫ e^(-5x²) dx.

Therefore, we have shown that the integral ∫ e^(-5t²) dt with limits of integration from 0 to x can be expressed as:

| (2/√π) ∫ e^(-5x²) dx = a erf(bx) |,

where a = √(2/π) and b = 1/√5. Here, erf(bx) denotes the error function evaluated at the argument bx.

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Answer:

x= -2 ...........

Step-by-step explanation:

0=x+2.......

x=-2........

Answer:

1/15 or 0.0667

Step-by-step explanation:

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bardai

chatgpt

red marble on the first draw is 2/6, or 1/3

red marble on the second draw, given that the first marble was red, is 1/5

(1/3) * (1/5) = 1/15

Answer:

4 paintings in a full hour

Work:

Carly painted 6/7 of a picture in 3/14 hours:

6/7=3/14

Which means Carly painted 2/7 of a picture in 1/14 hours:

2/7=1/14

We need to find how many paintings she can paint in 1 full hour, or 14/14 of an hour, how do you get from 1/14 to 14/14? You do multiplication:

1/14 x 14 = 14/14

but there is a rule that says what you do to one side of the equation, you need to do it to the other side too so:

2/7 x 14=1/14 x 14

28/7=14/14

28/7=4  

The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is given as follows:

0.5874 = 58.74%.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The parameters for this problem are given as follows:

\(\mu = 17.2, \sigma = 2.5, n = 40, s = \frac{2.5}{\sqrt{40}} = 0.3953\)

The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is the p-value of Z when X = 18.1 subtracted by the p-value of Z when X = 17.1, hence:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem:

\(Z = \frac{X - \mu}{s}\)

Z = (18.1 - 17.2)/0.3953

Z = 2.28

Z = 2.28 has a p-value of 0.9887.

Z = (17.1 - 17.2)/0.3953

Z = -0.25

Z = -0.25 has a p-value of 0.4013.

Hence:

0.9887 - 0.4013 = 0.5874 = 58.74%.

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EXPLANATION

Applying the rotation about the origin 180 degrees counterclockwise give us the following figure:

Answer:

In geometry, the circumference is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length around any closed figure.

Step-by-step explanation:

Answer:

1. Circumference = 87.92

2.Circumference = 43.96

Step-by-step explanation:

The first problem it had a radius. So in order to find the circumference you will have to use the formula 2πr. When you plug in the 14 yd in the radius spot it will look like 2π(14) when you solve it the answer will be 87.92

The second one has a diameter so the equation you will have to use is πd. Now you will have to plug the 14 cm where the diameter is which will look like π(14) when you solve it the answer will come out as 43.96

Answer:

\(\frac{5}{n+1}\times \frac{n+1}{n+3}=\frac{5}{n+3}\)

Step-by-step explanation:

Given the expression

\(\frac{5}{n+1}\times \frac{n+1}{n+3}\)

Let us simplify

\(\frac{5}{n+1}\times \frac{n+1}{n+3}\)

\(\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}\)

\(=\frac{5\left(n+1\right)}{\left(n+1\right)\left(n+3\right)}\)

\(\mathrm{Cancel\:the\:common\:factor:}\:n+1\)

\(=\frac{5}{n+3}\)

Therefore,

\(\frac{5}{n+1}\times \frac{n+1}{n+3}=\frac{5}{n+3}\)

Answer:

C

Step-by-step explanation:

5n+1/n+3

To solve for x, we need to isolate x on one side of the equation. To do this, we can first move all the terms that do not contain x to the right side of the equation by adding 3x and 2 to both sides:

2x - 2 + 3x + 2 = -3x + 13 + 3x + 2

5x = -3x + 15

8x = 15

Dividing both sides by 8, we get:

x = 15/8

= 1.875

Therefore, the value of x is approximately 1.875.

The value of x in equation 2x-2= -3x+13 is 3

To solve this equation we need to find the value of x so that all x terms should be one side and all constants should be at ones side:

2x+3x=13+2

5x=15

Now divide both side with 5 then, we get:

5x/5=15/5

x=3

Therefore, the value of x is 3

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Answer:

C. (3,25) and (7,9)

Step-by-step explanation:

1. Jada's data set has a mean of 5, Diego's data set has a mean of 6, and Lin's data set has a mean of 4.

2. The data set that has the greatest variability is Lin's data set because it has the highest standard deviation of 3.6.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

Question 1.

In this scenario and exercise, we would determine the mean of the three data sets based on the number of text messages sent by Jada, and Diego, and Lin over 6 days as follows;

Mean number of text for Jada = (4 + 4 + 4 + 6 + 6 + 6)/6

Mean number of text for Jada = 30/6

Mean number of text for Jada = 5.

Mean number of text for Diego = (4 + 5 + 5 + 6 + 8 + 8)/6

Mean number of text for Diego = 36/6

Mean number of text for Diego = 6.

Mean number of text for Lin = (1 + 1 + 2 + 2 + 9 + 9)/6

Mean number of text for Lin = 24/6

Mean number of text for Lin = 4.

Question 2.

In Statistics, variability is a measure of the spread of a data set. Also, we would use standard deviation to determine the variability in each data set as follows;

Standard deviation = √(1/n × ∑(xi - u₁)²)

Standard deviation for Jada = √(1/6 × [(4 - 5)² + (4 - 5)² + (4 - 5)² + (6 - 5)² + (6 - 5)² + (6 - 5)²]

Standard deviation for Jada = √(6/6) = 1

Standard deviation for Diego = √(1/6 × [(4 - 6)² + (5 - 6)² + (5 - 6)² + (6 - 6)² + (8 - 6)² + (8 - 6)²]

Standard deviation for Diego = √(14/6) = 1.53

Standard deviation for Lin = √(1/6 × [(1 - 4)² + (1 - 4)² + (2 - 4)² + (2 - 4)² + (9 - 4)² + (9 - 4)²]

Standard deviation for Lin = √(76/6) = 3.6

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

To find the equation in slope-intercept form, we shall begin by finding the slope of the line.

First step is to identify two different points on the line. Observe carefully that when x equals 0, y equals 2. Therefore we have (0, 2). Also when x equals 2, y equals negative 6. Therefore, the other point is (2, -6). With these two points we can now calculate the slope as follows;

With the slope derived as -4, we can now determine the value of b (the y-intercept). We shall take any of the points above, hence let use the first point;

The equation therefore is y = -4x + 2

Step-by-step explanation:

hmph................