Approximate the following square root to the nearest integer.
√10~

Check the picture below.

Answer:

∠ U = 12°

Step-by-step explanation:

the inscribed angle RST is half the measure of its intercepted arc RT , then

arc RT = 2 × ∠ RST = 2 × 30° = 60°

the secant- tangent angle U is equal to half the difference of its intercepted arcs, that is

∠ U = \(\frac{1}{2}\) ( RS - RT ) = \(\frac{1}{2}\) × (84 - 60)° = \(\frac{1}{2}\) × 24° = 12°

Answer:

The fulton county has fewer pitches.

Step-by-step explanation:

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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Answer:

C. 0.48

Step-by-step explanation:

Probability = number of required outcome

_______________________

number of possible outcome

= total volleyball game events

_______________________

total sophomore + junior

= 66/137

= 0.48

Answer: D) 0.31

Step-by-step explanation:

Let A denote the event that a person is a sophomore.

Let B denote the event that a person has attended volleyball game.

A∩B denote the event that a person is a sophomore and attend volleyball game.

Let P denote the probability of an event.

We are asked to find:

P(A∩B)

From the table provided to us we see that:

A∩B=42

Hence,

P(A∩B)=42/137=0.3065 which is approximately equal to 0.31. Therefore ur answer will be 0.31.

Answer:

1. Given.

2. Definition of vertical angles.

3. Vertical angles theorem.

4. Definition of corresponding angles.

5. Corresponding angles postulate.

6. Transitive property of congruence.

Explanation:

1. This statement is the given part of the problem

2. vertical angles are the pair of opposite angles that are formed when two line segments intersect. Angles 1 and 3 verify this definition, thus they're vertical angles.

3. The vertical angles theorem states that a pair of two vertical angles have the same measure.

4. Corresponding angles are the angles that are formed in matching corners with the transversal when two parallel lines are intersected by another line. Thus, angles 1 and 5 are corresponding angles.

5. The corresponding angles postulate states that, when two parallel lines are cut by a transversal, the resulting corresponding angles are congruent. Thus, angles 1 and 5 are congruent.

6. The transitive property of congruence states that if a is congruent to b and b is congruent to c, then a is congruent to c.

This means:

The number of suspects had less than two prior arrests are 3.

Given that, While reviewing the previous day’s arrest report.

Let x be the number of suspects have been arrested once before and y be the number of suspects arrested twice before.

Here, x+y=5 -----(i)

2x+3y=12 -----(ii)

From equation (i), x=5-y in equation (ii), we get

2(5-y)+3y=12

10-2y+3y=12

10+y=12

y=2

Substitute y=2 in equation (i), we get

x+2=5

x=3

Therefore, the number of suspects had less than two prior arrests are 3.

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Answer:

y=-1

Step-by-step explanation:

14-(.5*30) same as dividing 30 by 2

14-15=-1   combine

Answer:

Step-by-step explanation:

Y=1

Answer:

0 because there is no black socks.

Step-by-step explanation:

Answer:

0 because there are already some in one drawer

The system has the following solution: \(x_1=-4,\ x_2=3,\ x_3=1\). The vector xequals can be used to represent the answer.

A statement in mathematics demonstrating the equality of two expressions is called an equation. Two phrases with the same value are normally separated by the equals sign (=). Finding the area of a circle and predicting planetary motion are only two examples of the many practical issues that equations are used to address.

The linear system's augmented matrix, which is determined by the matrix equation A x = b is given by:

Aequals

\(\left[\begin{array}{ccc}1&-3&4\\2&-3&2\\-3&3&4\\-7&15&-4\end{array}\right]\)

Part 2:

Aequals

Write the system's solution as a vector after solving it.

We can use Gaussian Elimination to solve this system.

Step 1:

\(\left[\begin{array}{ccc}1&1&0\\2&-1&1\\-3&0&1\\-7&8&3\end{array}\right]\)

Step 2:

Aequals

\(\left[\begin{array}{ccc}1&0&0\\0&1&0\\3&1&0\\-4&3&1\end{array}\right]\)

The system's solution is \(x_1=-4,\ x_2=3,\ x_3=1\). The vector xequals represents the answer.

The matrix is,

\(\left[\begin{array}{ccc}-4\\3\\1\end{array}\right]\)

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Answer:

A=25% B=75%

Step-by-step explanation:

So first lets make a sample space. (Im using red, blue, green, and yellow)

rr, rb, rg, ry

br, bb, bg, by

gr, gb, gg, gy

yr, yb, yg, yy

So for A its 4/16 or 1/4=25%

For B its 12/16=3/4=75%

Answer:

x = 20

Step-by-step explanation:

The triangle shown is an equilateral triangle.  An equilateral triangle has angles that are all the same.  Therefore, the expression 4x-20 equals the value of the angle, which is 60 degrees.  To find x, you just have to do some simple algebra.

4x - 20 = 60 ..... set the expression equal to 60, that's what the angle equals

4x = 80 .... add 20 to both sides

x = 20 .... divide both sides by 4, and you get your answer

Hope this helps! :)

Answer:

D. 12°

Step-by-step explanation:

80° + 5x = 140°

or, 5x = 140° - 80°

or, x = 60°/5

:. = 12° Ans

Answer:

D (12).

Step-by-step explanation:

To find x, you would need to set up an equation. Since the whole angle, without the angle bisector, is 140, and one part of the angle with the bisector is 80, you would subtract 140-80, which would give you 60. Since the other angle is 5x, you would divide 60/5, which would give you 12, thus resulting in D as your answer.

Finding \(g(x)\) given that we know \(f(x)\) and the graphs for both functions. The correct option is D:

\(g(x) = (x/3)^2\)

Looking at the graph on the image, we notice that \(f(x)\) and \(g(x)\) are two quadratic functions, and \(g(x)\) is just a dilation o f\(f(x)\).

This means that:

\(g(x) = A*f(x)\)

Where A is a real number.

We know that:

\(f(x) = x^2\)

By looking at the graph in the image, we know that \(g(3) = 1\).

Then we can write:

\(g(3) = A*f(3) = A*3^2 = 1\)

We can now solve for A:

\(A*3^2 = 1\)

\(A*9 = 1\)

\(A = 1/9\)

We will have:

\(g(x) = (1/9)*f(x) = (1/9)*x^2 = (x/3)^2\)

Therefore, the correct option is D.

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Complete question in image attached.

Answer: 3 , 4 and 5 are correct options

Step-by-step explanation:

Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

Answer:

Yes you are correct

Step-by-step explanation:

we could go ahead and check its slope and so forth, OR we can just take a peek that the y-coordinates are the same -5, hmmmm well, hell that's just a horizontal line, Check the picture below.

The value of the inverse function f-¹ (3) is (e) 11

From the question, we have the following parameters that can be used in our computation:

f(x) = x - 8

To calculate the inverse value at f-¹ (3)

We set the value to 3

using the above as a guide, we have the following:

x - 8 = 3

Evaluate the like terms

x = 11

Hence, the value of the inverse function is (e) 11

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Complete question

if f(x) = x - 8, what is the value of f-¹ (3)?

Answer: 2, 4, and 5

Step-by-step explanation:

Answer:

2, 4, and 5

Step-by-step explanation:

The equation of line is,

⇒  y = - 1/5x - 1

We have to given that;

Two points on the line are (-5, 0) and (5, -2).

Now,

Since, The equation of line passes through the points (-5, 0) and (5, -2).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 2 - 0) / (5 - (-5))

m = - 2 / 10

m = - 1/5

Thus, The equation of line with slope - 1/5 is,

⇒ y - 0 = - 1/5 (x - (-5))

⇒ y = - 1/5 (x + 5)

⇒ y = - 1/5x - 1

Therefore, The equation of line passes through the points (-5, 0) and

(5, -2) will be;

⇒ y = - 1/5x - 1

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Answer:

y = -(1/2)x+1

Step-by-step explanation:

-2Y - X = -2

Add x to both sides:

-2Y = X - 2

Divide both sides by -2:

Y = -(1/2)x+1

You could also use the shortcuts:

For Ay+Bx=C, the slope is -B/A and the y-intercept is C/A.

Slope = -B/A = -(-1)/(-2) = 1/-2 = -(1/2)

Y-intercept = C/A = (-2)/(-2) = 1

y = mx + b ---> y = -(1/2)x + 1

Answer:

y = -1/2x +1

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

-2y -x = -2

Solve for y

Add x to each side

-2y = x-2

Divide by -2

-2y/2- = x/-2 -2/-2

y = -1/2x +1

Answer:

95% of the confidence interval for the proportion of smokers who have tried to quit within the past year    

(0.47228 , 0.49868)

Step-by-step explanation:

Step(i):-

Given that the National Center for Health Statistics interviewed 5409 adult smokers in 2015

and 2626 of them said they had tried to quit smoking during the past year

proportion

                            \(P = \frac{x}{n} = \frac{2626}{5409} =0.48548\)

                          Q = 1-P = 1 - 0.48548 = 0.5146

Step(ii):-

95% of the confidence interval for the proportion of smokers who have tried to quit within the past year      

\((P - Z_{\alpha } \sqrt{\frac{PQ}{n} } , P+ Z_{\alpha } \sqrt{\frac{PQ}{n} } )\)      

\((0.48548 - 1.96 \sqrt{\frac{0.48548 X 0.51452}{5409} } , 0.48548+ 1.96\sqrt{\frac{0.48548 X 0.51452}{5409} } )\)

( 0.48548 - 0.0132 , 0.48548 +0.0132)

(0.47228 , 0.49868)

Final answer:-

95% of the confidence interval for the proportion of smokers who have tried to quit within the past year    

(0.47228 , 0.49868)

Answer:

Step-by-step explanation:

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Let's begin by listing out the information given to us:

The length of the side opposite to the reference angle is 7.77 units.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

If we take the reference angle 45°, The side 'x' is opposite and the side having a length of 11 units is the hypotenuse.

We know, sin = opposite/hypotenuse.

Therefore,

sin45° = x/11.

1/√2 = x/11.

x = 11/√2.

x = 7.77 units.

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Answer:

\(6\sqrt{2}\)

Step-by-step explanation:

formula

AB=\(\sqrt{(x_{a}-x_{b})+(y_{a}-y_{b})}\)

Answer:

Step-by-step explanation:

To rewrite the equation x² + 18x + 7 = 4 in the form (x - p)² = q, we need to complete the square by adding and subtracting a constant term.

First, we subtract 4 from both sides of the equation:

x² + 18x + 7 - 4 = 0

Simplifying, we get:

x² + 18x + 3 = 0

To complete the square, we need to add and subtract the square of half the coefficient of x, which is (18/2)^2 = 81:

x² + 18x + 81 - 81 + 3 = 0

Simplifying, we get:

(x + 9)² - 78 = 0

Now, we can rewrite the equation in the desired form by adding 78 to both sides:

(x + 9)² = 78

Therefore, the values to be entered in the boxes are:

1: (x + 9)

2: 78