If tan t=−7/24 and π/2 < t < π, find sin t, cos t, sec t, csc t, cot t.
Enter the exact answers.

To prove the converse of the Vertical Angles Theorem, we need to show that if angles LDBC and LABE are congruent and points D, B, and E are on opposite sides of line AB, then they must be collinear.

Given: ∠LDBC ≅ ∠LABE

To Prove: D, B, and E are collinear

Proof:

1. Assume that points D, B, and E are not collinear.

2. Let BD intersect AE at point X.

3. Since D, B, and E are not collinear, then X is a point on line AB but not on line DE.

4. Consider triangle XDE and triangle XAB.

5. By the Alternate Interior Angles Theorem, ∠XAB ≅ ∠XDE (corresponding angles formed by transversal AB).

6. Since ∠LDBC ≅ ∠LABE (given), we have ∠LDBC ≅ ∠XAB and ∠LABE ≅ ∠XDE.

7. Therefore, ∠LDBC ≅ ∠XAB ≅ ∠XDE ≅ ∠LABE.

8. This implies that ∠XAB and ∠XDE are congruent vertical angles.

9. However, since X is not on line DE, this contradicts the Vertical Angles Theorem, which states that vertical angles are congruent.

10. Therefore, our assumption that D, B, and E are not collinear must be false.

11. Thus, D, B, and E must be collinear. Therefore, the converse of the Vertical Angles Theorem is proven, and we can conclude that if ∠LDBC ≅ ∠LABE and D, B, and E are on opposite sides of line AB, then D, B, and E are collinear.

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The slope for the least-squares line is 0.067 and the y-intercept is 2.63.
To find the slope and y-intercept for the least-squares line, we will use the given correlation coefficient (0.944), the means, and standard deviations of both the explanatory and response variables.

Slope (b1) = r * (Sy/Sx)
where r is the correlation coefficient, Sy is the standard deviation of the response variable, and Sx is the standard deviation of the explanatory variable.

Slope (b1) = 0.944 * (1.64/29.51) = 0.0522 (rounded to the hundredths place)

Next, we find the y-intercept (b0) using the following formula:

Y-intercept (b0) = Ymean - (b1 * Xmean)
where Ymean is the mean of the response variable and Xmean is the mean of the explanatory variable.

Y-intercept (b0) = 9.65 - (0.0522 * 149.4) = 1.88 (rounded to the hundredths place)

So, the correct slope and y-intercept for the least-squares line are 0.0522 and 1.88, respectively.

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The exact expression for the electrostatic potential at a point P in the x, y plane at a distance r from the center of the quadrupole is given by V(r) = k [Q/(r2 + D2)1/2 – Q/[(r2 + 2d + D2)1/2]] + k [-2Q/D].

Let's consider that three charges are placed in a straight line along the z-axis, and the charges are +Q on z=+D, -Q on z=-D, and -2Q at z=0.

To find the electrostatic potential at a point P in the x, y plane at a distance r from the center of the quadrupole, let's proceed with the following steps:

To find the electrostatic potential at a point P in the x-axis, we need to consider that the distance from the charges that are on the axis is r, and the distance from the charges that are on the axis and are at +D and -D is d.

The distance from the charges on the axis and at 0 is x. Now we can write,

V(x) = k [Q/(x2 + D2)1/2 – Q/[(x + d)2 + D2]1/2] + k [-2Q/D].

Now, we can substitute the values in the above expression and obtain,

V(x) = k [Q/(x2 + D2)1/2 – Q/[(x + d)2 + D2]1/2] + k [-2Q/D] .

Now, we need to use symmetry to argue that we can switch from x to r, which is given by r2 = x2 + y2.

Thus, the exact expression for the electrostatic potential at a point P in the x, y plane at a distance r from the center of the quadrupole is given by V(r) = k [Q/(r2 + D2)1/2 – Q/[(r2 + 2d + D2)1/2]] + k [-2Q/D].

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Answer:

the answers below:

1: (3,-2)

2: ( -3,2)

Answer:

Option D) -9

Step-by-step explanation:

Here (6 , n) corresponds to an ordered pair solution that is (x , y) so we have the value of x that is 6 but we need the value of y which is f(x) so we insert the value of x into the function to get the value of n like this,

\(f(x)=-2x+3\\f(6)=-2(6)+3\\n=-12+3\\n=-9\\\)

because f(x) corresponds to y and hence f(6) corresponds to n

It will take the golf ball 12 seconds to hit the ground using the kinematic equation for vertical motion.

To determine the time it takes for the golf ball to hit the ground, we can use the kinematic equation for vertical motion:

\(h = ut + (1/2)gt^2\)

Where:

h is the height (0 feet, as the ball is on the ground)

u is the initial velocity (192 feet per second)

g is the acceleration due to gravity (-32 feet per second squared, considering downward direction)

t is the time we want to find

Plugging in the given values, we get:

\(0 = (192)t + (1/2)(-32)t^2\)

Simplifying the equation, we have:

\(-16t^2 + 192t = 0\)

Factoring out t, we get:

t(-16t + 192) = 0

Setting each factor equal to zero, we have:

t = 0 (not applicable in this case)

-16t + 192 = 0

Solving for t, we get:

-16t = -192

t = 12

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The time it takes for the golf ball to hit the ground is approximately 11.92 seconds.

The time it takes for the golf ball to hit the ground can be determined using the equation of motion. We can use the formula:

h0 = 0

v0 = 192

g = 32.2

a = 16.1

b = 192

t1 = 0

t2 = -b / a

t(-16t + 192) = 0

Setting each factor equal to zero, we have:

t = 0 (not applicable in this case)

-16t + 192 = 0

Solving for t, we get:

-16t = -192

t = 12

t2 >= 0:

   time_to_hit_ground = t2

   time_to_hit_ground = t1

The time it takes for the golf ball to hit the ground is approximately", round(time_to_hit_ground, 2 seconds.

The time it takes for the golf ball to hit the ground is approximately 11.92 seconds.

Since time cannot be negative in this context, we discard the negative solution. Therefore, the time it takes for the golf ball to hit the ground is approximately 11.92 seconds.

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Answer:

BA = 11

Step-by-step explanation:

CB + BA = CA , substitute values

7x - 2 + 5x + 1 = 23, that is

12x - 1 = 23 ( add 1 to both sides )

12x = 24 ( divide both sides by 12 )

x = 2

Thus

BA = 5x + 1 = 5(2) + 1 = 10 + 1 = 11

Answer: 3/2

Did this on I ready

The speed of Becca for the given data is 3/2 miles per hour.

The distance that an object travels in relation to the amount of time it takes to do so can be used to define speed. In other terms, it is a measurement of an object's motion's speed without direction The term "velocity" refers to the combination of direction and speed.

Given the hiking distance of Becca = 9/10 miles

time taken = 3/5 hours

to find the speed,

speed = distance/time

speed = (9/10) ÷ (3/5)

speed = 9/10 x 5/3

speed = 3/2 miles per hour

Hence the speed of Becca is 3/2 miles per hour.

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A two-tailed test is considered to be more powerful than a one-tailed test. Therefore, Option D (a two-tailed test) is the correct answer.

The one-tailed test and the two-tailed test are two sorts of hypothesis tests. The number of tails, as the name implies, is the fundamental distinction between the two sorts of hypothesis tests. The tails are the areas under the probability distribution curve that are beyond the critical values or the cut-off points.

The one-tailed test is one of the types of hypothesis testing in which an alternative hypothesis is generated in a specific direction. In comparison to two-tailed tests, they are simpler to conduct. The one-tailed test is less likely to reject the null hypothesis since it only tests one of the tails. On the other hand, the two-tailed test tests both tails of the distribution, making it more powerful since it is more inclusive than the one-tailed test.

The two-tailed test is more effective since it tests for discrepancies on both sides of the distribution, whereas the one-tailed test only tests for discrepancies on one side of the distribution.

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Answer:

bro it's blurry

Step-by-step explanation:

why is it so blurry

the answers are

1) all 3 angles

2) all 3 angles

3) similar

Step-by-step explanation:

h(x) = (x + 9)(x² - 10x + 25) = (x + 9)(x - 5)²

When h(x) = 0, (x + 9) = 0 or (x - 5)² = 0.

=> x = -9 or x = 5.

Hence there are 2 distinct real roots of h(x).

Answer:

2 seconds

Step-by-step explanation:

When the ball hits the ground, its height (h) will be 0. You can therefore set up the following equation:

\(0=-16t^2+20t+30 \\\\-4(4t^2-5t-6)=0\)

Factor:

\(-4(4t+3)(t-2)=0 \\\\t=-\dfrac{3}{4}, 2\)

Since the time must be positive, it hits the ground after 2 seconds. Hope this helps!

Answer: jasmine earns more than richardo she earns 30 more dollars

Step-by-step explanation:

ricardo

dived 4 from 40 you get 10 then times by 18 which equals 180

jasmine

then you divide 8 and 40 then you get then you times it by 42 and you get 210

Answer:

Angle 1 = 99

Angle 2 = 91

Angle 3 = 81

99 + 91 - 81 = 109

I hope this helps!

Answer: the answer is 4.08

Step-by-step explanation:

Answer:

4.08

Step-by-step explanation:

2.29+2.59-0.50-0.30 is equal to 4.08

it's just addition and subtraction haha

Answer:

$1.35

Step-by-step explanation:

7 x 0.65 = 4.55

5.90 - 4.55 = 1/35

Answer:

1.35

Step-by-step explanation:

$0.65 x 7= 4.55

then u do $4.55 - $5.90

= $1.35

61

Answer:

5²+6²=5*5+6*6=25+36=61 is a required answer.

Answer:

61 is the answer

Step-by-step explanation:

\( {5}^{2} = 5 \times 5 = 25 \\ {6}^{2} = 6 \times 6 = 36 \\ \\ {5}^{2} + {6}^{2} = 25 + 36 \\ = 61\)

Step-by-step explanation:(a) To find two other pairs of polar coordinates of (3, π/4):

One with r > 0: (3, 9π/4)

One with r < 0: (-3, 5π/4)

To plot the point (3, π/4), we start at the origin and move 3 units along the line that makes an angle of π/4 radians with the positive x-axis.

(b) To find two other pairs of polar coordinates of (2, -2π/3):

One with r > 0: (2, 4π/3)

One with r < 0: (-2, π/3)

To plot the point (2, -2π/3), we start at the origin and move 2 units along the line that makes an angle of -2π/3 radians (which is the same as 4π/3 radians) with the positive x-axis.

(c) To find two other pairs of polar coordinates of (-2, π/6):

One with r > 0: (2, 7π/6)

One with r < 0: (-2, 19π/6)

To plot the point (-2, π/6), we start at the origin and move 2 units in the direction that makes an angle of π/6 radians with the positive x-axis, but since r is negative, we move in the opposite direction. So we end up at a point on the line that makes an angle of 7π/6 radians with the positive x-axis.

Answer:

x < - 3

Step-by-step explanation:

Given the interval (- ∞, - 3 )

The parenthesis on both ends indicates that x cannot equal the end values.

Thus

x < - 3 represents the interval

Check the picture below.

Answer:

Step-by-step explanation:

Your answer

About all the sides are equal so we can say (10x + 44) side's triagle is twice than another triangle

So, 10x + 44 = 2( 8x - 23)

..... 10x +44 = 16x -46

...... X = 15

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Answer:

1. ∠YZX = 37°

2. ∠YXZ = 53°

3. XZ = 30 meters

Step-by-step explanation:

1. To solve for an unknown angle, we need to utilize the inverse of a trigonometric function.

⭐What are the inverses of the trigonometric functions?

To know which inverse of the trigonometric functions we use, we have to see the type of side lengths we are given (opposite, adjacent, or hypotenuse)

We are given side length XY, which is opposite of ∠YZX, and we are given side length YZ, which is adjacent to ∠YZX. Therefore, we will use \(tan^-1 (opposite/adjacent) =\)

Substitute the values we are given into the function:

\(tan^-1 (18/24) =\)

Compute this equation using a scientific calculator. I recommend using the Desmos Scientific Calculator:

\(= 37\)

∴ ∠YZX = 37°

2. We already know 2 angles (∠YZX = 37°, and ∠ZYX = 90°) Therefore, to find ∠YXZ, we have to utilize the triangle sum theorem.

⭐ What is the triangle sum theorem?

Substitute the angles we know already (∠YZX and ∠ZYX), and solve for ∠YXZ.

\(< YZX + < ZYX + < YXZ = 180\)

\(37 + 90 + YXZ = 180\)

\(127 + YXZ = 180\)

\(< YXZ = 53\)

∴ ∠YXZ = 53°

3. We already know 2 side lengths (ZY = 24 meters, and XY = 18). Therefore, to find XZ, we have to utilize the Pythagoras' theorem.

⭐ What is the Pythagoras' theorem?

Substitute the values of the side lengths into the formula:

\((XZ)^2 = (XY)^2 + (ZY)^2\)

\((XZ)^2 = 18^2 + 24^2\)

Solve for XZ:

\((XZ)^2 = 324 + 576\)

\((XZ)^2 = 900\)

\(\sqrt{(XZ)^2} = \sqrt{900}\)

\(XZ = 30\)

∴ XZ = 30 meters

Answer:

C. 17 feet

Step-by-step explanation:

I apologize if this is inaccurate, as I have not done this material in awhile. But, I hope it helps and is accurate! Have a great day! :D

Answer:

The correct answer is A

Step-by-step explanation:

The center of gravity of the gymnast is located at approximately (0.1596 m, 0.0371 m).  The COG of the gymnast can be calculated by finding the weighted average of the individual segment COGs.

To locate the center of gravity (COG) of the gymnast shown in figure (a), we can use the data provided along with the coordinate system shown in figure (b). The COG of the gymnast can be calculated by finding the weighted average of the individual segment COGs.

Let's calculate the x-coordinate and y-coordinate of the COG separately.

For the x-coordinate (xcg), we can use the equation:

xcg = (m1*x1 + m2*x2 + m3*x3 + m4*x4) / (m1 + m2 + m3 + m4),

where m1, m2, m3, and m4 are the masses of the arms, torso, thighs, and legs, respectively, and x1, x2, x3, and x4 are the x-coordinates of their respective COGs.

Substituting the given values:

xcg = (6.89*0 + 33.6*0.337 + 14.1*0.145 + 7.50*0.227) / (6.89 + 33.6 + 14.1 + 7.50).

Calculating this expression:

xcg ≈ 0.1596 m.

For the y-coordinate (ycg), we can use the equation:

ycg = (m1*y1 + m2*y2 + m3*y3 + m4*y4) / (m1 + m2 + m3 + m4),

where y1, y2, y3, and y4 are the y-coordinates of the respective COGs.

Substituting the given values:

ycg = (6.89*0.236 + 33.6*0 + 14.1*0 + 7.50*0) / (6.89 + 33.6 + 14.1 + 7.50).

Calculating this expression:

ycg ≈ 0.0371 m.

Therefore, the center of gravity of the gymnast is located at approximately (0.1596 m, 0.0371 m) in the coordinate system shown in figure (b).

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Answer:Each pair of alternate interior angles is congruent, and each pair of alternate exterior angles is congruent.

Step-by-step explanation:

The right Riemann sum for arctan(1 + xdx) is Σ[arctan(1 + iΔx)]Δx, where i ranges from 1 to n and Δx is the width of each subinterval. The correct answer among the options provided is (arctan(1 + Δx) + arctan(1 + 2Δx) + ... + arctan(1 + nΔx))Δx.

In a right Riemann sum, the function is evaluated at the right endpoint of each subinterval. Therefore, we add up the values of arctan(1 + iΔx) at the endpoints of the subintervals, where i ranges from 1 to n. The width of each subinterval is Δx, so we multiply the sum by Δx to get the approximate value of the integral.

The provided expression (arctan(1 + Δx) + arctan(1 + 2Δx) + ... + arctan(1 + nΔx))Δx satisfies the conditions of a right Riemann sum, where the function is evaluated at the right endpoint of each subinterval. Therefore, this is the correct option among the given choices.

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