PLEASE! I WILL MARK YOU BRAINIEST!!!!
In ΔTUV, the measure of ∠V=90°, VT = 45 feet, and TU = 90 feet. Find the measure of ∠T to the nearest degree.

When a sequence has a common difference, then the sequence is arithmetic

The next two terms are -5 and -9

The sequence is given as: 11, 7, 3, -1

The above sequence have a common difference.

This is calculated by subtracting a term from the next term.

i.e.

\(\mathbf{d = T_2 - T_1 = T_3 - T_2 = T_{n+1} - T_n}\)

So, we have:

\(\mathbf{d = 7 - 11}\)

\(\mathbf{d = -4}\)

The nth term of an arithmetic sequence is:

\(\mathbf{T_n = T_1 + (n - 1)d}\)

So, we have:

\(\mathbf{T_n = 11 + (n - 1)(-4)}\)

\(\mathbf{T_n = 11 -4n +4}\)

Evaluate like terms

\(\mathbf{T_n = 15 -4n }\)

The next two terms are the 5th and the 6th terms.

So, we have:

\(\mathbf{T_5 = 15 -4 \times 5 = -5}\)

\(\mathbf{T_6 = 15 -4 \times 6 = -9}\)

Hence, the next two terms are -5 and -9

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Answer: Median is 5

Step-by-step explanation: To find the median, we first need to arrange the numbers in order from least to greatest:

0 0 3 7 10 27

The median is the middle number, or the average of the two middle numbers if there are an even number of values. In this case, there are 6 values, so the median is the average of the two middle numbers:

median = (3 + 7) / 2

median = 5

Therefore, the median of the given numbers is 5.

Answer:

66

Step-by-step explanation:

The sum of all of the angles in a triangle is 180. So all three angles would add up to 180:

(a + 21) + 57 + (a - 30) = 180

Combine like terms:

2a + 48 = 180

2a = 132

a = 66

Answer:

a+21+57+a-30=180(angle of triangle)

2a+48=180

2a=180-48

2a=132

a=132/2

a=66

then,a+21=66+21 =87

a-30=66-30 =36

Step-by-step explanation:

I think this is the answer

Answer:

w - 8.8 > 27

Step-by-step explanation:

The coordinates of point D in the parallelogram ABCD are (15, 10).

To find the coordinates of point D, we can use the properties of a parallelogram. In a parallelogram, opposite sides are parallel and congruent. Therefore, we can use this information to determine the coordinates of point D.

Let's consider the given points:

A(-3, 5)

B(7, 12)

C(5, 3)

Since opposite sides of a parallelogram are parallel, the vector connecting points A and B should be equal to the vector connecting points C and D. We can express this as:

AB = CD

To find the vector AB, we subtract the coordinates of point A from the coordinates of point B:

AB = (7 - (-3), 12 - 5)

= (10, 7)

Now, we can express the vector CD using the coordinates of point C and the vector AB:

CD = (5, 3) + (10, 7)

= (15, 10)

Therefore, the coordinates of point D are (15, 10).

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Answer:

x=61.71428 or 61 5/7

Step-by-step explanation:

We can use a ratio to solve

7 pieces              12 pieces

-----------------   = ---------------

36 seconds          x seconds

Using cross products

7x = 36*12

7x = 432

Divide by 7

7x/7 = 432/7

61 5/7

x=61.71428

Answer:

66

Step-by-step explanation:

Answer:

36h + 75 < 1200

solve:

36h + 75 = 1200

36h = 1125

h = 1125 divided by 36 = 31.25.

Therefore, Traci has to dance a minimum of 31.25 hours to raise $1200

okjajsjajajamaakqkaka

It will take both machines approximately 1.71 hours or 1 hour and 42 minutes to produce widgets together.

To solve this problem, we can use the formula:

1 / time taken by machine 1 + 1 / time taken by machine 2 = 1 / time taken by both machines

Let's denote the time taken by the old machine as x hours and the time taken by the new machine as y hours.

From the problem statement, we know that the old machine can produce widgets in 3 hours, so we have:

1 / x = 1 / 3

Solving for x, we get:

x = 3

Similarly, we know that the new machine can produce widgets in 4 hours, so we have:

1 / y = 1 / 4

Solving for y, we get:

y = 4

Now, we can plug in the values of x and y into the formula and solve for the time taken by both machines:

1 / 3 + 1 / 4 = 1 / t

Multiplying both sides by 12t, we get:

4t + 3t = 12

7t = 12

t = 12 / 7

Therefore, it will take both machines approximately 1.71 hours or 1 hour and 42 minutes to produce widgets together.

In conclusion, we used the formula for the combined work rate of two machines to calculate the time taken by both machines to produce widgets. We first found the individual work rates of the old and new machines and then substituted those values into the formula to solve for the time taken by both machines working together.

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The largest interval I over which the solution is defined is (-∞, ∞).               I = (-∞, ∞)

To solve the given initial-value problem, we can use the method of separation of variables as follows:
1. Separate the variables by moving all terms with y to the left side of the equation and all terms with x to the right side:
y/y' = ex/x
2. Integrate both sides of the equation with respect to their respective variables:
∫y/y' dy = ∫ex/x d
ln(y) = ex + C
3. Solve for y:
y = e^(ex + C)
4. Use the initial condition y(1) = 9 to find the value of C:
9 = e^(e + C)
C = ln(9) - e
5. Substitute the value of C back into the equation for y:
y = e^(ex + ln(9) - e)
6. Simplify the equation:
y = 9e^(ex - e)
7. The largest interval I over which the solution is defined is (-∞, ∞), since there are no restrictions on the values of x or y therefore, the solution to the initial-value problem is y(x) = 9e^(ex - e) and the largest interval I over which the solution is defined is (-∞, ∞).

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Answer:

b≤3

Step-by-step explanation:

For this problem, you want to solve it similarly to linear equations.

We start with 4b+6≤18.

Subtracting 6 from both sides gives 4b≤12.

From there, in order to isolate the b, we must divide both sides by 4, leaving b≤3.

**This content involves solving linear inequalities, which you may wish to revise. I'm always happy to help!

The solution to the expression 4+(−634) is -630

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

4+(−634)

Rewrite the expression properly

So, we have the following representation

4 + (−634)

Remove the bracket in the above expression

This gives

4 + (−634) = 4 - 634

Evaluate the difference

4 + (−634) = -630

Hence, the solution is -630

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The equation of circle M is (x - 5)^2 + (y - 3)^2 = 20.

To find the equation of a circle, we need the coordinates of its center and its radius. In this case, we can determine the center of the circle by finding the midpoint of the line segment with endpoints K(1, 5) and W(9, 1).

The midpoint formula is given by:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Using the given coordinates, we can calculate the midpoint as follows:

Midpoint = ((1 + 9) / 2, (5 + 1) / 2)

= (10 / 2, 6 / 2)

= (5, 3)

The coordinates of the center are (5, 3).

Next, we find the radius, which is half the length of the diameter. The length of the diameter can be calculated using the distance formula:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using the coordinates of K(1, 5) and W(9, 1), we have:

Distance = sqrt((9 - 1)^2 + (1 - 5)^2)

= sqrt(8^2 + (-4)^2)

= sqrt(64 + 16)

= sqrt(80)

= 4√5

The radius is half the length of the diameter, so the radius of circle M is:

Radius = (1/2) * 4√5

= 2√5

Now that we have the center (5, 3) and the radius 2√5, we can write the equation of circle M in standard form as:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) represents the center coordinates and r represents the radius. Substituting the values, we get:

(x - 5)^2 + (y - 3)^2 = (2√5)^2

(x - 5)^2 + (y - 3)^2 = 20

Therefore, the equation of circle M is (x - 5)^2 + (y - 3)^2 = 20.

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Answer:

Luke = 12 games

Naliba = 6 games

Step-by-step explanation:

Luke and naliba are playing squash

Luke wins twice as many games as naliba

They play a total of 18 games

Luke= 2x

naliba = x

2x +x= 18

3x= 18

x= 18/3

x= 6

Luke= 2(6)

= 12

naliba= 6

Hence luke wins 12 games and naliba wins 6 games

Answer:

Slope-intercept form of equation of line is, y = mx + c

Equation of line L is,  y = 5x - 5

From given figure, it is observed that line L is passing through point (0, -5) and (1, 0).

First we have to find slope (m) of line.

So, equation of line becomes,

Since, line passing through (1, 0). Therefore, substituting point (1, 0) in above equation of line.

We get,     c = - 5

Thus, equation of line is,  

Step-by-step explanation:

Slope-intercept form of equation of line is, y = mx + c

Equation of line L is,  y = 5x - 5

From given figure, it is observed that line L is passing through point (0, -5) and (1, 0).

First we have to find slope (m) of line.

So, equation of line becomes,

Since, line passing through (1, 0). Therefore, substituting point (1, 0) in above equation of line.

We get,     c = - 5

Thus, equation of line is,  

Answer:

y = \(\frac{5}{2}\) x + 10

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 4, 0) and (x₂, y₂ ) = (0, 10) ← 2 points on the line

m = \(\frac{10-0}{0-(-4)}\) = \(\frac{10}{0+4}\) = \(\frac{10}{4}\) = \(\frac{5}{2}\)

the line crosses the y- axis at (0, 10 ) ⇒ c = 10

y = \(\frac{5}{2}\) x + 10 ← equation of line

When testing the null hypothesis with an alpha value of 0.05, the critical value will be larger than if you were testing with an alpha value of 0.01.

If you are testing the null hypothesis with an alpha value of 0.05, the critical value will be smaller than if you were testing the alpha value of 0.01. This is because a smaller alpha value means a more stringent test of significance, which requires stronger evidence to reject the null hypothesis.

Therefore, the critical value is larger for a smaller alpha value to reflect the higher level of evidence required for rejection. Conversely, a larger alpha value allows for a less stringent test of significance, requiring weaker evidence to reject the null hypothesis, which results in a smaller critical value.

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Answer:

3.2

Step-by-step explanation:

3.2/1

Given planes,x+y+2z=4 and 2x+2y+z=8 in the first octant.

We need to find the volume of the region between these planes in the first octant.

Here are the steps to find the volume of the region between two planes in the first octant:

First, we need to find the intersection of two planes:

x + y + 2z = 4.. (1)

2x + 2y + z = 8.. (2)

Multiplying equation (1) with 2 and subtracting equation (2) from it, we get,

2x + 2y + 4z = 8 - 2x - 2y - z

=> 3z = 4

=> z = 4/3

Now, substituting the value of z in equations (1) and (2), we get;

x + y = -2/3.. (3)

2x + 2y = 8/3

=> x + y = 4/3.. (4)

Solving equations (3) and (4), we get, x = 2/3 and y = -2/3.

Therefore, the intersection of two planes is a line (2/3, -2/3, 4/3).

The volume of the region between two planes in the first octant is given as

Volume = ∫∫[2x + 2y - 8] dx dy

Here, the limits for x is 0 to 2/3 and for y is 0 to -x + 4/3.

Putting these limits in the above equation, we get,

Volume = ∫[0 to 2/3] ∫[0 to -x + 4/3] [2x + 2y - 8] dy dx

On solving,

Volume = 4/3 cubic units

Therefore, the volume of the region between the planes x+y+2z=4 and 2x+2y+z=8 in the first octant is 4/3 cubic units.

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The probability If no letter can be used twice, 32292000 ways different pass word options are there .

What is probability?

 Mathematical branch known as probability deals with determining the possibility of an event occurring. Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. The possibility of the result of any random event is known as probability. This phrase refers to determining the likelihood that any given event will occur.

Here a password contains 4 letters followed by 2 numbers.

Total number of alphabets = 26

If without repetition the words can be arranged as,

=> 26*25*24*23

Total numbers = 0 to 9 = 10

if without repetition the numbers can be arranged as ,

=> 10 * 9

If no letter can be used twice, number of  different pass word options are,

=> 26*25*24*23*10*9=32292000

Therefore there are 32292000 ways different password options available.

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Answer:

-5b <= -34

Step-by-step explanation:

The inequality phrase, "at most" is same as "less than or equal to". So the algebraic inequality would be -5b <= -34. To solve for b, divide both sides by -5 and make sure to switch the inequality symbol to >= when dividing or multiplying inequalities by a negative number. So b >= 34 / 5.

The angle whose vertex is on the circle and the sides of the angle are the chords is called an Inscribed Angle .

What is an Inscribed Angle ?

An inscribed angle in the circle is formed by the two chords which have a common end point on circle and this common end point is called the vertex of inscribed angle.

The arc formed by the inscribed angle in the circle is called as the intercepted arc .

also the Inscribed Angle Theorem states that inscribed angle on the circle is half the measure of central angle that subtends the same arc .

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Answer:

multiply input number by 2

Step-by-step explanation:

So, this is our function

y=2x===>

(3, 6), (4, 8), (5, 10), (6, 12), (7, 14)

so according to this functionality the output part is equal to input part multiplied by 2

we need to find the line equation for the dashed line. Since we have 2 points of the line, its slope is

where we used the slope formula:

Then, our searched line has the form:

where b is the y-intercept. We can finde b by substituting point (0,-3) into the last equation:

then, the searched line in slope-intercept form is

Therfore, the given area can be modeled as

because when a line is dashed it doesn't belong to the given area.

Answer:

Step-by-step explanation:

A line that is perpendicular will have a slope that is the negative inverse of the reference line slope.  Rewrite y-2x+9=0 as y =mx+b:

y = 2x-9   This line has a slope of 2 and a y-intercept of -9.  A perpendicular line to this will have a slope that is the negative inverse of 2, that is, -(1/2).

y=-(1/2)+b

We don't know b, but can find it by entering the x and y for the known point and solve for b:

Point:  (7, -6)

y=-(1/2)+b  

-6 = -(1/2)*(7)+b

-6 = -(7/2) + b

b = -6 + (7/2)

b = -2.5

The equation is y = -(1/2)x - 2.5

Answer:

The volume of the prism is 243 cm³

Step-by-step explanation:

The volume of the prism is V = B × H, where

∵ The prism is a triangular prism

∴ Its base is a triangle

∵ The base of it is a right triangle

∴ Its area B = \(\frac{1}{2}\) b h, where b and h are the legs of the right angle

→ We have one leg of the right angle and the hypotenuse, so we

   must use the Pythagoras Theorem to find the other leg

∵ (5.4)² + h² = (7.8)²

∴ 29.16 + h² = 60.84

→ subtract 29.16 from oth sides

∴ h² = 31.68

→ Take √  for both sides

∴ h = 5.6284989 cm

→ Now find the area of the base

∵ B = \(\frac{1}{2}\) (5.4)(5.6284989)

∴ B = 15.196947 cm²

→ Let us use the rule of the volume above

∵ V = B × H

∵ H = 16 cm

∴ V = 15.196947 × 16

∴ V = 243.151153 cm³

→ Round it to 3 significant figures

∴ V = 243 cm³

∴ The volume of the prism is 243 cm³