The midpoint of a segment is (2, -8) and one of the endpoints is (3,6). What are the coordinates of the other endpoint?

The exact values are:

sin(α + β) = (-6√5 - 8)/25

cos(α + β) = (4√5 - 6)/25

sin(α - β) = (-6√5 + 8)/25

tan(α - β) = (-9√5 + 45)/4

We have,

Recall the trigonometric identities:

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

tan(a - b) = (tan(a) - tan(b))/(1 + tan(a)tan(b))

Using these identities, we can find the exact values of the expressions given.

(a) Sin (α + β)

sin(α + β) = sin(α)cos(β) + cos(α)sin(β)

= (√5/5)(-3/5) + (2/5)(-4/5) (using the values given for sin and cos)

= -6√5/25 - 8/25

= (-6√5 - 8)/25

(b) Cos (α + β)

cos(α + β) = cos(α)cos(β) - sin(α)sin(β)

= (2/5)(-3/5) - (√5/5)(-4/5) (using the values given for sin and cos)

= -6/25 + 4√5/25

= (4√5 - 6)/25

(c) Sin (α - β)

sin(α - β) = sin(α)cos(β) - cos(α)sin(β)

= (√5/5)(-3/5) - (2/5)(-4/5) (using the values given for sin and cos)

= -6√5/25 + 8/25

= (-6√5 + 8)/25

(d) tan (α - β)

tan(α - β) = (tan(α) - tan(β))/(1 + tan(α)tan(β))

= ((√5/5) - (-4/5))/(1 + (√5/5)(-4/5)) (using the values given for sin and cos)

= (9√5/5)/(1 - 4/5√5)

= (-9√5 + 45)/4

Therefore,

The exact values are:

sin(α + β) = (-6√5 - 8)/25

cos(α + β) = (4√5 - 6)/25

sin(α - β) = (-6√5 + 8)/25

tan(α - β) = (-9√5 + 45)/4

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\( \leadsto \sf {k}^{ - \frac{1}{6} } \)

\( \\ \)

\( \leadsto \sf \dfrac{1}{{k}^{ - \frac{1}{6} }} \)

\( \\ \\ \)

\( \leadsto \sf \dfrac{1}{ \sqrt[6]{k} } \)

Answer:

(k^-1)^1/6

\(\sqrt[6]{k ^-1}\)  

Step-by-step explanation:

for second one -1 is coefficient sry can't format it

The dimensions of the rectangular box with largest volume if the total surface area is given as 100 cm2: x = y = z = 2.449 cm.

Given that:

Total surface area of the rectangular box or cuboid = 100 cm²

A rectangular box with largest volume is a cube.

The total surface area of a cube = 6 times square of one edge length.

Let the edge length = given dimensions; x, y, z

So,

x = y = z

6x^2 = 100

x^2 = 100 / 6

x = √ 100 / 6

x = 10 / √ 6 cm

x = 2.449 cm

Hence, dimensions of the rectangular box with largest volume if the total surface area is given as 100 cm2: x = y = z = 2.449 cm.

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Question

If you draw scaled copies of this triangle using the scale factors in the

table, what will the areas of these scaled copies be?

Answer: Hi, There! Mika-Chan

The Answer for the Scale Factor is....

→1 Scale and 36 Units ←

Hope this Helps!

Answer

0.6 • 25 = x

Step-by-step explanation:

60/100 x 25

0.6 x 25

Answer:

3

Step-by-step explanation:

i changed 1/2 into 0.5 and 3/2 into 1.5 then 0.5 times 4 times 1.5 and got 3

pls mark me branilest

Answer:

9.8

Step-by-step explanation:

I checked on google

Answer:

9.8

Step-by-step explanation:

Answer:

-8x+14 ≥ 60

Inequality Form:

x< -23/4

Interval Notation:

(−∞,−23/4)

Answer:

Therefore, there will be 18,225 house flies in 1 year. (It's kind of a joke/trick question since House Flies only live 28 days (range 15-30 days). So, in reality, you'll have to take that into consideration.

Step-by-step explanation:

Since the population triples every 2 months, we can express the population as:

P = 25 * 3^(t/2)

Where P is the population size after t months.

To find the population size after 1 year, we need to substitute t = 12 into the equation:

P = 25 * 3^(12/2)

P = 25 * 3^6

P = 25 * 729

P = 18225

Therefore, there will be 18,225 house flies in 1 year.

When we talk of a line of symmetry, we mean a line that passes through a plane shape and divides the shape into exactly two equal halves.

Any line that passes through a shape and gives us two other shapes which are complements of each other such that when they are joined together gives back the original shape.

In the question, we can identify three lines , l , m and n and we want to select which of these lines are lines of symmetry.

How do we go about this?

We simply look at both sides of the line, if what we have on both lines are equal, then what we have is a line of symmetry.

Looking at each line drawn , we can see that only line m divides the shape in a way that the two pieces can be overlapped.

Although the other two lines cut the shape into two, they do not give that overlapping image that line m would give

Hence, for this shape, line m is the line of symmetry

Answer:

180

Step-by-step explanation:

The area of a parallelogram is given by the formula A = b × h, where b is the base and h is the height. In this case, the base is 10 and the height is 18. Therefore, the area is:

A=10×18

A=180

The area of the parallelogram is 180 square units

Answer:

3n squared+n+2

Answer:

the nth term of the sequence is 2n² + 4T

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Step-by-step explanation:

he sequence represents a quadratic function, the nth term of the sequenceis 2n² + 4 

The nth term of a quadratic sequence is :an² + bn + c c = zeroth term ; a = second difference ÷ 2

From the sequence :First difference = 6, 10, 14, 18Second difference = 4, 4, 4

 First difference between terms in position 1 and 0 :6 - 4 = 2 

Zeroth term = First term in sequence - 2 = 6 - 2 = 4a = 4/2 = 2

Plugging the values into the equation :2n² + bn + 4 Using the 2nd term :n = 22(2)² + 2b + 4 = 128 + 2b + 4 = 12 2b = 12 - 12 2b = 0b = 0

Hence, the nth term of the sequence is 2n² + 4

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Answer:

1.) Unbalanced

Step-by-step explanation:

have a great day

Answer:

x = 4

m<AXC = 150

Step-by-step explanation:

m<1 + m<2 = m<AXC

102 + 10x + 8 = 6(6x + 1)

10x + 110 = 36x + 6

26x = 104

x = 4

m<AXC = 6(6x + 1)

m<AXC = 6(24 + 1)

m<AXC = 150

The slope of the line passing through the points (−8, -4) and (−8, 8) is undefined.

The slope of the line passing through the points (3, 4) and (−3, 4) is equal to 0.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given points into the slope formula, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (8 - (-4))/(-8 - (-8))

Slope (m) = (8 + 4)/(-8 + 8)

Slope (m) = 12/0

Slope (m) = undefined.

For line B, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (4 - 4)/(-3 - 3)

Slope (m) = 0/6

Slope (m) = 0.

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Given the point (5, 7) and the slope 2, using the point-slope form we have the equation of the line:

Where m is the slope and x₀ and y₀ are the coordinates of the given point. From this problem, we identify m = 2, x₀ = 5, and y₀ = 7. Then:

The slope-intercept form is given by:

Where m is the slope and b is the y-intercept. Using equation (1):

as 20+11>30 it is a triangle

now for angle

let us consider a=20,b=30,c=11 and their opposite angle be A,B,C respectively

then B =cos-inverse((a^2 +c^2-b^2)/2ac))

p.s We are calculating value of B because it is opposite of largest side b so it will be highest angle

or B = cos-inverse((400+121-900)/(2*30*11))

B = 125.04 degree

since B> 90 the triangle is obtuse triangle

Answer:

obtuse

Step-by-step explanation:

Given the 3 sides 20, 30 and 11

For the sides to form a triangle then the sum of any 2 sides must be greater than the third side.

20 + 30 = 50 > 11

20 + 11 = 31 > 30

30 + 11 = 41 > 20

Thus the 3 sides form a triangle

To determine what type of triangle it is

let c be the longest side and a, b the other 2 sides

• If a² + b² = c² then triangle is right

• If a² + b² > c² then triangle is acute

• If a² + b² < c² then triangle is obtuse

Here c = 30, a = 20, b = 11

c² = 30² = 900

a² + b² = 20² + 11² = 400 + 121 = 521

Since a² + b² < c² then triangle is obtuse

We are told that the group traveled an average of 12 miles per day. So, for example, after 1 day of travel, the traveled distance would be 12. After day two, they would have traveled 12 extra miles. That is

So note that to calculate the traveled distance, we take the number of days and multiply it by the average rate of miles per day (12 miles per day). Let x be the total amount of days the group took to travel 2000 miles. So , according to what we just described, we have the equation

so, by dividing both sides by 12 we get

so, the group took about 167 to travel the entire trail.

The solution of the inequality equation is x > -π/2 or x > 3π/2.

The value of x in the inequality is calculated by applying the following formula as follows;

Given 0 ≤ x < 2π,

tan (x/2) > - 1

To determine the value of x take the arc tan of (-1) as follows;

x/2 > arc tan (-1)

x/2 > -π/4

x > -π/2

In the interval π/2 ≤ x < π:

x/2 > arc tan (-1)

x/2 > 3π/4

x > 3π/2

Thus, the solution of the inequality equation is x > -π/2 or x > 3π/2.

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The given function is:

Start by evaluating the function in the extreme values of the interval:

The intermediate value theorem states: if a function f is continuous in an interval [a,b], and k is any number between f(a) and f(b), then there exists a number c between a and b such that f(c)=k.

As k=13 and it is between 1 and 43, then there is a number c such that f(c)=13.

Now, replace f(c) by 13 and solve for c:

Let's find the factored form to find the c-values:

As -4 is not in the interval, thus the value of c guaranteed by the theorem is c=3.

Answer:

-----------------------------------

Simplify the equation by distribution, then substitute the value of d and solve for c:

Answer:

2

Step-by-step explanation:

We have a multiplication problem within a whole number and a fraction.

When multiplying fractions with whole numbers, you always multiply the whole number with the numerator of the fraction.

\(\frac{numerator}{denominator}\)

\(\frac{4}{8} *4\)

\(\frac{4*4}{8}\)

\(\frac{16}{8}\)

Divide 16 by 8 :

\(2\)

from,

m = y - y1

x - x1

m = 2 - 5

4 - 1

m = -3 = -1

3

then,

y - y1 = m(x - x1)

using coordinates (1, 5)

y - 5 = -1(x - 1)

y = -x + 1 + 5

y = -x + 6.

Answer:

yeah 6×3=18 by multiplying 6 and 3

Answer:

Jeremy has gotten more than half of the test's questions correctly.

Step-by-step explanation:

To get half of the questions correctly, Jeremy needed at least 40, and Jeremy got more than 40, meaning he got more than half.

Answer: 6 feet and 2 yards are the same distance because each yard is 3 feet

Step-by-step explanation: