Complete the following proof.
Prove: In an equilateral triangle the three medians are equal.
+a
e-(.*)-(
2a
P=
- (0 + 2ª + )-( ₂² )-(.)
?
2
0+
2-(+)-()
|− a)² + (
R-
C(a. b)
PC
=
(2a, 0)
√3 (with side - 2a)
QA-
- √(₁-2)* ·-(- -)
J(J
9a² 8²
a² (√3)²
B
(Height of equalateral A = b)
X
RB
a²3
√3
(²-²)² + (- - -)*
-J* · ·
()*(3
√√3

Using a trigonometric identity, it is found that the secant and the cotangent of the angles are given as follows:

The following identity is used, considering an angle [tex]\theta[/tex].

[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]

In this problem we are given the sine, then the cosine can be found as follows:

[tex]\left(-frac{5}{8}\right)^2 + \cos^2{\theta} = 1[/tex]

[tex]\cos^2{\theta} = 1 - \frac{25}{64}[/tex]

[tex]\cos^2{\theta} = \frac{39}{64}[/tex]

[tex]\cos{\theta} = \pm \sqrt{\frac{39}{64}}[/tex]

In the fourth quadrant, the cosine is positive, hence:

[tex]\cos{\theta} = \frac{\sqrt{39}}{8}[/tex].

The secant of an angle [tex]\theta[/tex] is one divided by the cosine of the angle, hence:

[tex]\sec{\theta} = \frac{1}{\cos{\theta}} = \frac{1}{\frac{\sqrt{39}}{8}} = \frac{8}{\sqrt{39}} \times \frac{\sqrt{39}}{\sqrt{39}} = \frac{8\sqrt{39}}{39}[/tex]

The cotangent of an angle [tex]\theta[/tex] is the cosine divided by the sine of the angle, hence:

[tex]\cot{\theta} = \frac{\cos{\theta}}{\sin{\theta}} = \frac{\frac{\sqrt{39}}{8}}{-\frac{5}{8}} = -\frac{\sqrt{39}}{5}[/tex]

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Using proportions, the cost of the 17-ounce sundae is of $5.95.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Considering the 12-ounce sundae bought for $4.2, the cost per ounce is given by the following proportion:

$4.2/12 = $0.35.

Hence the cost of a 17-ounce sundae is:

$0.35 x 17 = $5.95.

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Second time john wins the race because he runs in the race with constant speed as same speed they run in 1st race.

According to the statement

We have given that the John and Peter, are running a 100-meter race.

In the first race that they run John beats Peter by 5 meters. and the next time they race John stands 5 meters behind the starting line.

Here the both participant's speed remain same in both races.

So, We have to find that the If they run at the constant speed as the first race, who will win the second race

So, for this purpose

According to the statement

in first race john beats the peter and wins the race and if they start the second race with the same speed then it is clear that the second time john won the race.

So, Second time john wins the race because he runs in the race with constant speed as same speed they run in 1st race.

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The complete statements are:

The complete question is added as an attachment

The roots are given as:

x = 0 second

and

x = 9.8 seconds

x = 0 implies that the height of the arrow was 0 meters above his bow after 0 seconds

x = 9.8 implies that  it takes approximately 9.8 seconds for the arrow to return to the height of the bow.

The x-value of the vertex is

x = (0 + 9.8)/2

Evaluate

x = 4.9

Approximate

x = 5

This means that the vertex is approximately 5 seconds

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The diameter of a new ball is 4.0ft

According to the statement

we have given that the the company wants to spend a maximum of $1 each.

And we have to find a diameter of a new ball.

Remember that for a sphere of diameter D, the surface area is

A = 4*pi*(D/2)^2

In this case, the cost is $0.02 per square foot, and the company wants to expend (at maximum) $1 per ball, so first we need to solve:

$0.02*A = $1

A = $1/$0.02 = 50

So the surface of the ball must be 50 square feet.

Then we solve:

50ft^2 = 4*3.14*(D/2)^2

D = 2*√(50 ft^2/(4*3.14)) = 4.0 ft

here the diameter of a ball is 4.0ft.

So, The diameter of a new ball is 4.0ft

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Answer:

-2+i

Step-by-step explanation:

-7+4i represents (-7,4) and 3-2i represents (3,-2).

So, the midpoint is (-2,1), which represents -2+i.

Answer:

$600

Step-by-step explanation:

For 8 hours she makes $120

For 1 hour she makes $120÷8 = $15

For 40 hours she makes $15 × 40 = $600

Our final answer is $600

Hope this helped and have a good day

Answer:

y = -2x + 2

Step-by-step explanation:

slope is found with (change in y/change in x), or in this case, (-4--2,3-2), which is -2

with the equation y = -2x + b, solve for b by plugging in the x and y values of one of the points

using (2, -2):

-2 = -2(2) +b

b = 2

so the equation is y = -2x + 2

Answer:

9 weeks.

Step-by-step explanation:

m = 11w + 67

m = 17w + 13

So:

11w + 67 = 17w + 13

67 - 13 = 17w - 11w

54 = 6w

w = 9.

The expression which shows the total cost is 2.50+0.4x and the cost of riding 20 miles is $10.50.

Given a taxi charges $2.50 for the first mile and $0.40 for each mile

We are required to make an expression showing total cost and total cost of a 20 mile ride.

let the miles ride by tax be x.

Total cost of the product or service=Number of units*price of one units.

We have been given that $2.50 is fixed so we will not multiply our variable charge with $2.50 and multiply 0.40 with x.

So,the expression showing looks like 2.50+0.40x.

Now to find the cost when taxi travels 20 miles, we have to put x=20,

Cost=2.50+0.40*20

=2.50+(40*20)/100

=2.50+800/100

=2.50+8

=$10.50

Hence the expression which shows the total cost is 2.50+0.4x and the cost of riding 20 miles is $10.50.

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The  accounting principle she would use to value the assets of the company at their original cost is historical cost accounting.

Historical cost accounting is an accounting method for recording the value of fixed assets under US GAAP where the value of an asset on a balance sheet is equal to the cost of acquiring the asset.

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Answer:

XPY = 15π m

Step-by-step explanation:

XPY is 3/4 of the circumference of the circle.  The perimeter of a circle is given by 2πr, with r = 10m.

C = 2πr

C = 2π(10)

C = 20π

3/4 of C is (3/4)(20π)

XPY = 15π m

Answer: y=[tex]-\frac{5}{2} x+2[/tex]

Step-by-step explanation:

Use the equation of the line format: y = mx + b

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

[tex]m=\frac{-3-(7)}{2-(-2)}[/tex]

[tex]m=\frac{-10}{4}[/tex]

simplified

[tex]m=\frac{-5}{2}[/tex]

in order to find B:

[tex]y = -(\frac{5}{2}) *(-2)+b[/tex]

Insert value of y:

[tex]7 = (-\frac{5}{2} ) * (-2) +b[/tex]

Rewrite:

[tex]-\frac{5}{2} * -2 - b=7[/tex]

Cancel the common factor of 2:

[tex]-5 * -1 +b = 7[/tex]

Multiply -5 by -1:

[tex]5 + b= 7[/tex]

Subtract 5 from both sides:

[tex]b = 7-5\\b=2[/tex]

Now substitute values of m, and the final answer is:

[tex]y = -\frac{5}{2}x + 2[/tex]

Hello,

52% of 230 = 52/100 × 230 = 0,52 × 230 = 119,6

Answer:

230 : 100 * 52 =

Step-by-step explanation:

Which expression can be used to find 52% of 230?

The expression is: 230 : 100 * 52 =

That year FTE was 26.

According to statement

Labor hours worked that year = 55,267

Total number of hours paid that year = 59,995

The total number of hours during the year

8 hours × 5 days × 52 weeks = 2080 hours

Now we find the FTE per year

So, FTE/YEAR = Labour works on that year / total number of hours in year

Substitute the values in it then

FTE/YEAR = 55267/2080

FTE/YEAR = 26

So, That year FTE was 26.

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Find 3π/4 in degrees

Referance angle

Option A

Answer:

The measure of the reference angle is 45°.

[tex]\sin(\theta)=\dfrac{\sqrt{2}}{2}[/tex]

Step-by-step explanation:

Reference Angle:  The smallest possible angle made by the terminal side of the given angle and the x-axis. The reference angle is always between 0° and 90° (0 and π/2 radians).

To convert radians to degrees, multiply by 180/π:

[tex]\implies \sf \theta=\dfrac{3\pi}{4} \cdot \dfrac{180}{\pi}=135^{\circ}[/tex]

Positive angles are drawn in a counterclockwise direction from the x-axis.

(See attached for diagram of the angle θ and its reference angle).

Angles on a straight line sum to 180°.

Therefore, to calculate the reference angle, subtract the measure of the angle from 180°:

[tex]\implies \sf Reference\:angle=180^{\circ}-135^{\circ}=45^{\circ}[/tex]

The angle 135° lies between 90° and 180° and so is in Quadrant II.

Therefore, the exact trigonometric ratios for 135° are:

[tex]\sin 135^{\circ}=\dfrac{1}{\sqrt{2}} \textsf{ or }\dfrac{\sqrt{2}}{2}\\\\ \textsf{(Since sine function is positive in the Quadrant II)}[/tex]

[tex]\cos 135^{\circ}=-\dfrac{1}{\sqrt{2}} \textsf{ or }-\dfrac{\sqrt{2}}{2}\\\\\textsf{(Since cosine function is negative in the Quadrant II)}[/tex]

[tex]\tan135^{\circ}=-1\\\\\textsf{(Since tangent function is negative in the Quadrant II)}[/tex]

Therefore, the true statements are:

  The measure of the reference angle is 45°.

  [tex]\sin(\theta)=\dfrac{\sqrt{2}}{2}[/tex]

Answer:

A=P(1+in)

A=13000(1+6/100×9)

A=press calculator

Answer:

department

Step-by-step explanation:

A "task force" group is another name for a command group.

We have,

A task force is a temporary grouping of individuals or units with a specific objective or mission.

It is typically formed to address a particular task or problem and is led by a designated commander or leader.

Task forces can be assembled from different departments or organizations to collaborate and work together towards a common goal.

Thus,

A "task force" group is another name for a command group.

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The expected outcome of spins based on the probability information is 60.

From the information, Joey decides to spin the wheel 60 times. Therefore, the expected outcome of spins is 60.

The thing that the booth owner can do to make the wheel more profitable for himself is to make winning probability less than that of losing.

Here, the booth owner do makes the wheel more profitable for himself as the winning is smaller.

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Answer:

Step-by-step explanation:

We will assume that the first two columns are the numbers sold for Plain Wrapping and Decorative Wrapping.  The third colum does not equal the sum of the first two, so we'll assume it is the total paid for both options.  Let set the price of Plain Wrapping to x and the Decorative Wrapping to y.  The number of gift wrappings times the cost per warpping is the product of x or y timers the number wrapped as shown in columns 1 and 2.

Take the first row and set it as an equation:

10x+9y = 47   [10 Plain Wraps and 9 Decorative Wraps bring a total of $47]

Do the same for the second and third rows:

25x + 12y = 86, and

16x +12y =  68

===========

We can take any equation and rearrange it to isolate one of the 2 variables, x or y.  I'll pick 10x = 47-9y and isolate x:

10x = 47-9y

x = (47-9y)/10

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

Now use this definition of x in another equation.  I'll use 25x + 12y = 86.

25x + 12y = 86

25(47-9y)/10 + 12y = 86     [since x = (47-9y)/10 from above]

117.5 - 22.5y + 12y = 86

-10.5y = -31.5

y = 3                                     [the price for decorative wrapping is $3]

If y = 3, then we can use this in any of the equations to find x:

x = (47-9y)/10

x = (47-9(3))/10     [Use y = 3]

x = (47-27)/10

x = 2                              [The price for plain wrapping is $3]

======================

Check to see if these values will expalin the total value of the three rows of numbers:

CHECK:

______UNITS____         $2 each          $3 each

PlainW DecG Total      PlainW ($)      DecG ($)      Total ($)

   x           y                          x                       y

   10         9        $47          $20                    $27              $ 47         OK

   25        12       $86          $50                    $36              $ 86         OK

   16        12       $68          $32                    $36              $ 68         OK

The values work.  Merry Christmas.

Answer:

The team charged $2 to wrap a gift with no bow and $3 to wrap a gift with a bow.

Step-by-step explanation:

just did it in edg

The point that is 5 units from W is (A) (-5, 2)

The point is given as:

W= (-5, -3)

A point 5 unit from W can be any of the following

W' = (-5 ± 5, -3)

W' = (-5, -3 ± 5)

When the above expressions are evaluated, we have:

W' = (0, -3), (-10, -3), (-5, 2) and (-5, -8)

Hence, the point that is 5 units from W is (A) (-5, 2)

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Take the prime factorization of [tex]x[/tex].

[tex]x = 7\times24\times48 = 7\times(2^3\times3)\times(3\times2^4) = 2^7\times3^2\times7[/tex]

If [tex]xy[/tex] is a perfect cube, then the smallest [tex]y[/tex] that makes this happen is [tex]y=2^2\times3\times7^2 = \boxed{588}[/tex]. We "complete" the cube by introducing just enough factors to get each prime power to be a multiple of 3.

Answer: 588

Step-by-step explanation:

Answer:

90 approximately because if AB is 80 then DC should be 90 because AB come before DC in letters

Answer:

112.6 degrees and 105 feet.

Step-by-step explanation:

took the assignment

Answer:

x ≤ 2

Step-by-step explanation:

We are given the inequality:

[tex]\displaystyle{2x-3 \leq \dfrac{x}{2}}[/tex]

First, get rid of the denominator by multiplying both sides by 2:

[tex]\displaystyle{2x\cdot 2-3\cdot 2 \leq \dfrac{x}{2}\cdot 2}\\\\\displaystyle{4x-6 \leq x}[/tex]

Add both sides by 6 then subtract both sides by x:

[tex]\displaystyle{4x-6+6 \leq x+6}\\\\\displaystyle{4x \leq x+6}\\\\\displaystyle{4x-x \leq x+6-x}\\\\\displaystyle{4x-x \leq 6}\\\\\displaystyle{3x \leq 6}[/tex]

Then divide both sides by 3:

[tex]\displaystyle{\dfrac{3x}{3} \leq \dfrac{6}{3}}\\\\\displaystyle{x \leq 2}[/tex]

Therefore, the answer is x ≤ 2

Answer: [tex]x \leq 2[/tex]

Step-by-step explanation: Given [tex]2x - 3 \leq \frac{x}{2}[/tex], we multiply 2 by both sides to cancel out the 2 in the denominator (multiplying by a number in a fraction turns it into 1, and since the denominator is one, it is the same as saying the number [or variable] on the numerator by itself.)

We then get [tex]4x - 6 \leq x[/tex].

Adding 6 to both sides, we get [tex]4x \leq x + 6[/tex].

Subtracting x from both sides, we get [tex]3x \leq 6[/tex]

Dividing by 3 from both sides, we get [tex]x \leq 2[/tex]

Hope this helped!

Considering that we have an isosceles triangle, the length of the missing side is of 11 inches.

An isosceles triangle is a triangle that has two congruent sides.

Researching this problem on the internet, the triangle has two sides of 4 in and 11 in, and one missing side. The missing side is opposite to the side of 4 in, with the same scale, hence the length of the missing side is of 11 inches.

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The statement which best explains whether the family will have enough money in 4 years is; The family will not have enough money. They will have saved only $19,200.

Amount saved in 4 years = Amount Hartman family saves monthly × Number of months

= $400 × 48

= $19,200

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The statement which best explains whether the family will have enough money in 4 years is; The family will not have enough money. They will have saved only $19,200.

Amount saved in 4 years = Amount Hartman family saves monthly × Number of months

= $400 × 48

= $19,200

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The linear function in slope-intercept form for the cost of a visit of x hours is given as follows:

C(x) = 9x + 31.

A linear function is modeled by:

y = mx + b

In which:

In this problem, the rate means that the slope is of m = 9. When x = 3, C(x) = 58, hence the y-intercept is found as follows:

C(x) = 9x + b

58 = 9(3) + b

b = 31.

Hence the equation is:
C(x) = 9x + 31.

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Answer:

No.  They cannon be on the same straight line.

Step-by-step explanation:

As explained in the attached graphic, the slopes are slightly different between the three points.

Based on the test by result, Alex did better in the test by scoring 66.67%

Percentage scored by Alex = 40/60 × 100

= 0.66666666666666 × 100

= 66.6666666666666

= 66.67%

Therefore, Alex did better in the test

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