5. in the following figure, GE= r.
where ris the radius of the circle.
a) What is the nature of the triangle GEO? Justify your answer.
b) By calculating SEG in two different ways. using ares of the ​

Answer:

  3 1/2 square units

Step-by-step explanation:

For this small triangle whose vertices are on grid points, the use of Pick's theorem will give the area with the least work.

__

Pick's theorem says that the area is ...

  A = i +b/2 -1

where i is the number of grid points inside the boundary, and b is the number of grid points on the boundary.

Here, only the given coordinates are boundary points that are on grid points. (b = 3)

The figure shows us three grid intersections inside the boundary of the triangle. (i = 3)

That means the area is ...

  A = 3 +3/2 -1 = 3 1/2 . . . . square units

_____

Alternate solution

The triangle is bounded by a square 3 units on a side. From that, we can subtract a 2×3 triangle at upper left, a 1×2 triangle at upper right, and a 3×1 triangle at the bottom. That leave a figure area of ...

  A = 3² -1/2(2×3) -1/2(1×2) -1/2(3×1) = 9 -3 -1 -3/2 = 3 1/2 . . . . square units

(The area of a triangle is 1/2bh, where b and h are the base and height of the triangle.)

__

Another alternate solution can be had by using a formula with the vertex coordinates:

  A = 1/2|(x1)(y2 -y3) +(x2)(y3 -y1) +(x3)(y1 -y2)|

  = 1/2|(-8)(3 -5) +(-5)(5 -2) +(-6)(2 -3)| = 1/2|16 -15 +6| = 3 1/2 . . . square units

The equation [tex]\frac{5-3-2}{1+4+6+7+8+9}[/tex]  = 0 is true

In arithmetic, a number expressed as a quotient, in which a numerator is divided by a denominator.

Using digits 0 to 9, no more than once each.

we want to place them in such a way that the division will be zero.

As we know that a quotient is equal to zero iff the numerator is equal to zero and the denominator other than zero.

So if we put some numbers on the numerator in such a way by adding them gives 0.

So, 5 - 3 - 2 = 0

Use all the other numbers in the denominator.

[tex]\frac{5-3-2}{1+4+6+7+8+9}[/tex]  = 0

which is true.

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Answer:

3k+1

Step-by-step explanation:

Answer:

The correct answer is 3k + 1

Step-by-step explanation:

Hope this helps:) Goodluck!

Answer:

5

Step-by-step explanation:

When you are looking for a pattern, look at one of the examples, makeup the pattern, then check it on the other examples.

Wrong answers may work on one, but not all the completed examples.

The right answer will work on all of the examples, then use that rule on the incomplete one.

So, I looked at the second one in the top row. The two bottom numbers, 5 + 13 makes 18. And 18÷3 (the top number, gives the center number) Check on other examples.

bottom + bottom=_

_÷top=center.

8+4=12, 12÷3 =4.

9+5=14, 14÷2=7

Both of these work.

So use the rule for the last one.

Add the bottom numbers, divide by the top number, fill it in the middle.

14+6=20

20÷4=5

Fill in 5.

Answer:

C.

Step-by-step explanation:

According to the volume equation of a sphere (V=4/3πr³)

8.4/2 equals a radius of 4.2, which when cubed equals 74.088 (base area). You then multiply your base area by the numerator of 4/3, giving you 296 when rounded or 296.352 when not rounded. Giving you the answer of C.

Answer:

Option 2

Step-by-step explanation:

Making the terms based on the words :

⇒ n/3 - 3 (3 is subtracted from one third of a number n)

⇒ < 6 (less than 6)

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

The inequality is :

⇒ n/3 - 3 < 6

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

The solution :

⇒ n/3 - 3 < 6

⇒ n/3 < 9

⇒ n < 27

Answer: the height is 18 cm.

Step-by-step explanation:

The equation for the volume of a cone is the following: V = 1/3 × B × h, where B (base) = πr². Because we are given the radius of the base, but not the base’s area itself, we will use V = 1/3πr²h.

Here, we are trying to solve for h, the height, so first we can first rearrange the equation to solve for h:

1) V = 1/3πr²h

2) h = V ÷ 1/3πr² (divide both sides by 1/3πr²h)

Now, we just need to input the given values: V = 471, π = 3.14, r = 5

h = 471 ÷ 1/3(3.14)(5²)

= 471 ÷ 1/3(3.14)(25)

= 471 ÷ 1/3(78.5)

= 471 ÷ (78.5/3)

= 18 cm

Answer:

the answer is ABC was translated right 4 units and down 4 units. hope this helped

Answer:

160in³

Step-by-step explanation:

V = lwh

V = 5(4)(8)

V = 40(4)

V = 160in³

The conditional probabilities that are correct are P(D | F) =  6/34, P(E | D) = 7/25 and P(F | E) = 8/18

The formula to compute the conditional probability P(A|B) is:

P(A | B) = P(A and B)/P(B)

The above means that the probability of event A such that the event B has already occurred

When the above formula is applied to the give data in the complete, we have:

P(D | F) = 6/34

P(E | D) = 7/25

P(D | E) = 7/18

P(F | E) = 8/18

P(E | F) = 8/34

Hence, the conditional probabilities that are correct are P(D | F) =  6/34, P(E | D) = 7/25 and P(F | E) = 8/18

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Answer: a,b,d

Step-by-step explanation:

trust

Answer & Step-by-step explanation:

These questions are wanting you to find the sequence and solve for the nth term in said sequence.

The easiest way to do this is to just see the difference between each number, and continue adding or subtracting to the nth term the question is asking for.

For example, the first one is decreasing by 3 every time, so the 7th term will be -4, (the 4th term), subtracted by 3, three more times.

5, 2, -1, -4, -7, -10, -13

The other way to do this is to find the rule, and subsitute in what term is required.

For letter c (the second c), the sequence is 30, 24, 18, 12

The rule is to subtract 6 every time, so -6 n

Since we start our 1st sequence from 30, our rule must start from 30 + 6, the opposite of our rule, which gives us 36.

Our rule is 36 - 6n

So since we are looking for the 11th term, we substutute in 11 into our equation.

36 - 6 n
36 - 6 (11)

36 - 66

-30

This way of thinking will work for the whole set of questions you have here

Observe that

y = x² - 2kx = x (x - 2k)

has roots at x = 0 and x = 2k. Since the leading coefficient is 1 > 0, the parabola opens upward, and in particular this means the x-axis lies above the curve.

We can compute the area of R by integrating:

[tex]\displaystyle \int_0^{2k} |x^2-2kx| \, dx = - \int_0^{2k} (x^2-2kx) \, dx \\\\ = kx^2 -\frac{x^3}3 \bigg|_{0}^{2k} \\\\ = \frac{4k^3}3[/tex]

Solve for k :

[tex]\dfrac{4k^3}3 = 36 \implies k^3 = 27 \implies \boxed{k=3} ~~~~ (B)[/tex]

Answer:

Step-by-step explanation:

Thanks Okay

Answer:

m<1 = 48 m<2=12.6 m<3= 48

Step-by-step explanation:

96 ÷ 2 =48

38÷3= 12.6

48

Answer:

-4 C (Negative 4 C)

Step-by-step explanation:

If its 20 C less in Moscow, then it must be 16-20 = - 4 C in Moscow.

Look up rules on subtracting large numbers from small numbers to understand how I got - 4.

Answer:

multiply the number with 4

Step-by-step explanation:

2 8 32 128

2x4 =8

8×4=32

32×4=128

128×4=512

[tex]\text{First term,}~ a =2\\\\\text{Common ratio,}~ r = \dfrac{8}2 = 4\\\\\text{Nth term} = ar^{n-1}\\\\\text{7th term} = 2 \cdot 4^{7-1} = 2 \cdot 4^6=8192\\ \\\text{Hence, the 7th term in the geometric series is 8192.}[/tex]

Answer:

[tex]KL=45.6[/tex]

Step-by-step explanation:

Property of a Rectangle: Opposite sides are equal.

This means:

[tex]KL = JM \text{ where JM = 45.6}[/tex]

[tex]KL = 45.6[/tex]

Answer:

A. 20.5

Step-by-step explanation:

The measure of an inscribed angle is half the measure of the intercepted arc. For example, If the intercepted arc is 11 then the Inscribed angle is 1/2 or 5.5! hope this helps ya!

Answer:

The answer is21

Answer:

$82.50

Step-by-step explanation:

25% of $110.00 is $27.5, which means 110.0 - 27.5 is equal to = 82.50.

Answer:82.50

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

The scale factor shows the proportion of a number to another one

The side lengths for triangle ABC: 12-4-2

The side lengths for triangle LMN: 6-2-1

if we write them as fractions

12/6 = 2

4/2 = 2

2/1 = 2 so the answer is in third option.

Answer:

See below

Step-by-step explanation:

Part A:

⇒ Y represents the amount of swimming

⇒ X represents the amount of tennis

Now, creating to equations:

Part B:

⇒ First equation is substituted for X in the other equation.

Gives us the plug in:

⇒ Y = 35 minutes of swimming

⇒ Adding :

35 + 40 = 75 minutes of swimming per day.

Part C:
No, due to the equation ⇒  70 + (70 - 40) = 100

Therefore, making this statement impossible.

Answer:

The diameter is 6.76

Please read the exaplanation... it always helps!

Step-by-step explanation:

Area of circle = r^2 pi

if the area is 36 then...

36 = r^2 pi           to solve for r divide both sides by pi

36/pi = r^2

11.45 = r^2             take the square root of both sides

√11.45 = r                 RADIUS = 3.38

then multiply by two since the diameter is 2 (radius) and you get...

diameter = 6.76

i hope this helpssssss!!!!!!!

Answer:

[tex]area = \pi {r}^{2} [/tex]

[tex]36 = 3.14 \times {r}^{2} [/tex]

[tex] \frac{36}{3.14} = {r}^{2} [/tex]

[tex] {r}^{2} = 11.46[/tex]

[tex]r = \sqrt{11.46} [/tex]

[tex]r = 3.39[/tex]

[tex]diameter = 2 \times radius[/tex]

[tex]diameter = 3.39 \times 2[/tex]

[tex] = 6.78[/tex]

Answer:

b) 95 degrees

Step-by-step explanation:

Remember that the internal angles of a triangle add up to 180°.

Solving :

Let that angle be x

Apply angle sum property

Answer:

Part A: (2x−5)(x+2)

Part B: (5/2,0) and (-2,0)

Part C: The graph of f(x) has both "ends" of the graph pointing upward. You can describe this as heading toward infinity.

Part D: To graph function we can use x-intercepts and "ends" to sketch.In order to graph better use one more point of parabola that you can find as the average of x-intercepts: (-2+5/2)/2 =1/4.This is just x coordinate and you need to plug in 1/4 in the f(x) and find y coordinate -10 1/8. You can use y-intercept (0,-10) as well to graph.

Step-by-step explanation:

2x^2-3x-5=y

(2x-5)(x+1)=y

(2x-5)(x+1)=0

2x-5=0

2x=5

x=2.5

x+1=0

x=-1

you have an even degree (2) and a positive coefficient (2)

therefore as x---> -∞, f(x)----> +∞

also, as x----> +∞, f(x)----> +∞

also notice that this is a parabola that opens upwards so both "ends" approach positive infinity

plot the x-intercepts, find the vertex using h=-b/2a and substituting this value into the equation to find k and make a table of values to graph the parabola unless you only want a rough sketch of the graph-you know the x-intercepts and you found the vertex using h=-b/2a

Step-by-step explanation:

Answer: hes right

Step-by-step explanation: i took the test

Answer:

4°C

Explanation:

Equation: y = -0.36x + 12.6

Simplify

y = -0.36(23)+12.6

y = 4.32°C

y = 4°C       (rounded to nearest degree)

Answer:

11

Step-by-step explanation:

First, order the numbers in the given set from least to greatest:

8 , 9 , 9 , 10 , 12 , 14 , 15 , 15

The median is the number found in the middle of the given set. If the amount of numbers in the set are even (as in this case), then you will find the mean of the two middle numbers.

In this case, the middle numbers are 10 & 12:

Find the mean. The mean is found by adding all the numbers together and dividing by the amount of numbers there is:

(10 + 12)/2 = (22)/2 = 11

11 is your median.

~

Answer:

11.

Step-by-step explanation:

12, 10, 14, 9, 8, 9, 15, 15

Arrange in ascending order:

8 9 9 10 12 14 15 15

Here, the median is the mean of the 2 middle numbers:

= (10+12) = 11.

We conclude that the distance between the home plate and the second base is 107.48 feet.

We know that the distance will be equal to the diagonal of the square. Remember that for  a square of side length S, the diagonal is:

D = S*√2

In this case, the side length is S = 76ft, then the diagonal is:

D = 76ft*√2 = 107.48ft

From this, we conclude that the distance between the home plate and the second base is 107.48 feet.

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