Which of the following statements must be true based on the diagram below? Select
all that apply. (Diagram is not to scale.)
L
K
O
M M
P
N
OP is a segment bisector.
OP is a perpendicular bisector.
OOP is an angle bisector.
O is the vertex of a pair of congruent angles in the diagram.
O is the vertex of a right angle.
Pis the midpoint of a segment in the diagram.

Hi! I'm happy to help!

This expression is an exponent, or repeated multiplication. 3^3 is three multiplied by itself (3), 3 times, or 3×3×3

So, our non-exponent expression will be 3×3×3.

I hope this was helpful, keep learning! :D

Answer:

182

Step-by-step explanation:

First, we can say that ∠ACB and ∠BCF are opposite angles because they are not next to each other and are formed by intersecting lines. Therefore, ∠ACB = ∠BCF

Next, angles correspond with the side opposite of it. This means that, for example, ∠ACB corresponds with line AB and ∠BCF corresponds with line BF. Because ∠ACB and ∠BCF are equal and the triangles are similar, we can say that their corresponding sides have a ratio with each other. Similarly, ∠CAB corresponds to CB, ∠ABC corresponds to AC, ∠CWV corresponds to CV, and ∠CVW corresponds to CB.

Because the triangle CVW is isosceles, we can say that the angles whose corresponding sides are equal are equal as well, so ∠CAB = ∠ABC and ∠CVW = ∠CVW. Next, because ∠ACB and ∠BCF are equal and correspond to each other, and the other two angles in each triangle are equal to each other, we can say that the other two angles must be equal. Another way of putting this is like this:

Say that x = ∠CAB. Then,

∠CAB + ∠ABC + ∠ACB = 180

x + x + ∠ACB = 180

2x + ∠ACB = 180

subtract ∠ACB from both sides

180 - ∠ACB = 2x

Similarly, if y = ∠CWV,

180 - ∠WCV = 2y. Therefore, 2y=2x and y=x, so ∠CAB = ∠ABC = ∠CWV = ∠CVW.

Given this, we can say that sides CV and CW correspond with BC and AC. This means that the ratio between, for example, CV and BC is equal to the ratio between CW and AC. Therefore,

CV/BC = CW/AC

84/182 = 84/?

Filling in the blank, 84/182 is equal to 84/182, so ? = 182

(92.50-55)/15 =2.5 hours

Step-by-step explanation:

92.5 (total) -55 (trip charge) = 37.50(hour charge)

37.50(hour charge)/15{per hour charge)=2.5(hours)

Answer:

The answer is in the image above

Answer:

Step-by-step explanation:

The antiderivative for b is definitely incorrect, as stated in the comments section.

[tex]\int\limits {\frac{1}{2x^2}+\sqrt{x} } \, dx \\\frac{1}{2} \int\limits{\frac{1}{x^2} } \, dx+\int\limits {x^{\frac{1}{2}} } \, dx[/tex]  That's a bit more simplified. One more important simplification and then we can integrate one term at a time:

[tex]\frac{1}{2}\int\limits{x^{-2}} \, dx +\int\limits{x^{\frac{1}{2} } \, dx[/tex]  and here we go:

[tex]\frac{1}{2}(\frac{x^{-2+1}}{-2+1})+(\frac{x^{\frac{1}{2}+\frac{2}{2}} }{\frac{1}{2}+\frac{2}{2} })+C[/tex] and

[tex]\frac{1}{2}(\frac{x^{-1}}{-1})+(\frac{x^{\frac{3}{2}} }{\frac{3}{2} })+C[/tex] and finally,

[tex]-\frac{1}{2x}+\frac{2}{3}x^{\frac{3}{2}}+C[/tex]

Answer:

Step-by-step explanation:

Factorize both numbers:

Common factors are:

So HCF is:

[tex]\Large \red \mid \: \underline {\rm {{{\color{blue}{Explanation...}}}}} \: \red \mid[/tex]

As per Euclid Division Algorithm.

[tex] \longrightarrow \: \Large\underbrace {\rm {{{\color{red}{ \: a \: = \: bq \: + \: r \: }}}}} [/tex]

[tex]\large\bf{\purple{ \hookrightarrow \: }} \tt \: \: 900 \: = \: 270 \: \times \: 3 \: + \: 90[/tex]

[tex]\large\bf{\orange{ \implies \: }} \: \:r \: \neq \: 0[/tex]

Again Applying Euclid Division Algorithm

[tex]\large\bf{\purple{ \hookrightarrow \: }} \tt \: 270 \: = \: 90 \: \times \: 3 \: + \: 0[/tex]

[tex]\large\bf{\orange{ \implies \: }} \: \:r \: = \: 0[/tex]

As the reminder is 0 , 90 will be the greatest common divisor for the two given numbers.

[tex]{\boxed{ \Large{ \blue{ \bf{ \underline{ HCF \: = \: 90}}}}}}[/tex]

Answer:

60% or 3/5

Step-by-step explanation:

Add up how many students take the bus: 50, and how many walk:10

Put that number over 100 and simplify: 60/100=6/10=3/5

Answer:

-13=5×1+5×4m-2m

-13=5+20m-2m

-13-5=18m

-18=18m

18m=-18

m=18÷18

m=1

Answer:

[tex]\frac{55}{4}[/tex]

Step-by-step explanation:

let the number be n the multiply by - 4 is - 4n and add 5 gives

- 4n + 5 = - 50 ( subtract 5 from both sides )

- 4n = - 55 ( divide both sides by - 4 )

n = [tex]\frac{-55}{-4}[/tex] = [tex]\frac{55}{4}[/tex]

The number is [tex]\frac{55}{4}[/tex] or 13.75 if you prefer

Answer:

Step-by-step explanation:

23550=15000(1+.0475t)

t=12

Answer:

$150.60

Step-by-step explanation:

$984.20-$381.80= $602.40

Take $602.40 and divide by 4 which equals $150.60 which is the 1/4 $ Charlie has in his savings account.

Answer:

Your final grade will be 78.67 %

Step-by-step explanation:

67% of your grade will be from your test average which is 79 (higher)

33% of your grade will be from your homework average which is 78.

Calculating:

(67×79+33×78) / (67+33) = 7867 / 100 = 78.67

Answer:

Step-by-step explanation:

The midpoint formula is

[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex] and we have the coordinates of the midpoint and the coordinates of one endpoint. Filling that in we have:

[tex](-5,-4)=(\frac{-4+x_2}{2},\frac{-7+y_2}{2})[/tex] and we will solve for the missing values one at a time. x first:

[tex]-5=\frac{-4+x_2}{2}[/tex] and

-10 = -4 + x₂ so

-6 = x₂ and do the same for y:

[tex]-4=\frac{-7+y_2}{2}[/tex] and

-8 = -7 + y₂ so

-1 = y₂

Thus, the coordinates of point g are (-6, -1)

Answer:

h(-5) = (-2)^2 + 5 = 9

h(-1) = (2)^2 + 5  = 9

(9-9)/4 = 0

average rate of change is 0

Step-by-step explanation:

Answer:

8!

Step-by-step explanation:

Basically, you would use the phythagorean theorem to find the answer plugging in the values that you already have to find the missing side (a^2 + b^2 = c^2)

since you have the length of the hypothenuse (c in the equation) and one of the legs of the triangle (a or b, it doesn't matter, but for the sake of the equation we'll plug in 6 for a), we can insert these numbers to find b!

Plugging it into the equation:

A^2 + b^2 = c^2

(6)^2 + b^2 = (10)^2

36 + b^2 = 100

subtract both sides to get b^2 = 64

then square root both sides b = 8

Answer:

x = 10

Step-by-step explanation:

AC = AB + BC

Substitute the values for the line segments:

50 = (2x) + (x + 20)

50 = 2x + x + 20

Combine like terms:

50 = 3x + 20

Subtract 20 from both sides:

30 = 3x

Divide both sides by 3:

10 = x

Check your work:

50 = 2(10) + 10 + 20

50 = 20 + 30

50 = 50

Correct!

Answer:x+20

Step-by-step explanation:

Answer:

3/7

Step-by-step explanation:

21w - 21 = -12

21w = -12 +21

21w = 9

w = 9/21

i.e w= 3/7

Step-by-step explanation:

21w-21= -12

21w= -12 + 21

w=9/21

Answer:

Step-by-step explanation:

Answer:

n+2 represemts the number of sides in the polygon for the nth member of the sequence

Answer:

Just study and pay attention in class and take good notes. I would say that you should pay more attention when they teach you the trigonometry unit.

Answer:

8x-16y

Step-by-step explanation:

Answer:

8x - 16y and a + 3b - 2c

Step-by-step explanation:

(a)

8(x - 2y) ← multiply each term in the parenthesis by 8

= 8x - 16y

(b)

[tex]\frac{6a+18b-12c}{6}[/tex] ← factor out 6 from each term in the numerator

= [tex]\frac{6(a+3b-2c)}{6}[/tex] ← cancel the 6 on numerator/ denominator

= a + 3b - 2c

Insert grouping symbols to make each number sentence true 3+8-2*5=45

Answer:

3+2+8×5

Answer:

137027.1 Rupees

Step-by-step explanation:

(125200+5302) * 0.05 = 6525.1

130502+6525.1 =  137027.1

Answer:

y = -1/2x + 6

Step-by-step explanation:

The slope of a parallel line will remain the same. The only thing that is different is the y-intercept but we can solve that using the point given, the slope, and the slope intercept form equation [ y = mx + b ].

0 = -1/2(12) + b

0 = -6 + b

6 = b

Now input the data we were given and solved for back into the formula.

y = -1/2x + 6

Best of Luck!

Answer:

13x + 10

Step-by-step explanation:

Rafael's hot-water tank holds:

[tex]17x + 11[/tex]

Gallons of hot water.

Rafael used:

[tex]4x + 1[/tex]

Gallons of hot water.

And we want to determine which binomial represent the amount of hot water remaining in the tank.

The amount remaining R in the tank will be the amount taken by Rafael subtracted from the total amount. Hence:

[tex]\displaystyle R = (17x+11) - (4x + 1)[/tex]

Simplify. Distribute:

[tex]\displaystyle R = (17x + 11) + (-4x - 1)[/tex]

Rearrange:

[tex]R = (17x - 4x) + (11 - 1)[/tex]

Combine like terms:

[tex]R = 13x + 10[/tex]

In conclusion, 13x + 10 gallons remain in the tank.

Answer:

AB= AC+CB

50 = (2x – 2 ) + 4(x+1)

50 = (2x – 2) + ( 4x+4)

50 = 6x +2

6x = 50 – 2

6x = 48

x= 48/6

x= 8

So; x=8 Q.E.D.

I hope I helped you^_^

Answer:

10.71

Step-by-step explanation:

0.15*71.40

Answer:

a = Maize takes up 17.5 Hectares, Beans takes up 16 Hectares, and  Potatoes takes up 12 hectares

b = Beans takes up 17.8 hectares, and Potatoes takes up 10.2 Hectares

Step-by-step explanation:

A: 50/100 = .5

.5 is = to 1% of the farm

Maize = .5*35

Maize = 17.5 Hectares

Beans = .5*32

Beans = 16 Hectares

Potatoes = .5*24

Potatoes = 12 hectares

B: Beans: 16*1.1125 = 17.8 hectares

Potatoes: 12*.85 = 10.2 Hectares

Answer:

The forest will cover an area of approximately 2994 square kilometers after 10 years.

Step-by-step explanation:

A forest covers an area of 5000 square kilometers. Each year, the area of the forest decreases by 5%. We want to determine its area after 10 years.

We can write an exponential function to represent the situation. The standard exponential function is given by:

[tex]\displaystyle f(x) = a(r)^x[/tex]

Where a is the initial value, r is the rate, and x is the time that has passed (in this case in years).

Since the original area is 5000 square kilometers, let a = 5000.

Each year, the area decreases by 5%. In other words, for each subsequent year, the forest's area will be 100% - 5% = 95% = 0.95 of its previous year. Hence, r = 0.95.

Thus, our function is:

[tex]\displaystyle f(x) = 5000(0.95)^x[/tex]

Then after 10 years (x = 10), the area will be:

[tex]\displaystyle f(10) = 5000(0.95)^{(10)}= 2993.6846...\approx 2994\text{ km}^2[/tex]

In conclusion, the forest will cover an area of approximately 2994 square kilometers after 10 years.