11 12 13 14 15 16 17 18 19 20 Given: AB = BC Prove: B is the midpoint of AC. A line contains point A, B, C. A flow chart has 3 boxes that go from top to bottom. The first box is labeled given and contains A B = B C. The second box is labeled definition of congruent segments and contains Line segment A B is-congruent-to Line segment B C. The third box is labeled definition of a midpoint and contains B is the midpoint of Line segment A C. What is the format of this proof? two-column proof one-paragraph proof flowchart proof two-paragraph proof Mark this and return

The value of x = 15.

The equation given is \(3^{14}\) + \(3^{14}\) + \(3^{14}\) = \(3^{x}\).

We can simplify this equation by adding the three terms on the left-hand side, which gives us 3(\(3^{14}\)) =\(3^{15}\).

Therefore, x = 15.

To understand why this is the case, we need to remember the laws of exponents.

The law of exponents states that when we multiply two numbers with the same base, we can add their exponents.

So, for example, \(3^{2}\) * \(3^{3}\) = \(3^{2+3}\) = \(3^{5}\).

Using this law, we can see that \(3^{14}\) +\(3^{14}\) + \(3^{14}\) is the same as 3 * \(3^{14}\).

And since 3 is also a factor of \(3^{15}\), we can combine the terms to get \(3^{15}\).

Therefore, x = 15.

We arrived at this conclusion by using the law of exponents to combine the terms on the left-hand side of the equation.

know more about law of exponents here:

https://brainly.com/question/11761858

#SPJ11

Answer:

To find the fraction of the total audience that were students or teachers, you need to add the fractions of students and teachers and simplify the result.

5/12 + 1/8 = (53) / (123) + (16) / (86) = 15/36 + 6/48 = 15/36 + 3/24 = 18/36 + 3/24 = (18+3) / (36+24) = 21/60

So 21/60 of the total audience were students or teachers.

The probability of the complement of the event is 0.05.

The complement of an event is the probability of that event not occurring. The relationship between the probability of an event and its complement is that they always add up to 1.

Therefore, if the probability of an event occurring is p, then the probability of its complement not occurring is 1-p.

In the case where the probability of an event is 0.95, the probability of its complement not occurring would be 1-0.95 = 0.05. This means that the probability of the complement of the event is 0.05.

This concept is important in probability theory and is used to calculate the probabilities of events and their complements. It allows us to consider all possible outcomes of a given situation and calculate the likelihood of each of them.

for such more question on probability

https://brainly.com/question/13604758

#SPJ11

Answer:

B

Step-by-step explanation:

given scale is 1 inch represents 7.5 feet

then we require to calculate how many 7.5 feet there are in each dimension.

to obtain this divide each dimension by 7.5, that is

13 ÷ 7.5 ≈ 1.73 ( to 2 decimal places )

26 ÷ 7.5 ≈ 3.47 ( to 2 decimal places )

then dimensions are approximately 1.73 inches by 3.47 inches

The actual distance represented by 23.7 cm on the map is 355.5 km.

To find the ratio of the amount of money Mabaso has to the amount of money Thabo has and the amount of money Ally has, we can divide each amount by the smallest amount (which is R35) to simplify the ratio.

Mabaso has R140, Thabo has R70, and Ally has R35.

The ratio of Mabaso's money to Thabo's money is:

R140 ÷ R35 = 4

The ratio of Mabaso's money to Ally's money is:

R140 ÷ R35 = 4

Therefore, the ratio of the amount of money Mabaso has to the amount of money Thabo has and to the amount of money Ally has is 4:1:1.

To calculate the percentage discount of a steel table, we need to find the difference between the original price and the discounted price, and then divide it by the original price. Finally, we multiply the result by 100 to get the percentage.

Original price: R750

Discounted price: R600

Discount: R750 - R600 = R150

Percentage discount: (R150 ÷ R750) × 100 = 20%

So, the table has a 20% discount on Black Friday.

To convert 125 grams to kilograms, we divide the amount in grams by 1,000 (since there are 1,000 grams in a kilogram).

125 g ÷ 1,000 = 0.125 kg

Therefore, 125 grams is equal to 0.125 kilograms.

If a green grocer packs 12 apples in a plastic bag and has 285 apples, we divide the total number of apples by the number of apples per bag to determine the number of bags needed.

Number of bags needed: 285 apples ÷ 12 apples/bag = 23.75 bags

Since we can't have a fraction of a bag, we round up to the nearest whole number. Therefore, the green grocer would need 24 bags.

If the scale of a map is 1,500,000 and the measurement on the map is 23.7 cm, we can use the scale to determine the actual distance.

1 cm on the map represents 1,500,000 cm in reality.

23.7 cm on the map represents x cm in reality.

x = 23.7 cm × 1,500,000 cm = 35,550,000 cm

To convert cm to km, we divide by 100,000 (since there are 100,000 cm in a kilometer).

35,550,000 cm ÷ 100,000 = 355.5 km

For more such questions on distance

https://brainly.com/question/30395212

#SPJ8

for example, let's find the 7.25% of "x"

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7.25\% of x}}{\left( \cfrac{7.25}{100} \right)x}\implies \stackrel{ \textit{in decimal form} }{\text{\LARGE 0.0725}}\times x\implies 0.0725x\)

Answer: x=0

Step-by-step explanation:

2(2)=4

4+x=4

-4 on both sides

so x=0

Answer:

B) x = 0

Step-by-step explanation:

We will get our equation in here first. Our equation is:

2 * 2 + x = 4

We simplify the multiplication giving us:

4 + x = 4

Finally, we subtract 4 from both sides to find the value of x. We get:

x = 0.

So the correct answer is B) x = 0.

Hope this helped!

Answer:

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

We are given that:

Find the value of y by substituting the given values into formula:

Answer: 39

Step-by-step explanation:

30-8=22

22/2=11

11+2=13

13 times 3 =39

Answer:

Yes

Step-by-step explanation:

To compare the variability of the measured sugar content for each day, we can estimate the standard deviation using the Range rule.

Standard Deviation =\(\dfrac{\text{Maximum Value-Minimum Value}}{4}\)

Day 1

5.0, 4.8, 5.1, 5.1, 4.8, 5.1, 4.8, 4.8, 5.0, 5.2, 4.9, 4.9, 5.0

Standard Deviation =\(\dfrac{5.2-4.8}{4}\)

=0.1

Day 2

5.8, 4.7, 4.7, 4.9, 5.1, 4.9, 5.4, 5.3, 5.3, 4.8, 5.7, 5.1, 5.7

Standard Deviation =\(\dfrac{5.8-4.7}{4}\)

=0.275

Day 3

6.3, 4.7, 5.1, 5.9, 5.1, 5.9, 4.7, 6.0, 5.3, 4.9, 5.7, 5.3, 5.6

Standard Deviation =\(\dfrac{6.3-4.7}{4}\)

=0.4

Since the estimated standard deviation of the third day is higher than that of the second day, the variability of the process is greater on the third day than on the second day.

We may determine from the principle of congruence that ΔTSV ≅ ΔRSV.

The proof to show that ΔTSV ≅ ΔRSV is called the Midsegment Theorem.

To prove this theorem, we can use the following steps:

Draw segment VR.

Since V is the midpoint of TR, VR is a midsegment of ΔTSV.

Since ∠TVS ≅ ∠RVS are right angles, and VR is a midsegment of ΔTSV, then ΔTSV is a right triangle.

Similarly, since VS bisects ∠RST, then VR is a midsegment of ΔRSV as well.

Since VR is a midsegment of both triangles, and both triangles are right triangles, then by the definition of a midsegment, we can conclude that the lengths of the midsegments are proportional to the lengths of the corresponding sides.

Since TS ≅RS, then the lengths of the corresponding sides of the two triangles are also equal.

Therefore, by the definition of congruence, we can conclude that ΔTSV ≅ ΔRSV.

This is valid proof of the Midsegment Theorem.

Learn more about congruent triangles here:

brainly.com/question/4364353

#SPJ1

The exact value of sin(5π/12) is (√6 + √2)/4

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

sin 5pi/12

Express properly

So, we have

sin(5π/12)

Convert the angle to degrees

This gives

sin(5π/12) = sin(5/12 * 180)

Evaluate

sin(5π/12) = sin(75)

The actual value of sin(75) is (√6 + √2)/4

This means that

sin(5π/12) = (√6 + √2)/4

Hence, the exact value of sin(5π/12) is (√6 + √2)/4

Read more about trigonometry function at

https://brainly.com/question/24349828

#SPJ1

The exact value of sin 5π/12 is (√6 + √2)/4

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Angle in trigonometry can be measured in either degree or radian.

π is a measurement in radian which is equivalent to 180° in degrees.

Therefore:

5π/12 = 5 × 180/12

= 75°

Therefore sin5π/12 = sin75°

sin75 = sin( 45+30) = sin45cos30+ cos 45sin30

= 1/√2 × √3/2 + 1/√2 × 1/2

= √3/2√2 + 1/2√2

= (√3+1)/2√2

rationalizing;

(2√6 + 2√2)/8

dividing through by 2

=(√6 + √2)/4

therefore tan75 =(√6 + √2)/4

learn more about trigonometric functions from

https://brainly.com/question/25618616

#SPJ1

Answer:

22.7%

Step-by-step explanation:

= difference / original *100

= (27000 - 22000) / 22000 * 100

= 5000/22000 *100

=22.727....

to 3sf

=22.7%

Answer:

$34.70

Explanation:

$3.47 x 10 = 34.7

Hope this helps  ^-^

-Isa

Answer:

H= -35/4

Decimal form: -8.75

Explanation:

The simplification of the given expression results as √5K/3.

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given expression is √10K²/√18k.

It can be evaluated as follows,

Write √10 and √18 in terms of prime factors as,

√10 = √(5 × 2)

And, √18 = √(3 × 3 × 2) = 3√2

Plug these values in the given expression to obtain,

⇒ √10K²/√18k

⇒  √(5 × 2)K²/3√2K

⇒ √5K/3

Hence, the given expression can be simplified as √5K/3.

To know more about algebraic expression click on,

brainly.com/question/953809

#SPJ1

Answer:

3.5g/ml or 3.5g/cm³

Step-by-step explanation:

1cm³=1ML

Volume of the irregular shaped stone = New Volume of water in cylinder -initial Volume of water in cylinder

Volume of irregular shaped stone = 8ml-2ml

Volume of irregular shaped stone =6ml

Denisty =Mass/Volume

Density = 21g/6ml

Density = 3.5g/ml

Answer:

1) 7/8     8/7

2) 4.4

3) 3.7

4) 2.8

Step-by-step explanation:

Length of bottom side of Figure A: 8 cm

Length of bottom side of Figure B: 7 cm

From Figure A to Figure B, the scale factor is 7/8.

7/8

8/7

5 × 7/8 = 35/8 = 4.375

4.4

3.2 × 8/7 = 3.657...

3.7

3.2 × 7/8 = 2.8

2.8

The radius of the circle, marked p on the diagram, is approximately 5.8 cm.

Radius is a term used in geometry to describe the distance from the center of a circle to any point on the circumference. It is a line segment that has its two endpoints at the center of the circle and at any point on the circumference.

The area of a sector is equal to the fraction of the circle's area that the sector occupies multiplied by the area of the entire circle.
Therefore, the area of the sector is equal to (θ/360) × πr^2.
Since the area of the sector is given as 85 cm^2, we can rearrange the equation to get:
85 = (θ/360) × πr^2
Rearranging further, we get:
r^2 = (85 × 360)/(πθ)
Taking the square root of both sides, we get:
r = √((85 × 360)/(πθ))
Since the angle θ is not given, we cannot solve for r. However, we can approximate the angle θ to be equal to 360° since the sector occupies the entire circle.
Therefore, the radius of the circle is equal to:
r = √((85 × 360)/(π × 360))
r = √(85/π)
r ≈ 5.8 cm
Therefore, the radius of the circle, marked p on the diagram, is approximately 5.8 cm.

To learn more about radius
https://brainly.com/question/29614115
#SPJ1

Answer: a = 2 and r=-1.

Step-by-step explanation:

Answer:

m<B = 58 degrees, m<C = 63 degrees

Step-by-step explanation:

let's find y!

angles B and A are complementary, so they should equal 90

therefore, B + A = 90

substitute

4y + 8y - 6 =90

12y = 96

y=8, and m<B = 8y-6; so m<B = 58

angles C and D are equal because of vertical angles

therefore, C = D

substitute

7x=5x+18

2x=18

x=9

m<C = 7x, so m<C = 63

Answer:

Area of the given regular pentagon is 61.5 cm².

Step-by-step explanation:

Area of a regular polygon is given by,

Area = \(\frac{1}{2}aP\)

Here, a = Apothem of the polygon

P = Perimeter of the polygon

Apothem of the regular pentagon given as 4.1 cm.

Side of the pentagon = 6 cm

Perimeter of the pentagon = 5(6)

                                             = 30 cm

Substituting these values in the formula,

Area = \(\frac{1}{2}(4.1)(30)\)

        = 61.5 cm²

Therefore, area of the given regular pentagon is 61.5 cm².

Answer: y + 3x + 2 = 0

Step-by-step explanation:

The formula for that is

y - y₁

-------     = -3 where x₁ = -3, y₁ = 7

x - x₁

Therefore cross multiply and solve

y - 7 = -3[( x - (-3)]

y - 7 = -3( x + 3 )

y - 7 = -3x - 9

y + 3x -7 + 9 = 0

y + 3x + 2 = 0

Answer:

y=-3x-2

Step-by-step explanation:

Answer:

S = ( 6, 12, 18, 24, 30, 36......)

T = ( 2, 4, 6, 8, 10, 12, 14, 16, 18......)

Step-by-step explanation:

Pick any point on the graph below for a solution:

Answer:

$585/month

Step-by-step explanation:

To determine how much money Mr. Smith has left over monthly to put into savings, we need to first calculate his monthly income and his monthly expenses, including taxes.

Mr. Smith's hourly rate is $20, and he works full time, which is typically 40 hours per week. Therefore, his weekly income is:

$20/hour x 40 hours/week = $800/week

To find his monthly income, we multiply his weekly income by the number of weeks in a month:

$800/week x 4 weeks/month = $3,200/month

To find his monthly expenses, we add up the amounts for his household and automobile expenses:

$1,410/month (household) + $405/month (automobile) = $1,815/month

Since Mr. Smith gets about 25% of his income taken out for taxes, we need to calculate the amount of taxes he pays each month:

$3,200/month x 0.25 = $800/month (taxes)

Now we can subtract his monthly expenses and taxes from his monthly income to find out how much money he has left over to put into savings:

$3,200/month - $1,815/month - $800/month = $585/month

Therefore, Mr. Smith has $585/month left over to put into savings after paying his expenses and taxes.

Im diying:(

dont be mean man

given ,

a circle of radius 12 inches

and \(\theta\) = 45°

now we know that ,

\(\\{Area \: of \: sector = \frac{\theta}{360\degree} \times \pi \: r {}^{2} } \\ \\ \)

let's now plug in the values of radius and theta as 12 inches and 45° respectively ,

\(\\\dashrightarrow \: \frac{45}{360} \times \frac{22}{7} \times 12 \times 12 \\ \\ \dashrightarrow \: \frac{1}{8} \times \frac{22 \times 12 \times 12}{7} \\ \\ \dashrightarrow \: \frac{22 \times 12 \times 12}{56} \\ \\ \dashrightarrow \: \frac{3168}{56} \\ \\ \dashrightarrow \: 56.57 \: inches {}^{2} (approx.)\)

hope helpful :D

Since the coordinate 3 has a weight of 2, and the coordinate 9 has a weight of 1 the weighted average is 6

We are required to find the weighted average

The weighted average of a variable is given by w = ∑wₙxₙ/∑w  where

wₙ = weight of variable xₙ,

xₙ = n th variable and

∑w = sum of weights

Given that the coordinate 3 has a weight of 2, and the coordinate 8 has a weight of 3, we find the weighted average

So, w = (w₁x₁ + w₂x₂)/(w₁ + w₂)

where

w₁ = 2,

x₁ = 3,

w₂ = 1 and

x₂ = 9

So, substituting the values of the variables into the equation, we have

w = (w₁x₁ + w₂x₂)/(w₁ + w₂)

w = (2 × 3 + 1 × 9₂)/(2 + 1)

w = (6 + 9)/3

w = 15/3

w = 5

So, the weighted average is 5

Learn more about weighted average here:

brainly.com/question/14432034

#SPJ1