Which property justifies this statement?

If x=3, then x−3=0.

Answer:

The triangle inequality states that the sum of the lengths of the two shortest sides of a triangle must be greater than the length of the largest side. Because 4 + 12 > 17 is not a true statement, the answer is "This triangle does not exist because the sum of 4 and 12 is less than 17."

Answer:

This triangle does not exist due to the fact that the sum of 4 and 12 is less than 17

Step-by-step explanation:

The triangle formaction rule states that the 2 smaller sides must be able to combine and be greater than the greatest side.

Triangle

Sides - 3, 4, 5

3+4=7

Meaning the two smaller sides add up to because greater than 5.

Non-Triangle

Sides - 5, 6, 13

5+6=11

This means that this is not a triangle because the smaller sides ‘5 and 6’ do not add up to become greater than 13.

Gemma’s Triangle

Sides - 4, 12, 17

4+12=16

Hence, Gemma‘s figure is not a triangle because the 2 smaller sides ‘4 and 12’ don‘t add up to be greater than 17.

Answer:

-26 ft  or 26 ft below the surface

Step-by-step explanation:

Starting at the surface

0

Descending 20 ft

0 -20 = -20

Rose 12 ft

-20 +12 = -8

Descends 18 ft

-8 -18= -26 ft

Answer:

1

Step-by-step explanation:

Answer:

No.

Step-by-step explanation:

They are giving us the information that Imani has 5 fewer wins than Jamie and they combine for 30 wins total. The question is asking us is it possible for Jamie to have one 11 games. To find how many games Imani won, we have to subtract 5 from Jamie's wins. 11-5 = 6. To then see if the wins add up to 30, we have to add Jamie's and Imani's wisn together, 11 + 5 ≠ 30, so therefore it is not possible for Jamie to have won 11 games.

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Explanation:

For any parallelogram, the opposite sides are the same length. Think of a rectangle, though we could have angles that aren't 90 degrees.

(5n-6) and (3n-2) are the lengths of the opposite sides. Set them equal to one another and solve for n.

5n-6 = 3n-2

5n-3n = -2+6

2n = 4

n = 4/2

n = 2

We can use this to find the length of the opposite sides

5n-6 = 5*2-6 = 10-6 = 4

3n-2 = 3*2-2 = 6-2 = 4

We get 4 each time which helps confirm we have the correct value for n.

The opposite sides are 4 cm each. The other side is

2n+3 = 2*2+3 = 4+3 = 7

Looking at adjacent sides (sides that are next door neighbors), we see 4 cm and 7 cm.

We could easily say "7 cm and 4 cm" as order doesn't matter. Though this isn't listed so we'll go with "4 cm and 7 cm" instead.

Answer:

UW=41

Step-by-step explanation:

the tangent line and the radius always meet at a right angle(90 degrees)

UWV is a right angle triangle, apply the Pythagorean theorem:

a²+b²=c² (a=40, b=9, c=UW)

40²+9²=c²

c=√40²+9²=√1600+81=√1681

c= 41

Answer:

36x^2 -1

Step-by-step explanation:

6x times 6x= 36x^2

6x times 1= 6x

-1 times 6x= -6x

-1 times 1= -1

so, ...

36x^2+6x+(-6x)+(-1) = 36x^2 -1

Alan will be 50 yrs old and Aron will be 20 yrs old

Answer:

x > or equal to 0

Step-by-step explanation:

you're welcome

Answer:

x > or equal to 0

Answer:

Probability of the teacher or other staff is 0.7143

Step-by-step explanation:

pr(teacher or other staff) = pr(teacher) + pr(other staff) - pr(teacher and other staff)

Total number of tickets = 1050

Number of tickets sold to teachers = 515

Number of tickets sold to other staff = 235

pr(teacher) = [tex]\frac{515}{1050}[/tex]

                 = 103 [tex]\frac{2}{10}[/tex]

                 = 0.4905

pr(other staff) = [tex]\frac{235}{1050}[/tex]

                    = 47 [tex]\frac{2}{10}[/tex]

                  = 0.2238

Since the picking of the wining ticket is mutually exclusive, then;

pr(teacher and other staff) = 0

Thus,

pr(teacher or other staff) = 0.4905 + 0.2238 - 0

                                         = 0.7143

Answer:

The correct option is;

A'(4, 4), B'(0, 4), C'(8, 8).

Step-by-step explanation:

The beginning coordinates are;

A -2, 2

B - 0, 2

C - 4, 4

Given that triangle ABC is dilated by 2, the center of dilation being the origin, (0, 0), we have;

Given that the center of dilation is the origin, we multiply the x, and y values by the scale factor as follows;

(x, y) → (2·x, 2·y)

Which gives;

A - (2, 2) → A'(2×2, 2×2) = A'(4, 4)

B - (0, 2) → B'(2×0, 2×2) = B'(0, 4)

C - (4, 4) → C'(2×4, 2×4) = C'(8, 8)

The correct option is A'(4, 4), B'(0, 4), C'(8, 8).

Answer:

Hey there!

We have the angle is equal to half the measure of the arc of 120 degrees. (Just another rule for circles)

7x-10=0.5(120)

7x-10=60

7x=70

x=10

Hope this helps :)

Answer:

x = 10

Step-by-step explanation:

Tangent Chord Angle = 1/2 Intercepted Arc

7x-10 = 1/2 ( 120)

7x -10 = 60

Add 10 to each side

7x -10+10 = 60+10

7x = 70

Divide by 7

7x/7 = 70/7

x = 10

Answer:

Option C is the correct option.

Step-by-step explanation:

√ 8 • √ 5

Calculate the product

[tex] = \sqrt{40} [/tex]

Simplify the radical expression

[tex] = \sqrt{2 \times 2 \times 10} [/tex]

[tex] = 2 \sqrt{10} [/tex]

Hope this helps...

Best regards!!

Answer:

Step-by-step explanation:

We have the equation

[tex] 2(3^t) = 1458[/tex]

Dividing by 2 on both sides we get

[tex] 3^t = 729[/tex]

Taking the natural logarithm on both sides we get

[tex] t \ln(3) = \ln(729)[/tex]

So t = \frac{\ln(729)}{\ln(3)} = 6.

So at 6 weeks we get 1458 infected people.

Answer:

40 m

Step-by-step explanation:

The perimeter of the flat, orange shape is the sum of all the sides that forms a boundary around the shape.

The shape is made up of 4 triangles having 2 equal side lengths each, which surrounds the center square.

Each side length of the triangle, that forms a boundary round the shape = 5 m.

There are 8 of this equal side length.

Perimeter = 8(5m) = 40 m

Answer:

45.29 miles per hour

Step-by-step explanation:

Speed is the distance over time.  To find the average rate of speed for a trip, we simply need to take the total distance divided by the total time.

Avg. Speed = (188 miles + 197 miles) / (4 hours + 4.5 hours)

Avg. Speed = 45.29 miles per hour

Hence the average rate of speed for the trip was 45.29 miles per hour.

Cheers.

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Edit:  Thanks to Chegsnut36 for calculation correction

Answer:

≅45.29

Step-by-step explanation:

Hey there!

To find the average rate speed we need to add all the same number.

188 + 197 = 385

4 + 4.5 = 8.5

Now to find the average rate we do,

385 ÷ 8.5 ≅ 45.29

Hope this helps :)

Answer:

64π

Step-by-step explanation:

Since the diameter of the circle is 16, the radius is half of that which is 8.

Area = πr² = 64π

Answer:

Step-by-step explanation:

Radius = 8 cm

Now, finding the area of circle:

[tex]\pi \: {r}^{2} [/tex]

Plug the values

[tex] = 3.14 \times {8}^{2} [/tex]

Evaluate the power

[tex] = 3.14 \times 64[/tex]

Calculate the product

[tex] = 200.96 \: {cm}^{2} [/tex]

Hope this helps..

Best regards!!

Answer:

1000

Step-by-step explanation!

The formula for the amount accrued [ƒ(x)] on an investment earning compound interest is f(t) = P(1 + r)^t where:

P = the amount of money invested (the principal)

r = the interest rate per payment period expressed as a decimal fraction

t = the number of periods

Your formula is

f(x) = 1000(1 + 0.05)^x

In comparison, we can see that the term that represents the amount of money originally invested is 1000.

Answer:

(A) 1,000

Step-by-step explanation:

i just took the test

Answer:

3.6hours

Step-by-step explanation:

kevin-6hrs

so he gets 1/6 called in 1 minute

Anne-9 hrs

so she gets 1/9 called in 1 minute

together

1/6+1/9=5/18 called in one minute

so what about all which are 18/18

you get 3.6 hrs I guess

Answer: m∠E = 20.5°

              m∠GPF = 47°

Step-by-step explanation: An inscribed angle is an alge formed with its vertex on the circle. Its relation with arc is that the measure of an inscribed angle is half the measure of the intersected arc. For that reason:

m∠E = [tex]\frac{arcFG}{2}[/tex]

m∠E = [tex]\frac{41}{2}[/tex]

m∠E = 20.5°

Angle in F is:

m∠F = [tex]\frac{arcEH}{2}[/tex]

m∠F = [tex]\frac{53}{2}[/tex]

m∠F = 26.5°

The angle GPF is external to the triangle EPF, so the angle can be found by the following definition: The measure of an external angle of a triangle equals the sum of the non-adjacent angles, i.e.:

m∠GPF = m∠E + m∠F

m∠GPF = 20.5 + 26.5

m∠GPF = 47°

Answer:

b

Step-by-step explanation:

Answer:

0.92 and 1.25 respectively

Step-by-step explanation:

0.92 and 1.25 respectively

first the mean of each value which is 9.7 and 9.8 respectively

standard deviation = square root of the mean deviation of each value

then deduct the mean from each element

and square each value and add them together. not you should square each deviation value before you add them

at last divide the result by the number of frequency and find it's square root

Answer:

0.92 and 1.25

Step-by-step explanation:

My other answer was deleted, I'm not sure why.

Answer:

w = 18

Step-by-step explanation:

w-3=15

Add 3 to each side

w-3+3=15+3

w = 18

Answer:

w = 18.

Step-by-step explanation:

w - 3 = 15

w = 15 + 3

w = 18

Check your work!

18 - 3 = 15.

Hope this helps!

Answer:

Option (4)

Step-by-step explanation:

In the given picture,

Trapezoid PQRS has two points T and U as the midpoints of sides PS and RQ.

Segment TU joins the midpoints of the sides PS and RQ.

Mid-segment theorem states that "If a line joining midpoints of a trapezoid is parallel to the bases, length of this segment is half the sum of lengths of the bases."

Therefore, m(TU) = [tex]\frac{1}{2}(m\text{PQ}+m\text{SR})[/tex]

7x - 26 = [tex]\frac{1}{2}[(3x+23)+(9x-3)][/tex]

7x - 26 = 6x + 10

7x - 6x = 26 + 10

x = 36

m(TU) = 7x - 26

          = 7(36) - 26

          = 252 - 26

          = 226

Therefore, Option (4) will be the answer.

Answer:

4th one

Step-by-step explanation:

The first digit can be 1 or 2.

For each one ...

The second digit can be 1 or 2.

For each one ...

The third digit can be 1 or 2.

That's (2•2•2)= 8 different possibilities.

Answer:

1521 pi in^3

radius x radius x height x pi = volume

13 x 13 x 9 = 1521

We do not multiply by pi because it is already included

Hope this helps

Step-by-step explanation:

Answer:

Excess of income over expenditure is ₹1,185,500.

Step-by-step explanation:

Note: The data in this question are merged together. They are therefore sorted before answering this question. See the attached pdf file for the sorted question.

The question is now answered as follows:

Question: Prepare Income and Expenditure A/c. for the year ending 31-03-2014.

Answer and explanation:

Note: See the attached excel file for the Income and Expenditure A/c. for the year ending 31-03-2014.

Both receipts and payments account and income and expenditure account are prepared by not-for-profit organizations such as charity organizations, human right campaign, clubs, etc.

Receipts and payments account is an account gives a summary of all the cash transitions, cash received and paid, that the organization engaged in during a particular period. It is similar to the cash book prepared by profit making organizations. The receipts and payments account is prepared in or to determine the balance of cash in hand or at bank or bank overdraft at the end of the period.

Income and expenditure account is an account gives a summary of all incomes and expenses of an organization during a particular period. It is similar to the trading and profit and loss account prepared by profit making organizations. The income and expenditure account is prepared in order to determine whether there is a surplus or a deficit balance during the period.

Round this however you need to

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Explanation:

The reference angle is 56 degrees. The side 26.5 is adjacent to this angle as it is the leg closest to the angle (in contrast to the opposite leg or opposite side that is furthest from the reference angle)

The hypotenuse is d. The hypotenuse is always the longest side. The longest side is always opposite the largest angle of a triangle.

We will use the cosine ratio as it is the ratio of adjacent over hypotenuse

cos(angle) = adjacent/hypotenuse

cos(56) = 26.5/d

d*cos(56) = 26.5

d = 26.5/cos(56)

d = 47.3897287242421

You use your calculator for the last step shown above. Make sure your calculator is in degree mode. Round that value however you need to.

Here is the formula of sin cos tan :

sin x = opposite/hypotenuse

cos x = adjacent / hypotenuse

tan x = opposite / adjacent

d = hypotenuse

x = the angle known in your pic

like example if in your picture:

adjacent = 26.5

if want to find the d

cos x = adjacent / hypotenuse

cos 56 = 26.5 / d

d = 26.5 : cos(56)

d = 47.390 (3 significant figures)

and if want to find the opposite

tan x = opposite/adjacent

tan 56 = opposite/ 26.5

opposite = 26.5 × tan(56)

opposite = 39.288

-> Sorry if im wrong