True or False
3 is a factor of n(n + 2)(n − 1) by mathematical induction.
Explain why.

Answers:

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

Explanation:

The template for a 30-60-90 triangle is that the short leg x leads to hypotenuse 2x, and longer leg x*sqrt(3). If x = 4, then we get the sides 4, 8, 4*sqrt(3) which are the short leg, hypotenuse, and long leg in that order.

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

The template for a 45-45-90 triangle is that we have x as the leg length and x*sqrt(2) as the hypotenuse. If x = 6, then we end up with the sides 6, 6, 6*sqrt(2)

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

The triangle with sides 6, 8, 10 is a right triangle because a = 6, b = 8, c = 10 makes a^2+b^2 = c^2 true. I'm using the converse of the pythagorean theorem. We don't have a special right triangle because these sides do not fit the templates mentioned in the previous two sections above.

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

The triangle with sides a = 7, b = 8, c = 10 on the other hand will not make a^2+b^2 = c^2 true. Note that a^2+b^2 = 7^2+8^2 = 113 which is not the same as 10^2 = 100. However, a triangle is possible because adding any two sides leads to a sum larger than the third side (triangle inequality theorem).

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

We cannot form a triangle with sides 7, 12, 19 because the sides 7 and 12 add to 7+12 = 19 but that's not longer than the third side 19.

The triangle inequality theorem says that if you want to form a triangle with sides a,b,c then the following three inequalities must all be true

a+b > c

a+c > b

b+c > a

Answer: 3 quart

Step-by-step explanation:

Given

Jason poured 1 gallon 1 quart of water into an empty 2 gallon bucket

1 gallon can be written as 4 quart

So, 2 gallon can be written as 8 quart

Subtract 1 gallon 1 quart(5 quart) from 2 gallon(8 quart) to get the volume added

[tex]\Rightarrow 8-5\\\Rightarrow 3\ \text{quart}[/tex]

So, 3 quart of water must be added to reach 2 gallon capacity.

Answer:

Area of the composite figure = 42 in²

Step-by-step explanation:

Composite area of the given figure = Area of the rectangle + Area of the right triangle

Area of the rectangle = Length × Width

                                    = 6 × 5

                                    = 30 in²

Area of the right triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

                                         = [tex]\frac{1}{2}(4)(6)[/tex]

                                         = 12 in²

Area of the composite figure = 30 + 12

                                                  = 42 in²

Answer:

6 (24÷3) -2

6 (8) -2

48-2

=46

Brackets of division multiplication add and subtract

Answer: the answer is 51.41281

Step-by-step explanation:

Sin=opp/hyp. sin(40)=x/69. x=69sin(40). x=51.41281

Answer:

320 square inches

Step-by-step explanation:

10*8=80

80*4=320

final answer: 320 square inches

Answer:

y = -2

Step-by-step explanation:

The formula for point-slope is as follows:

y - y1 = m(x - x1)

We are given the slope, m, or 0, and we are given the point (8, -2), which we can substitute into the point (x1, y1):

y + 2 = 0(x - 8)

y + 2 = 0

y = -2

Answer:

10

Step-by-step explanation:

=2.5(6*4)/6

=2.5*4(6 and 6 gets cancel)

=10

Answer: 3.9047 rounded to the nearest thousandth is 3.9050, or 3.905.

Step-by-step explanation:

You round 47 up to 50, which gets you to 3.9050, which you can then reduce it to 3.905.

Answer:

1/16

Step-by-step explanation:

There is a 1/2 chance to flip a heads.

So, in this case, we would multiply 1/2 four times in reference to the coins being flipped a total of 4 times to find its probability.

1/2 x 1/2 x 1/2 x 1/2 = 1/16

Thus, there is a 1/16 chance that you'd get heads four times in a row.

Answer:

answer is 20................................

Answer:

x=32

Step-by-step explanation:

To make the lines parallel, the sum of the angles must be equal to 180. 2x+3x+20=180, 5x=160, x=32

Answer:

$34.8

Step-by-step explanation:

Given data

Cost of apartment= $870 per month

increase= 20%

Discount= 8%

Let us find the amount of increase

=20/100*870

=0.2*870

=$174

New cost = 870+174

=$1044

New cost of apartment for 18 month

=1044*18

=$18792

He gave them 8% discount

=8/100*18792

=0.8*18792

=$15033.6

Hence the monthly fee will be

=15033.6/18

=$835.2

Therefore the difference in price is

=870-835.2

=$34.8

Answer:

By the Pythagorean theorem, it follows that the hypotenuse of this triangle has length c = √a2 + b2, the same as the hypotenuse of the first triangle. Since both triangles' sides are the same lengths a, b and c, the triangles are congruent and must have the same angles. ... If a2 + b2 = c2, then the triangle is right.

Step-by-step explanation:

Answer:

(5, 6, 9)

Step-by-step explanation:

The domain is basically the set of all x values while the range is the set of all y values, in this case, it's the values of f(x). To find the range, we can plug the x values into the equation:

f(-2) = 9

f(-1) = 6

f(0) = 5

f(1) = 6

f(2) = 9

Since we can't have repeats in the range, it would be: (5, 6, 9)

Answer:

Choice 3

Step-by-step explanation:

The third fraction (third refers to the answer number) is incorrect. As written, the cups won't cancel. The correct way to do this is to invert the fraction.

4 tablespoons

===========

1/4 cup

This is an extremely important procedure to know. Make sure you understand what the basis of it is. Often  times in higher physics, you don't have a proper relationships and this method (called dimensional analysis) is the only tool you have to work with.

So each term has at least 1 cancelation that occurs with the prior term. And it is the units that you look to cancel, and that determines which way to put the intermediate steps.

Answer:

Step-by-step explanation:

the circumference you make it using the diameter , pi times ( 3.142 times)

C = 13* 3.142 = 40.846

Answer:

yes it's true because 3 groups of 8 is 24

Answer:

A=h(b)b/2

Step-by-step explanation:

Answer:

49×66+49×34 = 49× (66+34)

Answer:

49×66+49×34 = 49× (66+34)

Step-by-step explanation:

Answer:

272 feets

Step-by-step explanation:

Badwater Basin = 279 feets below sea level = - 279 feets (relative to sea level)

New Orleans = 7 feets below sea level = - 7 feets (relative to sea level)

Hence,

New Orleans is higher Than Badwater Basin by :

279 feets - 7 feets

= 272 feets

Answer:

324.13°

Step-by-step explanation:

Applying,

cosA = 4/5

To find the value of A, we find the inverse of the cosine of both side,

(cosA)cos⁻¹ = cos⁻¹(4/5)

A = cos⁻¹(0.8)

A = 36.87° (First quadrant)

The above value of A is its value in the first quadrant

To find the value of A in the fourth quadrant, we use the expression

∅₄ = 360-∅₁............... Equation 1

Where ∅₄= value of A in the fourth quadrant, ∅₁ = value of A in the first quadrant.

Therefore,

∅₄ = 360-36.87

∅₄ = 324.13°

Hence the value of A in the fourth quadrant is 324.13°

Answer:

What do you need help with?

Answer: [tex]5\dfrac{1}{4}\ \text{cups of flour}[/tex]

Step-by-step explanation:

Given

Klarissa requires [tex]1\ \frac{3}{4}[/tex] cups of flour to make a recipe

Convert mixed numeral to fraction

[tex]\Rightarrow 1\dfrac{3}{4}=\dfrac{4+3}{4}\\\\\Rightarrow \dfrac{7}{4}[/tex]

If she wants to triple the recipe then,

[tex]\Rightarrow 3\times \dfrac{7}{4}=\dfrac{21}{4}\\\\\Rightarrow \text{or}\ 5\dfrac{1}{4}\ \text{cups of flour}[/tex]

depth at point B = 5 m

Step-by-step explanation:

y = -(2/5)x - 1

Point C is located 10 m from the origin O which means that x = 10. Using this value in our equation,

y = -(2/5)(10) - 1

= -4 - 1

= -5