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Gwar [14]
2 years ago
10

Prove that, for all positive values of n,

Mathematics
2 answers:
alekssr [168]2 years ago
7 0

\frac{(2n+3)^{2}-(2n+1)^{2}}{6n+6} \\ \\ =\frac{(4n^{2}+12n+9)-(4n^{2}+4n+1)}{6n+6} \\ \\ =\frac{4n^{2}+12n+9-4n^{2}-4n-1}{6n+6} \\ \\ =\frac{8n+8}{6n+6} \\ \\ =\frac{4(2n+2)}{3(2n+2)} \\ \\ =\frac{4}{3} \\ \\ \therefore \boxed{a=4, b=3}

max2010maxim [7]2 years ago
5 0

Answer:

vos te burlabas de mi

vos estás desgastado como un criminal sacado

exceso de flow

no se que será

que les paso?

sintieron un golpe en la nuca? ese fui yo..

siente tengo el estilo

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What is the length of s?​
vovangra [49]

Answer:

s = 16.97 units

Step-by-step explanation:

Since this is a right triangle, we can use trigonometry to figure out the lengths of the sides.

Look at the 45 degree angle. We can use the opposite side (12) and the hypotenuse (s) to solve for s.

Opposite and hypotenuse is sine, so we are using sine. The sine of 45 degrees is 0.70710678118. Make an equation like so:

  • 0.70710678118 = \frac{12}{s}, and we are solving for s.

Put a 1 in the denominator of sine(45 degrees) so you can cross-multiply.

  • \frac{0.70710678118}{1} =\frac{12}{s}

Cross multiply.

  • 0.70710678118s = 12

Divide both sides by sine(45 degrees).

  • s = 16.97

The length of side s is 16.97 units.

Another way to have done this problem is to use the Pythagorean theorem: a^2 + b^2 = c^2

Substitute 12 for a and b and solve for c, the hypotenuse.

  • (12)^2 + (12)^2 = c^2

Evaluate the exponents.

  • 144 + 144 = c^2

Add them together.

  • 288 = c^2

Square root 288 to solve for c.

c = 16.97, which is the same answer as you got using trigonometry.

6 0
3 years ago
4^3 > 6^2 Is this right or not right if not what other sign needs to go there.
Bess [88]

Answer:

that is right

Step-by-step explanation:

because 4×4×4 equals 64 and 6×6 equals 37 so it is 4^3>6^2

6 0
2 years ago
Read 2 more answers
Describe what each transformation does to pre image to create its image
Kamila [148]
A rotation rotates the pre image an x amount of degrees
a translation shifts a pre image up and down or left and right
a reflection reflects an image across an x or
y axis
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7 0
3 years ago
Solve the equation.<br> 4s=2/5<br><br> s=<br> (Type a whole number, fraction, or mixed number.)
BabaBlast [244]

Answer:

s = 1/10

Step-by-step explanation:

First, divide both sides by 4 to get s by itself.

(2/5) / 4 = 1/10

s = 1/10

6 0
3 years ago
Find the dimensions of an American football field. The length is 200 ft more than the width, and the perimeter is 1,040 ft. Find
natka813 [3]

Answer:

The width of the football field is 160 feet.

The length of the football field is 360 feet.

Step-by-step explanation:

Let w represent width of the football field.

We have been given that the length is 200 ft more than the width, so the length of the field would be w+200.

We are also told that the perimeter is 1,040 ft. We know that football field is in form of rectangle, so perimeter of field would be 1 times the sum of length and width. We can represent this information in an equation as:

2(w+w+200)=1040

Let us solve for w.

2(2w+200)=1040

4w+400=1040

4w+400-400=1040-400

4w=640

\frac{4w}{4}=\frac{640}{4}

w=160

Therefore, the width of the football field is 160 feet.

Upon substituting w=160 in expression w+200, we will get length of field as:

w+200\Rightarrow 160+200=360

Therefore, the length of the football field is 360 feet.

7 0
3 years ago
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