Help meeee pleasssseeee

Answer:

2+4+6+...+2k+2(k+1) = k(k+1) + (k+1)(k+1)

Step-by-step explanation:

Proved case for n

2+4+6+...+2n = n(n+1) ................(1)

for n = k + 1, we replace n by k and add n = k+1 on both sides (

2+4+6+...+2k+2(k+1) = k(k+1) + 2(k+1))

rearrange by factoring the right-hand-side

2+4+6+...+2k+2(k+1) = (k+1)(k+2)

which if we substitute n=k+1, we get back

2+4+6+...+2(n-1) + 2(n) = n(n+1)  ...............(2)

This means that equation (1) is applicable to case n+1, and the proof by induction is completed.

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

Proved

Step-by-step explanation:

Given

[tex]p = 80[/tex] ---- perimeter

[tex]a \to area[/tex]

Required

[tex]x^2 + 40x + a = 0[/tex]

The perimeter is calculated as:

[tex]p = 2(x + y)[/tex]

Where

[tex]x,y \to[/tex] the rectangle dimension

So, we have:

[tex]2(x + y) = 80[/tex]

Divide by 2

[tex]x + y = 40[/tex]

Make y the subject

[tex]y = 40 - x[/tex]

The area of the rectangle is:

[tex]a = xy[/tex]

[tex]a = x * (40 -x)[/tex]

[tex]a = 40x -x^2[/tex]

Equate to 0:

[tex]x^2 - 40x + a = 0[/tex]

Answer:

3.141

Step-by-step explanation:

3 decimals is .xxx, and you round the last digit up, so it becomes 3.141

Answer:

3.141

Step-by-step explanation:

since the forth number behind the decimal place is bigger than 5 we round up the third number.

I hope this helps in anyway.

Answer:

A) 3 ways

B) sorry don't know.

Step-by-step explanation:

2 P and 2 N

3P and 1 N

4P

So 3 ways.

Answer:

Cannot be factored

Step-by-step explanation:

Given

[tex]\frac{x^2}{9} + 1 + \frac{9}{x^2}[/tex]

Required

Factorize

Take LCM

[tex]\frac{x^2}{9} + 1 + \frac{9}{x^2} = \frac{x^4+9x^2+81}{9x^2}[/tex]

The expression cannot be factored

Answer:

Step-by-step explanation:

make it 1 triangle and trapezium

1) 1/2 x 7 x 8 = 28 in2

Answer:

56 in^2

Step-by-step explanation:

A = b* h

A = (8) * (7)

A = 56

A = 56 in ^2

Hope this helps!

Given:

x-intercepts of the hyperbola are ±4.

The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].

Center of the hyperbola is at origin.

To find:

The equation of the hyperbola.

Solution:

The general equation of a hyperbola:

[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex]            ...(i)

Where, (h,k) is the center of the hyperbola, ±a are x-intercepts, [tex](\pm c,0)[/tex] are foci.

Center of the hyperbola is at origin. So, h=0 and k=0.

x-intercepts of the hyperbola are ±4. So,

[tex]\pm a=\pm 4[/tex]

[tex]a=4[/tex]

The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].

[tex]\pm c=\pm 2\sqrt{5}[/tex]

[tex]c=2\sqrt{5}[/tex]

We know that,

[tex]a^2+b^2=c^2[/tex]

[tex](4)^2+b^2=(2\sqrt{5})^2[/tex]

[tex]16+b^2=20[/tex]

[tex]b^2=20-16[/tex]

[tex]b^2=4[/tex]

Taking square root on both sides, we get

[tex]b=\sqrt{4}[/tex]                    [b>0]

[tex]b=2[/tex]

Substituting [tex]h=0,k=0,a=4,b=2[/tex] in (i), we get

[tex]\dfrac{(x-0)^2}{4^2}-\dfrac{(y-0)^2}{2^2}=1[/tex]

[tex]\dfrac{x^2}{4^2}-\dfrac{y^2}{2^2}=1[/tex]

Therefore, the correct option is (d).

Answer:

hiiooioudzzxuxojxoufxodyzufxufxyfxuoxudr tztdxhxfuoxir d and

Answer: Graph B

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

Explanation:

Point A appears to be at (2.5, -1)

If we shift 6 units to the left, then we subtract 6 from the x coordinate. So the new x coordinate is now 2.5-6 = -3.5

If we shift 4 units up, then we add 4 to the y coordinate to go from -1 to -1+4 = 3

Overall, the point A(2.5, -1) moves to A'(-3.5, 3)

Graph B is the answer because of this. The other points B and C will follow the same pattern as point A does.

Answer:

Step-by-step explanation:

The element decay percentage rate of change 2.22% per minute.

Radioisotope, radionuclide, or radioactive nuclide, any of several species of the same chemical element with different masses whose nuclei are unstable and dissipate excess energy by spontaneously emitting radiation in the form of alpha, beta, and gamma rays.

Here, mass decreases by 73% every hour.

Weight of element X is 680 grams.

According to question,

f(t) = 680 (1 - 73%)ⁿ

f(t) = 680 (1 - 0.73)ⁿ

f(t) = 680 X 0.27ⁿ

f(t) = 680 X 0.9778ⁿ

f(t) = 680 X (1 - 0.02322)ⁿ

Thus, the element decay percentage rate of change 2.22% per minute.

Learn more about radioactive isotope from:

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Answer:

28/16=14/8 true

3/5=9/15 true

4/32=10/78 false

3/4=12/16 true

Step-by-step explanation:

DID IT ON BRIDGE

See the graph in the attached image.

Answer:

Step-by-step explanation:

The formula to find the angle between 2 vectors is

[tex]cos\theta=\frac{u*v}{|u||v|}[/tex] which is the dot product of u*v over the (magnitude of u times the magnitude of v). We also know that θ = [tex]\frac{\sqrt{2} }{2}[/tex]. Filling in that formula requires us to find the dot product of u and v, which is

u·v = (2×(-6)) + (a×8) so

u·v = -12 + 8a. Then we need the magnitudes of both u and v:

[tex]|u|=\sqrt{2^2+a^2}=\sqrt{4+a^2}[/tex] and

[tex]|v|=\sqrt{(-6)^2+8^2}=\sqrt{100}=10[/tex]

Putting all of together looks like this:

[tex]\frac{\sqrt{2} }{2}=\frac{-12+8a}{10\sqrt{4+a^2} }[/tex] . Cross multiply to get

[tex]10\sqrt{2}(\sqrt{4+a^2})=2(-12+8a)[/tex] which is tricky to simplify. You really need to know the rules for multiplying radicals to do this correctly. The simplification is

[tex]10\sqrt{8+2a^2}=-24+16a[/tex] and we need to solve for a. Begin by squaring both sides to get rid of the square root to get:

100(8 + 2a²) = 256a² - 768a +576 and simplify some more by distributing through the parenthesis to get

800 + 200a² = 256a² -768a + 576. Combine like terms to come up with

0 = 56a² - 768a - 224 and we need to factor that. Assuming since you're this far in math (pre-calc or maybe late algebra 2) you know how to factor, when you do, you get values for a of - .285714... and 14.

Therefore, the value for a is 14. I checked it...it works

Answer:

a = 14, U = (2, 14)

Step-by-step explanation:

the other answer is correct.

just to add the solution path for the quadratic equation

0 = 56a² - 768a - 224

in general, a quadratic equation usually expressed in x

0 = ax² + bx + c

has its solution as

x = (-b ± sqrt(b² - 4ac))/(2a)

for us here this looks like this then

a = (768 ± sqrt(768² - 4×56×-224))/(2×56) =

= (768 ± sqrt(589824 + 4×56×224))/112 =

= (768 ± sqrt(589824 + 50176))/112 =

= (768 ± sqrt(640000))/112 = (768 ± 800)/112

a1 = (768 + 800)/112 = 1568/112 = 14

a2 = (768 - 800)/112 = -32/112 = -0.29

and the negative solution would be for a vector solution in the wrong direction (down instead of up). as V is pointing up left, and the angle is only 45 degrees (pi/4), also U has to point up.

so, 14 is the solution for U.

Answer:

here is your answer

Step-by-step explanation:

here is your answer

Answer:

1960 dancers

Step-by-step explanation:

your are on "ace" level and need help here ?

a pair is 2 people

4 pairs is therefore 4×2 people = 8

245 teams of 4 pairs or 8 people each means

245×8 = 1960 people

Answer:

The answer is 104 degrees.

Step-by-step explanation:

M is equivalent to N, which means x is also 104 degrees.

Answer:

its c my dude

Step-by-step explanation:

....................

answer is c because that is right plz brainliest and like plz

Answer:

She must buy more than 5 lbs

Step-by-step explanation:

First write the inequality

cost per pound * number of pounds >  total cost

8 * lbs > 40

Divide each side by 8

8 lbs /8 > 40/8

lbs > 5

She must buy more than 5 lbs

Answer:

Is 32,13

Step-by-step explanation:

Because one is not bigger than five so it disappears.

Answer:

1205.76 m^3

Step-by-step explanation:

given:

radius = 8m

height = 18 m

volume of a cone = πr2h/3

=3.14 * (8)^2 * 18/3

=3.14 *64 *18/3

=3617.28/3

=1205.76 m^3

Answer:

[tex]\% = 11.96\%[/tex]

Step-by-step explanation:

Given

See attachment for box plot

Required

Percentage greater than or equal to 233

From the box plot, the maximum is:

[tex]Max = 244[/tex]

The minimum is:

[tex]Min = 152[/tex]

Percentage greater than 233 is calculated as:

[tex]\% = \frac{Max - 233}{Max - Min}[/tex]

[tex]\% = \frac{244 - 233}{244-152}[/tex]

[tex]\% = \frac{11}{92}[/tex]

Express as percentage

[tex]\% = \frac{11}{92}*100\%[/tex]

[tex]\% = \frac{1100}{92}\%[/tex]

[tex]\% = 11.96\%[/tex]

Answer:

14w

Step-by-step explanation:

Hope this helps

Answer:

x=6.25 and y=1.5

Step-by-step explanation:

Given equation

2x+5y=20

y=0.4x-1

Putting the value of y in above equation

2x+5(0.4x-1)=20

2x+2x-5=20

4x-5=20

4x=20+5

4x=25

x=6.25

Now,

y=0.4x-1( Given)

Putting the value of x=6.25 in above equation y

y=0.4(6.25)-1

y=2.5-1

y=1.5

Answer:

31/5 as a mixed number: 6 and 1/5

-73/8 as a mixed number:-9 and 1/8

Step-by-step explanation:

Rewriting each mixed number as a sum of two signed numbers 3 1/5  and -7 3/8 are 3 and 1/5  and -8 and 5/8 respectively

The mixed number to rewrite as a sum of two signed numbers are as follows:

Rewriting as a sum of the two signed numbers can be represented as follows;

3 1/5 = 16 / 5

-7 3/ 8 = - 59 / 8

Therefore,

3 1/5  will be 3 and 1/5

-7 3/ 8 will be -8 and 5/8

Note

3 + 1/5 = 3 1/5

-8 + 5/8 = -7 3/8

learn more on fraction here: https://brainly.com/question/24645582

Answer:

There are more females dropping than males each year and that there are more females than males

Answer: You didnt mention how much Dan mows in 1 hour, but just do that divided by 60

Step-by-step explanation:

Answer:

[tex]( {x}^{2} + 12)(x + 2)[/tex]

Step-by-step explanation:

[tex] {x}^{3} +2 {x}^{2} +12x+24[/tex]

[tex]( {x}^{3}+2 {x}^{2} )+12x+24[/tex]

[tex] {x}^{2} (x+2)+12(x+2)[/tex]

[tex]( {x}^{2} + 12)(x + 2)[/tex]