Can someone tell me the answers to these 3 questions plzzz

Problem 61

Refer to this link where I solved the problem earlier

https://brainly.com/question/24517029

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Problem 62

T(n) = nth triangular number

T(n) = n(n+1)/2 = 0.5n(n+1)

That squares to (0.5n(n+1))^2 = 0.25n^2(n+1)^2

The next triangular number after T(n) is

T(n+1) = 0.5(n+1)(n+1+1) = 0.5(n+1)(n+2)

That squares to 0.25(n+1)^2(n+2)^2

Notice how each squared result has 0.25 and (n+1)^2 found buried in them.

Let's say A = 0.25(n+1)^2

That would mean the first result 0.25n^2(n+1)^2 becomes An^2

The second result 0.25(n+1)^2(n+2)^2 becomes A(n+2)^2

Let's add those to see what happens

An^2+A(n+2)^2

An^2+A(n^2+4n+4)

A(n^2+n^2+4n+4)

A(2n^2+4n+4)

0.25(n+1)^2*(2(n^2+2n+2))

0.5(n+1)^2(n^2+2n+1+1)

0.5(n+1)^2((n+1)^2+1)

0.5k(k+1)

We see that the result is a triangular number where k = (n+1)^2

This shows that adding the squares of consecutive triangular numbers gets us another triangular number.

A few examples

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Problem 63

I'll borrow some of the ideas from problem 62

We found that after squaring the nth and (n+1)th triangular numbers, we got An^2 and A(n+2)^2 respectively. We let A = 0.5(n+1)^2

Subtract those expressions to get...

A(n+2)^2 - An^2

A(n^2+4n+4)-An^2

A(n^2+4n+4-n^2)

A(4n+4)

4A(n+1)

4*0.5(n+1)^2*(n+1)

(n+1)^3

This proves that the difference between the squares of consecutive triangular numbers is a perfect cube, aka a cube number.

A few examples:

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Problem 64

Refer to this link where I solved the problem earlier

https://brainly.com/question/24517029

Answer:

19683

plsss mark me brainliest

Step-by-step explanation:

term to term rule ×3

Answer:

A. the slope value is 1/4

B. 0

C. y = 1/4x

Step-by-step explanation:

A: the slope can be calculated with the formula

[tex]m = \frac{rise}{run} = \frac{y2 - y1}{x2 - x1} [/tex]

m is the slope

(x1, y1) is your first coordinate point (any point will work)

(x2, y2) is your second coordinate point (any point will work)

Plug in your values, in this case I chose (0,0) and (4,1) as the two coordinates:

[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{1 - 0}{4 - 0} = \frac{1}{4} [/tex]

B: the y-intercept is the y-coordinate of where the graph touches the y-axis and in this case the coordinate is (0,0) where the y coordinate is 0.

C:

the equation of the graph is y = mx + b.

m is the slope = 1/4

b is the y-intercept = 0

Therefore the equation is y = 1/4x

Answer:

D. be congruent

Step-by-step explanation:

vertical angles are angles that are across from each other on intersecting lines and they are always congruent

Step-by-step explanation:

a

[tex]area \: of \: circle = \pi{r}^{2} \\ = 22 \div 7{ \times (35 \div 2)}^{2} \\ = 3.14 \times 306.25 \\ = 961.625 {cm}^{2} [/tex]

Answer:

a.14

Step-by-step explanation:

2+2 =4

7+7= 14

I hope it helpful

Answer:

4a + 7 = SIMPLIFIED

4a = -7

a= -1.75 ANSWER OF EXPONENT IF NEEDED

Answer:

[tex] - 2(4x + 4) - 3x - 2 = 34 \\ \\ - 8x - 8 - 3x - 2 = 34 \\ \\ - 8x - 3x = 34 + 8 + 2 \\ \\ - 11x = 34 + 8 + 2 \\ \\ - 11x = 44 \\ \\ x = - \frac{44}{11} \\ \\ x = - 4[/tex]

Answer:

[tex]−2(4x+4) - 3x - 2 = 34 \\ - 8x - 8 - 3x - 2 = 34 \\ - 11x - 10 = 34 \\ - 11x = 34 + 10 \\ - 11x = 44 \\ \frac{ - 11x}{ - 11} = \frac{ - 44}{ - 11} \\ x = -4 [/tex]

Answer:

Tn=4n+1

4(100)+1

400+1

=401

Answer: i d k

Step-by-step explanation:

Answer:

x - 4

Step-by-step explanation:

[tex] \sf \bigg( \dfrac{ {x}^{4} }{ {x}^{3} } \bigg) - 4[/tex]

[tex] \sf \bull \dfrac{{a}^{m} }{ {a}^{n} } = {a}^{m - n} [/tex]

[tex] \sf \: {x}^{4 - 3} - 4[/tex]

[tex] \sf{x}^{1} - 4[/tex]

[tex] \sf \: x - 4[/tex]

Step-by-step explanation:

[tex]( \frac{ {x}^{4} }{ {x}^{3} } ) ^{ - 4 } \\ ( {x}^{4 - 3} ) ^{ - 4} \\ (x ^{1} ) ^{ - 4} \\ x ^{1 \times - 4} \\ x ^{ - 4} [/tex]

Answer:

[tex]\frac{49}{50}[/tex]

Step-by-step explanation:

First, divide it by 100.

[tex]\frac{98}{100}[/tex]

Then, simplify. (They both can be divided by 2 since it is their GCF)

[tex]\frac{49}{50}[/tex]

Answer: [tex]\frac{49}{50}[/tex]

Answer:

3x=15

Step-by-step explanation:

theres 3 classes

x=the price of each

15$ is the total

Answer:

4190 m

Step-by-step explanation:

3500-560=2940

2940+1250=4190

Answer:

-14

Step-by-step explanation:

!

Answer:

-14

Step-by-step explanation:

(-6)(2) + (-8/4) =

-12 - 2 =

-14

Answer:

This is the correct answer

Answer:

Step-by-step explanation:

The formula for the y-intecept form is [tex]y=mx+b[/tex]

Plugin the m and the b we have

[tex]y=-4x+5[/tex]

Answer:

y=-4x+5

Step-by-step explanation:

Answer:

Step-by-step explanation:

9) a = 2 ; b = 6

a) a + b =  2 + 6 = 8

b) b - a = 6 - 2 = 4

c) ab = 2 * 6 = 12

10) c = 12 ; d = 4

a) c ÷ d = 12 ÷ 4 = 3

b) c + d = 12 + 4 = 16

c) c - d = 12 - 4   = 8

Answer:

Step-by-step explanation:

10-512                                                                                                                                                      = -502                                                                                                                                         = -2.251

Answer:

A. No solution.

Step-by-step explanation:

Absolute values can never be negative. So there is no value of "x" that can make the absolute value negative.

Answer:

Step-by-step explanation:

Please see this link to get answer

Answer:

60×8 = 480 + 140 = 620

80×8 = 640

Answer:

3604

Step-by-step explanation:

68 km/hr

53 hours = 68*58 (if this helped pls give brainliest ty!)

Answer:

Speed = 68 km/h

Time = 53 hours

Distance = Speed × Time

Distance = 68 × 53

Distance = 3,604 km

answer is option B 480 because it is getting reduced by 4 times at Evey step

Answer:

30*4=120

120*4=480

answer=480

Step-by-step explanation:

Answer:

1. Center of rotation is (0,0), the origin. And you can label the green triangle's points PQR. it doesn't matter where you start just put P, Q, & R on each points of the green triangle

2. Reflection line is y = 0. And you can label the red triangle's points XYZ. it doesn't matter where you start just put X, Y, & Z on each points of the red triangle

Catch up with school before it's too late!

Answer:

See below.

Step-by-step explanation:

Substitute the values for x.

h(-5) = 4(-5) - 5 = -25

h(-1) = 4(-1) - 5 = -9

h(2) = 4(2) - 5 = 3

h(3) = 4(3) - 5 = 7

h(5) = 4(5) - 5 = 15

Hello!

Are you in algebra?

Here is how to solve and graph.

First, look for the slope and y-intercept of your equation.

y = - 1/2r-6

The y intercept is, -6

The slope is -1/2

the variable r, is another way to represent x, as it is just a variable.

now that you have all that information, plot -6 on the graph, -6 should be on the y- axis.

from that point, move down one space and move right two space. complete this step multiple times.

Now please look at the photo, and Here's what the graph should look like.

Answer:

(-12,8)

Step-by-step explanation: