3. The first four terms of a sequence are:
T2 = 12+ 22
T3 = 12 + 22 + 32
T4 = 12 + 22 + 32 +42
T1 = 12
The n" term is given by Tn=n(n + 1)(2n + 1).
Work out the value of T23.

Answer:

Mauricio nació en el año 2000.

Step-by-step explanation:

Supóngase que el cumpleaños se celebra en el año 2020, si [tex]x[/tex] es la edad actual de Mauricio, entonces la expresión matemática que traduce el enunciado del problema es:

[tex]\frac{(x+13)-10}{23} +20 = 21[/tex]

Ahora, se desarrolla y se simplifica la ecuación:

[tex]\frac{x+3}{23}+20 = 21[/tex]

[tex]\frac{x+3}{23} = 1[/tex]

Se despeja [tex]x[/tex]:

[tex]x +3 = 23[/tex]

[tex]x = 20[/tex]

Mauricio tiene 20 años.

Ahora, el año de nacimiento de Mauricio es la sustracción de la edad de Mauricio del año actual:

[tex]y = 2020-20[/tex]

[tex]y = 2000[/tex]

Mauricio nació en el año 2000.

Answer:

1408.5 acres

Step-by-step explanation:

If 55% of the land is federally owned, then 100 - 55 = 45% of the land is not federally owned.

We need to find how many acres are not federally owned, in other words, we need to find how many acres represent 45% of the total 3129 acres. So, to do this we can apply a rule of three:

3129 acres ---- 100%

x acres     ------ 45%

[tex]x=\frac{(3129)(45)}{100} =3129(0.45)= 1408.05[/tex]

Therefore, the total of acres that are not federally owned are 1408.5 acres.

Answer:

8

Step-by-step explanation:

8 can be divisible by 8. Therefore, it would be a multiple of 8.

The first multiple of a number is always that number.

All other options given are not multiples of 8.

Hope this helps.

One day is equivalent to 86400 seconds.

So 86400÷20=4320 gallons

Answer:

Step-by-step explanation:

B

Step-by-step explanation:

x2 + 10x + 25

x2 + 5x + 5x + 25

x(x + 5) + 5(x + 5)

(x + 5)(x+ 5) are the factors

x2 - 36

Both are squares so

x2 - (4)2

Answer:

no

Step-by-step explanation:

Answer:

The scalar used does not exist in the real number system.

Step-by-step explanation:

The ratio 16:14 is not equivalent to the ratio 64:60 because the scalar used does not exist in the real number system.

Note, that the ratio 64:60 can be scaled down by 4 to be the ratio 16:15, which is not the ratio 16:14.

In order to scale 64:60 to 16:14 or vise versa, you'd have to use a number that simply does not exist in the real number system.

Cheers.

Answer:

See explanation

Step-by-step explanation:

Usually, I just find the quadratic formula the easiest to go, but here are some tips to tell if which you should use.

1. First see if you can get integer values for the roots to multiply to c and add to b.

This is the easiest way to solve a quadratic equation, and I always check for whether I can easily find the roots by multiply two numbers for c and adding them for b.

For instance, the Quadratic [tex]x^2 + 5x + 6[/tex]

I can easily see that 2 and 3 are the roots here - as [tex]2\cdot3=6[/tex] and [tex]2+3=5[/tex]. If you can do this and receive integer values, then great! I'd definitely stick with this.

2. See if you can complete the square

If you have a quadratic which is a perfect square, you'll be able to tell if c is a perfect square, and b is twice that number. This will be easiest. Any quadratic equation can be solved by completing the square, but I personally stick to this method only if I can tell it's a perfect square quadratic.

3. Stick to the Quadratic Formula

If all else fails, go with the Quadratic formula. It's not that hard and it gets the job done. I would highly discourage going with graphing, as it takes too much time and it's quite a hassle unless you have a graphing calculator.

I really hope this helped!

Answer:

In my preferred order, ...

Step-by-step explanation:

My personal favorite is to use a graphing calculator. If it shows the zeros are whole numbers, your solution is at hand. If it shows the zeros are recognizable decimal fractions*, the solution is also at hand. If it shows the zeros are unrecognizable as fractions, they are likely irrational. Then the vertex of the graph gets you most of the way to an exact solution.

If the quadratic's coefficients are not integers, then the quadratic formula is least likely to give difficulty.

Example

The attached is a graph of the quadratic ...

  y = 2x^2 -3x -4

We can see from the x-intercepts that the roots are irrational (none are fractions with a denominator that is a factor of 2). The vertex of the graph is (3/4, -5 1/8), so the vertex form of the equation for this graph is ...

  y = 2(x -3/4)^2 -(5 1/8)

Solving this for y=0, we find ...

  0 = 2(x -3/4)^2 -(5 1/8)

  5 1/8 = 2(x -3/4)^2 . . . . . .add the constant (vertex y-value)

  (5 1/8)/2 = (x -3/4)^2 . . . . divide by 2 (the leading coefficient)

  2 9/16 = (x -3/4)^2

  x = 3/4 ± √(41/16) . . . . . . . add the horizontal offset (vertex x-value)

  x = (3 ± √41)/4 . . . . . . . . . . simplify

If you see what we've done here, you can write down the answer from the vertex and the leading coefficient:

  x = (3/4) ± √((5 1/8)/2) . . . . . vertex (3/4, 5 1/8), leading coefficient 2

__

With a little practice, factoring can be a relatively simple way to find the solution. As a preliminary step, the equation should be divided by any common factor of the coefficients, so they are all relatively prime. It helps immensely to know your times tables thoroughly. I like this method, because it can get a solution with fewer steps than using the quadratic formula.

The product of two binomials is ...

  (ax +b)(cx +d) = acx^2 +(ad+bc)x +bd

The product of the leading coefficient (ac) and the constant (bd) is abcd. It has factors of ad and bc, whose sum is the coefficient of the linear term. So, if you can factor the product of the leading and trailing coefficients and find a sum of factors that is the middle coefficient, you're home free. Sometimes the factors jump out at you, and sometimes you need to list a bunch of them before you see what you need.

In our example, we would be looking for factors of 2(-4) = -8 that have a sum of -3.

  -8 = (-8)(1) = -4(2) = (-2)(4) = (-1)(8)

These pairs have sums of -7, -2, 2, 7. None of the sums is -3, so factoring by integers is not possible. You can see that it is unnecessary to list the pairs with positive sums in this case.

Once you have the values ad and bc, you can see that 'a' is the greatest common divisor of ac and ad. Then ad/a = d, and ac/a = c. Now you know 3 of the 4 numbers in the binomial factors.

_____

* The Rational Root Theorem can tell you what reasonable fractions might be for your quadratic. You should be familiar with the decimal equivalents of fractions with small integer denominators.

Answer:

144

Step-by-step explanation:

Subtract 2 from 7 to get 5.

5×24+34−10=144

Multiply 5 and 24 to get 120.

120+34−10=144

Add 120 and 34 to get 154.

154−10=144

Subtract 10 from 154 to get 144.

The result of the given expression is 144

Expression has different terms separated by mathematical signs

Given the expression

(7−2)24+34−10

Using the PEDMAS rule

Parethesis first to have:

(7−2)24+34−10

= 5(24) + 34 - 10

Followed by multiplication

= 120 + 34 - 10

Then followed by Addition

= 154 - 10

Finally subtraction

154 - 10 = 144

The result of the given expression is 144

Learn more here: https://brainly.com/question/17788156

Answer:

X= -5

Step-by-step explanation:

5x -3 = -28

Add 3 to both sides

5x= -25

divide by 5 on both sides to isolate x

x=-5

Answer:

It would be losing 300.

Step-by-step explanation:

The opposite of gaining is losing the integer would be -300

Answer:

-300

Step-by-step explanation:

Answer:

$257

Step-by-step explanation:

First we multiply the rate by time

8.5*32=$272

then we subtract the uniform fee

272-15=$257

(plz give brianliest ty)

Answer:

8.50x-15

Step-by-step explanation:

Flat rate is 15 so you subtract from income made. 8.50x is how much you make depending on how many hours you work. Thus income-fee= how much you make first week.

Step-by-step explanation:

I try my best I not a math expert

Answer:

v=16/3

Step-by-step explanation:

3(2v-9)=5

Multiply 2v and -9 with 3

6v-27=5

Add 27 to both sides

6v=32

Divide both sides by 6

v=16/3

Answer:

[tex]\Huge \boxed{-50}[/tex]

Step-by-step explanation:

25 is subtracted from -25.

[tex]\Rightarrow -25-25 \\ \\ \\ \Rightarrow -50[/tex]

The value is -50.

Answer: The donated $18

Step-by-step explanation:

If each jacket cost $150  then multiply 150 by 4 to find out the total that the store received.

150 * 4 = 600  

Now find 3% of 600 to find out how much they donated to the charity.

3% * 600 = $18

Answer:

15+n

Step-by-step explanation:

Let the number be 'n'

Fifteen=15

increased by= +

a number= n

Hope this helps ;) ❤❤❤

Answer:

It could be 15+ (any varible)=?

Step-by-step explanation:

Answer: The formula solved for L is E/100M = L.

Step-by-step explanation:

So far we have the givens:

E, is measured by the formula E = 100M/L, where M = number monsters and L= level of monsters and solve for L.

Thus, isolate L to solve for it.

E = 100M/L

Divide each side by 100M to get rid of it and to free L.

E/100M = L

Hence your answer!

Answer: 50M/E is correct

Step-by-step explanation: I got it right :D

Answer:

78

Step-by-step explanation:

Mode = number that appears most in a set of numbers

The number that appears the most in this set is 78. So, the mode is 78. Hope it helps!

Answer:

Step-by-step explanation:

arrange in ascending order

39,43,43,50,55,61,75,78,78,78

mode=78

Answer:

x=-3/5

Step-by-step explanation:

3(x + 5) = 2(4x + 9) ​

First, distribute:

3(x)+3(5)=2(4x)+2(9)

3x+15=8x+18

-5x= 3

x= -3/5

Answer:

Angle A is 30

Angle B is 150

Step-by-step explanation:

So we have the supplementary angles A and B. In other words:

[tex]A+B=180[/tex]

We are also told that Angle B is 30 more than four times Angle A. In an equation, this is:

[tex]B=30+4A[/tex]

We now have a system of equations. Solve by substitution of B into the first equation:

[tex]A+B=180[/tex]

[tex]A+(30+4A)=180[/tex]

Combine like terms:

[tex]5A+30=180[/tex]

Subtract 30:

[tex]5A=150[/tex]

Divide by 5:

[tex]A=30[/tex]

So, Angle A is 30 degrees.

And since the angles are supplementary, this means that Angle B is 180 minus 30 or 150 degrees.

Answer:

0.85x - $50

Step-by-step explanation:

Given that :

Brandon wants to buy a new bike. The model he likes is on sale for 15% off its original price. His parents agree to pay for $50 of the cost. If the original cost of the bike is x dollars, which of the expressions below represent the amount Brandon has to pay

Discount on price = 15%

Amount parents agreed to pay = $50

Cost of bike = x

Discount on bike = 0.15x

Cost after discount is removed = (x - 0.15x) = 0.85x

Parent pays $50 of cost price, amount Brandon will have to pay equals :

(0.85x - $50)

Answer:

0.85x - $50

Step-by-step explanation:

Answer:

[tex]\bold{\dfrac{6}{7}}[/tex]

Step-by-step explanation:

Given ratio is:

8 gal to [tex]9\frac{1}3[/tex] gal

To find:

Ratio in Lowest form with whole numbers in numerator and denominator.

Solution:

First of all, let us convert [tex]9\frac{1}3[/tex] to simple [tex]\frac{p}{q}[/tex] form:

Formula:

[tex]a\dfrac{b}{c} = \dfrac{a\times c+b}c[/tex]

Using the formula, we get:

[tex]9\dfrac{1}{3} = \dfrac{9\times 3+1}{3} = \dfrac{28}{3}[/tex]

Now, let us have a look at the ratio:

[tex]8 : \dfrac{28}{3}[/tex]

Any ratio, [tex]p:q[/tex] can be written as [tex]\frac{p}{q}[/tex].

Writing given ratio as per above:

[tex]\dfrac{8}{\dfrac{28}{3}}\\\Rightarrow \dfrac{8 \times 3}{28}\\\Rightarrow \dfrac{2\times 3}{7}\\\Rightarrow \bold{\dfrac{6}{7}}[/tex]

Therefore, the answer is

[tex]\bold{\dfrac{6}{7}}[/tex]

Answer:

coffee is the best answer in my mind

Area of a rectangle= length*width

So:

Area of the playground= (6x)(4x+4)

Use distributive property.

Area of the playground= (6x*4x)+(6x*4)

=24x^2+24x

Answer: 24x^2+24x

Answer:

2x5-4x2-25

Step-by-step explanation:

First you distribute the negative sign to the second equation which makes each number it's opposite

Which would result in 4x5-13x2-10-2x5+9x2-15

Then you combine like terms and get 2x5-4x2-25

Answer:

-23

Step-by-step explanation: