1. x/5 + 10 = 40
2. 4x - 36 = -2
i would really appreciate it if you'd help me

The Sequence:

1 , 1+2 , 1+2+3 , 1+2+3+4, ...

here, every term is an AP. finding the general formula for the sum of the elements of each term is:

Sₙ = [tex]\frac{x}{2}(2a + (x-1)d)[/tex]        [where x = number of term, a = first term and d = common difference]

here, the first term is always 1 and so is the common difference.

Sₙ = [tex]\frac{x}{2}(2 +x-1)[/tex]

Sₙ = [tex]\frac{x}{2}(1 +x)[/tex] = [tex]\frac{1}{2}(x + x^{2})[/tex]

which is the formula for a general term in our series

now, we need to find the sum of the first n terms of this series

[tex]\displaystyle\sum_{x=1}^{n} [\frac{1}{2}(x + x^{2})][/tex]

[tex]\displaystyle\frac{1}{2} [\sum_{x=1}^{n} (x) + \sum_{x=1}^{n}(x^{2})][/tex]

in this formula, for the first term, it's just an AP from x = 1 to x = n

for the second term, we have a general formula [tex]\frac{n(n+1)(2n+1)}{6}[/tex]

[tex]\frac{1}{2}[\frac{n}{2}(2a + (n-1)d)+ \frac{n(n+1)(2n+1)}{6} ][/tex]

in this AP (first term), the first term and the common difference is 1 as well

[tex]\frac{1}{2}[\frac{n}{2}(2 + n-1)+ \frac{n(n+1)(2n+1)}{6} ][/tex]

[tex]\frac{1}{2}[\frac{n}{2}(n+1)+ \frac{n(n+1)(2n+1)}{6} ][/tex]

[tex][\frac{n}{4}(n+1)+ \frac{n(n+1)(2n+1)}{12} ][/tex]

[tex]\frac{n}{4}(n+1) [1+\frac{(2n+1)}{3} ][/tex]

[tex]\frac{n}{4}(n+1) [\frac{(3+2n+1)}{3} ][/tex]

[tex]\frac{n}{4}(n+1) [\frac{(2n+4)}{3} ][/tex]

[tex]\frac{n}{2}(n+1) [\frac{(n+2)}{3} ][/tex]

[tex]\frac{n(n+1)(n+2)}{6}[/tex]

which is the sum of n terms of the given sequence

9514 1404 393

Answer:

Step-by-step explanation:

The given expression says ...

  [tex]t_n+1=3\\\\t_n=2\qquad\text{for any value of n}\\\\t_2=2\\\\t_3=2[/tex]

Answer:

[tex]here \: tn + 1 = 3 \\ tn = 2 \\ put \: n = 1 \\ t1 = 2 \\ n = 2 \\ t2 = 2 \\ n = 3 \\ t3 = 2 \\ for \: all \: n \: values \: = 2 \\ thank \: you[/tex]

Answer:

x^4-9x^3+39x^2-225x+350

Step-by-step explanation:

The simplest polynomial you can get with that roots are (x-5i)(x+5i)(x-2)(x-7)=x^4-9x^3+39x^2-225x+350

The length of the canvas where Melany will mark the position of the hanger is 1.6 feet.

The given parameters:

length of the canvas = 8 feet

dimension of the hanger = [tex]\frac{1}{5} \ of \ the \ shoe's \ length[/tex]

To find:

The length of the canvas where Melany will mark the position of the hanger is calculated as follows:

[tex]location \ of \ the \ hanger = \frac{1}{5} \times 8\ ft\\\\location \ of \ the \ hanger = 1.6 \ ft[/tex]

Thus, the length of the canvas where Melany will mark the position of the hanger is 1.6 feet.

Learn more here: https://brainly.com/question/17765207

Answer:

64 ivy stems

Step-by-step explanation:

72 ivy stems / 18 centerpieces = 4 ivy stems / 1 centerpiece

Create an equation with x being the amount of ivy stems needed.

x / 16 = 4

x = 64

Answer:

500pounds×1.23euros

Step-by-step explanation:

to find y intercept, put x to be 0

hence,y int is -36

also, to find x int put y to be 0 and factorise the equation

hence, x are - 9 and 4

finally, the answer in a co ordinate are

(4,-36) , (-9,-36)

Hi there!

[tex]f(x)+f(x+1)=4f(x)[/tex]

There are 3 parts to this equation:

f(x)

f(x+1)

4f(x)

We must first determine these three parts separately.

1) f(x)

We're given that  [tex]f(x)=3^x[/tex]:

⇒ [tex]f(x)=3^x[/tex]:

2) f(x+1)

Now, we must find f(x+1). To do so, add 1 to x in the original function [tex]f(x)=3^x[/tex]:

⇒ [tex]f(x+1)=3^x^+^1[/tex]

3) 4f(x)

To find 4f(x), multiply the original function [tex]f(x)=3^x[/tex] by 4:

[tex]4f(x)=4*3^x[/tex]:

4) Put it all together

Now, plug each of the three parts into the equation [tex]f(x)+f(x+1)=4f(x)[/tex]:

[tex]f(x)+f(x+1)=4f(x)[/tex]

[tex]3^x+3^x^+^1=4*3^x\\3^x+3^x*3=4*3^x[/tex]

Factor the left side

[tex]3^x*(1+3)=4*3^x[/tex]

Divide both sides by 3^x

[tex]1+3=4\\4=4[/tex]

Because this equation is true, [tex]f(x)+f(x+1)=4f(x)[/tex] is therefore true.

I hope this helps!

USE (m a t h w a y) its real easy to use

Step-by-step explanation:

Answer:

1)C 2)A  3)D

Step-by-step explanation:

Answer:

-2, 2

Step-by-step explanation:

Answer:

21x4 + 8x3 - 40x2 + 15

Step-by-step explanation:

expand using distributive property.

Answer:

19.6

Step-by-step explanation:

the answer to the question is 19.6

Answer:

19.6

Step-by-step explanation:

We have to do long devision:

5 goes into 9 how many times? Once. So our first number will be one.

9 - 5(1) = 4

Bring the 4 down. Then bring the 8 from 98 down.

5 goes into 48 how many times? Nine times. So our second number will be nine.

48 - 5(9) = 3

Bring the 3 down. Since there is no numbers left from 98, add a decimal and then a zero to make the number 98.0.

5 goes into 30 how many times? Six times. So our third number will be six. Don't forget to add the decimal before the six!

30 - 5(6) = 0

Answer:

[tex]x=5\\z=94[/tex]

Step-by-step explanation:

As they are vertical angles

∴[tex]7x+51=86\\=>7x=35\\x=5[/tex]

And,

∴[tex]86+86+z+z=360\\=>2z=188\\z=94[/tex]

I have added an image for your further observation

Hope you have understood this.....      

ask me if you have any confusion.....      

if you liked it pls mark it as the brainliest

Answer:

I don't understand please can you explain to me

Answer:

four lines axes of symmetry does a square have

The drawing instruments required for a construction, is dependent on the type of construction performed

The straightedge and the compass moves required to construct the line CD in the diagram are;

Learn more about technical drawing here:

https://brainly.com/question/157137

Answer:

Move 1: Place the compass at point A and draw circle A with center at A and radius AB

Move 2: Place the compass at any point of the circumference of circle A and label the point, at point B. Draw a second circle with the same radius AB and center at point B with the compass

Move 3: Label the point the two circles intersect as points C and D

Move 4: Place the straightedge at points C and D and construct the straight line CD

Step-by-step explanation:

Answer:

1/c^102

Step-by-step explanation:

C^-24 * c^9 * c^-87

When we multiply exponents with the same base, we add the exponents

c^(-24+9+-87)

c^(-102)

We know that a^-b = 1/a^b

1/c^102

Answer:

Step-by-step explanation:

[tex]a^{m} *a^{n} = a^{m+n}\\\\\ a^{-m}=\dfrac{1}{a^{m}}\\\\\\c^{-24}*c^{9}*c^{-87}=c^{-24+9-87}\\\\=c^{-102}\\\\=\dfrac{1}{c^{102}}[/tex]

Answer:

Carlos and Pamela drove 120 miles on the first day, 240 miles on the second day, and 290 miles on the third day.

Step-by-step explanation:

Let x be the number of miles driven on the first day.

Then they drove twice as many miles, or 2x on the second day

and 50 miles more than the second day's, so 2x + 50

The total is 650 across all three days, so we'll take the sum.

x + 2x + (2x + 50) = 650

Combine like terms on the left

5x + 50 = 650

Subtract 50 on both sides

5x = 600

Divide by 5 on both sides

x = 120

Check work:

120 + 2(120) + 2(120) + 50 = 650

120 + 240 + 240 + 50 = 650

600 + 50 = 650

650 = 650

So they drove 120 miles on the first day

2*120 = 240 miles on the second day

and 2*120 + 50 = 240 + 50 = 290 miles on the third day

Answer:

93.5

Step-by-step explanation:

Also you only wrote down four numbers not 5 so I calculated it using those four numbers

Answer: 193.5

Step-by-step explanation:

184 + 190 + 198 + 202 = 774

first we add all the numbers together

774/4 = 193.5

then we divide the numbers by the amount of things we have in this case we have four players (last basketball player height not given) so we divide that by our added number and get 193.5cm

Answer:

D

Step-by-step explanation:

Step-by-step explanation:

[tex]thank \: you[/tex]

Answer:

47

Step-by-step explanation:

Do long division.

7 goes into 32, 4 times.

32 - 28= 4

7 goes into 49, 7 times.

Therefore 47 is correct.

Answer:

1/3

a dice has 6 sides and the probability of getting 4 or 5 is just 2/6 which simplifies to 1/3

A data summation is a collection of values.

Answer:

D

Step-by-step explanation:

Substitute the co-ordinates if a and b in the distance formula and you will get the answer as sq root of 90 which is D