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[tex]10=2d[/tex]

Given:

The sum of the first three terms of a sequence Is 42.

The fourth term is 24.

To find:

The  u₁ and the common difference

Step-by-step explanation:

nth term of a sequence is

[tex]u_n=u_1+(n-1)d[/tex]

where, u₁ is first term and d is common difference.

4th term is 24.

[tex]u_4=u_1+(4-1)d[/tex]

[tex]24=u_1+3d[/tex]           ...(i)

Sum of nth term of an AP is

[tex]S_n=\dfrac{n}{2}[2u_1+(n-1)d][/tex]

Sum of first three terms is 42.

[tex]S_3=\dfrac{3}{2}[2u_1+(3-1)d][/tex]

[tex]42=\dfrac{3}{2}[2u_1+2d][/tex]

Divide both sides by 3.

[tex]14=u_1+d[/tex]          ...(ii)

On subtract (ii) from (i), we get

[tex]10=2d[/tex]

[tex]5=d[/tex]

Put d=5 in equation (ii).

[tex]14=u_1+5[/tex]

[tex]14-5=u_1[/tex]

[tex]9=u_1[/tex]

Therefore, the first term is [tex]u_1=9[/tex] and common difference is [tex]d=5[/tex] .

Answer:

8x+11

Step-by-step explanation:

1. 6x+3+2x+8

2. 8x+11

Answer:

8x + 11

Step-by-step explanation:

3(2x+1)+2(x+4)

distribute the 3 & 2 within the parentheses. first, multiply 3 and 2x, then multiply 3 and 1 to get 6x + 3. next, multiply 2 and x, then multiply 2 and 4 to get 2x + 8. this gives you:

6x + 3 + 2x + 8

then add like terms (6x + 2x and 3 + 8) to get your simplified final answer:

8x + 11

Answer:

The domain is all of the x values for which the function has a y value and visa versa for the range. So the domain is the minimum x value to the maximum x value and the range is from the minimum y value to the maximum y value. Filled in circles include the point its on and open circles do not. You can show this difference using parentheses and brackets. brackets include the point, parentheses.

Step-by-step explanation:

Solution,

Given; x^3-7x^2-x+7=0

Using factor theorem,

we have,

i)x^3-7x^2-x+7=0

let's check whether 1 is the factor of given equation or not by replacing the value of x by one..

or, 1^3-7.1^2-1+7=0

or, 1-7-1+7=0(.°. Cancellation of +1&-1 and +7&-7 in equation)

.°.0=0

which proves that 1 is one of the factor of x

therefore(x-1) is a factor of x^3-7x^2-x+7=0.

Now,

Expanding the x^3-7x^2-x+7=0 to get (x-1) as a factor...

ii)x^3-7x^2-x+7=0

or,x^3-x^2-6x^2+6x-7x+7

or,x^2(x-1) - 6x(x-1) - 7(x-1) = 0

or,(x-1) (x^2-6x-7)w = 0

or,,(x-1) (x^2-(7-1)x-7) =0

or,,(x-1) (x^2-7x + x -7) =0

or,(x-1) [x(x-7)+1(x-7)] = 0

or,(x-1) (x+1) (x-7) = 0

Either,

i) x - 1=0

.°.x = 1

And,

ii)x + 1 = 0

.°. x = -1

Or,

iii) x - 7 = 0

.°.x =7

Hence, the required value of x are -1 ,+1 & 7.

Answer:

-25b + 30y + 5

Step-by-step explanation:

I hope this helps!

Answer:

The expected profit on the listing is $5031.96

Step-by-step explanation:

Given that:

The probability of selling the house in 6 months is p = 0.37

The probability of not selling the house = 1 - 0.37 = 0.63

Suppose Y represents the profit on the listing,

Then: the expected profit on the listing can be computed as:

E(X) = ($20283* 0.37) - ($3925*0.63)

E(X) = $7504.71 - $2472.75

E(X) = $5031.96

Thus, the expected profit on the listing is $5031.96

The expected profit on the listing is $5031.96.

Since

The probability of selling the house in 6 months is p = 0.37

The probability of not selling the house = 1 - 0.37 = 0.63

here Y means the profit on the listing,

So, the expected profit is

E(X) = ($20283* 0.37) - ($3925*0.63)

E(X) = $7504.71 - $2472.75

E(X) = $5031.96

Thus, the expected profit on the listing is $5031.96.

Learn more about profit here: https://brainly.com/question/24673559

Answer:

that question kinda have alot of answers but try y=-25x+31

Step-by-step explanation:

Answer:

7(x-1)2+3

Step-by-step explanation:

Answer:

h=

3x2−24x+53 orver x

Step-by-step explanation:

Answer:

Step-by-step explanation:

Kindly find a simple sketch of a baseball pitch, the circle with a dot inside represents the first base coach(don't mind my drawing please I will improve).      

So, from the diagram, we can see that the expression that describes the distance and the first base coach is

y=90+3

y=93

so the distance  between Roberto Clemente and the first base coach is 93ft                                  

Answer:

between 8-9

Step-by-step explanation:

I just used my calculator lol

Answer:

keep in coming it is easy it is 14

y-y1= m(x-x1)

y+12=3/4(x-8)

y+12=3/4x-6

y=3/4x+6

i think that's it

Answer:

2333

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

6,12,18,14,30,35 only four numbers that are between 15-35

Answer:

x = 2

Step-by-step explanation:

The line goes straight through the x axis

Answer: x=2

Step-by-step explanation:

The line goes up and down, which is, Horizontal and Vertical Lines

Vertical lines go up and down and have a slope that is undefined. Graphs of horizontal lines are parallel to the x-axis. Graphs of vertical lines are parallel to the y-axis.

3 = 2 by z property

Step-by-step explanation:

Congruence criteria for triangles

If two sides and the angle between them in one triangle have the same measures as two sides and the angle between them in another triangle, then the triangles are congruent.

Please mark as brainliest

Answer: a = 40 degrees and b = 104 degrees

Step-by-step explanation:

Since a is directly across from 40 degrees those are vote equal. Now that we know a is 40 we also have b which lies on a straight line, meaning that it is a part of 180 degrees. We also have a and a 36 degree angle on that line. Since we know a is 40 we can add angle a and 36 to get 76 degrees. Now that we know part of the 180 degrees is 76, we subtract that from 180 to get angle b, meaning that b=106.

Answer:

a^2/3

Step-by-step explanation:

the numerator simplifies to 5a^3 and the bottom is 15a. we can use our exponent rules to subtract exponents, so it is 1/3(a^2). this simplifies to a^2/3.

Answer:

a^2

------

3

Step-by-step explanation:

5 a^3  / 15a

Simplify the numbers

5/15 = 1/3

Simplify the variables

a^3 /a = a^2

Putting it back together

a^2

------

3

9514 1404 393

Answer:

  4

Step-by-step explanation:

Substitute the given value for g(x) and solve the 2-step equation for x.

  g(x) = 3 + 5x

  23 = 3 +5x

  20 = 5x . . . . . . subtract 3

  4 = x . . . . . . . .  divide by 5

The value of x is 4 when g(x) is 23.

Answer: T-rex

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

AB + BC = AC

4m - 15 + 5m - 6 = 15

m - 21 = 15

m = 36

Answer:

14/30 gallons

Step-by-step explanation:

Answer:

X=-3

Step-by-step explanation:

-3^3 is -27

Answer:

x³ = -27

x³×⅓ = -3³

x = -3³×⅓

x = -3

Answer:

6 * k2

Step-by-step explanation:

Answer:

95.703

Step-by-step explanation:

If you could subscribe to penny_pg3d that would be great :>

Answer:

Your answer is 95.703!

Step-by-step explanation: To explain, It's easier to break apart the decimals and multiply that way step by step. I hope this helps you in future situations! Good luck on your test!

Answer:

zero

Step-by-step explanation:

if their are no students then how will the likes are given ...

Answer:

if their are no students then how will the likes are given ...

Step-by-step explanation:

Answer:

8.50 for 2 lb of ham is corecct it is less

Step-by-step explanation:do 4.29+4.29 which eqauls8.58

Answer:

8.50 for 2 pounds is a better deal

Step-by-step explanation:

If you went with 4.29 per pound you would have to pay 8¢ more than 8.50 . You would have to pay 8.58 instead

Answer:

It will take him 90 seconds

Step-by-step explanation:

Divide 72 by 4 and then multiply that by 5. that will show you  how many seconds it take him to walk 73 yards