1.) 2x + y = 3 2.) x - 2y = -1 If equation 1 is multiplied by 2 and then the equations are added, the result is

BaLLatris [955]

Here , we are provided with a table which shows 5 consecutive terms of an arithmetic sequence . But before solving further , let's recall that ;

The n'th term of a Arithmetic Sequence let's say it be ${\sf T_n}$ is given by ;

${\boxed{\bf T_{n}=T_{1}+(n-1)d}}$

Where , d is the common difference

Now , here we are given with ;

${\quad \qquad \sf \blacktriangleright \blacktriangleright \blacktriangleright T_{1}=8 \: and \: T_{5}=-4}$

We have to find the 2nd , 3rd and 4th term respectively ,

Now , by using the above formula , 5th term can be written as ;

${: \implies \quad \sf T_{1}+(5-1)d=T_{5}}$

Putting the values and transposing 1st term to RHS , we have ;

${: \implies \quad \sf 4d = -4-8}$

${: \implies \quad \sf d=-\dfrac{12}{4}}$

${: \implies \quad \sf d=-3}$

Now , as we got the common difference , so we can find out the missing terms now ;

${: \implies \quad \sf T_{2}= T_{1}+(2-1)d}$

${: \implies \quad \sf T_{2}= 8 +d}$

${: \implies \quad \sf T_{2}= 8-3}$

${: \implies \quad \bf \therefore \: T_{2}= 5}$

Now

${: \implies \quad \sf T_{3}= T_{1}+(3-1)d}$

${: \implies \quad \sf T_{3}= 8 +2d}$

${: \implies \quad \sf T_{3}= 8-6}$

${: \implies \quad \bf \therefore \: T_{3}= 2}$

Also ,

${: \implies \quad \sf T_{4}= T_{1}+(4-1)d}$

${: \implies \quad \sf T_{4}= 8 +3d}$

${: \implies \quad \sf T_{4}= 8-9}$

${: \implies \quad \bf \therefore \: T_{4}= -1}$

Now , The given table can be written as ;

${\begin{array}{|c|c|c|c|c|c|}\cline{1-6} \bf n & \sf 1 & 2 & 3 & 4 & 5 \\ \cline{1-6} \bf T_{n} & \sf 8 & 5 & 2 & -1 & -4 \end{array}}$

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8 0

2 years ago

Martina took out a loan for 7 months and was charged simple interest at an annual rate of 7.2%. The total interest she pald on t

ycow [4]

Answer:

70 thats it bro

8 0

2 years ago

Triangles PQR and XYZ are similar triangles. Which are the other two angle measures of triangle XYZ?

Julli [10]

Angle Z = Angle R = 35 degrees

Angle Y = 180-70-35 = 180-105 = 75

35 & 75 degrees

5 0

3 years ago

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What is the average (arithmetic mean) of eleven consecutive integers? (1) the average of the first nine integers is 7. (2) the a

laiz [17]

Since eleven is odd, there must be a centra element, which in this case is the sixth. So, we can write 11 consecutive integers as

$x-5, x-4, x-3, x-2, x-1, x, x+1, x+2, x+3, x+4, x+5$

Since the arithmetic mean is the sum of the values, divided by how many they are, we have

$M = \dfrac{x-5, x-4, x-3, x-2, x-1, x, x+1, x+2, x+3, x+4, x+5}{11} = \dfrac{11x}{11} = x$

So, the mean of 11 consecutive integers is the 6th integer.

4 0

3 years ago

Riko wants to find the distance between the points (−2, −3) and (2, −5). His work is shown. StartAbsoluteValue negative 3 EndAbs

swat32

Answer:

Riko is wrong because she uses the wrong formula.

Step-by-step explanation:

Given the coordinate points (-2, -3) and (2, -5)

We are to find the distance between the two points

Using the formula:

D = √(x2-x1)²+(y2-y1)²

From the coordinates x1 = -2, y1 = -3, x2 = 2 and y2 = -5

Substitute

D = √(2-(-2))²+(-5-(-3))²

D= √(4)²+(-2)²

D = √16 + 4

D = √20

D = √4*√5

D = 2√5

This shows that Riko is wrong because she uses the wrong formula.

7 0

2 years ago

Read 2 more answers