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3 years ago

Find the sum of the first 50 terms of the sequence -6, -2, 2, 6

Mathematics

1 answer:

monitta3 years ago

4 0

Answer:

4600

Step-by-step explanation:

STEP 1: Determine type of progression

$d1 = - 2 - ( - 6) \\ d1 = 4 \\ \\ d2 = 2 - ( - 2) \\ d2 = 4$

Since d1 = d2, it is Arithmetic progression, with a common difference of 4

STEP 2: Evaluate the sum

$s = \frac{n}{2} (2a + (n - 1)d) \\ s = \frac{50}{2} (2( - 6) + (50 - 1)4) \\ s = 4600$

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Find equation of a line through (1,4) and (1,6)

Elena L [17]

Notice the picture below

no matter what value "y" may have, "x" will always be 1

4 0

3 years ago

3(x - 6) + 6 = 5x - 6. what is the solution

4vir4ik [10]

Answer:

x=-3

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3(x−6)+6=5x−6

(3)(x)+(3)(−6)+6=5x+−6(Distribute)

3x+−18+6=5x+−6

(3x)+(−18+6)=5x−6(Combine Like Terms)

3x+−12=5x−6

3x−12=5x−6

Step 2: Subtract 5x from both sides.

3x−12−5x=5x−6−5x

−2x−12=−6

Step 3: Add 12 to both sides.

−2x−12+12=−6+12

−2x=6

Step 4: Divide both sides by -2.

−2x

−2

x=−3

7 0

3 years ago

Read 2 more answers

If the area of a rectangle in terms of x is x2 + 15x + 26 / 6x2 and its width is x2 - 3x - 10 / 30x3 Find the length of the rect

Veseljchak [2.6K]

Answer:

The length of the rectangle is;

5x(x+13)/(x-5)

Step-by-step explanation:

Mathematically, we know that the area of a rectangle is the product of the length and width of the triangle

To find the length of the rectangle, we will have to divide the area by the width

we have this as;

(x^2 + 15x + 26)/6x^2 divided by (x^2-3x-10)/30x^3

thus, we have ;

(x^2 + 15x + 26)/6x^2 * 30x^3/(x^2-3x-10)

= (x^2+15x+ 26)/(x^2-3x-10) * 5x

But;

(x^2 + 15x + 26) = (x+ 2)(x+ 13)

(x^2-3x-10) = (x+2)(x-5)

Substituting the linear products in place of the trinomials, we have;

(x+2)(x+13)/(x+2)(x-5) * 5x

= 5x(x+13)/(x-5)

4 0

3 years ago

Round to the nearest hundredth 42.052

Vera_Pavlovna [14]

42.052

place value and digits:

4 = tens
2 = ones
0 = tenths
5 = hundredths
2 = thousandths

5 is in the hundredths place. To find if you round up or down, look at the digit to the right (thousandths in this case). It is a 2, which is less than 5, so you round down.

42.052 rounded to the nearest hundredth is 42.05

hope this helps

8 0

3 years ago

Ella invested $2,700 in an account paying an interest rate of 5.4% compounded

Dmitry [639]

Answer:

The account will take 7 years to reach a value of $4,020

Step-by-step explanation:

Compound Interest

When it occurs interest in the next period is then earned on the principal sum plus previously accumulated interest.

The formula is:

$A=P\left(1+{\frac {r}{n}}\right)^{nt}$