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Arte-miy333 [17]

3 years ago

7

Find the area of each shape. Give awnser correct to one decimal place.

1 answer:

castortr0y [4]3 years ago

6 0

Whats the numbers to solve

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Ralph is an electrician. He charges an initial fee of $26, plus $31 per hour. If Ralph earned $119 on a job, how long did the jo

lubasha [3.4K]

3 hours

You can turn this into an equation:

F = 26 + 31t
Where F is the money Ralph earned, and t is the number of hours he worked.

Plugging in the 119 for F, we get
119 = 26 + 31t

93 = 31t

3 = t

5 0

3 years ago

The sum of two terms of gp is 6 and that of first four terms is 15/2.Find the sum of first six terms.

Gnoma [55]

Given:

The sum of two terms of GP is 6 and that of first four terms is $\dfrac{15}{2}.$

To find:

The sum of first six terms.

Solution:

We have,

$S_2=6$

$S_4=\dfrac{15}{2}$

Sum of first n terms of a GP is

$S_n=\dfrac{a(1-r^n)}{1-r}$ ...(i)

Putting n=2, we get

$S_2=\dfrac{a(1-r^2)}{1-r}$

$6=\dfrac{a(1-r)(1+r)}{1-r}$

$6=a(1+r)$ ...(ii)

Putting n=4, we get

$S_4=\dfrac{a(1-r^4)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1-r^2)(1+r^2)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1+r)(1-r)(1+r^2)}{1-r}$

$\dfrac{15}{2}=6(1+r^2)$ (Using (ii))

Divide both sides by 6.

$\dfrac{15}{12}=(1+r^2)$

$\dfrac{5}{4}-1=r^2$

$\dfrac{5-4}{4}=r^2$

$\dfrac{1}{4}=r^2$

Taking square root on both sides, we get

$\pm \sqrt{\dfrac{1}{4}}=r$

$\pm \dfrac{1}{2}=r$

$\pm 0.5=r$

Case 1: If r is positive, then using (ii) we get

$6=a(1+0.5)$

$6=a(1.5)$

$\dfrac{6}{1.5}=a$

$4=a$

The sum of first 6 terms is

$S_6=\dfrac{4(1-(0.5)^6)}{(1-0.5)}$

$S_6=\dfrac{4(1-0.015625)}{0.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Case 2: If r is negative, then using (ii) we get

$6=a(1-0.5)$

$6=a(0.5)$

$\dfrac{6}{0.5}=a$

$12=a$

The sum of first 6 terms is

$S_6=\dfrac{12(1-(-0.5)^6)}{(1+0.5)}$

$S_6=\dfrac{12(1-0.015625)}{1.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Therefore, the sum of the first six terms is 7.875.

5 0

3 years ago

Math problem need help if do 5 stars

NNADVOKAT [17]

Answer:

The ordered pair (15, 12) means that 15 pounds of beans cost $12.

Step-by-step explanation:

We know that the x-axis is the pounds of beans and the costs are the y-axis.

4 0

2 years ago

What is the length of the side opposite ZB?<br> 3 units<br> 4 units<br> 5 units<br> 6 units

Sedbober [7]

5 units is the length of the side opposite ZB

4 0

3 years ago

Find the common ratio and the explicit formula <br><br>-3, 9, -27, 81,

Fofino [41]

Answer:

see explanation

Step-by-step explanation:

These are the terms of a geometric sequence with n th term

$a_{n}\\$ = a $(r)^{n-1}$

where re a is the first term and r the common ratio

r = 9 ÷ - 3 = - 27 ÷ 9 = 81 ÷ - 27 = - 3 ← common ratio

and a = - 3, thus

[te x]a_{n}[/tex] = - 3 $(-3)^{n-1}$ ← explicit formula

6 0

3 years ago