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3 years ago

Write the following equation in the general form Ax+ By + C= 0.

Mathematics

1 answer:

Mama L [17]3 years ago

6 0

Answer:

1/2 y - 1/3 x -1 = 0

Multiply through by the LCD -6 to clear the fractions and the negative coefficient with the 'x'.

-3y + 2x + 6 = 0

Then reorder

2x - 3y + 6 = 0

Step-by-step explanation:

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The first two terms in an arithmetic progression are -2 and 5. The last term in the progression is the only number in the progre

Rudik [331]

Given:

The first two terms in an arithmetic progression are -2 and 5.

The last term in the progression is the only number in the progression that is greater than 200.

To find:

The sum of all the terms in the progression.

Solution:

We have,

First term : $a=-2$

Common difference : $d = 5 - (-2)$

$= 5 + 2$

$= 7$

nth term of an A.P. is

$a_n=a+(n-1)d$

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

$a_n=-2+(n-1)(7)$

According to the equation, $a_n>200$ .

$-2+(n-1)(7)>200$

$(n-1)(7)>200+2$

$(n-1)(7)>202$

Divide both sides by 7.

$(n-1)>28.857$

Add 1 on both sides.

$n>29.857$

So, least possible integer value is 30. It means, A.P. has 30 term.

Sum of n terms of an A.P. is

$S_n=\dfrac{n}{2}[2a+(n-1)d]$

Substituting n=30, a=-2 and d=7, we get

$S_{30}=\dfrac{30}{2}[2(-2)+(30-1)7]$

$S_{30}=15[-4+(29)7]$

$S_{30}=15[-4+203]$

$S_{30}=15(199)$

$S_{30}=2985$

Therefore, the sum of all the terms in the progression is 2985.

6 0

3 years ago

Type the correct answer in the box.

Akimi4 [234]

Answer:

$\huge\boxed{-8+8i}$

Step-by-step explanation:

$2(-36-3i)+(5+2i)(12-2i)\\\\\text{use the distributive property and FOIL}\\\\=(2)(-36)+(2)(-3i)+(5)(12)+(5)(-2i)+(2i)(12)+(2i)(-2i)\\\\=-72-6i+60-10i+24i-4i^2\\\\i=\sqrt{-1}\to i^2=-1\\\\=-72-6i+60-10i+24i-4(-1)=-72-6i+60-10i+24i+4\\\\=(-72+60+4)+(-6-10+24)=-8+8i$

7 0

3 years ago

Carla has already written 10 pages of a novel. she plans to write 15 additional pages per month until she is finished. write and

grin007 [14]

Linear Equation: 15m+10=w
15 pages written for every month for 5 months plus the 10 pages she has already written is equal to the total number of pages written in 5 months.
m= number months written. In this case, it is 5 months.
w= number of pages written in 5 months
15(5)+10=w
75+10=w
85 pages written=w
Carla will have written 85 pages in 5 months.

4 0

3 years ago

each row has a starting cart that it 4 feet long if this row is 43 feet long how many total carts are in it

Margaret [11]

Answer:

43/4 = 10.25 which rounds to the nearest whole number of 10 total carts

5 0

2 years ago

Please someone help, give the right answer it’s important

KonstantinChe [14]

Step-by-step explanation:

Please see the attached picture and I hope I have given the right answer.