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2 years ago

*REMEMBER THAT IN STANDARD FORM YOU DONT USE FRACTIONS!!

Mathematics

1 answer:

Basile [38]2 years ago

3 0

Standard form for a linear equation (highest degree is 1), is Ax+By=C;

y-1=(-2/3)(x-4) <-- expand and isolate y
y-1=-2/3x+8/3
y=-2/3x+(8/3+1)
y=-2/3x+(8/3+3/3)
y=-2/3x+11/3 <---remove fraction;
3y=-2x+11 <-- rearrange to given format
2x+3y=11

Hope I helped :)

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PLEASE HELP ILL MARK BRAINLIEST !!!

Alexus [3.1K]

Answer:

a) the common difference is 20

b) $x_8=115 , x_{12}=195$

c) the common difference is -13

d) $a_{12}=52, a_{15}=13$

Step-by-step explanation:

a) what is the common difference of the sequence xn

Looking at the table, we get x_3=16, x_4=36 and x_5= 56

Deterring the common difference by subtracting x_4 from x_3 we get

36-16 =20

So, the common difference is 20

b) what is x_8? what is x_12

The formula used is: $x_n=x_1+(n-1)d$

We know common difference d= 20, we need to find $x_1$

Using $x_3=16$ we can find $x_1$

$x_n=x_1+(n-1)d\\x_3=x_1+(3-1)d\\15=x_1+2(20)\\15=x_1+40\\x_1=15-40\\x_1=-25$

So, We have $x_1 = -25$

Now finding $x_8$

$x_n=x_1+(n-1)d\\x_8=x_1+(8-1)d\\x_8=-25+7(20)\\x_8=-25+140\\x_8=115$

So, $\mathbf{x_8=115}$

Now finding $x_{12}$

$x_n=x_1+(n-1)d\\x_{12}=x_1+(12-1)d\\x_{12}=-25+11(20)\\x_{12}=-25+220\\x_{12}=195$

So, $\mathbf{x_{12}=195}$

c) what is the common difference of the sequence $a_m$

Looking at the table, we get a_7=104, a_8=91 and a_9= 78

Deterring the common difference by subtracting a_7 from a_8 we get

91-104 =-13

So, the common difference is -13

d) what is a_12? what is a_15?

The formula used is: $a_n=a_1+(n-1)d$

We know common difference d= -13, we need to find $a_1$

Using $a_7=104$ we can find $x_1$

$a_n=a_1+(n-1)d\\a_7=a_1+(7-1)d\\104=a_1+7(-13)\\104=a_1-91\\a_1=104+91\\a_1=195$

So, We have $a_1 = 195$

Now finding $a_{12}$ , put n=12

$a_n=a_1+(n-1)d\\a_{12}=a_1+(12-1)d\\a_{12}=195+11(-13)\\a_{12}=195-143\\a_{12}=52$

So, $\mathbf{a_{12}=52}$

Now finding $a_{15}$ , put n=15

$a_n=a_1+(n-1)d\\a_{15}=a_1+(15-1)d\\a_{15}=195+14(-13)\\a_{15}=195-182\\a_{15}=13$

So, $\mathbf{a_{15}=13}$

5 0

3 years ago

Which of the following expression has a terminating decimal?

mrs_skeptik [129]

Answer:

1.# = 119.2 2.# = 869.545454545 3.# = 443.66666666 4.# = 13501.3939394

Step-by-step explanation:

i don't know about the 2 one and 3 and 4 one that came up a very big number. I used a calculator though.exactly way you tired to tipe it in sorry it took so long to answer the problem!!!.

7 0

2 years ago

Given two terms in artimetic sequence find the common difference, the 52 term, and the explicit formula. A15=139 and A30=259

quester [9]

139, 149, 159, 169, 179, 189, 199, 209, 219, 229, 239, 249, 259.

The common difference is 13.

Let n = 52

Let d = common difference

a_52 = 139 + (52 - 1)(13)

a_52 = 139 + (51)(13)

a_52 = 139 + 663

a_52 = 802

4 0

3 years ago

Write an expression for: 9 less than the product of 12 and a number x

Aleksandr [31]

The product of 12 and x can be displayed as 12x

9 less than 12x is displayed as 12x - 9

Answer: 12x - 9

8 0

3 years ago

Help me on number problem 1 please

Mandarinka [93]

Answer: y = 3x-1

Step-by-step explanation: I was never the best at doing this, but here it goes...

first start with the formula Y2-Y1/X2-X1 for this problem, lets say your Y2 is -1, your Y1 is 5, your X2 is 0, and your X1 is 2, making your equation -1-5/0-2 which equals -6/-2, which can be qritten as 3. this is your slope.

now take the equation Y-Y1 = M (X-X1) m is your slope, which is 3 in this case as stated above. your X1 is2, your Y1 is 5. plug this in and you get

y-5 = 3 (x-2) which you put into slope intercept form, which is y = mx + b

your answer should be y = 3x-1

6 0

2 years ago