5/10 + 3/10 plz help!

(Sugg<br> eous equations.<br> 3x + 2y = 12<br> 4x – y = 5

Ostrovityanka [42]

Answer:

1 × (3x + 2y = 12)

2 × (4x - y = 5)

3x + 2y = 12

+ (8x - 2y = 10)

= 11x = 22

divide both sides by the coefficient of 'x' (11)

Therefore x = 2

put (x = 2) in equation 1

3(2) + 2y = 12

6 + 2y = 12

2y = 12 - 6

2y = 6

divide both sides by the coefficient of 'y'(2)

Therefore y = 3

7 0

3 years ago

<img src="https://tex.z-dn.net/?f=%24a%2Ba%20r%2Ba%20r%5E%7B2%7D%2B%5Cldots%20%5Cinfty%3D15%24%24a%5E%7B2%7D%2B%28a%20r%29%5E%7B

riadik2000 [5.3K]

Let

$S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n$

where we assume |r| < 1. Multiplying on both sides by r gives

$r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}$

and subtracting this from $S_n$ gives

$(1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}$

As n → ∞, the exponential term will converge to 0, and the partial sums $S_n$ will converge to

$\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}$

Now, we're given

$a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a$

$a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}$

We must have |r| < 1 since both sums converge, so

$\dfrac{15}a = \dfrac1{1-r}$

$\dfrac{150}{a^2} = \dfrac1{1-r^2}$

Solving for r by substitution, we have

$\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)$

$\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}$

Recalling the difference of squares identity, we have

$\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}$

We've already confirmed r ≠ 1, so we can simplify this to

$\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15$

It follows that

$\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12$

and so the sum we want is

$ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}$

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

7 0

2 years ago

I don’t understand this at all

LUCKY_DIMON [66]

Answer:

I think the answer is - 2 + ( 3/4) =2 3/4

Step-by-step explanation:

first of all we can take out the =-1 1/4 and - 1 3/4 email it's not it the correct place also - 2 1/4 because of the 1/4

4 0

3 years ago

PLEASE HELP WILL MARK BRAINLIEST!

nlexa [21]

Answer:

He did the equation backward. He did $\frac{x_2-x_1}{f(x_2)-f(x_1)}$ , which is wrong.

The actual equation for average rate of change is:

$\frac{f(x_2)-f(x_1)}{x_2-x_1} =$

$=\frac{18-8}{10-6}$

$=\frac{10}{4}$

$=\frac{5}{2}$

6 0

3 years ago

Read 2 more answers

A newsletter publisher believes that less than 29% of their readers own a Rolls Royce. Is there sufficient evidence at the 0.02

Lerok [7]

Answer:

For this case they want to proof if the proportion of readers own a Rolls royce is less than 0.29 and that wuld be the alternative hypothesis. The complement would represent the null hypothesis. Then the system of hypothesis for this case are:

Null hypothesis: $p \geq 0.29$

Alternative hypothesis: $p< 0.29$

Step-by-step explanation:

For this case they want to proof if the proportion of readers own a Rolls royce is less than 0.29 and that wuld be the alternative hypothesis. The complement would represent the null hypothesis. Then the system of hypothesis for this case are:

Null hypothesis: $p \geq 0.29$

Alternative hypothesis: $p< 0.29$

3 0

4 years ago