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3 years ago

For each line, state its slope and its y-intercept. x+4y=1

1 answer:

6 0

You want to write this in y=mx+b slope therefore isolate the y.
4y=-x+1 then simply divide by 4 to get y by itself.

y=-x/4+1/4.

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Devin used what he learned in clas to determine that for every 8 grams of oxygen in water, there is 1 gram of hydrogen

MAXImum [283]

And?... is that the question or is there more?

6 0

3 years ago

If $a$, $b$, $c$, and $d$ are replaced by four distinct digits from $1$ to $9$, inclusive, then what's the largest possible valu

Alexxx [7]

Answer:

Step-by-step explanation:

for the value of difference to be largest, the minuend should be maximum(most possibly) and the subtrahend should be minimum

[in A-B=X, A is minuend and B is subtrahend ]

so, $a.b should be maximum. as there is a condition that 4 digits should be distinct, the product will be maximum if we choose 2 maximum valued numbers from the given numbers. so, one of them should be 9 and the other should be 8.

therefore, $a.b=9*8=72

as mentioned above, c.d$ should be minimum. this will be possible only when we choose 2 minimum valued numbers from the given numbers. so, one of them should be 1 and the other should be 2.

therefore, c.d$ = 1*2 = 2

hence, the difference = 72-2 = 70

thus, the largest possible value of the difference $a.b - c.d$ = 70

7 0

3 years ago

Help me asap! I will give you marks

Law Incorporation [45]

Recall the binomial theorem.

$(a+b)^n = \displaystyle \sum_{k=0}^n \binom nk a^{n-k} b^k$

1. The binomial expansion of $\left(1+\frac x3\right)^7$ is

$\left(1 + \dfrac x3\right)^7 = \displaystyle\sum_{k=0}^7 \binom 7k 1^{7-k} \left(\frac x3\right)^k = \sum_{k=0}^7 \binom 7k \frac{x^k}{3^k}$

Observe that

$k = 1 \implies \dbinom 71 \left(\dfrac x3\right)^1 = \dfrac73 x$

$k = 2 \implies \dbinom 72 \left(\dfrac x3\right)^2 = \dfrac73 x^2$

When we multiply these by $8-9x$ ,

• $8$ and $\frac73 x^2$ combine to make $\frac{56}3 x^2$

• $-9x$ and $\frac73 x$ combine to make $-\frac{63}3 x^2 = -21x^2$

and the sum of these terms is

$\dfrac{56}3 x^2 - 21x^2 = \boxed{-\dfrac73 x^2}$

2. The binomial expansion is

$\left(2a - \dfrac b2\right)^8 = \displaystyle \sum_{k=0}^8 \binom 8k (2a)^{8-k} \left(-\frac b2\right)^k = \sum_{k=0}^8 \binom 8k 2^{8-2k} a^{8-k} b^k$

We get the $a^6b^2$ term when $k=2$ :

$k=2 \implies \dbinom 82 2^{8-2\cdot2} a^{8-2} b^2 = 28 \cdot2^4 a^6 b^2 = \boxed{448} \, a^6b^2$

6 0

1 year ago

8+3(5-1) =20 I am very confused on how this equals 20, someone please explain. thanks

soldier1979 [14.2K]

Step-by-step explanation:

first you have to do the subtraction in the parentheses so it's 8+3(4) and then you multiply the 3 by 4 (only the 3 because the 8 isn't next to the multiply) and then you have 12, add 8 and it's 20

7 0

3 years ago

58 = 7/4x well, basically I am really bad with fractions, and I'm supposed to do this on a computer, I don't have a calculator I

KiRa [710]

58=7/4x
Multiply both sides by 4 so the fraction cancels out:
232=7x
Divide both sides by 7:
x=33.14 (rounded)

Hope this helps :)

4 0

4 years ago