All categories

3 years ago

7x^2-31x+20 I Know The Answer, I Just Don't Know The Steps To Solving This Equation.

2 answers:

7 0

$7x^2-31x+20=0$
First, remove the coefficient by division
So
$\frac{7x^2}{7}-\frac{31x}{7}+\frac{20}{7}=0$
Then, cancel out $\frac{20}{7}$
So,
$x^2-\frac{31x}{7}+\frac{20}{7}-\frac{20}{7}=-\frac{20}{7}$
Then take half of the coefficient, then square it.
$\frac{-\frac{31}{7}}{2}=\frac{37}{14}$
$(-\frac{37}{14})^2=\frac{961}{196}$
So, The equation already looks like this:
$x^2-\frac{31}{7}+\frac{961}{196}=-\frac{20}{7}+\frac{961}{196}$
So,
$x^2-\frac{31}{7}+\frac{961}{196}=\frac{401}{196}$
Then factor the left side of the equation:
$(x-\frac{31}{14})^2=\frac{401}{196}$
Then square both sides:
$x-\frac{31}{14}=\sqrt{\frac{401}{196}}$

svet-max [94.6K]3 years ago

5 0

$7x^2-31x+20=0\\
\\
\Delta=(-31)^2-4.7.20=961-560=401\\
\\
x=\frac{31 \pmsqrt{401}}{2*7}=\frac{31 \pm\sqrt{401}}{14}$

You might be interested in

Ben is the youngest of four children. Bob is 5 years older than Ben, Bridget is twice as old as Bob, and Brian is 3 years younge

TEA [102]

Answer:tD

Step-by-step explanation:

5 0

3 years ago

Nancy walked 516 yards in 6 minutes and then another 368 yards in 4 minutes. What was Nancy's average speed? * A. 89 yd/min B. 8

Rina8888 [55]

Average speed = (total distance covered) / (time to cover the whole distance)

Total distance = (516 + 368) = 884 yards
Total time = (6 + 4) = 10 minutes

Average speed = (884 yards) / (10 minutes)

Average speed = 88.4 yards/minute (C)

Other ways to write the same speed:

-- 4.42 feet/second
-- 265.2 feet/minute
-- 53.04 inches/second
-- 5,304 yards/hour
-- 3.014 mph (rounded)
-- 810.07 furlong/fortnight

7 0

3 years ago

Find dy/dx by implicit differentiation for x + 2y = xy.

Stella [2.4K]

Ok to find dy/dx of x+2y=xy we take derivative of both sides with respect to x

1+2dy/dx = x*dy/dx +y*dx/dx
1+ 2dy/dx = x*dy/dx + y* 1
2dy/dx +1 = x*dy/dx + y

2y’ + 1 = xy’ + y

2y’ + 1 - xy’ = y

2y’ -xy’ = y - 1

y’(2-x) = y - 1

so we get finally

y’= (y-1)/(2-x)

Hope this helps you understand the concept! Any questions please ask! Thank you so much!!

4 0

3 years ago

How many terms of the arithmetic sequence {1,22,43,64,85,…} will give a sum of 2332? Show all steps including the formulas used

MA_775_DIABLO [31]

There's a slight problem with your question, but we'll get to that...

Consecutive terms of the sequence are separated by a fixed difference of 21 (22 = 1 + 21, 43 = 22 + 21, 64 = 43 + 21, and so on), so the n-th term of the sequence, a (n), is given recursively by

• a (1) = 1

• a (n) = a (n - 1) + 21 … … … for n > 1

We can find the explicit rule for the sequence by iterative substitution:

a (2) = a (1) + 21

a (3) = a (2) + 21 = (a (1) + 21) + 21 = a (1) + 2×21

a (4) = a (3) + 21 = (a (1) + 2×21) + 21 = a (1) + 3×21

and so on, with the general pattern

a (n) = a (1) + 21 (n - 1) = 21n - 20

Now, we're told that the sum of some number N of terms in this sequence is 2332. In other words, the N-th partial sum of the sequence is

a (1) + a (2) + a (3) + … + a (N - 1) + a (N) = 2332

or more compactly,

$\displaystyle\sum_{n=1}^N a(n) = 2332$

It's important to note that N must be some positive integer.

Replace a (n) by the explicit rule:

$\displaystyle\sum_{n=1}^N (21n-20) = 2332$

Expand the sum on the left as

$\displaystyle 21 \sum_{n=1}^N n-20\sum_{n=1}^N1 = 2332$

and recall the formulas,

$\displaystyle\sum_{k=1}^n1=\underbrace{1+1+\cdots+1}_{n\text{ times}}=n$

$\displaystyle\sum_{k=1}^nk=1+2+3+\cdots+n=\frac{n(n+1)}2$

So the sum of the first N terms of a (n) is such that

21 × N (N + 1)/2 - 20N = 2332

Solve for N :

21 (N ² + N) - 40N = 4664

21 N ² - 19 N - 4664 = 0

Now for the problem I mentioned at the start: this polynomial has no rational roots, and instead

N = (19 ± √392,137)/42 ≈ -14.45 or 15.36

so there is no positive integer N for which the first N terms of the sum add up to 2332.

4 0

2 years ago

If the measure of angle 4 is 43 degrees, then the measure of angle 6 is -------

marta [7]

Answer:

degrees and the measure of angle 5 is -------- degrees. The measure of angl

Step-by-step explanation:

3 0

3 years ago