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3 years ago

What is the discriminant of 9х2 + 2 = 10x?

1 answer:

5 0

$\bf 9x^2+2=10x\implies 9x^2-10x+2=0 \\\\[-0.35em] ~\dotfill\\\\ \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{9}x^2\stackrel{\stackrel{b}{\downarrow }}{-10}x\stackrel{\stackrel{c}{\downarrow }}{+2}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}~~\checkmark\\ negative&\textit{no solution} \end{cases} \\\\\\ (-10)^2-4(9)(2)\implies 100-72\implies 28$

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Helena wrote the equation using point-slope form for the line that passes through the points (5, 1) and (3, 5). Analyze the step

viva [34]

Answer:

In step 2, she didn’t use an x and y from the same coordinate pair

Step-by-step explanation:

see the attached figure to better understand the problem

we have the points (5, 1) and (3, 5)

step 1

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute

$m=\frac{5-1}{3-5}$

$m=\frac{4}{-2}$

$m=-2$

step 2

The equation of the line in point slope form is

$y-y1=m(x-x1)$

take the point (3,5)

$m=-2$

substitute

$y-5=-2(x-3)$

$y-5=-2x+6$

$y=-2x+6+5$

step 3

$y=-2x+11$

therefore

In step 2, she didn’t use an x and y from the same coordinate pair

3 0

3 years ago

Read 2 more answers

Ted has $3.90. He has only dimes and quarters. He has 27 coins altogether. How many of each does he have

mestny [16]

Answer: 8 quarters 19 dimes

Step-by-step explanation:

we already know 8+19=27, if 4 quarters equals a dollar then you use 4 quarters each to create 2 dollars.

then, use 10 dimes to create another dollar summing it up to $3. now all we have to do is make 90 cents, and we've already used 18 coins.

if we used another 9 dimes, that would equal 90 cents.

in conclusion, 4+4= 8

8+10= 18

18+9= 27, and having $3.90

6 0

3 years ago

Solve for q. 3(q − 7) = 27 q =

Whitepunk [10]

Answer:

The answer is, q = 16.

Step-by-step explanation:

1) Divide both sides by 3.

$q - 7 = \frac{27}{3}$

2) Simplify 27/3 to 9.

$q - 7 = 9$

3) Add 7 to both sides.

$q = 9 + 7$

4) Simplify 9 + 7 to 16.

$q = 16$

Therefor, the answer is q = 16.

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3 years ago

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Alabama Instruments Company has set up a production line to manufacture a new calculator. The rate of production of these calcul

umka21 [38]

Answer:

The number of calculators is 4871

Step-by-step explanation:

If we integrate dx/dt we get x, which is the number of calculators. To find the number of calculators between the beginning of third week to the end of fourth week (the beginning of fifth week), this integration must be evaluated at t between 3 and 5.

$x=\int\limits^5_3 {\frac{dx}{dt}} \, dt =\int\limits^5_3 {5000(1-\frac{100}{(t+10)^2})} \, dt$