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Math Knowledge

Solve for x:
x² - 5x - 6 = 0

-1 or 6

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

x² - 5x - 6 = 0
(x + 1)(x - 6) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (x + 1) or (x - 6) must equal zero:

If (x + 1) = 0, x must equal -1
If (x - 6) = 0, x must equal 6

So the solution is that x = -1 or 6

Arithmetic Reasoning

On average, the center for a basketball team hits 50% of his shots while a guard on the same team hits 60% of his shots. If the guard takes 25 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?

If the guard hits 60% of his shots and takes 25 shots he'll make:

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{60}{100} \) = \( \frac{60 x 25}{100} \) = \( \frac{1500}{100} \) = 15 shots

The center makes 50% of his shots so he'll have to take:

shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)

to make as many shots as the guard. Plugging in values for the center gives us:

center shots taken = \( \frac{15}{\frac{50}{100}} \) = 15 x \( \frac{100}{50} \) = \( \frac{15 x 100}{50} \) = \( \frac{1500}{50} \) = 30 shots

to make the same number of shots as the guard and thus score the same number of points.

Electronics Information

Use Ohm's Law to calculate the value of current in this circuit if voltage is 240 volts and resistance is 40 Ω.

6 A

Ohm's law specifies the relationship between voltage (V), current (I), and resistance (R) in an electrical circuit: V = IR.

Solved for current, I = \( \frac{V}{R} \) = \( \frac{240}{40} \) = 6 A

General Science

Which of these parts of digestion takes place in the mouth?

breaking down starches

Digestion begins in the mouth where the teeth and tongue break down food mechanically through chewing and saliva, via the enzyme salivary amylase, starts to break starches down chemically. From the mouth, food travels down the esophagus where contractions push the food into the stomach.

Arithmetic Reasoning

What is \( \frac{3}{3} \) - \( \frac{5}{5} \)?

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]. The first few multiples they share are [15, 30, 45, 60, 75] making 15 the smallest multiple 3 and 5 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{3 x 5}{3 x 5} \) - \( \frac{5 x 3}{5 x 3} \)

\( \frac{15}{15} \) - \( \frac{15}{15} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{15 - 15}{15} \) = \( \frac{0}{15} \) =

Word Knowledge

Nurture most nearly means:

foster

To further the development of.

Electronics Information

The valence shell of a semiconductor is how full of electrons?

half full

Semiconductors have valence shells that are exacly half full and can conduct electricity under some conditions but not others. This property makes them useful for the control of electrical current.

General Science

In cell biology, cytokinesis results in two separate:

cells

During cell division, the cytokinesis phase occurs when cytoplasm and cell membranes complete their separation resulting in two separate cells.

Shop Information

A __________ is driven by a motor and used to shape and form edge contours.

router

A router is a tool that a worker uses to rout (hollow out), shape, or contour an area in relatively hard material like wood or plastic.

Word Knowledge

Turmoil most nearly means:

chaos

Extreme confusion, agitation.