Academic Q & A

Question 1

Christian V. asked: An isosceles trapezoid has a perimeter of 35 km. Its shorter base measures 12 km and its longer base measures 15 km. The two remaining sides have the same length; what is that length?

Accepted Answer

A great way to begin the process of solving this type of (geometry) question is to visualize/draw it. Draw an isosceles trapezoid and label the 4 sides with the information provided: 2 of the side lengths are equal but unknown, so "x" for each. The perimeter of your trapezoid = the sum of the lengths of its 4 sides (x + x + 12 + 15 = 35). Simplified that's
2x + 27 = 35 >>>2x = 35 - 27 >>>2x = 8 >>>x = 4.

Question 2

ESL class asked: Are there times where "wanna" sounds weird in everyday speech? To illustrate: She wants to try the new ice cream & She wanna try the new ice cream. Are both equally common in everday speech?

Accepted Answer

Use "wanna" ONLY in everyday/informal speech. Or avoid it in everyday speech but be prepared to hear it. You're not gonna find it, I mean not going to find it, in anything formal (a business letter or email, on your resume, in a job interview)

That said, "I wanna try the ice cream" is pretty common

"She wanna try the ice cream" sounds weird

"You wanna come with me?" and "Does she wanna come with us?" sound pretty common

"I'm gonna go to the beach on Sunday" and "She's gonna go to the beach on Sunday" both sound "OK" to me (again, as a question of everyday/informal speech)

Or this one: "I'ma say that I'm sure you're gonna wanna try the new flavor of ice cream. It's sooo good!"

Question 3

Araceli G. asked: The clown's flamboyant costume sparkled with sequins, rustled with ribbons, and sported a dozen bright colors. Based on context clues in the sentence, what does flamboyant mean: Expensive, Handmade, Pretty, or Gaudy?

Accepted Answer

The sentence is full of context clues that should grab your attention: "sparkled, " "sequins," "rustled with ribbons," and "a dozen bright colors." Those clues should call to mind a picture of something over-the-top, extravagant, glittery, shiny, etc. IOW, an elaborate, colorful display.

If you're not sure what "gaudy" means, can you effectively eliminate the other 3 choices based on the context clues?

Question 4

Abhi B. asked: The first side of a triangle is 6 cm shorter than the second side. The third side is three times the first side. If the perimeter of the triangle is 31 cm, how long is each side?

Accepted Answer

Since side 1 is compared to side 2, call side 2 "x" and go from there

Length of side 1 is 6 cm shorter than side 2, side 2 is "x", so side 1 = x -6

Length of side 3 is three times the length of side 1, side 1 = x - 6, so side 3 = 3(x-6) = 3x-18

Now, add all three sides and set equal to the given perimeter (31)

(x) + (x -6) + (3x -18) =31

Combine like terms: 5x-24=31

Add 24 to both sides: 5x =55

Divide by 5 on both sides, solve for x

x = 11 (second side length)

You can now solve for the other 2 sides

Check that the sum of your 3 sides = 31

Question 5

Lilly R. asked: What are 2 numbers that have a sum of -2 and a product of -48?

Accepted Answer

Here's a good start. While you might be able to run a few numbers through your head (the factors of 48, for example) and “trial & error" your way to a solution, you (your teacher) want to solve it algebraically. A sum of -2 means two numbers add to -2 or x + y = -2. A product of -48 means the two numbers multiply to -48 or xy (x times y) = -48. This is a system of equations problem: x+y=-2 & xy=-48. Solve for x in the first equation: (x = -2-y). Substitution . . . if x=-2-y, you can substitute that into the product equation. Here xy = -48 becomes (-2-y)(y) = -48. Distribute the y: -2y-y^2 = -48. Gather the terms on the left side of the equation and multiply through by -1 to get: y^ 2 + 2y -48 = 0. You can solve this obvious quadratic equation using the Quadratic Formula . . . but first . . . check to see if you can factor (Hint: Don't use the quadratic formula!) Here's where I'll leave it to you. Did you get it? If you need help with factoring and/or using the QF, don’t hesitate to contact me

Question 6

Deepa J. asked: Mandy read 365 pages in a day. She read 4 times as many pages at night as in the morning. How many pages did she read in the morning?

Accepted Answer

Bar modeling is a great approach here. Draw one bar/box to represent the pages Mandy read in the morning and four equal sized bars/boxes for the night (she read four times as many pages at night). Each of the five bars/boxes represents the same # of pages read (i.e., 1/5 of the total). The sum of the five bars/boxes = 365 pages. The question re: pages read in the morning asks, in effect, "What is one of your 5 bars/boxes worth?" Think: 5 times "something" = 365 or . . . 365 divided by 5 = # of pages read in the morning. Once you get the # of pages read in the morning, multiply that by 4 to get # of pages read at night. Add the two (morning pages + evening pages) and you should get 365. Here’s where I’ll leave it to you.
If you're looking for a strictly algebraic solution, consider: x + 4x = 365; 5x = 365; x = 73 (morning) and 4x = 292 (night)

Question 7

Jennifer M. asked: The square of the distance between a guy wire and a pylon along the ground is 90,000 feet. The square of the height of the pylon is 160,000 feet. What is the length of the guy wire from the top of the pylon to the ground?

Accepted Answer

The word problem is laying out the Pythagorean Theorem (a^2+b^2=c^2 ). Sketch a right triangle with these measurements: a = base of right triangle (distance along the ground), b = height of pylon, c = hypotenuse (side opposite the right angle, the longest of the 3 sides, in this case c = guy wire). Now, a^2 = 90,000 (given), b^2 = 160,000 (given), and 90,000 + 160,000 = c^2 (length of guy wire^2 ). 250,000 = c^2 Take the √ of both sides of the equation. Guy wire length = _____ ft. Here’s where I’ll leave it to you. Did you get it? If you need help with the Pythagorean Theorem or geometry in general, don’t hesitate to contact me