Samuel bought 8 shirts for a total of $58. If tee shirts cost $6 and long sleeve shirts

Fernando has two equally-sized containers of clay which he is using to build a pyramid-like structure. The finished structure wi

evablogger [386]

Answer:

Fernando does not have enough clay to finish the structure since, the expressions for the volume left are not the same.

Step-by-step explanation:

Let w be the length of the longest slab. Since each slab is 2 inches less than the one beneath it, we have the width of the other 3 slabs as w - 2, w - 2 - 2 = w - 4 and w - 4 - 2 = w - 6 respectively.

Since the base of each slab is a square and has thickness 2 inches, the volume of each slab from largest to smallest is thus 2w², 2(w - 2)², 2(w - 4)² and 2(w - 6)² respectively.

We have that we have half of the container of clay left after forming the first two slabs(which are the bottom-most slabs). Let V be the volume of each clay container. Since we have half left, that is V/2, we have used 2V - V/2 = 3V/2 to make the two bottom-most slabs.

So, 3V/2 = 2w² + 2(w - 2)²

= 2w² + 2(w² - 4w + 4)

= 2w² + 2w² - 8w + 8

= 4w² - 8w + 8

= 4(w² - 2w + 2) (1)

Also we want to know if V/2 is equal to the volume of the two top-most slabs.

So, V/2 = 2(w - 4)² + 2(w - 6)²

= 2(w² - 8w + 16) + 2(w² - 12w + 36)

= 2w² - 16w + 32 + 2w² - 24w + 72

= 4w² - 40w + 104

= 4(w² - 10w + 26)

From (1) V/2 = 4(w² - 2w + 2)/3 ≠ 4(w² - 10w + 26)

<u>Since the expressions for the remaining volume are not the same, Fernando does not have enough clay to finish the structure.</u>

4 0

3 years ago

The students in Ms. Lorenzo’s class collected the following numbers of bottle caps:

gladu [14]

I am not sure how to show you how to do a dot plot on this website, but to see how to do a dot plot

b) Put everything in order and find the middle
10, 10, 10, 20, 30, 30, 30, 30, 40, 50, 50, 50, 60, 60, 70, 70, 2040
^^
So 40 is in the middle, making it the median

c) Add all of the values together and divide by the total number of values.
10 + 10 + 10 + 20 + 30 + 30 + 30 + 30 + 40 + 50 + 50 + 50 + 60 + 60 + 70 + 70 + 2040 = 2660
2660 / 17 = 156.5

5 0

3 years ago

What is 12 to 44 simlified

elena-s [515]

$\frac{12}{44}$ simplified is $\frac{3}{11}$

I got this by dividing both the numerator and denominator by 4

Hope this helps

-AaronWiseIsBae

7 0

3 years ago

Read 2 more answers

45 degreese is used in a pie chart to reperesent 6 people. How many people were there altogehter?

KatRina [158]

We can solve this problem by the rule of three.
A complete pie chart has 360º.

45º----------------------6 people
360º-------------------- x

x=(360º*6 people) / 45º=48 people.

Answer; 48 people.

6 0

4 years ago

1. Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the

Sveta_85 [38]

Answer:

#1) y = -4x + 1; #2) parallel; #3) y = -1/2x + 5/2; #4) y = 2x + 4; #5) Never

Step-by-step explanation:

#1) We want a line that passes through (1, -3) and is parallel to y = 2-4(x-1). First we simplify our equation using the distributive property:

y = 2-4(x-1) = 2-4(x) -4(-1) = 2-4x--4 = 2-4x + 4 = -4x + 6

Lines that are parallel have the same slope; this means we want a line through (1, -3) with a slope of -4. Using point-slope form,

$y-y_1=m(x-x_1)\\\\y--3=-4(x-1)\\\\y+3=-4(x)-4(-1)\\\\y+3=-4x+4\\\\y+3-3=-4x+4-3\\\\y=-4x+1$

#2) We must first write our second equation in slope-intercept form by isolating the y term:

2x+y=7

Subtract 2x from each side"

2x+y-2x = 7-2x

y = -2x+7

This means the slope is -2; the slopes are the same, so the lines are parallel.

#3) The slope of our given equation is 2. To be perpendicular, the second line must have a slope that is a negative reciprocal (flipped and opposite signs); this makes it -1/2. Using point-slope form,

$y-0=\frac{-1}{2}(x-5)\\\\y=\frac{-1}{2}(x)+\frac{-1}{2}(-5)\\\\y=\frac{-1}{2}x+\frac{5}{2}$

#4) The slope of Main Street on the diagram, found by using rise/run, is 2. This means the bike path will also have a slope of 2 in order to be parallel. The park entrance is at (0, 4). This makes the equation y = 2x+4.

#5) Two lines with the same slope are always parallel. They are never perpendicular.

3 0

3 years ago

Read 2 more answers