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AlexFokin [52]
3 years ago
6

Reed uses 8 pieces of glass per square foot to make a stained glass window. How many pieces of glass will he need to make a wind

ow that is 864 square inches?
Mathematics
1 answer:
laiz [17]3 years ago
8 0
To solve the problem posed in the statement we need to know the equivalence between squared foot and squared inches, and that is:
1 square foot = 144 square inches
So Reed uses 8 pieces of glass per 144 squared inches as well.
Now we can use a rule of three, simple and direct proportion to solve the question, it goes like this:
144 squared inches ------> 8 pieces glass
864 squared inches ------> x

x = (864)(8)/144
x = 48
Hence, Reed will use 48 pieces of glass to make a window that is 864 square inches.
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Just write an equation on each one
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What's a pair of equal ratios
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Y= 2x + 2 and y= 2x - 1
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Which rule represents the translation from the pre-image, ΔABC, to the image, ΔA'B'C'?
cluponka [151]

The rule represents the translation from the pre-image, ΔABC, to the image, ΔA'B'C' is (x, y) → (x + 7, y - 6).

<h3>What is translation?</h3>

When a line is translated, it means the line is moved from one position to another. The coordinate for triangle ABC are A(-3 ,4) , B(-4,1) and C(-2,1).

The coordinate of triangle A'B'C' is A'(4,-2), B'(3,-5), and C'(5,-5).

From above, it can be seen that the image A'B'C' is obtained from the pre-image ABC by translating the vertices of the image by 7 units to the right and 6 units down.

Therefore, the rule represents the translation from the pre-image, ΔABC, to the image, ΔA'B'C' is (x, y) → (x + 7, y - 6)

Hence, the rule represents the translation from the pre-image, ΔABC, to the image, ΔA'B'C' is (x, y) → (x + 7, y - 6).

Learn more about translation on:

brainly.com/question/12861087

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7 0
2 years ago
What property does the statement show? (4x8)x3=(8x4)x3
Mariana [72]
1. commutative property states that : a + b = b + a 

<span>2. 3x - 5 = 5x - 17 -- add 5 to both sides </span>
<span>3x = 5x - 17 + 5 -- subtract 5x from both sides </span>
<span>3x - 5x = -17 + 5 -- combine like terms </span>
<span>-2x = -12 -- divide both sides by -2 </span>
<span>x = 6 </span>

<span>3. slope formula : slope = (y2 - y1) / (x2 - x1) </span>
<span>(3,-1) x1 = 3 and y1 = -1 </span>
<span>(-2,-5) x2 = -2 and y2 = -5 </span>
<span>now we sub </span>
<span>slope = ((-5 - (-1)) / (-2 -3) </span>
<span>slope = (-5 + 1) / -5 </span>
<span>slope = -4/-5 </span>
<span>slope = 4/5 </span>

<span>4. x = first integer </span>
<span>x + 2 = 2nd integer </span>
<span>x + x + 2 = 80 -- combine like terms </span>
<span>2x + 2 = 80 -- subtract 2 from both sides </span>
<span>2x = 80 - 2 </span>
<span>2x = 78 -- divide both sides by 2 </span>
<span>x = 39 <== this is the smallest number </span>
<span>x + 2 = 41 </span>

<span>5. p = 1/2g - 3 </span>

<span>6. The union of two sets is all the numbers in both sets, no need to copy the same number more then once. Answer is : (1,2,3,4,5,6,8,10) </span>

<span>7. 2x + 3y <= 6 -- put in y = mx + b form </span>
<span>3y <= -2x + 6 </span>
<span>y <= -2/3x + 2 </span>
<span>In y = mx + b form, the y intercept is in the b position. So the y intercept is (0,2) </span>
<span>To find the x intercept, sub in 0 for y (change inequality sign to equal sign) </span>
<span>2x + 3y = 6 </span>
<span>2x + 3(0) = 6 </span>
<span>2x = 6 </span>
<span>x = 3 </span>
<span>x intercept is (3,0) </span>
<span>So plot your points (3,0) and (0,2) </span>
<span>Connect the points with a solid line because there is an equal sign in there. </span>
<span>Shade below the line because it is less then. </span>

<span>8. 3x + 6y = 8 </span>
<span>6y = -3x + 8 </span>
<span>y = -1/2x + 4/3 </span>

<span>y = 2x - 8 </span>

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<span>9. 7x + 3y - 2 + 6x + 1 + y^2 </span>
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<span>y = mx + b </span>
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<span>6 = 0(-2) + b </span>
<span>6 = b </span>

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<span>11. x + y = 5 -- put this in y = mx + b form, and the m position is your slope </span>
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<span>13. |a| + b --- (a = -1.4 and b = -2.7) </span>
<span>absolute values, whether they have a negative or not, they are always positive </span>
<span>|a| + b </span>
<span>|-1.4 | + (-2.7) </span>
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<span>14. I cannot see the problem </span>

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<span>-10y = 50 -- divide by -10 </span>
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<span>now sub -5 in for y in either of the original equations </span>
<span>x + 2y = -9 </span>
<span>x + 2(-5) = -9 </span>
<span>x - 10 = -9 </span>
<span>x = -9 + 10 </span>
<span>x = 1 </span>
<span>answer : x = 1 and y = -5 or (1,-5) </span>


<span>I was really bored so I thought I would just help out :)</span>
3 0
4 years ago
Read 2 more answers
Find all pairs of real numbers $(x,y)$ such that $x + y = 6$ and $x^2 + y^2 = 28$. if you find more than one pair, then list you
vivado [14]
1. x^2+y^2=28 and x+y=6

2.  x^2+y^2 and x+y remind us of the formula: (x+y)^{2}= x^2+y^2+2xy

substituting we get: 

 6^{2}= 28+2xy

2xy=36-28
xy=8/2=4

3 Let's solve the system of equations i)x+y=6 and ii)xy=4

substitute y=4/x in (i): 

x+ \frac{4}{x} =6

multiply all sides by x:

x^{2} +4=6x

x^{2} -6x+4=0

complete the square:

x^{2} -6x+4=x^{2} -2*3x+9-9+4= (x-3)^{2}-5=0

x-3=\sqrt{5} or x-3=-\sqrt{5} 

x=3+\sqrt{5} or x=3-\sqrt{5}

so from x+y=6, y=6-x

case 1,  x=3+\sqrt{5} gives y=3-\sqrt{5}

case 2, x=3-\sqrt{5} gives y=3+\sqrt{5} 


Answer: 

(3-\sqrt{5}, 3+\sqrt{5}), (3+\sqrt{5},  3-\sqrt{5})
3 0
3 years ago
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