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tia_tia [17]
3 years ago
8

A and B are supplementary angles. If A= (4x – 30)° and m

Mathematics
1 answer:
AfilCa [17]3 years ago
3 0

Answer:

82 degrees

Step-by-step explanation:

Hope this helps! ^^

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If <img src="https://tex.z-dn.net/?f=%20300cm%5E%7B2%7D%20" id="TexFormula1" title=" 300cm^{2} " alt=" 300cm^{2} " align="absmid
Artist 52 [7]
Check the picture below.  Recall, is an open-top box, so, the top is not part of the surface area, of the 300 cm².  Also, recall, the base is a square, thus, length = width = x.

\bf \textit{volume of a rectangular prism}\\\\&#10;V=lwh\quad &#10;\begin{cases}&#10;l = length\\&#10;w=width\\&#10;h=height\\&#10;-----\\&#10;w=l=x&#10;\end{cases}\implies V=xxh\implies \boxed{V=x^2h}\\\\&#10;-------------------------------\\\\&#10;\textit{surface area}\\\\&#10;S=4xh+x^2\implies 300=4xh+x^2\implies \cfrac{300-x^2}{4x}=h&#10;\\\\\\&#10;\boxed{\cfrac{75}{x}-\cfrac{x}{4}=h}\\\\&#10;-------------------------------\\\\&#10;V=x^2\left( \cfrac{75}{x}-\cfrac{x}{4} \right)\implies V(x)=75x-\cfrac{1}{4}x^3

so.. that'd be the V(x) for such box, now, where is the maximum point at?

\bf V(x)=75x-\cfrac{1}{4}x^3\implies \cfrac{dV}{dx}=75-\cfrac{3}{4}x^2\implies 0=75-\cfrac{3}{4}x^2&#10;\\\\\\&#10;\cfrac{3}{4}x^2=75\implies 3x^2=300\implies x^2=\cfrac{300}{3}\implies x^2=100&#10;\\\\\\&#10;x=\pm10\impliedby \textit{is a length unit, so we can dismiss -10}\qquad \boxed{x=10}

now, let's check if it's a maximum point at 10, by doing a first-derivative test on it.  Check the second picture below.

so, the volume will then be at   \bf V(10)=75(10)-\cfrac{1}{4}(10)^3\implies V(10)=500 \ cm^3

6 0
3 years ago
Is 33, 56, and 66 and right triangle
GenaCL600 [577]

Answer:

No

Step-by-step explanation:

If you mean they are the sides lengths,

33^2+ 56^2 != 66^2

3136 != 4356

7 0
3 years ago
Triangle ABC is located on a coordinate plane. Triangle ABC is transformed to create triangle A'B'C using the rule described bel
lara [203]

Answer:

What grade is this

Step-by-step explanation:

I can give you the answer but you have to be patient like 30 min

3 0
3 years ago
I need help ASAP!!!!
Ad libitum [116K]

Step-by-step explanation:

Kindly find 4 attached files

The proportionality is determined by the lines that only passes through the origin

And all the lines drawn are passing through the origin

So by either one of the 2 ways

By using rule of direct variation y=kx that has no y intercept

Or by finding the equation of straight line and find the slope with neglecting the y intercept since it's 0

5 0
2 years ago
Anthony has 15 coins, all of which are quarters and dimes. In all, they're worth $3.60. How many of each kind of coin does Antho
Usimov [2.4K]

Answer:

1 Dime

14 Quarters

Step-by-step explanation:

d + q = 15

0.10d + 0.25q = 3.60

d = 15 - q

0.10d + 0.25q = 3.60

0.10(15 - q) + 0.25q = 3.60

1.5 - 0.10q + 0.25q = 3.60

0.15q = 3.60 - 1.5

0.15q = 2.1

0.15q/0.15 = 2.1/0.15

q = 14

d = 15 - q

d = 15 - 14

d = 1

8 0
3 years ago
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