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2 years ago

The interior angle measures of a convex pentagon are consecutive multiples of 4. find the measure of each interior angle.

Mathematics

1 answer:

lawyer [7]2 years ago

3 0

Answer:

100°, 104°, 108°, 112°,116°

Step-by-step explanation:

Let the smallest angle be $4x$ . Since, the interior angles are consecutive, the other angles are $4(x+1)$ , $4(x+2)$ , $4(x+3)$ and $4(x+4)$ .

Sum of interior angles = 540°

$4x+4(x+1)+4(x+2)+4(x+3)+4(x+4)=540$ °

$20x+40=540$ °

$20x=(540-40)$ °

$20x=500$ °

$x=(500/20)$ °

$x=25$

Using the value of x to calculate the angles:

$4x=4*25=100$ °

$4(x+1)=4*26=104$ °

$4(x+2)=4*27=108$ °

$4(x+3)=4*28=112$ °

$4(x+4)=4*29=116$ °

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walnut grower estimates from past records that if 20 trees are planted per acre, then each tree will average 60 pounds of nuts p

laila [671]

Answer:

5 trees should be planted to maximize the yield per acre,

The maximum yield would be 1250

Step-by-step explanation:

Given,

The original number of trees per acre = 20,

Average pounds of nuts by a tree = 60,

Let x be the times of increment in number of trees,

So, the new number of trees planted per acre = 20 + x

∵ for each additional tree planted per acre, the average yield per tree drops 2 pounds,

So, the new number of pounds of nut = (60 - 2x)

Thus, the total yield per acre,

$Y(x) = (20+x)(60-2x)$

Differentiating with respect to t ( time ),

$Y'(x) = (20+x)(-2) + 60 - 2x = -40 - 2x + 60 - 2x = 20 - 4x$

Again differentiating with respect to t,

$Y''(x) = -4$

For maxima or minima,

$Y'(x) = 0$

⇒ 20 - 4x = 0

⇒ 20 = 4x

⇒ x = 5,

For x = 5, Y''(x) = negative,

Hence, Y(x) is maximum for x = 5,

And, maximum value of Y(x) = (20+5)(60 - 10) = 25(50) = 1250,

i.e. 5 trees should be planted to maximize the yield per acre,

and the maximum yield would be 1250 pounds

4 0

2 years ago

A farmer ordered 3/4 ton of soil. He wants to divide it evenly into 8 flower beds. How much will he have for each bed?

nasty-shy [4]

We know that
<span>Total soil--------> 3/4 ton
</span><span>divide it by 8
(3/4)/8----> 3/(4*8)----> 3/32 ton----> 0.09375 ton----> multiply by 1000---> 93.75 kg

the answer is
</span>93.75 kg f<span>or each bed</span>

7 0

2 years ago

I need help with these please... anyone?

Svetlanka [38]

The total measure of the interior angles of each figure will be:

180 (n-2) = 180 (4 - 2) = 360

Now add all those angles and set them equal to 360.

41 + 133 + 86 + x = 360

x is the unknown angle.

260 + x = 360
x = 100

The missing angle that is Not labeled in any of the figure is 100°

Hope this helps :)

8 0

2 years ago

Equivalent to 4^7•4^-5

nekit [7.7K]

Answer:

Step-by-step explanation:

$\text{Use}\ a^n\cdot a^m=a^{n+m}\\\\4^7\cdot4^{-5}=4^{7+(-5)}=4^{7-5}=4^2=4\cdot4=16$