9514 1404 393
Answer:
10°, 80°
Step-by-step explanation:
<em><u>Setup</u></em>
Let x and y represent the measures of the two acute angles in the right triangle.
From your knowledge of right triangles, you know the two acute angles are complementary:
x + y = 90
The problem statement gives you another relation:
x = 2(y + 30) . . . . twice the sum ...
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<em><u>Solution</u></em>
The second equation gives you an expression for x that can be substituted into the first equation.
(2(y +30)) + y = 90
3y +60 = 90 . . . . . . . . collect terms
3y = 30 . . . . . . . . . subtract 60
y = 10 . . . . . . . . divide by 3
x = 2(y +30) = 2(40) = 80
The two angles are 10° and 80°.
You need to subtract the two cutouts on each side, so the side of the box would be 24- 2x. X would then become the height of the box once folded.
The volume is found by multiplying the 4 dimensions:
The volume becomes x(24-2x)^2
Now take the derivative of the formula to solve for x
Dv/dx= (24-2x)^2 + x^2(24-2x)*-2
= 24-2x(24-2x-4x)=0
X =12 or 4
24-2x = 24-2(4) = 24-8=16
Volume = 16 x 16 x 4 = 1024 cubic inches.
Answer:
Step-by-step explanation:
Since the smaller triangles have a side of the same length, they share one side, and the included angle is 90°, the triangles are congruent.
This means the length of the side to the left is also x as shown in the image below.
The bigger triangle is also right and has side lengths of x, x, and 6 (the hypotenuse), thus:
Operating:
Since 18=9*2
The options are not clear enough, so I cannot make a choice.
Answer:
The margin of error of the poll is 8%.
Step-by-step explanation:
This is a confidence interval. A confidence interval has both a lower end and an upper end.
The true proportion is the midpoint between the two ends.
The margin of error is the absolute difference between the proportion and the ends(which is the same, upper end - proportion = proportion - lower end),
In this problem, we have that:
The lower end is 52%.
The upper end is 68%.
The proportion is (52 + 68)/2 = 60%.
The margin of error is 60 - 52 = 68 - 60 = 8%.
9514 1404 393
Answer:
16
Step-by-step explanation:
The values in each row of the table have a total of 45. If Hans plants 29 daisies, he likely will plant ...
45 -29 = 16 . . . snapdragons
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One can also find the answer by extending the table 2 more rows. Each x entry increases by 1 as each y entry decreases by 1. Then the number of snapdragons listed in the second added row will be 14+2 = 16.
