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Romashka-Z-Leto [24]

3 years ago

8

Explain the difference between AAS congruence and ASA

1 answer:

Orlov [11]3 years ago

7 0

ASA - If two pairs of angles of two triangles are equal in measurement, and the included sides are equal in length, then the triangles are congruent.

AAS - If two pairs of angles of two triangles are equal in measurement, and a pair of corresponding non-included sides are equal in length, then the triangles are congruent.

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Can someone help me with one of these or both ?

kifflom [539]

Answer: 280 for number 2

Step-by-step explanation: I think I ain’t not % sure

3 0

3 years ago

A box with a square base and open top must have a volume of 157216 cm3. We wish to find the dimensions of the box that minimize

shepuryov [24]

Answer:

Base Length of 68cm
Height of 34 cm.

Step-by-step explanation:

Given a box with a square base and an open top which must have a volume of 157216 cubic centimetre. We want to minimize the amount of material used.

Step 1:

Let the side length of the base =x

Let the height of the box =h

Since the box has a square base

Volume $=x^2h=157216$

$h=\dfrac{157216}{x^2}$

Surface Area of the box = Base Area + Area of 4 sides

$A(x,h)=x^2+4xh\\$Substitute h=\dfrac{157216}{x^2}\\A(x)=x^2+4x\left(\dfrac{157216}{x^2}\right)\\A(x)=\dfrac{x^3+628864}{x}$

Step 2: Find the derivative of A(x)

$If\:A(x)=\dfrac{x^3+628864}{x}\\A'(x)=\dfrac{2x^3-628864}{x^2}$

Step 3: Set A'(x)=0 and solve for x

$A'(x)=\dfrac{2x^3-628864}{x^2}=0\\2x^3-628864=0\\2x^3=628864\\x^3=314432\\x=\sqrt[3]{314432}\\ x=68$

Step 4: Verify that x=68 is a minimum value

We use the second derivative test

$If\:A(x)=\dfrac{x^3+628864}{x}\\A''(x)=\dfrac{2x^3+1257728}{x^3}\\$When x=68\\A''(x)=6$

Since the second derivative is positive at x=68, then it is a minimum point.

Recall:

$h=\dfrac{157216}{x^2}\\h=\dfrac{157216}{68^2}=34$

Therefore, the dimensions that minimizes the box surface area are:

Base Length of 68cm
Height of 34 cm.

3 0

3 years ago

Jay currently has a balance of $2,375 on her credit card. If she must make a minimum monthly payment of 5.8% of her total balanc

Papessa [141]

Answer:

$137.75

Step-by-step explanation:

question is 'what is 5.8% of 2375'

'what' means assign a variable

'is' means an equal sign

'of' means to multiply

p = .058 x 2375

p = 137.75

*You could do the following: p = 5.8 x 2375 and get 13775 but you have to remember to move the decimal point two places to the left

4 0

3 years ago

In an arithmetic sequence, the first term, a1, is equal to 3, and the fourth

777dan777 [17]

Answer:

a4=a1+(n-1)d

33=3+3d

30=3d

d=30/3

d=10

6 0

3 years ago

Which is the answer?

Tom [10]

Answer:

y=3x

Step-by-step explanation:

y=3x is the one according to values in the table

8 0

3 years ago