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3 years ago

Name one addition piece of information that is sufficient to prove that the triangles are similar. Please explain!

Mathematics

1 answer:

Sophie [7]3 years ago

8 0

Answer:

the given triangles are right triangles which is enough to prove them 'similar'

but not congruent.

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Round off the following numbers to the nearest thousand. 19. 674,620 20. 355,500

Oksana_A [137]

Answer:

1) 675,000.

2) 356,000

Step-by-step explanation:

There are some rules to round off to the nearest thousand.

1. While rounding off to the nearest thousand, if the digit in the hundreds place is between 0 – 4 i.e., < 5, then the hundreds place is replaced by ‘0’.

2. If the digit in the hundreds place is = to or > 5, then the hundreds place is replaced by ‘0’ and the thousands place is increased by 1.

We have given two numerals:

1) 674,620

According to the second rule defined the digit at the hundreds place is greater than 5 than the thousands place will be increased by 1.

The answer is 675,000.

2) 355,500

According to the second rule defined the digit at the hundreds place is greater than 5 than the thousands place will be increased by 1.

The answer is 356,000....

4 0

3 years ago

Please help me solve 8x+2y=32 and 10x-5y=-20

Tju [1.3M]

Answer:

(2,8)

x = 2

y = 8

Step-by-step explanation:

The steps are shown in the picture

7 0

3 years ago

If 30,000 cm2 of material is available to make a box with a square base and an open top, what is the largest possible volume (in

Cloud [144]

Answer:

The largest possible volume of the box is 2000000 cubic meters.

Step-by-step explanation:

The volume ( $V$ ), in cubic centimeters, and surface area ( $A_{s}$ ), in square centimeters, of the box with a square base are described below:

$A_{s} = l^{2}+h\cdot l$ (1)

$V = l^{2}\cdot h$ (2)

Where:

$l$ - Side length of the base, in centimeters.

$h$ - Height of the box, in centimeters.

By (2), we clear $h$ within the formula:

$h = \frac{V}{l^{2}}$

And we apply in (1) and simplify the resulting expression:

$A_{s} = l^{2}+ \frac{V}{l}$

$A_{s}\cdot l = l^{3}+V$

$V = A_{s}\cdot l -l^{3}$ (3)

Then, we find the first and second derivatives of this expression:

$V' = A_{s}-3\cdot l^{2}$ (4)

$V'' = -6\cdot l$ (5)

If $V' = 0$ and $A_{s} = 30000\,cm^{2}$ , then we find the critical value of the side length of the base is:

$30000-3\cdot l^{2} = 0$

$3\cdot l^{2} = 30000$

$l = 100\,cm$

Then, we evaluate this result in the expression of the second derivative:

$V'' = -600$

By Second Derivative Test, we conclude that critical value leads to an absolute maximum. The maximum possible volume of the box is:

$V = 30000\cdot l - l^{3}$

$V = 2000000\,cm^{3}$

The largest possible volume of the box is 2000000 cubic meters.

4 0

2 years ago

A vehicle is purchased for $18,000, with a down payment of $6,098. The balance in financed for three years at an annual rate of

mestny [16]

The Present value of an annuity is given by PV = P(1 - (1 + r/t)^-nt)/(r/t)
where: P is the monthly payment, r is the annual rate = 7% = 0.07, t is the number of periods in one year = 12 and n is the number of years = 3.

18,000 - 6,098 = P(1 - (1 + 0.07/12)^-(3 x 12)) / (0.07/12)
11,902 = P(1 - (1 + 0.07/12)^-36) / (0.07/12)
P = 0.07(11,902) / 12(1 - (1 + 0.07/12)^-36) = 367.50

Therefore, monthly payment = $367.50

7 0

2 years ago

Y equals 8 X equals 575 Solve for slope intercept y equals mx + b

zhannawk [14.2K]

y = 8

x = 575

We want to solve for b in the slope-intercept form y = mx + b.

To complete this problem, we need the value of m, the slope. If you know m, then just plug into y = mx + b this way:

8 = 575m + b

3 0

2 years ago