The longest side of an isosceles obtuse triangle measures 20 centimeters. The other two side lengths are congruent but unknown.What is the greatest possible whole-number value of the congruent side lengths?

A.9 cm
B.10 cm
C.14 cm
D.15 cm

Answers

Answer 1

Answer:

Since 9+9=19<20 and 10+10=20=20, the triangles with sides 9, 9, 20 and 10, 10, 20 cannot exist.

Use the cosine theorem to check which option C or D is true:

$20^2=14^2+14^2-2\cdot 14\cdot 14\cos \theta,\n 400=196+196-392\cos \theta,\n 8=-392\cos \theta,\n \n \cos \theta=-(8)/(392) =-(1)/(49)$ .

You have that cosine of the greatest angle (opposite to the greatest side) is negative, this means that angle is obtuse.

$20^2=15^2+15^2-2\cdot 15\cdot 15\cos \theta,\n 400=225+225-450\cos \theta,\n -50=-450\cos \theta,\n \n \cos \theta=(50)/(450) =(1)/(9)$ .

Here you have that cosine of the greatest angle (opposite to the greatest side) is posiative, this means that angle is acute.

Answer: the greatest possible whole-number value of the congruent side lengths is 14 (choice C)

Answer 2

Answer:

Answer:

Step-by-step explanation:

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Answers

well 3/5 = 0.60 in decimal form
and 4/12 when simplified is 1/3 which is .33 in decimal form
so jr shaded more.

Mary did she paid 0.33 or 1/3

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Answers

Answer:

540

Step-by-step explanation:

Answer:

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Step-by-step explanation:

have a amazing day peep's :]

Isla walked 3/4 miles each way to and from the school Wednesday. How many miles did Isla walk that day?

Answers

All you have to do is multiply 3/4 of a mile times two because she walked round trip. The answer is 1.5 miles

1 1/2 is the answer 1 and 1 half

Whats the gcf of 48 and 78

Answers

The greatest common factor (GCF) of 48 and 78 is: 6

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 78: 1, 2, 3, 6, 13, 26, 39

The common factors between the two numbers are 1, 2, 3, and 6, but considering 6 is the highest number out of them, it is the greatest common factor.

we must find prime factoriztion 4 getting GCF

FACTORS OF 48 : 1,2,3,4,6,8,12,16,24 & 48
FACTORS OF 78 : 1,2,3,6,13,26,39 & 78

WE can see the common factors of 48 and 78 are: 1,2,3 & 6
it means the GCF of 78 & 48 is 6

Describe how you regroup when you find the sum of 64 + 43?

Answers

To regroup, you simply break up the bigger numbers into smaller numbers that are more easily added together. We often regroup into numbers that end with 0 because they're easier to add. For example, you can break up 64 into 60 + 4 and 43 into 40 + 3. This will make addition easier, because you can first add together 60 and 40, which will equal 100. Then, you can add the smaller digits: 100 + 4 + 3 = 107.

Final answer:

Regrouping in addition, as in 64 + 43, involves adding numbers column by column from right to left. If the addition in a column results in a value of 10 or more, a 'carry over' or regrouping is done to the next column. The final resultant sum is 107.

Explanation:

To regroup when you find the sum of 64 + 43, you need to add the numbers column by column, moving from right (units) to left (tens, hundreds, etc.). In this case, add the right column (4 from 64 and 3 from 43) to get 7. Next, add the left column (6 from 64 and 4 from 43). The sum is 10. Since 10 is a two-digit number, the number in tens place (1) is carried over or regrouped to the tens column. To get the final answer, add the numbers in the tens column (including the carryover). This results in 107. In general, regrouping is a technique used in addition and subtraction to simplify calculations and solve problems more easily.