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hammer [34]
2 years ago
6

How did the beetle uncover the ants secret plan?

Mathematics
1 answer:
SpyIntel [72]2 years ago
8 0
It bugged its phone.
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In isosceles △ABC (AC = BC) with base angle 30° CD is a median. How long is the leg of △ABC, if sum of the perimeters of △ACD an
SIZIF [17.4K]

Note necessary facts about isosceles triangle ABC:

  • The median CD drawn to the base AB is also an altitude to tha base in isosceles triangle (CD⊥AB). This gives you that triangles ACD and BCD are congruent right triangles with hypotenuses AC and BC, respectively.
  • The legs AB and BC of isosceles triangle ABC are congruent, AC=BC.
  • Angles at the base AB are congruent, m∠A=m∠B=30°.

1. Consider right triangle ACD. The adjacent angle to the leg AD is 30°, so the hypotenuse AC is twice the opposite leg CD to the angle A.

AC=2CD.

2. Consider right triangle BCD. The adjacent angle to the leg BD is 30°, so the hypotenuse BC is twice the opposite leg CD to the angle B.

BC=2CD.

3. Find the perimeters of triangles ACD, BCD and ABC:

P_{ACD}=AC+CD+AD=2CD+CD+AD=3CD+AD;

P_{BCD}=BC+CD+BD=2CD+CD+AD=3CD+AD;

P_{ABC}=AC+BC+AB=2CD+2CD+AD+BD=4CD+2AD.

4.  If sum of the perimeters of △ACD and △BCD is 20 cm more than the perimeter of △ABC, then

P_{ACD}+P_{BCD}=P_{ABC}+20,\\ \\3CD+AD+3CD+AD=4CD+2AD+20,\\ \\6CD+2AD=4CD+2AD+20,\\ \\2CD=20.

5. Since AC=BC=2CD, then the legs AC and BC of isosceles triangles have length 20 cm.

Answer: 20 cm.

8 0
2 years ago
Read 2 more answers
What does the digit 7 represent in 170,280?
Sidana [21]

Answer:

that is the ten thousands place

Step-by-step explanation:

3 0
2 years ago
The price of products may increase due to inflation and decrease due to depreciation. Derek is studying the change in the price
BaLLatris [955]
For product A, the product is increasing, for the bigger the number you plug into x (due to the fact that the numbers become bigger because of the time: year 1, year 2, etc)
Product A is 82% change rate, while 
product B is 983.45/4 = 245.8625,  1756.16/3 = <span>585.3867</span>
Product B is 245.8625/585.3867
product B is 42% change rate

Product A change rate is higher than Product B by 40%

hope this helps
3 0
2 years ago
a car rental service rently purchased all new vehicles .to help cover the cost ,rental rates have to increase 26% from the norma
ruslelena [56]

Answer:

The new rate should be $56.67 per day

Step-by-step explanation:

Proportion states that the two fractions or ratios are equal.

As per the statement:

Normal rate per day = $45

To find the new rate:

Let new rate be x per day

By definition of proportion:

\frac{126}{100} = \frac{x}{45}

By cross multiply we have;

100x = 126 \times 45

Divide both sides by 100 we get;

x = \frac{126 \times 45}{100}

Simplify:

x = $56.7

Therefore, the new rate should be $56.7 per day




5 0
2 years ago
Find the x value 2x=6
sleet_krkn [62]

Answer:

x = 3

Step-by-step explanation:

2x = 6

x = 3 (Because we divide on both sides by 2 so that the x is by itself, 6/2 = 3)

7 0
2 years ago
Read 2 more answers
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