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vagabundo [1.1K]
3 years ago
10

In the diagram below, m A = 59°, m B = 55° and m C = 78°. Find m D.​

Mathematics
1 answer:
masya89 [10]3 years ago
3 0

Answer:

D=36

Step-by-step explanation:

All angles of the triangle add up to 180. Subtract 180-59-55=66

Then the missing measurement is a vertical which means that E=66.

So then 180-78-66=36

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Two children own two-way radios that have a maximum range of 3 miles. One leaves a certain point at 1:00 P.M., walking due north
Grace [21]

Answer:

The answer is 21 minutes

Step-by-step explanation:

We use the equation Xf = Xo + vt

1) At 1:00 PM, child one leaves the starting point heading north at a constant velocity of 6 mi/hr or .1 [mi/min] (divide by 60 to convert from [mi/hr] to [mi/min])

2) He walks for 15 minutes before kid 2 starts walking. In 15 minutes he is able to cover 1.5 [mi]

  • x_{1f1} =x_{o} +v_{1} t_{1} \\x_{1f1} =0+.1(15)\\x_{1f1} =1.5 [mi]

3) Now, child 2 starts walking and we know that when the range reaches 3 miles, they won´t be able to communicate. So the sum of the final position of child 1 and child 2 must be 3[mi]

  • Child 1 final position => x_{1f} = x_{1f1} +v_{1} t\\x_{1f} =1.5+v_{1} t
  • Child 2 final position => x_{2f} =0+v_{2} t

4) Sum the equations and equate to 3

  • x_{1f} +x_{2f} =3

5) Substitute the values we already know

  • 1.5+v_{1} t+v_{2}t=3\\ 1.5+.1t+.15t=3\\1.5+.25t=3\\t=\frac{3-1.5}{.25} \\t=6 [min]

6) in 15 + 6 minutes they will be 3miles apart

7) In 21 minutes they will still be able to communicate with one another.

7 0
3 years ago
An expecting mother wants to convert a corner of the nursery in her house into a rectangular playpen by enclosing the corner of
Elena-2011 [213]

  10=1+9            1x9=9
   =2+8            2x8=16
   =3+7            3x7=21
   =4+6            4x6=24
   =5+5            5x5=25
↑ Left: the possible measurements of the two fences, Right: the possible areas

out of the areas calculated, 25 sq feet is the maximum. :)

Ans: 25 square feet


5 0
3 years ago
3x^2 -5x -2=0
Kipish [7]

Answer:

Step-by-step explanation:

1. Find two numbers that add to make the coefficient of x (in this case, -5) and that multiply to make the constant term multiplied by the coefficient of x^2 (in this case, -2 x 3 = -6)

Two numbers that work are -6 and +1

-6 x +1 = -6

-6 + -1 = -5

2. Split the middle term into the two numbers that you found.

3x^2 -6x +x -2 = 0

I've put the -6 on the left side because in our next step, when we factorise, it will be easier than having the numbers the other way around.

3. Factorise the left side by taking out common factors from each pair. The pairs I'm talking about here are '3x^2 and -6x', and 'x and -2'

3x (x-2) +1 (x-2) = 0

4. You now have two numbers both being multiplied by the term x-2. We can rearrange this equation to give us two brackets being multiplied by each other.

(3x + 1) (x-2) = 0

5. According to the Null Factor Law, if two terms are multiplied together and the result is 0, then one of those terms must be 0. Make both terms equal to 0 and solve each for x.

3x + 1 = 0              x-2 = 0

3x = -1                   x = 2

x = -1/3

6. The solutions to this equation are x = 2 and x = -1/3

6 0
3 years ago
Read 2 more answers
The real car is 8 feet long and the model is 6 inches long. What is the ratio of the length of the car to the length of the mode
Lubov Fominskaja [6]
6 : 8
hope this helps ^^
8 0
2 years ago
The average hourly wage of computer programmers with 2 years of experience has been $21.80.Because of high demand for computer p
svp [43]

Answer:

d. H0: μ <= 21.80 Ha: μ > 21.80

Step-by-step explanation:

We set the null hypothesis as what is already given . We are already informed that the average wage is equal to  μ <= 21.80 against the claim that is required. It is required to test whether the average wage of the computer programmers is greater than μ > 21.80

So option d is the best answer.

Hypotheses testing is done  using an observation and a claim. The observation is set as a null hypothesis and claim is set as an alternative hypothesis. The null and alternative hypotheses must be chosen wisely to get the correct results.

The critical region is dependent on the claim set.

5 0
3 years ago
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