(20pts=5pts each) For parts (a)–(d) answer the questions and complete the statements in the space provided: line EC ∩ line AC ∩ line BC = C , m∠ECA=32°, m∠CEF=150°

Answer:

3/4   and  2/5 have a common denominator of 20, so re-write

15/20x - 2 = 8/20       Now multiply both sides by 20

15x-40 = 8

Step-by-step explanation:

Answer:

The minimum amount of time required is 74.7 seconds.

Step-by-step explanation:

The question can be solved in two cases:

i. diagonal swimming of Brandon across the river

ii. Running of the rest distance by Brandon.

Case I: Since he would swim diagonally across the river, then the diagonal distance can be determined by applying appropriate trigonometric function.

Let the diagonal be represented by x, an included angle θ = [tex]45^{o}[/tex] is formed at his starting point (angle formed by the diagonal and the length of the width of the river).

So that:

Cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]

Cos [tex]45^{o}[/tex] = [tex]\frac{70}{x}[/tex]

x = [tex]\frac{70}{Cos 45^{o} }[/tex]

  = 98.995

x = 99 m

The diagonal distance covered by Brandon is 99 m.

The time to cover this distance can be calculated by:

speed = [tex]\frac{distance}{time}[/tex]

time = [tex]\frac{distance}{speed}[/tex]

Given that his swimming rate is 2 m/s, then:

time = [tex]\frac{99}{2}[/tex]

        = 49.5

The time taken by Brandon to swim diagonally is 49.5 seconds.

Case II: Since he want to cover a total distance of 250 m;

remaining distance to be covered = 250 - 99

                                                         = 151

time = [tex]\frac{distance}{speed}[/tex]

Given that he runs at 6 m/s, then;

time = [tex]\frac{151}{6}[/tex]

       = 25.1667

The time taken by Brandon to run the remaining distance is 25.2 seconds.

The minimum amount of time required = time taken by Brandon to swim diagonally + time taken by Brandon to run the remaining distance

                                 = 49.5 + 25.2

                                 = 74.7

The minimum amount of time required is 74.7 seconds.

Minimum amount of time to reach the desired point is   79.5 s

Brandon is on one side of a river

The width of the river =  70 m

Brandon wants to reach a point that is 250 m downstream of opposite side as quickly as possible by swimming diagonally across the river then running the rest of the way.

The swimming speed of Brandon =   2 m/s

The speed of running of Brandon = 6 m/s

Let us consider that the included angle be 45°

[tex]\rm cos \; \theta = \dfrac{70}{x} \\\\cos \; 45 = \dfrac{70}{x} \\\x = \dfrac{70}{0.707} \approx 99[/tex]

So the distance traveled by Brandon in water is 99 m

As the swimming speed of Brandon is given 2 m/s

So the time taken by Brandon to cross the river is given as follows

[tex]\rm Time = \dfrac{Distance}{Speed}[/tex]

[tex]\rm Time \; to\; cross\; the\; river = \dfrac{99}{2} = 49.5 \; s[/tex]

Let the horizontal distance covered by Brandon by swimming is H

So from Pythagorean theorem we can write

[tex]\rm H = \sqrt{99^2 -70^2 } = 70[/tex]

The distance that is left to be traveled by running is  250 - 70 = 180 m  

So  Time taken in running to reach the point by running = 180/6 = 30 s

So the  time to reach the desired point = 49.5 + 30 =   79.5 s

For more information please refer to the link given below

https://brainly.com/question/14930619

Answer:

42

Step-by-step explanation:

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Answer:

2/3

Step-by-step explanation:

The fractions which are equivalent to the fraction [tex]\frac{9}{6}[/tex] from the given options are [tex]\frac{3}{2}[/tex] and [tex]\frac{12}{8}[/tex], which are options (A) and (C).

Given a fraction [tex]\frac{9}{6}[/tex].

It is required to find the fraction which is equivalent to the given fraction.

If two fractions are equivalent, then they will be proportional.

The fraction [tex]\frac{9}{6}[/tex] can be written as [tex]\frac{3*3}{2*3}[/tex].

Here, when 3 gets canceled, the resulting fraction is [tex]\frac{3}{2}[/tex].

So, [tex]\frac{3}{2}[/tex]  is equivalent to [tex]\frac{9}{6}[/tex].

And, [tex]\frac{3}{2}[/tex] is the simplest fraction that cannot be simplified further.

So, any number multiplied by it both on the numerator and denominator will be an equivalent fraction.

Multiplying both the numerator and denominator of the fraction [tex]\frac{3}{2}[/tex] by 4, the resulting fraction is [tex]\frac{12}{8}[/tex].

Hence, the correct options are (A) and (C).

Learn more about Fractions here :

https://brainly.com/question/29796627

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The complete question is given below.

Which fractions are equivalent to [tex]\frac{9}{6}[/tex]?

(A) [tex]\frac{3}{2}[/tex]

(B) [tex]\frac{4}{5}[/tex]

(C) [tex]\frac{12}{8}[/tex]

(D) [tex]\frac{10}{8}[/tex]

Answer:

I think it's 4 gigabytes

Step-by-step explanation:

He only wants to pay 65$ and he already spends 45$ on his phone already. So you only have 20 dollars until his grand totaly of 65$ so 5x4= 20 so he can only use 4 gigabytes. Does that make sense? Hope I helped eheh

Answer:

-150 points cause 200-350= -150

Step-by-step explanation:

Can i have brainliest i've never got one before

Answer: the are no values of y that make it true

Step-by-step explanation: no solution

Answer:

-4/7

Step-by-step explanation:

Answer:

The slope would be 2

Step-by-step explanation:

Answer:

82.19

Step-by-step explanation:

Answer:

108quartz

Step-by-step explanation:

Volume of a cylinder = πr²h

r is the radius

h is the height

If A cylindrical container can hold 4 quarts of water, then;

4 = πr²h ...... 1

Let the volume be x of the radius and height at tripled

h1 = 3h

r1 = 3r

X = πr1²h1

X = π(3r)²(3h)

X = 9πr²(3h)

X = 27πr²h .... 2

Divide 1 by 2

4/x = πr²h/27πr²h

4/x = 1/27

Cross multiply

x = 4×27

x = 108

Hence the container can hold 108quartz of water of the radius and height was tripled.

Answer:

5 twenty's 1 five

Step-by-step explanation:

20 x 5 = 100

100 = 5 = 105

Answer:

hb=4√3

Step-by-step explanation:

Answer:

AB = 8, HB = 6, Area of ∆ABC = 8[tex]\sqrt{3}[/tex], Perimeter of ∆ABC = 12 + 4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

To find AB:

∆ABC is an 30,60,90∆

Using the theorem, you can find AB = 2AC = 2*4 = 8

AB = 8

To find HB:

You need to find AH to subtract from AB

Construct CH, a perpendicular bisector to side AB

From before you can put together that m∠CAB = 60°

∆ACH is an 30,60,90∆

Using this method again, AH = AC/2 = 4/2 = 2

Then you subtract AH from AB = 8-2 = 6

HB = 6

To find the area of ∆ABC:

You use the (base*height)/2 method

base = AB = 8

to find the height, CH, you need to use the Pytha Theorem

and get [tex]AH^{2}+CH^{2}=AC^{2}[/tex]

then substitute, and get [tex]2^{2} + CH^{2} = 4^{2}[/tex]

calculate and get CH = 2[tex]\sqrt{3}[/tex]

then the height = CH =  2[tex]\sqrt{3}[/tex]

solve the area and get

Area of ∆ABC = 8[tex]\sqrt{3}[/tex]

(optional perimeter)

to find perimeter of ∆ABC:

you add AC + CB + AB

you find CB by using opposite to 30°

CB = CH*2 = 2[tex]\sqrt{3}[/tex]*2 = 4[tex]\sqrt3}[/tex]

so AC + CB + AB = 4 + 4[tex]\sqrt3}[/tex] + 8

Perimeter of ∆ABC = 12 + 4[tex]\sqrt3}[/tex]

Hope this helps!!

Answer:

y = 2x + 6

slope = 2

y intercept = 6

Answer:

15/41

There are 41 marbles and 15 of them are red so you have a 15/41 chance to pick out a red as that is how many of them there are as compared to the total

Answer:

D

Step-by-step explanation:

Subtract 60 from 80 to get 20, and divide 20 by 80 to get 1/4, which can be converted to 25%.

Answer:

i think its D but im not exactly sure

Answer:

1/4 en pedazos seria 1/4 en pedazos

Step-by-step explanation:

la pregunta no tiene sentido

Answer: La fracción un cuarto, escrita en símbolos como 1/4, significa "una pieza, donde se necesitan cuatro piezas para formar un todo". La fracción un cuarto, escrita en símbolos como 1/4, significa "una pieza, donde se necesitan 4 piezas para formar un todo".

Step-by-step explanation:

Answer:

0.4% people

Step-by-step explanation:

Convert fraction (ratio) 24 / 6,000 Answer: 0.4%

Answer:

0.4%

Step-by-step explanation:

Answer:

4.5 ounces of yellow and 7.5 ounces of blue will create 12 ounces of the perfect shade of green.

Step-by-step explanation:

1.5 + 2.5 = 4 ounces.

Multiply by 3

4.5 + 7.5 = 12 ounces

So, she needs 4.5 ounces of yellow.

Answer:

huh

Step-by-step explanation:

Answer:

mid point=(-1/2,-5)

Step-by-step explanation:

c? i think its c (Sorry if iim wrong)

Answer:

The answer is D

Step-by-step explanation:

Answer:

892 Books.

Step-by-step explanation:

It says there are three times as many books in the town library than the school, which means you would have to divide the amount of books in the town library by three.

Answer:

-33

Step-by-step explanation:

2(-2)^3 -7(-2)^2 -5(-2) +1

-16 -28 +11

= -33

I hope it is helpful for you

Answer:

the answer is 1

Step-by-step explanation: i took the test on k12 hope this helps

Answer:  [tex]b^2[/tex]

You can write this as b^2

===================================================

Work Shown:

[tex]c = \frac{(ab^5)^{1/2}}{(ab)^{1/2}}\\\\c = \left(\frac{ab^5}{ab}\right)^{1/2}\\\\c = \left(b^4\right)^{1/2}\\\\c = b^{4*1/2}\\\\c = b^{2}\\\\[/tex]

there could be a calculator online to solve it