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2 years ago

What three points are solutions to 2x-y =4

Mathematics

1 answer:

DochEvi [55]2 years ago

5 0

Answer:

Attached file

Step-by-step explanation:

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Lily swims for 5 hours in stream that has a current of 1 mph. She leaves her dock, swims upstream for 2 miles and then swim back

antiseptic1488 [7]

Answer:

Swimming speed in still water is approximately 1.5 mph

Step-by-step explanation:

Given the speed of the current = 1 mph

distance she swims upstream =2 miles,

the total time = 5 hours.

She swam 2 miles upstream against the current and 2 miles back to the dock with the current. The formula that relates distance, time, and rate is $d = r t\ \ \ \ or \ \ \ t= \frac{d}{r}$

Let x be the speed in still water.

Then her speed with the current is x + 1, and

her speed against the current is x – 1.

Total time is equal to 2 miles with upstream and 2 miles downstream.

$\frac{2}{x+1}+\frac{2}{x-1}=5\\\\\frac{2(x-1)}{(x+1)(x-1)}+\frac{2(x+1)}{(x-1)(x+1)}=5\\\\\frac{2x-2}{(x^2-1)}+\frac{2x+2)}{(x^2-1)}=5\\\\\frac{2x-2+2x+2)}{(x^2-1)}=5\\\\4x=5(x^2-1)\\4x= 5x^2-5\\0= 5x^2-4x-5$

Now Using quadratic formula to solve above equation we get;

$x= \frac{-b \±\sqrt{b^2-4ac}} {2a}\\\\here \ \ a= 5,b=-4,c=-5\\\\x= \frac{-(-4) \±\sqrt{(-4)^2-4\times 5\times-5}} {2\times5}\\\\x=\frac{4 \±\sqrt{16+100}} {10}\\\\x=\frac{4 \±\sqrt{116}} {10}=x=\frac{4 \±2\sqrt{29}} {10}= x=\frac{2 \±\sqrt{29}} {5}\\ x \approx 1.5 \ or \ x = -0.7$

Since speed must be positive, Hence speed of still water is about 1.5 miles per hour.

3 0

3 years ago

Find the value of x in the isosceles triangle shown below.

Reptile [31]

Answer:

x=10

Step-by-step explanation:

We can use the Pythagorean theorem to find x

The height meets the base at a right angle

The base is bisected ( cut in half) so the base is 6 the height is 8

a^2 + b^2 = c^2

6^2 + 8^2 = x^2

36+64 = x^2

100 = x^2

Taking the square root of each side

sqrt(100) = sqrt(x^2)

10 = x

4 0

3 years ago

Read 2 more answers

PLS HELP ASAP What pattern do you notice about the exponents when dividing two powers with the same base?

Tanya [424]

Answer:

subtract the exponents

Step-by-step explanation:

To divide powers of the same base, you can subtract the exponents.

4 0

2 years ago

A student factors 10x2 + 3x – 27 to the following. (2x – 3)(5x + 9) Which statement about (2x – 3)(5x + 9) is true? The expressi

77julia77 [94]

Answer:

The answer is A

Step-by-step explanation:

A. The expression is equivalent, and it is completely factored.

7 0

3 years ago

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Need help with this question; What is the measure of one leg of a right angle given that the hypotenuse measure 14cm and the oth

melamori03 [73]

Answer:

11.5 cm

Step-by-step explanation:

The dimensions of a right angled triangle can be determined using Pythagoras theorem

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c = hypotenuse

a² + 8² = 14²

a² + 64 = 196

a² = 196 - 64

a² = 132

find the square root of 132

a = 11.5 cm

3 0

2 years ago