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2 years ago

I need help on 5-7. Its a little confusing for me

Mathematics

1 answer:

Len [333]2 years ago

8 0

Answer:

5. x = 5, y = 3

6. x = 0, y = 4

7. x = -1, y = 1

Step-by-step explanation:

5. substitute 3(value of y) into the equation y = x - 2:

=> 3 = x - 2

=> x = 5

6. substitute 0(value of x) into the equation y = x + 4:

=> y = 0 + 4

=> y = 4

7. substitute 1(value of y) into the equation y = 2x + 3:

=> 1 = 2x + 3

=> 2x = -2

=> x = -1

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The hypotenuse of an isosceles right triangle is centimeters longer than either of its legs. Find the exact length of each side.

Varvara68 [4.7K]

Question

The hypotenuse of an isosceles right triangle is 11 centimeters longer than either of its legs. find the exact length of each side.

Answer:

$Hypotenuse:37.56$

$Other\ Legs: 26.56$

Step-by-step explanation:

Let the hypotenuse be y and the other legs be x.

So:

$y = 11 + x$

Required

Determine the exact dimension of the triangle

Using Pythagoras theorem;

$y^2 = x^2 + x^2$

$y^2 = 2x^2$

This gives:

$(11+x)^2 = 2x^2$

Open bracket

$121 + 22x + x^2= 2x^2$

Collect like terms

$2x^2 - x^2 -22x - 121 = 0$

$x^2 -22x - 121 = 0$

Using quadratic formula:

$x = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}$

$x = \frac{-(-22)\±\sqrt{(-22)^2 - 4*1*-121}}{2*1}$

$x = \frac{-(-22)\±\sqrt{968}}{2*1}$

$x = \frac{22\±31.11}{2}$

Split

$x = \frac{22+31.11}{2}\ or\ x = \frac{22-31.11}{2}\\$

$x = \frac{53.11}{2}\ or\ x = \frac{-9.11}{2}$

x can not be negative.

So:

$x = \frac{53.11}{2}$

$x = 26.56$

Recall that:

$y = 11 + x$

$y = 11 + 26.56$

$y = 37.56$

Hence, the dimensions are:

$Hypotenuse:37.56$

$Other\ Legs: 26.56$

6 0

3 years ago

Number 6 and 7 asap please help

netineya [11]

Hello!

We will write and solve this equation below.

x-24=35

Add 24 to both sides.

x=59

4c=28

Divide both sides by 4.

c=7

I hope this helps!

3 0

2 years ago

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An urn contains six red balls numbered 1, 2, 3, 4, 5, 6, two white balls numbered 7, 8, and two black balls numbered 9, 10. A ba

Svetradugi [14.3K]

Answer:

2/10 = 1/5

Step-by-step explanation:

To figure out the probability of something, we can take

(number of outcomes of that something) / (number of total outcomes)

Here, we are trying to find the probability that the ball is white. The number of outcomes that are possible with the ball being white is 2, as there are two white balls and you can only pick one. You can pick either of the two white balls, but there is no way to pick one of them two times, pick two of them at once, or pick any other ball and have it be white.

The number of total outcomes is 10. There are 10 balls, and you can only pick one ball at a time. There are only 10 options to choose from.

Therefore, we can plug our numbers into the formula above and get 2/10 = 1/5 as our probability

8 0

2 years ago

Find the value of x. Round to the nearest tenth. The diagram is not drawn to scale.

VladimirAG [237]

x = 11 x cos(22)

x = 10.199

x = 10.2

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2 years ago

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