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3 years ago

The perimeter of an equilateral triangle is 27 centimeters. Find the altitude of the triangle

1 answer:

4 0

7.79cm It is an equilateral triangle so it has 3 equal sides. That means each side is 9cm. 
Now draw a line from the top of the equilateral triangle to the base, and dividing it into two. You will have made two smaller triangles, with sides 9, 4.5, and h (the one you want to find).

A line drawn from the apex of an equilateral triangle to the midpoint of the base is perpendicular to the base, so you can use Pythagoras' Theorem!

4.5^2 + h^2 = 9^2
h = sqrt(9^2 - 4.5^2)
Therefore, the height is 7.79cm (2 decimal places)

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Which of the following is an extraneous solution of sqrt 4x + 41 = x+5

stiv31 [10]

Answer:

x=-8

Step-by-step explanation:

$\sqrt{4x+41}=x+5$

on squaring both sides

$4x+41=(x+5)^2\\\\4x+41=x^2+10x+25\\\\x^2+6x-16=0\\\\x^2+8x-2x-16=0\\\\x(x+8)-2(x+8)=0\\\\(x-2)(x+8)=0$

either x-2=0 or x+8=0

either x=2 or x=-8

Putting x=2 in original equation, we get

$\sqrt{4\times 2+41}=2+5$

7=7 hence, it is not an extraneous solution

Putting x=-8 in original equation

$\sqrt{4\times (-8)+41}=-8+5$

i.e. 3=-3

Hence, x=-8 is an extraneous solution (since it doesn't satisfy the original equation)

3 0

3 years ago

Read 2 more answers

Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to f

Angelina_Jolie [31]

Answer:

$P(z>1.51) =1-P(Z$

And i fwe look into the normalstandar dtable we can find the desired probability:

$P(z>1.51) =1-P(Z$

And then the The area to the right of z = 1.51 is 0.0655

Step-by-step explanation:

For this case we want to find the following probability:

$P(z>1.51)$

And for this case we can use the normal standard distribution and the complement rule and we have this:

$P(z>1.51) =1-P(Z$

And i fwe look into the normalstandar dtable we can find the desired probability:

$P(z>1.51) =1-P(Z$

And then the The area to the right of z = 1.51 is 0.0655

7 0

3 years ago

25x = 125x + 3 x = −10 x = −9 x = −3 x = 3

ICE Princess25 [194]

Answer:

x=-9

Step-by-step explanation:

first you make the coefficients equal to each other by doing a common factor which in this case is 5. Then you have to do the variable for each time the common number is repeated which is 5^x * 5^x= 5^(x+3)*5^(x+3)*5^(x+3) This would make it equal to 5^2x=5^(3x+9). Since the non exponents are common factors you can get rid of them and solve for the exponent by doing 2x=3x+9. You solve that equation to get x=-9.

8 0

3 years ago

PLEASE ANSWER ASAP *picture attached*

SVETLANKA909090 [29]

Answer:

$x^{2} -2x-8$