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3 years ago

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Mathematics

1 answer:

vladimir1956 [14]3 years ago

5 0

Step-by-step explanation:

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A right triangle has a side of length 1 fourth and a hypotenuse of length 1 third. What is the length of the other side?

Marina86 [1]

Answer:

The other side = $\frac{1}{12}$ units

Step-by-step explanation:

A right triangle has a side of length $\frac{1}{4}$ units and;

the hypotenuse is $\frac{1}{3}$

According to Pythagorean theorem,

a² + b² = c² , where a and b are the two legs of a triangle and c is the hypotenuse.

Lets say a² = $(\frac{1}{4}) ^2$ and c² = ( $(\frac{1}{3} )^2$

b² = c² - a²

b² = $\frac{1}{9}$ - $\frac{1}{16}$ = $\frac{1}{144}$

So b = $\sqrt{1/144}$ = $\frac{1}{12}$ units.

So the other side = $\frac{1}{12}$ units.

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3 years ago

An archery target consists of a circular bull's-eye with radius x, surrounded by four rings with width y. What is the area of th

amid [387]

given:
bull's eye radius= x
width of surrounding rings=y

solution:
Radius of the circle=x+4y
Area of the outermost ring=Area of the circle-Area of the penultimate ring =Ď€(x+4y)^2-Ď€(x+3y)^2
=Ď€(x^2+8xy+16y^2-x^2-9y^2-6xy)
=Ď€(2xy+7y^2)
hence the area of the outermost ring in terms of x and y is Ď€(2xy+7y^2).

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3 years ago

30+ Points!!! 5. Solve the following inequalities. a) 2 log3x – 2 logx3 -3 <0

Ilya [14]

Answer:

I answered your last question also

2 log3x – 2 logx3 -3 <0

$\mathrm{Subtract\:}2\log ^3\left(x\right)\mathrm{\:from\:both\:sides}$

$2\log ^3\left(x\right)-2logx^3-3-2\log ^3\left(x\right)$

$\mathrm{Simplify}$

$-2logx^3-3$

$\mathrm{Add\:}3\mathrm{\:to\:both\:sides}$

$-2logx^3-3+3$

$\mathrm{Simplify}$

$-2logx^3$

$Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)$

$\left(-2logx^3\right)\left(-1\right)>-2\log ^3\left(x\right)\left(-1\right)+3\left(-1\right)$

$\mathrm{Simplify}$

$2lx^3og>2\log ^3\left(x\right)-3$

$\mathrm{Divide\:both\:sides\:by\:}2lx^3o;\quad \:l>0$

$\frac{2lx^3og}{2lx^3o}>\frac{2\log ^3\left(x\right)}{2lx^3o}-\frac{3}{2lx^3o};\quad \:l>0\\$

$\mathrm{Simplify}$

$g>\frac{2\log ^3\left(x\right)-3}{2lx^3o};\quad \:l>0$

Step-by-step explanation:

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3 years ago

An equation is shown. 2x-4y=8 solve the equation for x in terms of y

horrorfan [7]

2x-4y=8

Add 4y to each side to separate the variables, since you want to solve for x let be on the left

2x=4y+8

Divide the entire equation by 2 to allow x to stand alone

x=2y+4

And I have to type some more so it will let me answer the question so here ya go

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3 years ago

Combine like terms. y + 3 + 9(y + 5) =

Mnenie [13.5K]

Answer:

The answer is 10y + 48.

Step-by-step explanation:

First you have to get rid of brackets by expanding :

$y + 3 + 9(y + 5) \\ = y + 3 + 9y + 45$