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3 years ago

13

What is the value of this expression?

1 answer:

Mila [183]3 years ago

4 0

Answer:

1/4

Step-by-step explanation:

1)2²= 4

2)4²= 16

3)3x2/3=2

4)6+2-4/8=1/4

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HOW DO THE PROPERTIES OF A DILATION TRANSFORMATION DIFFER FROM THE OTHER TRANSFORMATIONS YOU HAVE LEARNED ABOUT?

Alexxandr [17]

It differs because dilation changes the shape but not the orientation or place the shape is located.

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3 years ago

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Simplify<br> x + x + y x y?

saw5 [17]

Answer: $2x+y^2$

Step-by-step explanation:

$x\:+\:x\:+\:y\:\cdot \:y$

$x+x+yy$

$2x+yy$

$2x+y^2$

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3 years ago

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30 POINTS I WILL GIVE U BRAINLIEST AND THANKS AND 5 STARS please help this is very important this is a big part of my grade

mars1129 [50]

Answer:

$1.\:2^x=64, x=\boxed{6},\\2.\:x=\left(\frac{2}{3}\right)^3,x=\boxed{\frac{8}{125}}\\3.\:3\cdot (3^4)=3^x, x=\boxed{5}\\4.\:\frac{16}{25}=x^2,x=\boxed{\frac{4}{5}},$

Step-by-step explanation:

$1.\\\\2^x=64,\\\log 2^x=\log64,\\x\log 2=\log 64,\\x=\frac{\log 64}{\log 2}=\boxed{6}$

$2.\\x=\left(\frac{2}{5}\right)^3=\frac{2^3}{5^3}=\boxed{\frac{8}{125}}$

3. This problem incorporates an exponent property.

Exponent property used: $a^b\cdot a^c=a^{(b+c)}$ , yielding an answer of $\boxed{5}$

$4.\\\\\frac{16}{25}=x^2,\\x=\sqrt{\frac{16}{25}}=\frac{\sqrt{16}}{\sqrt{25}}=\boxed{\frac{4}{5}}$

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3 years ago

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Which of these functions has an inverse function? Select all that apply.

ElenaW [278]

ANSWER

y=x

y=x³

EXPLANATION

A function, f(x) has an inverse if and only if

$f(a) = f(b) \Rightarrow \: a = b$

Thus, the function is one to one.

For y=x or

$f(x) = x$

$f(a) = f(b) \Rightarrow \: a = b$

Hence this function has an inverse.

For the function y=x² or f(x)=x².

$f(a) = f(b) \Rightarrow \: {a}^{2} = {b}^{2} \Rightarrow \: a = \pm \: b$

This function has no inverse on the entire real numbers.

For the function y=x³ or f(x)=x³

$f(a) = f(b) \Rightarrow \: {a}^{3} = {b}^{3} \Rightarrow \: a = b$

This function also has an inverse.

For y=x⁴ or f(x) =x⁴

$f(a) = f(b) \Rightarrow \: {a}^{4} = {b}^{4} \Rightarrow \: a = \pm \: b$

This function has no inverse over the entire real numbers.

5 0

3 years ago

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A piece of wire 28 ft long is cut into two pieces. One piece is used to form a square, and the remaining piece is used to form a

marusya05 [52]

Answer:

Wire should be cut in two parts with the length = 15.69 ft and 12.31 ft

Step-by-step explanation:

Length of the wire = 28 ft has been cut in two pieces.

One piece is used to form a square and remaining piece to form a circle.

Let the length of the wire which forms the square is 'l' ft.

Area of the square = (side)²

Perimeter of the square = 4(side) = l

Length of one side = $\frac{l}{4}$

So, the area of the square = $\frac{l^{2}}{16}$ ft²

Now length of the remaining part = perimeter of the circle = (28 - l) ft

2πr = (28 - l)

r = $\frac{28-l}{2\pi }$

Area of the circle formed = πr²

= $\frac{\pi(28-l)^{2} }{4(\pi )^{2} }$

= $\frac{(28-l)^{2}}{4\pi }$

Combined area of the square and circle

= $\frac{l^{2}}{16}$ + $\frac{(28-l)^{2}}{4\pi }$

= $\frac{l^{2}}{16}$ + $\frac{(28-l)^{2}}{4\pi }$

Now to maximize the area we will find the derivative of the area with respect to l.

$\frac{dA}{dl}=\frac{d}{dl}[\frac{l^{2}}{16}+\frac{(28-l)^{2}}{4\pi}]$

= $\frac{d}{dl}[\frac{l^{2}}{16}+\frac{(28)^{2}+l^{2}-56l }{4\pi }]$

= $\frac{2l}{16}+\frac{(2l-56)}{4\pi }$

Now equate the derivative to zero.

$\frac{2l}{16}+\frac{(2l-56)}{4\pi }$ = 0

$(2l-56)=-\frac{2l}{16}\times 4\pi$

$(2l-56)=-\frac{\pi l}{2}$

$2l+\frac{\pi l}{2}=56$

$\frac{(4l+l\pi )}{2}=56$

l(4 + π) = 112

l(4 + 3.14) = 112

l = $\frac{112}{7.14}$

l = 15.69 ft

Length of the other part = 28 - 15.69 = 12.31 ft

Therefore, wire should be cut in two parts with the length = 15.69 ft and 12.31 ft

8 0

3 years ago