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3 years ago

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Mathematics

2 answers:

liq [111]3 years ago

5 0

Answer:

Part 1) $f(x)=\sqrt{x-1}$ -----> Graph C

Part 2) $g(x)=-\sqrt{x}$ ----> Graph D

Part 3) $h(x)=\sqrt{x}$ -----> Graph A

Part 4) $j(x)=-\sqrt{x-1}$ ---> Graph E

Step-by-step explanation:

Part 1) we have

$f(x)=\sqrt{x-1}$

Find the domain of the function

The radicand must be positive

$x-1\geq 0$

Solve for x

$x\geq 1$

The domain is the interval -----> [1,∞)

All real numbers greater than or equal to 1

Find the range

For x=1

$f(1)=\sqrt{1-1}=0$

The range is the interval ----> [0,∞)

All real numbers greater than or equal to 0

therefore

The function represent Graph C

Part 2) we have

$g(x)=-\sqrt{x}$

Find the domain of the function

The radicand must be positive

$x\geq 0$

The domain is the interval -----> [0,∞)

All real numbers greater than or equal to 0

Find the range

For x=0

$f(0)=-\sqrt{0}=0$

The range is the interval ----> (-∞,0]

All real numbers less than or equal to 0

therefore

The function represent Graph D

Part 3) we have

$h(x)=\sqrt{x}$

Find the domain of the function

The radicand must be positive

$x\geq 0$

Solve for x

$x\geq 0$

The domain is the interval -----> [0,∞)

All real numbers greater than or equal to 0

Find the range

For x=0

$f(0)=\sqrt{0}=0$

The range is the interval ----> [0,∞)

All real numbers greater than or equal to 0

therefore

The function represent Graph A

Part 4) we have

$j(x)=-\sqrt{x-1}$

Find the domain of the function

The radicand must be positive

$x-1\geq 0$

Solve for x

$x\geq 1$

The domain is the interval -----> [1,∞)

All real numbers greater than or equal to 1

Find the range

For x=1

$f(1)=-\sqrt{1-1}=0$

The range is the interval ----> (-∞,0]

All real numbers less than or equal to 0

therefore

The function represent Graph E

pashok25 [27]3 years ago

4 0

Answer:

Graph A → y=√x.

Graph B → y=(√x) - 1.

Graph C → y=√(x-1).

Graph D → y= -√x.

Graph E → y= -√(x-1)

Step-by-step explanation:

The graph 'A' intercepts the y-axis at (0, 0). Therefore it belongs to the function y=√x.

The graph 'D' is exactly the same graph 'A' but reflected across the x-axis. Therefore, it belongs to the function y=-√x.

The function 'C' is exactly the same function y=√x but translated one unit to the right, therefore, the solution function is y=√(x-1)

The graph 'E' is exactly the same graph 'C' but reflected across the x-axis, therefore the function is: y= -√(x-1)

In the options you have two times the function y=√x. I assume that's a mistake. The graph 'B' corresponds to y = (√x) - 1

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A ball has a volume of 128 cubic inches. Find the diameter of the ball.

Natalija [7]

$\bf \textit{volume of a sphere}\\\\
V=\cfrac{4\pi r^3}{3}~~
\begin{cases}
r=radius\\
-----\\
V=128
\end{cases}\implies 128=\cfrac{4\pi r^3}{3}\implies 128(3)=4\pi r^3$

$\bf \cfrac{128(3)}{4\pi }=r^3\implies \sqrt[3]{\cfrac{128(3)}{4\pi }}=r^3\implies \sqrt[3]{\cfrac{96}{\pi }}=r\implies \sqrt[3]{\cfrac{8\cdot 12}{\pi }}=r
\\\\\\
\sqrt[3]{\cfrac{2^3\cdot 12}{\pi }}=r\implies 2\sqrt[3]{\cfrac{12}{\pi }}=r\\\\
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7 0

4 years ago

Need help with step by step explanation pls

sesenic [268]

Answer:

$5 \sqrt{2}$

Step-by-step explanation:

$\sqrt{50} - \sqrt{32} + 2 \sqrt{8} \\ 5 \sqrt{2} - 4 \sqrt{2} + 4 \sqrt{2} \\ \sqrt{2} + 4 \sqrt{2} \\ 5 \sqrt{2}$

5 0

3 years ago

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 6.9 years, and standard deviation of

Lostsunrise [7]

ANSWER

0.9738 or 97.38%

EXPLANATION

Given:

$\begin{gathered} mean(\mu)=6.9 \\ Standard\text{ }Deviation(\sigma)=1.6 \end{gathered}$

Desired Outcome:

Probability that it will last 10 years

z-score for the sample:

$\begin{gathered} z-score=\frac{X-\mu}{\sigma} \\ z-score=\frac{10-6.9}{1.6} \\ z-score=1.9376 \end{gathered}$

p-value

For the z-score of 1.9376, the p-value is 0.9738 or 97.38%

Hence, the probability that it will last longer than 10 years if you randonly purchase one item is 97.38%

7 0

1 year ago

A 55% decrease followed by a 25% increase

Lina20 [59]

Let's say the item starts off at $100.

A 55% decrease means 100%-55% = 45% of the value is still there. The item is now worth 0.45*100 = 45 dollars.

Now increase this by 25%. The long way to do this is to add 25% of 45 onto 45

(25% of 45) + (45) = 0.25*45+45 = 11.25+45 = 56.25

Or, we can multiply 45 by 1.25 since the multiplier 1.25 represents a 25% increase

1.25*45 = 56.25

-----------------------------------------------------

The item was $100, it drops to $45 after the 55% decrease, then it is $56.25 after the 25% increase.

Let's compute the percent difference

A = 100 = old value

B = 56.25 = new value

C = percent difference

C = 100*(B-A)/A

C = 100*(56.25-100)/100

C = -43.75%

The negative C value indicates a percent decrease.

So combining a 55% decrease and a 25% increase leads to an overall decrease of 43.75%

-----------------------------------------------------

A shortcut is to multiply 0.45 and 1.25 to get 0.5625

Then subtract this from 1 to get 1-0.5625 = 0.4375

This is another way to see we have a 43.75% decrease.

8 0

4 years ago

A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder increases and the radius, r, decr

stepan [7]

Answer:

The radius is decreatsing at a rate 0.78 cm per second.

Step-by-step explanation:

We are given the following in the question:

$\dfrac{dl}{dt} = 0.7\text{ cm per second}$

Instant radius,r = 2 cm

Instant length,l = 9cm

The radius of the cylinder decreases.

Volume of cylinder =

$V =\pi r^2l$

Since the volume of the cylinder does not changes, we can write:

$\dfrac{dV}{dt}=0$

Rate of change of volume:

$\dfrac{dV}{dt} = \pi(2r\dfrac{dr}{dt}l + r^2\dfrac{dl}{dt})$

Puttiung values, we get

$0 = \pi(2(2)\dfrac{dr}{dt}(9) + (2)^2(0.7))\\\\\dfrac{dr}{dt}=-\dfrac{4\times 0.7}{4\times 9} \approx -0.78$

Thus, the radius is decreatsing at a rate 0.78 cm per second.

5 0

4 years ago