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zalisa [80]
3 years ago
15

Write a formula for the function g(x) obtained when the graph of f(x)= square root x is shifted up 1 unit and to the left 9 unit

s .
Mathematics
1 answer:
ch4aika [34]3 years ago
4 0

\bf ~~~~~~~~~~~~\textit{function transformations}
\\\\\\
f(x)= A( Bx+ C)+ D
\\\\
~~~~y= A( Bx+ C)+ D
\\\\
f(x)= A\sqrt{ Bx+ C}+ D
\\\\
f(x)= A(\mathbb{R})^{ Bx+ C}+ D
\\\\
f(x)= A sin\left( B x+ C \right)+ D
\\\\[-0.35em]
~\dotfill\\\\
\bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\
\bullet \textit{ flips it upside-down if } A\textit{ is negative}\\
~~~~~~\textit{reflection over the x-axis}
\\\\
\bullet \textit{ flips it sideways if } B\textit{ is negative}


\bf ~~~~~~\textit{reflection over the y-axis}
\\\\
\bullet \textit{ horizontal shift by }\frac{ C}{ B}\\
~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}\\\\
~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\
\bullet \textit{ vertical shift by } D\\
~~~~~~if\ D\textit{ is negative, downwards}\\\\
~~~~~~if\ D\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{ B}


with that template in mind, let's take a peek.


\bf f(x)=\sqrt{x}~\hspace{7em}\stackrel{\textit{up by 1}}{D=1}\qquad \stackrel{\textit{left by 9}}{C=9}
\\\\[-0.35em]
~\dotfill\\\\
g(x)=\stackrel{A}{1}\sqrt{\stackrel{B}{1}x+\stackrel{C}{0}}+\stackrel{D}{0}\implies \stackrel{\textit{shifted}}{g(x)=\stackrel{A}{1}\sqrt{\stackrel{B}{1}x+\stackrel{C}{9}}+\stackrel{D}{1}}\implies \blacktriangleright g(x)=\sqrt{x+9}+1 \blacktriangleleft

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Brass is made up of copper and zinc. 100 grams of brass contains 20 grams of zinc.
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Answer:

A.  12 grams Zn

B.  280 g of copper.

Step-by-step explanation:

100 grams of brass

20 grams of zinc

100 grams of brass has 20 grams of Zn.

20/100 = 0.200  Zn   <u>20% Zn  and 80% copper</u>.

A.  (60 g brass)*(0.2) = 12 grams Zn

B.  (350 g brass)*(0.80) = 280 g of copper.

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2 years ago
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anyanavicka [17]

Answer:

16.8 + (-18.6)

Step-by-step explanation:

A subtraction symbol and adding a negative are the same

8 0
3 years ago
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A triangular prism is shown. a cylinder is cut out of the center of the prism. the triangular base has side lengths of 14 and 10
Whitepunk [10]

The expression that represents the volume, in cubic units, of the shaded region of the composite figure is: A. One-half(14)(10)(8) – π(2.52)(8).

<h3>Expression</h3>

Given:

Base side length=14 and 10 units

Height=8 units

Diameter=5 units


Hence:

Expression= 1-( half 14)(10)(8) - π(2.52)(8)

Expression=1-(7) (10)(8) - π(2.52)(8)

Expression=1- (560)- 63.33

Expression=-559-63.33

Expression=-622.33

Therefore the expression that represents the volume, in cubic units, of the shaded region of the composite figure is: A. One-half(14)(10)(8) – π(2.52)(8).

Learn more about expression here:brainly.com/question/723406

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Using the distance formula, calculate how far Tre threw the ball. (4 points: 2 points for setup, 1 for calculation, 1 for the an
sergij07 [2.7K]

Answer:

D = 63.717

Step-by-step explanation:

The details that complete the question are:

(x_1,y_1) = (0,42.78)

and

(x_2,y_1)=(90,42.78)

Required

Determine how far the ball travelled

Distance is calculated using:

D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Substitute values for x's and y's

D = \sqrt{(42.78 - 0)^2+(42.78-90)^2}

D = \sqrt{42.78^2+(-47.22)^2

D = \sqrt{1830.1284+2229.7284

D = \sqrt{4059.8568

D = 63.717

<em>Hence, the ball travelled a distance of 63.717 units</em>

6 0
3 years ago
I’ve done question a. But can you help me on b and c
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Answer:

Step-by-step explanation:

b) Diameter of Mercury = 4.88 * 10³ = 4.88 * 1000 = 4880 km

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Mass of Saturn = 5.68 * 10²⁶

Difference  = 18.98 * 10²⁶ - 5.68*10²⁶

                   = (18.98 - 5.68) * 10²⁶

                   = 13.30 * 10²⁶

                   = 1.330 * 10²⁷

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