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2 years ago

Write an equation that represents a horizontal translation 10 units left of the graph of g(x) = |x|

Mathematics

2 answers:

Vika [28.1K]2 years ago

7 0

Answer: h(x) = |x+10|

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Explanation:

To shift the graph 10 units to the left, we replace x with x+10. What's really going on is that the xy axis shifts 10 units to the right (because x is now x+10; eg, x = 2 ---> x+10 = 2+10 = 12) so it appears that the graph is moving to the left. The general rule is h(x) = g(x+10).

So,
g(x) = |x|
g(x+10) = |x+10| ... every x has been replaced with x+10
h(x) = g(x+10)
h(x) = |x+10|

We can use a graphing tool like GeoGebra to visually confirm we have the right answer (see attached). Note how a point like (0,0) on the green graph moves to (-10,0) on the red graph.

prisoha [69]2 years ago

4 0

To move a graph c units to the right, minus c from every x
to move a graph c units to the left, add c to every x

g(x)=|x|
move to left 10 units
add 10 to every x
h(x)=|x+10| is the equation of g(x) translated 10 units to the left

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1 year ago

200 students attend a school which offers French and History. 10% of those who take History also take French and 4 times as many

SIZIF [17.4K]

Answer: P(hist& french)=16/200=0.08

Step-by-step explanation:

To find the required probability we have to know what is the number of students that take both History and French ( Intersection of 2 circles in Venn diagram)

1. Lets find the number of students that take History or French or both.

We know that 8% from 200 take neither History or French. So number or students who take History or French or both is 200-200*0.08=184

2. Let number of students that takes French (or both Fr+Hist)=x (left circle)

So number of students that takes History (or both Fr+Hist)=4x (right circle)

So number of students that take both French+History= 10% from 4x or

0.1*4x=0.4x (circles' intersection)

3. Now we have the equation as follows:

x+4*x-0.4*x = 184

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x=40 students takes French (or both French+ History)

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2 years ago

Mrs. Stevens wants to have $18,000 in the bank in 3 years. If she deposits $9500 today at 4% compounded quarterly for 3 years, h

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$\bf \qquad \textit{Compound Interest Earned Amount}
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A=P\left(1+\frac{r}{n}\right)^{nt}
\qquad 
\begin{cases}
A=\textit{current amount}\\
P=\textit{original amount deposited}\to &\$9500\\
r=rate\to 4\%\to \frac{4}{100}\to &0.04\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{quarterly, 4 quarters a year}
\end{array}\to &4\\

t=years\to &3
\end{cases}$

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2 years ago

Read 2 more answers

Most states categorize possession of cocaine charges by weight. Possessing less than a gram will result in the lowest level of f

AleksAgata [21]

Answer:

Over 2 oz. Class A-II felony

Step-by-step explanation:

One would need to carefully weigh the material.*

0.06 kg ≈ 2.12 oz

Note that .06 kg is 1 significant figure, so this rounds to 2 oz (1 significant figure). Given the precision of the reported weight, there is insufficient precision to say the amount is actually over 2 oz.

If you take the numbers at face value, the suspect is in possession of over 2 oz, so will be charged with a Class A-II felony.

_____

* 2.00 ounces translates to about 0.0567 kg, which rounds to 0.06 kg.