URGENT!!!! 60 POINTS TO WHOEVER HELPS ME!!!<br><br> Factor each completely:

Describe two different sequences of transformations that will map ABCD to EFGH.

Harlamova29_29 [7]

The orientation of the figure has been changed by 90°, but the points are not all rotated around the same center. Translation is involved.

Translation before rotation:
.. translate down 5 units
.. rotate counterclockwise 90° about the origin

Translation after rotation:
.. rotate counterclockwise 90° about the origin
.. translate right 5 units

This can also be accomplished by a double reflection.
.. reflect across the line y=x
.. reflect across the line x=2.5

Or,
.. reflect across the line y=2.5
.. reflect across the line y=x

3 0

4 years ago

A motorboat that travels with a speed of 20 km/hour in still water has traveled 20 km against the current and 180 km with the cu

Gala2k [10]

Recall your d = rt. distance = rate * time.

let's say the speed of the current is "c".

keeping in mind that, when the boat is going against the current, the boat is not really going at 2kmh, but instead at " 20 - c ", because the current is subtracting speed from it.

Likewise when is going with the current, is going at a speed of " 20 + c ".

if the boat took say "t" hours on the way over, on the way back it took the slack from the whole 8 hours and "t", namely it took " 8 - t " hours.

$\bf \begin{array}{lccclll}
&\stackrel{km}{distance}&\stackrel{kmh}{rate}&\stackrel{hours}{time}\\
&------&------&------\\
\textit{against the current}&20&20-c&t\\
\textit{with the current}&180&20+c&8-t
\end{array}
\\\\\\
\begin{cases}
20=(20-c)(t)\implies \frac{20}{20-c}=t\\
180=(20+c)(8-\stackrel{\downarrow }{t})\\
--------------\\
180=(20+c)\left( 8- \stackrel{\downarrow }{\frac{20}{20-c}}\right)
\end{cases}
\\\\\\
180=(20+c)\left( \cfrac{(160-8c)-20}{20-c} \right)$

$\bf 180=(20+c)\left( \cfrac{140-8c}{20-c} \right)\implies 180(20-c)=(20+c)(140-8c)
\\\\\\
3600c-180c=2800-160c+140c-8c^2
\\\\\\
3600c-180c=2800-20c-8c^2
\\\\\\
3600c-180c-2800+20c+8c^2=0\implies 8c^2-160c+800=0
\\\\\\
c^2-20c+100=0\implies (c-10)(c-10)=0\implies \boxed{c=10}$

8 0

3 years ago

Santosh is four more than three times the age of his cousin. If Santosh is 49 years old, then what is the age of his cousin?

Valentin [98]

Let cousin = x
Santos. =(3x+4)
Santos. ........49
=>3x+4=49
3x=49
x=15
=> cousin is 15yrs

5 0

3 years ago

Read 2 more answers

a display at an aquarium has sea stars to wolf eels in a ratio 4 : 5. It also has 5/8 as many rockfish as sea stars. there are 4

r-ruslan [8.4K]

The number of sea stars is 64.

What is a ratio?

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other.

In general, a: b, which can be interpreted as "a is to b," is used to denote a ratio between two quantities, let's say "a" and "b."

This ratio is expressed in fraction form as a/b. We utilize the same method for further simplifying a ratio as we use for further simplifying a fraction.

According to the question,

Ratio of sea stars to wolf eels = 4:5

Number of rock fish= 5/8 (Number of sea stars)

Number of wolf eels - Number of rock fish = 40

Using the given information, we get,

Number of sea stars = 8/5 (Number of rock fish)

On simplification,

Number of wolf eels = 80

So, number of sea stars = (4/5)*80

= 64

Learn more about ratios here:

brainly.com/question/2328454

#SPJ1

7 0

3 years ago

What is the inverse of the following conditional?

alexdok [17]

Answer:

I think it'd be "If Eric is ordering a pizza, it does not have mushrooms."

Step-by-step explanation:

While slightly jumbled, the given sentence is clearly trying to tell us that for whatever reason, Eric will never order a pizza with mushrooms on it.

Please don't get mad if it's wrong, I tried my best.

8 0

3 years ago

URGENT!!!! 60 POINTS TO WHOEVER HELPS ME!!! Factor each completely: