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Rus_ich [418]
2 years ago
5

The figure shows two triangles on a coordinate grid:

Mathematics
2 answers:
Afina-wow [57]2 years ago
3 0
IT IS CORRECT 5 UNIT DOWN TRANSLATION 180 DEGREE COUNTERCLOCKWISE ROTATION
Jobisdone [24]2 years ago
3 0

Answer: A translation 5 units down followed by a 180-degree counterclockwise rotation about the origin .

Step-by-step explanation:

From the given figure, the coordinates of ΔABC are A(-3,4), B(-3,1), C(-2,1) and the coordinates of ΔA'B'C' are A'(3,1), B'(3,4), C'(2,4).

When, a translation of 5 units down is applied to  ΔABC, the coordinates of the image will be

(x,y)\rightarrow(x,y-5)\\A(-3,4)\rightarrow(-3,-1)\\ B(-3,1)\rightarrow(-3,-4)\\ C(-2,1)\rightarrow(-2,-4)

Then applying 180° counterclockwise rotation about the origin, the coordinates of the image will be :-

(x,y)\rightarrow(-x,-y)\\(-3,-1)\rightarrow(3,1)\\(-3,-4)\rightarrow(3,4)\\(-2,-4)\rightarrow(2,4) which are the coordinates of ΔA'B'C'.

Hence, the set of transformations is performed on triangle ABC to form triangle A’B’C’ is " A translation 5 units down followed by a 180-degree counterclockwise rotation about the origin ".

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A study analyzed the average yearly salt intake in the United States from 2012 thru 2017. The data is summarized in the table:
Ugo [173]

Answer:Is an estimate of the average grams of salt used in 2012

Step-by-step explanation: Let

x ---> the number of years since 2012

f(x) ---> is the total amount of salt ingested in grams

we have

This is a linear equation in slope intercept form

where

The slope is equal to

The y-intercept or initial value is equal to

The y-intercept is the value of the function f(x) when the value of x is equal to zero

In this context, the y-intercept is the average amount of grams of salt ingested  in the year 2012

The exact value of the average amount of grams of salt ingested  in the year 2012 is 3,554 grams (see the data in the table)

Compare the exact value with the y-intercept

therefore

3,548 grams Is an estimate of the average grams of salt used in 2012

7 0
3 years ago
what’s the correct answer for this?
Gnoma [55]

Answer:

A.

Step-by-step explanation:

98%

The probability of not winning the raffle is 100% - 2% = 98%

5 0
2 years ago
Multiply.<br> 2x(x2 + 2x - 6)
Stels [109]
<span>2x(x2 + 2x - 6)
</span>First add what is in the "(" wich is 2x+2x
<span>2x(4x - 6)
</span>Second multiply the 2x by the 4x & -6
<span>8x-12x
Now subtract the -12x from the 8x
8x-12x = -4x


</span>
8 0
3 years ago
Read 2 more answers
Need step by step detailed answer
kolezko [41]

Answer:

y = -4x - 4

Step-by-step explanation:

If we have two lines in slope intercept form as

y = m_1x + c_1 \text{ and}\\y = m_2x + c_2\\

then the product of the slopes m_1m_2 = -1

In other words, m_2 = -\frac{1}{m_1}

We have the first line as

y = \frac{1}{4}x + 5\\\\

The slope of this line is \frac{1}{4}

The slope of a perpendicular line will be the negative of the reciprocal of this line

Reciprocal of 1/4 is 4

So slope of perpendicular line is -4 which implies

y = -4x + c

We have to determine c

Since the line passes through (-3, 8), plug in these values for x and y in the equation and solve for c

8 = (-4)(-3) + c

8 = 12 + c

c = -4

So the equation of the perpendicular line is y = -4x - 4 (Answer)

It is always a good idea to plot these graphs and see if they fit the data provided

The attached plot shows the two graphs and you can see they are perpendicular to each other and the perpendicular line(the answer) passes through point (-3,8)

4 0
1 year ago
Help I need it I’m almost done
sesenic [268]

Answer:

E

Step-by-step explanation:

3 0
3 years ago
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