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nikdorinn [45]
3 years ago
5

Make a table with the domain of {2,3,4,5,6} and draw a graph of the absolute value function y = 2|x-4| + 3.

Mathematics
2 answers:
Basile [38]3 years ago
7 0

Answer:

Table for y = 2|x-4| + 3 on domain {2,3,4,5,6} is given as:

x                           y

2         2|x-4| + 3 = 2|2-4| + 3 = 7

3         2|x-4| + 3 = 2|3-4| + 3 = 5

4         2|x-4| + 3 = 2|4-4| + 3 = 3

5         2|x-4| + 3 = 2|5-4| + 3 = 5

6         2|x-4| + 3 = 2|6-4| + 3 = 7

The graph of the absolute value function y = 2|x-4| + 3 for the given domain is attached.

Step-by-step explanation:

The absolute value parent function, written as function(x) = | x |, is defined as:

|x| = x          and           |-x| = x

In our case;

For x = 2        

y = 2|x-4| + 3

= 2|2-4| + 3

= 2|-2| + 3

= 2*2 + 3

= 4 + 3

= 7

Similarly, for all other values of x in the given domain, value of y can be calculated.

Jet001 [13]3 years ago
5 0

Answer:

<h2>In the attachment.</h2>

Step-by-step explanation:

|a|=\left\{\begin{array}{ccc}a&for\ a\geq0\\-a&for\ a

Put each value of x from the set {2, 3, 4, 5, 6}

to the equation y = 2|x - 4| + 3:

x = 2 → y = 2|2 - 4| + 3 = 2|-2| + 3 = 2(2) + 3 = 4 + 3 = 7 → (2, 7)

x = 3 → y = 2|3 - 4| + 3 = 2|-1| + 3 = 2(1) + 3 = 2 + 3 = 5 → (3, 5)

x = 4 → y = 2|4 - 4| + 3 = 2|0| + 3 = 2(0) + 3 = 0 + 3 = 3 → (4, 3)

x = 5 → y = 2|5 - 4| + 3 = 2|1| + 3 = 2(1) + 3 = 2 + 3 = 5 → (5, 5)

x = 6 → y = 2|6 - 4| + 3 = 2|2| + 3 = 2(2) + 3 = 4 + 3 = 7 → (6, 7)

Mark the points in the coordinates system.

The domain is only five numbers, therefore the graph of this function is only five points.

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Write the equation of a line perpendicular to 9xplus7yequals6 that passes through the point ​(9​,negative 7​).
andrew11 [14]

k:\ y=m_1x+b_1\\\\l:\ y=m_2x+b_2\\\\k\ ||\ l\iff m_1=m_2\\\\k\ \perp\ l\iff m_1m_2=-1

We have:

k:\ 9x+7y=6\ \ \ |-9x\\\\7y=-9x+6\ \ \ \ |:7\\\\y=-\dfrac{9}{7}x+\dfrac{6}{9}\to m_1=-\dfrac{9}{7}\\\\l:\ y=m_2x+b\\\\l\ \perp\ k\iff-\dfrac{9}{7}m_2=-1\ \ \ \ |\cdot\left(-\dfrac{7}{9}\right)\\\\m_2=\dfrac{7}{9}\to\ l:\ y=\dfrac{7}{9}x+b

We know. The line <em>l</em> passes throught the point (9, -7). Substitute the coordinates of the poin to the equation of line<em> l </em>:

-7=\dfrac{7}{9}\cdot9+b\\\\-7=7+b\ \ \ \ |-7\\\\b=-14

y=\dfrac{7}{9}x-14\ \ \ \ |\cdot9\\\\9y=7x-126\ \ \ \ |-9y\ |+126\\\\7x-9y=126

Answer: y=\dfrac{7}{9}x-14\to7x-9y=126


7 0
3 years ago
A dog weighs two pounds less than three times the weight of a cat. The dog also weights twenty-two more pounds than the cat. Wri
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Answer:

Weight of dog: 34 pounds,

Weight of cat: 12 pounds.

Step-by-step explanation:

Let d represent weight of dog and c represent weight of cat.

We have been given that a dog weighs two pounds less than three times the weight of a cat.

3 times weight of cat: 3c

We can represent the given information in an equation as:

d=3c-2...(1)

We are also told that the dog also weights twenty-two more pounds than the cat. We can represent the given information in an equation as:

d=c+22...(2)

Equate both equations:

3c-2=c+22

3c-c-2=c-c+22

2c-2=22

2c-2+2=22+2

2c=24

\frac{2c}{2}=\frac{24}{2}

c=12

Therefore, the weight of cat is 12 pounds.

Substitute c=12 in equation (2)

d=c+22

d=12+22

d=34

Therefore, the weight of dog is 34 pounds.

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3 years ago
24 + 8x + 10(2x)<br> Terms:<br> Constants:<br> Coefficients:
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Terms: 24, 8x, 10(2x)
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<h3>How to solve the equation</h3>

Since Katrina averages fifteen passengers every twenty minutes and Stefon also works for the airline and averages fifteen passengers every twenty-five minutes, this can be represented this:

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Divide through by 9

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telo118 [61]

Answer:

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Step-by-step explanation:

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