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3 years ago

Describe the graph of the function.y = |x – 4| – 7

Mathematics

2 answers:

faltersainse [42]3 years ago

5 0

<h2>Answer with explanation:</h2>

We are given a function as:

$y=|x-4|-7$

We know that this function is a transformation of the parent function y=|x| i.e. the modulus function.

The rule that holds in this transformation is:

It is a translation of the parent function 4 units to the right and 7 units down.

Also, the graph of the function is attached to the answer.

juin [17]3 years ago

3 0

This is always ''interesting'' If you see an absolute value, you always need to deal with when it is zero:

(x-4)=0 ===> x=4,

so that now you have to plot 2 functions!

For x<= 4: what's inside the absolute value (x-4) is negative, right?, then let's make it +, by multiplying by -1:

|x-4| = -(x-4)=4-x
Then:

for x<=4, y = -x+4-7 = -x-3

for x=>4, (x-4) is positive, so no changes:

y= x-4-7 = x-11,

Now plot both lines. Pick up some x that are 4 or less, for y = -x-3, and some points that are 4 or greater, for y=x-11

In fact, only two points are necessary to draw a line, right? So if you want to go full speed, choose:

x=4 and x= 3 for y=-x-3

And just x=5 for y=x-11

The reason is that the absolute value is continuous, so x=4 works for both:

x=4===> y=-4-3 = -7

x==4 ====> y = 4-11=-7!

abs() usually have a cusp int he point where it is =0

Hope it helps, despite being this long!

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Applying the the properties of Congruence.

kolbaska11 [484]

Answer:

$LM = 35cm$ and $m \angle H = 98^o$

Step-by-step explanation:

For this problem, it is critical to understand what the opening statement means.

$Quadrilateral GHJK \cong quadrilateral LMNP$ means that each pair of <u>corresponding sides</u> between shapes are congruent (they have equal length), and each pair of <u>corresponding angles</u> between shapes are congruent (they have equal measure -- or same number of degrees when measured with a protractor).

So, it's important to be able to determine which pairs are the <u>corresponding</u> parts. When the congruence is given like $Quadrilateral GHJK \cong quadrilateral LMNP$ the letters are in a particular order. That order explains the order in which the shape is drawn out, and they put them in the same order for both shapes to mean that those are the letters that correspond with each other.

So, the first letter of each are a corresponding pair, the second letter of each are a corresponding pair, ... etc

In other words, point G and L correspond, point H and K correspond, etc.

To find the corresponding sides, the sides for these shapes are defined by a two adjacent letters (two letters next to each other in the name, or ... as it wraps around the end of the name... the first and last letter).

$\overline{GH} \cong \overline{LM}\\ \overline{HJ} \cong \overline{MN} \\\overline{JK} \cong \overline{NP}\\\overline{KG} \cong \overline{PL}$

While all of that is true, we only have a few sides with any information in them. Notice that side GH in the first shape, and sides PL & LM in the second shape are the only sides with anything written. So, we just need to determine which sides correspond (and thus, are congruent), so that we know how to move forward. Looking at the list of congruent sides above, we see that $\overline{GH} \cong \overline{LM}$

Since the sides (line segments) are congruent, their lengths are equal

$GH = LM$

...so we can substitute the expressions for each angle into the equation and solve for the unknown value "x"

$GH = LM\\(4x+3)=(6x-13)$

$(4x+3)+13=(6x-13)+13\\4x+16=6x$

$(4x+16)-4x=(6x)-4x\\16=2x$

divide both sides by 2

$\frac{16}{2}=\frac{2x}{2}\\8=x$

So, to find the length, LM, we just need to look back at the expression for LM:

$LM = 6x-13\\LM = 6(8)-13\\LM = 48-13\\LM = 35$

remembering that the lengths are measured in centimeters (as indicated on the diagram): $LM = 35cm$

To find the corresponding angles, the angles for these shapes are defined by a single letter, so since the points correspond in order, the names of the shapes tell which angles are congruent.

$\angle G \cong \angle L\\\angle H \cong \angle M\\\angle J \cong \angle N\\\angle K \cong \angle P$

While all of that is true, we only have a few angles with any information in them. Notice that ∠H in the first shape, and ∠L & ∠M in the second shape are the only angles with anything written. So, we just need to determine which angles correspond (and thus, are congruent), so that we know how to move forward. Looking at the list of congruent angles above, we see that

$\angle H \cong \angle M$

Since the angles are congruent, their measures are equal

$m\angle H = m\angle M$

...so we can substitute the expressions for each angle into the equation and solve for the unknown value "y"

$m\angle H = m\angle M\\(9y+17)=(11y-1)$

subtract 1 from both sides

$(9y+17)+1=(11y-1)+1\\9y+18=11y$

subtract 9y from both sides

$\\(9y+18)-9y=(11y)-9y\\18=2y$

divide both sides by 2

$\frac{18}{2}=\frac{2y}{2}\\9=y$

So, to find angle H, we just need to look back at the expression for the measure of angle H:

$m\angle H = 9y+17\\m\angle H = 9(9)+17\\m\angle H = 81+17\\m\angle H = 98$

remembering that the angle is measured in degrees (as indicated on the diagram): $m \angle H = 98^o$

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2 years ago

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Reika [66]

Step-by-step explanation:

for each top equation, there is a y value and an x value. You could plug in the bottom equation for y in the top equation since y=5x+23. Then you do order of operations and get your y-value. Then you do order of operations again and get your x-value. then its ordered pair, (x,y)

Right? I am so sorry if I am wrong <3

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3 years ago

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mina [271]

Factors of 26 are 1, 2, 13, 26 all you have to do is figure out which numbers can go until a number and in this case the number is 26.

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romanna [79]

Answer:

Step-by-step explanation:

I say it is 3 because 2 * 3 = 6

6/2=3

I hope this helps you:)

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3 years ago

A jeweler who buys a ring from a jewelry maker for $125 marked with the price by 135% for sale in the store what is the selling

siniylev [52]

Marked up by 135% means
new price=original price+(original price times markup) =125+(125 times 1.35)=293.75
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4 years ago

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