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3 years ago

Use the vertical line test to determine if the graph represents a function. Explain.

Mathematics

2 answers:

tatuchka [14]3 years ago

6 0

Answer:

Is it possible to pass a single vertical line through more than one point on the horizontal line?The answer to this question is: No it is not possibleSince we cannot have a vertical line cross through more than one point, this graph passes the vertical line test making it a function. Any input (x) leads to exactly one output (y)

Step-by-step explanation:

nadezda [96]3 years ago

5 0

Ask yourself this: Is it possible to pass a single vertical line through more than one point on the horizontal line?

The answer to this question is: No it is not possible

Since we cannot have a vertical line cross through more than one point, this graph passes the vertical line test making it a function. Any input (x) leads to exactly one output (y)

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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): $m \angle H = 98^o$

6 0

2 years ago

When a number is decreased by 7.3%, the result is 60. What is the original number to

marishachu [46]

Answer:

Original Number = let we assume it is x

Number after decremented = y = 60

Total decrease = z = x-y = x-60

% of decrease = ((x-60)/x)*100 = 7.3

(x-60)*100 = 7.3x

100x -6000 = 7.3x

100x-7.3x = 6000

92.7x = 6000

x = 6000/92.7 = 64.73

Original Number = 64.73

Step-by-step explanation:

4 0

3 years ago

Vectors; please help: 2y+w-u=?

andreyandreev [35.5K]

Answer:

idkdikdidkidkidk

Step-by-step explanation:

5 0

3 years ago

P=2 (w+h) h the subject

UkoKoshka [18]

P=2(w+h)
remember you can do anythig to an equaotn as lng as you do it to both sides
divide both sides by 2
P/2=w+h
subtract w
(P/2)-w=h

7 0

3 years ago

Read 2 more answers

In 2015 as part of the General Social Survey, 1289 randomly selected American adults responded to this question:

Radda [10]

Answer:

B (0.312, 0.364)

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence interval $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$

For this problem, we have that:

1289 randomly selected American adults responded to this question. This means that $n = 1289$ .

Of the respondents, 436 replied that America is doing about the right amount. This means that $\pi = \frac{436}{1289} = 0.3382$ .

Determine a 95% confidence interval for the proportion of all the registered voters who will vote for the Republican Party. 

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3382 - 1.96\sqrt{\frac{0.3382*0.6618}{1289}} = 0.312$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3382 + 1.96\sqrt{\frac{0.3382*0.6618}{1289}} = 0.364$

The 95% confidence interval is:

B (0.312, 0.364)

5 0

3 years ago