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kondor19780726 [428]
3 years ago
7

Select the postulate or theorem that you can use to conclude that the triangles are similar.

Mathematics
1 answer:
insens350 [35]3 years ago
8 0

Answer: SAS similarity postulate

Step-by-step explanation:

According to SAS postulate of similarity, two triangles are called similar if two sides in one triangle are in the same proportion to the corresponding sides in the other, and the included angle are congruent.

In triangles, QNR and MNP,

\frac{QN}{MN} = \frac{QM+MN}{MN} = \frac{10+8}{8} = \frac{18}{8} = \frac{9}{4}

\frac{NR}{NP} = \frac{NP+NR}{NP} = \frac{10+8}{8} = \frac{18}{8} = \frac{9}{4}

\implies \frac{QN}{MN} = \frac{NR}{NP}

Also,

\angle QNR\cong \angle MNP  (Reflexive)

Thus, By SAS similarity postulate,

\triangle QNR\sim\triangle MNP

⇒ Option first is correct.

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Andru [333]

Answer:

the first one

Step-by-step explanation:

2x+у=3

3x-y=2

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3 years ago
Draw the graph for f(x)=x-1/x^2-x-6 and state:a. the x-intercept(s).b. the y-intercept.c. the equation(s) of any vertical asympt
Zigmanuir [339]

ANSWER:

a. (1, 0)

b. (0, 1/6)

c. x = -2. x = 3

d. y = 0

e. The asymptotes have the form of a line and divide the function into 3 parts.

f.

\begin{equation*} \text{Domain: }\left(-\infty\:,\:-2\right)\cup\left(-2,\:3\right)\cup\left(3,\:\infty\:\right) \end{equation*}

g.

\text{Range}(-\infty,\infty)

STEP-BY-STEP EXPLANATION:

We have the following function:

f\left(x\right)=\frac{x-1}{x^2-x-6}

The graph corresponding to the function is the following:

We determine in each case what the statement asks for, like this:

a. the x-intercept(s):

\begin{gathered} \text{ in this case y = 0, therefore:} \\  \\ \frac{x-1}{x^2-x-6}=0 \\  \\ x-1=0\cdot(x^2-x-6) \\  \\ x=1 \\  \\ \text{The x-intercept is \lparen1, 0\rparen} \end{gathered}

b. the y-intercept:

\begin{gathered} \text{ in this case x = 0, therefore } \\  \\ y=\frac{0-1}{0^2-0-6} \\  \\ y=\frac{-1}{-6} \\  \\ y=\frac{1}{6} \\  \\ \text{ The y-intercept is }\:\left(0,\frac{1}{6}\right) \end{gathered}

c. the equation(s) of any vertical asymptote(s). The horizontal asymptotes are the values that x cannot take since the function would be discontinuous for those values.

In this case, since it is a rational function, it would be when the denominator is 0, therefore, we solve the following:

\begin{gathered} x^2-x-6=0 \\  \\ (x-3)(x+2)=0 \\  \\ x-3=0\rightarrow x=3 \\  \\ x+2=0\operatorname{\rightarrow}x=-2 \\  \\ \text{ The equation\lparen s\rparen of any vertical asymptote are:} \\  \\ x=3,x=-2 \end{gathered}

d. the equation of the horizontal asymptote. If the degree of the denominator is greater than that of the numerator, the horizontal asymptote is the x-axis, that is:

y=0

e. information about the behavior at the asymptote(s).

In this case the behavior of the asymptotes are straight lines that represent values that the function cannot take or cannot reach, divide the function into 3 parts.

f and g.

In this case, the domain is the interval of values that x can take and the range is the interval of values that y can take.

Therefore:

\begin{gathered} \text{Domain: }\left(-\infty\:,\:-2\right)\cup\left(-2,\:3\right)\cup\left(3,\:\infty\:\right) \\  \\ \text{Range:}\:\left(-\infty\:,\:\infty\:\right) \end{gathered}

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Find the measure of x.
snow_lady [41]

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That means

∠C+∠A=180⁰

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Answer: x=96⁰.

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3 years ago
The measure of an angle is 12°. What is the measure of its supplement?<br> *No answer just number*
Elena-2011 [213]

Answer:

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Step-by-step explanation:

5 0
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Answer:

$52091.95

Step-by-step explanation:

From the given information:

The number of  cities visited = 14

Cost of each cooking demonstration = $3450

The total cost of cooking demonstration = $3450 × 14

= $48300

Book signing material = $1475

∴

The total cost of cooking demonstration and book material is:

= $48300 + $1475 = $49775 ---- (i)

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However; suppose the weekly rental fee fine = $x  &

the change per mile = $y

Then

y*540 + x = 1188.15    --- (ii)

y*880 + x = 1310.55   --- (iii)

From equation (ii) and (iii)

y *340 = 122.4

y = 122.4/340

y = 0.36

From (ii)

y × 540 + x = 1188.15

(0.36)540 + x = 1188.15

x = 1188.15 - (0.36)540

x = 993.75

Hence, the total cost of travelling by RV camper = $1993.75 + 3120 × (0.36)

= $2116.95

Thus, the total amount the publisher should budget = $49975.0 + $2116.95

= $52091.95

8 0
3 years ago
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