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3 years ago

2. What is the value of x? Show your work.

Mathematics

2 answers:

kirza4 [7]3 years ago

8 0

Answer:

x=7

Step-by-step explanation:

We are given that

$\angle K=\angle N$

$\angle J=\angle M$

Therefore, $\triangle JKL\sim \triangle MNP$

By AA similarity postulate

AA similarity: When two angles of one triangle are equal to its corresponding angles of other triangle then , two triangles are similar by AA similarity.

When two triangles are similar then the ratio of their corresponding sides are equal.

Therefore, $\frac{JK}{MN}=\frac{JL}{MP}$

We have JK=25 units,MN=30 units

JL=20 units,MP= $4x-4$

Substitute the values then we get

$\frac{25}{30}=\frac{20}{4x-4}$

$\frac{5}{6}=\frac{20}{4(x-1)}=\frac{5}{x-1}$

$x-1=\frac{5\times 6}{5}$

$x-1=6$

$x=6+1=7$

Hence, the value of x=7

trapecia [35]3 years ago

4 0

The answer will be 7.....value of x is 7 i believe

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Answer:

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To reflect a linear function in the line y=x, find points on f(x) and then swap their x and y coordinates.

Points on f(x): (0, -4) (2, 0) (5, 6)

Points reflected in line y=x: (-4, 0) (0, 2) (6, 5)

Plot points (-4, 0) (0, 2) (6, 5) and connect to form a straight line - this is the inverse of the function: $f^{-1}(x)$

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Using the slope-intercept form: y = mx + b

(where m is the slope and b is in the y-intercept)

From inspection of the graph, we can see the line crosses the y-axis at -4,

⇒ f(x) = 2x - 4

As the line is actually a line segment (with endpoints (0, -4) and (5, 6), then

f(x) = 2x - 4, 0 ≤ x ≤ 5

To determine the equation of $f^{-1}(x)$ :

Rewrite f(x) as $y = 2x - 4$

Swap the x and y: $x = 2y - 4$

Rearrange to make y the subject: $y= \dfrac{1}{2}(x + 4)$

Replace y with $f^{-1}(x)$

So the equation of the inverse is: $f^{-1}(x)= \dfrac{1}{2}(x + 4)$

As the original function is a segment, then

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(shown in blue on the attached diagram)

** I can't see any points labelled E and F on the original function. If they are the endpoints of the line segment of f(x), then they are (0, -4) and (5, 6) **

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