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Illusion [34]
3 years ago
12

Solve similar triangles

Mathematics
2 answers:
nalin [4]3 years ago
5 0

Answer:

7.5 ?

Step-by-step explanation:

jeka943 years ago
4 0

Answer:

7.5

Step-by-step explanation:

We are given information that the two triangles are similar and we want to work out the length of "t" . Since these 2 triangles are similar, it means that a scale factor is used to enlarge the sides, we can work out the scale by dividing QP by LJ and RP by KJ so,

QP ÷ JK = 25 ÷ 5 = 5

RP ÷ JL = 22.5 ÷ 4.5 = 5

So we can see the scale factor is 5, now all we need to do is multiply the scale factor by 1.5 to find the value of t

1.5 × 5 = 7.5

The value of t is 7.5

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Write the equation in slope-intercept form then change it to standard form with integer coefficients.
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Answer:

1. Slope-intercept form:   y = 2x - 4

Standard form:   2x - y = 4

2. Slope-intercept form:  y = \dfrac12x - 1

Standard form:             x - 2y = 2

3. Slope-intercept form:   y = \dfrac45x + \dfrac{21}{5}

Standard form:            4x -5y = - 21

Step-by-step explanation:

Slope intercept form:   y = mx + b

where:

  • y = y-coordinate
  • m = slope
  • x = x-coordinate
  • b = y-intercept

Standard form:  Ax + By = C

\textsf{1.  as} \ m=2: \ \ y = 2x + b

   \textsf{at} \  (6, 8): \ \ 8 = 2(6) + b

   \implies b = -4

Slope-intercept form:   y = 2x - 4

Standard form:   2x - y = 4

\textsf{2.  as} \  \ m = \dfrac12: \ \ y = \dfrac12x + b

    \textsf{at} \  (4, 1): \ \ 1 = \dfrac12(4) + b

    \implies b = -1

Slope-intercept form:  y = \dfrac12x - 1

Standard form:             x - 2y = 2

\textsf{3.  as} \  \ m = \dfrac45: \ \ y = \dfrac45x + b

   \textsf{at} \  (1,5): \ \ 5 = \dfrac45(1) + b

   \implies b = \dfrac{21}{5}

Slope-intercept form:   y = \dfrac45x + \dfrac{21}{5}

Standard form:            4x -5y = - 21

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