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netineya [11]
3 years ago
6

In △FEG , point H is between points E and F, point J is between points F and G, and HJ¯¯¯¯¯∥EG¯¯¯¯¯ .

Mathematics
1 answer:
CaHeK987 [17]3 years ago
5 0

Answer:

FJ=39\ units

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

△FEG is similar with △FHJ -----> by AA Similarity Theorem

so

\frac{FE}{FH}=\frac{FG}{FJ}

we have

FE=HF+EH=26+14=40\ units

FH=HF=26\ units

FG=60\ units

substitute the given values

\frac{40}{26}=\frac{60}{FJ}

FJ=26(60)/40\\FJ=39\ units

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What's slope Line
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Rema spent 6 days reading her book, completing the same fraction of the book each day, if she read a total of 8/9 of her book af
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Using the completing-the-square method, rewrite f(x) = x2 + 10x + 7 in vertex form
mr Goodwill [35]

Answer:

f(x) = (x - (-5))^2 + (-18)

Step-by-step explanation:

Given:

f(x) = x^2 + 10x + 7

Rewrite f(x) in vertex form

Solution:

f(x) = ax^2 + bx + c is a quadratic function.

The vertex form of f(x) is a(x - h)^2 + k, where (h, k) is the vertex.

=> f(x) = x^2 + 10x + 7

          = x^2 + 10x + 25 - 18

          = (x + 5)^ - 18

          = (x - (-5))^2 + (-18)

=> f(x) can be rewritten in form of a(x - h)^2 + k, where (h, k) is the vertex, with a = 1, h = -5, k = -18

6 0
3 years ago
Write the following series in sigma notation.<br> 7 + 16 + 25 +34 +43 +52 + 61
Solnce55 [7]

The series 7 + 16 + 25 +34 +43 +52 + 61 is an illusration of arithmetic series

The sigma notation of the series is: \sum\limits^7_{n=1} {9n - 2}

<h3>How to write the series in sigma notation?</h3>

The series is given as:

7 + 16 + 25 +34 +43 +52 + 61

The above series is an arithmetic series, with the following parameters

  • First term, a = 7
  • Common difference, d = 9
  • Number of terms, n = 7

Start by calculating the nth term using:

a(n) = a + (n - 1) * d

This gives

a(n) = 7 + (n - 1) * 9

Evaluate the product

a(n) = 7  - 9 + 9n

Evaluate the difference

a(n) = 9n - 2

So, the sigma notation is:

\sum\limits^7_{n=1} {9n - 2}

Read more about arithmetic series at:

brainly.com/question/6561461

3 0
2 years ago
What is the slope of the line that passes through the points (-3, 6) and (1,2)
Nadya [2.5K]

Answer:

the slope is -1

m = -1

Step-by-step explanation:

y2 - y1     y

--------- = ----

x2 - x1     x

= y/x = m

2 - 6

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1 - - 3

= -4/4

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8 0
3 years ago
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