In the figure below, D is the midpoint of AB, E is the midpoint of BC, and F is the midpoint of AC. Find the perimeter of triangle ABC.
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(( E )) is the midpoint of BC ,
Thus ;
[tex]BE = CE = 6[/tex]
So :
[tex]BC = 12[/tex]
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[tex] \frac{AC}{2} = DE \\ [/tex]
[tex] \frac{AC}{2} = 7.5 \\ [/tex]
Multiply sides by 2
[tex]2 \times \frac{AC}{2} = 2 \times 7.5 \\ [/tex]
[tex]AC = 15[/tex]
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[tex] \frac{AB}{2} = EF \\ [/tex]
[tex] \frac{AB}{2} = 8 \\ [/tex]
Multiply sides by 2
[tex]2 \times \frac{AB}{2} = 2 \times 8 \\ [/tex]
[tex]AB = 16[/tex]
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[tex]∆ABC \: \: Perimeter =
AB + BC + AC \\ [/tex]
[tex]
∆ABC \: \: Perimeter = 16 + 12 + 15 \\ [/tex]
[tex]
∆ABC \: \: Perimeter = 43[/tex]
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Done...
The perimeter of triangle ABC is 43.
The calculation is as follows:Since BE = CE = 6
So, BC = 12
Now
[tex]AC \div 2 = DE\\\\AC\div 2 = 7.5[/tex]
Now multiplied sides by 2
So,
[tex]2\times AC \div 2 = DE\\\\AC\div 2 = 7.5 \times 2[/tex]
AC = 15
Half of AB = EF
AB = 16
Now the perimeter is
= AB + BC + AC
= 16 + 12 + 15
= 43
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B. 4/11
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Gradient=(y1-y2)/(x1-x2)
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What is an equation of the line that passes through the points (4,−1) and (8, 5)? Put your answer in fully reduced form.
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Answers
Answer:
y=2/3x-7
Step-by-step explanation:
The slope intercept formula is
y=mx+b
(m) is the slope (rate of change)
(b) is the y intercept (where the line crosses the y axis [vertical])
We need to find the slope and the y intercept. First we will find the slope.
The formula for slope is y1-y2/x1-x2
In and ordered pair the first value is the (x) and the second is the (y).
(x, y)
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6/4 Simplify
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Now we apply out new slope into our y=mx+b
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Now we need to find the (b) which is the y intercept.
To do this we need to use one of our given points, you can choose either but for this I'll use (4, -1).
In this ordered pair 4 is the (x) and -1 is the (y)
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Science, technology, engineering and mathematics or STEM education was an initiative developed by the________________.
A. National Science Foundation
B.National Scholar Foundation
C. National Schools Foundation
D. National Secondary Foundation
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Answers
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The graph below shows the relationship between the distance and the amount of time that Theo's family traveled.
Answers
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Malcom's family travel 15 miles per hour faster than Theo's
Step-by-step explanation:
See attachment for complete question
Given
Malcom's Family:
[tex]d = 65t[/tex]
To determine the equation of Theo's family, we refer to the attached graph.
From the graph:
[tex]t = 1; d = 50[/tex]
[tex]t = 2; d = 100[/tex]
First, we determine the slope, m:
[tex]m = \frac{d_2 - d_1}{t_2 - t_1}[/tex]
[tex]m = \frac{100 - 50}{2- 1}[/tex]
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Next, we determine equation for Theo's family using:
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[tex]d =50t[/tex]
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SSS
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