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3 years ago

What value of t makes the following equation true? 3(t−2)=−1

Mathematics

2 answers:

USPshnik [31]3 years ago

8 0

Answer:

Step-by-step explanation:

3(t-2)=-1

3t-6=-1

3t-6+6=-1+6

3t=5

t=5/3

adell [148]3 years ago

8 0

Answer:

5/3

Step-by-step explanation:

3(t - 2) = -1

3t - 6 = -1

3t = -1 + 6

3t = 5

t = 5/3 <==

lets check it..

3(5/3 - 2) = -1

3(5/3 - 6/3) = -1

3(-1/3) = -1

-3/3 = -1

-1 = -1 (correct)...it checks out

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1 year ago

GJ is a midsegment of triangle DEF, and HK is a midsegment of triangle GFJ. What is the length of HK?

loris [4]

Answer:

Option B) 4 centimeters

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the value of n

we know that

a) GJ is a midsegment of triangle DEF

then

G is the midpoint segment DF and J is the midpoint segment EF

DG=GF and EJ=JF

b) HK is a midsegment of triangle GFJ

then

H is the midpoint segment GF and K is the midpoint segment JF

GH=HF and JK=KF

In this problem we have

HF=7 cm

GH=7 cm

GF=GH+HF ----> by addition segment postulate

GF=7+7=14 cm

Remember that

DG=GF

substitute the given values

$2n-1=14$

solve for n

$2n=14+1$

$2n=15$

$n=7.5\ cm$

step 2

Find the length of GJ

we know that

The <u><em>Midpoint Theorem</em></u> states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side

$GJ=\frac{1}{2}DE$

we have

$GE=2n+1=2(7.5)+1=16\ cm$

substitute

$GJ=\frac{1}{2}16=8\ cm$

step 3

Find the length of HK

we have that

$HK=\frac{1}{2}GJ$ ----> by the midpoint theorem

we have

$GJ=8\ cm$

substitute

$HK=\frac{1}{2}8=4\ cm$

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