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harina [27]
3 years ago
13

Triangle DEF is similar to triangle GHK. What is the value of DF if GK is 3.4 inches, EF is 2.25 inches, and HK is 9 inches?

Mathematics
1 answer:
kap26 [50]3 years ago
4 0
DF=3.4 because it's congruent to GK
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The measure of one angle of a right angle is 50 more then the measure of the smallest angle
Nataly_w [17]

Answer:

70° and 20°

Step-by-step explanation:

let x be the measure of one angle then x + 50 is the measure of the other angle, thus

x + 50 + x = 90

2x + 50 = 90 ( subtract 50 from both sides )

2x = 40 ( divide both sides by 2 )

x = 20

The smallest angle is 20° and the other angle is 20 + 50 = 70°

5 0
3 years ago
In the 1990s the demand for personal computers in the home went up with household income. For a given community in the 1990s, th
WITCHER [35]

Answer:

a) 0.5198 computers per household

b) 0.01153 computers

Step-by-step explanation:

Given:

number of computers in a home,

q = 0.3458 ln x - 3.045 ;   10,000 ≤ x ≤ 125,000

here x is mean household income

mean income = $30,000

increasing rate, \frac{dx}{dt} = $1,000

Now,

a) computers per household are

since,

mean income of  $30,000 lies in the range of 10,000 ≤ x ≤ 125,000

thus,

q = 0.3458 ln(30,000) - 3.045

or

q = 0.5198 computers per household

b) Rate of increase in computers i.e \frac{dq}{dt}

\frac{dq}{dt} = \frac{d(0.3458 ln x - 3.045)}{dt}

or

\frac{dq}{dt}=0.3458\times(\frac{1}{x})\frac{dx}{dt} - 0

on substituting the values, we get

\frac{dq}{dt}=0.3458\times(\frac{1}{30,000})\times1,000

or

= 0.01153 computers

6 0
3 years ago
Solve the system of linear equations by substitution.<br><br> −2x−5y=3<br><br> 3x+8y=−6
DochEvi [55]

Answer:

x=6 y=-3

Step-by-step explanation:

7 0
3 years ago
Three consecutive intergers have a sum of 84. Find the intergers<br><br> ___,___,___,
Fudgin [204]

Answer:

27 + 28 + 29 = 84

Step-by-step explanation:

x + (x+1) + (x+2) = 84

3x + 3 = 84

84 - 3 = 81

81 / 3 = 27

8 0
4 years ago
A triangle has a side length of 4in in an area of 18 square inches and a larger similar triangle has a corresponding side length
Harman [31]

Answer:

72

<em>s1</em><em> </em><em>:</em><em>s2</em><em> </em><em>=</em><em> </em><em>A1</em><em> </em><em>:</em><em> </em><em>A2^</em><em>2</em>

<em>So</em><em> </em><em>the</em><em> </em><em>factor</em><em> </em><em>of</em><em> </em><em>the</em><em> </em><em>sides</em><em> </em><em>is</em><em> </em><em>2</em><em>.</em><em> </em><em>Now</em><em> </em><em>you</em><em> </em><em>multiply</em><em> </em><em>the</em><em> </em><em>area</em><em> </em><em>by</em><em> </em><em>2</em><em> </em><em>squared</em><em>.</em>

5 0
3 years ago
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