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Alex
3 years ago
13

Determine whether the lines l1 and l2 given by the vector equations are parallel, perpendicular, or neither. L1: r(t) = (-4 + 3t

)i + (5 + t)j l2: r(s) = (5 + 2s)i + (1 - 6s)j
Mathematics
1 answer:
Vilka [71]3 years ago
4 0

Over which interval(s) is the function decreasing?

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Suppose the lengths of two sides of a right triangle are represented by 2x and 3 (x + 1), and the longest side is 17 units. Find
densk [106]

Answer:

x=4

Step-by-step explanation:

<u>Step 1</u>:-

given the lengths of two sides of a right angle are represented by 2x and 3(x+1) and longest side is 17 units.

AB = 2x and BC = 3(x+1) and longest side AC= 17

by using Pythagoras theorem

AC^2 = AB^2 + BC^2

<u>step 2:-</u>

The hypotenuse is longest side is AC = 17 units

(17)^2 = 4x^2 +9(X+1)^2

on simplification, we will use formula

(a + b)^2 = a^2 +2ab+b^2

289 = 4x^2 +9(x^2+2x+1)

13x^2 +18x-280 = 0

finding factors  70 X 52 = 3640

13x^2 +70x-52x-280 = 0

13x^2 -52x+ 70x-280 = 0

Taking common , we get

13x(x-4)+70(x-4)=0

x-4=0 and 13x+70=0

x=4 and 13x =-70

x=4 and x=\frac{-70}{13}

we can not choose negative value so x value is 4

Final answer:- x = 4

<u>verification:-</u>

<u></u>AC^2 = AB^2 + BC^2<u></u>

289 = 4(4)^2+9(4+1)^2

289 = 64 +9(25)

289=289

6 0
3 years ago
Read 2 more answers
I'm confused can someone help me
Dafna11 [192]

Answer: M∠2 just mean measure of angle 2,

Step-by-step explanation: So I worked it out and the awnser is B.

3 numbers/the degrees of all 3 sides always add up to 180 degrees.

Side 1 is 60 degrees and the left side is 20, so 20 + 60 + 3 (unkown    number) = 180

60 - 20 = 100,

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3 years ago
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The second term in a geometric sequence is 20. The fourth term in the same sequence is 45/4 or 11.25. What is the common ratio i
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\bf \begin{array}{ccll}&#10;n&term&value\\&#10;\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\&#10;2&a_2&20\\&#10;3&a_3&20r\\&#10;4&a_4&20rr\\&#10;&&20r^2\\\\&#10;&&\frac{45}{4}&#10;\end{array}\implies \stackrel{4^{th}~term}{20r^2=\cfrac{45}{4}}\implies r^2=\cfrac{45}{80}&#10;\\\\\\&#10;r^2=\stackrel{simplified}{\cfrac{9}{16}}\implies r=\sqrt{\cfrac{9}{16}}\implies r=\cfrac{\sqrt{9}}{\sqrt{16}}\implies r=\cfrac{3}{4} 
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HELPP PLEASE <br><br> let f(x)=2x^2+3x+1 and g(x)=x^2 +8. Find g(f(x)). Show each step
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Answer:

When applicable, state the domain restriction. g(f(x)) 4 x2 + 1 16 x2 + 3 4 x2 + 7 16 x2 - 8 x + 3 Please help. I thinks that it is 16 x2 + 3. College Algebra. Consider the function f(x)=4 - x^2 for the domain [ 0,∞). Find f^−1 (x), where f^−1 is the inverse of f

Step-by-step explanation:

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