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Helen [10]
3 years ago
10

Find the value of the variable and YZ if Y is between X and Z. XY=4n+3, YZ=2n-7,XZ=22

Mathematics
1 answer:
ruslelena [56]3 years ago
7 0

Answer:

\large \boxed{n = \dfrac{13}{3}; YZ = \dfrac{5}{3}}}

Step-by-step explanation:

I think you have the situation shown in the diagram below.

1. Calculate the value of n

\begin{array}{rcl}XY + YZ & = & XZ\\4n+ 3 + 2n - 7 & = & 22\\6n - 4 & = & 22\\6n & = & 26\\n & = & \dfrac{26}{6}\\\\& = & \mathbf{\dfrac{13}{3}}\\\end{array}\\\large \boxed{\mathbf{n = \dfrac{13}{3}}}

2. Calculate the value of YZ

\begin{array}{rcl}YZ & = & 2n - 7\\& = & 2\left (\dfrac{13}{3}\right ) - 7 \\\\& = & \dfrac{26}{3} - 7\\\\& = & \dfrac{26}{3} - \dfrac{21}{3}\\\\& = & \dfrac{5}{3} \\\\\end{array}\\\large \boxed{YZ = \mathbf{ \dfrac{5}{3}}}

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Answer:

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8 0
2 years ago
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Please help. What is the circumference of the circle? <br><br> (X+4)^2+(y-5)^2=81
PIT_PIT [208]

the radius: r^2 = 81

r =9

c = 2*pi*r

 = 2 * pi * 9

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Answer: 18*pi or approximately 56.62

8 0
3 years ago
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If the length of a rectangle is a two-digit number with identical digits and the width is 1/10 the length and the perimeter is 2
Oksanka [162]

If the length of a rectangle is a two-digit number with identical digits and the width is 1/10 the length and the perimeter is 2 times the area of the rectangle, what is the the length and the width

Solution:

Let the length of rectangle=x

Width of rectangle=x/10

Perimeter is 2(Length+Width)

= 2(x+x/10)

Area of Rectangle= Length* Width=x*x/10

As, Perimeter=2(Area)

So,2(x+x/10)=2(x*x/10)

Multiplying the equation with 10, we get,

2(10x+x)=2x²

Adding Like terms, 10x+x=11x

2(11x)=2x^2

22x=2x²

2x²-22x=0

2x(x-11)=0

By Zero Product property, either x=0

or, x-11=0

or, x=11

So, Width=x/10=11/10=1.1

Checking:

So, Perimeter=2(Length +Width)=2(11+1.1)=2*(12.1)=24.2

Area=Length*Width=11*1.1=12.1

Hence, Perimeter= 2 Area

As,24.2=2*12.1=24.2

So, Perimeter=2 Area

So, Answer:Length of Rectangle=11 units

Width of Rectangle=1.1 units

7 0
3 years ago
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If you roll a fair six-sided die and a fair four-sided die, what is the probability that neither die shows a 1?
Masja [62]
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For the second die, 3 out of 4 are not 1. 
That is 3/4.  
Multiply 5/6 by 3/4 to get the probability.
5/6 x 3/4 = 20/72 
Simplify once to get 10/36. 
Do it again to get 5/18. 
In decimal form it is 0.2777 and in percent form it is 27.77%. 
Hope this helps!

3 0
3 years ago
Bobby biked 12/3 hours on monday 21/3 hours on tuesday and 22/3 hours on wednesday. what is the total number of hours bobby spen
serg [7]
The fractions you're given can be simplified down, so you get (12 ÷ 3) 4 hours on Monday, (21 ÷ 3) 7 hours on Tuesday, and (22 ÷ 3) 7 1/3 hours on Wednesday. You can now add these up and get your answer as 18 1/3 hours, or 18.33.

I hope this helps!
8 0
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