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AleksandrR [38]
3 years ago
14

Find the value of the variable if P is between J&K JP=8z-17; PK=5z+37; JK=17z-4

Mathematics
1 answer:
pochemuha3 years ago
5 0
Because P it between J and K it means that JP+PK = JK. That means:
8z-17+5z+37=17z-4
13z+20=17z-4
4z=24
z=6

<span>The value of the variable is 6.</span>
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A is correct.

-8, -4, 0, 2

-|-4| becomes -(4) which becomes -4.
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Solve for h.<br><br> –2 − 10h = –11h − 20
Delvig [45]

。☆✼★ ━━━━━━━━━━━━━━  ☾  

-2 - 10h = -11h - 20

+ 2

- 10h = -11h - 18

+ 11h

h = -18

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Is it true that 5 + 4 = 4 + 5 ? Explain why.
vfiekz [6]
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7 0
3 years ago
Each train car holds 71 passengers. About how many train cars
gulaghasi [49]

567/71 because passengers/(train cars/passengers) = train cars

71 x 7 = 497 (not enough)

71 x 8 = 568 (enough)

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7 0
2 years ago
6. Two observers, 7220 feet apart, observe a balloonist flying overhead between them. Their measures of the
MaRussiya [10]

Answer:

The ballonist is at a height of 3579.91 ft above the ground at 3:30pm.

Step-by-step explanation:

Let's call:

h the height of the ballonist above the ground,

a the distance between the two observers,

a_1 the horizontal distance between the first observer and the ballonist

a_2 the horizontal distance between the second observer and the ballonist

\alpha _1 and \alpha _2 the angles of elevation meassured by each observer

S the area of the triangle formed with the observers and the ballonist

So, the area of a triangle is the length of its base times its height.

S=a*h (equation 1)

but we can divide the triangle in two right triangles using the height line. So the total area will be equal to the addition of each individual area.

S=S_1+S_2 (equation 2)

S_1=a_1*h

But we can write S_1 in terms of \alpha _1, like this:

\tan(\alpha _1)=\frac{h}{a_1} \\a_1=\frac{h}{\tan(\alpha _1)} \\S_1=\frac{h^{2} }{\tan(\alpha _1)}

And for S_2 will be the same:

S_2=\frac{h^{2} }{\tan(\alpha _2)}

Replacing in the equation 2:

S=\frac{h^{2} }{\tan(\alpha _1)}+\frac{h^{2} }{\tan(\alpha _2)}\\S=h^{2}*(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})

And replacing in the equation 1:

h^{2}*(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})=a*h\\h=\frac{a}{(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})}

So, we can replace all the known data in the last equation:

h=\frac{a}{(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})}\\h=\frac{7220 ft}{(\frac{1 }{\tan(35.6)}+\frac{1}{\tan(58.2)})}\\h=3579,91 ft

Then, the ballonist is at a height of 3579.91 ft above the ground at 3:30pm.

6 0
2 years ago
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