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2 years ago

13

Make z the subject 9d= 6z - 5d

1 answer:

yarga [219]2 years ago

4 0

Answer:

$z=2\frac{1}{3}d$

Step-by-step explanation:

$9d=6z-5d$

$6z=9d+5d$

$6z=14d$ (combine like terms)

$z=2\frac{1}{3}d$

Hope this helps :)

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Kristen lives directly east of the park. The football field is directly south of the park. The library sits on the line formed b

guajiro [1.7K]

With that information you can determine how far the park is from the football field.

Call h the height of the triangle, x the distance from the park to the football field and y the distance from the park to the home of Kristen.

Using Pithagora's theorem, ou can state this system of equations:

1) From the complet triangle: x^2 + y^2 = (8 + 2)^2 = 10^2 = 100

2) From the triangle whose hypotenuse is the distance from the park to the football field:

x^2 = 8^2 + h^2

3) From the triangle whose hypotenuse is the distance from the park to the home of Kristen:

y^2 = 2^2 + h^2

To solve the system start by subtracting equation 3) from equation 1) =>

x^2 + y^2 = 100
y^2 = 4 + h^2
---------------------
x^2 = 100 - 4 - h^2

x^2 = 96 - h^2

Now sum this result to equation 2

x^2 = 96 - h^2
x^2 = 64 + h^2
---------------------
2x^2 = 96 + 64

2x^2 = 160

=> x^2 = 80

=> x = 8.94

Answer: 8.94 miles

6 0

3 years ago

R (-3,1) and S (-1,3) are points on a circle. If RS is a diameter, find the equation of the circle.

ELEN [110]

Answer:

$\sf (x+2)^2+(y-2)^2=2$

Step-by-step explanation:

If RS is the diameter of the circle, then the midpoint of RS will be the center of the circle.

$\sf midpoint=\left(\dfrac{x_s-x_r}{2}+x_r,\dfrac{y_s-y_r}{2}+y_r \right)$

$\sf =\left(\dfrac{-1-(-3)}{2}+(-3),\dfrac{3-1}{2}+1 \right)$

$\sf =(-2, 2)$

Equation of a circle: $\sf (x-h)^2+(y-k)^2=r^2$

(where (h, k) is the center and r is the radius)

Substituting found center (-2, 2) into the equation of a circle:

$\sf \implies (x-(-2))^2+(y-2)^2=r^2$

$\sf \implies (x+2)^2+(y-2)^2=r^2$

To find $\sf r^2$ , simply substitute one of the points into the equation and solve:

$\sf \implies (-3+2)^2+(1-2)^2=r^2$

$\sf \implies 1+1=r^2$

$\sf \implies r^2=2$

Therefore, the equation of the circle is:

$\sf (x+2)^2+(y-2)^2=2$

4 0

2 years ago

Gh bisects fgi. solve for fgi,fgh,hgi solve for x Simplify all answers

Lelechka [254]

Answer:

fgi = 48

fgh = 24

hgi = 24

Step-by-step explanation:

Bisection divides an angle into two equal angles,

So,

4x - 20 = 3x - 9

4x - 3x = - 9 + 20

x = 11

fgi = 3x - 9 + 4x - 20

= 3x + 4x - 20 - 9

= 7x - 29

= 7 ( 11 ) - 29

= 77 - 29

fgi = 48

fgh = 3x - 9

= 3 ( 11 ) - 9

= 33 - 9

fgh = 24

hgi = 4x - 20

= 4 ( 11 ) - 20

= 44 - 20

hgi = 24

5 0

2 years ago

Five hundred yards of fence is to be used to enclose a rectangular area next to a straight river. The river bank acts as one sid

fenix001 [56]

Answer:

the requirements are missing:

express the height of the rectangle in terms of w
express the area of the rectangle in terms of w

1) the height of the rectangle is:

w + h + h + w = 500 + w

2w + 2h = 500 + w

2h = 500 + w - 2w = 500 - w

h = (500 - w) / 2 = 250 - 0.5w

2) the are of the rectangle is:

w x h = w x (250 - 0.5w) = 250w - 0.5w²

3 0

2 years ago

The mclntosh family went apple picking.They picked a total of 115 apples.The family ate a total of 8 apples each day.After how m

aleksklad [387]

Answer:

its b i took the test

Step-by-step explanation:

5 0

2 years ago