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2 years ago

10

On a coordinate plane, a line is drawn from Rock to Tree. The x- and y-axes are labeled feet. Rock is at (3, 2) and Tree is at (

16, 21).
A treasure map says that a treasure is buried so that it partitions the distance between a rock and a tree in a 5:9 ratio. Marina traced the map onto a coordinate plane to find the exact location of the treasure.

x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1

y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1

What are the coordinates of the treasure? If necessary, round the coordinates to the nearest tenth.

(11.4, 14.2)
(7.6, 8.8)
(5.7, 7.5)
(10.2, 12.6)

2 answers:

-Dominant- [34]2 years ago

6 0

Answer:

The second choice $(7.6,8.8)$

Step-by-step explanation:

The missing image is attached

We use the section formula:

$(x,y)=(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

We substitute $x_1=3,x_2=16,y_1=2,y_2=21$ and m=5, n=9

$(x,y)=(\frac{5*16+9*3}{5+9},\frac{5*21+5*2}{9+5})$

We simplify to get:

$(x,y)=(\frac{80+27}{14},\frac{105+10}{14})$

This simplifies to:

$(x,y)=(\frac{107}{14},\frac{125}{14})$

In decimals we get:

$(x,y)=(7.6,8.8)$

ladessa [460]2 years ago

4 0

Answer:

(7,6, 8,8)

Step-by-step explanation:

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3 years ago

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Using the given information, give the vertex form equation of each parabola.

Amanda [17]

Answer:

The equation of parabola is given by : $(x-4) = \frac{-1}{3}(y+3)^{2}$

Step-by-step explanation:

Given that vertex and focus of parabola are

Vertex: (4,-3)

Focus:( $\frac{47}{12}$ ,-3)

The general equation of parabola is given by.

$(x-h)^{2} = 4p(y-k)$ , When x-componet of focus and Vertex is same

$(x-h) = 4p(y-k)^{2}$ , When y-componet of focus and Vertex is same

where Vertex: (h,k)

and p is distance between vertex and focus

The distance between two points is given by :

L= $\sqrt{(X2-X1)^{2}+(Y2-Y1)^{2}}$

For value of p:

p= $\sqrt{(X2-X1)^{2}+(Y2-Y1)^{2}}$

p= $\sqrt{(4-\frac{47}{12})^{2}+((-3)-(-3))^{2}}$

p= $\sqrt{(\frac{1}{12})^{2}}$

p= $\frac{1}{12}$ and p= $\frac{-1}{12}$

Since, Focus is left side of the vertex,

p= $\frac{-1}{12}$ is required value

Replacing value in general equation of parabola,

Vertex: (h,k)=(4,-3)

p= $\frac{-1}{12}$

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3 years ago

Read 2 more answers

Drag a description to match each equation.

AnnZ [28]

Given:

The descriptions and equations. The equations are

$y=4x$

$y=x+4$

To find:

The correct description for each equation and match them.

Solution:

We know that, "+" is used for more and "×" is used for times.

Additive: y is 4 more than x.

$y=x+4$

Additive: x is 4 more than y.

$x=y+4$

Multiplicative: y is 4 times x.

$y=4x$

Multiplicative: x is 4 times y

$x=4y$

Therefore, the correct description for the equation $y=4x$ is "Multiplicative: y is 4 times x " and the correct description for the equation $y=x+4$ is "Additive: y is 4 more than x. "

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3 years ago