A city map is placed on a coordinate grid. The post office is located at the pointP ( 5, 35) , the library is located at the point L (15, 10) , and the fire station is
located at the point F  (9, 25) . What is the ratio of the length of PF to the length of
LF ?
A 2 : 3
B 3 : 2
C 2 : 5
D 3 : 5

Answers

Answer 1

Answer: The distance between two points:
$d=√((x_2-x_1)^2+(y_2-y_1)^2)$
(x₁,y₁), (x₂,y₂) - the coordinates of the points

$P(5,35) \nL(15,10) \nF(9,25) \n \n\overline{PF} = √((9-5)^2+(25-35)^2)=√(4^2+(-10)^2)=√(16+100)= \n=√(116)=√(4 * 29)=2√(29) \n \n\overline{LF}=√((9-15)^2+(25-10)^2)=√((-6)^2+15^2)=√(36+225)= \n=√(261)=√(9 * 29)=3√(29) \n \n\frac{\overline{PF}}{\overline{LF}}=(2√(29))/(3√(29))=(2)/(3)=2:3$

The answer is A.

Answer 2

Answer:

Final answer:

The ratio of the length of PF to the length of LF on the coordinate grid can be found by using the distance formula. After calculation, we find that the ratio is approximately 2:3.

Explanation:

To answer this question, you need to know how to calculate the distance between two points on the coordinate grid, which can be found using the distance formula. The distance formula is √[(x2-x1)² + (y2-y1)²] where (x1, y1) and (x2, y2) are the coordinates of two points on a plane.

First, calculate the length of PF as follows:

PF = √[(9-5)² + (25-35)²] = √[16 + 100] = √116≈10.77

Next, calculate the length of LF as follows:

LF = √[(15-9)² + (10-25)²] = √[36 + 225] = √261≈16.155

Hence, the ratio of the length of PF to the length of LF is approximately 10.77:16.155 which approximately reduces to 2:3.

Therefore, the answer is A: 2:3.

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This is hard for me, can someone please help? Loren solved the equation 10 = StartFraction 19 Over 9 EndFraction (149) + b for b as part of her work to find the equation of a trend line that passes through the points (1, 130) and (10, 149). What error did Loren make? She should have solved 10 = StartFraction 9 Over 19 EndFraction (149) + b for b. She should have solved 1 = StartFraction 19 Over 9 EndFraction (130) + b for b. She should have solved 149 = StartFraction 19 Over 9 EndFraction (10) + b for b. She should have solved 130 = StartFraction 9 Over 19 EndFraction (1) + b for b.

Answers

The solution is, the equations of line passes through two points:(1,130), (10.149) is:

149=19/9 (10) +b

130=19/9(1)+b

What is a straight line?

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

for Loren to find a line passes through two points:(1,130), (10.149)

1) find slope: m=y2-y1/x2-x1 =149-130/10-1=19/9

m=19/9

to find b in the equation y=mx+b for point (1,130)

y=130, x=1, m=19/9

130=19/9(1)+b

for point (10,149)

149=19/9 (10) +b

you have two options

Hence, The solution is, the equations of line passes through two points:(1,130), (10.149) is:

149=19/9 (10) +b

130=19/9(1)+b

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Answer:

149=19/9 (10) +b

130=19/9(1)+b

Step-by-step explanation:

for Loren to find a line passes through two points:(1,130), (10.149)

1) find slope: m=y2-y1/x2-x1 =149-130/10-1=19/9

m=19/9

to find b in the equation y=mx+b for point (1,130)

y=130, x=1, m=19/9

130=19/9(1)+b

for point (10,149)

149=19/9 (10) +b

you have two options

Which value, when placed in the box, would result in a system of equations with infinitely many solutions?y=2x-5
2y - 4x =
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5
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Answers

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Step-by-step explanation:

If x = 2, find the value of 3x^3 - 3x - 2.

Answers

Answer:

Step-by-step explanation:

3x^3-3x-2

x=2

3(2)^3-3(2)-2

3×8-6-2

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Understand?

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