Plot c so its distance from the origin is 1. Plot poin e 4/5 closer to the origin than c. What is its cooridinate?
Answers
Answer:
[tex]C = (1,0)[/tex]
[tex]E = (0.8,0)[/tex]
See attachment for C and E
Step-by-step explanation:
Given
[tex]O= (0,0)[/tex] --- Origin
[tex]CO = 1[/tex] --- distance of C to O
Solving (a): Plot point C
Calculate the coordinates of C using distance formula:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 -y_1)^2}[/tex]
Where:
[tex]O= (0,0)[/tex] ---[tex](x_1,y_1)[/tex]
[tex]C = (x,y)[/tex] -- [tex](x_2,y_2)[/tex]
[tex]d = CO = 1[/tex]
So, we have:
[tex]1 = \sqrt{(x - 0)^2 + (y -0)^2}[/tex]
[tex]1 = \sqrt{x^2 + y^2}[/tex]
Square both sides
[tex]1^2 = x^2 + y^2[/tex]
[tex]x^2 + y^2 =1[/tex]
For this solution, we assume y = 0
[tex]x^2 + 0^2 =1[/tex]
[tex]x^2=1[/tex]
Solve for x
[tex]x = 1[/tex]
So, the coordinates of C is: (1,0)
[tex]C = (1,0)[/tex]
Solving (b): Plot point E
We have that E is 4/5 closer to the origin.
This implies that, the ratio is:
[tex]m : n = 4/5:1/5[/tex]
Multiply by 5
[tex]m : n = 4:1[/tex]
So, E is at 4:1 between O and C
Calculate the coordinates of E using:
[tex]E = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})[/tex]
Where
[tex]O= (0,0)[/tex] ---[tex](x_1,y_1)[/tex]
[tex]C = (1,0)[/tex] --- [tex](x_2,y_2)[/tex]
[tex]m : n = 4:1[/tex]
[tex]E = (\frac{4*1 + 1 * 0}{4 + 1},\frac{4*0 + 1*0}{4 + 1})[/tex]
[tex]E = (\frac{4}{5},\frac{0}{5})[/tex]
[tex]E = (0.8,0)[/tex]
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Answers
Answer:
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Step-by-step explanation:
Find the 30% decrease:
21*0.3 = 6.3
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Answer:
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Step-by-step explanation:
First, we need to convert the percentage to a decimal. 30% = .30
Now we multiply the price times the decimal, 21 x .30 = 6.3
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
Use the slope equation. (Refresh if you cant see below.)
[tex]\frac{y_2-y_1}{x_2-x_1}\\\text{Substitute two points into the equation. We can use the first two, (3, 5), and (5, 0).}\\\frac{0-5}{5-3}\\\text{Subtract.}\\-\frac{5}{2}[/tex]
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Answers
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Step-by-step explanation:
From the question given, we are informed that Gephart is traveling from his house to the history museum and that the distance from home to the history museum is six and seven-tenths kilometers.
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Answers
Answer:
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Step-by-step explanation:
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Answers
(x-p)^2+(y-q)^2=r^2
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"p" and "q" represent the coordinates of the centre of the circle.
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Answer:
Solution given:
centre(h,k)=(-2,3)
radius(r)=6 units
we have
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(x-h)²+(y-k)²=r²
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D 8.5 units
Answers
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Step-by-step explanation:
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Step-by-step explanation:
Answer:
B=69
Step-by-step explanation:
Supplementary angles have a sum of 180. Set up your formula as
180=(2x+27)+(x+27)
180=2x+27+x+27
180-27-27=3x
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Answers
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
Answer:
n = -20
Step-by-step explanation:
n/-4 = 5
n/-4 (-4) = 5(-4)
n = -20
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What’s the answer to this everbody should know
Answers
Answer:
x<12
Step-by-step explanation:
Let's solve your inequality step-by-step.
x−3<9
Step 1: Add 3 to both sides.
x−3+3<9+3
x<12
Answer:
x<12
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Answers
[tex]3{x}^{2} - 2 = 11x \\ + 11x \: \: \: \: \: \: + 11x \\ 3 {x}^{2} + 11x- 2 = 0 \\ quadratic \: formula \: goes \: fom \: this \: : a {x}^{2} + bx + c = 0 \\ to \: this : x = \frac{- b \ \frac{ + }{ \: } \: \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
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