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]
Related Questions
Nico practiced drums 1.5 fewer hours than he practiced piano. If Nico practiced the piano for 4 hours, how many hours did Nico practice the drums
Answers
Answer:
2.5 hours
Step-by-step explanation:
4 - 1.5 = 2.5
You must subtract 1.5 from the amount of hours he plays piano, which is 4. This is because he spends 1.5 hours less playing drums than he does playing piano.
A shirt cost $21 last month. This month the price decreased by 30%. What is the new price?
Answers
Answer:
$14.70
Step-by-step explanation:
Find the 30% decrease:
21*0.3 = 6.3
Find new price:
21-6.3 = 14.7
Answer:
$14.7
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
We subtract this amount from the previous cost. 21 - 6.3= $14.7
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Answers
Answer:
y= -2x+ 5
Step-by-step explanation:
parallel with y= -2x+ 1 means the lines have the same slope m= -2
from point (-1, 7) we go with a slope of -2 until we find the y-intercept (0, 5)
y= mx+b is the general formula
y= -2x+ 5
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Answer:
angle 2=81 degree
angle 1 =126 degree
Step-by-step explanation:
Edgar pay $67.86 for 7.8 pounds of fertilizer. What is the price per pound of fertilizer?
(Write in dollars & cents.)
Answers
Answer:
He pays $8.70
Step-by-step explanation:
You would do $67.86 divided by 7.8 lbs
Which of the following shows the quadratic formula correctly used to solve the
polynomial equation 3x^2 - 2 =11x
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]
so now you just plug in the numbers to their corresponding letter:
[tex]x = \frac{ - 11 \frac{ + }{ \: } \sqrt{ {11}^{2} - 4(3)( - 2)} }{2(3)} [/tex]
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Answers
Carol measured her windows for new curtains. She measured the width to be 34 in when it was actually 36 inches. Which was carols approximate percent error in her window measurement .
A. 2.0%
B. 2.8%
C. 5.6%
D. 5.9%
Answers
Answer:5.9
Step-by-step explanation: Clarification from teacher
Write a sentence in which the relative frequency of the letter E (or e) is exactly 10%.
Answers
Answer:
I'd try to do that, but it cannot be done.
Step-by-step explanation:
The above sentence contains 30 letters, including 3 "e"s, so the frequency of e is 3/30 = 0.1 = 10%
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Answer:
B)
Step-by-step explanation:
Volume is expressed in
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Answer:
Cubic Units
Step-by-step explanation:
Find the missing lengths of the leg AND the hypotenuse in simpilest radical form.
Answers
Answer:
Above picture is the solution for your question
Step-by-step explanation:
Use relation of trignometric ratios
Mr. Gephart is traveling from his house to the history museum. How many meters will he travel to the museum? The distance from home to the history museum is six and seven-tenths kilometers.
Answers
Answer: 6700 meters
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.
In order to know the distance in meters
that he will travel to the museum, we have to multiply the convert the distance given in kilometers to meters. This will be:
1000 meters = 1 kilometer
Therefore, 6 7/10km = (6 7/10 × 1000m)
= 6 7/10 × 1000
= 67/10 × 1000
= 67 × 100
= 6700 meters
He'll travel 6700 meters to the museum.
Find the area of the figure.
Answers
Answer:
The answer is 28.5
Step-by-step explanation:
Right triangle: 4.5
Top triangle: 6
Rectangle: 18
Your welcome :)
A 4-cup bottle of vegetable oil costs $2.88. What is the price per fluid Ounce?
Answers
Explanation:
What is the length of the hypotenuse
Answers
Answer:
15
Step-by-step explanation:
The Pythagorean's Theorem states that a^2 + b^2 = c^2, so 81 + 144 = 225, and 225 square rooted is 15.
Answer:
15
Step-by-step explanation:
So, to find the hypotenuse you must use the pythagreons theorm:
A^2+B^2=C^2
Now, we knowt hat A and B is the side lengths.(9 and 12)
The hyoptenuse is C.
So, lets plug in our values for A and B, and find C:
A^2+B^2=C^2
=
9^2+12^2=C^2
Now lets square each number except for C, since its a unknown value:
81+144=C^2
Now combine the 144 and 81:
225=C^2
Finally, square root both sides so C^2 becomes C:
15=C
So the answer for the hyotenuse is 15!
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Logan inherited $8,000 from his grandmother. He split the money and placed the amounts in the two accounts below. Find the total amount of money he will have in the accounts combined after 5 years. x Account A: earns 7% interest compounded quarterly x Account B: earns 5.5% interest compounded annually
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Answer:
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Step-by-step explanation:
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Answer: go
Step-by-step explanation:
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Answers
A.) -2/5
Because x increases by positive two and y decrease by negative five
Answer:
Your answer is -5/2.
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]
Sonia has a hat collection. The ratio of white hats to
blue hats in her hat collection is 10:9. Which ratio is
equivalent to 10:9?
Answers
Answer:
20:18 30:27 40:36 etc..
Step-by-step explanation:
To find equivalent ratios you multiply both 10 and 9 by the same number to find equivalent ratios.
one side of a triangle is 50 and the other side is 120 what is the length of the third side?
this is exterior angle theorem.
Answers
I think it 10
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If each unit on the graph measures 1 inch, how far is the
inchworm from the ladybug? (Hint: The Pythagorean
theorem can be used because the x-axis, y-axis, and z-
axis each intersect at a right angle.)
O 5 in.
O 7 in.
0 12 in.
25 in.
Answers
Answer:
A. 5
Step-by-step explanation:
just did the quiz on .
Which value(s) is a solution for the inequality
f < 4?
Answers
Answer:
665
Step-by-step explanation:
kmnbvcxsdrftyuiol,m nbvcxsdftgyhuio
Answer:
s = s
f < 4 = s
Step-by-step explanation:
The length of segment PK is 4 units and the length of segment PQ is 2 units. What is the approximate
perimeter of shaded triangle PQL
A 10.0 units
B 9.5 units
C 9.0 units
D 8.5 units
Answers
Answer:
9.5
Step-by-step explanation:
There are 3 liters of orange juice at a school party. 10 students want to drink all of the orange juice, and they all want to get exactly the same amount. How much orange juice can each get? (enter your answer as a fraction or mixed number)
Write a number sentence that represents the problem.
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Answer:
0.3
Step-by-step explanation:
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Answer:
0.3
Step-by-step explanation:
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The function r(n) = 5n² + 1 represents the value of the nth term in a sequence.
What is the sum of the 1st and 3rd terms of the sequence?
Answers
Step-by-step explanation:
a_n=5n²+1
➜a_1=5(1)²+1
➜5×1+1
➜5+1
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Answers
Answer:
2x+27+x+27=180
3x+54=180
3x=180-54
x=126/3
x=42
angle B=x+27
=42+27
=69 degree
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
126=3x
126/3=x
42=x
Now substitute 42 in place of x for Angle B
Angle B = x+27
B = 42+27
B=69
Check your work by doing the same for Angle A
Angle A = (2x+27)
A=2*42+27
A=84+27
A=111
Now add both together and if you did it right, your answer is 180
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What is the equation of a circle with a radius of 6 and a center at ( -2 , 3 )?
Answers
(x-p)^2+(y-q)^2=r^2
The radius is given (r=6), as well as the centre of the circle (-2;3).
"p" and "q" represent the coordinates of the centre of the circle.
So it would look like this -
(x-p)^2+(y-q)^2=r^2
p=x-coordinate (-2)
q=y-coordinate (3)
r=6
(x-(-2))^2+(y-(3))^2 =6^2
(x+2)^2 + (y-3)^2 = 36
***"^" means "to the power of"
Hope this helped~
Answer:
Solution given:
centre(h,k)=(-2,3)
radius(r)=6 units
we have
equation of a circle is:
(x-h)²+(y-k)²=r²
(x+2)²+(y-3)²=6²
(x+2)²+(y-3)²=36 is required equation of a circle.
9. The quotient of n and -4 is 5. What is the
value of n?
Answers
Answer:
n=-20
Step-by-step explanation:
Answer:
n = -20
Step-by-step explanation:
n/-4 = 5
n/-4 (-4) = 5(-4)
n = -20
-20/-4 = 5
X-3<9
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