Given :
Two equations :
y = t³
x = t + 5
To Find :
Rectangular equation formed by eliminating the parameter.
Solution :
Putting value of t from second equation to first equation.
We get :
[tex]y = ( x-5)^3[/tex]
Also, t from equation first :
[tex]t = \sqrt[3]{y}[/tex]
Putting the value of t and equation two, we get :
[tex]x = \sqrt[3]{y}+5[/tex]
Therefore, rectangular equation is formed by eliminating the parameter is :
y = ( x - 5)³ and x = ∛y + 5 .
The rectangular equation is y = (x - 5)³ which is obtained from the parametric equations y = t³ and x = t + 5 option (3) y = (x - 5)³ is correct.
What are parametric equations?A parametric equation in mathematics specifies a set of numbers as functions of one or more independent variables known as parameters.
The options are:
y = (x + 5)³x = (y + 5)³y = (x - 5)³y = (x - 5)²It is given that:The parametric equations are:
y = t³
x = t + 5
From the second equation that is x = t + 5
Take the value of t and plug in the equation y = t³:
t = x - 5
y = (x - 5)³
The above equation represents a cubic equation.
Thus, the rectangular equation is y = (x - 5)³ which is obtained from the parametric equations y = t³ and x = t + 5 option (3) y = (x - 5)³ is correct.
Learn more about the parametric function here:
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WILL MARK BRAINLIEST
One side of a triangle is twice as long as a second side. The remaining side is 3 larger than the second side. The perimeter is 39m. Find the length of each side.
Answer:
Lengths all the three sides are 9m, 18m and 12m
Step-by-step explanation:
Let us assume the length of the second side to be x m
According to the question:
first side = 2x
third side = x + 3
Applying the formula of perimeter:
Perimeter = length + breadth + height
39 = 2x + x + (x + 3)
39 = 2x + x + x + 3
39 = 4x + 3
39 - 3 = 4x
4x = 36
x = [tex]\frac{36}{4}[/tex]
x = 9
length of the first side (x) = 9 m
length of the second side (2x) =2 × 9 =18 m
length of the third side (x + 3) = 9 + 3 = 12 m
∴ lengths all the three sides are 9m, 18m and 12m
26.25 rounded to the nearest tenth
Answer: 26.3
Step-by-step explanation:
Feliks joins a local recreation center to play basketball the reception charges $20 annual fee plus additional $15 per month for the usage of the basketball courts Feliks prepays by writing a check for 3185 for how many months did he prepays for
Answer:
211 months
Step-by-step explanation:
Feliks joins a local recreation center to play basketball the reception charges $20 annual fee plus additional $15 per month for the usage of the basketball courts Feliks prepays by writing a check for 3185 for how many months did he prepays for
Let the number of months that he prepays for be represented by m
Hence, we have the equation
$20 + $15 × m = $3185
Hence:
20 + 15m = 3185
Collect like terms
15m = 3185 - 20
15m = 3165
m = 3165/15
m = 211 months
A construction worker places a compass at various positions on a wall until the compass needle deflects to one direction. What is the worker most likely using a compass to find
Answer:
Sources of electrical current
Step-by-step explanation:
Based on the information given the reason why
He/ She places a compass at different positions on a wall until the compass needle change to a direction was because the construction worker
was most likely using the compass to find the Sources of an ELECTRICAL CURRENT or where the ELECTRICAL CURRENT originated from reason been that ELECTRICAL CURRENT is the movement of electric charge from cathode to anode .
Answer:
D. Sources of electrical current
Step-by-step explanation:
I just took the test
Does anyone know how to do this?
Answer:
y= Ix-3I (that says absolute value btw)
Step-by-step explanation:
This is the result of starting with y = |x|, then shifting it three units to the right. Replacing x with x-3 moves the xy axis three units to the left, giving the illusion the V shaped curve moved 3 spots to the right.
We don't shift up or down since the vertex is on the x axis.
We also don't vertically compress or stretch the graph either.
Side note: the vertex for this graph is (3,0) which is the lowest point of the curve.
Anyone please help me to do 4 ) f
Best answer gets brainliest hurry ASAP
Answer:
42 minutes
Step-by-step explanation:
When graphing on the complex plane , which quadrant will the complex number 10 - 13i be found in ?
Answer:
The complex number would be in the 4th quadrant.
Step-by-step explanation:
We know that a complex number is a number that can be expressed in the form of a + bi,
where
'[tex]a[/tex]' and b are real numbers, and '[tex]i[/tex] represents the imaginary unitGiven the complex number
10 - 13i
Here,
Coefficient of the real part of the complex number = 10Coefficient of the imaginary part of complex number = -13As the coefficient of the imaginary part holds a negative sign, and the real part holds a positive sign.
Thus, the complex number would be in the 4th quadrant.
Question 5 please help out
Answer:
B
Step-by-step explanation:
try typing into ur calc. that is the answr u get!!
Hope this helps!! Pls mark me brainliest!!
Please I really need help
Answer:
Extreme fitness: y=10x+50
Ultimate fitness:y=15x+30
Step-by-step explanation:
The graph represents function 1, and the equation represents function 2: A graph with numbers 0 to 4 on the x-axis and y-axis at increments of 1. A horizontal straight line is drawn joining the ordered pairs 0, 3 and 4, 3. Function 2 y = 7x + 1 How much more is the rate of change of function 2 than the rate of change of function 1? 5 6 7 8
Answer:
its 7 i got it right on the test :)
what method is this?
Which object has a GREATER unit rate of change as shown in the graph?
Answer: A
Step-by-step explanation:
Michelle ordered shirts to sell at the school carnival. She paid $2.80 per shirt, she adds a
150% markup to the total price she paid for the shirts.
What is the selling price of each shirt?
PLEASE HELP!! Any help will be greatly appreciated!
Answer:
The selling price is $7
Step-by-step explanation:
Step one:
Given information
She paid $2.80 per shirt
She adds a 150% markup to the total price she paid for the shirts
Let us find 150% of $2.80
=150/100*2.8
=1.5*2.8
=$4.2
Hence the selling price is the markup price plus the cost price
=4.2+2.8
=$7
Trey takes the angle shown, places the point of his compass on S, and draws an arc with an arbitrary radius intersecting the rays of the angle at P and R. Trey claims that as long as he draws two more arcs by placing the needle of his compass on P and then on R, drawing a ray from S through the point at which the arcs intersect, he will be able to bisect ∠S. Is Trey correct?
A. Trey is correct. Since the initial arc was drawn with the point of the compass on S, RS=PS.
B. Trey is not necessarily correct. He will need to ensure that the compass width remains the same for each arc drawn from P and R.
C. Trey is correct. Since the compass is placed on the points P and R to draw the remaining two arcs, the ray drawn through their intersection will bisect the angle.
D. Trey is not necessarily correct. He will need to ensure that the distance from S to P and the distance from S to R are equal.
Answer:
b
because he isnt fight nor wrong
Step-by-step explanation:
A banks loan officer writes applications for credit the ratings are normally distributed with a mean of 200 and a standard deviation of 50 fine P 60 the score which separates the lower 60% from the top 40% round to 1 Decimal Pl.
Answer:
212.7
Step-by-step explanation:
Calculation to Find P60 the score which separates the lower 60% from the top 40%
First step is to find z of 60% using the invNorm distribution
Hence,
z=0.6=0.2533
Now let Find P60 which is the score which separates the lower 60% from the top 40% using this formula
x<=>z
Where,
Standard deviation=50
Mean=200
z=0.2533
Let plug in the formula
x=0.2533*50+200
x=12.665+200
x=212.665
x=212.7(Approximately)
Therefore the score which separates the lower 60% from the top 40% is 212.7
Rewrite the expression using the division symbol and as a fraction. The quotient of m and 11
M÷11 M/11
Step-by-step explanation:
when you find the quotient you divide so when you divide with a fraction you take what number you were given first and out it on top of the number you were given second
write a linear function f with the values f(-2)=8 and f(1)=-10
Answer:
The linear function f(x) = -6x - 4
Step-by-step explanation:
The equation of the linear function f(x) is y = m x + b, where
y = f(x)m is the slope of the line represents the functionb is the y-intercept ⇒ value y at x = 0The rule of the slope is m = [tex]\frac{y2-y1}{x2-x1}[/tex] , where
(x1, y1) and (x2, y2) are two points on the line∵ f(x) = y ⇒ is the function of the set of ordered pairs (x, y)
∴ f(-2) = 8 is the point (-2, 8)
∴ f(1) = -10 is the point (1, -10)
∴ x1 = -2 and y1 = 8
∴ x2 = 1 and y2 = -10
→ Substitute them in the rule of the slope to find it
∵ m = [tex]\frac{-10-8}{1--2}[/tex] = [tex]\frac{-18}{1+2}[/tex] = [tex]\frac{-18}{3}[/tex]
∴ m = -6
→ Substitute it in the form of the equation above
∵ y = -6(x) + b
∴ y = -6x + b
→ To find b substitute x by 1 and y by -10
∵ x = 1, y = -10
∴ -10 = -6(1) + b
∴ -10 = -6 + b
→ Add 6 to both sides
∵ -10 + 6 = -6 + 6 + b
∴ -4 = b
∴ b = -4
→ Substitute it in the equation
∴ y = -6x + -4
∴ y = -6x - 4
∵ y = f(x)
∴ The linear function f(x) = -6x - 4
Helppppppppppppppppppppppppppp
A group of 5 friends want to buy a flat-screen TV for $210. The tax comes to $15. Write and solve a multiplication equation to find how much money each person should pay if each person pays the same amount.
Answer:
$45
Step-by-step explanation:
In order to create a multiplication equation, we would need to use a single variable that represents the amount that each friend will pay. This can be represented by the variable x. We multiply this variable by the number of friends which should equal the total of the TV with the tax included. Like so...
$210 + $15 = 5x
Now that we have the equation we can go ahead and solve it by adding the total and the tax, and then dividing both sides by 5 in order to isolate x.
$210 + $15 = 5x
$225 = 5x
$45 = x
Finally, we can see that each friend will pay the same amount which is $45
The Steelers beat the Seahawks by 10 points. The total points scored between both teams was 44. How many points did the Seahawks have?
Answer:
17
steelers had 27
Step-by-step explanation:
Drake needs to drill holes in a wooden plank. The holes will have a diameter of 0.5 millimeters, with an error allowance of 0.05 millimeters. Which equation can be used to find the minimum and maximum acceptable diameters?
Answer:
|x − 0.5| = 0.05
Step-by-step explanation:
Here x represents the diameter,
Since, an error of 0.05 millimeters is allowance in diameter,
Thus, the maximum acceptable diameter = x + 0.05,
And, the minimum acceptable diameter = x - 0.05
According to the question,
The holes will have a diameter of 0.5 millimeters,
Thus, x - 0.05 < 0.5 and 0.5 < x + 0.05
⇒ x - 0.5 < 0.05 and x - 0.5 > - 0.05
⇒ x - 0.5 < 0.05 and -(x -0.5) < 0.05
⇒ |x-0.5| < 0.05
⇒ Option D is correct.
Which expression has the same value as -18\(-9)?
-18\2
-12\(-3)
-10\5
-8\(-4)
Answer:
Step-by-step explanation:
Well -8/-4 is 2 so that is the same
Kamal got married 5 years ago. Today his age is 1 1/4 times his age at the time of marriage. His sons age is 1/10 times his present age. What is hisson's age ?
Answer:Son's age =2.5 years old
Step-by-step explanation:
Step 1
Let the age of Kamla at marriage be represented as x
Age after five years = x+5
Given that today his age is 1 1/4 times his age at marriage, Our equation to express his age at marriage will be
x+ 5= (5/4)x
Multiplying 4 by both sides gives
4(x+5) = (5/4 x 4 )x
4x+20 = 5x
20=5x-4x
x= 20 years at Marriage
Therefore his present age = 20+5= 25
Step 2
Son' s age = 1/10 times his present age
Son's age = 1/10 x 25= 2.5 years old
12 + 6x -18
Helpppp!!
Answer:
6x - 6
Step-by-step explanation:
The only step necessary here is to simplify. We can subtract 18 from 12 since they are like terms.
6x - 6.
That's it! That's your final answer.
Please help!!!
Find the value of x for which l || m.
Answer:
i can't see the pic clearly
Step-by-step explanation:
Helpppp fasttt!!!!!!!!
Answer:answer is the first one
Step-by-step explanation:
Collect like terms such as grouping the t and s variables together. The -3 should be included in the equation. Solution in pic below.
If the fifth term in a geometric sequence is 1∕27 and the common ratio is 1∕3, find the explicit formula of the sequence.
Question 18 options:
A)
an = (1∕3)n – 1 for n ≥ 1
B)
an = (1∕27) ⋅ (1∕3)n – 1 for n ≥ 1
C)
an = (3) ⋅ (1∕3)n – 1 for n ≥ 1
D)
an = (3) ⋅ (3)n – 1 for n ≥ 1
Answer:
B
Step-by-step explanation:
5x - 2y = 33
5x + 8y = 18
Solve the simultaneous equations.
x=__
y=__
Answer:
x=6
y=-3/2
Hope this helps
Plz plz help plz plz I’ll give brainlist
Answer: 10
Step-by-step explanation:
hope this helps!
Answer 2 2/19
there is you answer