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.
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Does Anyone Know This
Answer:
1 g-h
2 g^2-h
3 gh
4 g+h
5 h-g
6 g+h^2
Step-by-step explanation:
A grounds keeper needs grass to cover a circular field 290 feet in diameter.a store sells 50 pound bags of grass seed. One pound of grass seed covers about 400 square feet of field. What is the smallest number of bags the groundskeeper must buy to cover the circular field? Explain ir show your reasoning
Answer:The smallest number of bags the groundskeeper must buy to cover the field is 165 bags.
Given:
A groundskeeper needs grass seed to cover a circular field, 290 feet in diameter.
A store sells 50 pound bags of grass seed. One pound of grass seed covers about 400 square feet of field.
To find:
The smallest number of bags the groundskeeper must buy to cover the field.
Solution:
Diameter of the field = 290 feet, radius = 145 feet
Step-by-step explanation:
please help me !!!!!!!!!!!!!!!!!!!!!!!!
Answer:
20
Step-by-step explanation:
15 is the mid so +5 is 20 thus 20 is the anser
Classify the triangle. Check all that apply
Acute
Obtuse
Right
Scalene
Isoceles
Equilateral
Equiangular
None of the above
Answer:
The answer is Right because of the tiny square in the right corner and scalene because none of the three sides are equal in length.
Step-by-step explanation:
I hope this helps!
If r is the radius of a circle and d is its diameter, which of the following is an
equivalent formula for the circumference C = 2 pie r?
A. C= pie d
B. C= 2 pie d
C. C=2 pie d^2
D. C = 2 pie rd
Answer:
A
Step-by-step explanation:
because r is 1/2 of d so you would have 1 d instead of 2 r
Which relation is a function?
A) {(2,3). (5,8).(-4,-1). (9.7), (2.1)}
B) {(2,3). (5,8).(-4-1). (9.7). (5,7)}
C) {(2,3). (5.8).(-4,-1). (9.7).(-2.1)}
D) {(2,3). (5.8).(-4,-1). (5,7), (-2,1)}
Guys plz help plz on both plzzzzz
Answer:
The first one is 9/50 and the second one is 1/2
Step-by-step explanation:
you multiply the numerators by each other then you multiply the denominators by each other then you should have your answer :)
D is 13. What is the length of the line.
Answer:
D
Step-by-step explanation:
You have to use pythagorean theorem to solve this.
Answer:
D
Step-by-step explanation:
use pytherogream theory
sides, 5 and 12
pytherogream triple 5, 12, 13
Raj polled 100 students in his class to compare the number of hours that boys and girls played video games each week. The results of his survey are shown below. Which gender shows greater variability in their playing time?
Hours of Video Game Time per Week for Boys
A box-and-whisker plot. The number line goes from 0 to 28. The whiskers range from 0 to 28, and the box ranges from 9 to 17. A line divides the box at 14.5.
Hours of Video Game Time per Week for Girls
A box-and-whisker plot. The number line goes from 0 to 28. The whiskers range from 0 to 28, and the box ranges from 3 to 15. A line divides the box at 6.
Boys show greater variability because the 3rd quartile for boys is 17 but only 15 for girls.
Boys show greater variability because the median playing time for boys is 14.5 but only 6 for girls.
Girls show greater variability because the interquartile range for girls is 12 for girls but only 8 for boys.
Girls show greater variability because the data for the girls is skewed toward the lower end of the box plot.
Answer:
c is the correct answer i took the test
Step-by-step explanation:
The gender that shows greater variability in their playing time is C. Girls show greater variability because the interquartile range for girls is 12 for girls but only 8 for boys.
How to find the interquartile range?For the males, the interquartile range will be:
= Third quartile - First quartile
= 17 - 9
= 8
For the females, the interquartile range will be:
= Third quartile - First quartile
= 15 - 3
= 12
Therefore, girls show greater variability because the interquartile range for girls is 12 for girls but only 8 for boys.
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What is w²+2xy if x= - 3, w= - 2, and y=1?
Answer:
-10
Step-by-step explanation:
w2 is -2x-2
2xy is getting times together -3x1
Help me classify the triangles by its sides and measuring its angles :)
actually answer this
Answer:
1. isosceles
2. Right
Step-by-step explanation:
Here, we want to give the kind of triangle in each of the diagrams
1. From what we can see, we have two sides equal to each other using the given markings. More specifically, the base sides are equal and that makes the triangle an isosceles triangle
2. From what we can see here, we have an angle of 90 degrees on one of the sides of the triangle. In other words, we have a right angle on one of the sides.
This makes the triangle, a right triangle
please answer this questioncould u please answer this question
Answer:
3
Step-by-step explanation:
3p - 1 = 5(p-1) -2(7-2p)
(simplify)
3p -1 = 5p-5-14+4p
3p-1 = 9p-19
(make p the subject)
3p-9p = -19+1
-6p = -18
p = -18/-6
p = 3
es 6
Step-by-step explanation:
3p-1= 5p-5-14mas4p
3p-4p-5p= -5-14mas1
3p-4p-5p= -18
3p-9p=-18
_3p=-18
p=-18:-3
p=6
The sum of two numbers is 23. The larger number y is 1 less than twice the smaller number x. Write and solve a system of linear equations to find the two numbers.
Answer:
15 and 8
Step-by-step explanation:
NEED ASAPPPP
The linear equation below describes the graph of a line.
4x – 3y = -12 Which of these is a point on the graph of the line?
Answer:
(-3,4)
Step-by-step explanation:
to solve for x, make y=0
to solve for y, make x=0
Well, you didnt give answer choices, BUT go onto desmos and use the graphing calculator to figure it out :)
30 men repair a road in 56 days by working 6 hours daily. in how many days 45 men will repair same road by working 7 hours daily?
Answer:
Case1:
Men : 30
Work : 1
Time (day×hr): 56×6 = 336 hr.
Case2:
Men : let it be m men.
Work: 1
Time: 45×7 = 315 hr.
Work being constant in both cases, men and time are in inverse proportion i.e, more men take less time.
Product of men and time is constant in both cases.
Therefore, 30×336=m×315
Or, 30×336/315 = m
Or, m = 32.
Hence, required number of men is 32.
Step-by-step explanation:
what is the bill for 10 day rental b = 45.95d + 38.5
Answer:
b = 498
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
b = 45.95d + 38.5
d = 10 days
Step 2: Evaluate
Substitute: b = 45.95(10) + 38.5Multiply: b = 459.5 + 38.5Add: b = 498Answer:
498 dollars
Step-by-step explanation:
So just plug in the 10 in the equation for D
45.95*10+38.5
Now just solve using order of operations
You would get 498
PLS ANSWER
Which number line represents the solutions to-2|x| =-6?
o
-8
8
7. 3, 19 25..
Find the formula for the nth term of the following sequence
Answer:
a+(n-1)d is the formula to calculate
Abby spent 22 minutes working on her science project yesterday 34 minutes working on today. how many minutes did Abby spend working on her science project altogether
The number of minutes that Abby spend working on her science project altogether is 56 minutes.
How to calculate the value?From the information, Abby spent 22 minutes working on her science project yesterday and 34 minutes working on today.
Therefore, the time used altogether will be the addition of the time used for both occasions
= 22 minutes + 34 minutes
= 56 minutes
This illustrates addition.
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32 + 5a = -8(4a - 4)
Answer:
a=0
Step-by-step explanation:
Answer:
44=-1a
Step-by-step explanation:
32+5a=-8-4+4a
32+12=-5a+4a
44=-1a
Kayla won 37 super bouncy balls
playing hoops at her school's game night
Later, she gave two to each
of her friends. She only has 7
remaining. How many friends does she have?
Answer:
15 friends
Step-by-step explanation:
37 - 7=30 so then you divide 30 by 2 which equals 15 so there is your answer.
A circular mirror measures 24 cm in diameter.
The cake is cut in half. Work out the perimeter of half of the mirror.
Answer:
The perimeter or circumference of a half mirror = 37.68 cm
Step-by-step explanation:
The diameter of circular measure = 24 cmWe know that the perimeter of a circular shape is called the 'circumference', with the formula
Circumference of a circle = C = 2πrWhen the mirror is cut into half, the diameter gets half as well.
Thus, the diameter of a half mirror = 24/2 = 12 cmWe know that radius = r = diameter / 2 = 12/2 = 6 cm
Thus, the perimeter of half of the mirror = C = 2πr
= 2(3.14)6
= 37.68 cm
Therefore, the perimeter or circumference of a half mirror = 37.68 cm
Plz help with math plzlzlzlzl
How to find the discount
Write the equation, in slope-intercept form, of the line that passes through (-2,0) and is parallel to the line represented by 5x-3y=-17 .
Answer:
[tex]y=\frac{5}{3}x+\frac{10}{3}[/tex]
Step-by-step explanation:
Firstly we rewrite the equation that is parallel to the line we need because parallel lines have the same slope by the rule
[tex]m_1=m_2[/tex]
so we rewrite the equation in slope-intercept form:
[tex]5x-3y=17\\-3y=-5x+17\\y=\frac{-5x+17}{-3}\\\\y=\frac{-5x}{-3}+\frac{17}{-3} \\\\y=\frac{5}{3}x-\frac{17}{3}[/tex]
and now we compare it with our slope-intercept form equation:
[tex]y=mx+b[/tex]
the coefficient of x which is m is the slope and since parallel lines have equal slopes the line that we need would also have the same slope which is 5/3.
now the next step is the line that we need passes through the point (-2,0) so it means that it should satisfy that specific point so we insert that point into our slope-intercept form and insert the slope which is 5/3 which is m.
[tex]y=mx+b\\y=\frac{5}{3}x+b\\\\0=\frac{5}{3}(-2)+b\\\\0=\frac{-10}{3}+b\\\\b=\frac{10}{3}\\[/tex]
now we know that the y-intercept(b) of the line we need is 10/3 and slope(m) is 5/3 insert these values into our slope-intercept form:
[tex]y=mx+b\\y=\frac{5}{3}x+\frac{10}{3} \\[/tex]
so this is our given line.
what is the expression for "the difference of 3 and 5times a number"?
answering
3 - 5n
(3 - 5)n
5 - 3n
Answer:
3-5n is the correct answer
what’s the quotent of -3/8 and -1/4
Answer:
1.5
Step-by-step explanation:
-3/8=-0.375
-1/4=-0.25
the negatives cancel each other out so it is 0.375/0.25
.25 goes into .375 1.5 times, so the answer is 1.5
Have a good day!
helpppppppppppppppppp
The 1st option is correct.
Answer:
m/15=-3
Step-by-step explanation:
When you see quotient it means to divide
is means equal
I hope this helps
Is 14/950 more or less than 1/2 and why!
ABCD is a rectangle. Find the mCED
Answer:8.5...
Step-by-step explanation: