Answer: The required equation of the line is [tex] y=-\dfrac{5}{2}x-1.[/tex]
Step-by-step explanation: We are given to find the equation of the line that is parallel to the following line and passes through the point (-2, 4) :
[tex]5x+2y=12~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
the slope-intercept form of the equation of a straight line is given by
[tex]y=mx+c,[/tex]
where m is the slope of the line.
From equation (i), we have
[tex]5x+2y=12\\\\\Rightarrow 2y=-5x+12\\\\\Rightarrow y=-\dfrac{5}{2}x+6.[/tex]
So, the slope of line (i) is given by
[tex]m=-\dfrac{5}{2}.[/tex]
We know that the slopes of two parallel lines are equal. So, the slope of the new line will be
[tex]m=-\dfrac{5}{2}.[/tex]
Since the line passes through the point (-2, 4), so its equation will be
[tex]y-4=m(x-(-2))\\\\\\\Rightarrow y-4=-\dfrac{5}{2}(x+2)\\\\\\\Rightarrow y-4=-\dfrac{5}{2}x-5+4\\\\\\\Rightarrow y=-\dfrac{5}{2}x-1.[/tex]
Thus, the required equation of the line is [tex] y=-\dfrac{5}{2}x-1.[/tex]
The volume of the cylinder is 392 cm cubed work out the length
Find the volume of this
Then net folds into s cube. Which two letters appear on the opposite faces?
Select all that apply.
(xyz)2 = _____
The expression without exponents is?
xyz⋅xyz
x•x•y•y•z•z
x2 •y2 •z2
xy•xy•xy
Answer:
xyz⋅xyz
x•x•y•y•z•z
Step-by-step explanation:
Select all that apply.
(xyz)2 = _____
The expression without exponents is?
xyz⋅xyz
x•x•y•y•z•z
x2 •y2 •z2
xy•xy•xy
Odyssey
In the diagram, △ABC ≅ △WRS. What is the perimeter of △WRS?
10 units
11 units
12 units
13 units
Answer: Third option is correct.
Step-by-step explanation:
Since we have given that
△ABC ≅ △WRS
So, Perimeter of △ABC is given by
AB+BC+CA
here, AB = 3 units
BC = 4 units
AC = x
By pythagorus theorem, we get that
[tex]AC^2=AB^2+BC^2\\\\x^2=3^2+4^2\\\\x^2=9+16\\\\x^2=25\\\\x=\sqrt{25}\\\\x=5\ units[/tex]
So, perimeter of △ABC is
3+4+5=12 units
So, the perimeter of △WRS is also 12 units as they are similar triangles .
Hence, Third option is correct.
Answer:
The Answer Is 12
Step-by-step explanation:
Sabastian is driving 400 miles to meet his friend. He travels 100 miles in the first two hours of his trip. If he continues at the same rate, how long will it take to drive the remaining distance?
Leyla drops a penny from a height of 150m.
How long will it take for the penny to hit the ground? Round to the nearest tenth of a second.
Answer:
5.5
Step-by-step explanation:
3.8 is misinformation
Write a quadratic function f whose zeros are 3 and 8
If Chloe has $3,200 in weekly sales, she will earn more money with
The volume of a rectangular box is found by multiplying its length, width, and height: V = lwh. A certain box has a volume of b 3 + 3b 2 - 4b - 12. Factor the four-term polynomial to find the dimensions of the box. Hint: Use factoring by grouping to factor the four term polynomial first.
Answer:
The dimensions of the box are (b+3), (b-2) and (b+2).
Step-by-step explanation:
The volume of a rectangular box is
[tex]V=l\times w\times h[/tex]
The volume of a certain box is
[tex]V=b^3+3b^2-4b-12[/tex]
First of all find the factors of above expression by grouping method.
[tex]V=b^2(b+3)-4(b+3)[/tex]
[tex]V=(b+3)(b^2-4)[/tex]
[tex]V=(b+3)(b^2-2^2)[/tex]
[tex]V=(b+3)(b-2)(b+2)[/tex] [tex][\because a^2-b^2=(a+b)(a-b)][/tex]
Volume of a rectangle is the product of its dimensions, therefore the dimensions of the box are (b+3), (b-2) and (b+2).
A bag contains 3 red marbles and 4 blue marbles.A marble is taken out from the bag and replaced. Another marble is taken from the bag. Work out the probability that the two marbles taken from the bag are the same colour.
which definitions or properties would you use to simplify the expression
[tex]( {4}^{8} \times {4}^{ - 4} {)}^{ - 2} [/tex]
explain
Jennifer wants to rent a car for 5 days, and she’s interested in a the loss damage waiver but not the collision damage wavier.If the daily rate is $39 and LDW is $65 for the rental period,what is her total cost?
APEX $260 is correct answer.
What is the equation of the line that is perpendicular to the line and passes through the point (6, 2)?
Step [tex]1[/tex]
Find the slope of the line perpendicular to the given line
we have
the equation of the given line is
[tex]y=\frac{1}{2}x+7[/tex]
we know that
if two lines are perpendicular
then
the product of their slopes is equal to minus one
so
[tex]m1*m2=-1[/tex]
in this problem the slope m1 of the given line is
[tex]m1=\frac{1}{2}[/tex]
so
[tex]m2=-\frac{1}{m1}[/tex]
[tex]m2=-2[/tex]
Step [tex]2[/tex]
Find the equation of the line with slope m2 and passes through the point [tex](6, 2)[/tex]
we know that
the equation of the line is
[tex]y-y1=m*(x-x1)\\ y-2=-2*(x-6)\\y=-2x+12+2\\ y=-2x+14[/tex]
therefore
the answer is the option A
the equation of the line is [tex]y=-2x+14[/tex]
see the attached figure to better understand the problem
Determine whether each pair of angles is a pair of vertical angles, a linear pair of angles, or neither. Select the correct answer for each lettered part.
Answer:
Linear Pair, Neither, Vertical.
Its also in the attached PNG just in case the question you have decides to put them out of order. You are all welcome! I hope this helps you people in the future
A jar of dimes and quarters contains $15.25. there are 103 coins in all. how many quarters are in the jar?
Between which 2 consecutive numbers is radical 46
Please help me Idk what I’m doing thanks
What value of x makes the denominator of the function equal zero? y = 6/4x-40
Describe how you would estimate the square root of a number that is not a perfect square without using a calculator. lets say n was the imperfect square number and the square root is w. the square root of n = n+w squared/ 2w.
An antique car was purchased for $7400 and is not worth $10,600. What is the approximate percent of change
The approximate percentage of change will be 43.24%.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
An antique car was purchased for $7400 and is not worth $10,600.
Then the approximate percent of change will be given as,
P = [(10600 - 7400) / 7400] x 100
P = (3200 / 7400) x 100
P = 0.4324 x 100
P = 43.24%
The approximate percentage of change will be 43.24%.
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.help me please thank you.
**HELP!**
El Generico public high school got a new flag pole. But they completely forgot to buy a cord and NO ONE knows how tall the flagpole is! To find out, they decided to use similar figures! As the sun was setting, Bob the janoitor set up a 5-foot stick next to the flagpole and compared shadows. The 5 foot stick cast an 8-foot shadow. The shadow of the flagpole was 32-feet long.
Use rules of similar polygons to figure out how tall the flagpole is! HINT: this will involve proportions!
solve the following question: |x|=3/4
Please help !! Thank you :)
i need to know the equations
A dad has two daughters – wendy and julia. wendy is twice as old as julia. the man is now five times as old as wendy, and in 4 years he will be six times as old as julia. find the present age of the father.
Answer: 50
Step-by-step explanation:
Anna started a race at 9:30am. She ran for 3 hours and 47 minutes. What time did she finish her race?
The solution is, the race ends at 12h50 (noon)
What is addition?It can be stated as, Addition is a way of combining things and counting them together as one large group.We know that, Addition in math is a process of combining two or more numbers.
here, we have,
Anna started a race at 9:30am. She ran for 3 hours and 47 minutes.
so we know the time she start and how many time the race was so let's add them together to get the end time
now,
9:03+3h47
=12h50
so the race ends at 12h50 (noon)
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Find the area of the following circle. (Round answer to the nearest hundredth.)
d = 15 in
area = _____ square inches
circumference = ______ inches
The area of circle is,
⇒ 176.62 in²
And, ⇒ Circumference = 47.1 in.
What is mean by Circle?
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The diameter of circle is,
d = 15 in.
Hence, Radius of circle is.
r = 15 / 2
r = 7.5 in,
Thus, Area of circle is,
⇒ πr²
⇒ 3.14 × 7.5²
⇒ 176.62 in²
And, Circumference = 2πr
⇒ Circumference = 2 × 3.14 × 7.5
⇒ Circumference = 47.1 in.
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Suppose the graph of a cubic polynomial function has the same zeroes and passes through the coordinate (0, –5).
Write the equation of this cubic polynomial function.
Recall that the zeroes are (2, 0), (3, 0), and (5, 0). What is the y-intercept of this graph?
-5
The linear factors of the cubic are
The cubic polynomial equation which passes through the coordinate (0,-5) and whose zeroes are (2 , 0), (3 , 0), and (5 , 0) is: [tex]y = \dfrac{1}{6}(x-2)(x-3)(x-5)[/tex] and it can be determine by arithmetic operations.
Given :
A cubic polynomial whose zeroes are (2 , 0), (3 , 0), and (5 , 0).Cubic polynomial equation passes through (0 , -5).Arithmetic operations can be used to determine the cubic polynomial equation. The generalised cubic polynomial equation is given by:
[tex]y = K(x-a)(x-b)(x-c)[/tex]
Where, K is constant and a, b, and c are the zeroes of the cubic polynomial equation. Therefore, the value of a, b, and c are 2, 3, and 5 respectively.
[tex]y = K(x-2)(x-3)(x-5)[/tex] ----- (1)
It is given that cubic polynomial equation passes through (0 , -5). So, put x = 0 and y = -5 in equation (1) to evaluate the value of K.
[tex]-5=K(0-2)(0-3)(0-5)[/tex]
[tex]5=30K[/tex]
[tex]K = \dfrac{1}{6}[/tex]
Therefore the cubic polynomial equation is given by:
[tex]y = \dfrac{1}{6}(x-2)(x-3)(x-5)[/tex]
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