Answer:
It should take about 4.75 min.
Step-by-step explanation:
Hope this helps and could you mark me as the brainliest
plz help me im stuck
A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum height of 10 mm halfway across a horizontal distance of 80 mm.
Part A: Write the equation of the parabola in standard form that models the spider's jump. Show your work. (4 points)
Part B: Identify the focus, directrix, and axis of symmetry of the parabola. (6 points)
The spider's movement is an illustration of a parabola.
The equation of a parabola is: [tex]\mathbf{y = -\frac{1}{160}(x - 40) + 10}[/tex]The focus of a parabola is: (40,-30)The axis of symmetry is: [tex]\mathbf{x = 40}[/tex]The directrix is:[tex]\mathbf{y = 50}[/tex](a) The equation
The spider passes through the origin.
So, we have:
[tex]\mathbf{(x,y) = (0,0)}[/tex]
The spider jumps to a maximum height of 10mm, midway 80mm.
So, the vertex is:
[tex]\mathbf{(h,k) = (40,10)}[/tex]
The equation of a parabola is:
[tex]\mathbf{y = a(x - h)^2 + k}[/tex]
So, we have:
[tex]\mathbf{0 = a(0 - 40)^2 + 10}[/tex]
Subtract 10 from both sides
[tex]\mathbf{a(0 - 40)^2 =- 10}[/tex]
[tex]\mathbf{1600a =- 10}[/tex]
Solve for a
[tex]\mathbf{a =- \frac{1}{160}}[/tex]
Substitute [tex]\mathbf{a =- \frac{1}{160}}[/tex] and [tex]\mathbf{(h,k) = (40,10)}[/tex] in [tex]\mathbf{(h,k) = (40,10)}[/tex]
[tex]\mathbf{y = -\frac{1}{160}(x - 40) + 10}[/tex]
(b) The focus, directrix and the axis of symmetry
The focus of a parabola is:
[tex]\mathbf{Focus= (h, k + p)}[/tex]
Where:
[tex]\mathbf{p = \frac{1}{4a}}[/tex]
So, we have:
[tex]\mathbf{p = \frac{1}{4 \times -1/160}}[/tex]
[tex]\mathbf{p = -\frac{160}{4}}[/tex]
[tex]\mathbf{p = -40}[/tex]
So, we have:
[tex]\mathbf{Focus = (40,10-40)}[/tex]
[tex]\mathbf{Focus = (40,-30)}[/tex]
The axis of symmetry is:
[tex]\mathbf{x = h}[/tex]
So, we have:
[tex]\mathbf{x = 40}[/tex]
The directrix is:
[tex]\mathbf{y = k - p}[/tex]
[tex]\mathbf{y = 10 + 40}[/tex]
[tex]\mathbf{y = 50}[/tex]
Read more about parabolas at:
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Solve √3x+4−2=3
The square root covers the 4 but not the -2
[tex] \sqrt{3} x + 4 - 2 = 3 \\ = > \sqrt{3} x = 3 - 4 + 2 \\ = > \sqrt{3} x = 1 \\ = > x = \frac{1}{ \sqrt{3} } \\rationalising \: \: \: the \: \: \: denominator \\ = > x = \frac{1}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } \\ = > x = \frac{ \sqrt{3} }{3} \\ [/tex]
Answer:[tex] \frac{ \sqrt{3} }{3} [/tex]
Answer: x = 7
Step-by-step explanation:
[tex]\sqrt{3x+4}=3+2[/tex]
[tex]\sqrt{3x+4}=5[/tex]
[tex]3x+4 =25[/tex]
[tex]3x = 21[/tex]
[tex]x=7[/tex]
Please give me a brainliest answer
HELPP PLEASE will put brainliest
Answer:
Slope of function A is equal to slope of function B
Step-by-step explanation:
Function A
[tex]y =\dfrac{2}{5}x+1\\\\\\slope=\dfrac{2}{5}[/tex]
Function B:
[tex]Slope=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\dfrac{3-[-1]}{5-[-5]}\\\\=\dfrac{3+1}{5+5}\\\\\\=\dfrac{4}{10}\\\\\\=\dfrac{2}{5}[/tex]
Express (3/5+ 3)^2
as a trinomial in simplest form.
Hey there!
Fun fact:
• MONOMIAL contains ONE term because MONO- means 1
• BINOMIAL contains TWO terms because BI- means 2
• TRINOMIAL contains THREE terms.. because TRI- means 3.
• POLYNOMINAL contains FOUR or MORE terms because POLY- means 4 or more
ANSWERING YOUR QUESTION
(3/5x + 3)^2
= (3/5x)(3/5x) + (3/5x)(3) + (3/5x)(3) + 3(3)
• 3/5x(3/5x) = 9/25x
• 3/5x(3) = 9/5x
• 3(3) = 9
= 9/25^2 + 9/5x + 9/5x + 9
• COMBINE the LIKE TERMS
= (9/25)x^2 + 18/5x + 9
Therefore, your answer is:
“9/25x^2 + 18/5x + 9”
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
6.
Find the area of a rectangle with
length 2x - 7 and width 3x +4.
Answer:
[tex]A=6x^{2} -13x-28[/tex]
Step-by-step explanation:
A=L(W)
A=2x-7(3x+4)
Use distributive property
[tex]A=6x^{2} +8x-21x-28[/tex]
Combine like terms
[tex]A=6x^{2} -13x-28[/tex]
What is the justification for each step in the solution of the equation?
5x−4/2=2x−1
Select from the drop-down menus to correctly justify each step.
5x−42=2x−1 Given
5x−4=2(2x−1) Choose...
5x−4=4x−2 Choose...
5x=4x+2 Addition or Subtraction Property of Equality
x=2 Choose...
Options
Addition or subtraction property of equality
Multiplication or division property of equality
Distributive property of equality
Combine like terms
The "/" Is for a fraction.
Answer:
5x-2=2x-1
5x-2x=-1+2
3x=1
3/3x=1/3
x=1/3 or 1.3333...
help pls im in need!!
Answer:
x=-23
Step-by-step explanation:
-0.48x+0.28=4.6
-0.2x=4.6
x=-23
Answer:
it’s -0.2x =4.6
Step-by-step explanation:
X = -23 is the answer for the equation but
your asking for what the number is before the x right
it’s -0.2x =4.6
than multiple both sides by 10
divide both sides by -2
simplify
X=-23
A quadratic function y = f(x) is plotted on a graph and the vertex of
the resulting parabola is (3, -5). What is the vertex of the function
defined as g(x) = f(-x) + 3?
Answer:
the vertex is (0,3)
Step-by-step explanation:
using vertex form: y=a(x-h)^2+k you can find the vertex
h: the horizontal <----------->
and
k: the vertical |
so, there is no h, but there is a k, which is 3, so the answer is (0,3) I believe
Which equation in slope-intercept form has a graph with an x-intercept at 3 and a y-intercept at -2?
Answer:
a
Step-by-step explanation:
A is the answer, since when you graph it, you are able to visualize y crossing -2 and x crossing 3.
how to use solution of an inequality in the real world?
They seek to describe the way nature flows. Many of the simpler equations also describe financial concepts, like exponential growth. Exponential growth can describe the cultivation of microorganisms as well.
Addition and substraction is used in shopping.
Much of mathematics are also used in programming in order to make smart software.
You basically used equations everyday without even notice. Like when you have to calculate “How many dollars does the sum of your grocery stuffs equal to?”. Or a more complicated situation, if you need to be in the meeting at 9:30am, the travel distance is 10km and you can only leave after 8:30am, your driving speed should equal “x” km/h.”
Inequalities are used for comparison. “He is taller than me.” or “The iPhone with larger memory capacity is more expensive.”. A more complicated example is also with calculating your driving speed. “Now if there is expected traffic jam for 2km. You get out of the traffic jam at 9:00am, you have to drive faster than
“x” km/h to compensate for your loss time.”
Just some simple examples. There are a lots more out there, just look around.
Answer:
by using injustices or by subtracting
I need help with this question
Answer:
b
Step-by-step explanation:
f (x) = x +11. Find the inverse of f(x).
O A. f-1(2) = x3 + 11
O B. f-'(x) = (x + 11)3
O c. f-1(x) = 23 – 11
O D. f-1(x) = (2x – 11)3
Answer:
y = x - 11
Step-by-step explanation:
f (x) = x + 11
y = x + 11
x = y + 11
x - 11 = y
What is 191 divided by 5 with a remainder
Answer:
your answer is 38 with a remainder of 1
Step-by-step explanation:
Nominator
191
Denominator
5
38.2= 38 Remainder 1
The result of 191/5 is a terminating decimal with 1 digit to the right of the decimal point.
191 divided by 5 in decimal = 38.2
191 divided by 5 in fraction = 191/5
191 divided by 5 in percentage = 3820%
On dividing 191 by 5, the remainder is 1.
The divisor is the integer that divides a given number. The resultant number is sometimes referred to as the quotient. The residual is the number that the divisor leaves after partially dividing the original integer.
Dividend = Divisor x Quotient + Remainder
On dividing 191 by 5
Step 1: Divide 191 into 5 parts: 191/5 = 38(integer part only)
Step 2: Divide the quotient you just calculated by the divisor (5).
38 × 5 = 190
Step 3: Subtract the result from the initial dividend from step 2 (191) (191):
191 - 190 = 1
Step 4: The remainder is the outcome of step 3:
1 is the result of dividing 191 by 5.
Therefore, the remainder after dividing 191 by 5 is 1.
Learn more about the mathematical operation, here:
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Please help I will make you Brainliest if correct (you don't have to do number two if you don't want to)
Answer:
120?
Step-by-step explanation:
Might be incorrect. -_-
Answer: question 1, all you had to do was divide the shpaes up by simply finding the missing numbers and separating the two shapes.
The rectangle has a area of 96
The square has a area of 16. if we add this up we get a area of 112
so the area is 112cm^2
Happy To Help :)
Question 2. 8 x 2 is 16
2 x 10 is 20.. add that up we get 36m
An airline carries 9,000 passengers per day. How many passengers will the airline carry in 9 days?
Answer:
I think it would be 81,000 hope this helps ;)
Step-by-step explanation:
Kylie signed up for a streaming music service where there's a fixed cost for a monthly membership and a cost per song downloaded. Her total cost is given by the linear graph below. What does the slope of the line represent?
Answer:
we need the linear graph ._.
Step-by-step explanation:
10x−25y Factor the expression using the GCF
Answer: 2x-5y
Step-by-step explanation:
The common term in this expression (GCF) is 5. When you take out the 5, you get 2x-5y. This is the answer.
:)
Robin earned $4,581 in 9 weeks. How much does he earn per week?
Answer:
$509 per weekStep-by-step explanation:
Well, in order to find the unit rate we simply do the following steps:
4,581 ÷ 9 = 509
So to answer the question, each week Robin earns $509.
Hope this helps! : )
Answer:
they earn 509 a week
Step-by-step explanation:4581 divided by 9
Home Find the slope of the roof of a home that rises 8 feet for every horizontal change of 24 feet.
Answer:
1/3
Step-by-step explanation:
to find slope
m=(vertical distance)/(horizontal distance)
m=8/24
m=1/3
PLEASE PLEASE HELP ILL MARK BRAINLIEST!!!!
Answer:
done this before
Step-by-step explanation:
cant see full picture but of what i know of is he spent 35 dollars on apples for his shop...?
Answer: 3x+5y=$33
X+y=9
Step-by-step explanation: X= number of pounds of apples y= number of ponds of oranges.
What is an equation of the line that passes through the point (-4,-6) and is
perpendicular to the line 2c – y = 6?
Answer:
y = -1/2c - 8
Step-by-step explanation:
2c - y = 6
2c -6 = y
Slope: 2. Slope of the perpendicular line: -1/2
Point (-4,-6)
y-intercept = -6 - (-1/2)(-4)
b = -6 -2 = -8
The equation of the line that passes through the point [tex](-4,-6)[/tex] and is
perpendicular to the line [tex]2c - y = 6[/tex] is [tex]2x_{2} -y_{2} +2=0[/tex].
What is equation of the line ?Equation of the line: The general equation of a straight line is [tex]y = mx + c[/tex]. This variable [tex]'c'[/tex] is called the intercept on the [tex]y-axis[/tex]. And [tex]y = c[/tex] is the value where the line cuts the [tex]y-axis[/tex].
Here,
[tex]m=[/tex] the gradient,
[tex]c=[/tex] the intercept on the y-axis
We have,
An equation of the line that passes through the point [tex](-4,-6)[/tex] and is
perpendicular to the line [tex]2c - y = 6[/tex] .
So,
Line [tex]2c - y = 6[/tex]
[tex]2c - y = 6[/tex]
⇒ [tex]y=2c-6[/tex]
and [tex]y = mx + c[/tex]
On comparing above two equations
[tex]m=2[/tex]
and Slope [tex]=-\frac{1}{m}[/tex]
So, Slope [tex]=-\frac{1}{2}[/tex]
Now,
Slope of the equation [tex](m)=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
Slope of required equation [tex]=\frac{-1}{Slope \ of \ 2c-y=6}[/tex]
[tex]=\frac{-1}{\frac{(-1)}{2} }=2[/tex]
Now,
Equation of line with slope [tex]2[/tex] and passing through point [tex](-4,-6)[/tex] ,
Slope of the equation [tex](m)=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
[tex]2=\frac{y_{2} -(-6) }{x_{2} -(-4) }[/tex]
[tex]2x_{2} +8=y_{2} +6[/tex]
[tex]2x_{2} -y_{2} +2=0[/tex]
So, the equation of the line is [tex]2x_{2} -y_{2} +2=0[/tex] .
Hence, we can say that the equation of the line that passes through the point [tex](-4,-6)[/tex] and is perpendicular to the line [tex]2c - y = 6[/tex] is [tex]2x_{2} -y_{2} +2=0[/tex].
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Miss Weight's recipe for Soup calls for
1 1/4 teaspoons of salt. She wants to
use 1/2
that amount. How much salt
Will she use?
Answer: 5/8 of a teaspoon of salt
Step-by-step explanation:
half of 1 is 1/2 or 4/8
half of 1/4 is 1/8
4/8 + 1/8 = 5/8
I NEED HELP ASAP I WILL MARK BRAINLIEST :’]
The question is “Find the equation of the line. Use exact numbers.”
Answer:
y=x-5
Step-by-step explanation:
69632 + 69469 - 59303
Answer: 79798
Step-by-step explanation:
139101 - 59303
= 79798
please give me a brainliest answer
Answer:
79798
Step-by-step explanation:
69632
+ 69469
= 139101
- 59303
= 79798
Hope this helps :)
In a neutral atom that has an atomic mass of 22 and atomic number of 12, how many neutrons does this element have?
Given :
In a neutral atom that has an atomic mass of 22 and atomic number of 12.To Find :-
The number of neutrons .Solution :-
As we know that,
n(neutrons) + n(protons) = A n(neutrons) + 12 = 2 2n(neutrons) = 22-12n(neutrons) = 10Hence the required answer is 10.
Answer:
10 neutrons
Step-by-step explanation:
no.of neutrons = atomic mass - Atomic number
no.of neutrons= 22-12
=10
What is Two-thirds divided by StartFraction 4 Over 5 EndFraction?
A fraction bar labeled 1. Under the 1 are 5 boxes labeled one-fifth. Under the 5 boxes are 3 boxes containing one-third. Under the 3 boxes are 15 boxes labeled StartFraction 1 Over 15 EndFraction.
Two-thirds
StartFraction 5 Over 6 EndFraction
1 and one-fifth
3 and one-third
Answer:
B
Step-by-step explanation:
Answer:
b?
Step-by-step explanation:
i think thats it sorry if wrong!
Please help me solve this problem
Answer:
30
Step-by-step explanation:
If you subtract 30 - 12 you would get 18 and multiply by -3 would get you -54
180
9. What is the value of x below?
A.
B.
1362
C.
D.
→ K
g
136
90
54
t
Answer:
icifzuez8t
Step-by-step explanation:
f8x8s3w557t6jeflfrjj5xg
z4usti
jayo4i
zirstodtpd
dry
fumc
Riley finds a recipe for bubble solution that uses one cup water, 1/4 cup dish soap, and 1 tablespoon corn syrup. She uses 2 cups of dish soap. How much water should she use? Show ur work
HRLP PLZ
Answer:8
Step-by-step explanation: