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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Put the in order 7/16 1/2 3/8 9/32 5/16 15/32 ??? Put from greatest to least
ebgjwbjhkjfhdsn wmiuehdbnsmkji
Answer:
im srry what
Step-by-step explanation:
DYK?
— Pretty face is everywhere, but a woman who cheer you up at your weakest and stay after knowing about your flaws and bad sides are rare, so you better keep her dude!.
#moodchallenge
A bottle of grape juice costs 6.50$ of you buy 6 bottles you can get 10%discount workout how much you save if you buy 6 bottles
Need help with question 1 and 2
Solve for x: 16 = x + 32
Answer:
-16
Step-by-step explanation:
Use everyone's favourite thing: ALGEBRA!!!
16=x+32
16-32=x
-16=x
Hope that helps
Step-by-step explanation:
16=x+32
16-x=32
-x=32-16
-x=16
X=-16
Explain the parts of an angle
Answer:
line segments are the lines
rays are line segments that have one vertex
a vertex is the endpoint of a line(usually represented by a dot)
Step-by-step explanation:
Pls help
bobik: yes, or no
Answer:
yes
Step-by-step explanation:
Answer:
?? Yes??
Step-by-step explanation:
Plzzz help!! just atleast look at my question!! plzz I really need help!
no
Step-by-step explanation:
-2 - -3 doesn't equal -5
Answer:
no
Step-by-step explanation:
-2 - -3 = 1 not 5
please help me its due in 3 mins
Answer:
p = 35°
Step-by-step explanation:
Angles on a straight line add up to 180° so:
2p + 5 + 3p = 180° (simplify)
5p + 5 = 180° (subtract 5 from both sides)
5p = 175° (divide both sides by 5)
p = 35°
Hope this helps!
Answer:
p=35
Step-by-step explanation:
You have to add the two together and set them equal to 180, so 2p+5+3p=180 so 5p=175, so p=35.
i need help. ill mark brain to the first to answer.
Answer:
a and f
Step-by-step explanation:
1500 is double 750, which is the combined calories of lunch and breakfast, which is only 1 third.
Answer:
1st and 2nd options
Step-by-step explanation:
Daily total = (400+350)*3 = 2250
Dinner = 2250 * 2/3 = 1500
equation: 2/3*(x+400+350) = 2/3 * daily total = Dinner = x
what is the equation for the line that is perpendicular to the x-axis and passes through the point (4, -7)?
Step-by-step explanation:
perpendicular means to cross at a right angle (90 degrees).
so, any line perpendicular to the x-axis is parallel to the y-axis.
and any line parallel to the y-axis has only a defining x value. all points on that line have the same x value (while any value for y from -infinity to +infinity is valid).
the y-axis itself is
x = 0
the specified point here has an x value of 4.
so, the line we are looking for is
x = 4
to point out : this is NOT a function, because for the same x value we get more than 1 valid y values.
I need help ASAP!!! (please look at the image and explain how you got the answer, please and thanks)
Answer:
114
Step-by-step explanation:
so lets call shelf 1 x
shelf 2 is twice size + 18 of shelf 1 so it is 2(x)+18
shelf 3 is 12 less than shelf 1 so x-12
shelf 4 is four more so x+4
Add them all together and it should be 5x+10= 2.5 m or 250 cm
Solve for x using cm
then plug into shelf 2 equation
mat.................................................
Answer: it should be B.
Step-by-step explanation:
Answer:
The answer is B. please let me know if I'm wrong.
Have a nice day/night!
Step-by-step explanation:
~King from 7 deadly sins~
Solve the equation x2-81 = 0.
Answer:
40.5
Step-by-step explanation:
x2 - 81 = 0 --> + 81 to both sides
2x = 81 --> divide by 2 on both sides
x = 40.5
Answer:
2x-81=0
2x=0+81
2x=81
x=81
2
x=40.5 ANSWER.
MARK ME AS A BRAINLIST PLZ.
60% of a mussems fossils are from the jurassic period if the number of fossils from the jurassic period is 15 what is the total of number of fossils ate the musuem ?
The total number of fossils at the museum are, 25
What is -(x + 4) - 3x = x in Distributive property?
Answer:
x = -4/5
Step-by-step explanation:
Original equation: -(x+4)-3x=x
Remember distributive property allows us to get rid of the parenthesis by bringing a multiplication from outside to inside a parenthesis.
-(x+4) = -x-4
= -x-4-3x=x
Now we combine like terms in this case we have (-x) and (-3x)
= -4x-4=x
Subtract x from both sides
= -4x-4=x
-x -x
----------------
-5x-4=0
Add 4 to both sides
-5x-4=0
+4 +4
---------------
-5x=4
Our final step is to divide both sides by -5
-5x=4
---- ----
-5 -5
x = -4/5
Hope this helps!!!
The price of a notebook has risen to $3.45 today. Yesterdays price was $3.20. find the percentage increase, round your answer to the nearest tenth of a percent.
Answer:
7.8%
Step-by-step explanation:
Yesterday’s price =$3.20
Today’s price =$3.45
Increase =today’s price - yesterday’s price
That’s $3.45 - $3.20
= $0.25
Percentage increase = increment /yesterday’s price x 100%
That’s $0.25/$3.20 x 100%
0.0781 x 100%
7.81
7.8%
Simplify (a – b)(a2 – 5ab + 2)
Answer:
5ab^2-6a^2b+a^3-2b+2a
Step-by-step explanation:
The simplified expression of expression (a – b)(a² – 5ab + 2) is a³ – 6a²b + 5ab² + 2a – 2b
What is Expression?An expression is combination of variables, numbers and operators.
To simplify the expression (a – b)(a² – 5ab + 2), we need to apply the distributive property, which states that:
(a + b)(c + d) = ac + ad + bc + bd
Using this property, we can multiply the two binomials as follows:
(a – b)(a² – 5ab + 2) = a(a² – 5ab + 2) – b(a² – 5ab + 2)
Now we can distribute the terms of each binomial:
= a³ – 5a²b + 2a – a²b + 5ab² – 2b
Simplifying the terms, we can combine like terms:
= a³ – 6a²b + 5ab² + 2a – 2b
Therefore, the simplified expression is a³ – 6a²b + 5ab² + 2a – 2b
To learn more on Expressions click:
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helping my sister with her homework
Answer:
5 : 10
6 : 12
7 : 14
8 : 16
9 : 18
Step-by-step explanation:
10/5=2
there is only one number in between 7 and 5
so now you have to go up 2 each time in the right collum and go up once in the left collum.
please help me do this
Answer:
125
Step-by-step explanation:
add 21 and 34. with that you get 55. then subtract 180 from 55 then get 125
Write an equation of the line that is parallel to the y-axis and passes through the point (−3,1). Then determine whether the slope of the line is positive, negative, zero, or undefined.
Answer:
equation : x = -3
slope : undefined
Step-by-step explanation:
The equation says that it is parallel to y-axis, meaning all the x values are the same. the slope is undefined because of (HOY / VUX)
what is green and blue? HELP
Answer:
green horizontal asymptote: y = -2
blue horizontal asymptote: y = -4
Step-by-step explanation: Exponential functions have a horizontal asymptote
Solve the inequality. Graph the solution
Answer:
1. y > -3/5 and y < 7/5 Direction to graph 1 below.
2. r > 1 and r < 13/3 Direction to graph 2 below
Step-by-step explanation:
|5y - 2| + 5 > 0
Case 1 Positive || Case 2 Negative ||
5y - 2 + 5 > 0 -(5y - 2) + 5 > 0
5y +3 > 0 -5y + 2 +5 > 0
5y > -3 -5y + 7 > 0
y .> -3/5 -5y > -7
-y > -7/5
y < 7/5 y value negative, change sign
The graph 1: open circle at -3/5; close circle at 7/5; shade between these two numbers.
2. |8-3r|< 5
Case I Case II
8 - 3r < 5 -(8-3r) < 5
-3r < 5 - 8 -8 + 3r < 5
-3r < -3 3r < 5 + 8
-r < -3/3 3r < 13
r >1 r is negative, change r < 13/3
the direction of the sign
Graph 2: Open circle at 1; open circle at 13/3; shade between the two numbers.
What do I choose? PLEASE HELP!! Ill give brainlist, five stars and a thanks for whoever's answer is right. Please!!!!!
Answer:
6 3/4
Step-by-step explanation:
If Sarah uses 3/4 of ribbon to make one hair bow, you would need to multiply 3/4 by 9.
3/4 × 9 = 6 3/4
She will need 6 3/4 yards of ribbon.
Hope this helps! Brainliest would be really appreciated!
Molly has 3 pounds of blueberries. She is freezing the berries into 1 half pound portions. How many smaller portions of blueberries will Molly make
Answer:
6 smaller portions
Step-by-step explanation:
1 pound (lb) = 16 ounces (oz)
3 lbs = 48 oz
1/2lb = 8oz
48oz (total)/8oz (amount in each portion) = 6 portions
How many solutions does the nonlinear system of equations graphed below have?
A. One
B. Four
C. Two
D. Three
Answer:
There are three possible types of solutions for a system of nonlinear equations involving a parabola and a line.
Step-by-step explanation:
From the graph, write the linear equation in slope-intercept form
Answer:
y= [tex]\frac{2}{5}[/tex](x)+2
Step-by-step explanation:
First take two points from the line (x-int (-5,0) and y-int (0,2)). Once you get that you want to find the slope using the formula [tex]\frac{Y_{2} -Y_{1} }{X_{2}- x_{1} }[/tex]. Substitute the values and find the slope. Once you find the slope (m) to be [tex]\frac{2}{5}[/tex], take any of the two points and apply it to the slope intercept formula (y=mx+b) to find b. I took the point (0,2) and applied it to the formula. It should look like 2= [tex]\frac{2}{5}[/tex](0)+b. Solve for b by multiplying 2/5 by zero and your left with 2=b. Plugin the missing varibles for the equation and it should come out to be y= [tex]\frac{2}{5}[/tex](x)+2.
HELPP AND SHOW YOUR WORK!!!
4. −10(x − 3)
A) −15x + 30
B) −10x + 30
C) −15x + 35
D) −15x + 37
Answer:
B) [tex]-10x+30[/tex]
Step-by-step explanation:
You distribute:
-10 times X minus 3 ( -10*x-3)
Which gives you:
Answer: -10x+30
Hope this helps!
Answer:
-10x+30Step-by-step explanation:
[tex]\sf -10(x -3)[/tex]
[tex]\sf -10x-\left(-10\right)\times \:3[/tex]
[tex]\sf -10x+30[/tex]
What are the values of v and w ?
Answer:
V = 72 & W = 72
Step-by-step explanation:
All angles of a triangle will be equivalent to 180 degrees.
We start by subtracting first.
180 - 36 = 144
Look back at the triangle. FG and HG are congruent, which means the values of V and W will be the same.
The last step is to divide.
144 / 2 = 72
V = 72 & W = 72
Solve for x step by step: -4=v/20-5
Answer:
WALA PO AKONG ALAM SA MATH EHH HEHEH