The spider's movement is an illustration of a parabola.
The equation of the parabola is: [tex]\mathbf{y = -\frac{1}{320}(x - 80)^2 + 20}[/tex]The focus of the parabola is [tex]\mathbf{Focus = (80 ,-60)}[/tex]The directrix is: [tex]\mathbf{y = 100}[/tex].The axis of symmetry is: [tex]\mathbf{x = 80}[/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 20mm, midway 160mm.
So, the vertex is:
[tex]\mathbf{(h,k) = (80,20)}[/tex]
The equation of a parabola is:
[tex]\mathbf{y = a(x - h)^2 + k}[/tex]
So, we have:
[tex]\mathbf{0 = a(0 - 80)^2 + 20}[/tex]
[tex]\mathbf{0 = 6400a + 20}[/tex]
Subtract 20 from both sides
[tex]\mathbf{6400a =- 20}[/tex]
Solve for a
[tex]\mathbf{a =- \frac{1}{320}}[/tex]
Substitute [tex]\mathbf{a =- \frac{1}{320}}[/tex] and [tex]\mathbf{(h,k) = (80,20)}[/tex] in [tex]\mathbf{y = a(x - h)^2 + k}[/tex]
[tex]\mathbf{y = -\frac{1}{320}(x - 80)^2 + 20}[/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 -1/320}}[/tex]
[tex]\mathbf{p = -\frac{320}{4}}[/tex]
[tex]\mathbf{p = -80}[/tex]
So, we have:
[tex]\mathbf{Focus = (80 , 20-80)}[/tex]
[tex]\mathbf{Focus = (80 ,-60)}[/tex]
The axis of symmetry is:
[tex]\mathbf{x = h}[/tex]
So, we have:
[tex]\mathbf{x = 80}[/tex]
The directrix is:
[tex]\mathbf{y = k - p}\\[/tex]
So, we have:
[tex]\mathbf{y = 20+80}[/tex]
[tex]\mathbf{y = 100}[/tex]
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Geometry questions need some help
Step-by-step explanation:
8) x=23sin(48) =17.1m
9) x=11cos42=8.2ft
what is the volume of the prism?
Answer:
Step-by-step explanation:
h = 3 ft
l*b = 25 sq.ft
Volume = l*b *h
= 25 * 3
= 75 cubic feet
Answer:
75ft
Step-by-step explanation:
First you mupilply [tex]25 x 3 = 75ft[/tex]
and that is it.
A pack of 24 crayons costs the manufacturer $0.05 to make and is sold to the stores for $0.25. The
stores sell the crayons for $0.50 during Back to School week.
An equation that represents the mark up cost by the manufacturer is (Select]
. An equation that represents the store mark up cost is (Select]
. A
V
composition of these two functions is (Select)
. It represents
[ Select]
The answers is P(C)=2c P(C) =5c P(C) =10c
We want to find equations for the different markups for the manufacturer and the stores that sell the crayons.
We know that a pack of 24 crayons costs $0.05 to make.
Is sold to stores for $0.25
The stores sell it for $0.50
Now we want to get the markup equation for the manufacturer, this is:
Markup = 100%*(price - cost)/(cost) = 100%*($0.25 - $0.05)/$0.05 =400%
For the store it is:
Markup = 100%*($0.50 - $0.25)/($0.25) = 100%
For the composition of these two I assume you refer to the total markup (notice that these are not functions, we can't make a composition if we do not have a variable).
Comp = 100%*($0.50 - $0.05)/($0.05) = 900%
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Guys can u please help i can explain it so i gotta send a photo i always give hearts and 5 stars :D the photo is down below
Answer:
5x cm
Step-by-step explanation:
Total length of AE = 2x + 3x
= 5x cm
Sensei Umeh’s ""Active Hands"" karate program grew from 8 members to 15 last week. What is the percent of change?
Answer:
187.5% increase
Step-by-step explanation:
Percent change formula: [tex]\frac{x_{2}-x_{1}}{x_{1}}[/tex]
Initially, the program had 8 members and ended with 15 so [tex]\frac{15-8}{8}=\frac{7}{8}=0.875=87.5[/tex]
Please answer for last question
Step-by-step explanation:
since you know already that it is a linear equation with a constant change rate (slope), you don't know the equation itself yet ?
you found the change rate (slope).
it is x goes up by 2, and y goes down by 6.
the slope is the ratio y/x representing the y and x changes, and it is always the factor of x.
"down" or "left" means "-","up" or "right" means "+".
the slope here is therefore
-6/2 = -3/1 = -3
so, we know the line function looks like
y = -3x + b
to get b we use one of the x y pairs like (1. 4)
4 = -3×1 + b
7 = b
and the full line function is
y = -3x + 7
Kira is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.
Company A charges an initial fee of $35 and an additional 60 cents for every mile driven.
Company B charges an initial fee of $42 and an additional 50 cents for every mile driven.
For what mileages will Company A charge less than Company B?
Write your answer as an inequality, using m for the number of miles driven.
Answer:
m < 0.7
Miles less than 0.7
Step-by-step explanation:
Company A: 60m + 35
Company B: 50m + 42
60m + 35 < 50m + 42
60m - 50m < 42 - 35
10m < 7
m < 7/10 (0.7)
Sally brought the pizza shown above for lunch which was cut into 10 equal slides what percentage of the pizza did tell they eat if she had four slices
Answer:
25%
Step-by-step explanation:
Answer:
Sally ate 40% of the pizza and there was 60% of the pizza leftover.
Step-by-step explanation:
A percentage is a rate, number, or amount in each hundred.
There were 10 slices of pizza, she ate 4.
4/10 = 40/100 multiplied by 10, which would let us find the percentage.
Therefore, Sally ate 40% of the pizza and left 60% back.
Hope This Helps!
Find the simple interest.
Principal
$160
Rate
5.5%
Time
4 years
The simple interest is
(Simplify your answer.)
Answer:
$35.20
Step-by-step explanation:
S.I. = (P×R×T)/100
=(160×5.5×4) /100
= (640×55) / 100×10
= (64×55) / 100
= 3520 / 100
= $ 35.20
brainliest plz
Help please help me
Answer:Hi
Step-by-step explanation:
Lines AB and CD are parallel. Find the measures of the three angles in triangle ABF,Measurement of angle FAB
Answer:
not enough information
Step-by-step explanation:
in order to even think about solving this we need at 2/3 measurements
like aas, sas, sss ect
Could I get help with 8-11 please :(
Answer:
8. m∠1 = 64, m∠2 = 26, m∠3 = 36
9. m∠1 = 73, m∠2 = 58, m∠3 = 107, m∠4 = 49, m∠5 = 131
10. m∠1 = 34, m∠2 = 52, m∠3 = 38, m∠4 = 94, m∠5 = 56, m∠6 = 38
11. m∠1 = 62, m∠2 = 71, m∠3 = 109, m∠4 = 35, m∠5 = 109, m∠6 = 29, m∠7 = 47, m∠8 = 62
Step-by-step explanation:
8. m∠1 = 180 - (75 + 41) = 180 - 116 = 64
m∠2 = 90 - 64 = 26
m∠3 = 90 - 54 = 36
9. m∠3 = 180 - 73 = 107
m∠1 = 73
m∠2 = 180 - (73 + 49) = 180 - 122 = 58
m∠4 = 49
m∠5 = 180 - m∠4 = 180 - 49 = 131
10. m∠6 = 90 - 52 = 38
m∠3 = m∠6 = 38, m∠2 = 52
m∠5 = 180 - (86 + 38) = 180 - 124 = 56
m∠1 = 90 - 56 = 34
m∠4 = 180 - (34 + 52) = 180 - 86 = 94
11. m∠2 = 71
m∠3 = m∠5 = 180 - 71 = 109
m∠1 = 180 - (47 + 71) = 180 - 118 = 62
m∠4 = m∠2 - 36 = 71 - 36 = 35
m∠6 = m∠2 - 42 = 71 - 42 = 29
m∠7 = 47
m∠8 = m∠1 = 62
[tex]\sf 300+200+200[/tex]
Step-by-step explanation:
300+200+200 = 700.
so simple
hope this helps you.
what is the equation for the line that is parallel to the y-axis and passes through the point (2, -5)?
Answer:
X = 2
Step-by-step explanation:
please help me this is due tomorrow and I can't figure this out (IXL CC.2 8th grade)
The answer is suppose to look like this (_____,___) AND IF YOU CAN TAKE A SCREENSHOT OF THE GRAPH( picture provided) AND SHOW ME WERE THE LINES MEET.
Answer:
at point (4,4)
Step-by-step explanation:
Answer:
( 4 , 4 )
Step-by-step explanation:
The polynomial of degree 5, P(2), has leading coefficient 1, has roots of multiplicity 2 at x = 4 and
x = 0, and a root of multiplicity 1 at 3 3.
Find a possible formula for P(x).
P(x)
Answer:
[tex]P(x)=x^{5} +x^{4} -5x^{3} +3x^{2}[/tex]
Step-by-step explanation:
Each root corresponds to a linear factor, so we can write:
[tex]P(x)=x^{2} (x-1)^{2} (x+3)\\=x^{2} (x^{2} -2x+1(x+3)\\\\=x^{5} +x^{4} -5x^{3} +3x^{2}[/tex]
Any polynomial with these zeros and at least these multiplicities will be a multiple (scalar or polynomial) of this [tex]P(x)[/tex]
Footnote
Strictly speaking, a value of [tex]x[/tex] that results in [tex]P(x)=0[/tex] is called a root of
[tex]P(x)=0[/tex] or a zero of [tex]P(x)[/tex] . So the question should really have spoken about the zeros of [tex]P(x)[/tex] or about the roots of [tex]P(x)=0[/tex]
Distance describes how far an object has moved along its path.
Displacement describes how far an object has moved from its starting point to its final position.
Step-by-step explanation:
Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion. Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position.
Answer:
Distance travelled by skateboard is 1.5 miles.
Displacement is 1 mile.
Kerri sold her purse for $351. She had originally purchased it for $316. Calculate her profit or loss percentage.
Answer:
$35 profit
Step-by-step explanation:
351-316=35
Answer:
$35
Step-by-step explanation:
she bought it for $316 and sold it for more than she bought it for so we know that she made money.
so all we have to do is subtract 351 from 316
Please Help Me
The ratio of the number of combinations (2n+2) of different objects taken n at a time to the number of combinations of (2n-2) of different objects taken n at a time is 99:7. Find the value of n.
The expected value of n is 1.152
The question states that ratio of 2n+2 and 2n-2 = 99:7. This means that
2n+2:2n-2 = 99:7, this also means that
[tex]\frac{2n+2}{2n-2}[/tex] = [tex]\frac{99}{7}[/tex]
If that is so, we can cross multiply so that
99 * (2n - 2) = 7 * (2n + 2), on expanding the bracket, we have
198n - 198 = 14n + 14
198n - 14n = 14 + 198
184n = 212, dividing both sides by 184, we have
n = 212/184
n = 1.152
Therefore, the value of n is 1.152
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can someone please help me with this
Answer:
∠ R = 58° , ∠ Q = 32°
Step-by-step explanation:
Complementary angles sum to 90°
∠ Q is 26° less than ∠ R , so ∠ Q = ∠ R - 26° , then
∠ Q + ∠ R = 90° , that is
∠ R - 26° + ∠ R = 90°
2 ∠ R - 26° = 90° ( add 26° to both sides )
2 ∠ R = 116° ( divide both sides by 2 )
∠ R = 58°
∠ Q = 58° - 26° = 32°
[tex]x/6=7/2x=[/tex]
Answer:
x = √21, x = -√21
3 pls pls pls help me
Answer:
I think the answer is c
Step-by-step explanation:
Emily went to soccer practice 6 times last month. Each practice is 90 minutes long.
How long did Emily spend at soccer practice last month?
Answer:
74 days. thanks me later lol nag check out
Answer:
What is 540 minutes or 9 hours spent practicing soccer
Step-by-step explanation:
90*6=540 minutes
540/60(minutes in 1 hour)
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PLEASE HELP!!
Identify the type of transformation to triangle ABC.
Glide
reflection
Reflection
Rotation
Translation
Answer:
Step-by-step explanation:
A-Reflection
B-Translation
C-Rotation
D- Glide Reflection
Answer Asap!
<3 THX <3
XOXO Also giving out brainliest!
Answer:
4,3 becomes 0,0 after the changes
Answer:
32
Step-by-step explanation:
28 29 30
There are five red, 3 blue and a white marble in a jar. What is the probability of selecting
a white marble, replacing it, then selecting a white marble again?
Answer:
1/81 I think now 100% sure though
Please provide the answer for the x and z as seen in the image
pls help!!!!! i will give brainliest!!!!!
Answer:
-2
Step-by-step explanation:
all you gotta do is look to see where the line intersects the y axis which is -2 here
please help i need help
Answer:
fractions
d
its right answer
Answer:
The answer to your question is D Fractions
Step-by-step explanation:
Fractions and decimals are two different ways to represent parts of a whole number.
I hope this helps!
why is 3/8 bigger than 3/12
Answer:
3/8 is is bigger then 3/12
Step-by-step explanation:
The reason is that 3/12 is equivalent to 2/8 and 3/8 is equivalent to 6/16
Sorry if its wrong! ^^""
As, 0.375> 0.25, so, 3/8 is greater than 3/12.
Here, we have,
To get the answer, we first convert each fraction into decimal numbers.
We do this by dividing the numerator by the denominator for each fraction as illustrated below:
3/8 = 0.375
3/12 = 0.25
Then, we compare the two decimal numbers to get the answer.
0.375 is greater than 0.25.
i.e. 0.375> 0.25, as 0.375 - 0.25 = 0.125
Therefore, 3/8 is greater than 3/12.
Hence, As, 0.375> 0.25, so, 3/8 is greater than 3/12.
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