Given:
The image of a lens crosses the x-axis at –2 and 3.
The point (–1, 2) is also on the parabola.
To find:
The equation that can be used to model the image of the lens.
Solution:
If the graph of polynomial intersect the x-axis at c, then (x-c) is a factor of the polynomial.
It is given that the image of a lens crosses the x-axis at –2 and 3. It means (x+2) and (x-3) are factors of the function.
So, the equation of the parabola is:
[tex]y=k(x+2)(x-3)[/tex] ...(i)
Where, k is a constant.
It is given that the point (–1, 2) is also on the parabola. It means the equation of the parabola must be satisfy by the point (-1,2).
Putting [tex]x=-1, y=2[/tex] in (i), we get
[tex]2=k(-1+2)(-1-3)[/tex]
[tex]2=k(1)(-4)[/tex]
[tex]2=-4k[/tex]
Divide both sides by -4.
[tex]\dfrac{2}{-4}=k[/tex]
[tex]-\dfrac{1}{2}=k[/tex]
Putting [tex]k=-\dfrac{1}{2}[/tex] in (i), we get
[tex]y=-\dfrac{1}{2}(x+2)(x-3)[/tex]
Therefore, the required equation of the parabola is [tex]y=-\dfrac{1}{2}(x+2)(x-3)[/tex].
Note: All options are incorrect.
There is a bag filled with 5 blue and 6 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 of the same colour?
Answer:
The probability of getting two of the same color is 61/121 or about 50.41%.
Step-by-step explanation:
The bag is filled with five blue marbles and six red marbles.
And we want to find the probability of getting two of the same color.
If we're getting two of the same color, this means that we are either getting Red - Red or Blue - Blue.
In other words, we can find the independent probability of each case and add the probabilities together*.
The probability of getting a red marble first is:
[tex]\displaystyle P\left(\text{Red}\right)=\frac{6}{11}[/tex]
Since the marble is replaced, the probability of getting another red is: [tex]\displaystyle P\left(\text{Red, Red}\right)=\frac{6}{11}\cdot \frac{6}{11}=\frac{36}{121}[/tex]
The probability of getting a blue marble first is:
[tex]\displaystyle P\left(\text{Blue}\right)=\frac{5}{11}[/tex]
And the probability of getting another blue is:
[tex]\displaystyle P\left(\text{Blue, Blue}\right)=\frac{5}{11}\cdot \frac{5}{11}=\frac{25}{121}[/tex]
So, the probability of getting two of the same color is:
[tex]\displaystyle P(\text{Same})=\frac{36}{121}+\frac{25}{121}=\frac{61}{121}\approx50.41\%[/tex]
*Note:
We can only add the probabilities together because the event is mutually exclusive. That is, a red marble is a red marble and a blue marble is a blue marble: a marble cannot be both red and blue simultaneously.
what is the length of side X in the above right triangle
Answer:
x = 12
Step-by-step explanation:
Leg 1 = 9
Leg 2 = x
Hypotenuse = 15
Using Pythagorean Theorem;
A² + B² = C²
9² + x² = 15²
81 + x² = 225
x² = 225 - 81
x² = 144
x = [tex]\sqrt{144}[/tex]
x = 12
Hope this helps!
Answer:
x ≈ 12
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
x² + 9² = 15²
x² + 81 = 225 ( subtract 81 from both sides )
x² = 144 ( take the square root of both sides )
x = [tex]\sqrt{144}[/tex] = 12
How many quarters are there in 5 and 3/4
Answer:
23
Each 1 has 4 quarters
5*4=20
20+3
23
Step-by-step explanation:
A water tank is in the shape of a cylinder with a diameter of 20 feet and a height of 20 feet. The tank is 70% full. About how many gallons of water are in the tank?
Answer:
32901 gallons
Step-by-step explanation:
First, we find the volume of the cylindrical water tank when it is full.
The volume of a cylinder is given as:
V =
where r = radius and h = height of the cylinder
The diameter of the tank is 20 feet, hence, its radius is 10 feet.
Volume, V, is therefore:
V =
This is the volume of the tank, when it is full.
When it is 70% full, the volume will be:
1 cubic foot () is 7.48 gallons.
Therefore, the volume of the 70% full tank in gallons will be:
4398.23 * 7.48 = 32901.05 gallons ≅ 32901 gallons
The tank contains 32901 gallons of water.
Answer:
approximately 32,900 gallons
Step-by-step explanation:
volume water in tank
v = πr²h * .70
v = π * 10² * 20 * .70
v = 4,398.2297150257 ft³
1 ft³ = 7.48 gallons
gallons in tank
4,398.2297150257 * 7.48 = 32,898.7582683922
~ 32,900 gallons
What is the value of x?
Answer:
Solution given:
sin 47=opposite/hypotenuse
Sin 47=x/18
x=sin47*18
x=13.16ft
Answer:
ammaamakamamMN8181(18736
Step-by-step explanation:
88271(1(1+1+382(2(#!#
Please help I need the answer right
Answer:
B) 4 inches
Step-by-step explanation:
Since ABC is congruent to EFG then AB is congruent to EF, and BC is congruent to FG.
BC = 4 in
FG = 4 in
Someone Help if they can ASAP!
Answer:
The answer is D.
Step-by-step explanation:
Since (4x+20) and 60 are vertically opposite angles. They both are equal. Hope this helped!
Two angles are complementary. If one angle measures 48°, what is the measure of the other angle?
a
42°
b
48°
c
132°
d
52°
Answer:
A
Step-by-step explanation:
The sum of two complementary angles is 90 degrees
x + 48 = 90
x = 90 -48
x = 42 degrees
Can anyone please help with this question? Would much appreciate it
please help with this !!!!
Answer:
0
Step-by-step explanation:
this is just to confuse us.
"t" is used instead of "x" (probably because the formula has something to do with "time"). but it does not matter.
and 3 different functional definitions have been given based on the value of the argument "t".
we need the functional value for t=2.
is 2 = 8 ? no. therefore the first definition does not apply.
is 2 = 10 ? no. therefore the second definition does not apply either.
is 2 unequal to 8 or 10 ? yes, 2 is 2 and not 8 and not 10.
so, the third definition applies :
f(2) = 2² - 3×2 + 2 = 4 - 6 + 2 = 0
What is the volume of the square pyramid? Enter in the box ___m^3
Answer:
V = 400 m^3
Step-by-step explanation:
The volume of a square pyramid is
V = 1/3 Bh where B is the area of the base and h is the height
B = 10 *10 = 50
V = 1/3 (100)* 12
V = 400 m^3
PLEASE PLEASE PLEASE HELP ME
EXPLAINING YOUR ANSWER WILL GIVE YOU BRAINLIEST
I REALLY NEED HELP AND ACCURATE ANSWERS
Answer:
the area of sector is
[tex] \frac{126}{360} \times \pi \times ( \frac{16}{2} ) {}^{2} = \frac{112}{5} \pi[/tex]
Answer:
Step-by-step explanation:
126/360 × pi× radius²= Area of the sector
1. If one leg gets longer the other leg must also
get longer in order to keep the hypotenuse the
same.
TRUE
FALSE
Người ta dự định chuyển 78452 lít dầu từ kho A sang kho B Trong 4 ngày đầu mỗi ngày chuyển được 18214 lít dầu hỏi còn phải chuyển bao nhiêu lít dầu nữa
Answer:
5596 liters of oil still need to be transferred.
Step-by-step explanation:
Total oil = 78452 liters
oil transferred each day for 4 days = 18214 liters
The amount of oil transferred in 4 days = 4 x 18214 = 72856 liters
The mount of oil left in ware house A
= 78452 - 72856
= 5596 liters
Simplify the expression
3(5x+8)
Answer:
Solution given:
3(5x+8)
distribute
15x+8*3
15x+24 is a required answer.
Answer:
15x + 24
Step-by-step explanation:
Apply the Distributive Property of Multiplication. Multiply each of the two terms inside parentheses by 3:
3(5x + 8) = 15x + 24
Write the number 10 000 000 as a power of 10.
Answer:
10⁷
Step-by-step explanation:
Just count the number of zero and raise the counted number of zero.
Kiera and her brother, Desmond, are making trail mix to bring on their family's camping trip. Kiera uses 2 cups of raisins and 5 cups of nuts in her trail mix. Desmond uses 3 cups of raisins and 6 cups of nuts in his trail mix. Whose trail mix has a lower ratio of raisins to nuts?
Answer:
Kiera has a lower ratio of raisins to nuts. (2:5)
Step-by-step explanation:
To find this, you would have to make the number of nuts the same in each to accurately compare them.
It starts with Kiera's 2 cups of raisins and 5 cups of nuts. So it will be 2:5 (raisins first then nuts.)
Desmond will be 3:6 (have to make it the same order, raisins and then nuts.)
So I multiplied both the 2 and the 5 in 2:5 by 6 first.
Then multiply both the 3 and 6 in 3:6 by 5 to make the number of nuts the same in both.
So Kiera will have 12:30 and Desmond will have 15:30.
Then you can conclude that Kiera has the lower ratio.
Every tenth customer to Macy's end of the season sale gets a $10
coupon. Every twenty-fifth customer gets a free gift bag. Which customer
will be the first one to get both the $10 off coupon and the gift bag?
Answer:
50th
Step-by-step explanation:
10 multiply by 5 is 50
And 25 multiply by 2 is 50
50 is the first to appear on both sides
help with the questions below!
Answer:
b
Step-by-step explanation:
A kite is flying 78 ft off the ground, and its string is pulled taut. The angle of elevation of the kite is 41°. Find the length of the string. Round your answer to the
nearest tenth.
PLZ HELP BEEN STUCK FOR A HOUR!!!
Answer:
Length of kite string = 118.9 feet (Approx.)
Step-by-step explanation:
Given:
Height of kite = 78 feet
Angle of elevation = 41°
Find;
Length of kite string
Computation:
Height of kite = Perpendicular
Length of kite string = Hypotenuse
Using trigonometry function;
Sinθ = Perpendicular / Hypotenuse
Sin 41 = Height of kite / Length of kite string
0.656 = 78 / Length of kite string
Length of kite string = 78 / 0.656
Length of kite string = 118.9 feet (Approx.)
A triangle in the coordinate plane has vertices of (2,6).(-4,-4), and (0,-6). The triangle is dilated with a scale factor of 2. What are the new coordinates?
(1,3), (-2,-2), and (0, -3)
(4,12).(-8, -8), and (0, -12)
(0,4),(-6, -6), and (-2,-8)
(4,8).(-2,-2), and (2,-4)
Answer:
To solve this problem you have to multiply all of the coordinates by 2
So your answers are
(2,6) ---> (4,12)
(-4,-4) ---> (-8,-8)
(0,-6) ---> (0,-12)
Could you please make brainly :)
Hope this helps ;)
Step-by-step explanation:
Please answer this and get ez 25 points
Answer:
13. 10%
14. 43/50
Step-by-step explanation:
13. P(1000) = 5/50 × 100% = 10%
14. P(not 100) = (50-7) /50 = 43/50
Select the rule for each piece. Rule for piece 1: Rule for piece 2:
Answer:
Rule for piece 1: y=-x
Rule for piece 2: y=1
Rule for piece 3: y = 2-x
Step-by-step explanation:
17. There are 25 squares in the pattern.
What fraction of the squares have these
numbers of edges free?
a) 1 edge b) 2 edges c) 3 edges
Arrange the functions in ascending order, starting with the function that eventually has the least value and ending with the function that eventually has the greatest value.
3x + 8
4x + 3
x2 + 6
3x
4x
x2
↓
↓
↓
↓
↓
Answer:
3x < 4x < 3x + 8 < 4x + 3 < x² < x² + 6
Step-by-step explanation:
This is because as x → ∞
3x → 3∞ ,
Also, as x → ∞
4x → 4∞ ,
Also, as x → ∞
3x + 8 → 3∞ + 8,
Also, as x → ∞
4x + 3 → 4∞ + 3 ,
Also, as x → ∞
x² → ∞²,
Also, as x → ∞
x² + 6 → ∞² + 6
and 3∞ < 4∞ < 3∞ + 8 < 4∞ + 3 < ∞² < ∞² + 6
Thus as x → ∞
3x < 4x < 3x + 8 < 4x + 3 < x² < x² + 6 in ascending order
Answer:
i am not 100% sure but i think it is
3x < 3x + 8 < 4^x < 4^x + 3 < x^2 < x^2 + 6
Step-by-step explanation:
I just got this because one of the other answers said replace x with infinite. Their answer would have been wrong because the actual question is supposed to be 4^x and 4^x + 3 which is different than just 4x and 4x + 3. :)
Noah says that 2^4 • 3^2 = 6^6.
Tyler says that 2^4 • 4^2 = 16^2
Do you agree with Noah? Explain or show your reasoning.
Do you agree with Tyler? Explain or show your reasoning.
Answer: 5/6
Step-by-step explanation:
Help,anyone can help me do quetion
Answer:
B1: x = 51
C1: x = 73, y = 34
Step-by-step explanation:
B1:
By exterior angle theorem:
x° + 54° = 105°
x° = 105° - 54°
x° = 51°
x = 51
C1
x° = 73°(Alternate angles)
x = 73
y° = 34° (corresponding angles)
y = 34
what is 94.2 and 87 averaged out
Answer: 90.5
Step-by-step explanation:
Answer:
90.6
Step-by-step explanation:
If you mean "what is the average of 94.2 and 87," that is found as follows:
94.2 + 87
------------------ = 90.6
2
We say, "the average" (or "the mean") of 94.2 and 87 is 90.6." 90.6 lies exactly halfway between 87 and 94.2.
Your math test scores have been: 73, 86, 91,88 Just from these scores, your current grade is 84.5 You just scored a 67 on the last test. What is your new grade?
Answer:
[tex]81[/tex]
Step-by-step explanation:
The average of a set of [tex]n[/tex] values is equal to the sum of the values in that set divided by [tex]n[/tex].
Therefore, the average of your 5 scores is equal to [tex]\frac{73+86+91+88+67}{5}=\boxed{81}[/tex]. Since evidently your grade is represented by the average of all your scores, your new grade is 81.
Al vender una refrigeradora, gané s/. 580. Si después de la venta gasté s/. 1 260 y me queda s/. 480, ¿Cuánto costó la refrigeradora?
Answer:
english plz
Step-by-step explanation: