The image of a parabolic lens is projected onto a graph. The image crosses the x-axis at –2 and 3. The point (–1, 2) is also on the parabola. Which equation can be used to model the image of the lens?
y = (x – 2)(x + 3)
y = (x – 2)(x + 3)
y = (x + 2)(x – 3)
y = (x + 2)(x – 3)
Answer:
[tex]y =-\frac{1}{2}(x +2)(x - 3)[/tex]
Step-by-step explanation:
Given
[tex]x_1 = -2[/tex]
[tex]x_2 = 3[/tex]
[tex](x,y) = (-1,2)[/tex] --- a point on the parabola
Required
The equation
First, calculate the equation from the zeros
[tex]y =k(x - x_1)(x - x_2)[/tex]
Substitute [tex]x_1 = -2[/tex] and [tex]x_2 = 3[/tex]
[tex]y =k(x - -2)(x - 3)[/tex]
[tex]y =k(x +2)(x - 3)[/tex]
To solve for k, we substitute [tex](x,y) = (-1,2)[/tex]
[tex]2 = k(-1+2)(-1-3)[/tex]
[tex]2 = k(1)(-4)[/tex]
[tex]2 = -4k[/tex]
Divide by -4
[tex]k=\frac{2}{-4}[/tex]
[tex]k=-\frac{1}{2}[/tex]
So, the equation is:
[tex]y =k(x +2)(x - 3)[/tex]
[tex]y =-\frac{1}{2}(x +2)(x - 3)[/tex]
Answer:
C
Step-by-step explanation:
What is the area of the triangle shown below?
(please help, im trying to bring my grades up)
Answer:
65 units²
Step-by-step explanation:
10 × 13 = 130
130 ÷ 2 = 65
Answer:
5²+x² =13²
x². =169-25
x² =144
x. =√144
x. =12
area of the triangle=1/2×10×12
=60 units²
Help a bab out please?
Answer:
the answer is 55
Step-by-step explanation:
if you have a straight line each side equals 180 degrees so take 60+65 which equals 125 then do 180-125 and you get 55
A small auditorium has 20 seats in the first row and each successive row contains 2
additional seats. If there are 12 rows in the auditorium, how many seats are in this
auditorium?
O 384
O 372
O 330
O 264
Answer:
330.
Step-by-step explanation:
Count all the way up. The first row is 20, then goes, 22,24,26,28,30,32,34,36,38,40. These are the number of seats for all 12 rows, since we added 2 each row. Add them all together including 20 to get 330 seats. The whole auditorium has 330 seats.
Hope this helps!
As per arithmetic Progression, there are 372 seats in the given auditorium.
What is an arithmetic progression?"Arithmetic Progression is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value."
Given, the auditorium has 20 seats in the first row.
Then, each successive row contains 2.
We can assume it as an arithmetic progression.
Here, the first term(a) is 20.
The common difference(d) is 2.
Total number of terms(n) is 12.
Therefore, the sum of all the terms is
[tex]= \frac{n}{2}[2a + (n-1)d]\\= \frac{12}{2}[2(20) + (12-1)2]\\= 6[40+(11)2)]\\= 6(40+22)\\= 6(62)\\= 372[/tex]
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The length of a rectangle is 5 more than 3 times the width. Write and solve an equation to find the width (w) if the length is 12.5 cm.
Answer:
Length = 42.5 cm
Step-by-step explanation:
length of rectangle = 5 + 3w
So l = 5 + 3w where w = 12.5
Equation:
L = 5 + 3(12.5)
Solving the Equation:
L = 5 + 3(12.5)
L = 5 + 36 + 1.5
L = 42.5
Length: 42.5 cm
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Please help me with this problem
Answer:
3.14 x 4 x 4
= 3.14 x 16
= 50.24
Answer:
50.24
Step-by-step explanation:
A=πr²
= (3.14)(4)²
= 50.24
PLEASE HELPPPPPP FINDING CIRCUMFERENCE AND AREA OF A CIRCLE
Answer:
The circumference of the circle is 28.26 m.
The area of the circle is 63.585 [tex]m^{2}[/tex].
Step-by-step explanation:
To solve for the circumference of the circle, start by using the circumference formula of a circle, which is [tex]C= 2\pi r[/tex]. However, 3.14 will be used instead of [tex](\pi)[/tex] for this formula.
First, the radius of the circle needs to be found. To find the radius of the circle, divide the diameter by 2 because the radius equals half of the diameter. The radius is 9 m divided by 2, which equals 4.5 m.
Next, plug in the radius into the formula, and the formula will look like [tex]C=(2)(\pi )(4.5 m)[/tex]. Then, solve the equation, and the answer will be 28.26 m.
To solve for the area of the circle, start by using the area formula of a circle, which is [tex]A=\pi r^{2}[/tex]. However, 3.14 will be used instead of [tex](\pi)[/tex] for this formula.
For the area, plug the radius into the formula, and the formula will look like [tex]A= (3.14)(4.5m)^{2}[/tex]. Then, solve the equation, and the answer will be 63.585 [tex]m^{2}[/tex].
a cell phone plan charges a base fee of $62 and an overage charges $30 per gigabyte of data that exceeds 2 GB
Analyze the diagram below and complete the instructions that follow.
Find the exact value of tan(M).
Explanation:
Recall that tangent = opposite/adjacent.
For reference angle M, the side ON = 5 is the opposite side and MN = 12 is the adjacent side. We don't need the hypotenuse.
Answer:
C or 5/12
Step-by-step explanation:
Which graph represents
y= -2x?
Answer:
The second one
Step-by-step explanation:
An artist is preparing to open a gallery, but wants to have 35 finished works of
art before he opens. He creates 4 new works each week. If he already has 19
works prepared, how many weeks until he is ready to open?
Answer:
tic ishaan t,x Germany ruff hero
an architects cWhat is the domain of this relation?
(12, 5)
(20, 0)
(20, 20)
(–13, 0)
Answer:
Domain { -13,12,20 }
Step-by-step explanation:
The domain is the input values
Domain { -13,12,20 }
We list them in order from smallest to largest and do not list repeats
if sec theta = 5/3 and the terminal point determined by theta is in quadrant 4, then:
Answer:
A. csc 0 = -5/4 or B. cos 0 = 3/5
Answer:
B or A
Step-by-step explanation:
sec(theta) = 1/cos(theta)
cos(theta) = adjacent side / hypotenuse.
The csc(theta), the sin(theta) and the tan(theta) in quad 4 are all minus
Since the cos(theta) is positive in quad 4, B is going to be the answer.
The value for sin(theta) should be sin(theta) = - 4/5 not 2/5
Tan(theta) = - 4/3
Note: 4 is found by using the Pythagorean Theorem because the trigonometric functions are all defined by the sides of a right triangle.
a^2 + b^2 = c^2
a = the adjacent side = 3
b = the opposite side = b
c = the hypotenuse = 5
3^2 + b^2 = 5^2
9 + b^2 = 25
b^2 = 16
b = 4
Whats the measure of
Answer:
C. 80°
Step-by-step explanation:
Recall: SOH CAH TOA
Reference Angle = J
Opposite = 60
Adjacent = 11
Hypotenuse = 61
Apply trigonometric function, SOH, which is:
Sin J = Opp/Hyp
Sin J = 60/61
[tex] J = sin^{-}(\frac{60}{61}) [/tex]
J = 79.6111422°
J = 80° (nearest degree)
Can someone help me please?
Step-by-step explanation:
Given that,
No. of heads = 40
No. of tails = 60
We know that,
Probability = (no. of favourable outcomes)/(total no. of outcomes)
Experimental probability of getting heads,
no. of favourable outcomes = 40
Total no. of outcomes = 40+60 = 100
So,
[tex]P=\dfrac{40}{100}[/tex]
She has taken 60 on denominator. She should have taken 100 instead of 60.
what is the correct answer
Answer:
We can solve this with the Pythagorean Theorem.
The Pythagorean theorem states that a2 + b2 = c2 in a right triangle where c is the longest side. You can use this equation to figure out the length of one side if you have the lengths of the other two.
Just square the sides, add them, and then take the square root. Here's an example:
We can solve it like this ~ [tex]30^2+60^2 = y[/tex]
= 2,500
y = [tex]\sqrt{2500}[/tex]
= 50
Therefore, the correct answer is 50.
What is the solution to the equation fraction 1 over 4 x = 5? (5 points) x = fraction 4 over 5 x = fraction 5 over 4 x = 20 x = 1
Answer:
your question was barely readable, but I'll try it anyways. hope it helps you to understand the concept.
[tex] \frac{1}{4} x = 5[/tex]
multiply each side of the equation by 4
[tex]x = 20[/tex]
sorry, the test really doesn't make much sense as a question. try to photograph the problem if possible. but take care not to photograph personal information
what is the length of BC?
A. 9 units
B. 11 units
C. 15 units
D. 16 units
Answer:
15units
Step-by-step explanation:
BC is: 5x=5×3=15 units. so,Length of BC=15 units
What is least common multiple of 15, 14, and 7
Answer:
210
Step-by-step explanation:
15 = 3 x 5
14 = 2 x 7
7 = 7
LCM = 3 x 5 x 2 x 7 = 210
Answer:
210
Explanation:
find the least common multiple of two numbers is to first list the prime factors of each number. Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs.
Every point on a circle is the same distance from a single location. What is
that location called?
Answer:
The center.
Step-by-step explanation:
That point is the center of the circle.
Hope that this helps!
What is the factorization of 49b2 − 81?
Step-by-step explanation:
The factorisation of 49b^2 - 81 is (7b - 9)(7b + 9). This is because 49 and 81 are the squares of 7 and 9 respectively, so these must be multiplied together. b^2 is b x b. Finally, it must be -9 and +9 to make -81, because when the signs are the same the result is a positive number
Answer:
(7b - 9)(7b + 9)
Step-by-step explanation:
49b2 - 81
49 - 7 x 7
b2 - b x b
81 - 9 x 9
(a + b) (a - b) = a2 - b2
(7b - 9)(7b + 9)
Find the measures of angles 1, 2, & 3.
Answer:
1=68 (Vertically opposite angles are equal)
2= 112 (sum of angles on a straight line gives 180°)
3=112 (vertically opposite angles are equal)
What are the names of the segments in the figure
Answer:
C. The three segments are segments AB, CA, and AC
A 9 year old boy has $12 saved.
He decides to start saving on a regular basis because he selss aluminum
cans
He figures out that he can save $2.50 per day.
What is the total amount he will have saved after 1 day?
2 days?
3 days?
17days?
X days?
Organize the information however you think is best and find out the totals.
Do...
g
in
Answer:
.............................
The quantity five times a number y decreased by twelve. Group of answer choices 5y - 12 12 - 5y 12y - 5 12 + 5y
Answer:12 - 5y
Step-by-step explanation:
The quantity five times a number y decreased by twelve means that 5 multiplied by a number is subtracted from 12, it also means that 12 minus 5 times a number y and can be written mathematically as
12 - 5y
what is a kite? what are its properties? what is its use in our daily life?
Answer:
Well, in geometry, the properties would be that the angles produced by the intersection of the diagonals are right angles. A kite is basically entertainment, made by cloth and string
A kite is a four sided shape. Like an elongated rectangle.a kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other. In contrast, a parallelogram also has two pairs of equal-length sides, but they are opposite to each other instead of being adjacent. Kite quadrilaterals are named for the wind-blown, flying kites, which often have this shape and which are in turn named for a bird. Kites are also known as deltoids, but the word "deltoid" may also refer to a deltoid curve, an unrelated geometric object.Kites have been used for human flight, military applications, science and meteorology, photography, lifting radio antennas, generating power, aerodynamics experiments, and much more.
What is point A on the coordinate plane
Answer:
4,1
Step-by-step explanation:
Answer:
(4,1)
Step-by-step explanation:
Ez
There are x students trying out for a solo in a chorus concert. Only 6 will be chosen. How many students will not be chosen? Please write down the Algebra expression and answer please and thank you.
We need to solve this question using Algebraic expressions. The answer for the given question is x-6.
How do you solve Algebraic Expressions?A mathematical expression with variables and/or numbers is called an algebraic expression. It can be simplified even if it cannot be solved since it lacks an equals sign (=). Algebraic equations, which have algebraic expressions divided by an equals sign, can be solved. Recognize the distinction between an algebraic equation and an algebraic expression. A mathematical expression called an algebraic expression can have variables or integers in it. be able to combine similar phrases. Adding up (or removing) the terms with the same degree is all that is required to combine related terms. All x2 terms can be mixed with other x2 terms, and all x3 terms can be coupled with x3 terms, according to this.
Calculationx students are trying in a chorus concert.
Only 6 students will be chosen.
so the answer for the given question=x-6
We need to solve this question using Algebraic expressions. The answer for the given question is x-6.
To refer more about Algebraic expressions, visit:
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57.
Peter shared the cost of dinner equally with 3 of his friends. When he was calculating the
amount that each of them should pay, he divided the cost by 2 instead of 4. In the end, each
boy paid $11.40. Find the correct amount for each share.
Answer:
$5.70
Step-by-step explanation:
→ Find the total amount they needed to pay
11.40 × 2 = 22.80
→ Divide the total by 4
22.80 ÷ 4 = $5.70
HELPpppp
A standard deck of 52 playing cards contains 13 cards in each of four suits: hearts, diamonds, clubs, and spades. Four cards are drawn from the deck at random.
What is the approximate probability that exactly three of the cards are diamonds???
Answer:
0.25 is the probability
Step-by-step explanation:
If there are 13 diamonds in a deck of 52 cards, dividing 13 by 52 will get you 0.25. This is the probability of getting a diamond from the deck of 52 cards.