The focus is the point inside a parabola that helps determine the shape of the curve.
What is a parabola?A parabola is an equation of a curve, such that any point on the curve is equidistant from a fixed point called the focus and a fixed line called the directrix of the parabola.
The equation of a parabola:
y = a(x - h)² + k
We have,
A parabola is a type of curve that is formed when a plane intersects a cone at an angle that is parallel to one of the cone's sides.
One of the key defining features of a parabola is that all points on the curve are equidistant from a fixed point, known as the focus, and a fixed line, known as the directrix.
The focus is located inside the parabola, and its distance from the directrix is equal to the distance from any point on the parabola to the directrix.
This property allows us to use the focus and directrix to determine the shape and location of the parabola.
Thus,
The focus is the point inside a parabola that helps determine the shape of the curve.
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PQ, QR, RS, and SP are tangent to ⨀ X. Find RS.
Answer:
Step-by-step explanation:
rewrite these sets in listing method
a) A=(letters of the word "COLLECTION")
PLEASE DO IT IN LISTING METHOD
Explanation:
We simply list each letter one time. Any duplicates are tossed. If you sorted the letters alphabetically, then you'd get {C, E, I, L, N, O, T}. However, the order doesn't matter with sets.
Note: This listing method is another name for "roster method". Think of how sports teams list their roster, which is basically just a list of the players' names.
What are the next 3 terms in the following geometric sequence:
512, 256, 128, ___, ___, ___
A. 92, 66, 28
B. 1024, 2048, 4096
C. 64, 32, 16
D. 32, 8, 2
Answer:
C. 64, 32, 16
Step-by-step explanation:
This geometric sequence is made by dividing the numbers by 2:
512 ÷ 2 = 256
256 ÷ 2 = 128
Hence, the next term will be
128 ÷ 2 = 64
64 ÷ 2 = 32
32 ÷ 2 = 16
Therefore, the correct answer is C.
The next 3 terms in the given geometric sequence are 64, 32, and 16, respectively. The correct option is C.
What is geometrical series?A geometric series is the collection of an unlimited number of terms with a fixed ratio between them.
The given series is a geometric sequence, therefore, the common ratio between any two terms will be the same. Therefore, we can write, the ratio as,
Common ratio, r = a₂ / a₁ = 256 / 512 = 1/2
Now, the nth term of the given sequence can be defined as,
aₙ = a₁ × r⁽ⁿ⁻¹⁾
= 512 × (1/2)⁽ⁿ⁻¹⁾
Therefore, the next term of the given geometric progression will be,
a₄ = 512 × (1/2)³ = 64
a₅ = 512 × (1/2)⁴ = 32
a⁶ = 512 × (1/2)⁵ = 16
Hence, the next 3 terms in the given geometric sequence are 64, 32, and 16, respectively.
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Plz help me tyvm :/
10 points
(no links)
(no wrong or guessed answers)
Answer:
2y
Step-by-step explanation:
2x-3=2y
2x-2y=3
Answer:
x = 3, y = 1.5
Step-by-step explanation:
Given the 2 equations
x + 2y = 6 → (1)
2x - 3 = 2y → (2)
In (2) subtract 2y from both sides and add 3 to both sides
2x - 2y = 3 → (3)
Adding (1) and (3) term by term will eliminate the y- term
3x = 9 ( divide both sides by 3 )
x = 3
Substitute x = 3 into either of the 2 equations and solve for y
Substituting into (1)
3 + 2y = 6 ( subtract 3 from both sides )
2y = 3 ( divide both sides by 2 )
y = 1.5
2) through:(-1,-1), slope = -4
Need help seriously
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Vowels: A, E, I, O, U
There are only 2 vowels out of 8 on the spinner, which means that 6 out of 8 aren't vowels.
[tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex]
Hope this is helpful
Anyone know the answer to this ??
Answer:
18 i think sorry if i am wrong
Step-by-step explanation:
please I need this question fast please
We have a linear function y=kx+b and we know that [tex]\displaystyle\bf \left \{ {{5*1+c=2} \atop {5p+c=-2}} \right.=>\left \{ {{c=-3} \atop {5p+c=-2}} \right. => 5p-3=-2 => p=\frac{1}{5}[/tex] [tex]\displaystyle\bf Answer: \boxed{C) \quad p=\frac{1}{5} }[/tex]
which linear inequality is represented by the graph
Answer:
Step-by-step explanation:
PLEASE HELP!! I’ve added an attachment. Please help me find the type of statement for this mathematical question. TYSM!!
Answer:
Step-by-step explanation:
Statements Reasons
1). AD ≅ BC 1). Given
2). ∠D ≅ ∠C 2). Given
3). ∠DEA ≅ ∠CEB 3). Vertically opposite angles
4). ΔADE ≅ Δ BCE 4). AAS postulate of congruence
5). AE ≅ BE 5). CPCTC
Hence, proved.
which choices are equivalent to the expressions below ? Check all that apply
√5 × √5
y-5 = -3 (x+2) in standard form
Answer:
maybe y - -3x = -11?
Step-by-step explanation:
im rushing so i may have did it wrong sorry
Solve question no. A and B
Answer:
Mean A=7
median B=3/4 .75
Answer:
Step-by-step explanation:
mean = sum of data / no of data
= 4+7+5+9+11+6 /6
=42 / 6
=7
mean = 7
to find median arrange the data from ascending to descending order
Data = 3,4,6,8,10,12
median = (N +1) / (N means no of data)
=(6 +1) / 2
=7/2
=3.5
= 3 rd term + 4 th term / 2
=6 + 8 / 2
=14 / 2
=7
median = 7
Rachel draws a trend line through the following data
points. Did she draw the line correctly?
Answer:
i think its A but im not sure its correct
Step-by-step explanation:
find the subsets of ( S,Q,L,R)
Answer:
{}, {s} {q} {l} {r} {s,q} {s, l} {s, r} {q, l} {q, r} {l, r} {s, q, l} {s,l,r} {s, q, r} {q, l, r} {s, q, l, r}
In ΔNOP, the measure of ∠P=90°, NP = 35, ON = 37, and PO = 12. What ratio represents the sine of ∠N?
Answer:
12/37
Step-by-step explanation:
SOH - CAH - TOA
O = opposite
A = adjacent
H = hypotenuse
Sin = O/H
Sin N = 12/37
Answer:Find sin N
sinN=
hypotenuse/opposite
12/37
Step-by-step explanation:
P, Q & R form a right-angled triangle.
R, S & P lie on a straight line.
PS = SQ and ∠SQR = 36°.
Work out
∠RPQ
Answer:
∠RPQ = 27
Step-by-step explanation:
In ΔSRQ,
∠R = 90
∠SQR = 36°
∠R + ∠SQR + ∠RSQ = 180 {Angle sum property of triangle}
90 + 36 + ∠RSQ = 180
126 + ∠RSQ = 180
∠RSQ = 180 - 126
∠RSQ = 54°
∠PSQ +∠RSQ = 180 {Linear pair}
∠PSQ + 54 = 180
∠PSQ = 180 - 54
∠PSQ = 126
In ΔPSQ,
SQ = PS ,
So, ∠SQP = ∠SPQ {Angles opposite to equal sides are equal}
∠SQP = ∠SPQ =x
∠PSQ + x +x = 180 {Angle sum property of triangle}
126 + 2x = 180
2x = 180 - 126
2x = 54
x = 54/2
x = 27
∠RPQ = 27°
solve the equation (1÷49)^x + 2 =(7)^x - 3
9514 1404 393
Answer:
x = -1/3
Step-by-step explanation:
Maybe you mean ...
(1/49)^(x +2) = 7^(x -3)
Taking logarithms base 7, we have ...
-2(x +2) = x -3
-2x -4 = x -3 . . . . . eliminate parentheses
-1 = 3x . . . . . . . . . . add 3+2x
x = -1/3 . . . . . . . . . divide by the coefficient of x
This is confirmed by a calculator in the first attachment.
_____
As written, the equation is ...
((1/49)^x) +2 = (7^x) -3
Multiplying both sides by 7^(2x) gives us ...
1 + 2·7^(2x) = 7^(3x) -3·7^(2x)
Subtracting the left side gives us the cubic equation in 7^x:
(7^x)^3 -5·(7^x)^2 -1 = 0
This has one irrational real root (found using a graphing calculator). The solution is ...
x ≈ 0.83111881051
This answer is confirmed in the second attachment. (10^-16 is essentially zero for this purpose.)
__
Additional comment
Part of the reason for going to the trouble to solve the "as written" equation is to show you that it is possible, though messy. What we'd like to emphasize here is that grouping symbols are needed when exponents contain math operations.
In typeset text, the superscript font indicates the grouping of parts of an exponent. In plain text, we cannot tell if 7^x-3 means (7^x)-3 or 7^(x-3). The Order of Operations tells us to interpret it the first way: (7^x) -3, because exponentiation is done before addition. That leads to trouble in this problem.
Consider the following simple regression model: y = 0 + 1 x 1 + u. In order to obtain consistent estimators of 0 and 1, when x and u are correlated, a new variable z is introduced into the model which satisfies the following two conditions: Cov( z, x) 0 and Cov ( z, u) = 0. The variable z is called a(n) _____ variable. 答案选项组 dummy instrumental lagged dependent random
Answer:
Instrumental variable
Step-by-step explanation:
cov(z,u) shows that the instrumental variable is exogenous. An instrumental variable can also be regarded as a third variable, It is included in the model if you have an issue of endogeneity in your regression model. An endogeneity problem arises if there are other variables are being influenced by other independent variable in the same regression model. we use z to account for these behaviours in the model. this variable controls for measurement errors as well as confounding errors.
Express x^2 + 4x - 7 in the form (x + a)^2 - b where a and b are intergers
Answer:
[tex]x^2+4x-7=(x+4)^2-23[/tex] where [tex]a=4[/tex] and [tex]b=-23[/tex]
Step-by-step explanation:
Given: [tex]x^2+4x-7[/tex]
Complete the square: [tex](x^2+4x+16)-23[/tex]
Reduce trinomial: [tex](x+4)^2-23[/tex]
Therefore, [tex]x^2+4x-7=(x+4)^2-23[/tex] where [tex]a=4[/tex] and [tex]b=-23[/tex].
the slope of the line below is -5/7 write a point slope equation of the line using the coordinates of the labeled point (6,2)
Evaluate the expression. r = <5, 9, -4>, v = <3, 3, -8>, w = <9, -6, -1> v ⋅ w (5 points)
<-15, -27, -32>
0
17
<27, -18, 8>
Answer:
s
Step-by-step explanation:
i don’t understand how to find the number that goes into the blank box.
Answer:
8
Step-by-step explanation:
It asks for the y-intercept. The y-intercept is (0,?) the slope is -3 which means it's decreasing by 3. 5+3=8 so 8 is the y-intercept.
Hope this helps and pls tell if it's correct.
Find f(4) if f(x) = 3x + 13
We are given the linear function below:
[tex] \large{f(x) = 3x + 13}[/tex]
To find f(4), simply substitute x = 4 in the equation.
[tex] \large{f(4) = 3(4) + 13} \\ \large{f(4) = 12 + 13} \\ \large \boxed{f(4) = 25}[/tex]
Answer
f(4) = 25Which of the following statements is false? PLEASE HELP ASAP!
Answer:
C
Step-by-step explanation:
Question 2 Multiple Choice Worth 1 points)
(01.04 LC)
Choose the missing step in the given solution to the inequality -X – 10 > 14 + 2x.
-X - 10 > 14 + 2x
-3x - 10 > 14
X<-8
Answer:
see below
Step-by-step explanation:
-X – 10 > 14 + 2x.
Subtract 2x from each side
-x-2x -10 > 14+2x-2x
-3x -10 > 14
Add 10 to each side
-3x -10+10 > 14+10
-3x > 24
Divide each side by -3, remembering to flip the inequality
-3x/-3 < 24/-3
x < -8
Which is the Value if this expression when m = 3 and n = -5
A = (-123) + 77 + (-257) + 23 – 43
Answer:
[tex]A=-323[/tex]
Step-by-step explanation:
A = (-123)+77+(-257)+23-43
A = -46+(-257)+23-43
A = -303+23-43
A = -280-43
A = -323
Hope this helps
Please solve the following simultaneous equations.
3 + y - 2x = 0
3x2 + 2y2 – 4xy = 9
Answer:
(3, 3) (1, -1)
Step-by-step explanation:
Answer:
(1, - 1) , (3, 3 )
Step-by-step explanation:
Given the 2 equations
3 + y - 2x = 0 → (1)
3x² + 2y² - 4xy = 9 → (2)
In (1) subtract 3 - 2x from both sides
y = 2x - 3 → (3)
Substitute y = 2x - 3 into (2)
3x² + 2(2x - 3)² - 4x(2x - 3) = 9 ← distribute and simplify left side
3x² + 2(4x² - 12x + 9) - 8x² + 12x = 9
3x² + 8x² - 24x + 18 - 8x² + 12x = 0
3x² - 12x + 18 = 9 ( subtract 9 from both sides )
3x² - 12x + 9 = 0 ( divide through by 3 )
x² - 4x + 3 = 0 ← in standard form
(x - 1)(x - 3) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x - 3 = 0 ⇒ x = 3
Substitute these values into (3) for corresponding values of y
x = 1 : y = 2(1) - 3 = 2 - 3 = - 1 ⇒ (1, - 1 )
x = 3 : y = 2(3) - 3 = 6 - 3 = 3 ⇒ (3, 3 )
On acm grid, point p has the coordinates (3,-1) and point q has the coordinates (-5,6)
Calculate the shortest distance between p and q
Answer:
√113
Step-by-step explanation:
√(x2 - x1)² + (y2 - y1)²
√(-5 - 3)² + [6 - (-1)]²
√(-8)² + (7)²
√(64) + (49)
√113