[tex]y = 2x -2 ~~~~.....(i) \\\\y = x^2 -4 x +3 ~~~~ .....(ii) \\\\\\x^2-4x +3 = 2x -2\\\\\implies x^2 -4x -2x +3 +2 =0\\\\\implies x^2 -6x +5 =0\\\\\implies x^2 -5x -x +5 =0\\\\\implies x(x-5) -(x-5) =0\\\\\implies(x-5)(x-1) =0\\\\\implies x = 5 ~~ \text{or}~~ x = 1 \\\\\\\text{Substitute x = 1 in equation (i):}\\\\y = 2 -2 =0\\\\ \text{Substitute x = 5 in equation (i):}\\\\\\y = 2(5) -2 = 10 -2 =8 \\\\\text{Hence,}~~ (x,y) = (1,0) ~ \text{and} ~ (x,y) = (5,8)[/tex]
. Consider the set {7,8,9), a subset of this set includes:
{2,3}
b. {5,63
c. none of these
d. {10,11
Answer:
Option "C" none of these is the correct answer.
Step-by-step explanation:
The subset of the set {7, 8, 9} must have the elements of this set only.
Hope this helps :)
The quadratic function f(x)=ax^2+4x+c has a maximum at the point (1, 9) . What are the values of a and c?
Answer: a = -2 and c = 7
Step-by-step explanation:
(this answer uses some basic calculus)
We know that [tex]f'(x) = 2ax + 4[/tex], and since [tex](1,9)[/tex] is a maximum of [tex]f[/tex], then [tex]f'(1) = 0[/tex]. That means [tex]2a + 4 = 0[/tex], so [tex]\boxed{a = -2}[/tex]. Then since [tex]f(1) = 9[/tex], we have [tex]-2(1)^2 + 4(1) + c = 9[/tex], so [tex]\boxed{c = 7}[/tex].
Answer:
a = -2
c = 7
Step-by-step explanation:
Given the quadratic function, f(x) = ax² + 4x + c, for which its vertex is the maximum point occurring at (1, 9), and b = 4.
Solve for the value of a:Since the x-coordinate of the vertex, x = 1, can be calculated using the formula, [tex]x = \frac{-b}{2a}[/tex]:
We can substitute the value of the x-coordinate and b = 4 into the formula, and solve for the value of a:
[tex]x = \frac{-b}{2a}[/tex]
[tex]1 = \frac{-4}{2a}[/tex]
Multiply both sides by 2a:
(2a) 1 = [tex]\frac{-4}{2a} (2a)[/tex]
2a = -4
Divide both sides by 2 to solve for a:
[tex]\frac{2a}{2} = \frac{-4}{2}[/tex]
a = -2
Therefore, the value of a = -2.
Solve for the value of c:Next, to solve for c, substitute the coordinate values of the vertex, (1, 9) into the given quadratic function:
f(x) = ax² + 4x + c
9 = -2(1)² + 4(1) + c
9 = -2 + 4 + c
9 = 2 + c
Subtract 2 from both sides to isolate c:
9 - 2 = 2 - 2 + c
7 = c
Double-check:In order to double-check the validity of our values for a and c, substitute a = -2, and c = 7 into the function, along with the coordinates of the vertex, (1, 9):
f(x) = -2x² + 4x + 7
9 = -2(1)² + 4(1) + 7
9 = -2 + 4 + 7
9 = 9 (True statement).
Therefore, the correct answers are: a = -2, and c = 7.
Helppppp Pleaseeeeeee
Answer:
what is the question
Step-by-step explanation:
Multiply (4-5i)(4+i)
Answer:
this is the correct answer happy
Find complex numbers z=(x,y) such that
[tex]z ^{2} = - 5 - 12i[/tex]
Answer:
I don't know..,.............,,.,.......,
Find the measure of angle
9514 1404 393
Answer:
(b) 62°
Step-by-step explanation:
Let x represent the measure of the angle.
The complement is (90 -x).
The supplement is (180 -x).
The relationship between the supplement and the complement is ...
(180 -x) = 6 +4(90 -x)
180 -x = 6 +360 -4x
3x = 186
x = 62
The measure of the angle is 62°.
Do you think you could use a multiply a 4 digit number by a 1 digit number
Answer:
line them up straight with the bottom number and the top number.
Help!!!! neeed someone to answer this question please!! its due today!
Answer:
1.)
a.)The correlation coefficient is determined by dividing the covariance by the product of the two variables' standard deviations.
b.)Medications such as naproxen, ibuprofen, and acetaminophen are most effective in reducing pain and swelling associated with muscle-related lower back pain. However, OTC medication is less likely to alleviate symptoms that stem from nerve compression or disc problems.
Step-by-step explanation:
I HOPE ITS HELP YOU
Find The nth Term of this number sequence
18, 16, 14, 12
a = 18
d = 16 - 18 = -2
an = a + (n - 1) × d
an = 18 + (n - 1) × (-2)
an = 18 - 2n + 2
an = -2n + 20
1. 2y +8x =70
2. 2y = 8x- 70
3. y= 8x- 70
What’s the slope and y intercept for these equations?
Can you give me some hint please
Help me please!!!!!!!!!!!
Two more than the quotient of a number and 4 equals 6
Answer:
2 + (n/4) = 6
Step-by-step explanation:
Answer:
2+(n÷4)= 6
Step-by-step explanation:
hope it helps u
plzz plzzzz plzzzz mark as brainliest
A parabola can be drawn given a focus of (-11, -4) and a directrix of x=11. Write the equation of the parabola in any form.
Answer:
Step-by-step explanation:
This will open to the left and the vertex will be at (0, -4).
Equation us (y + 4)^2 = -4*-11x
44x = (y + 4)^2
Order of operations and cross
reduce:
I got 20/3 but I think I’m wrong
Answer:
130/81
simplified: 1 49/81
Step-by-step explanation:
I did the math
What is the equation of the line that has a slope of 3 and goes through the point (-3,5)?
A. Y=3x +4
B. Y= 3x - 14
C. Y= 3x - 4
D. Y= 3x + 12
Answer:
C. y=3x-4
Step-by-step explanation:
I just know trust me
What property is illustrated by the statement? 5(- 7 10 )=(- 7 10 )5 A) Commutative Property of Multiplication B) Commutative Property of Addition C) Associative Property of Multiplication D) Associative Property of Addition
Answer:
commutative property of multiplication
Step-by-step explanation:
Name the property used: commutative property of multiplication
Answer: commutative property of multiplication
Describe how the point-slope formula is useful when writing the equation of a trend line
Step-by-step explanation:
if you observe the graph the y values increase as the x value increase.
so it has a possitive association.
if the value of y increase as the value of the x increase then data has positive association.
Function or non functional? Pls help ty :3
sole the inequality x-8>-4
Answer:
[tex]x>4[/tex]
Based on this, we know the correct number line will be an empty bubble with a line going to the right of 4.
Step-by-step explanation:
[tex]x-8>-4[/tex]
add 8 to both sides of the inequality
[tex]x>4[/tex]
Suppose that we compute a 90% confidence interval for an unknown population mean . Which of the following is a correct interpretation?
90% of all possible
How much is 2+10.
Please help me i dont know
Will give brainliest
Answer: 12
2 + 10
12
:)
Answer: 12
Step-by-step explanation: just add 2 to 10
name the parts mentioned in the figure below
please answer this
Answer:
O - point
CD- chord
AB- diametre
I dont know PO sorry
Answer:
O is the center.
AB is the diameter.
OP is a radius.
CD is a tangent.
By the way the combination of letters is the two points that it relates too.
Step-by-step explanation:
hope this helps. . .<3
Given f(x) = 2x - 5 , find the average rate of change of f(x) from x = 2 to x = 5?
[tex]slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)=2x - 5 \quad \begin{cases} x_1=2\\ x_2=5 \end{cases}\implies \cfrac{f(5)-f(2)}{5-2}\implies \cfrac{[2(5)-5]~~ - ~~[2(2)-5]}{3} \\\\\\ \cfrac{5-(-1)}{3}\implies \cfrac{5+1}{3}\implies 2[/tex]
Find the missing term 81:18=?:8
Answer:
81/10 or 10
Step-by-step explanation:
81:18 - 8 = 81/10 simplified
sorry if am wrong i tried :L
Solve for w.
16w–w–12w–2w=13
w=
Answer:
w = win
Step-by-step explanation:
w=13
Answer:
w = 13
Step-by-step explanation:
16w - w = 15w
15w - 12w = 3w
3w - 2w = w
w = 13
5. A 32 foot tree casts a 60 foot shadow as shown below. A man next to the tree casts a 12 foot shadow. How tall
is the man? Justify your solution
Answer:
Step-by-step explanation:
The shadow length will be proportional to height
12 / 60 = h / 32
h = 12(32)/60 = 6.4 ft or 6 ft 4.8 inches
find the point (x,y) on the curve where dy/dx = 0
a. By the chain rule,
[tex]\dfrac{dy}{dx} = \dfrac{dy}{dt}\cdot\dfrac{dt}{dx} = \dfrac{dy}{dt}\cdot\dfrac{1}{\frac{dx}{dt}}[/tex]
Given that [tex]y=e^t+e^{-t}[/tex] and [tex]x=e^{-t}[/tex], we have the derivatives
[tex]\dfrac{dy}{dt} = e^t -e^{-t}[/tex]
[tex]\dfrac{dx}{dt} = -e^{-t}[/tex]
and so
[tex]\dfrac{dy}{dx} = \dfrac{e^t - e^{-t}}{-e^{-t}} = 1-e^{2t}[/tex]
Set this equal to zero and solve for t :
[tex]1-e^{2t} = 0[/tex]
[tex]1 = e^{2t}[/tex]
[tex]\ln(1) = \ln\left(e^{2t}\right)[/tex]
[tex]0 = 2t \ln(e)[/tex]
[tex]0 = 2t[/tex]
[tex]t=0[/tex]
This value of t corresponds to x = e⁰ = 1 and y = e⁰ - 1/e⁰ = 1 - 1 = 0. So the only point on the curve where the derivative dy/dx is zero is (1, 0).
b. Compute the second derivative. Since dy/dx is a function of t, we'll momentarily replace it with f(t). By the chain rule,
[tex]\dfrac{d^2}{dx^2} = \dfrac d{dx} \dfrac{dy}{dx} = \dfrac{df}{dx} = \dfrac{df}{dt}\cdot\dfrac{dt}{dx} = \dfrac{df}{dt}\cdot\dfrac{1}{\frac{dx}{dt}}[/tex]
We have
[tex]\dfrac{df}{dt} = -2e^{2t}[/tex]
and we've already committed dx/dt. So
[tex]\dfrac{d^2}{dx^2} = \dfrac{-2e^{2t}}{-e^{-t}} = 2e^{3t} [/tex]
Substitute the first and second derivative into the differential equation:
[tex]\left(\dfrac{d^2y}{dx^2}\right)^2 + \dfrac{dy}{dx} - 1 = 0[/tex]
[tex]\left(2e^{3t}\right)^2 + (1-e^{2t}) - 1 = 0[/tex]
[tex]4e^{6t} -e^{2t}= 0[/tex]
[tex]e^{2t} (4e^{4t} - 1) = 0[/tex]
[tex]4e^{4t} - 1 = 0[/tex]
[tex]4e^{4t} = 1[/tex]
[tex]e^{4t} = \dfrac14[/tex]
[tex]\ln\left(e^{4t}\right) = \ln\left( \dfrac14\right)[/tex]
[tex]4t \ln(e) = -\ln(4)[/tex]
[tex]4t = -\ln(4)[/tex]
[tex]t = -\dfrac{\ln(4)}4[/tex]
In Martin's class of 20 students, 4 students report that social studies is their favorite class and 75% of the students report that PE is their favorite class. Show your work to explain how to determine whether more students prefer social studies or PE. (5 points)
pls Help!
Answer:
More students like PE
Step-by-step explanation:
100÷20=5
1 student = 5%
4×5=20
20% students favourite is social studies
75%>20%
List all the factors pairs in the table 64
(1, 64), (2, 32), (4, 16), (8, 8).
Answer:
1 x 64
2 x 32
4 x 16
8 x 8
Step-by-step explanation:
Factors of 64: 1, 2, 4, 8, 16, 32 and 64.
Pairs:
1 x 64
2 x 32
4 x 16
8 x 8
Hope this helps :)
Can someone explain the distributive property to me in simple terms? Thanks
Answer:
Im not sure
Step-by-step explanation: