Answer:
Step-by-step explanation:
To evaluate the derivative of this function you need the chain rule. The pattern I teach to my calculus students is to find
u =
u' =
f(u) =
f'(u) =
First pick your "u". u will be the inner function, the one inside the parenthesis.
u' will then be the derivative of u.
f(u) is the function in terms of u, and
f'(u) is the derivative of the function in terms of u.
The derivative then, finally, will be u' * f'(u). Let's begin.
Our u, or the part of the function inside the parenthesis is 3 - 2x; hence,
u = 3 - 2x
The derivative, u', then is
u' = -2
f(u) is the function in terms of u, so
f(u) = [tex]u^{-\frac{1}{2}[/tex] and the derivative in terms of u is
f'(u) = [tex]-\frac{1}{2}u^{-\frac{3}{2}[/tex]
u' * f'(u) then is
[tex]-\frac{1}{2}u^{-\frac{3}{2}*(-2)[/tex] Simplify that by subbing back in for u and multiplying -2 by -1/2 to get
[tex]y'=(3-2x)^{-\frac{3}{2}[/tex]
Solve the system of equations by substitution.
y=-1/2x-7
2 x - y = -16
Answer:
Point Form:
( − 46 /3 , − 44 /3 )
Equation Form:
x = − 46 /3 , y = − 44 /3
Step-by-step explanation:
Combine 1 /2 and x .
y = x /2 − 7
2 x − y = − 16
Replace all occurrences of y in 2 x − y = − 16 with x /2 − 7 .
y = x /2 − 7
2 x − ( x /2 − 7 ) = − 16
Simplify
2 x − ( x /2 − 7 ) .
y = x /2 − 7
3 x /2 + 7 = − 16
Solve for
x
in the second equation.
y = x /2 - 7
x = − 46 /3
Replace all occurrences of x in y = x /2 − 7 with − 46 /3 .
y = − 46 /3 /2 − 7
x = − 46 /3
Simplify − 46 /3 /2 − 7 .
y = − 44 /3
x = − 46 /3
The solution to the system of equations can be represented as a point.
( − 46 /3 , − 44 /3 )
The result can be shown in multiple forms.
Point Form:
( − 46 /3 , − 44 /3 )
Equation Form:
x = − 46 /3 , y = − 44 /3
A line contains the point (8,-5). If the slope of the line is write the equation of the line using point-slope form
Answer:
[tex]\bold{y+5=\frac57(x-8)}[/tex]
Step-by-step explanation:
[tex]y-y_1=m(x-x_1)[/tex] - point-slope form of Equation of the Line
[tex](8,-5)\ \ \implies x_1=8\,,\ y_1=-5\\\\m=\frac57\\\\equation:\\{}\qquad\qquad y-(-5)=\frac57(x-8)\\\\{}\qquad\qquad y+5=\frac57(x-8)[/tex]
Two similar triangles are shown.
to create
AXYZ was dilated, then
AQAG
translated
reflected
dilated
rotated
Answer: reflected
Step-by-step explanation:
The triangle ΔXYZ was dilated and then it was reflected to create ΔQAG.
What are the types of translations?There are three types of translations -
reflectionrotationdilationGiven is a triangle ΔXYZ.
It is asked to find the type of translation that would result in ΔQAG.It can be seen in the figure that the triangle XYZ is reflected across the given line to form triangle QAG.So, we can we can replace the blank with Option - 2 : reflected.Therefore, the triangle ΔXYZ was dilated and then it was reflected to create ΔQAG.
To solve more questions on graph rotation, visit the link below-
https://brainly.com/question/19527326
#SPJ7
Definition:A sailboat set a course of N 25° E from a small port along a shoreline that runs north and south. Sometime later the boat overturned and the crew sent out a distress call. They estimated that they were 12 miles away from the nearest harbor, which is 28 miles north of the port they had set sail from. If a rescue team leaves from the harbor, find all possible courses the team must follow in order to reach the overturned sailboat.
Answer:
S 75°E
S 55°E
Step-by-step explanation:
Take the law if sines of a triangle:
[tex] \frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC} [/tex]
Where,
a = 28 miles
B = 25°
b = 12 miles
First solve for A, using the law of sines:
[tex] \frac{a}{sinA} = \frac{b}{sinB} [/tex]
[tex] \frac{28}{sinA} = \frac{12}{sin25} [/tex]
Cross multiply:
[tex] 28 sin25 = 12 sinA [/tex]
[tex] 11.83 = 12 sinA [/tex]
[tex] Sin A = \frac{11.83}{12} [/tex]
[tex] Sin A = 0.986 [/tex]
[tex]A = sin^-^1(0.986)[/tex]
[tex] A = 80.44 degrees [/tex]
Since A = 80.44° find A supplement, A`:
A` = 180 - 80.44
A` = 99.56°
If A` + B < 180°, find C.
Thus,
A` + B = 99.56 + 25 = 124.56
We can see that A` + B < 180
Find C:
C = 180 - (80.44+25) = 74.56° ≈ 75°
C` = 180 - (99.56+25) = 55.44° ≈ 55°
Rewrite in bearing form:
S 75°E
S 55°E
14 of 46
E Sa
Function Transformations: Tutorial
Part B
Open the graphing tool, and compare the functions using the sliders. What can be said about the domain of
y= VX - kand the domain of y = VX + k?
Answer:
Therefore, domain of y = [tex]\sqrt{x-k}[/tex] ; Domain = [k, ∞)
Domain of y = [tex]\sqrt{x}+k[/tex] ; Domain = [0, ∞)
Step-by-step explanation:
Two functions are,
y = [tex]\sqrt{x-k}[/tex]
and y = [tex]\sqrt{x}-k[/tex]
Let the value of k = 1
Then we find the graph of the functions attached.
By analyzing these graphs,
y = [tex]\sqrt{x-1}[/tex] when shifted 1 unit right and 1 unit down we get a new function,
y = [tex]\sqrt{x}+1[/tex]
Therefore, domain of y = [tex]\sqrt{x-1}[/tex] ; Domain = [1, ∞)
Domain of y = [tex]\sqrt{x}+1[/tex] ; Domain = [0, ∞)
Similarly, domain of y = [tex]\sqrt{x-k}[/tex] ; Domain = [k, ∞)
And domain of y = √x + k ; Domain = [0, ∞)
Simplify √18. Help!!! I am on a test on ingenuity. 2√3 2√9 3√2 9√2
What’s are the answers for both?
Answer:
d = 8g = 2Step-by-step explanation:
8d + 4 = 5d + 28
Group like terms
That's
8d - 5d = 28 - 4
3d = 24
Divide both sides by 3
d = 8
[tex] \frac{7(7g + 8)}{4} = 38.5[/tex]
Cross multiply
we have
7(7g + 8) = 38.5(4)
49g + 56 = 154
49g = 154 - 56
49g = 98
Divide both sides by 49
g = 2
Hope this helps you
sketch the graph for the following quadratic function.
[tex] - x ^{2} + 4x + 12[/tex]
it's ok if it's wrong.i just wanna see how the work done to do this
Answer:
Please refer to the attached image for the graph of given function.
Step-by-step explanation:
Given the equation:
[tex]-x^{2} +4x+12[/tex]
Let us rewrite by letting it equal to [tex]y[/tex].
[tex]y=-x^{2} +4x+12[/tex]
Now, we can see that it is a quadratic equation and it is known that a quadratic equation has a graph of parabola.
Let us compare the given equation with standard quadratic equation:
[tex]y=ax^{2} +bx+c[/tex]
we get:
[tex]a = -1\\b = 4\\c = 12[/tex]
Coefficient of [tex]x^{2}[/tex] is negative 1, so the parabola will open downwards.
Axis of symmetry: It is the line which will divide the parabola in two equal congruent halves.
Formula for axis of symmetry is:
[tex]x = -\dfrac{b}{2a}[/tex]
[tex]x = -\dfrac{4}{2(-1)}\\\Rightarrow x=2[/tex]
It is shown as dotted line in the image attached in the answer area.
Axis of symmetry will also contain the vertex of the parabola.
It is a downward parabola so vertex will be the highest point on this parabola.
Putting x = 2 in the equation of parabola:
[tex]y=-2^{2} +4\times 2+12\\\Rightarrow y =16[/tex]
So, vertex will be at P(2, 16).
Now, let us find points of parabola to sketch graph:
put x = 0, [tex]y=-0^{2} +4\times 0+12=12[/tex]
Another point is Y(0,12)
Now, let us put y = 0, it will give us two points because the equation is quadratic in x.
[tex]0=-x^{2} +4x+12\\\Rightarrow -x^{2} +6x-2x+12=0\\\Rightarrow -x(x -6)-2(x-6)=0\\\Rightarrow (-x-2)(x-6)=0\\\Rightarrow x = -2, 6[/tex]
So, other two points are X1(-2, 0) and X2(6,0).
If we plot the points P, Y, X1 and X2 we get a graph as attached in the image in answer area.
Is 2+4x-5x^2 in standard form?!
Answer:
y=-5x^2+4x+2
Step-by-step explanation:
Answer:
-5x² + 4x + 2
Step-by-step explanation:
Standard Form: ax² + bx + c
All you need to do is rearrange to have the highest degree first.
Please please help!!! Study the diagram of circle Z. Points P, O, Q, and R lie on circle Z in such a way that OP¯¯¯¯¯¯¯¯≅QR¯¯¯¯¯¯¯¯. If m∠QZR=(2x+9)∘ and m∠PZO=(4x−11)∘, what is the value of x?
x=3.3
x=15.3
x=10
x=12
Answer:
The correct option is
x = 10
Step-by-step explanation:
in a circle Given that chord [tex]\overline {OP}[/tex] is congruent to [tex]\overline {QR}[/tex], we have;
Measured angle m∠RZQ is congruent to measured angle m∠PZO
Congruent chords are subtended by congruent angles at the center of the circle
Therefore we have;
4·x - 11 is equal to 2·x + 9
4·x - 2·x = 9 + 11
2·x = 20
x = 10
The value of the measured angles are;
4·x - 11 = 4×10 - 11 = 40 - 11 = 29°
The value of x is 10°.
Answer:
x=10
Step-by-step explanation:
4·x - 11 is equal to 2·x + 9
4·x - 2·x = 9 + 11
2·x = 20
x = 10
The value of the measured angles are;
4·x - 11 = 4×10 - 11 = 40 - 11 = 29°
The value of x is 10°
The question i want to know is linked below. Please help :)
Answer:
Hey there!
To solve this problem, we want to find the LCM (least common multiple) of the two numbers.
The numbers are 25 and 30.
25=5x5
30=2x3x5
LCM is 5x5x2x3, or 150.
Thus, in 150 minutes is when the next bus will leave.
150 mins is equal to 2 hours and 30 mins, or 2.5 hours.
8 AM + 2.5 hrs = 10:30 AM.
Thus, the next time the busses leave together would be at 10:30 AM.
Let me know if this helps :)
PLZ HELP QUICK............
Answer:
[tex]4^m[/tex]
Step-by-step explanation:
When you exponent an exponent, you multiply the powers together.
When you divide exponents, you subtract the powers.
Step 1: Convert to same base
log₄64 = 3
Step 2: Rewrite equation
[tex]\frac{(4^3)^{0.5m}}{4^{0.5m}}[/tex]
Step 3: Simplify
[tex]\frac{4^{1.5m}}{4^{0.5m}}[/tex]
Step 4: Simplify
[tex]4^m[/tex]
Let's consider the scenario: You bring a hunting rifle to forest, and you see a tree full of birds. You count 15 birds total. You shoot 1 down. HOw mAny are left?
Answer:
0( no birds)
Step-by-step explanation:
if you shoot one, the rest will fly away
Answer:
14 alive birds, but 15 in total.
Step-by-step explanation:
15-1=14, or 15-0=15. the dead one still exists
Dave ran 3.52 miles in the same time
that Eric ran 2.44 miles. How much
further did Dave run than Eric?
The coefficient of x in the expansion of the following is (x+3)^3 a) 1 b) 3 c) 18 d) 27 e) 9
Answer:
d) 27
Step-by-step explanation:
The expanded form of (a+b)³ is ...
(a +b)³ = a³ +3a²b +3ab² +b³
When we are expanding (x +3)³, the x-term is ...
3(x)(3²) = 27x
The coefficient of x in the expansion is 27.
Find the area of this triangle..
Answer:
Step-by-step explanation:
For this problem, we have to use Heron's Formula.
S= (a + b + c)
over 2
And then √S( S-a) (S-b) (S-c)
That's the formula, now to plug in the numbers.
S= 12+12+21.2
over 2
that equals 45.2/ 2= 22.6'
Now we found s, so we can plug in the second step of the formula...
√22.6 ( 22.6 - 12 ) ( 22.6 - 12 ) ( 22.6 - 21.2 )
This equals √ 22.6 (10.6) (10.6) (1.4)
and that equals...
59.624411 = or rounded it up to 60.
Can someone help me solve this question? I'd appreciate it! Thank you.
Step-by-step explanation:
Side a = 63
Side b = 21
Side c = 66.40783 = 21√10
Angle ∠A = 71.565° = 71°33'54" = 1.24905 rad
Angle ∠B = 18.435° = 18°26'6" = 0.32175 rad
Angle ∠C = 90° = 1.5708 rad = π/2Area = 661.5
Perimeter p = 150.40783
Semiperimeter s = 75.20392
Height ha = 21
Height hb = 63
Height hc = 19.92235
Median ma = 37.85829
Median mb = 63.86901
Median mc = 33.20392
Inradius r = 8.79608
Circumradius R = 33.20392
Vertex coordinates: A[0, 0] B[66.40783, 0] C[6.64078, 19.92235]
Centroid: [24.34954, 6.64078]
Inscribed Circle Center: [12.20392, 8.79608]
Circumscribed Circle Center: [33.20392, 0]
Please help me!
30g of cornflakes contain 2.5g of fat
How many grams of fat are there in 566g of cornflakes?
Give your answer to 1 dp
Answer:
47 .2 Grams 0f FatStep-by-step explanation:
[tex]30g ----> 2.5g -fat\\566g ----> xg -fat\\30x = 1415\\\frac{30x}{30} =\frac{1415}{30} \\\\x = 47.1666\\\\x = 47.2g of Fat[/tex]
Which inequality is represented by this graph?
Help please :’/
Answer:A
Step-by-step explanation:
It is a solid line and the area below is shaded so it has to be less than the slope, hope this helped!
<!> Brainliest is appreciated! <!>
Answer:
Its A because you find the slope, -1/3 which is followed by x. The x intercept is 1 so you do plus one. Because the line is solid and negative, it makes it a less-than equal to sign. Hope this helps at all!
Step-by-step explanation:
In the diagram below, AB is parallel to CD. What is the value of x?
Answer:
A. 120 degrees.
Step-by-step explanation:
The two angles are alternate angles, which means they are congruent. So, x is also 120 degrees.
Hope this helps!
Which of the following is an arithmetic sequence?
Answer:
B
Step-by-step explanation:
An arithmetic sequence there will be a constant difference between terms.
Option A: this sequence is not an arithmetic sequence as the difference between the 1st term and the 2nd term is ×[tex]\frac{1}{2}[/tex], but the difference between the 3rd term to the 4th term is ×[tex]\frac{1}{4}[/tex].
Option B: this sequence is an arithmetic sequence as the differences between every two consecutive terms are +5.
Option C: this sequence is not an arithmetic sequence as the difference between the 1st term and the 2nd term is -8, but in the difference between the 2nd term and the 3rd is +8.
Option D: this sequence is a typical fibonacci sequence, and clearly we can see that the differences are different in every two consecutive terms.
I hope this helps, ask me any question if you do not understand :)
To Finance a Vacation in 4 years, Margo saves $530 at the begenning of the every month in an account paying interest at 3.9% compounded quarterly a. What will be the balance in her ac To Finance a Vacation in 4 years, Margo saves $530 at the begenning of the every month in an account paying interest at 3.9% compounded quarterly a. What will be the balance in her account when he takes the vacation? [4 marks] b. How much of the balance will be an interest? [2 marks] c. If she waits an additional year to start her vacation, continues to save the same amount of money, how much more money does she have to spend count when he takes the vacation? [4 marks] b. How much of the balance will be an interest? [2 marks] c. If she waits an additional year to start her vacation, continues to save the same amount of money, how much more money does she have to spend
i got this question too as my homework it so hard ill let you know if i find out the answer.
Amanda teaches violin lessons for $21.30 per hour. How many hours of lessons must Amanda give to make no less than $894.60?
No less than 42 lessons
No less than 35 lessons
No less than 45 lessons
No less than 33 lessons
Answer:
No less than 42 lessons
Step-by-step explanation:
To find the total numbers of hours needed to teach, divide the total amount of money needed by the amount of money made an hour.
$894.60/$21.30 = 42
Which are examples of binomials? Check all that apply.
Answer:
b,d,e,f and g
Step-by-step explanation:
A binomial is a polynomial with 2 terms
● a has only one term (15)
● b has two terms 15x and 2 so it is a binomial
● c has only one term so it's not a binomial
● d has two terms 512v^5+ 99w^5
● e has also two terms -6y^2 and (-79)x
● f= 2(3x+4) = 6x+8 so f has two terms then it's a binomial
● g has also two terms
Find the following System by the cramer's rule 4x-2y=8 3x+y=-4
Answer:
the value of x is 0 and y is -4.
hope it helps uh..
What is the area of the rhombus ABCD is AB is 11.2, diagonal AC is 17, and diagonal BD is 15
Answer:
117.5
Step-by-step explanation:
The formula for the area A of a rhombus is
A = ½d₁d₂,
where d₁ and d₂ are the lengths of the diagonals.
A = ½ × 17 × 15 = 117.5
Answer: 127.5 sq. units
Step-by-step explanation:
Please Help I will give out brainliest
Answer:
when y=1 then x=0.5
Step-by-step explanation:
The graph is provided.
The equation y=4x-1 can be graphed by first graphing the -1 which is the y-intercept in the y=mx+b form. 4=m that is our slope. you can find the lines second point by moving 4 up and 1 to the right. rise/run =4/1. So when you move 4 up and 1 right you get another point on the line (1,3).
You can find out x=0.5 when y=1 by just tracing your finger over the graph and the point when y equals 1 the line intercepts x=0.5. Another screenshot is given.
I hope this helps!
Which system below has no solution? y = 4x and y = 2x - 3 y = -4x and y = 2x - 3 y = -4x and y = 2x + 3 y = -4-x and y = 2x - 3
Answer:
y=4x
Step-by-step explanation:
this is because all other systems are defined and can be solved simultaneously...
pls lime and follow me ...i follow back...thanks
find the exact length of the third side
Answer:
8
Step-by-step explanation:
We will the pythagorian theorem :
let x be the third side x²+6²= 10²x²= 100-36 x=[tex]\sqrt{64}[/tex] x=8Answer:
b=8
Step-by-step explanation:
We can use the Pythagorean theorem since this is a right triangle:
a^2+ b^2 = c^2 where a and b are the legs and c is the hypotenuse
a=6 and b = 10
6^2 + b ^2 = 10^2
36+ b^2 = 100
b^2 = 100-36
b^2 = 64
Taking the square root of each side
sqrt(b^2) = sqrt(64)
b = 8
If AC =4.5 what is the measure of AB
Answer:
f
Step-by-step explanation:
f
Answer:
[tex]\boxed{AB = 9}[/tex]
Step-by-step explanation:
AB = 2(AC) {Because a line segment drawn from a center of a circle bisect the chord opposite to it}
So,
AB = 2(4.5)
AB = 9