Answer:
3 +4 i
Step-by-step explanation:
x + sqrt(yz)
Let x = 3 y=2 and z = -8
3 + sqrt(2*-8)
3+ sqrt(-16)
3 + sqrt(16) sqrt(-1)
We know sqrt(-1) = i
3 +4 i
What are the x-intercepts of the graph of the function f(x) = x2 + 5x - 36?
O (-4,0) and (9, 0)
O (4,0) and (-9,0)
O (-3,0) and (12, 0)
O (3,0) and (-12, 0)
Answer: (3,0) and (-12,0)
Step-by-step explanation:
The x-intercepts of the graph of f(x) = x² + 5x - 36 are (-9,0) and (4,0).
Option B is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
To find the x-intercepts of the function f(x) = x^2 + 5x - 36,
we need to set y = f(x) to 0 and solve for x.
So, we have:
x² + 5x - 36 = 0
We can factor the left side of the equation:
(x + 9)(x - 4) = 0
Using the zero product property, we get:
x + 9 = 0 or x - 4 = 0
Solving for x, we get:
x = -9 or x = 4
Therefore,
The x-intercepts of the graph of f(x) = x² + 5x - 36 are (-9,0) and (4,0).
Learn more about functions here:
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Find the linear function with the following properties.
f(0) = -10
Slope off = -5
Answer:
y = -5x -10
Step-by-step explanation:
plug the given values into the line equation: y = mx + b
where m is the slope and b is the y-intercept.
f(0) is the y-intercept (the point on the graph where x = 0)
The linear function with the properties f(0) = -10, Slope of -5 is f(X)=-5x-10.
To find the linear function with the given properties, we need to use the slope-intercept form of a linear function, which is:
y = mx + b
where:
y is the output (the value of the function)
x is the input (the independent variable)
m is the slope of the line
b is the y-intercept (the value of the function when x = 0)
We are given that f(0) = -10, which means when x is 0, the function value (y) is -10. This gives us the y-intercept (b = -10).
We are also given that the slope (m) is -5.
So, the linear function is f(x) = -5x - 10.
Hence, the linear function is f(x) = -5x - 10.
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Explain why a + b = d.
B
lbº
aº
dº
A
С C
find the volume of this the sphere round to the nearest tenth 7in [?]in*3
Answer:
1436.8
Step-by-step explanation:
4/3×π×7³
= 1372π/3
≈ 1436.8
Answered by GAUTHMATH
Answer: 1436
Step-by-step explanation:
I really need help please
Answer:
Step-by-step explanation:
We have two sides; the Adjacent and the Hypotnuse
Meaning we will use Cos
Cos = A/H
Cos X = 16/19
Use the inverse of Cos to find the angle
X = cos-1 (16/19)
X = 0.45499141546
X = 0.45
Please help me out!!!
Answer:
x = 76.9
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp side / adj side
tan 70 = x/28
28 tan 70 = x
x=76.92936
Rounding to the nearest tenth
x = 76.9
Answer:
76.9
Step-by-step explanation:
SOH: Sin(θ) = Opposite / Hypotenuse
CAH: Cos(θ) = Adjacent / Hypotenuse
TOA: Tan(θ) = Opposite / Adjacent
Tan 70 = [tex]\frac{x}{28}[/tex]
(28) tan 70 = x
76.929 = x
Divide x2 + 5x + 6 by x + 3.
Answer:
:D 7x+6 / x+3
Answer:
x+2
Step-by-step explanation:
To divide polynomials, one of the methods is to factor.
Take the numerator: x^2 + 5x + 6.
Factoring this numerator gives (x+3)(x+2)
Now, the question becomes (x+3)(x+2) / (x+3)
x+3 cancels out, leaving x+2 as the final answer.
Hope this helps!
(if you have other questions, leave them in the comment, and If I know how to do them, I will answer) :)
1+sin2a/1-sin2a=(1+tana/1-tana)^2
[tex] \Large \mathbb{SOLUTION:} [/tex]
[tex] \begin{array}{l} \dfrac{1 + \sin 2A}{1 - \sin 2A} = \dfrac{(1 + \tan A)^2}{(1 - \tan A)^2} \\ \\ \dfrac{1 + 2\sin A\cos A}{1 - 2\sin A\cos A} = \dfrac{(1 + \tan A)^2}{(1 - \tan A)^2} \\ \\ \because \sin 2A = 2\sin A\cos A\ (\text{Double Angle Identity}) \\ \\ \text{Divide both numerator and denominator of} \\ \text{LHS by }\cos^2 A. \\ \\ \dfrac{\frac{1 + 2\sin A\cos A}{\cos^2 A}}{\frac{1 - 2\sin A\cos A}{\cos^2 A}} = \dfrac{(1 + \tan A)^2}{(1 - \tan A)^2} \\ \\ \dfrac{\frac{1}{\cos^2 A} + \frac{2\sin A\cos A}{\cos^2 A}}{\frac{1}{\cos^2 A} - \frac{2\sin A\cos A}{\cos^2 A}} = \dfrac{(1 + \tan A)^2}{(1 - \tan A)^2}\\ \\ \dfrac{\sec^2 A + 2\tan A} {\sec^2 A- 2\tan A} = \dfrac{(1 + \tan A)^2}{(1 - \tan A)^2} \\ \\ \dfrac{1 + \tan^2 A + 2\tan A} {1 + \tan^2 A - 2\tan A} = \dfrac{(1 + \tan A)^2}{(1 - \tan A)^2} \\ \\ \because \sec^2 A = 1 + \tan^2 A\ (\text{Pythagorean Identity}) \\ \\ \text{Rearranging, we get} \\ \\ \dfrac{\tan^2 A + 2\tan A + 1} {\tan^2 A - 2\tan A + 1} = \dfrac{(1 + \tan A)^2}{(1 - \tan A)^2} \\ \\ \dfrac{(1 + \tan A)^2}{(1 - \tan A)^2} = \dfrac{(1 + \tan A)^2}{(1 - \tan A)^2}\\ \\ \text{LHS} = \text{RHS}_{\boxed{\:}}\end{array} [/tex]
Edgar accumulated $5,000 in credit card debt. If the interest rate is 10% per year and he does not make any payments for 3 years, how much will he owe on this debt in 3 years by compounding continuously?
the discrete compounding formula is f = p * (1 + r) ^ n
f is the future value
p is the present value
r is the interest rate per time period
n is then number of time periods
in your problem, you are given:
f = what you want to find
p = 5000
r = 30% per year / 100 = .3 per year (percent / 100 = rate).
n = 3 years
if you compound annually, the formula becomes:
f = 5000 * (1 + .3) ^ 3 = 10985
if you compound quarterly, the formula becomes:
f = 5000 * (1 + .3 / 4) ^ (3 * 4) = 11908.898
if you compound monthly, the formula becomes:
f = 5000 * (1 + .3 / 12) ^ (3 * 12) = 12162.67658
if you compound continuously, a different formula is used.
that formula is f = p * e ^ (r * n)
f is the future value
p is the present value
e is the scientific constant of 2.718281828.......
r is the interest rate per time period
n is the number of time periods.
with this formula, you leave the time periods in terms of years.
it will make no difference what time periods and compounding periods you use, the answer will be the same.
most of the time you will just give it the interest rate per year and the number of years.
the reason is as follows:
r * n = .3 * 3 = .9 when giving it rate and time in terms of years.
r * n = .3 / 4 * 3 * 4 = .9 when giving it rate and time in terms of quarters.
r * n = .3 / 12 * 3 * 12 = .9 when giving it rate and time in terms of months.
in your problem, the formula becomes f = 5000 * e ^ (.3 * 3) = 12298.01556.
the more compounding periods per year, the higher the future value.
the highest is when you compound continuously.
this is apparent from the data.
Can you please solve these equations by elimination? -10x -10y=20 , -7x -7y=14.
Answer:
-10x -10y=20
-10x - 20=10y
-10x - 20/10=y
-10x - 2=y
y=-10x-2
-7x -7y=14
-7x - 14 = 7y
-7x - 14/7=y
-7x - 2=y
y=-7x-2
A dump truck with 1500 gallons of soil arrives on campus to fill in the new planters on the quad. Each planter needs 2 cubic yards of soil. How many planters can be filled?
Answer:
3 planters can be filled, with 288,156 gallons left over.
Step-by-step explanation:
Given that a dump truck with 1500 gallons of soil arrives on campus to fill in the new planters on the quad, and each planter needs 2 cubic yards of soil, to determine how many planters can be filled the following calculation must be performed:
1 cubic yard = 201.974 gallons
2 cubic yards = 403.948 gallons
1500 / 403.948 = X
3.71 = X
1500 - (403.948 x 3) = 288.156
Therefore, 3 planters can be filled, with 288,156 gallons left over.
A baker is making 41/8 batches of cookies. If each batch requires 3/4 of a stick of butter, how much butter will her need for all 41/8 batches? Please explain/show ur work.
Answer:
Step-by-step explanation:
I assume that you mean 4⅛ batches, not 41/8 batches.
4⅛ batches × (¾ stick)/batch = 33/8 batches × (¾ stick)/batch
= 99/32 sticks
= 3 and 3/32 sticks
The circumference of a
square orchard is 1600
meters. How many square
meters does the orchard
cover? How many hectares?
Answer:
A square is 4 even sides.
the circumference around the square area is 1600 meters. This means that each side is 400 meters.
Square meters is the area of the square.
400 x 400 = 160000 m^2
To get to Hectares, you divide the squared measurement by 10,000.
Answer:
160000m^2 = 16ha
Step-by-step explanation:
Bit of a nit pick first the word is perimeter not circumference circumference only applies to circles. 1600/4=400 (divide by 4 because a square has 4 sides) 400^2=160000 (A=L*H the length and height are the same so you square it) 160000/10000=16 (1 hectare = 10000m^2), Hope this helps. :)
Find all the zeros of f(x).
f(x) = 2x3 + 7x2 - 28x + 12
Arrange your answers from smallest to largest. If
there is a double root, list it twice.
Plz help!
Answer:
The zeroes are -6, 1/2 and 2.
Step-by-step explanation:
f(x) = 2x3 + 7x2 - 28x + 12 = 0
From the first and last coefficient 2 and 12, one guess for a zero is x = 2.
So substituting x = 2:
f(2) = 16+ 28 - 56 + 12 = 0
So x = 2 is a zero and x - 2 is a factor of f(x)
Performing long division:
x - 2)2x3 + 7x2 - 28x + 12( 2x2 + 11x - 6 <------- Quotient
2x3 - 4x2
11x2 - 28x
11x2 - 22x
- 6x + 12
-6x + 12
.............
Now we solve
2x2 + 11x - 6 = 0
(2x - 1)(x + 6) = 0
2x - 1 = 0 or x + 6 = 0, so:
x = 1/2, x = -6.
Answer: -6, 1/2, 2.
Step-by-step explanation:
{(x) = 2x3 + 7x2 - 28x + 12 = 0
From the first and last coefficient 2 and 12, one
guess for a zero is x=2.
So substituting x=2:
{(2) = 16+ 28 - 56 + 12 = 0
So x = 2 is a zero and x - 2 is a factor of f(x)
Performing long division:
X - 2)2x3 + 7x2 - 28x + 12(2x2 + 11x - 6 <
Quotient
Sam can mow a lawn in 40 minutes. Melissa can mow the same lawn in 80 minutes. How long does it take for both Sam and Melissa to mow the lawn if they are working together?
Answer:
It will take them both 24 minutes to mow the lawn if they are working together.
Step-by-step explanation:
Given that Sam can mow a lawn in 40 minutes, and Melissa can mow the same lawn in 80 minutes, to determine how long does it take for both Sam and Melissa to mow the lawn if they are working together, the following calculation must be performed:
1/40 + 1/60 = 1 / X
3X + 2X = 120
X = 120/5
X = 24
Thus, it will take them both 24 minutes to mow the lawn if they are working together.
state the hundred thousands place for 7,832,906,215
Answer:
Step-by-step explanation:
6 is the thousands place
0 (right next to it) is the 10 thousands place
9 is the hundred thousands place. There is only 1 nine present so the answer is unique.
Does anyone know how to take the fuzzy stuff off
Answer:
???
Step-by-step explanation:
100 mice eat 100 cakes. If each big mouse eats 3 cakes, and 3 baby mice eat 1 cake, how many big mice and baby mice are there?
Find the missing side. Round your answer to the nearest tenth
Answer:
x = 24.8
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
Sin theta = opp / hypotenuse
sin 75 = 24 /x
x sin 75 = 24
x = 24/ sin 75
x=24.84662
Rounding to the nearest tenth
x = 24.8
A , B, C , D probability
Answer:
your laptop is nice really
Given limit f(x) = 4 as x approaches 0. What is limit 1/4[f(x)]^4 as x approaches 0?
Answer:
[tex]\displaystyle 64[/tex]
General Formulas and Concepts:
Calculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]
Limit Rule [Variable Direct Substitution Exponential]: [tex]\displaystyle \lim_{x \to c} x^n = c^n[/tex]
Limit Property [Multiplied Constant]: [tex]\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \lim_{x \to 0} f(x) = 4[/tex]
Step 2: Solve
Rewrite [Limit Property - Multiplied Constant]: [tex]\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = \frac{1}{4} \lim_{x \to 0} [f(x)]^4[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution Exponential]: [tex]\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = \frac{1}{4}(4^4)[/tex]Simplify: [tex]\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = 64[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Book: College Calculus 10e
Answer: C. 64
Step-by-step explanation:
Edge 100%
• The difference between a polynomial or rational equation and polynomial or rational inequality
Answer:
An equation has an equal sign between two expressions, while an inequality has a ≤ or ≥ sign.
The dual of the equation x(y + 1) is?
Answer:
x (y+1)
xy+1x
xy+x is theanswer.
I hope this will help you.
stay safe
how you could find the shortest distance from A(6, 5) to the line y = 5x – 10?
Answer:
The distance between two points (a, b) and (c, d) is given by:
[tex]d = \sqrt{(a - c)^2 + (b - d)^2}[/tex]
So the distance between the point (6, 5) and the line y = 5x - 10 can be thought as the distance between the point (6, 5) and the point (x, 5x - 10)
Where:
(x, 5x - 10) denotes all the points in the line y = 5x – 10
That distance is given by:
[tex]d = \sqrt{(x - 6)^2 + (5x - 10 - 5)^2} = \sqrt{(x - 6)^2 + (5x - 15)^2}[/tex]
Now we want to minimize this.
Because the distance is a positive quantity, we can try to minimize d^2 insted, so we have:
[tex]d^2 = (\sqrt{(x - 6)^2 + (5x - 15)^2})^2 = (x - 6)^2 + (5x - 15)^2}\\\\d^2 = x^2 - 2*x*6 + 36 + 25*x^2 - 2*15*x + (-15)^2\\\\d^2 = 26*x^2 - 42*x + 261[/tex]
Notice that this is a quadratic equation with a positive leading coefficient, which means that the arms of the graph will open upwards, then the minimum will be at the vertex of the parabola.
Remember that for a parabola:
y = a*x^2 + bx + c
the x-value of the vertex is:
x = -b/2a
Then for our parabola:
d^2 = 26*x^2 - 42*x + 261
The vertex is at:
x = -(-42)/(2*26) = 0.808
Then we just need to evaluate the distance equation in that value of x to get the shortest distance:
[tex]d = \sqrt{(0.808 - 6)^2 + (5*0.808 - 15)^2} = 12.129[/tex]
The shortest distance between the point A and the line is 12.129 units.
what is the image of ( 4, -8 ) after a dilation by a scale factor of 1/4 centered at the origin ?
what we know?:
* scale factor of 1/4
* the point (4, -8)
all we have to do is put 4/4 (because we are dilating by 1/4)
4/4= 1
same for the other one: -8/4= -2
FINAL ANSWER: (1, -2)
4x - 2 - 1 = 2 hep plz
Tolong bantuin pakai cara
Answer:
1364
Step-by-step explanation:
1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364
a1+a2 = a3, a2+a3=a4 etcetera..
1+3 =4
3+4 =7
4+7=11
.
.
a13+a14 = a15
521+843 = 1364
so, 1364 is the answer
Solve for X Solve for X Solve for X Solve for X Solve for X
Answer:
13.5
Step-by-step explanation:
We can use a ratio to solve
2 3
---- = ------
11 3+x
Using cross products
2(3+x) = 3*11
Distribute
6+2x = 33
Subtract 6
6+2x-6 = 33-6
2x = 27
Divide by 2
2x/2 = 27/2
x = 13.5
Now we have to,
→ solve for x
Then use a ratio to solve,
→ 2/11 = 3/3+x
Now see the further steps,
→ 2(3+x) = 3 × 11
→ 6+2x = 33
→ 2x = 33-6
→ 2x = 27
→ x = 27/2
→ x = 13.5
Hence, 13.5 is value of x.
Test for exactness. If exact, solve it directly. Otherwise, use integrating factors to solve it. Solve the IVP (if given). 2xy + (x^2) y' = 0
sin(x) cos(y) + cos(x) sin(y) y' = 0
(x^2) + (y^2) - 2xyy' = 0
e^(2x).(2 cos(y) - sin(y) y') = 0, where y(0) = 0
• 2xy + x ² y' = 0
This DE is exact, since
∂(2xy)/∂y = 2x
∂(x ²)/∂x = 2x
are the same. Then there is a solution of the form f(x, y) = C such that
∂f/∂x = 2xy ==> f(x, y) = x ² y + g(y)
∂f/∂y = x ² = x ² + dg/dy ==> dg/dy = 0 ==> g(y) = C
==> f(x, y) = x ² y = C
• sin(x) cos(y) + cos(x) sin(y) y' = 0
is also exact because
∂(sin(x) cos(y))/∂y = -sin(x) sin(y)
∂(cos(x) sin(y))/∂x = -sin(x) sin(y)
Then
∂f/∂x = sin(x) cos(y) ==> f(x, y) = -cos(x) cos(y) + g(y)
∂f/∂y = cos(x) sin(y) = cos(x) sin(y) + dg/dy ==> dg/dy = 0 ==> g(y) = C
==> f(x, y) = -cos(x) cos(y) = C
• x ² + y ² - 2xyy' = 0
is not exact:
∂(x ² + y ²)/∂x = 2x
∂(-2xy)/∂y = -2x
So we look for an integrating factor µ(x, y) such that
µ (x ² + y ²) - 2µxyy' = 0
becomes exact, which would require that these be equal:
∂(µ (x ² + y ²))/∂y = (x ² + y ²) ∂µ/∂y + 2µy
∂(-2µxy)/∂x = -2xy ∂µ/∂x - 2µy
Observe that if µ(x, y) = µ(x), then ∂µ/∂y = 0 and ∂µ/∂x = dµ/dx, so we would have
2µy = -2xy dµ/dx - 2µy
==> -2xy dµ/dx = 4µy
==> dµ/µ = -2/x dx
Integrating both sides gives
∫ dµ/µ = ∫ -2/x dx ==> ln|µ| = -2 ln|x| ==> µ = 1/x ²
So in the modified DE, we have
(1 + y ²/x ²) - 2y/x y' = 0
which is now exact and ready to solve, since
∂(1 + y ²/x ²)/∂y = 2y/x ²
∂(-2y/x)/∂x = 2y/x ²
We get
∂f/∂x = 1 + y ²/x ² ==> f(x, y) = x - y ²/x + g(y)
∂f/∂y = -2y/x = -2y/x + dg/dy ==> dg/dy = 0 ==> g(y) = C
==> f(x, y) = x - y ²/x = C
• exp(2x) (2 cos(y) - sin(y) y' ) = 0
is exact, since
∂(2 exp(2x) cos(y))/∂y = -2 exp(2x) sin(y)
∂(-exp(2x) sin(y))/∂x = -2 exp(2x) sin(y)
Then
∂f/∂x = 2 exp(2x) cos(y) ==> f(x, y) = exp(2x) cos(y) + g(y)
∂f/∂y = -exp(2x) sin(y) = -exp(2x) sin(y) + dg/dy ==> dg/dy = 0 ==> g(y) = C
==> f(x, y) = exp(2x) cos(y) = C
Given that y = 0 when x = 0, we find that
C = exp(0) cos(0) = 1
so that the particular solution is
exp(2x) cos(y) = 1
a river generates a spring flood about 40% of the time. Based on these records, what is the chance that it will flood for at least three years in a row sometime during the next five years