Answers
In order to find the values of x and y, let's compare the real part and the complex part in each side of the equation:
\(\begin{gathered} -12+18i+8x=-9-17i+13yi\\ \\ (8x-12)+(18)i=(-9)+(13y-17)i\\ \\ \begin{cases}8x-12={-9\rightarrow8x=3\rightarrow x=\frac{3}{8}} \\ 18={13y-17\rightarrow13y=35\rightarrow y=\frac{35}{13}}\end{cases} \end{gathered}\)Therefore the answer is x = 3/8 and y = 35/13.
Related Questions
when the spring is stretched and the distance from point a to point b is 5.3 feet, what is the value of θ to the nearest tenth of a degree?
a. 60.0
b. 35.2
c. 45.1
d. 55.5
Answers
When the spring is stretched and the distance from point a to point b is 5.3 feet, the value of θ is 53.13 degrees
The distance between point a to point b = 5.3 feet
The length of the top side = 3 feet
Therefore, it will form a right triangle
Here we have to use trigonometric function
Here adjacent side and the hypotenuse of the triangle is given
The trigonometric function that suitable for the given conditions is
cos θ = Adjacent side / Hypotenuse
Substitute the values in the equation
cos θ = 3 / 5
θ = cos^-1(3 / 5)
θ = cos^-1(0.6)
θ = 53.13 degrees
Therefore, the value of θ is 53.13 degrees
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a parabola had a vertex of (-5,0) and passes through the point (-3,1)
Answers
Answer:
Step-by-step explanation:
let the parabola be y=a(x+5)²+0
or y=a(x+5)²
∵ it passes through (-3,1)
1=a(-3+5)²
4a=1
a=1/4
so parabola is y=1/4(x+5)²
Find the distance from the point (3,4,6) to the yz-plane. Find the distance in exact form between the point P(−4,−3,4) and the point Q(4,−4,−1). Distance =
Answers
To find the distance from a point to the yz-plane, we can use the formula d = |Ax + By + Cz + D| / √(A^2 + B^2 + C^2), where A, B, C, and D are the coefficients of the equation of the plane. By substituting the coordinates of the point (3, 4, 6) into the formula, we can calculate the distance.
For the distance between two points, we can use the distance formula, d = √((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2), where (x1, y1, z1) and (x2, y2, z2) are the coordinates of the two points. By substituting the coordinates of P(-4, -3, 4) and Q(4, -4, -1) into the formula, we can calculate the distance.
1. Distance from a point to the yz-plane:
The equation of the yz-plane can be represented as x = 0. To find the distance from the point (3, 4, 6) to the yz-plane, we substitute the values into the distance formula:
d = |0(3) + 1(4) + 0(6) + D| / √(0^2 + 1^2 + 0^2)
Since the equation of the yz-plane is x = 0, the coefficients A = 0, B = 1, C = 0, and D = 0. Substituting these values into the formula, we get:
d = |4| / 1
d = 4
Therefore, the distance from the point (3, 4, 6) to the yz-plane is 4 units.
2. Distance between two points:
To find the distance between the points P(-4, -3, 4) and Q(4, -4, -1), we can use the distance formula:
d = √((4 - (-4))^2 + (-4 - (-3))^2 + (-1 - 4)^2)
d = √(8^2 + (-1)^2 + (-5)^2)
d = √(64 + 1 + 25)
d = √90
Therefore, the distance between the points P(-4, -3, 4) and Q(4, -4, -1) is √90 units.
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If (x - 4) varies inversely as (y + 3) and x = 8 when y = 2, what is x when y = - 1?
Answers
Answer:
\(x=14\)
Step-by-step explanation:
If two values are inversely proportional, their product must be maintained. That way, if one value goes up, the other goes down by the same extent.
Therefore, if \((x-4)\) and \((y+3)\) vary inversely, their product will be the same for all values of \(x-4\) and \(y+3\).
Let \(x=8\) and \(y=2\) as given in the problem. Substitute values:
\((8-4)(2+3)=(4)(5)=20\)
Hence, the maintained product is \(20\).
Thus, we have the following equation:
\((x-4)(y+3)=20\)
Substitute \(y=-1\) to find the value of \(x\) when \(y=-1\):
\((x-4)(-1+3)=20,\\(x-4)(2)=20,\\x-4=10,\\x=10+4=\boxed{14}\)
The estimated demand for a good is Q=25-5p+0.32m+12pr
where Q is the quantity demanded of the good, P is the price of the good, M is income, and PR is the price of related good R. If the price of the good falls by $4, the quantity demanded will ________ by ________ units.
increase 5 units
increase 20 units.
increase 50 units
increase 48 units
decrease 12 units
A theoretical restriction on the short-run cubic cost equation, TVC = aQ + bQ + cQ2, is
a > 0, b > 0, c > 0
a > 0, b < 0, c > 0
a > 0, b > 0, c < 0
a > 0, b < 0, c < 0
Answers
If the price of the good falls by $4, the quantity demanded will increase by 20 units. A theoretical restriction on the short-run cubic cost equation, \(TVC = aQ + bQ + cQ^2, is a > 0, b > 0, c < 0.\)
1. Quantity Demanded:
According to the estimated demand equation, \(Q = 25 - 5P + 0.32M + 12PR,\) where Q represents the quantity demanded, P is the price of the good, M is income, and PR is the price of a related good R.
If the price of the good falls by $4, we can substitute P - $4 into the equation to calculate the new quantity demanded:
\(Q' = 25 - 5(P - $4) + 0.32M + 12PR\)
Simplifying the equation, we have:
\(Q' = 25 + 20 - 5P + 0.32M + 12PRQ' = 45 - 5P + 0.32M + 12PR\)
Comparing this with the original equation, we see that the coefficient of P is -5. Therefore, a $4 decrease in price would increase the quantity demanded by 20 units.
2. Short-Run Cubic Cost Equation:
The theoretical restriction on the short-run cubic cost equation, \(TVC = aQ + bQ + cQ^2, is a > 0, b > 0, c < 0.\)
This restriction ensures that the total variable cost (TVC) increases as the quantity (Q) increases, as indicated by the positive coefficients of aQ and bQ. Additionally, the negative coefficient of cQ^2 ensures that the cost curve is concave, representing diminishing marginal returns in the short run.
Therefore, the answer is:
If the price of the good falls by $4, the quantity demanded will increase by 20 units. The theoretical restriction on the short-run cubic cost equation, \(TVC = aQ + bQ + cQ^2, is a > 0, b > 0, c < 0.\)
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We are interested in the first few Taylor Polynomials for the function
f(x) = 2x²+ 3e-*
centered at a = 0.
To assist in the calculation of the Taylor linear function, T₁(x), and the Taylor quadratic function, T₂(x), we need the following values:
f(0) =
f'(0) =
f''(0) =
Using this information, and modeling after the example in the text, what is the Taylor polynomial of degree one:
T₁(x) =
What is the Taylor polynomial of degree two:
T₂(x) =
Answers
Given function:f(x) = 2x²+ 3e-*To calculate Taylor polynomials for the function f(x), we need the following values:f(0) = ?f'(0) = ?f''(0) = ?Let's calculate these values one by one.f(x) = 2x²+ 3e-*.f(0) = 2(0)²+3e-0 = 3f(x) = 2x²+ 3e-*f'(x) = 4x +
0.f'(0) = 4(0) + 0 = 0.f''
(x) = 4.f''(0) = 4.Now, let's find the Taylor polynomials of degree one and two.Taylor polynomial of degree one: T₁(x) = f(a) + f'(a)(x-a)Let's take a = 0.T₁(x) = f(0) + f'(0)xT₁(x) = 3 + 0.x = 3Taylor polynomial of degree two:
T₂(x) = f(a) + f'(a)(x-a) + [f''(a)(x-a)²]/2
Let's take a = 0.T₂(x) = f(0) + f'(0)x + [f''(0)x²]/2T₂
(x) = 3 + 0.x + [4x²]/2T₂
(x) = 3 + 2x²So, the Taylor polynomial of degree one is T₁(x) = 3, and the Taylor polynomial of degree two is T₂(x) = 3 + 2x².
In mathematics, an expression is a group of representations, digits, and conglomerates that resemble a statistical correlation or regimen. An expression can be a real number, a mutable, or a combination of the two. Addition, subtraction, rapid spread, division, and exponentiation are examples of mathematical operators. Arithmetic, mathematics, and shape all make extensive use of expressions. They are used in mathematical formula representation, equation solution, and mathematical relationship simplification.
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is square root of 4 a irrational numbers
Answers
Answer:
yes
Step-by-step explanation:
if a even number can go into a even number a even number of times its a irrational number
Answer: no it is rational
Step-by-step explanation: A number is only irrational if it has endless decimals after it.
An item is regularly priced at $71. It is now priced at a discount of 35% off the regular price.
Answers
Answer:
$46.15
Step-by-step explanation:
So you can just multiply the 71 by 0.65 becuase your paying 65 percent of the price now since it’s 35 percent off and you’ll get 46.15
OR
You can just multiply 0.35 by 71 and get 24.85. Then subtract that form 71. You’ll get 46.15
Answer:
Discount amount: $24.85
New price with the discount included: $46.15
Step-by-step explanation:
I don't know what you are trying to solve, but here's the work for various things. You can pick the answers you need if you see them here.
1. Find the amount of the discount.
Multiply the retail price by the discount percentage.
$71 x 35% = $24.85
$24.85 is the total discount that was taken off of the original price.
2. Find the price of the item after the discount.
Subtract the amount of the discount from the original price.
$71.00 - $24.85 =$46.15
$46.15 is the new price.
What is 2/3 of 1 5/16
Answers
Answer:
7/8
Step-by-step explanation:
2/3 * 1 5/16 =
2/3 * (1 + 5/16)=
2/3 * (16/16 + 5/16)= -> common denominator numbers are easy to simplify
2/3 * (16+5)/16 =
2/3 * 21/16=
(2*21)/(3*16)=
42/48=
21/24=7/8
ctions: Choose the correct answer for each problem below.
1. Divide: 71.5+ 11
a. 65
b. 6.5
C. 0.65
d. 650
2. Divide: 495.06 +0.6
a. 825.1
b. 8,251
C. 82.51
d. 8.251
Answers
Suppose g : A → B and f : B → C are functions.a. Show that if f ◦g is onto, then f must also be onto.b. Show that if f ◦g is one-to-one, then g must also be one-to-one.c. Show that if f ◦g is a bijection, then g is onto if and only if f is one-to-one.
Answers
A function f from A to B is called one-to-one (or 1-1) if whenever f (a) = f (b) then a = b. No element of B is the image of more than one element in A.
a. To prove that if f ◦ g is onto, then f must also be onto, we assume f ◦ g is onto. This means that for every c ∈ C, there exists an a ∈ A such that (f ◦ g)(a) = f(g(a)) = c. Since g(a) ∈ B, we can say that for every c ∈ C, there exists a b = g(a) ∈ B such that f(b) = c. Hence, f is onto.
b. To prove that if f ◦ g is one-to-one, then g must also be one-to-one, we assume f ◦ g is one-to-one. This means that for any a1, a2 ∈ A, if g(a1) ≠ g(a2), then (f ◦ g)(a1) = f(g(a1)) ≠ f(g(a2)) = (f ◦ g)(a2). If g(a1) = g(a2), then we can conclude that a1 = a2 to maintain the one-to-one property of f ◦ g. Therefore, g must also be one-to-one.
c. If f ◦ g is a bijection, it means that it is both onto and one-to-one. From part a, we know that f must be onto. Now, to prove that g is onto if and only if f is one-to-one, we can use the contrapositive. If g is not onto, then there exists a b ∈ B that is not in the range of g. In that case, f(g(a)) cannot be one-to-one because there are multiple values of a that map to the same b. Similarly, if f is not one-to-one, then there exist b1, b2 ∈ B such that f(b1) = f(b2) but b1 ≠ b2. In this case, g(a) can't be one-to-one because there are multiple values of a that map to the same b. Therefore, g is onto if and only if f is one-to-one.
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A recipe calls for 8 oz of chocolate chip in each batch. how many pounds of chocolate chips do you need to make six batches? (1 pounds = 16 oz)
Answers
Answer:
Step-by-step explanation:
half a pound
Let the long-run profit function for a representative firm is given by π i
=p 2
−2p−399, where p is the price of computer. The inverse market demand for computer is given by p=39−0.009q, where q is unit of computers. Suppose technology for producing computers is identical for all firms and all firms face identical input prices. (a) Find the firm's output supply function. (b) Find the market-equilibrium price and the equilibrium number of firms. (c) Find the number of computers sold by each firm in the long run.
Answers
(a) The firm's output supply function is given by q = (p + 199) / 2.
(b) The market-equilibrium price is $32.56, and the equilibrium number of firms is 10.
(c) Each firm sells 70 computers in the long run.
To find the firm's output supply function, we need to maximize the firm's profit function, which is given by π = p^2 - 2p - 399. In the long run, firms will produce where marginal cost equals marginal revenue. Marginal revenue can be obtained by differentiating the inverse market demand function with respect to q, and marginal cost is equal to the derivative of the profit function with respect to q. Equating the two, we get:(39 - 0.009q) = (2q - 2) / q
Simplifying the equation, we find:
q = (p + 199) / 2
This represents the firm's output supply function.
To find the market-equilibrium price and the equilibrium number of firms, we need to find the intersection point of the market demand and supply. Substituting the output supply function into the inverse market demand function, we have:p = 39 - 0.009((p + 199) / 2)
Simplifying and solving for p, we get:
p ≈ $32.56
Substituting this price back into the output supply function, we find:
q = (32.56 + 199) / 2 ≈ 115.78
Given that each firm produces 70 computers in the long run, we can calculate the equilibrium number of firms:
Number of firms = q / 70 ≈ 10
Since each firm sells 70 computers in the long run, and there are 10 firms, the total number of computers sold by each firm is:70 * 10 = 700
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Graph the function:
y = -3x + 2
Answers
Answer:
Step-by-step explanation:
Avery leans a 24-foot ladder against a wall so that it forms an angle of 80
with the ground. How high up the wall does the ladder reach? Round your answer to the nearest tenth of a foot if necessary.
Answers
The height of the wall where the ladder reaches will be 23.6 feet.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
Avery leans a 24-foot ladder against a wall so that it forms an angle of 80° with the ground.
The height of the wall where the ladder reaches is given as,
\(\text{sin 80}^\circ \sf =\dfrac{h}{24}\)
\(\sf h = 24 \times \text{sin 80}^\circ\)
\(\sf = 24 \times \text{0.9848}\)
\(\sf h = 23.63\thickapprox\bold{23.6 \ feet}\)
The height of the wall where the ladder reaches will be 23.6 feet.
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Is the function periodic? If so, find the period.See imagea) yes; 4b) yes; 5c) yes' 6d) no
Answers
Recall that a periodic function is a function that repeats itself at regular intervals, and the period is the distance between the repetitions.
Notice that the given graph repeats itself regularly, then it must be periodic.
From the given diagram we get that the period of the given graph is:
\(2-(-4)=2+4=6.\)Answer: Option C.
find the value of given expression
\( \sqrt{401 - 1} \)
Answers
Step-by-step explanation:
\( \sqrt{400} \\ 20\)
Joan wants to have $250,000 when she retires in 29 years. How much should she invest annually in her sinking fund to do this if the interest is 4% compounded annually?
Answers
Joan should invest $4720 annually in her sinking fund to have $250,000 when she retires
Calculating the amount to investWe can use the future value formula for an annuity to solve this problem:
FV = PMT * [(1 + r)^n - 1] / r
Where:
FV = future valuePMT = annual paymentr = interest raten = number of periodsWe want to find PMT, so we can rearrange the formula:
PMT = FV * r / [(1 + r)^n - 1]
Plugging in the values we know:
FV = $250,000
r = 0.04
n = 29
PMT = $250,000 * 0.04 / [(1 + 0.04)^29 - 1]
PMT = $250,000 * 0.04 / 22.718
PMT = $4720
So Joan should invest approximately $4720 annually in her sinking fund to have $250,000 when she retires in 29 years, assuming an interest rate of 4% compounded annually.
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Factor the following expression completely… (Hint factor out the GCF first)
Answers
Given:
The expression is given
\(15x^4+55x^3+30x^2\)Explanation:
To factor out completely the expression.
Take common from the expression.
\(5x^2(3x^2+11x+6)\)Now factorize the quadratic equation in the bracket.
\(5x^2(3x+2)(x+3)\)Answer:
Hence the factor of the expression is
\(5x^2(3x+2)(x+3)\)Answer:
15x⁴ + 55x³ + 30x² = 5x² (x + 3) (3x + 2)
Step-by-step explanation:
Factorize:
15x⁴ = 3 * 5 * x⁴
55x³ = 11 * 5 * x³
30x² = 6 *5 * x²
GCF = 5x²
15x⁴ + 55x³ + 30x² = (5x²*3x²) + (5x² * 11x) + (5x² *6)
= 5x² (3x² + 11x + 6)
3x² +11x + 6
Sum = 11
Product = 3 *6 = 18
Factor = 2 , 9 {2 +9 = 11 & 2*9 = 18}
3x² + 11x + 6 = 3x² + 9x + 2x + 6 {Rewrite the middle term using factors}
= 3x(x + 3) + 2(x +3)
= (x + 3)(3x + 2)
15x⁴ + 55x³ + 30x² = 5x²(x + 3)(3x + 2)
which provides stronger evidence against the null hypothesis, a p-value of 0.02 or a p-value of 0.03? explain your answer.
Answers
A p-value is a measure of the strength of evidence against the null hypothesis in a statistical hypothesis test. It represents the probability of obtaining the observed data or more extreme results, assuming that the null hypothesis is true.
In general, a smaller p-value provides stronger evidence against the null hypothesis. Therefore, in the given scenario, a p-value of 0.02 would provide stronger evidence against the null hypothesis compared to a p-value of 0.03.
A p-value of 0.02 indicates that there is a 2% chance of obtaining the observed data or more extreme results if the null hypothesis is true. This suggests that the observed data is relatively unlikely under the assumption of the null hypothesis, providing stronger evidence against it.
On the other hand, a p-value of 0.03 indicates that there is a 3% chance of obtaining the observed data or more extreme results if the null hypothesis is true. Although this still suggests that the observed data is unlikely under the null hypothesis, it is not as strong evidence as a p-value of 0.02.
In summary, a lower p-value indicates that the observed data is less likely to occur under the null hypothesis, providing stronger evidence against it. Therefore, a p-value of 0.02 would provide stronger evidence against the null hypothesis compared to a p-value of 0.03.
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Find the volume of the triangular pyramid shown below
Answers
Answer:
B
Step-by-step explanation:
Use the graph below for this question:
what is the average rate of change from x = 0 to x = 2?
a) 3
b) -1
c) 2
d) -2
Answers
The average rate of change is the same as the slope. Even though this graph is a parabola, we still use the slope formula with the corresponding points. Had the question asked for the instantaneous rate of change, we would have needed to find a derivative.
Slope formula: (y2 - y1) / (x2 - x1)
Point 1: (0,4)
Point 2: (2,8)
(8 - 4) / (2 - 0)
4 / 2
2
The average rate of change from x = 0 to x = 2 is 2.
Hope this helps!
Consider a sample of tissue cells infected in a laboratory treatment. For 225 tissues, the standard deviation for the number of cells infected was 80 and the mean was 350. What is the standard error
Answers
Thus, standard error for this sample of tissue cells infected in a laboratory treatment is 5.33.
The standard error (SE) is a measure of how much the sample mean deviates from the population mean. It is calculated as the standard deviation of the sample divided by the square root of the sample size.
In this case, the sample size is 225, the standard deviation is 80, and the mean is 350. Therefore, the standard error can be calculated as follows:
SE = 80 / √(225)
SE = 80 / 15
SE = 5.33
The standard error for this sample of tissue cells infected in a laboratory treatment is 5.33. This means that the sample mean of 350 is likely to be within 5.33 units of the population mean.
The smaller the standard error, the more precise the estimate of the population mean. In this case, the standard error is relatively small compared to the standard deviation, which suggests that the sample mean is a relatively accurate estimate of the population mean.
However, it is important to note that the standard error only provides information about the precision of the estimate, not its accuracy. Other factors, such as sampling bias or measurement error, could still affect the accuracy of the estimate.
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The graph that is made up of two straight lines, which has an absolute maximum or absolute minimum, and is symmetric belongs to the
function family.
Answers
Answer:
This may be a function of the absolte value family.
f(x) = IxI.
f(x) = x if x ≥ 0
f(x) = -x if x ≤ 0
Where this is the parent function, and the graph is shown below in green.
If the coefficient is positive, then the lines open upwards, and we will have a minimum (in this case, when x = 0).
And also in this case, we have symmetry around the value x = 0.
Now, the vertex can also be an absolute maximum if the coefficient is negative, like in the example shown below in color blue (the equation for the blue graph is f(x) = -3*IxI )
Ms. Gallegos burns 236 calories riding her bike each hour. She wants to burn more than 590 calories riding her bike at the same rate.
Answers
Answer:
Step-by-step explanation:
590 cal × (1 hr)/(236 cal) = 2.5 hr
The cycle time for trucks hauling concrete to a highway construction site is uniformly distributed over the interval 50 to 70 minutes. What is the probability that the cycle time exceeds 60 minutes if it is known that the cycle time exceeds 55 minutes
Answers
The probability that the cycle time exceeds 60 minutes given that it exceeds 55 minutes is 2/1 or simply 1, which means it is certain that the cycle time exceeds 60 minutes if it exceeds 55 minutes.
Given that the cycle time for trucks hauling concrete to a highway construction site is uniformly distributed over the interval 50 to 70 minutes, we know that the probability density function is:
f(x) = 1 / (70 - 50) = 1/20, for 50 <= x <= 70
To find the probability that the cycle time exceeds 60 minutes given that it exceeds 55 minutes, we need to use conditional probability:
P(X > 60 | X > 55) = P(X > 60 and X > 55) / P(X > 55)
We can simplify this by noticing that if X is greater than 55, then it must be between 55 and 70, and therefore:
P(X > 55) = P(55 <= X <= 70) = (70 - 55) / (70 - 50) = 1/4
Similarly, we can rewrite the numerator as:
P(X > 60 and X > 55) = P(X > 60)
since if X is greater than 60, it is also greater than 55.
Now, to find P(X > 60), we integrate the density function from 60 to 70:
P(X > 60) = ∫60^70 (1/20) dx = (1/20) × (70 - 60) = 1/2
Putting it all together:
P(X > 60 | X > 55) = P(X > 60 and X > 55) / P(X > 55)
= P(X > 60) / P(X > 55)
= (1/2) / (1/4)
= 2
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Which equation in standard form has a graph that passes through the point (3,-9) and has a slope of 5/3?
Answers
Answer:
5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
because I did it and good night and sleep
Avery had $25.40 in her wallet. If she bought lunch with dollars from her wallet, how much money did she have in her wallet after lunch?
A. $18.15
B. $18.30
C. $17.15
Answers
Answer:
Step-by-step explanation:
This question doesn't say how much her lunch cost.
I need these answers please
Answers
I hope this helped!
What does y 3x 3 look like on a graph?
Answers
On a graph, y 3x 3 would be a line that is 3 units below the line y = 3x. It would have the same slope but lower y-intercept.
To graph y 3x 3, we can first graph y = 3x. To do this, we can pick any two points along the line and plot them. For example, if we choose (0,0) and (1,3), the line would look like this:
(0,0) -------------------------- (1,3)
Now, to graph y 3x 3, we want to move the line 3 units down. Therefore, the new points that we plot should be (0,-3) and (1,0). The graph should look like this:
(0,-3) -------------------------- (1,0)
This line is 3 units below the line y = 3x. It has the same slope, but a lower y-intercept.
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