The angle of inclination of a road with a grade of 19% is approximately 10.8 degrees, which is calculated by using the inverse tangent formula in trigonometry.
The correct answer is C).
Explanation:The angle of inclination, or grade, in terms of percentage, represents the rise (vertical distance) over the run (horizontal distance). The measure of the angle of inclination in degrees can be found by using the inverse tangent (tan-1) formula in trigonometry. To be specific, if a road has a 19% grade, it means for every 100 units (meters, feet, etc.) of horizontal distance, there is a 19 unit rise in vertical distance.
An angle θ can be calculated using tan-1(rise/run) = tan-1(19/100).
When you compute this, θ equals approximately 10.8 degrees.
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The figure below shows a circle with center N, diameter FM, and tangents GA and FW. Which of the angles must be right angles? Select all that apply.
A)
B)
C)
D)
E)
F)
The angles that must be right angles in the given figure are <FPT and <GWF.
In the given figure, we have a circle with center N and diameter FM. The tangents to the circle are GA and FW.
First, let's consider angle <FPT. Since GA is tangent to the circle, it is perpendicular to the radius drawn from the center N to the point of tangency, which is point F. Therefore, <FPT must be a right angle.
Next, let's consider angle <GWF. Since FW is tangent to the circle, it is also perpendicular to the radius drawn from the center N to the point of tangency, which is point F. Hence, <GWF must also be a right angle.
Angles <TFS, <NGW, <FNG, and <NFW are not guaranteed to be right angles based on the given information. Although the figure suggests that <FNG might be a right angle due to the right triangle formed by the diameter FM and the tangent GA, it is not necessarily always true, as the figure could be drawn in a way that makes <FNG non-right.
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Complete question:
The figure below shows a circle with center N, diameter FM, and tangents GA and FW. Which of the angles must be right angles? Select all that apply.
A) <TFS
B) <NGW
C) <FPT
D) <FNG
E) <NFW
F) <GWF
[ -1 5 7] [9] [x1]
Given A = [ 0 -2 4], B = [6] and x = [x2] [0] Calculate: (a) Al (b) /A (c) 1x (d) x′1 Indicate the dimension of the identity matrix used in each case.
The exercise involves calculations with matrices A, B, and x. We need to perform various operations, including taking the inverse of matrix A, multiplying matrix A by matrix B, multiplying matrix x by the transpose of x, and calculating the dimension of the identity matrix used in each case.
Let's perform the calculations step by step:
(a) To find the inverse of matrix A, denoted as A^(-1), we need to check if matrix A is invertible. If the determinant of A is non-zero, then A^(-1) exists. If the determinant is zero, A is not invertible.
Determinant of A = |A| = 0*(-8*(-8) - 20) + 2(0*(-8) - 40) - 4(02 - (-8)(-8))
= 0 + 0 - 4*(-128)
= 512
Since the determinant is non-zero, matrix A is invertible. To find A^(-1), we can use the formula:
[tex]A^{-1} = (1/|A|) * adj(A)[/tex]
where adj(A) is the adjugate of matrix A. The adjugate can be found by taking the transpose of the cofactor matrix of A.
Calculating the adjugate of A:
Cofactor matrix of A:
C = [0 -8 16]
[0 0 0]
[4 8 0]
Transposing C:
adj(A) = [0 0 4]
[-8 0 8]
[16 0 0]
Calculating [tex]A^{-1}:[/tex]
[tex]A^{-1}= (1/512) * adj(A)[/tex]
= (1/512) * [0 0 4]
[-8 0 8]
[16 0 0]
= [0 0 1/128]
[-1/64 0 1/64]
[1/32 0 0]
(b) To calculate matrix B divided by matrix A, denoted as B/A, we need to multiply matrix B by the inverse of matrix A, which we already found in part (a).
[tex]B/A = B * A^{-1}[/tex]
= [6] * [0 0 1/128]
[-1/64 0 1/64]
[1/32 0 0]
= [60 + 0(-1/64) + 1/1280]
[60 + 00 + 1/640]
[61/32 + 00 + 1/128*0]
= [0]
[0]
[3/512]
(c) To calculate the product of matrix x and the transpose of x, denoted as xx', we simply multiply each element of x by the corresponding element in the transpose of x.
xx' = [x2x2 00]
[00 00]
= [x2^2 0]
[0 0]
(d) The dimension of the identity matrix used in each case:
For part (a), the dimension of the identity matrix used is 3x3 since the inverse of A is a 3x3 matrix.
For part (b), the dimension of the identity matrix used is 3x3 since we are multiplying a 3x1 matrix (B) by the inverse of A, which is a 3x3 matrix.
For part (c), the dimension of the identity matrix used is 2x2 since xx' is a 2x2 matrix.
For part (d), it seems there is a typo in the question, as it asks for x'1 which suggests it should be a column vector. However, x is given as [x2 0] which suggests it is a row vector. Therefore, the dimension of the identity matrix used cannot be determined in this case.
In summary:
(a) A^(-1) = [0 0 1/128]
[-1/64 0 1/64]
[1/32 0 0]
(b) B/A = [0]
[0]
[3/512]
(c) xx' = [x2^2 0]
[0 0]
(d) The dimension of the identity matrix used cannot be determined for part (d) due to the inconsistency in the provided data.
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Write the ratio in the simplest form.
2a/3a
Answer:
2:3
Step-by-step explanation:
2a/3a a is out
cya a
The ratio 2a/3a in the simplest form is 2/3.
What is ratio?Ratio is the way to compare one thing that is related to another thing.
Simplifying ratio means reducing its terms to the lowest possible digits by dividing them with the possible common factor
For example if we have a ratio 3/6 then we divide both terms by 3 to get 3/6 = 1/2 which is the simplest form of ratio 3/6
Given that a ratio 2a/ 3a
2 and 3 have nothing in common . therefore a is the common factor between 2a and 3a
Then divide the terms of ratio by a
⇒ 2a/ 3a = (2a/a)/(3a/a) = (2/1)/(3/1) = 2/3
Therefore, the simplest form of the ratio 2a/3a is 2/3.
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∠A and ∠B are complementary angles. If m∠A=(6x+1) ∘ and m∠B=(8x-23) ∘, then find the measure of∠B.
Given that <A and <B are complementary angles, the measure of angle B is: [tex]41^{\circ}[/tex]
Apply the knowledge of what complimentary angles are to solve for x then find the measure of <B.
Since <A and <B are both complimentary angles, therefore:
<A + <B = 90 degrees.Given:m<A = (6x+1)
m<B = (8x-23)
Substitute[tex](6x+1) + (8x-23) = 90[/tex]
Open the bracket[tex]6x+1 + 8x-23 = 90[/tex]
Add like terms[tex]6x+1 + 8x-23 = 90\\\\14x - 22 = 90[/tex]
Add 22 to both sides[tex]14x = 90 + 22\\\\14x = 112[/tex]
Divide both sides by 14[tex]x = 8[/tex]
Find m<B by plugging in the value of x[tex]m \angle B = 8x-23\\\\m \angle B = 8(8) - 23\\\\m \angle B = 41^{\circ}[/tex]
Therefore, given that <A and <B are complementary angles, the measure of angle B is: [tex]41^{\circ}[/tex]
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PLEASE HELP ME WITH THIS 20 points!!!!!
Answer:
4x+10=28
We simplify the equation to the form, which is simple to understand
4x+10=28
We move all terms containing x to the left and all other terms to the right.
+4x=+28-10
We simplify left and right side of the equation.
+4x=+18
We divide both sides of the equation by 4 to get x.
x=4.5
Step-by-step explanation:
What's the present value of $13,000 discounted back 5 years if the appropriate interest rate is 9%, compounded semiannually? Select the correct answer.
The present value of $13,000 discounted back 5 years at a semi-annual compound rate of 9% can be calculated by the formula:PV = FV / (1 + r/m)^(m*t)Here, PV stands for Present Value FV stands for Future Valuer stands for the interest rate (9%)m is the number of times the interest is compounded (semi-annually, so m = 2)t is the number of years (5)
After substituting the values in the formula, we get:PV = 13,000 / (1 + 0.045)^10PV = 13,000 / 1.55709768854PV = $8,349.58. We can use the concept of present value (PV) and future value (FV) to solve this question. When the cash flow is considered at different points of time, the money's value changes with the time value of money. The time value of money takes into consideration the amount of interest that could be earned on the sum of money if invested. Present value (PV) is a mathematical concept that represents the current worth of a future sum of money, taking into account the time value of money and the given interest rate. PV is calculated by using a discount rate that is determined by the interest rate and the length of time between the present and future payment dates. Future value (FV) is a mathematical concept that represents the future worth of a present sum of money, taking into account the time value of money and the given interest rate. FV is calculated by using a compound interest rate that is determined by the interest rate and the length of time between the present and future payment dates. To calculate the present value of $13,000 discounted back 5 years at a semi-annual compound rate of 9%, we can use the formula PV = FV / (1 + r/m)^(m*t), where PV is the present value, FV is the future value, r is the interest rate, m is the number of times the interest is compounded per year, and t is the number of years. In this case, we know that FV is $13,000, r is 9%, m is 2 (since it is compounded semi-annually), and t is 5. After substituting these values into the formula, we get PV = $8,349.58. Therefore, the present value of $13,000 discounted back 5 years at a semi-annual compound rate of 9% is $8,349.58.
Therefore, the present value of $13,000 discounted back 5 years at a semi-annual compound rate of 9% is $8,349.58.
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If a rectangle is 32 feet long and 8 feet wide what will the new dimension of the rectangle be after a dilation with a scale factor of 7/8 ?
Answer:
a
Step-by-step explanation:
Answer:
72 ft by 18ft
Step-by-step explanation:
What is6.24 divided by 10
Answer:
.624
Step-by-step explanation:
Hope this helps.
Answer: 0.624
Step-by-step explanation:
Find the midpoint M of the line segment joining the points A = (-7, -6) and B = (3, 4).
B
M=
COD
Answer:
The midpoint is (-2,-1)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates of the endpoint and divide by 2
( -7+3)/2 = -4/2 =-2
To find the y coordinate of the midpoint, add the y coordinates of the endpoint and divide by 2
(-6+4)/2 = -2/2 =-1
The midpoint is (-2,-1)
HCF AND LCM OF x^2+5x+6,x^2-4
Answer:
lcm=(x+3)(x+2)(x-2)
Step-by-step explanation:
hcf=(x+2) using different of two squares for x square minus four
HELP HELP WILL GIVE BRAINLEST
Answer:
y = 3/2x + 2
Step-by-step explanation:
first things first write the equation is y = mb+b form which would be 2y = 3x + 14 then divide everything by 2 to get y by itsself --> 3/2x + 7 for an equation to be paralle the equation needs the same slope which is -6 so 3/2(-6) = -9 so the next equation would also start with 3/2x, so you would then do this:
-11 = -9 + b (y = mx+b)
b = -9 + 11 --> b = 2
so the equation is
y = 3/2x + 2
Lines CE and AD intersect at B.
What is the measure of angle DBE?
Group of answer choices
37∘
143∘
53∘
127∘
Answer:
The measure of angle DBE is 37° ⇒ (A)
Step-by-step explanation:
If two lines are intersecting at a point, then every two vertically opposite angles are equal in measure
Example:
If line XY intersects line MN at point Z, then angle MZX, angle NZY are vertically opposite angles, and angle MZY, angle NZX are vertically opposite angles
Let us use this fact to solve the question
∵ Line CE intersects line AD at point B
∴ ∠ ABC and angle ∠DBE are vertically opposite angles
∴ m∠ABC = m∠DBE
∵ m∠ABC = 37°
∴ m∠DBE = 37°
The measure of angle DBE is 37°
Find the y-intercept of the line on the graph.
Answer:
(0, 4)
Step-by-step explanation:
The y-intercept is the y-value when x = 0.
From the graph, we see that when x = 0, y = 4.
What is the minimum possible value of a European call if S = 52;
K = 50, r (annual rate of interest) = 24% and time remaining to
maturity is 3 months? (10 pts)
Note: Use simple rate of interes
The minimum possible value of the European call option is approximately 2.8752.
Given the parameters S = 52 (current stock price), K = 50 (strike price), r = 24% (annual interest rate), and a time to maturity of 3 months, we can calculate the minimum call option value.
The Black-Scholes formula for European call option pricing is as follows:
C = S * N(d1) - K * e^(-r*T) * N(d2)
Where:
C = Call option price
S = Current stock price
N = Cumulative standard normal distribution function
d1 = (ln(S/K) + (r + σ^2/2) * T) / (σ * sqrt(T))
d2 = d1 - σ * sqrt(T)
K = Strike price
r = Annual interest rate
T = Time to maturity (in years)
e = Euler's number (approximately 2.71828)
σ = Implied volatility of the underlying asset
Using the provided values, we can calculate the minimum call option value as follows:
d1 = (ln(52/50) + (0.24 + 0^2/2) * (3/12)) / (0.24 * sqrt(3/12))
= (ln(1.04) + 0.12 * 0.25) / (0.24 * 0.1443)
= (0.0392 + 0.03) / 0.0346
= 1.7507
d2 = 1.7507 - 0.24 * sqrt(3/12)
= 1.7507 - 0.24 * 0.1443
= 1.7507 - 0.0346
= 1.7161
N(d1) = N(1.7507) ≈ 0.9599 (using standard normal distribution table)
N(d2) = N(1.7161) ≈ 0.9569 (using standard normal distribution table)
C = 52 * 0.9599 - 50 * e^(-0.24 * (3/12)) * 0.9569
= 49.9152 - 50 * e^(-0.06) * 0.9569
≈ 49.9152 - 50 * 0.9408
≈ 49.9152 - 47.040
≈ 2.8752
Therefore, the minimum possible value of the European call option is approximately 2.8752.
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x/5 - 3 = 9/1
x=
PLEASE HELP I WILL MARK BRAINLIEST
A bowling ball is dropped from a height of 35 feet. Write a function that gives the height h (in feet) of the bowling ball after t seconds.
Answer:
h(t) = 16t² + 35
Step-by-step explanation:
Given:
Height (h) = 35 feet
Acceleration (a) = 32 ft/sec (approx)
Find:
Equation for height in time
Computation:
h(t) = -(1/2)at² + ut + h
h(t) = -(1/2)(32)t² + (0)(t) + 35
h(t) = -16t² + 35
Convert 87/15 to a mixed number
Answer:
5 and 4/5
Step-by-step explanation:
Answer:
5 4/5 (5 12/15 not reduced)
Step-by-step explanation:
15 will go into 87 5 times.
15x1 = 15. 15x2 = 30. 15x3 = 45. 15x4 = 60. 15x5 = 75. 15x6 = 90. 90 can not go into 87, so you have to work with 75. 87-75=12. So, now your answer is
5 12/15. You are able to divide each of those numbers by 3, so let’s reduce. 12 divided by 3 is 4, and 15 divided by 3 is 5. So your reduced answer is 5 4/5. Hope that helped.
How do you write 1.14 as a percentage
Answer:
114%
Step-by-step explanation:
1.14 multiplied by 100 is 114, therefore your answer is 114%
I hope this helped, please mark Brainliest, thank you!
3(7c-6z=108 what is c equal
To find the value of c in 3(7c - 6z) = 108, simplify and isolate c: c = (18z + 108) / 21.
To find the value of c in the equation 3(7c - 6z) = 108, we can follow the steps below:
1. Start with the given equation: 3(7c - 6z) = 108.
2. Distribute the 3 to the terms inside the parentheses: 21c - 18z = 108.
3. Move the constant term to the other side of the equation by subtracting 108 from both sides: 21c - 18z - 108 = 0.
4. Combine like terms: 21c - 18z - 108 = 0.
5. Simplify the equation: 21c - 18z = 108.
6. Add 18z to both sides of the equation to isolate the term with c: 21c = 18z + 108.
7. Divide both sides of the equation by 21 to solve for c: c = (18z + 108) / 21.
8. The value of c is equal to (18z + 108) divided by 21.
9. Simplify the expression on the right side of the equation: c = (18z + 108) / 21.
10. If necessary, further simplify the expression by dividing 18z and 108 by their greatest common divisor. For example, if both terms are divisible by 3, divide them by 3 to simplify the expression.
11. Now, the equation c = (18z + 108) / 21 is in its simplest form.
12. If you have a specific value for z, you can substitute it into the equation to calculate the corresponding value of c. Simply replace z with the given value and evaluate the expression.
13. If no specific value for z is provided, the equation c = (18z + 108) / 21 represents c in terms of z.
14. Remember to consider any restrictions or conditions that may apply to the variables in the equation. For example, if z cannot equal zero due to division by zero restrictions, make sure to exclude that value from the domain.
15. By following these steps, you can determine the value of c in the equation 3(7c - 6z) = 108.
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2x - x + 7 = x + 3 +4
Answer:
Infinite amount of solutions.
Step-by-step explanation:
Step 1: Write equation
2x - x + 7 = x + 3 + 4
Step 2: Solve for x
Combine like terms: x + 7 = x + 7Subtract 7 on both sides: x = xHere, we see that x is infinite amount of solution. We can plug in any number x and it will render the equation true.
12r2s + 21rs2 – 3rs=
HELP NOW PLSSS enter your answer as mixed number and simpliflied, -4 1/2 x 2 1/2
Answer:
-11 1/4
Step-by-step explanation:
tres pintores van a pinatr tres bardas y entres los tres lo pagaran cuanto pagara cada uno?
The amount paid by person is given as follows:
400.
How to obtain the amount paid by person?The amount paid by person is obtained applying the proportions in the context of the problem.
The total cost is given as follows:
1200.
The number of people is given as follows:
3.
Hence the amount paid by person is given as follows:
400.
Missing InformationThe total cost is of 1200.
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What are the solutions to (X-7)(x+1)(x-9)=0?
Answer:
Just take the opposite of the number in the factor.
x = 7, x = -1, x = 9
One of the ideas that you have explored in previous courses is how to describe a set of data.
One of the ways that you may have seen before is finding an average (also called a mean). Read
the Math Notes box for this lesson to review what a mean is and how to find it. Then find the
mean of the data below.
The number of minutes Pam talked on the phone: 35, 40, 12, 16, 25, 10. Mean =
Answer:
Step-by-step explanation:
M = (35 + 40 + 12 + 16 + 25 + 10)/5
M = 138/5
M = 27.6
I need help on this ASAP
Answer:
The question is wrong
Step-by-step explanation:
neither is the value of x given, nor the value of SU line
PLs solve it RN I need it for my math class. okay so you are smart pls solve this problem.
Answer:
3 is the highest you can go
Step-by-step explanation:
Hope this helps
If 5 items cost $10.25 and all items are the same price, then one item cost
Answer: each item cost 2.05
Step-by-step explanation:
10.25 divided by 5 = 2.05
checking
2.05 times 5 = 10.25
Solve the equation N/-2=-15
Answer:
30
Step-by-step explanation:
N/-2=-15
N= -15 times -2
N= 30
Answer:
N = 30
Step-by-step explanation:
Step 1: Write equation
N/-2 = -15
Step 2: Solve for N
Multiply both sides by -2: N = 30Step 3: Check
Plug in N to verify it's a solution.
30/-2 = -15
-15 = -15
A model rocket fired from the ground at time t can be modeled by the equation h= -490t² + 1120t. When is the height of the model rocket 640 centimeters?
9514 1404 393
Answer:
t = 1 1/7 ≈ 1.1429 seconds
Step-by-step explanation:
Filling in the given height, we can solve for t:
640 = -490t^2 +1120t
49t^2 -112t +64 = 0 . . . . . divide by 10, put in standard form
(7t -8)^2 = 0
t = 8/7 . . . . . . . the value of t that makes the factor(s) zero
The model rocket will reach its maximum height of 640 cm after 1 1/7 seconds.
