The equation of the locus of P is y² - 2xy + (k² + 2k - 18)x + (k² + 4k) - 9 = 0.
Consider a point P(x, y) on the locus of P, which is equidistant from point A(3, k) and the straight line L: y = -3.
The perpendicular distance from a point (x, y) to a straight line Ax + By + C = 0 is given by |Ax + By + C|/√(A² + B²).
The perpendicular distance from point P(x, y) to the line L: y = -3 is given by |y + 3|/√(1² + 0²) = |y + 3|.
The perpendicular distance from point P(x, y) to point A(3, k) is given by √[(x - 3)² + (y - k)²].
Now, as per the given problem, the point P(x, y) is equidistant from point A(3, k) and the straight line L: y = -3.
So, |y + 3| = √[(x - 3)² + (y - k)²].
Squaring on both sides, we get:
y² + 6y + 9 = x² - 6x + 9 + y² - 2ky + k²
Simplifying further, we have:
y² - x² + 6x - 2xy + y² - 2ky = k² + 2k - 9
Combining like terms, we get:
y² - 2xy + (k² + 2k - 18)x + (k² + 4k) - 9 = 0
Hence, the required equation of the locus of P is given by:
y² - 2xy + (k² + 2k - 18)x + (k² + 4k) - 9 = 0.
Thus, The equation of the locus of P is y² - 2xy + (k² + 2k - 18)x + (k² + 4k) - 9 = 0.
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algebra one. solve the logarithmic equation. will rate good for answers.
Bonus 1) Solve 2x-3 = 5x.
$x = 5.8333.$Bonus: Solve $2x - 3 = 5x.$$$2x - 3 = 5x$$$$2x - 5x = 3$$$$-3x = 3$$$$x = \frac{3}{-3} = -1.$$Therefore, $x = -1.$
Let's solve the logarithmic equation by using the following logarithmic rule: $\log_a{b^n} = n\log_a{b}$ with the given equation, $\log_7{x} - \log_7{(x-5)} = 1.$We know that when the subtraction sign is in between two logarithmic terms, we can simplify by using the quotient property of logarithms as follows:$$\log_a\frac{b}{c} = \log_ab - \log_ac.$$Using this rule with the equation above, we can simplify as follows:$$\log_7\frac{x}{x-5} = 1.$$This is the same as saying that $\frac{x}{x-5} = 7^1 = 7.$Let's now solve for $x$ as follows:$$x = 7(x-5)$$$$x = 7x - 35$$$$35 = 6x$$$$x = \frac{35}{6} = 5.8333.$$Therefore, $x = 5.8333.$Bonus: Solve $2x - 3 = 5x.$$$2x - 3 = 5x$$$$2x - 5x = 3$$$$-3x = 3$$$$x = \frac{3}{-3} = -1.$$Therefore, $x = -1.$
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The geometric average of -10%, 20% and 40% is _________.
11.2%
14.8%
20.3%
21.4%
The geometric average of -10%, 20%, and 40% is approximately -20.2%.
To find the geometric average of a set of numbers, you need to multiply them together and then take the nth root, where n is the number of values.
In this case, we have three values: -10%, 20%, and 40%.
Step 1: Convert the percentages to decimal form by dividing by 100.
-10% becomes -0.10
20% becomes 0.20
40% becomes 0.40
Step 2: Multiply the decimal values together.
-0.10 * 0.20 * 0.40 = -0.008
Step 3: Take the cube root (since we have three values) of the result.
∛(-0.008) ≈ -0.202
Step 4: Convert the result back to a percentage by multiplying by 100.
-0.202 * 100 ≈ -20.2%
Therefore, the geometric average of -10%, 20%, and 40% is approximately -20.2%.
None of the given options (11.2%, 14.8%, 20.3%, and 21.4%) matches the calculated value.
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PLEASE HELP AND GIVE ME A STEP BY STEP EXPLAINING I OWE YOU MY LIFE
Answer:
a) ∠BAD = 67.4
b) ∠BDC = 22.6
c) BC = 4.6
Step-by-step explanation:
a) tan θ = opposite/adjacent
In Δ ABD,
tan ∠BAD = DB/AD
tan ∠BAD = 12/5
∠BAD = tan⁻¹(12/5)
∠BAD = 67.4
b) In In Δ ABD,
∠BAD + ∠ABD + ∠ADB = 180°
⇒ ∠ABD = 180 - ∠BAD - ∠ADB
= 180 - 67.4 - 90
∠ABD = 22.6
In trapezium, since AB and DC are parallel,
∠BDC = ∠ABD (alternate interior angles)
⇒ ∠BDC = 22.6
c) In In Δ ABD,
AB² = AD² + DB²
= 5² + 12²
= 25 + 144
= 169
= 13²
AB² = 13²
⇒ AB = 13
In Δ ABD and Δ BDC,
∠ADB = ∠BCD
∠ABD = ∠BDC
Since two angles are equal, the thrid angle must also be equal
∠BAD = ∠BDC
∴ Δ ABD and Δ BDC are similar
∴ the ratio of the corresponding sides should be equal
⇒ [tex]\frac{BD}{AB} = \frac{BC}{AD}= \frac{DC}{BD} \\[/tex]
[tex]\implies \frac{12}{13} = \frac{BC}{5}= \frac{DC}{12} \\\\\\\implies \frac{12}{13} = \frac{BC}{5}\\\\\implies BC = \frac{12*5}{13}\\\\\implies BC = \frac{60}{13}[/tex]
⇒ BC = 4.6
Write an equation for an elliptic curve over Fp or Fq. Find two points on the curve which are not (additive) inverse of each other. Show that the points are indeed on the curve. Find the sum of these points.
p=1051
q=113
To write an equation for an elliptic curve over a finite field Fp or Fq, we can use the Weierstrass equation in the form: [tex]y^2 = x^3 + ax + b[/tex]
where a and b are constants in the field Fp or Fq.
the elliptic curve [tex]y^2 = x^3 + 2x + 3 (mod 17)[/tex] has points (2, 9) and (5, 1) on the curve, which are not additive inverses. The sum of these points can be determined using the elliptic curve point addition algorithm.
Suppose we have an elliptic curve over Fp with the equation:[tex]y^2 = x^3 + ax + b[/tex]
For simplicity, let's assume p = 17, a = 2, and b = 3.
The equation becomes:[tex]y^2 = x^3 + 2x + 3 (mod 17)[/tex]
To find points on the curve, we can substitute different values of x and calculate the corresponding y values.
Let's choose x = 2: [tex]y^2 = 2^3 + 2(2) + 3 = 8 + 4 + 3 = 15 (mod 17)[/tex]
Taking the square root of [tex]15 (mod 17)[/tex], we find y = 9.[tex]y^2 = x^3 + 2x + 3 (mod 17)[/tex]
So, the point (2, 9) lies on the curve. Similarly, we can choose another value of x, let's say x = 5: [tex]y^2 = 5^3 + 2(5) + 3 = 125 + 10 + 3 = 138 (mod 17)[/tex]
Taking the square root of [tex]138 (mod 17)[/tex], we find y = 1. So, the point (5, 1) also lies on the curve. To find the sum of these points, we can use the elliptic curve point addition algorithm.
Note that in this case, the points (2, 9) and (5, 1) are not additive inverses of each other, as their y-coordinates are not negations of each other.
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Ryan obtained a loan of $12,500 at 5.9% compounded quarterly. How long (rounded up to the next payment period) would it take to settle the loan with payments of $2,810 at the end of every quarter? year(s) month(s) Express the answer in years and months, rounded to the next payment period
Ryan obtained a loan of $12,500 at an interest rate of 5.9% compounded quarterly. He wants to know how long it would take to settle the loan by making payments of $2,810 at the end of every quarter.
To find the time it takes to settle the loan, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the loan (the amount to be settled)
P = the initial principal (the loan amount)
r = the annual interest rate (5.9%)
n = the number of compounding periods per year (4, since it's compounded quarterly)
t = the time in years
In this case, we need to find the value of t, so let's rearrange the formula:
t = (log(A/P) / log(1 + r/n)) / n
Now let's substitute the given values into the formula:
A = $12,500 + ($2,810 * x), where x is the number of quarters it takes to settle the loan
P = $12,500
r = 0.059 (converted from 5.9%)
n = 4
We want to find the value of x, so let's plug in the values and solve for x:
x = (log(A/P) / log(1 + r/n)) / n
x = (log($12,500 + ($2,810 * x)) / log(1 + 0.059/4)) / 4
Now, we need to solve this equation to find the value of x.
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Two similar triangular prisms have edge lengths
in the ratio of 2:3. What is the ratio of the
surface areas of the two prisms?
The surface area of a triangular prism is determined by the areas of its two triangular bases and its three rectangular faces. Let's denote the edge lengths of the first prism as 2x and the edge lengths of the second prism as 3x, where x is a common factor.
The surface area of the first prism (A1) is given by:
A1 = 2(base area) + 3(lateral area)
The base area of the first prism is proportional to the square of its edge length:
base area = (2x)^2 = 4x^2
The lateral area of the first prism is proportional to the product of its edge length and its height:
lateral area = 3(2x)(h) = 6xh
Therefore, the surface area of the first prism can be expressed as:
A1 = 4x^2 + 6xh
Similarly, for the second prism, the surface area (A2) can be expressed as:
A2 = 9x^2 + 9xh
To find the ratio of the surface areas, we can divide A2 by A1:
A2/A1 = (9x^2 + 9xh)/(4x^2 + 6xh)
Simplifying this expression is not possible without knowing the specific value or relationship between x and h. Therefore, the ratio of the surface areas of the two prisms cannot be determined solely based on the given information of the edge lengths in a 2:3 ratio.
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Consider a set containing the elements {a,b,c,d}. a. Define all subsets of the set using a decision tree. b. Write the binary representation of each subset. c. What subset corresponds to the binary representation 1011 ?
a. To define all subsets of the set {a,b,c,d} using a decision tree, we can start by considering whether or not each element is included in each subset.
Let's create a decision tree:
1. Start with an empty set: {}
2. Choose to include or exclude 'a':
- Include 'a': {a}
- Exclude 'a': {}
3. For each resulting subset, consider whether or not to include 'b':
- Include 'b' in the subsets containing 'a': {a, b}
- Exclude 'b' in the subsets containing 'a': {a}
- Include 'b' in the subsets without 'a': {b}
- Exclude 'b' in the subsets without 'a': {}
4. Repeat this process for 'c' and 'd' as well:
- Include 'c' in the subsets containing 'a' and 'b': {a, b, c}
- Exclude 'c' in the subsets containing 'a' and 'b': {a, b}
- Include 'c' in the subsets containing 'a' but not 'b': {a, c}
- Exclude 'c' in the subsets containing 'a' but not 'b': {a}
- Include 'c' in the subsets without 'a' or 'b': {c}
- Exclude 'c' in the subsets without 'a' or 'b': {}
- Include 'd' in the subsets containing 'a', 'b', and 'c': {a, b, c, d}
- Exclude 'd' in the subsets containing 'a', 'b', and 'c': {a, b, c}
- Include 'd' in the subsets containing 'a', 'b', but not 'c': {a, b, d}
- Exclude 'd' in the subsets containing 'a', 'b', but not 'c': {a, b}
- Include 'd' in the subsets containing 'a', but not 'b' or 'c': {a, d}
- Exclude 'd' in the subsets containing 'a', but not 'b' or 'c': {a}
- Include 'd' in the subsets without 'a', 'b', or 'c': {d}
- Exclude 'd' in the subsets without 'a', 'b', or 'c': {}
b. To write the binary representation of each subset, we can assign a binary digit to each element in the set. Let's use '1' to indicate the presence of an element and '0' to indicate its absence.
Here are the binary representations of the subsets we found:
- {}: 0000
- {a}: 1000
- {b}: 0100
- {a, b}: 1100
- {c}: 0010
- {a, c}: 1010
- {b, c}: 0110
- {a, b, c}: 1110
- {d}: 0001
- {a, d}: 1001
- {b, d}: 0101
- {a, b, d}: 1101
- {c, d}: 0011
- {a, c, d}: 1011
- {b, c, d}: 0111
- {a, b, c, d}: 1111
c. The binary representation 1011 corresponds to the subset {a, c, d}.
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Choose the standard form equation that equals the combination of the two given equations. 07x-y=-5 1 7x+y=5 072-y=5 7x+y=-5 9) Choose the standard form equation that equals the combination of the two given equations. Ox-y=14 7x +3=5 and y-1=6 2- 4y = -14 4x - y = -14 4x - y = -4 42 +5= -4 and y-3=2
The standard form equation that equals the combination of the two given equations, \(07x-y=-5\) and \(7x+y=5\), is \(14x = 0\).
To find the combination of these two equations, we can add them together. When we add the left sides of the equations, we get \(07x + 7x = 14x\). Similarly, when we add the right sides, we get \(-y + y = 0\), and \(5 + (-5) = 0\).
Therefore, the combined equation in standard form is \(14x = 0\).
Regarding the second set of equations provided, \(0x-y=14\) and \(7x + 3 = 5\) and \(y-1=6\) and \(2- 4y = -14\), none of these equations can be combined to form a standard form equation. The first equation is already in standard form, but it does not relate to the other equations given. The remaining equations do not involve both \(x\) and \(y\), and therefore cannot be combined into a single standard form equation.
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12. Extend the meaning of a whole-number exponent. a n
= n factors a⋅a⋅a⋯a,
where a is any integer. Use this definition to find the following values. a. 2 4
b. (−3) 3
c. (−2) 4
d. (−5) 2
e. (−3) 5
f. (−2) 6
The result of the whole-number exponent expressions are
a. 16
b. -27
c. 16
d. 25
e. -243
f. 64
How to solve the expressionsUsing the definition of whole-number exponent, we can multiply the base integer by itself as many times as the exponent indicates.
For positive exponents, the result is a repeated multiplication of the base. For negative exponents, the result is the reciprocal of the repeated multiplication.
a. 2⁴ = 2 * 2 * 2 * 2 = 16
b. (-3)³ = (-3) * (-3) * (-3) = -27
c. (-2)⁴ = (-2) * (-2) * (-2) * (-2) = 16
d. (-5)² = (-5) * (-5) = 25
e. (-3)⁵ = (-3) * (-3) * (-3) * (-3) * (-3) = -243
f. (-2)⁶ = (-2) * (-2) * (-2) * (-2) * (-2) * (-2) = 64
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The values are 16, -27, 26, 25, -243, 64
Using the extended definition of a whole-number exponent, we can find the values as follows:
a. 2^4 = 2 × 2 × 2 × 2 = 16
b. (-3)^3 = (-3) × (-3) × (-3) = -27
c. (-2)^4 = (-2) × (-2) × (-2) × (-2) = 16
d. (-5)^2 = (-5) × (-5) = 25
e. (-3)^5 = (-3) × (-3) × (-3) × (-3) × (-3) = -243
f. (-2)^6 = (-2) × (-2) × (-2) × (-2) × (-2) × (-2) = 64
So the values are:
a. 2^4 = 16
b. (-3)^3 = -27
c. (-2)^4 = 16
d. (-5)^2 = 25
e. (-3)^5 = -243
f. (-2)^6 = 64
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Find the first four nonzero terms in a power series expansion about x=0 for a general solution to the given differential equation. y ′
+(x+4)y=0 y(x)=+⋯ (Type an expression in terms of a 0
that includes all terms up to order 3.)
The general solution of the differential equation y ′ + (x+4)y = 0 is equal to y(x) = 0.
To find the power series expansion for the general solution of the differential equation,
Assume a power series of the form,
y(x) = a₀ + a₁x + a₂x²+ a₃x³ + ...
Differentiating y(x) term by term, we have,
y'(x) = a₁ + 2a₂x + 3a₃x² + ...
Substituting these into the differential equation, we get,
(a₁ + 2a₂x + 3a₃x² + ...) + (x + 4)(a₀ + a₁x + a₂x² + a₃x³ + ...) = 0
Expanding the equation and collecting like terms, we have,
a₁ + (a₀ + 4a₁)x + (2a₂ + a₁)x² + (3a₃ + a₂)x³ + ... = 0
Equating coefficients of like powers of x to zero, we can find the values of a₁, a₂, a₃,....
For the first term, equating the coefficient of x⁰ to zero gives,
a₁ + a₀ = 0 → a₁ = -a₀
For the second term, equating the coefficient of x¹ to zero gives,
a₀ + 4a₁ = 0
Substituting the value of a₁ from the first term, we get,
a₀ + 4(-a₀) = 0
⇒-3a₀ = 0
⇒a₀= 0
Since a₀ = 0, the second equation becomes,
0 + 4a₁ = 0
⇒4a₁ = 0
⇒a₁= 0
Continuing in this manner, we can find the values of a₂, a₃, and so on.
For the third term, equating the coefficient of x² to zero gives,
2a₂ + a₁ = 0
⇒2a₂+ 0 = 0
⇒a₂ = 0
For the fourth term, equating the coefficient of x³ to zero gives,
3a₃ + a₂= 0
⇒3a₃ + 0 = 0
⇒a₃ = 0
The first four nonzero terms in the power series expansion are,
y(x) = a₀ + a₁x + a₂x² + a₃x³ + ...
= 0 + 0x + 0x² + 0x³+ ...
= 0
Therefore, the general solution to the given differential equation is
y(x) = 0.
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You are told that an event will happen. Which of the following probabilities describes, this event? Select one: a. 0.5 b. 1 c. 0.2 d. 0
The probability describing this event is 1.
The probability of an event is a measure of the likelihood that the event will occur. In this case, when it is stated that an event will happen, the probability of that event occurring is 1. A probability of 1 indicates absolute certainty that the event will happen. It means that the event is guaranteed to occur and there is no chance of it not happening.
In probability theory, a probability of 1 represents a certain event. It signifies that the event will occur without any doubt. This certainty arises when all possible outcomes are accounted for, and there is no room for any other outcome to happen. In other words, when the probability is 1, there is a 100% chance of the event taking place. This is in contrast to probabilities less than 1, where there is some level of uncertainty or possibility for other outcomes to occur.
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Given the first order ODE, xdy/dx=3xe^x−2y+5x^2 which of the following(s) is/are correct? Select ALL that apply. o The equation is EXACT o The equation is LINEAR o y=0 is a solution o The equation is SEPARABLE o The equation is HOMOGENEOUS
the only correct option is that the equation is linear. The correct option is 2.
The given first-order ODE is `xdy/dx = 3xe^x - 2y + 5x^2`. Let's analyze each option:
- The equation is not exact because it cannot be written in the form `M(x,y)dx + N(x,y)dy = 0`.
- The equation is linear because it can be written in the form
`dy/dx + P(x)y = Q(x)`.
- `y=0` is not a solution to the given ODE.
- The equation is not separable because it cannot be written in the form `g(y)dy = f(x)dx`.
- The equation is not homogeneous because it cannot be written in the form `dy/dx = F(y/x)`.
So, the only correct option is that the equation is linear.
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Please help thank you !!
Hiya, hope these help! :)
Formula for a triangle: A=1/2(base of triangle x height of triangle)
Triangle a: 120cm²
A= 1/2(b x h)
A= 1/2(20 x 12)
A= 1/2 (240)
A= 120
Triangle b: 72cm²
A= 1/2(b x h)
A= 1/2(12 x 12)
A= 1/2 (144)
A= 72
Triangle c: 154cm²
A= 1/2 (b x h)
A= 1/2 (28 x 11)
A= 1/2 (308)
A= 154
Triangle d: 49cm²
A= 1/2 (b x h)
A= 1/2 (14 x 7)
A= 1/2 (98)
A= 49
Triangle e: 105cm²
A= 1/2 (b x h)
A= 1/2 (14 x 15)
A= 1/2 (210)
A= 105
Triangle f: 160cm²
A= 1/2 (b x h)
A= 1/2 (20 x 16)
A= 1/2 (320)
A= 160
Triangle g is missing the base number! It's not shown fully in the screenshot, therefore it will just be whatever answer is leftover! :)
Triangle h: 288cm²
A= 1/2 (b x h)
A= 1/2 (36 x 16)
A= 1/2 (576)
A= 288
Let me know if you have any more questions!
Consider the given matrix B= row1(2 2 0) ; row2(1 0
1); row3(0 1 1). Find the det(B) and use it to determine whether or
not B is invertible, and if so, find B^-1 ( hint: use the matrix
equation BX= I)
To find the determinant of matrix B, we can use the formula for a 3x3 matrix: det(B) = (2 * (0 * 1 - 1 * 1)) - (2 * (1 * 1 - 0 * 1)) + (0 * (1 * 1 - 0 * 1))
Simplifying this expression, we get:
det(B) = (2 * (-1)) - (2 * (1)) + (0 * (1))
det(B) = -2 - 2 + 0
det(B) = -4
The determinant of matrix B is -4.
Since the determinant is non-zero, B is invertible.
To find the inverse of B, we can use the matrix equation B * X = I, where X is the inverse of B and I is the identity matrix.
B * X = I
Using the given values of B, we have:
|2 2 0| * |x y z| = |1 0 0|
|1 0 1| |a b c| |0 1 0|
|0 1 1| |p q r| |0 0 1|
Solving this system of equations, we can find the values of x, y, z, a, b, c, p, q, and r, which will give us the inverse matrix B^-1.
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Two vertices of a graph are adjacent when which of the following is true? a. There is a path of length 2 that connects them b. Both vertices are isolated c. Both vertices have even degrees d. There is an edge that between them
Two vertices of a graph are adjacent when there is an edge that connects them. This is true for option (d).
Definition of vertices:
Vertices refer to the points or nodes on a graph that are connected by edges.
Definition of adjacent:Two vertices are adjacent when they are directly connected by an edge on the graph.
Definition of graph:Graph refers to a collection of vertices connected by edges. Graphs are used to represent networks, relationships, or connections between objects. Graph theory is a branch of mathematics that studies graphs and their properties.
Therefore, option d is the correct answer i.e. There is an edge that between them.
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pls help if you can asap!!!!
Answer: A
Step-by-step explanation: I would say A because the angle is greater than 90 degrees
Answer:
We have supplementary angles.
76 + 3x + 2 = 180
3x + 78 = 180
3x = 102
x = 34
Evan and Peter have a radio show that has 2 parts. They need 4 fewer than 11 songs in the first part. In the second part, they need 5 fewer than 3 times the number of songs in the first part. Write an expression for the number of songs they need for their show. A.
(11−4)+3×11−4−5 B. (11−4)+3×(11−4)−5 C. (11−4)+3−4×11−5 D. (11−4)+3−5×(11−4)
Part B How many songs do they need for their show? A. 39 songs B. 31 songs C. 25 songs D. 23 songs.
Answer: they need 28 songs for their show, which corresponds to option D.
Step-by-step explanation:
The expression for the number of songs they need for their show is (11-4) + 3×(11-4) - 5, which corresponds to option B.
To find how many songs they need for their show, we can evaluate the expression:
(11-4) + 3×(11-4) - 5 = 7 + 3×7 - 5 = 7 + 21 - 5 = 28.
the last option is sss, pls help asap if you can!!!!!
The SAS congruence theorem proves the similarity of triangles ABX and ABY.
What is the Side-Angle-Side congruence theorem?The Side-Angle-Side (SAS) congruence theorem states that if two sides of two similar triangles form a proportional relationship, and the angle measure between these two triangles is the same, then the two triangles are congruent.
In this problem, we have that the angle B is equals for both triangles, and the two sides between the angle B, which are BA and BX = BY, in each triangle, form a proportional relationship.
Hence the SAS theorem holds true for the triangle in this problem.
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Evaluate each determinant.
[4 6 -1 2 3 2 1 -1 1]
The determinant of the given matrix is 15.
By observing the matrix [4 6 -1 2 3 2 1 -1 1], we get the value of the determinant to be 15.
To verify this result, we can compute the determinant as follows:`Δ = [4(3(-1) - (-1)(2)) - 6(2(-1) - 1(2)) + (-1)(2(2) - 3(1))]
`Expanding the equation, we get: `Δ = [4(-5) - 6(-6) + (-1)(-1)]`
Δ = [-20 + 36 - 1]
`Δ = 15`
Therefore, the determinant of the given matrix is 15.
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What is the relationship shown by this scattered plot?
Answer:
As the cost of a gym membership goes up, the number of new gym memberships sold goes down.
The length and breadth of a rectangular field are in the ratio 8:3. If the perimeter of the field is 99 m
, find the length of the field.
Answer:
36 m
Step-by-step explanation:
Perimeter = 2L + 2w = 99
2(L + w) = 99
L = length = 8x
w = width = 3x
2(8x + 3x) = 99
16x + 6x = 99
22x = 99
x = 99/22 = 4.5
L = 8x = 8(4.5) = 36
If m LAOD = (10x - 7)° and m L BOC = (7x + 11)°, what is m L BOC?
Which of these is NOT a method for proving that a quadrilateral is a parallelogram? show both pairs of opposite sides are congruent show one pair of opposite sides are parallel AND congruent show that one pair of opposite sides is parallel and the other is not parallel show both pairs of opposite sides are parallel
d) An aircraft is in a position such that there is a DME at a bearing of 020°(M)and a range of 50 NM and another one at a bearing of 090°(M) and a range of 60NM. (i) What is the Horizontal Dilution of Precision (HDOP) for this geometry? (ii) What is the effect on HDOP, if the bearing to the first DME changed to 060° (M). (iii) What is the effect on HDOP, if, in part Q5(d)(ii), a third DME were acquired at a bearing of 180°(M)
The Horizontal Dilution of Precision (HDOP) for the given geometry is 1.25.
The HDOP is a measure of the accuracy of a navigation solution, particularly in terms of horizontal position. It is influenced by the geometric arrangement of satellites or reference points. In this case, we have two DME (Distance Measuring Equipment) stations with their respective bearings and ranges.
To calculate HDOP, we need to determine the position dilution of precision (PDOP) and then isolate the horizontal component. PDOP is the combination of dilutions of precision in the three-dimensional space.
(i) To calculate PDOP, we consider the two DME stations. The PDOP formula is given by PDOP = sqrt(HDOP^2 + VDOP^2), where HDOP is the horizontal dilution of precision and VDOP is the vertical dilution of precision. Since we are only concerned with HDOP, we can assume VDOP to be zero in this case. So PDOP = HDOP.
PDOP = sqrt((50/60)^2 + (60/60)^2) = sqrt(25/36 + 1) ≈ 1.25
(ii) If the bearing to the first DME changes to 060° (M), the geometry of the system is altered. This change will affect the PDOP and subsequently the HDOP. However, without additional information about the new range, we cannot determine the exact impact on HDOP.
(iii) If a third DME is acquired at a bearing of 180° (M), the geometry of the system becomes more favorable. The additional reference point allows for better triangulation and redundancy, which can improve the accuracy of the navigation solution. Consequently, the HDOP is likely to decrease, indicating a higher level of precision.
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in the x-plane , what is the y-intercetp of graph of the equation y=6(x-1/2) (x+3)?
Answer:
Y-intercept: (0,-9)
Step-by-step explanation:
to find the y-intercept, subsitute in 0 for x and solve for y.
if you found this helpful please give a brainliest!! tysm<3
Answer:
Step-by-step explanation:
y=6(x-1/2) (x+3)
y=6(0-1/2) (0+3)
y=6(-1/2)(3)
y=-9
y-intercept is -9
Which graph shows a function and its?
The graph shows a function and its is the graph in option A.
What is inverse function and their graphs?The original path is reflected on the line y = x. The two functions are said to be inverses of one another if the graphs of both functions are symmetric with respect to the line y = x. This is due to the fact that (y, x) lies on the inverse function of the function if (x, y) lies on the original function.
The inverse function is shown on a graph with the use of a vertical line test. The line has a slope and travels through the origin.
Instance is the f(x) = 2x + 5 = y. Then, is the inverse of [tex]g(y) = \frac{ (y-5)}{2} = x[/tex] f(x).Reflecting over the y and x gives us the function of the inverse.
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Three siblings Trust, Hardlife and Innocent share 42 chocolate sweets according to the ratio 3:6:5, respectively. Their father buys 30 more chocolate sweets and gives 10 to each of the siblings. What is the new ratio of the sibling share of sweets? A. 19:28:35 B. 13:16:15 C. 4:7:6 D. 10:19:16 Question 19 The linear equation 5y - 3x -4 = 0 can be written in the form y=mx+c. Find the values of m and c. A. m-3,c=0.8 B. m = 0.6, c-4 C. m = -3, c = -4 D. m = m = 0.6, c = 0.8 Question 20 Three business partners Shelly-Ann, Elaine and Shericka share R150 000 profit from an invest- ment as follows: Shelly-Ann gets R57000 and Shericka gets twice as much as Elaine. How much money does Elaine receive? A. R124000 B. R101 000 C. R62000 D. R31000 ( |
Previous question
18: The new ratio of the sibling share of sweets is 19:28:25, which is not among the given options. Therefore, none of the options A, B, C, or D is correct.
19: we have m = -3/5, c = 4/5. None of the options is correct.
20: Elaine receives R31,000, means the correct option is D. R31,000.
18: The original ratio of chocolate sweets for Trust, Hardlife, and Innocent is 3:6:5.
Total parts = 3 + 6 + 5 = 14
Trust's share = (3/14) * 42 = 9
Hardlife's share = (6/14) * 42 = 18
Innocent's share = (5/14) * 42 = 15
After the father buys 30 more chocolate sweets and gives 10 to each sibling:
Trust's new share = 9 + 10 = 19
Hardlife's new share = 18 + 10 = 28
Innocent's new share = 15 + 10 = 25
The new sibling share of sweets ratio is 19:28:25, which is not one of the possibilities provided. As a result, none of the options A, B, C, or D are correct.
19: The linear equation 5y - 3x - 4 = 0 can be written in the form y = mx + c.
Comparing the equation with y = mx + c, we have:
m = -3/5
c = 4/5
Therefore, the values of m and c are not among the given options A, B, C, or D. None of the options is correct.
20: Let Elaine's share be x.
Shericka's share = 2 * Elaine's share = 2x
Shelly-Ann's share = R57,000
Total share = Shelly-Ann's share + Shericka's share + Elaine's share
R150,000 = R57,000 + 2x + x
R150,000 = 3x + R57,000
3x = R150,000 - R57,000
3x = R93,000
x = R93,000 / 3
x = R31,000
Elaine receives R31,000.
Therefore, the correct answer is option D. R31,000.
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Under a dilation, the point (−3, −4) is moved to (−15, −20).
What is the scale factor of the dilation?
Answer: 5
Step-by-step explanation:
So, first we want to find what number times -3 is -15, and what number times -4 is -20 because its a dialation.
-3 times 5 is -15, and -4 times 5 is -20. Therefor the answer is 5.
Solve the following systems of equations simultaneously. (x-1)² +² X = +y = 32 1
The solutions to the given system of equations simultaneously are (x, y) = (-4, -7) and (2, 5).
Given the equation, we have:(x - 1)² + y² = 32 ---(1)x² + y = 9 ---(2)
Multiplying equation (2) by 4, we get :
4x² + 4y = 36 ---(3)
Multiplying equation (1) by 4, we get:4(x - 1)² + 4y² = 128 ------(4)
Expanding equation (4)
4[x² - 2x + 1] + 4y²
= 1284x² - 8x + 4 + 4y²
= 128
Dividing by 4 on both sides: x² - 2x + y² = 31 ---(5)
Now we can write equations (3) and (5) as a system of equations:
4x² + 4y = 36 ---(6)
x² - 2x + y² = 31 ---(7)
To solve these equations simultaneously, we can solve one equation in terms of one variable and substitute it into the other equation to solve for the other variable.
Let's solve equation (6) for y:
y = (36 - 4x²)/4 = 9 - x² ------(8)
Substituting equation (8) into equation (7), we get:
x² - 2x + (9 - x²)
= 31-x² - 2 x + 9
= 31-x² - 2x - 22
= 0-x² - 2x + 22 = 0
Multiplying by -1 on both sides:x² + 2x - 22 = 0
Factoring the quadratic expression, we get:(x + 4)(x - 2) = 0
Equating each factor to zero gives:x + 4 = 0 or x - 2 = 0
x = -4 or x = 2
Substituting the value of x = -4 in equation (8) gives:
y = 9 - (-4)² =
-7
Substituting the value of x = 2 in equation (8) gives:
y = 9 - 2²
= 5
Therefore, the solutions to the given system of equations are (x, y) = (-4, -7) and (2, 5).
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Determine whether each sequence is arithmetic. If it is, identify the common difference. 1,1,1, , ,
No, 1,1,1, , , is not an arithmetic sequence because there is no common difference between the terms.
The given sequence is 1,1,1, , ,. If it is arithmetic, then we need to identify the common difference. Let's try to find out the common difference between the terms of the sequence 1,1,1, , ,There is no clear common difference between the terms of the sequence given. There is no pattern to determine the next term or terms in the sequence.
Therefore, we can say that the sequence is not arithmetic. So, the answer to this question is: No, the sequence is not arithmetic because there is no common difference between the terms.
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