Answer:
90 degrees
Step-by-step explanation:
Same side interior angles, or consecutive angles, are supplementary (angle measures add up to 180 degrees). Since both angles have measures 3x degrees, the angles are congruent (same angle measure). In Geometry, when two angles are congruent and supplementary, the two angles are right angles (angles measuring 90 degrees). Therefore the angle measures of the two angles are 90 degrees and 90 degrees.
Or, to solve this algebraically, add 3x and 3x, let it equal to 180 degrees, solve for x, and find the angle measures by substituting x into the expression.
3x + 3x = 180
6x = 180
x = 30
3x = 3*30 = 90
Use the method of undetermined coefficients to solve the given nonhomogeneous system. x' = −1 5 −1 1 x + sin(t) −2 cos(t)
It looks like the system is
[tex]x' = \begin{bmatrix} -1 & 5 \\ -1 & 1 \end{bmatrix} x + \begin{bmatrix} \sin(t) \\ -2 \cos(t) \end{bmatrix}[/tex]
Compute the eigenvalues of the coefficient matrix.
[tex]\begin{vmatrix} -1 - \lambda & 5 \\ -1 & 1 - \lambda \end{vmatrix} = \lambda^2 + 4 = 0 \implies \lambda = \pm2i[/tex]
For [tex]\lambda = 2i[/tex], the corresponding eigenvector is [tex]\eta=\begin{bmatrix}\eta_1&\eta_2\end{bmatrix}^\top[/tex] such that
[tex]\begin{bmatrix} -1 - 2i & 5 \\ -1 & 1 - 2i \end{bmatrix} \begin{bmatrix} \eta_1 \\ \eta_2 \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix}[/tex]
Notice that the first row is 1 + 2i times the second row, so
[tex](1+2i) \eta_1 - 5\eta_2 = 0[/tex]
Let [tex]\eta_1 = 1-2i[/tex]; then [tex]\eta_2=1[/tex], so that
[tex]\begin{bmatrix} -1 & 5 \\ -1 & 1 \end{bmatrix} \begin{bmatrix} 1 - 2i \\ 1 \end{bmatrix} = 2i \begin{bmatrix} 1 - 2i \\ 1 \end{bmatrix}[/tex]
The eigenvector corresponding to [tex]\lambda=-2i[/tex] is the complex conjugate of [tex]\eta[/tex].
So, the characteristic solution to the homogeneous system is
[tex]x = C_1 e^{2it} \begin{bmatrix} 1 - 2i \\ 1 \end{bmatrix} + C_2 e^{-2it} \begin{bmatrix} 1 + 2i \\ 1 \end{bmatrix}[/tex]
The characteristic solution contains [tex]\cos(2t)[/tex] and [tex]\sin(2t)[/tex], both of which are linearly independent to [tex]\cos(t)[/tex] and [tex]\sin(t)[/tex]. So for the nonhomogeneous part, we consider the ansatz particular solution
[tex]x = \cos(t) \begin{bmatrix} a \\ b \end{bmatrix} + \sin(t) \begin{bmatrix} c \\ d \end{bmatrix}[/tex]
Differentiating this and substituting into the ODE system gives
[tex]-\sin(t) \begin{bmatrix} a \\ b \end{bmatrix} + \cos(t) \begin{bmatrix} c \\ d \end{bmatrix} = \begin{bmatrix} -1 & 5 \\ -1 & 1 \end{bmatrix} \left(\cos(t) \begin{bmatrix} a \\ b \end{bmatrix} + \sin(t) \begin{bmatrix} c \\ d \end{bmatrix}\right) + \begin{bmatrix} \sin(t) \\ -2 \cos(t) \end{bmatrix}[/tex]
[tex]\implies \begin{cases}a - 5c + d = 1 \\ b - c + d = 0 \\ 5a - b + c = 0 \\ a - b + d = -2 \end{cases} \implies a=\dfrac{11}{41}, b=\dfrac{38}{41}, c=-\dfrac{17}{41}, d=-\dfrac{55}{41}[/tex]
Then the general solution to the system is
[tex]x = C_1 e^{2it} \begin{bmatrix} 1 - 2i \\ 1 \end{bmatrix} + C_2 e^{-2it} \begin{bmatrix} 1 + 2i \\ 1 \end{bmatrix} + \dfrac1{41} \cos(t) \begin{bmatrix} 11 \\ 38 \end{bmatrix} - \dfrac1{41} \sin(t) \begin{bmatrix} 17 \\ 55 \end{bmatrix}[/tex]
Determine how much this home would cost to replace: 3,800 square feet at $102.00 per square foot
Answer: $
___
This is exactly what the questions look like, can’t find anything.
The minor arc measures of circle Z are shown in the figure.
Circle Z is shown. Radii Z Y, Z X, Z W, Z V, Z U, and Z T are shown. The arc measure of Y X is 71 degrees, the arc measure of X W is 32 degrees, the arc measure of W V is 71 degrees, the arc measure of V U is 78 degrees, the arc measure of U T is 54 degrees, and the arc measure of T Y is 54 degrees.
Use the drop-down menus to complete each statement.
Angle UZT is congruent to angle
.
Angle VZW is congruent to angle
.
The completed statement are:
Angle UZT is congruent to angle TZY.Angle VZW is congruent to angle YZX.What is the angle about?Part A:
Angle UZT is congruent to angle TZY.
Using the image attached figure, we can see that:
∠UZT = 54°
∠TZY = 54°
Hence one can say that ∠TZY = ∠UZT are both congruent angles.
Part B:
Angle VZW is congruent to angle YZX.
Using the image attached attached, we can see that:
∠VZW = 71°
∠YZX = 71°
Hence, ∠YZX = ∠VZW are both regarded as congruent angles .
Therefore, The completed statement are:
Angle UZT is congruent to angle TZY.Angle VZW is congruent to angle YZX.Learn more about Angles from
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Answer: a, c
Step-by-step explanation:
uh help please dont know whats wrong step by step will help a lot
let's keep in mind that i² = -1, and let's use the conjugate of the denominator.
[tex]\cfrac{2+5i}{3-2i}\cdot \cfrac{3+2i}{3+2i}\implies \cfrac{(2+5i)(3+2i)}{\underset{\textit{difference of squares}}{(3-2i)(3+2i)}}\implies \cfrac{6+4i+15i+10i^2}{(3)^2~~ - ~~(2i)^2} \\\\\\ \cfrac{6+19i+10(\stackrel{i^2}{-1})}{9~~ - ~~(2^2 i^2)}\implies \cfrac{6+19i-10}{9~~ - ~~4(\underset{i^2}{-1})}\implies \cfrac{-4+19i}{9+4}\implies -\cfrac{4}{13}+\cfrac{19i}{13}[/tex]
PLEASE HELP ME ASAP! BEING TIMED
If the tens digit of a number is 4 times the units digit and the hundreds digit is twice the tens digit, is the number even or odd?
The number is 841
So we can see that the number is odd.
Is the number even or odd?
Here we have a 3-digit number that can be written as:
a*100 + b*10 + c
Here we know that:
"the tens digit of a number is 4 times the units digit"
b = 4*c
"the hundreds digit is twice the tens digit"
a = 2*b
Now, remember that a, b, and c, are numbers on the set {0, 1, ..., 8, 9}
And if we replace the first equation into the second, we get:
a = 2*(4*c) = 8*c
Now, the only value of c that we can use such that a is a single digit whole number is c = 1
(if c = 0, then our number is zero)
a = 8*1 = 8
b = 4*1 = 4
c = 1
The number is 841
So we can see that the number is odd.
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Function a (b) relates the area of a trapeze with a given height of 14 and a base length of 5 with the length of its other base. it takes the other base value as input and returns the trapeze area as output. what equation below represents the inverse function b (a), which takes the trapeze area as input and returns the length of the other base as an output?
The function accepts the trapezoid's area as input and returns as output the length of the other base exists A(x)/7-5=x.
What is an area of a trapezoid?The function of the trapezoid area exists:
[tex]A(x)=(B+b)*h/2[/tex]
where B exists the bases
h stands the height.
Given a height of 14 and one base length of 5 with the length of its other base
With the given data:
h = 14B and b =5 and x (it may vary which one exists bigger)
So that function becomes:
[tex]$A(x)=(5+x)*14/2[/tex]
A(x) = (5 + x) [tex]*[/tex] 7
So if you want the inverse function, to find the value of x:
A(x) / 7 = 5 + x
A(x )/ 7 - 5 = x
Therefore, the function accepts the trapezoid's area as input and returns as output the length of the other base exists A(x)/7-5=x.
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Pls help
Write the equation for a parabola with a focus at (-4,3) and a directrix at y=5
Answer:
y=(1/-4)(x+4)^2 +4
Step-by-step explanation:
Don't ask
Need help! Someone please help!!!
Answer:
B. Ounces of water consumed compared with the number of same-size bottles dr*nk
Step-by-step explanation:
A constant rate of change means that the two values should be linear. Let's analyze why the other three options are wrong:
A. The distance between different airports can be very different (i.e the distance between Airport 1 and Airport 2 is 20 km and the distance between Airport 2 and Airport 3 is 500 km), meaning that the distance the airplane travels and the number of airports it visits are not linear.
C. Similar to A, the point scored in different quarters can be very different (i.e. 0 points scored in the 1st quarter, 35 points scored in the 2nd quarter, etc.)
D. Similarly, the number of fish in a pond can either be very large or very small, even if the volume of the pond stays the same
B is correct because the bottles are the same size, meaning that if you drink x bottles of 2-ounce bottles, you will always drink 2x ounces of water, no matter what, creating a linear function.
Could someone explain how to get the correct answer when trying to find the f(X) and g(X) on a graph like this? Thanks!
Answer:
f(3) = g (3)
Step-by-step explanation:
graphically, we notice that the graphs of f and g intersect
at the point of coordinates (3 , 0)
Then
f(3) = 6 = g(3)
Then
f(3) = g (3)
1. Part A. Graph the following coordinates on the grid below.
(4, 3), (4,-5), (-2, 3), and (-2,-5)
Answer:
Step-by-step explanation:
a) start at the origin (0,0) then go 4 boxes to the right, 3 up
b) start at the origin (0,0) then go 4 boxes to the right, 5 down
c) start at the origin (0,0) then go 2 boxes to the left, 3 up
d) start at the origin (0,0) then go 2 boxes to the left, 5 down
The chance of getting a viral infection is 0.0005. out of 10,000 people, about how many of them are expected to get infected?
The computation shows that the number of people expected to get infected is 5.
How to calculate the value?It should be noted that the chance of chance of getting a viral infection is 0.0005. out of 10,000 people.
Therefore, the number of people expected to get infected will be:
= 0.0005 × 10000
= 5
The number of people expected to get infected is 5.
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Select the correct answer. a number is selected at random from the set {2, 3, 4, ... 10}. which event, by definition, covers the entire sample space of this experiment?
[tex]( \: 2 \: 3 \: 4 \: 5 \:6 \: 7 \:8 \: 9 \: 10 \: )[/tex]
[tex]Event \: P \\P:"choosing \: a \: natural \: number \: from \: 2 \: to \: 10 \: inclusive"[/tex]
6. If x is the largest of three consecutive integers, represent the sum of the three integers.
a) If x is the largest of three consecutive integers, how do we represent the three integers?
b) How do we convert this information into a solvable equation?
c) Find the sum
Answer:
See below
Step-by-step explanation:
x = largest
x-1 previous
x -2 smallest
sum = x + x-1 + x-2
sum = 3x -3
An airplane covers 3500 km in three hours. What would be the distance covered by the plane in 4.5 hours if it flies at the same constant speed. ( I need the proportion equation please help ASAP.)
Answer:
5,250 km
Step-by-step explanation:
[tex]\frac{hours}{miles}[/tex] = [tex]\frac{hours}{miles}[/tex]
[tex]\frac{3}{3500}[/tex] = [tex]\frac{4.5}{x}[/tex] Cross Multiply
3x = (4.5)(3500)
3x = 15750 Divide both sides of the equation by 3
x = 5,250
The graph shows two lines, A and B:
A graph is shown with x and y axes labeled from 0 to 6 at increments of 1. A straight line labeled A joins the ordered pair 2, 6 with the ordered pair 5, 0. Another straight line labeled B joins the ordered pair 0, 2 with the ordered pair 6, 6.
Based on the graph, which statement is correct about the solution to the system of equations for lines A and B?
(3, 4) is the solution to both lines A and B.
(3, 4) is the solution to line A but not to line B.
(0, 2) is the solution to both lines A and B.
(0, 2) is the solution to line A but not to line B.
Answer:
Part A) The system has one solution
Part B) The solution is the point (4,4)
i believe
Let S1 be the amount allowing 10% discount on the price of some goods and then adding 10% VAT. Let S2 be the amount adding 10% VAT and then allowing 10% discount. Which of the following is true? (i) S1 > S2 (ii) S1 < S2 (iii) S1 = S2 (iv) Cant be decided
Using decimal multipliers, the correct statement is given by:
(iii) S1 = S2.
What is a decimal multiplier?Increases of a% or decreases of a% re represented by decimal values, as follows:
The equivalent multiplier for an increase of a% is given by: [tex]\frac{100 + a}{100}[/tex]The equivalent multiplier for an decrease of a% is given by: [tex]\frac{100 - a}{100}[/tex]Hence, in the context of this problem:
An increase of 10% is represented by 1.1.A decrease of 10% is represented by 0.9.The options are given as follows:
S1 = 0.9 x 1.1 = 0.99.S2 = 1.1 x 0.9 = 0.99.They are equal, hence option (iii) is correct.
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Based on these segment lengths, which group of segments cannot form a triangle? a. 12, 7, 8 b. 8, 7, 13 c. 1, 2, 3 d. 80, 140, 70
(D) 80°, 140°, and 70° group of segments cannot form a triangle.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC represents a triangle with vertices A, B, and C.In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane. In other words, the triangle is contained in just one plane, and every triangle is contained in some plane. There is just one plane and all triangles are enclosed in it if the entire geometry is merely the Euclidean plane; but, in higher-dimensional Euclidean spaces, this is no longer true.To find which group of segments cannot form a triangle:
80°, 140°, and 70° cannot form a triangle because the sum of the three angles is 290°, whereas the sum of the angles in a triangle is 180°.Therefore, (D) 80°, 140°, and 70° group of segments cannot form a triangle.
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Answer:
80, 140, 70
Step-by-step explanation:
-6 - (2x + 7) = -2(x +6) -1
Answer:
Infinite solutions
Step-by-step explanation:
You can put in any number for x and the 2 sides of the equation will equal each other.
Answer:
The equation has not solution, both parts of the equation correspond to the same line.
Step-by-step explanation:
-6 -(2x+7) = -2(x+6) - 1
-6 -2x - 7 = (-2*x + (-2*6)) - 1
-6 - 2x - 7 = -2x - 12 - 1
-2x - 13 = -2x - 13
-2x = - 2x
If m ABD = 61, and m DBC = 59, then m ABC = ? PLS ASAP
Given that angle ABD and angle DBC are adjacent angle, the value of angle ABC is 120 degrees.
What is the value of angle ABC?Given the data in the question;
Angle ABD = 61°Angle DBC = 59°Angle ABC = ?Since angle ABD and angle DBC are adjacent angle, there addition will give us the value of angle ABC.
∠ABD + ∠DBC = ∠ABC
We substitute in the given values
61° + 59° = ∠ABC
∠ABC = 120°
Given that angle ABD and angle DBC are adjacent angle, the value of angle ABC is 120 degrees.
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find the value of n: [tex]3n (\frac{1}{4} ) = 16 \frac{1}{2}[/tex]
[tex]\boldsymbol{\sf{3n\left(\dfrac{1}{4}\right)=16\dfrac{1}{2} } }[/tex]
Multiply both sides of the equation by 4, the lowest common denominator of 4.2.
[tex]\boldsymbol{\sf{ 12n\times\left(\dfrac{1 }{4}\right)=2(16\times2+1) }}[/tex]
Multiply 12 and 1/4, because once multiplied, we get the following 12/4.
[tex]\boldsymbol{\sf{\dfrac{12}{4}n=2(16\times2+1) \ \ \longmapsto \ \ [Divide \ 12 \div 4.] }}[/tex]
[tex]\boldsymbol{\sf{3n=2(16\times2+1) \ \ \longmapsto \ \ [ Multiply \ 16\times 2] }}[/tex]
[tex]\boldsymbol{\sf{3n=2(32+1) \ \longmapsto \ \ [Add] }}[/tex]
[tex]\boldsymbol{\sf{3n=2\times33 \ \ \longmapsto \ \ [Multiply] }}[/tex]
[tex]\boldsymbol{\sf{3n=66}}[/tex]
Divide both sides by 3.
[tex]\boldsymbol{\sf{n=\dfrac{66}{3} \ \longmapsto \ \ [Split] } }[/tex]
[tex]\boxed{\boldsymbol{\sf{n=22}}}[/tex]
Once the exercise is solved, we find that the value of n is 22.
Which is the greatest fraction in this list? 1/2,3/4,5/8,11/16
Answer:
3/4
Step-by-step explanation:
multiply each fraction by 100 or you could find the LCM
write a solution system for the inequality 3x-2>10
Answer:
x>4
Step-by-step explanation:
3x - 2 >10 add 2 to both sides
3x > 12 Divide both sides by 3
x >4
Answer:
[tex]x > \bf 4[/tex]
Step-by-step explanation:
To find a solution to this inequality, we have to rearrange this equation to make [tex]x[/tex] its subject:
[tex]3x - 2 > 10[/tex]
⇒ [tex]3x - 2 + 2 > 10 + 2[/tex] [Add 2 to both sides]
⇒ [tex]3x > 12[/tex]
⇒ [tex]\frac{3x}{3} > \frac{12}{3}[/tex] [Divide both sides by 3]
⇒ [tex]x > \bf 4[/tex]
please help if u cannot skip
The statement that is true about the function is D. it is discontinuous and non-differentiable at x = 3.
How to determine which statement is true?To determine which statement is true, we need to know the conditions for continuity and differentiablity of a function.
Conditions for continuity and differentiablity of a function.For a function f(x) to be continuous at a point x = a, then both the left hand limit of f(x) and the right hand limit of f(x) as x → a must be equal. That is [tex]\lim_{x \to a^{-} } f(x) = \lim_{x \to a^{+} } f(x)[/tex]. So, [tex]\lim_{x \to a^{} } f(x)[/tex] must exist since [tex]\lim_{x \to a^{-} } f(x) = \lim_{x \to a^{+} } f(x) = \lim_{x \to a^{} } f(x)[/tex]Also, for a function to be differentiable at a point x = a, it must also exist at x = a
So, since f(x) = {x² - 1 if -1 ≤ x ≤ 3 and x²/3 if 3 < x ≤ 8}
From the equality on the first condition,we see that f(x) is exists at x = 3 but is not continuous since f(x) changes to another function when x > 3. So,left hand limit of f(x) and the right hand limit of f(x) as x → 3 are not equal.
That is [tex]\lim_{x \to 3^{-} } f(x) \neq \lim_{x \to 3^{+} } f(x)[/tex] . Thus, the function is discontinuous at x = 3.
For differentiability, both conditions must be met. Since only one condition is met, it is non-differentiable.
So, the function is discontinuous and non-differentiable at x = 3.
So, the statement that is true about the function is D. it is discontinuous and non-differentiable at x = 3.
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Solve the equation. Write the smaller value of x. x^2-4x-5=0
Find the surface
7 in.
4 in.
4 in.
+
4 in.
5 in.
7 in.
5 in.
j
SA = [?]in.² please explain how you got it I’m stuck
Latoya has a lot of doctor’s visits coming up, and her children all need vaccinations for the upcoming school year. which type of insurance would be most helpful to her in this situation?
Health insurance would be most helpful to Latoya.
What is Health insurance?Health insurance, often known as medical insurance in South Africa, is a type of insurance that covers all or part of the risk of a person incurring medical expenses. Risk, like other types of insurance, is shared among many people. An insurer can design a routine finance structure, such as a monthly premium or payroll tax, to provide the money to pay for the health care benefits stipulated in the insurance agreement by calculating the overall risk of health risk and health system expenses over the risk pool.The benefit is managed by a central institution, such as a government agency, a private company, or a non-profit organization.Therefore, health insurance would be most helpful to Latoya.
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Find two positive numbers whose product is 81 and whose sum is a minimum. (enter your answers as a comma-separated list. )
Answer: 18
Step-by-step explanation: the smallest two positive numbers whose product is 81 are 9 and 9. 9+9 is equal to 18.
The prices for different lengths of ribbon sold at a fabric store are shown in the table.
Which statement best justifies whether or not the relationship between the length and price represents a function?
the correct option is the last option, the table represents a function because no length of ribbon has more than one price.
What is a function?
A function is a relationship that maps elements from a set, the domain (set of the inputs), into elements from another set, the range (set of the outputs).
Such that each element of the domain can be mapped into only one element of the range.
If we look at the table, we can see that each input (length of ribbon) is mapped into only one output (price). Then we conclude that this table represents a function.
Then the correct option is the last option, the table represents a function because no length of ribbon has more than one price.
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In the 2020 presidential election, Indiana had 11 electoral votes. That was 29 votes fewer than the number of electoral votes in Texas. Write and solve an equation to find the number of electoral votes in Texas.
Answer:
40
Step-by-step explanation:
11+29=40
Answer:
B)0 to 21 electoral votes
Step-by-step explanation:
edge 2023
Two equations are shown Y equals four over X +3 and Y equals negative 2X subtract four which statement best describes the graph of the two equations
The graph for the given system of equations is shown below
Graph of System of Linear equationsFrom the question, we are to determine the graph that describes the given system equations
First, we will graph the given system of linear equations.
The given equations are
Y equals four over X +3
and
Y equals negative 2X subtract four
That is,
y = 4/(x+3)
y = -2x -4
The graph for the given system of equations is shown below
The statement that best describes the graph of the two equations is the statement that describes the graph of the system of equations as shown below
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