Find the value of x.
OA. 66
OB. 122
OC. 98
O D. 76
SUBMIT

Given that angle ABD and angle DBC are adjacent angle, the value of angle ABC is 120 degrees.

Given the data in the question;

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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A function, C(x), to model the water used by the car wash on a shorter day will be (B) 3x³ + 4x² - 11x - 8.

To find a function, C(x), to model the water used by the car wash on a shorter day:

Given information -

Now the amount of water is cut from the total water usage so to find out the new model c(x) we need to subtract the decrease in water from the total water usage.

We are trying to find:

Therefore, a function, C(x), to model the water used by the car wash on a shorter day will be (B) 3x³ + 4x² - 11x - 8.

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The correct question is given below:

The water usage at a car wash is modeled by the equation W(x) = 4x3 + 6x2 − 11x + 7, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours.

Write a function, C(x), to model the water used by the car wash on a shorter day

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]

[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.

Using decimal multipliers, the correct statement is given by:

(iii) S1 = S2.

Increases of a% or decreases of a% re represented by decimal values, as follows:

Hence, in the context of this problem:

The options are given as follows:

They are equal, hence option (iii) is correct.

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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

Q1: For 30 minutes, a person jogged 10 times along the perimeter of a rectangular field at 12 kilometers per hour. Find the square meters of the field if its length is twice its width.

Q2: A car is traveling at a speed of 75 kilometers per hour. In one minute, how many meters does the car travel?

Q3: What is the length of 2000 millimeters in inches? Round your answer to the nearest hundredth.

Hope this helps =)

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)

 45° only the possible values for x.

What is the meaning of trigonometric ratio?

The given equation can be presented as follows;

[tex]\frac{cos (2 . x )}{cosine(x) + sin(x)} = 0[/tex]

We have that cos(2·x) = cos²(x) - sin²(x)

Also, we have, by the difference of two squares, the following relation;

cos²(x) - sin²(x) = (cos(x) - sin(x))(cos(x) + sin(x))

Therefore, the given equation can be written as follows;

[tex]\frac{cos (2 . x )}{cosine (x) + sin(x) } = \frac{(cos(x) - sin(x) * (cos(x) + sin(x)}{(cos(x) + sin(x))} = 0[/tex]

Crossing the common term, (cos(x) + sin(x)), in the numerator and the denominator, we have-

[tex]\frac{(cos(x) - sin (x) * (cos(x) + sin(x)}{(cos(x) + sin(x))} = cos (x) - sin(x) = 0[/tex]

From cos(x) - sin(x) = 0, we have;

Adding sin(x) to both sides of the equation

cos(x) - sin(x) + sin(x) = 0 + sin(x)

cos(x) = sin(x)

Therefore, the opposite leg and the adjacent leg of the right triangle formed with reference to the angle x are equal

∴ x = 90/2 = 45° only for 0° ≤ x ≤ 180°

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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

The equation be 2(x-2)-5=√x+3-1 then the graphical solution of the equations exists approximately x = 3 and x = 6.

The solution of an equation creates that equation true.

The equation of can be simplified, therefore:

2(x-2)-5=√x+3-1

simplifying the above equation, we get

2x -9 =√x+2

4 x²-37x + 79 = 0

The graphical solution of the equations exists at approximately x = 3 and

x = 6

In ending, the solution of an equation makes the equation true.

Therefore, the graphical solution of the equations exists approximately x = 3 and x = 6

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Answer:

3/4

Step-by-step explanation:

multiply each fraction by 100 or you could find the LCM

The length of each of the equal sides is become x = (3y-4) cm

According to the statement

we have given that the perimeter of the isosceles triangle and length of third side. and we have to find the length of same side of triangle.

So,

An isosceles triangle is a triangle that has two sides of equal length.

Let the equal sides of isosceles triangle be x cm each.

We know that the

Sum of sides of a triangle = perimeter

x+x+(3y-7) = 9y-15

2x = 9y-3y-15+7

After solving the equation it become

2x= 6y-8

x=(6y-8)/2

Now the length of equal sides is x=3y-4

So, The length of each of the equal sides is become x = (3y-4) cm

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Answer:

40

Step-by-step explanation:

11+29=40

Answer:

B)0 to 21 electoral votes

Step-by-step explanation:

edge 2023

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.

The number is 841

So we can see that the number is 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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Answer:

Part A) The system has one solution

Part B) The solution is the point (4,4)

i believe

Using it's concept, the domain of the function is given as follows:

{x| –2 ≤ x <= 5}

The domain of a function is the set that contains all possible input values for the function, that is, the values for which the function is defined.

The function described in this problem is defined from x = -2 until x = 5 hence the domain of the function is given as follows, by the interval:

{x| –2 ≤ x <= 5}

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Answer:

So I got 64 on my test, but it doesn't let you see what was right and what was wrong, so I guess we will never know☹️☹️☹️☹️.

BTW in was on edge

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.

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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Health insurance would be most helpful to Latoya.

Therefore, health insurance would be most helpful to Latoya.

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[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]

a3=9

assuming the pattern is constant, a3 is right in the middle of a1 and a5 so the answer would be right in the middle of 6 and 12. the average of 6 and 12 is 9, so a3=9.

hope this helps!

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

Answer:

x:12×2−6(a2+b2)x+3a2b2=0

Step-by-step explanation:

equation

Answer:

y=(1/-4)(x+4)^2 +4

Step-by-step explanation:

Don't ask

The value of A is A(1,-15) and the distance between AB is 8 so these are the correct answers.

According to the statement

We have given that the

AB = 8 and B lies at −7, and we have to find the position of the A on the number line.

Let a be a point on number line and b be the second point on number line.

And The distance between two numbers on number line is calculate by subtracting the smaller number from larger number.

Here

AB = 8

B = -7

We have to look at the options one by one.

For A = -1

As A>B

AB = -1-(7) = -1+7 = 6

For A = 1

As A>B so

AB = 1-(-7) = 8

So with A = 1 , AB = 8

This is one of the right answers.

For A=15

As A>B

AB = 15-(-7) = 22

For A=-15

As B>A

AB = -7 -(-15) = 8

As with A=1 and A=-15, the distance between AB is 8 so these are the correct answers.

So, The value of A is A(1,-15) and the distance between AB is 8 so these are the correct answers.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

Suppose A and B are points on the number line. If AB = 8 and B lies at −7, where could A be located?

Select ALL that apply.

A −1

B 1

C 15

D −15

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Answer:

3

Step-by-step explanation:

f(x) = 3x² - 2x + 1

f(x) = ax² + bx + c

a = 3

The completed statement are:

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:

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Answer: a, c

Step-by-step explanation: