If l is parallel to m, and line PQ is perpendicular to line RQ, then find the measure for each numbered angle.

m<1= _____
m<2= _____
m<3= _____
m<4= _____

If the inequality which can be used to determine x is 7.25 + 23.25x ≤ 170 and the number of people who can go the amusement park is 7

The maximum amount that he can spend = $170

The cost of the parking ticket = $7.25

The cost of the ticket including tax = $23.25 per person

Then the inequality will be

7.25 + 23.25x ≤ 170

Subtract both side of the inequality by 7.25

23.25x ≤ 162.75

Divide both side of the inequality by 23.25

23.25x / 23.25 ≤ 162.75/23.25

x ≤ 7.006

Hence, the inequality is 7.25 + 23.25x ≤ 170 and 7 people can go to the amusement park

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Using polar coordinates, the result for integral is - 0.448[tex]\pi[/tex]

What is polar co-ordinates?

In arithmetic, the polar coordinate system may be a two-dimensional organization within which every purpose on a plane is set by a distance from a indicator and an angle from a reference direction.

Main body:

The most used relation for polar coordinates is:

[tex]x^{2} +y ^{2} =r^{2}[/tex]

An integral in Cartesian coordinates is converted to polar using:

[tex]\int\int{f(x,y)} \, dA = \int\int{ f(r, \beta )d\beta[/tex]

In this problem:

f(x,y) = sin [tex]x^{2} +y^{2}[/tex]

thus

f(r,[tex]\beta[/tex]) = sin[tex]r^{2}[/tex]

Region between the circles with center at the origin and radii 1 and 3, thus the inner limits of integration are r =1  and r =3.

First quadrant, thus, the outer limits of integration are: [tex]\beta[/tex] = 0,[tex]\beta[/tex] = [tex]\pi /2[/tex].

The polar integral is:

I = [tex]\int\limits^3_1 {sinr^{2} r} \, dr[/tex]

Using substitution:

u =[tex]r^{2}[/tex] ⇒ du = 2rdr⇒ dr = du /2

I = 1/2[tex]\int\ {sin u} \, du[/tex]

 = -[tex]cos r^{2[/tex] /2     where limits are 3, 1

Applying the fundamental theorem of calculus:

I = [tex]-cos 5^{2} /2[/tex][tex]-cos1^{2}/2[/tex]

I = - 0.996

Then, the outer integral is:

O =[tex]\int\limits^\pi _0 {-0.996} \, d\beta[/tex]

O=  - 0.448[tex]\pi[/tex]

Hence the result for integral is - 0.448[tex]\pi[/tex]

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The propagated error in the measurement of the side of the cube is 0.001.

We know that,

the volume of a cube is dependent on the length of the edge, s, which is given by the equation,

V = [tex]s^{3}[/tex].

With this we determine that the given cube has an edge of 27 = [tex]s^{3}[/tex]

⇒ s = 3 inches.

Now we can acquire the differential of the equation for the volume of the cube with the following equations.

V = [tex]s^{3}[/tex]

dV = d([tex]s^{3}[/tex])

dV = 3[tex]s^{2}[/tex] ds

We have given that volume of the cube is 0.027.

That is dV = 0.027 and s = 3

we simply plug in the given and then solve for ds to determine the error in the measurement of the edge of the cube.

dV = 3[tex]s^{2}[/tex] ds

0.027 = 3(3)²ds

0.027 = 27ds

0.001 = ds

Therefore, there is an error in measurement of the edge of the cube up to 0.001 inches.

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Answer:

----------------------------

If the given function is f(x), then rules of translation by b units are:

Our function and its image are:

Therefore we have translation left by 3 units.

Correct choice is D.

Answer:

Translate each point of the graph of h(x) 3 units left.

Step-by-step explanation:

Translations

For a > 0

[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}.[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}.[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.[/tex]

Given functions:

[tex]h(x)= \log_6 x[/tex]

[tex]m(x)= \log_6(x+3)[/tex]

As m(x) = h(x+3),  to graph the function m(x), translate the function h(x) 3 units left.

Total kinetic energy that is generated will be 2025 joules

What is kinetic energy?

The K.E. of an object is that the energy that it possesses because of its motion. it's outlined because the work required to accelerate a body of a given mass from rest to its expressed velocity.

Main body:

According to question :

mass = 2 kg

velocity = 45 m/s

formula for kinetic energy = (1/2) mv²

substituting these values in formula,

K.E. = (1/2) 2* 45²

K.E. = 45²

K.E. = 2025 joules.

Hence kinetic energy generated is 2025 joules.

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The domain when the maximum number of people allowed in the movie theater is 60 people would be: B. 0 ≤ x ≤ 60.

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function or relation is defined. This ultimately implies that, a domain is the set of all possible input values (x-values) for a function while a range is the set of all possible output values (y-values) of a function.

Since the maximum number of people that are allowed in the movie theater is 60 people, we can logically deduce that the input values (x-values) for its function is less than or equal to 60. Therefore, the domain of the function on this graph is given by:

Domain = [0, 60]

Domain = 0 ≤ x ≤ 60.

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Complete Question:

The graph represents the money collected at the movie theater on Saturday. Find the domain when the maximum number of people allowed in the movie theater is 60 people.

40 ≤ y ≤ 160

0 ≤ x ≤ 60

40 ≤ x ≤ 160

0 ≤ y ≤ 60

Answer:

the answer is 0 is less than or equal to x which is less than or equal to 60

Step-by-step explanation:

Domain is the x value

Since the max amount of people is 60, and people is x value the answer i put above is a reasonable domain.

Hope this helps!

The measurement of the angles x, y, and z of the given triangles are;

x = 88°, y = 55° and z = 37°

We know that;

The sum of interior angles of any triangle is equal to 180 degree.

The sum of angles on a straight line is 180 degrees.

Thus;

x + y + z = 180°

Now, from the given diagram, we can see two pairs of parallel lines. This means that there will be some corresponding angles.

Thus;

y is a corresponding angle to 55° and as such we can say that;

y = 55°

Similarly, z° is a corresponding angle to 37° and as such we can say that;

z = 37°

Thus;

x + 55 + 37 = 180

x + 92 = 180

x = 180 - 92

x = 88°

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The speedup of a parallel algorithm will eventually reach some limit.

What is parallel algorithm?

An algorithm is a set of instructions that takes input from the user and, after doing some calculations, generates an output. A parallel algorithm is one that can carry out multiple operations simultaneously on various processing units and then combines all of the separate outputs to get the desired outcome.

An algorithm that can execute several instructions concurrently on various processing devices and then aggregate all of the individual outputs to produce the final result is known as a parallel algorithm.

Because a parallel algorithm's speedup is never equal to the number of processors, it ultimately reaches a limit beyond which it can no longer be accelerated. At that point, the algorithm will no longer be accelerated and the speedup will stop.

Hence, the speedup of a parallel algorithm will eventually reach some limit.

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Answer:

-6.1,-2.5,-0.4,3.4

Step-by-step explanation:

If we used a number line and graphed all the numbers, we could visually see that -6.1 is the farthest from zero followed by -2.5,-0.4 and 3.4. Because we are doing the coldest temperature to warmest and not the other way around the answer would be -6.1,-2.5,-0.4,3.4

Hope this was helpful!

Answer:

(-2,-4)

Step-by-step explanation:

3x+2=-2x-8

+2x.    +2x

5x+2=-8

   -2. -2

5x=-10

/5.  /5

x= -2

y=3(-2)+2

y=-6+2

y= -4

(-2,-4)

Hopes this helps please mark brainliest

a. [tex]123.1(1.069)^3 \approx 150.4[/tex]

b. [tex]123.1(1.069)^{20} \approx 467.5[/tex]

Based on the graphs of functions f(x) and g(x) = f(x) + k, the value of k is: B. k = -2.

In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

Since the graph of the line for function f(x) passes through the ordered pairs (0, 1) and (2, 6), its y-intercept is given by:

y = f(0) = 1.

Since the graph of the line for function g(x) passes through the ordered pairs (0, -1) and (2, 4), its y-intercept is given by:

y = g(0) = -1.

From the information provided above, we have the following function:

g(x) = f(x) + k

g(0) = f(0) + k

Making k the subject of formula, we have:

k = g(0) - f(0)

k = -1 - 1

k = -2.

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The expression that can be use to represent the amount owned on rental is 0.1x + 25y

Rick rents a car from a company that charges him $25 per day plus 10 cents per mile driven.

The expression that can be use to represent the amount owned on rental can be represented as follows:

let

x = number of miles driven

y = number of days

Let's convert cent to dollars

100 cents  = 1 dollars

10 cents = ?

cross multiply

amount in dollars = 10 / 100 = 0.1 dollars

Therefore,

the expression = 0.1x + 25y

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The relations which are functions as required to be identified in the task content are;

It follows from the task content that the relations which are functions among the given answer choices are to be identified.

Since the definition of a function is such that; a function is a special kind of relation in which case only one output value is assigned to each input values.

Put simply, a function has only one output value for each input value.

Therefore, it follows from the definition above that the relations which are functions among the given answer choices are as listed above.

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Answer:

D

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (4, 2) ← 2 points on the line

m = [tex]\frac{2-3}{4-(-2)}[/tex] = [tex]\frac{-1}{4+2}[/tex] = - [tex]\frac{1}{6}[/tex]

Answer:

-------------------------------

Find y:

Hamiltonian due to interaction of spin magnetic field:

H = -u.B

H = α/√2[tex]\left[\begin{array}{ccc}1&1\\1&-1\\\end{array}\right][/tex]

What is a matrix?

In mathematics, a matrix (multiple matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, and used to represent mathematical objects or properties of such objects. The

matrix represents a linear mapping without additional information and allows explicit computation in linear algebra. The study of matrices is therefore a large part of linear algebra, and most properties and operations in abstract linear algebra can be expressed in matrices. For example, matrix multiplication represents the construction of linear maps.

Not all matrices are related to linear algebra. This is especially true for graph theory, occurrence matrices, and adjacency matrices. This article focuses on matrices in the context of linear algebra. Unless otherwise stated, all matrices either represent linear maps or can be considered linear maps.

Square matrices (matrices with the same number of rows and columns) play an important role in matrix theory. Square matrices of a given dimension form non-commutative rings, one of the most common examples of non-commutative rings. The determinant of a square matrix is ​​the numerical value associated with the matrix that underlies the study of square matrices. For example, a square matrix has nonzero determinant and is invertible only if the eigenvalues ​​of the square matrix are the roots of the polynomial determinant.

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The expression 5(x + 7) has a sum of two terms 5x and 35.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, an expression 5(x + 7).

Now distributing 5 to x and 7 we get 5x + 35.

So, The expression 5(x + 7) has the sum of two terms.

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Work Shown:

[tex](x_1,y_1) = (-5,-3) \text{ and } (x_2,y_2) = (8,-1)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{-1 - (-3)}{8 - (-5)}\\\\m = \frac{-1 + 3}{8 + 5}\\\\m = \boldsymbol{\frac{2}{13}}\\\\[/tex]

A slope of 2/13 means we go up 2 units and to the right 13 units. If starting at (-5,-3) and following this movement pattern of "up 2, right 13", then we arrive at (8,-1).

The magnitude and the direction angle of the vector are given as follows:

The points that define the vector are given as follows:

m(-15, 16) and n(2,-6).

Considering m as the starting point and n as the endpoint, the vector is defined by the subtraction of the coordinates of n by the coordinates of m, hence:

v = (2 - (-15), -6 - 16) = (17, -22).

The magnitude of the vector is given by square root of the sum of the squares of the components, hence:

|v| = sqrt(17² + (-22)²) = 27.80.

The direction angle is the arc tangent of the division of the vertical component of the vector by the horizontal component of the vector, hence:

θ = arctan(-22/17)

θ = -52.3.

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Yes it is reasonable to save that the farm’s glass recycling could pay for their fuel oil.

Recycling is the process of turning trash into new products and materials. This idea frequently takes the recovery of energy from waste materials into account. The capacity of a substance to regain the qualities it had in its initial state determines how recyclable it is.

Both the environment and your community may benefit from recycling. It protects natural resources, minimizes greenhouse gas emissions, cleans up the air and water, and conserves energy.

In this question, there is a benefit to recycling. That is, the farm would be able to save more fuel. Hence it pays for the costs of fuel.

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The amounts of each solution needed are given as follows:

The percentage of paint when 5 liters of the thinned solution are added is of:

62%.

The variables to the system of equations are given as follows:

The painted needs 20 liters, hence:

x + y = 20.

The solution is 65%, hence:

0.5x + 0.75y = 0.65 x 20

0.5x + 0.75y = 13.

From the first equation, we have that:

x = 20 - y.

Hence the amount of liters of the 75% solution is obtained as follows:

0.5(20 - y) + 0.75y = 13.

0.25y = 3

y = 3/0.25

y = 12 liters.

Then the amount of liters of the 50% solution is of:

x = 20 - y = 20 - 12 = 8 liters.

When 5 liters of the 50% solutions are added, there would be 13 liters of the 50% solution, then the percentage would be of:

P = (0.5 x 13 + 0.75 x 12)/25 = 0.62 = 62%.

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Using a midpoint Riemann sum with 3 subintervals of equal length to approximate [tex]\int^{70}_{10}v(t)dt[/tex] is 2020 and [tex]\int^{70}_{10}v(t)dt[/tex] means the distance in feet, traveled by rocket A from t=0 seconds to t=70 seconds.

From the given question,

An initial height of 0 feet at time t=0 seconds.

The velocity of the rocket is recorded for selected values of over the interval 0 < t < 80 seconds.

(a) Using a midpoint Riemann sum with 3 subintervals of equal length to approximate [tex]\int^{70}_{10}v(t)dt[/tex].

[tex]\int^{70}_{10}v(t)dt[/tex]

A midpoint Riemann sum with 3 sub intervals so, n=3

∆t= (70-10)/3

∆t = 60/3

∆t = 20

Intervals: (10, 30), (30,50), (50,70)

Midpoint:      20        40         60

Midpoint Riemann Sum

[tex]\int^{70}_{10}v(t)dt[/tex] = ∆t[v(20+v(40)+v(60)]

From the table

[tex]\int^{70}_{10}v(t)dt[/tex] = 20[22+35+44]

[tex]\int^{70}_{10}v(t)dt[/tex] = 20*101

[tex]\int^{70}_{10}v(t)dt[/tex] = 2020

(b) Now we have to explain the meaning of v(t)dt in terms of the rocket's flight [tex]\int^{70}_{10}v(t)dt[/tex].

It means the distance in feet, traveled by rocket A from t=0 seconds to t=70 seconds.

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When he saved $80 in March, he saved $112 in April because he intended to save 140% more than he did.

In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage. Percentage, a relative number showing hundredth parts of any amount, is a relative measure that indicates how many questions on a test you correctly answered out of 100 (75/100). Since one percent (symbolized as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified. By dividing the total by the amount you wish to convert to a percentage. You would divide 2 by 5 in this case as 2 divided by 5 equals 0.4. The result of multiplying 0.4 by 100 is 40, or 40%.

Here,

Amount of money he saved in march=$80

Amount of money he wish to save in April,

=140%*80

=$112

He saved $112 in April when he saved $80 in March and he wanted to save 140% more than what he saved in March.

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a) Coordinates of the midpoint: (2,1)

b) Gradient of the line PQ = -2/3

c) n = 13

What is the midpoint  of a line segment?

The midpoint is defined as the point which divides the line segment into two equal halves.

Given P = (-1,3) , Q = (5,-1)

Coordinates of the midpoint are given by

X' = (X1+ X2)/2

Y' = (Y1+ Y2)/2

(X1,Y1 ) and (X2,Y2) are the endpoints of the line segment.

Putting the values in the above formula X' = (-1+5)/2 = 2

Y' = (3-1)/2 = 1

hence midpoint  = (2,1)

The Slope or Gradient of the line is given by = (Y2-Y1)/X2-X1)

= (-1-3)/(5-(-1))

= -4/6 = -2/3

Gradient = -2/3

Distance between 2 points is given by the formula

[tex]\sqrt{(x_{1}-x_{2}) ^{2}+(y_{1}-y_{2}) ^{2} }[/tex]

[tex]\sqrt{(-1-5)^{2}+(3-(-1))^{2} }[/tex]

[tex]\sqrt{6^{2}+4^{2} }[/tex]

= [tex]2\sqrt{13}[/tex]

hence n = 13

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Answer:

First option

Step-by-step explanation:

Hope this helps

Answer:

7

Step-by-step explanation:

649-531=118

We know that there are 118 more guests per hour.

Divide 826 by 118 to get 7.

Answer: 7

Step-by-step explanation:

The first line of the table is 2 and 236 if you divide 236 by 2 you get 118

Then after that you times it by any number after 5.5 until you get 826.

Answer:x=9/4 nine over 4 for improper fraction I hope this is helpful mark me brainlist if this sounds good

Step-by-step explanation:

7(x-1)=3x+2

Distribute through the parentheses

7x-7=3x+2

Move the variable to the left-hand side and change its sign

7x-7-3x=2

or Move the constant to the right-hand side and change its sign

7x-7-3x=2

Collect like terms

4x=2+7

And then Add the numbers

4x=9

Divide both sides of the equation by 4

x=9/4

Mixed number is 2 1/4

The angles in the intersected lines are as follows:

When lines intersect angle relationships are formed such as vertically opposite angles, linear angles etc.

Angle a is vertically opposite to angle b.

Vertically opposite angles are congruent.

Therefore,

∠a ≅ ∠b

Hence,

x + 8 = 100(vertically opposite angles)

x = 100 - 8

x = 92

b + x + 8 = 180(sum of angles on a straight line)

b + 92 + 8 = 180

b = 180 - 100

b = 80 degrees.

Hence,

a = 80 degrees

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