(Refer to the attached image)​

An ordered pair is a set of two values, (x,y), where x and y are the coordinates. In an ordered pair, the first element is typically referred to as the x-coordinate, or the "first component" and it represents the horizontal position of the point on a coordinate plane. The second element is typically referred to as the y-coordinate, or the "second component" and it represents the vertical position of the point on a coordinate plane.

So, to find the first and second element of a pair, you can refer to the first element as the x-coordinate or the first component and the second element as the y-coordinate or the second component.

For example, in the ordered pair (4,3), the first element is 4, which represents the x-coordinate, and the second element is 3, which represents the y-coordinate.

Answer:

31p+13

Step-by-step explanation:

After expanding: 21p+28+10p-15

After simplifying: 31p+13

Answer:

it’s A

Step-by-step explanation:

I graphed it out

A two-dimensional (2D) coordinate system is a system used to define the position of points in a two-dimensional plane.

A 2D coordinate system can also be used to represent other kinds of data, such as temperature, elevation, or pressure. In this case, the two coordinates are usually called the x-axis and y-axis, and they are both used to measure the same physical quantity.

It is most commonly used in mathematics and engineering to plot graphical data such as graphs, charts, and diagrams. In a 2D coordinate system, each point is represented by two numbers, called coordinates, which indicate the position of the point in relation to a fixed reference point, called the origin. These coordinates usually describe the horizontal (x) and vertical (y) distances between the point and the origin. The set of all points in the 2D coordinate system is called the coordinate plane.

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Answer: 1,176 miles

Step-by-step explanation:

490 / 5 = 98 miles

98 mph X 12 hours is 1,176

value of p = 7 and value of q = 10.

The word consecutive implies an unbroken sequence that means terms approaches forward by following a specific order. Within a consecutive sequence the gap between each term is the same.

given, 4, p, q, 13 are consecutive terms, find the value of P and Q.

As the above four are consecutive number so starting from the 4 we write the list in an unbroken sequence.

At first difference between highest and lowest number = 13- 4 = 9

now this difference is divided by the number of gaps between the sequence, we find there are 3 gaps between four numbers.

order of sequence = 9/ 3 = 3

now the next number after 4 will be 4+3 = 7

in the next, 7+3 =10

finally, we get 10+3 =13

so, the consecutive numbers are 4, 7, 10, 13.

As a result, p = 7 and q = 10

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Answer:

a. Write an inequality that demonstrates this situation

Let x be the number of $5 t-shirts Tyrone can buy

The inequality that demonstrates this situation is:

x*5 + 22 <= 95 - 15

b. solve your inequality

x5 + 22 <= 80

x5 <= 58

x <= 11.6

x <= 11

c. Explain what your answer means to Tyrone

Tyrone has $95 to spend, he already bought pants for $22, so he has $95-22 = $73 left to spend. He wants to have at least $15 left over after buying t-shirts, so he can buy up to $73-15 = $58 worth of t-shirts. Each t-shirt costs $5, so he can buy a maximum of 11 t-shirts (58/5=11.6) with no remainder. So Tyrone can buy 11 t-shirts and he will have $73-11*5 = $18 left. This means that Tyrone can buy 11 t-shirts and still have $18 left over.

Step-by-step explanation:

The power and the r m s value for each of the following signals are a)p=50w and  r m s =7.07 b)p=178w,  r m s =√178 c)p=51w, r m s =√51
d)p=25w, r m s =√25 e)p=25w, r m s  =√25  and f)p=1/2, r m s =√1/2.

(a) 5+10cos(100t+π/3)
=A cos(w0t+θ)
power of the signal
P=10^ 2/2=100/2=50w
p=50w
r m s value of the signal
=√50
=7.07

b) 10cos(100t+π/3)+16sin(150t+π/5)
power of the signal.
p=10^ 2/2+16^ 2/2
p=178w
r m s value of the signal=√178

c) (10+2sin(3t)cos10t
=10cos10t+2sin3tcos210t
=2sin3tcos10t
=1/2(sin(3+10)+sin(3-10))
(sin a cos b=1/2(sin(a + b)+sin(a-b))
=2x1/2(sin13t-sin7t)
=sin13t-sin7t
=10cos10t+sin13t-sin7t
power of the signal is
p=10^ 2/2+1^ 2/2+1^ 2/2
p=51w
r m s value of the signal=√51

d) 10 cos(5t)cos(10t)
=10(cos(5+10)T+ cos (5-10)t/2
(cos a cos b=1/2(cos a+ cos b)+cos(a-b))
=10(cos(15)t+ cos (-5)t/2
=5cos15t-5cost
power value of the signal
p=5^ 2/2+5^ 2/2
p=25w
r m s value of the signal=√25

e) 10 sin(5t)cos(10t)
=10(sin(5+10)t+ sin(5-10)t/2
=10/2(sin15t-sin5t)
=5sin15t-5sin5t
power of the signal
p=5^ 2/2+5^ 2/2
p=25w
r m s value of the =√25      

F) f) e^(jαt) cos(w0t)
=e jαt cos wot
=(cosαt+ cos wot+jsin2tcoswot
=(cos(α+wo)t+ cos(α-wo)t/2+j(sin(2+wo)t+ sin cos-wot/2
=1/2cos(α+wo)T+1/2cos(α-wo)T
power of the signal
p=(1/2)^ 2/2+(1/2)^ 2/2+(1/2)^ 2/2+(1/2)^ 2/2
p=1/2
r m s value=√1/2

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[tex]\pi[/tex]

Answer:

Step-by-step explanation:

its the next one down

So on solving provided question we can say that given coordinates are

(−6,4) and (−1,−8)so equation is x - y +10 = 0

A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is represented by the second number. like in (12.5), when there are 12 units below and 5 above.

given coordinates are

(−6,4) and (−1,−8)

so equation is

y-y1 = m(x-x1)

y-4 = x +6

x - y +10 = 0

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The equation of a line passes through the point (-6, 5) and

has a slope of 1/2 is y = (1/2)x + 8.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and equation of a line in slope-intercept form is y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given, A line passes through the point (-6, 5) and has a slope of 1/2.

First, we need to determine the y-intercept 'b'.

5 = (1/2)(-6) + b.

5 = - 3 + b.

b = 8.

y = (1/2)x + 8 is the required equation of the line.

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The missing first term of the expression that, when fully simplified, would be a binomial with a degree of 4 include the following:

A. 0

C. 9x^2y

E. 4xy^3

In Mathematics, a polynomial function simply refers to a type of mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations.

In Mathematics, the canonical form for a polynomial in one variable (x) is given by this mathematical expression:

[tex]a_n x^n + a_{n-1} x^{n-1} +a_1 x^1 +a_0=0[/tex]

Since the degree of a polynomial function is the sum of exponents in each of its term, the required answer options must have exponents that are equal to those of the given polynomial function and these include the following:

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Answer: A C E

Step-by-step explanation:

Answer:47.8125kg

Step-by-step explanation:

x: previous weight

x = 45+45x6.25% = 47.8125

Answer:

AB = 9.68, BC = 7.04

Step-by-step explanation:

AC/DC = 6.71/6.1 = 1.1    This is the proportionality factor

6.4(1.1) = BC = 7.04

8.8(1.1) = AB = 9.68

The minimum speed object must have at the top of the loop is 3.8m/s.

Friction is the force that resists the motion of an object, it works in the opposite direction of applied force. Centripetal force is the force applied to the center of the body moving in a circular motion, whereas gravitational force is the pull of gravity on a body i.e., it attracts a body toward the ground.

Diameter of loop= 3m

thus radius = 1.5m

Centripetal force =< gravitational attraction the object has.

Centripetal force ,F=mv^2/r ----1

where  M= mass v= velocity and r= radius

gravitational force is F=ma -----2

let 1=2

mv^2/r=ma

m is common so can be canceled out

a=v^2/r

for v= 9.8m/s^2

a= 9.8^2/1.5

a=3.834057903

Therefore, the minimum speed object must have at the top of the loop is 3.834m/s.

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Indeed, the values in the table back up his assertion.

This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.

We typically utilize this technique for math calculations.

This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.

According to our question-

2% of 250 = 5, 4% of 200 = 8, and 8% of 150 = 12.

5 + 8 + 12 = 25

Hence, Indeed, the values in the table back up his assertion.

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Jee's trip from New York to Boston would take approximately time 4.5 hours.

To calculate the time it would take Jee to travel from New York to Boston, we need to divide the total distance (approximately 280 miles) by the average speed (42 mph). This gives us a total time of 6.67 hours. We then need to subtract the time it took Jee to travel from Boston to New York (6 hours) to get the total time for the return trip. 6.67 hours - 6 hours = 4.5 hours. Therefore, Jee's trip from New York to Boston takes approximately time 4.5 hours. Jee's trip from New York to Boston would take approximately 4.5 hours.

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The inequality  6 > x + 1 > 3  is 'And' type Inequality.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

An 'Or' inequality is also referred to as a disjunction.

In other words, there is no connection on the number line between the range of values that meet either component of the inequality. Finding a truthful statement that satisfies either one of the inequality conditions or both inequality conditions is the aim whenever 'Or' compound inequalities are solved.

For example, x > 7 OR x < 3

Another name for a compound inequality with a 'And' is a conjunction. Compound inequality of this kind is stated as a long inequality, such as

3 > x > 9. Similar to 3>x and x > 9, this is.

The solutions to this and other compound inequalities fall within a range of potential values between 3 and 9. The range of values used to solve "And" inequalities must meet both requirements. These inequalities display a range of overlapping values.

So, the inequality is 'And' type of Inequality.

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The midline theorem in Geometry claims that cutting along the midline of a triangle creates a segment that is parallel to the base and half as long.

It is a theorem used in coordinate geometry and calculus. If P1(x1, y1) and P2(x2, y2) are the coordinates of a line, then the midpoint formula is given as Midpoint = [(x1 + x2)/2, (y1 + y2)/2]

Property of the midpoint theorem are:

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The value of the equation A = LW is A = 750

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The value of L = 50

The value of W = 15

A = LW   be equation (1)

Substituting the values of L and W in the equation , we get

A = 50 x 15

On simplifying the equation , we get

A = 750

Therefore , the value of A is 750

Hence , the equation is A = 750

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Answer: 11 Books, 6 Toys

Step-by-step explanation:

Let the number of books be B, and the number of toys be T

B+T=17

11B+6T=157

Let's use the elimination method:

11B+6T=157

6B+6T=102

And finally you get

5B=55

B=11

Use the value of B to get T

11+T=17

T=6

Therefore, the answer is

B=11,T=6

Answer:

21 cm

Step-by-step explanation:

An equilateral triangle has all 3 sides equal.

So the perimeter of the equilateral triangle

= 3 x side

= 3 x 7

= 21 cm

Hence,

The perimeter of the equilateral triangle is 21 cm.

Answer:

51,328

Step-by-step explanation:

5 11 12+2 1 6=51328

The amount that they will have saved after 2 weeks is $1,737.

Tom, you can refer to a quantity or number of something using the word "amount." It is typically used to refer to an amount of money, like when people discuss their income, but it can also be used to describe a quantity of something, such as the volume of water in a tank or the time required to complete a task.

We must divide the difference between Ezra and Haley's initial deposits by the difference between their weekly installments to figure out how many weeks it will take them to save the same amount of money. In this instance, their initial deposits differed by $804 ($862 - $58), while their weekly installments differed by $402 ($71 - $473). We can calculate that it will take them two weeks to save the same amount of money by dividing $804 by $402.

After two weeks, they will have $1,737 in savings. Haley will have $1,737 ($862 + $71 + $71 + $703) and Ezra will have $1,737 ($58 + $473 + $473 + $733) in their accounts after two weeks.

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The constant of proportionality, given that this is a proportional relationship, is 11. 7

To find the constant of proportionality, the following formula is used :

= Y value / Corresponding x value

The constant of proportionality can only be found for proportional relationships.

In this instance, we have x and y of ( 7, 81. 9 ).

The constant of proportionality is:

= 81 .9 / 7

= 11. 7

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Equality is a fundamental component of a just and equitable society. It encompasses legal, social, and economic aspects, all of which are essential to ensure that all citizens are treated fairly and have access to the same rights and opportunities.

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Yes, (3,4, -2) is a solution of the system. You can find the solution by substituting the values.

To check if (3,4,-2) is a solution of the system, we can substitute those values into each of the equations and see if they are true.

5x1 + 2x3 = 7

becomes

5(3) + 2(-2) = 7

which simplifies to

15 - 4 = 7

-2x1 + 6x2 + 9x3 = 0

becomes

-2(3) + 6(4) + 9(-2) = 0

which simplifies to

-6 + 24 - 18 = 0

-7x1 + 5x2 - 3x3 = -7

becomes

-7(3) + 5(4) - 3(-2) = -7

which simplifies to

-21 + 20 + 6 = -7

As we can see all the equation are true, (3,4,-2) is a solution of the system.

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The final solution after reducing the given number radical is; 9√2

The radical of a number is defined in the same way we define the root of a number. The root can be a square root, fourth root or even cube root, up to the nth root.

Now, we are given the number radical as; √162

Now, 162 can be broken down into its' factors as √(81 * 2)

We know from properties of surds that;

√(a * b) = √a * √b

Thus, we now have;

√162 = √81 * √2

This can be simplified further to get;

9√2

Thus, that is the final solution to the number radical simplification.

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When you multiply 4 with any number, you can use the doubling-up trick (that's the one you used for the two times table) twice. Here is an example: 2 x 4 is the same as 2 + 2 = 4 and then 4 + 4 = 8. So, 2 x 4 = 8.

Here is next double, double example are: 5 x 4 is the same as 5 + 5 = 10, so then 10 + 10 = 20. So, the answer is 5 x 4 = 20.

Here, is the table of four.

4×1=4

4×2=8

4×3=12

4×4=16

4×5=20

4×6=24

4×7=28

4×8=32

4×9=36

4×10=40

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