what are the ordered pairs of the solution for this system of equations f(x) = x^2 -2x+3 ; f(x) = -2x + 12

If (63, x, 105) generate a Pythagorean Triple, the value of x is 84.

Before starting to solve this problem we must know that the Pythagorean theorem is a theorem that realizes the sides of a right triangle and has many applications for it.

A Pythagorean Triple is a set of three integers that satisfy the Pythagorean Theorem, [tex]a^2 + b^2 = c^2[/tex]. In this case, 63 and 105 are two sides of a right triangle, and x is the third side. We can plug in the values and solve for x:
63² + x² = 105²
3969 + x² = 11025
x² = 7056
x = √7056
x = 84

Therefore, the value of x is 84, and the Pythagorean Triple is (63, 84, 105).

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on solving the provided question we can say that for parallel combination, the equation will be  1/R = 1/R1 + 1/R2.

A mathematical equation is a formula that links two assertions and signifies equivalence with the equals sign (=). In algebra, a mathematical statement that proves the equality of two mathematical expressions is referred to as an equation. The equal sign, for instance, separates the variables 3x + 5 and 14 in the equation 3x + 5 = 14. There is a mathematical formula that explains the link between the two phrases that appear on either side of a letter. Frequently, the symbol and the single variable are the same. like in 2x - 4 = 2, for example.

we have,

Total Resistance (R) = 1.403 kilo-ohm.

R1 = 2.0 Kilo-ohm.

1.403 kilo-ohm = 1403 ohm.

for parallel combination, the equation will be

1/R = 1/R1 + 1/R2

[tex]1/1403 = 1/2000 + 1/ R2\\.1/1043 - 1/2000 = R2\\2000 - 1403 / 1403 x 2000 = 1/R2\\597/ 1403 x 2000 = 1/R2\\R2 = 1403 x 2000 / 597 = 2806000 / 597 = 4700.16\\R2 = 4700.16 ohm[/tex]

103 ohm = 1 kilo-ohm =>  4700 ohm = 4.7 kilo-ohm

so, R2 = 4.7 kilo-ohm.

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Answer: For Jon, buying 3 shirts for $20 can be written as a rate as follows:

The number of shirts Jon buys per dollar spent = 3 shirts / $20 = 3/20 shirts/dollar

For Brenda, recording 76 songs on 4 albums can be written as a rate as follows:

The number of songs Brenda records per album = 76 songs / 4 albums = 19 songs/album

So, the rate of songs Brenda records per album can be written as 19 songs/album.

Step-by-step explanation:

The measure of angle B is given as follows:

<B = 295º.

Angles A and B in the context of this problem are reflex angles, meaning that the sum of their measures is of 360º.

The measures are given as follows:

Hence the measure of angle B is obtained as follows:

65 + <B = 360

<B = 360 - 65

<B = 295º.

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Jada can get 4 albums or she can get 80 individual songs for $20. The equation will be written as 0.25s + 5a = 20.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that It costs $0.25 to download an individual song and $5 to download an album. Jada has $20 to spend downloading music.

The equation will be written as,

0.25s + 5a = $20

The number of individual songs will be,

0.25s = 20

s = 20 / 0.25

s = 80

The number of albums,

5a = 20

a = 20 / 5

a = 4

The complete question is given below.

It costs $0.25 to download an individual song and $5 to download an album. Jada has $20 to spend downloading music.

a. Make a table showing three ways Jada can spend $20 downloading individual songs and albums. (s the being number of individual songs and a being the number of albums.)

b. Write an equation relating the number of individual songs (s) and the number of albums(a) in standard form.

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Answer:

Answer is 1/2. Box plot is split into quarters. So 1/4 + 1/4 = 1/2

The axis of symmetry, vertex, domain, and range of each of the quadratic function are as follows;

Axis of symmetry = 3.

Vertex = (3, 3).

Domain = {-∞, ∞}.

Range = {-∞, 3}.

Axis of symmetry = 4.

Vertex = (4, -2).

Domain = {-∞, ∞}.

Range = {-2, ∞}.

Mathematically, the axis of symmetry (vertex) of a quadratic function can be calculated by using this mathematical expression:

Axis of symmetry (vertex), Xmax = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

Note: The domain of a quadratic function (parabola) is always all real numbers on the x-axis of a cartesian coordinate.

For the given quadratic function y = -2x² + 12x - 15, we have:

Axis of symmetry (vertex), Xmax = -b/2a

Axis of symmetry (vertex), Xmax = -12/2(-2)

Axis of symmetry (vertex), Xmax = -12/-4 = 3.

Vertex (h, k) = (3, 3).

Domain = {-∞, ∞} or x ∈ R.

Range = {-∞, 3}.

x      y

1      2

1      4

3     3

For the given quadratic function y = 2x² - 16x + 30, we have:

Axis of symmetry (vertex), Xmax = -b/2a

Axis of symmetry (vertex), Xmax = -(-16)/2(2)

Axis of symmetry (vertex), Xmax = 16/4 = 4.

Vertex (h, k) = (4, -2).

Domain = {-∞, ∞} or x ∈ R.

Range = {-2, ∞}.

x      y

3     0

5     0

4     -2

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The length of line FG is 16 units

The length of FG is equal to length GH that is to say

line FG = line GH

From the problem, we have that

FG = x  + 11

GH = 3x + 1

Equation both lines

x + 11 = 3x + 1

collecting like terms

11 - 1 = 3x - 1

10 = 2x

rearranging and isolating x

2x = 10

x = 5

The line FG = x + 11 = 5 + 11 = 16 units

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A frequency distribution usually has equal bin widths is the true statement.

All the line charts are not used for the purpose of cross-sectional data. A scatter plot is very useful in this process of visualizing trends over time. A scatter plot essentially requires two quantitative variables (i.e., not categorical data).

The difference of the maximum and minimum values is divided by the number of bins.

1. Identify the maximum and minimum values of the quantitative data.

2. Subtract the minimum value from the maximum value to get the difference

3. Divide the difference by the number of bins to get the approximate width of each bin

The width of the bins in a frequency distribution of quantitative data can be estimated by dividing the difference between the maximum and minimum values of the data by the desired number of bins. This will provide an approximate size for each bin, that can then be used to construct the frequency distribution.

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Answer: $6

Step-by-step explanation:

Divide $390 by 65 to find $6 per ticket.

Answer:

$6

Step-by-step explanation:

$390/65=6

The four consecutive numbers which adds to give 130, are 31, 32, 33, 34

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers.

Given that, there are four consecutive numbers which adds to give 130,

According to the definition of consecutive numbers, we add 1 to each previous integer to get the successive integer,

Therefore, let us consider x, x+1, x+2, x+3 be the four consecutive numbers,

Therefore,

x+x+1+x+2+x+3 = 130

4x + 6 = 130

4x = 124

x = 31

Therefore, the required consecutive integers are, 31, 32, 33, 34

Hence, the four consecutive numbers which adds to give 130, are 31, 32, 33, 34

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The total area of the composite figure can be found to be 24. 52 cm ²

First, find the area of the first triangle :

= 1 / 2 x base x height

= 1 / 2 x 3 x 2. 7

= 4. 05 cm ²

The area of the second triangle :

= 1 / 2 x 3 . 4 x ( 6. 8 - 2 . 7 )

= 6. 97 cm ²

Then the area of the rectangle :

= 5 x 2. 7

= 13. 5 cm ²

The total area of the composite shape is :

= 13.5 + 6.97 + 4. 05

= 24. 52 cm ²

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The measure of angle X is given as follows:

40º.

We have two secants in this problem, and point C is the intersection of the two secants, hence the angle measure of x is half the difference between the angle measure of the largest arc by the angle measure of the smallest arc.

The arc angles are given as follows:

125º and 45º.

Hence the value of x is given as follows:

X = 0.5 x (125 - 45)

x = 40º.

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Answer:

23 degrees

Step-by-step explanation:

Sum of interior angles in a triangle = 180°

∴Sum of interior angles in the right- angled triangle in the question:
    67° + 90° + ? = 180°

= ? = 180° - 90° - 67°

∴ ? = Missing angle measurement = 23°

                                                           = 23 degrees

Answer:

Step-by-step explanation:

The best estimate of the speed Morris is traveling will be 48 miles per hour.

What is conversion?

Conversion means to convert the same thing into different units.

Aneesha travels at a rate of 50 miles per hour. Morris is traveling 3 feet per second less than Aneesha.

We know that 1 mile = 5,280 feet.

Then convert the feet per second to miles per hour. Then the speed of the Morries will be

⇒ 3 feet / 1 second

⇒ (3 / 5285) miles / (1 / 3600) hour

⇒ (3 / 5285) x (3600)

⇒ 2 miles per hour

Then the best estimate of the speed Morris is traveling will be

⇒ 50 - 2

⇒ 48 miles per hour

The best estimate of the speed Morris is traveling will be 48 miles per hour.

Answer: 8y=2h

Step-by-step explanation: you have to subtract the first 2 numbers then add the others and then add letters and boom

The value of m∠J in the triangle is 65°

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

We have triangle HIJ and m∠H = (4x + 1)°, m∠I = (2x-6)° and m∠J = (6x-7)°.

Since the sum of angle in a triangle is 180°. We can say:

m∠H +  m∠I +  m∠J = 180°

(4x + 1)° + (2x-6)° + (6x-7)° = 180°

4x + 1 + 2x-6 + 6x-7 = 180

12x - 12 = 180

12x = 180 + 12

12x = 192

x = 192/12

x = 16

To find m∠J = (6x-7)°, put x = 12 into  m∠J = (6x-7)°. That:

m∠J = 6(12) - 7

m∠J = 72 - 7

m∠J = 65°

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The original coordinates are P(-x, y), and it is on the second quadrant.

Remember that for a general point (a, b), a reflection about the x-axis changes the sign of the y-component, so we will get the image (a, -b)

Here we know that the image after the refection is P' = (-x, -y), then the coordinates of point P are (-x, y)

If we assume both x and y to be positive, then point P would be on the second quadrant.

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The temperature of an apple pie during the time it spends in the oven shows the continuous relationship.

In mathematics, a continuous function is a function that does not have discontinuities that means any unexpected changes in value. A function is continuous if we can ensure arbitrarily small changes by restricting enough minor changes in its input.

A function f(x) is said to be a continuous function in calculus at a point x = a if the curve of the function does NOT break at the point x = a.

A continuous function, on the other hand, is a function that can take on any number within a certain interval. For example, if at one point, a continuous function is 1 and 2 at another point, then this continuous function will definitely be 1.5 at yet another point.

Therefore, option C and E are the correct answers.

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In the image line segment SE is the tangent. The secant line making an angle with tangent line SE is NS. So the angle is ∠GSE. So option B is the correct answer.

Tangent is a line which intersect with only a single point on the curve. The point where the line meets is the point of tangency. Tangent line is always perpendicular to the radius drawn to the point of tangency. Here the tangent line is SE, point of tangency is S.

Secant lines are the lines which passes through two points of a curve. A chord drawn to the circle is a secant line. Here there are two secant lines NS and NA. Here only NS makes an angle with the tangent line.

So the angle made by a tangent and secant line is ∠GSE.

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The image for the question is attached below.

Answer:

The polygon has 8 sides, so the sum of its interior angles is 1080 degrees. Each interior angle is equal to 135 degrees

the interior angle of a regular polygon is equal to the total number of its sides minus two, multiplied by 180 degrees divided by the number of sides. For example, in a regular polygon with 8 sides, one interior angle would equal 1080 degrees (8 - 2) x 180/8 = 1080.

The brand that is the better buy based on their unit price is; Brand A

A unit price is defined as the price for one item or measurement, such as a pound, a kilogram, or a pint, which can be used to compare the same type of goods sold in varying weights and amounts.

It is also referred to as a product's average price which is the result of dividing the product's total sales revenue by the total units sold.

Thus;

Unit price of Brand A = 8.77/24 =$0.365 per pencil

Unit price of Brand B = 9.84/26 = $0.378 per pencil

The cheaper one is the better buy which is Brand A.

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We are are 95% confident that the true proportion of wins using the new strategy will be between 0.1812 and 0.242895 in first simulation and between 0.1948 and 0.2732 in second simulation.

A chess player ran a simulation twice to estimate the proportion of wins to expect using a new game strategy. Each time, the simulation ran a trial of 1,000 games. The first simulation returned 212 wins, and the second simulation returned 235 wins. Construct and interpret 95% confidence intervals for the outcomes of each simulation.

A 95% confidence interval gives us a range of values that we are 95% confident contains the true proportion of wins that the new game strategy will produce in the long run. To construct the confidence interval for each simulation, we can use the following formula:

CI = p ± 1.96 * sqrt(p * (1 - p) / n)

where p is the sample proportion of wins, n is the number of trials, and 1.96 is the z-score corresponding to a 95% confidence level.

For the first simulation, p = 212 / 1000 = 0.212 and n = 1000, so the confidence interval is:

CI = 0.212 ± 1.96 * sqrt(0.212 * (1 - 0.212) / 1000)

CI = (0.1812, 0.2428)

This means that we are 95% confident that the true proportion of wins using the new strategy will be between 0.1812 and 0.2428.

For the second simulation, p = 235 / 1000 = 0.235 and n = 1000, so the confidence interval is:

CI = 0.235 ± 1.96 * sqrt(0.235 * (1 - 0.235) / 1000)

CI = (0.1948, 0.2732)

This means that we are 95% confident that the true proportion of wins using the new strategy will be between 0.1948 and 0.2732.

In general, larger sample sizes lead to narrower confidence intervals. In this case, both confidence intervals overlap, indicating that the two simulations are consistent with each other. This gives us additional confidence in the estimated proportion of wins using the new strategy.

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Answer:

the confidence interval for the first simulation is (0.187, 0.237), and the confidence interval from the second simulation is (0.209, 0.261). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.187 and 0.237. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.209 and 0.261.

Step-by-step explanation:

got it right on the test :)

The required equation model for the given situation is 1/6 (c + 24) = 15. Option C is correct.

The concept of the equation model is a fundamental part of mathematics, and it is used in a wide range of applications. Here are some ways in which the equation model is used,
1. Solving equations    2. Modeling real-world situations 3.Understanding relationships between variables.

here,
According to the question let the Pokémon cards Mark intially had be c,
So as per the given condition, Mark has c + 24 card and he gives 1/6 of his card to his little brother, which is 15 cards
The equation model of the situation is given as,
1/6(c + 24) = 15

Thus, the required equation model for the given situation is 1/6 (c + 24) = 15. Option C is correct.

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The equation which represents the number of tickets sold in advance is 0.35 × 800

Total tickets sold for a play = 800

Percentage of tickets sold in advance= 35%

Number of tickets sold in advance= Percentage of tickets sold in advance × Total tickets sold for a play

= 35% × 800

= 0.35 × 800

= 280 tickets

In conclusion, 280 tickets were sold in advance.

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Carol pays a 10% deposit, it means the amount of deposit she pays is £234,900.

To work out the amount of deposit paid by Carol, we need to find 10% of the house price. We can do this by multiplying the house price by 10/100 or 0.10.

Here are the steps to find the amount of deposit paid by Carol:

1. Start with the house price: £2349000
2. Multiply by 0.10 to find 10% of the house price: £2,349,000 x 0.10 = £234,900
3. The amount of deposit paid by Carol is £234,900.

So, the answer is £234,900.

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Answer:

[tex]\sin A=\frac{a}{b}[/tex]

[tex]\cos A=\frac{c}{b}[/tex]

[tex]\tan A=\frac{a}{c}[/tex]

[tex]\csc A=\frac{b}{a}[/tex]

[tex]\sec A=\frac{b}{c}[/tex]

[tex]\cot A=\frac{c}{a}[/tex]

Step-by-step explanation:

Here are the definitions of the trig functions listed in the picture

[tex]\sin x=\frac{O}{H}[/tex]

[tex]\cos x=\frac{A}{H}[/tex]

[tex]\tan x=\frac{O}{A}[/tex]

[tex]\csc x=\frac{H}{O}[/tex]

[tex]\sec x=\frac{H}{A}[/tex]

[tex]\cot x=\frac{A}{O}[/tex]

Note:

[tex]A[/tex] = side adjacent to angle

[tex]O[/tex] = side opposite to angle

[tex]H[/tex] = hypotenuse

All 6 questions are about angle A.

The side adjacent to angle A is side c.

The side opposite to angle A is side a.

The hypotenuse is side b.

Therefore we can write

[tex]A=c\\O=a\\H=b[/tex]

Knowing that we can fill out the table.

[tex]\sin A=\frac{a}{b}[/tex]

[tex]\cos A=\frac{c}{b}[/tex]

[tex]\tan A=\frac{a}{c}[/tex]

[tex]\csc A=\frac{b}{a}[/tex]

[tex]\sec A=\frac{b}{c}[/tex]

[tex]\cot A=\frac{c}{a}[/tex]

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Answer:

x ≈ 73.4°

Step-by-step explanation:

using the sine ratio in the right triangle

sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{23}{24}[/tex] , then

x = [tex]sin^{-1}[/tex] ([tex]\frac{23}{24}[/tex] ) ≈ 73.4° ( to the nearest tenth )

Graph of y = cosec x is attached below.

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

Given function,

y = cosecx

when x = (π/2)

y = cosec (π/2)

y = 1

when x = π

y = cosec π

y = ∞

when x = 3π/2

y = cosec 3π/2

y = -1

By the calculation, graph of y = cosecx is drawn as follows.

Hence, graph of y = cosecx is attached below.

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The two figures (i.e. triangles) are similar triangles

Let's create a triangle with the following coordinates:

A = (0, 0)

B = (3, 0)

C = (0, 4)

To get the new coordinates, we need to multiply the y-coordinate of each point by 4:

A' = (0, 0 * 4)

B' = (3, 0 * 4)

C' = (0, 4 * 4)

So the new points are:

A' = (0, 0)

B' = (3, 0)

C' = (0, 16)

To determine if the two figures are similar, we need to check if they have the same shape but different sizes.

Specifically, the new triangle is four times larger in the vertical direction but has the same shape and angles as the original triangle.

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