what is the slope of line 2x-3y=19.
​

By applying operations for complex numbers, we have these:

Herein we must apply the operations of summing two complex numbers, multiplying two complex numbers and multiplying a complex number by a real number, which are defined below:

Addition between two complex numbers

(a + i b) + (c + i d) = (a + c) + i (b + d)     (1)

Multiplication between two complex numbers

(a + i · b) · (c + i d) = (a · c - b · d) + i (b · c + a · d)

Multiplication of a complex number by a real number

k · (a + i b) = k · a + i k · b      (2)

Now we proceed to find the equivalent expressions:

- 5 · x + y = - 5 · (3 + i 8) + (7 - i) = (- 15 - i 40) + (7 - i) = - 8 - i 41

- x · y = - (3 + i 8) · (7 - i) = (- 3 - i 8) · (7 - i) = (- 21 - 8) + i (- 56 + 3) = - 29 - i 53

x · 2 · y = (3 + i 8) · 2 · (7 - i) = (3 + i 8) · (14 - i 2) = (42 + 16) + i (112 - 6) = 58 + i 106

2 · x - 3 · y = 2 · (3 + i 8) - 3 · (7 - i) = (6 + i 16) + (- 21 + i 3) = - 15 + i 19

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Answer:

Step-by-step explanation:

Discussion

First draw FH

<FOH and <FGH share the end points of the chord FH

<FOH is a central angle.

<FGH touches the circumference of the circle in the on the same side of the point of angle <FOH is closest to

Therefore <FGH  is 1/2 <FOH. That is always true of central angles and the smaller angle touching the circumference that <FOH points to

Conclusion

<FGH = 1/2 < FOH

58 = 1/2 <FOH

Therefore <FOH = 2 * 58 = 116

y = < FOH

Answer

y = 116

The true statement is (b) It is a reduction because 0 < n < 1.

The scale factor of dilation is given as:

n = 1/3

When the scale factor (n) is between 0 and 1, then the dilation is considered reduction or compression;

Otherwise, the dilation is considered enlargement or stretch

Because n is between 0 and 1, then the dilation is a reduction

Hence, the true statement is (b) It is a reduction because 0 < n < 1.

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Answer:

b

Step-by-step explanation:

The solution to the system of equations is the point of intersection of the two lines which is at; (0.88, 0.65)

The two simultaneous equations of the line are given as:

y = -²/₅x + 1 -----(1)

y = 3x – 2   -----(2)

Subtracting equation 1 from equation 2 gives;

3.4x - 3 = 0

3.4x = 3

3.4x/3.4 = 3/3.4

x = 0.88

Substitute x = 0.88 in equation 2 to get;

y = 3(0.88) - 2

y = 2.65 - 2

y = 0.65

Thus, the solution to the system of equations is the point of intersection of the two lines which is at (0.88, 0.65).

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The standard form using integers of the equation is 6y - x = 42

Note that solving in standard form means writing it as a simple equation

Given y = 1/6x + 7

Find the LCM of the right side, we have

y = [tex]\frac{x + 42}{6}[/tex]

Cross multiply

6 × y = x + 42

6y = x + 42

Make the variables move to the left side

6y - x = 42

Thus, the standard form using integers of the equation is 6y - x = 42

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Step-by-step explanation:

angle J is also 67 deg since the triangle is an isosceles triangle

angle T is 67 deg since the 2 triangles are congruent

angle G = 180 - 2x67 = 46 deg

ST is 5cm

HJ is 3.7cm

Answer:

What are the missing measures in the diagram?

m∠J =

✔ 67

°

m∠T =

✔ 67

°

m∠G =

✔ 46

°

ST =

✔ 5

cm

HJ =

✔ 3.7

cm

Step-by-step explanation:

The piecewise functions that are represented by the graph are; g(x) = −2, x < −2; g(x) = −2x + 6, x ≥ 1; g(x) = x/2 + 1, –2 ≤ x < 1

From the attached graph of the piecewise function, we can access each option as follows;

A) g(x) = −2x, −2 < x < 0

This is not represented by the graph because g(x) = −2x has negative slope which means it goes downward. There's also no y-intercept in g(x) = −2x.

B)  g(x) = −2, x < −2;

This is represented by the graph because g(x) = −2 is a horizontal line which is only on the left side of x = -2.

C) g(x) = x − 2, −2 < x < 1;

This is not represented by the graph because g(x) = x − 2 has y-intercept at y = -2 and slope of 1 which means that graph of g(x)= x - 2 must be going upward and crossing at y = -2.

D) g(x) = −2x + 6, x ≥ 1

This is represented by the graph because g(x) = −2x+6 satisfies the graph which is going downward.

E) g(x) = x/2 + 1, –2 ≤ x < 1

This is represented by the graph because g(x) = (x/2) + 1 satisfies the graph which is going downward.

The options are;

g(x) = −2x, −2 < x < 0

g(x) = −2, x < −2

g(x) = x − 2, −2 < x < 1

g(x) = −2x + 6, x ≥ 1

g(x) = x/2+ 1, –2 ≤ x < 1

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Answer:

The number that could not be a value of y if y = 4x² - 6 is -12.

Step-by-step explanation:

The value of y for which a function f(x) = y = 4x² - 6 can be determined by knowing the smallest value of y for which x is equal to zero.

So, from the equation y = 4x² - 6, we will replace the value of x with zero to determine the smallest value of y.

y = 4(0) - 6

y = 0 - 6

y = -6

Thus, any number smaller than -6 could not be a value of y for the equation y = 4x² - 6.

Therefore, we can conclude that the number that could not be a value of y if y = 4x² - 6 is -12.

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

If x=-5, what is y is y=4-x²?

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

Put in the value of x.

[tex]\bf{y=4-(-5)^2}[/tex] | evaluate using Bodmas

[tex]\bf{y=4-25}[/tex] | subtract

[tex]\bf{y=-21}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

             [tex]\bf{=y=-21}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic \not1 \theta l}}[/tex]

The common difference for the arithmetic sequence in the task content is; -5.

The common difference of the sequence which is arithmetic can be evaluated as the difference between each successive term.

Hence, it follows that the common difference is;

-1-(-6) = 4-(-1) = 9-4 = 5.

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60+90+ angle U = 180 {sum of angle of triangle}

or, 150+ U= 180

or, angle U = 30°

From here we got that ,

angle U is smallest.

We know that, side opposite to the shortest angle is shortest side. So , short leg is side PM

In right angled triangle PMU,

hypotenuse(h) = 10

angle theta = 60°

perpendicular (PM)= ?

NOW,

sin theta = Perpendicular/ hypotenuse

or, sin 60° = P/10

[tex] \\or \frac{ \sqrt{3} }{2} = p \div 10[/tex]

[tex] or\frac{10 \sqrt{3} }{2} = p[/tex]

[tex]or \: 5 \sqrt{3 } = p[/tex]

Therefore,

[tex]short \: leg = 5 \sqrt{3} [/tex]

Hello !

We solve this system:

[tex]\begin{cases} 2y + 2 &=3y - 9 \: \: \: \: (1)\\ 3x + 6 &=y + 4 \end{cases}[/tex]

[tex](1) : 2y + 2 = 3y - 9 \\ - y + 2 = - 9 \\ - y = - 11\\ y = 11[/tex]

We replace y by 11 in the second equation:

[tex]3x + 6 = 11 + 4 \\ 3x + 6 = 15 \\ 3x = 9 \\ x = \frac{9}{3} = 3[/tex]

_____________

[tex]x = 3[/tex]

[tex]y = 11[/tex]

Have a nice day ;)

Answer:

x = 3

y = 11

Step-by-step explanation:

Since DRWH is a parallelogram

Then ,the opposite sides are congruent

Then , DR = HW and DH = RW

………………………………………………

DR = HW

⇔ 2y + 2 = 3y - 9

⇔ 9 + 2 = 3y - 2y

⇔ 11 = y

⇔ y = 11

DH = RW

⇔ 3x + 6 = y + 4

⇔ 3x + 6 = 11 + 4

⇔ 3x + 6 = 15

⇔ 3x = 15 - 6

⇔ 3x = 9

⇔ x = 9/3

⇔ x = 3

Answer: See attached.

Step-by-step explanation:

   For [a], we graph the parent function (y = x²), but shift it downwards 2 units.

   For [b], we graph the parent function (y = x²), but shift it downwards 6 units, shift it to the right 2 units, and apply a compress factor of 3.

The accuracy in the research done by university is 0.81, sensitivity is 0.93, specificity is 0.81 and precision is 0.047.

Given sample size of 58205 and proportion of people donated 576. Cutoff is 0.5.

Probability is the chance of happening an event among all the events possible. It lies between 0 and 1.

TP=total people donated in sample, TN=total number of people,FP=donation,FN=No donation

Accuracy is calculated as under:

=(TP+TN)/(TP+TN+FP+FN)

=(268+23439)/(238+23439+5375+20)

=23707/29102

=0.81

Accuracy=0.81

Sensitivity is calculated as under:

=TP/(TP+FN)

=268/(268+20)

=268/288

=0.93

Precision is calculated as under:

=TP/(TP+FP)

=268/(268+5375)

=268/5643

=0.047

Their values are the probabilities in itself.

Hence accuracy is 0.81, sensitivity is 0.93, specificity is 0.81 and precision is 0.047.

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The value of x from the given circle is 12

Angle at the vertex of the circle is half the angle at its intercepted arc.

From the given circle;

The measure of <DEF = 80/2 = 4x -8

Equate both angles

4x - 8 = 80/2

Add 8 to both sides

4x - 8 + 8 = 40 + 8

4x = 48

x =12

Hence the value of x from the given circle is 12

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Answer:

[tex]x^{16}[/tex]

Step-by-step explanation:

In this situation, you would add the two exponents (the little numbers at the top) together for the answer.

Answer:

x¹⁶

Step-by-step explanation:

x⁷ × x⁹ = x⁷⁺⁹ = x¹⁶

The ratio of the combined volume of these pyramids to the volume of the prism as a fraction is equal to 1/3.

Mathematically, the volume of a pyramid can be calculated by using this formula:

Volume = 1/3 × b × h

Where:

Since both pyramids have the same base area as the prism, their combined volume is given by:

Combined volume = (1/3 × b × h) + (1/3 × b × h)

Combined volume = 2/3 × b × h

Also, the volume of this prism = 1/2 × b × h

Thus, the ratio is given by:

Ratio = (2/3 × b × h)/(1/2 × b × h)

Ratio = 2/3 × 1/2

Ratio = 1/3.

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Answer:

18484.3

Step-by-step explanation:

[tex]\frac{10^2}{0.00541}[/tex]

[tex]\frac{100}{0.00541}[/tex]

18484.3

After applying algebraic analysis we find the right choices for each case, all of which cannot be presented herein due to length restrictions. Please read explanation below.

In this problem we have a rational function, whose features can be inferred by algebraic handling:

Holes - x-values that do not belong to the domain of the rational function:

x³ + 8 · x² - 9 · x = 0

x · (x² + 8 · x - 9) = 0

x · (x + 9) · (x - 1) = 0

x = 0 ∨ x = - 9 ∨ x = 1

But one root is an evitable discontinuity as:

y = (9 · x² + 81 · x)/(x³ + 8 · x² - 9 · x)

y = (9 · x + 81)/(x² + 8 · x - 9)

Thus, there are only two holes. (x = - 9 ∨ x = 1) Besides, there is no hole where the y-intercept should be.

Vertical asymptotes - There is a vertical asymptote where a hole exists. Hence, the function has two vertical asymptotes.

Horizontal asymptotes - Horizontal asymptote exists and represents the end behavior of the function if and only if the grade of the numerator is not greater than the grade of the denominator. If possible, this assymptote is found by this limit:

[tex]y = \lim_{x \to \pm \infty} \frac {9\cdot x + 81}{x^{2}+8\cdot x - 9}[/tex]

y = 0

The function has a horizontal asymptote.

x-Intercept - There is an x-intercept for all x-value such that numerator is equal to zero:

9 · x + 81 = 0

x = - 9

There is a x-intercept.

Lastly, we have the following conclusions:

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The actual dimensions of the Great Pyramid include a height of 146.6m and a base of 230.33m.

The Great Pyramid is the largest Egyptian pyramid and also the tomb of rge Fourth dynasty Pharaoh.

It should be noted that the actual dimensions of the Great Pyramid include a height of 146.6m and a base of 230.33m.

It is also the oldest of the seven wonders of the world.

A scale scale drawing using an exact proportion between the pyramid will be 147 to 230.

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Answer:

The actual dimensions of the Great Pyramid include a height of 146.6m and a base of 230.33m.

How to illustrate the information?

The Great Pyramid is the largest Egyptian pyramid and also the tomb of the Fourth dynasty Pharaoh.

It should be noted that the actual dimensions of the Great Pyramid include a height of 146.6m and a base of 230.33m.

It is also the oldest of the seven wonders of the world.

A scale drawing using an exact proportion between the pyramid will be 147 to 230.

Answer:

I don't know

Step-by-step explanation:

980-788711758c75ds47c75c70rz76vyif7cuc8f58x85c7f85f8c

3²×5, 2⁴×5, 2²×3×5×7, 5⁴ and 3⁴ are the index notations of the numbers 45, 80, 420, 625 and 81 respectively. This can be obtained by taking the factors of these numbers and wring as the powers as shown below.

It is a method of representing numbers and variables that are multiplied by themselves a number of times.

For example, 7³, a²

The given numbers can be represented as the following:

(1) 45 =3×3×5 = 3²×5

(2) 80 =2×2×2×2×5 = 2⁴×5

(3) 420 =2×2×3×5×7 = 2²×3×5×7

(4) 625 =5×5×5×5 = 5⁴

(5) 81 =3×3×3×3 = 3⁴

Hence 3²×5, 2⁴×5, 2²×3×5×7, 5⁴ and 3⁴ are the index notations of the numbers 45, 80, 420, 625 and 81 respectively.

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6) ∠FOC is vertical to ∠EOD

7) m∠POF is complementary to M∠FOB.

8) m∠AOC = 30°

6) Vertical angles are angles that are opposite of each other when two lines cross. Thus;

∠FOC is vertical to ∠EOD

7) Given that m∠POF + M∠FOB = 90

Two angles are called complementary when their measures add to 90 degrees. Thus;

m∠POF is complementary to M∠FOB.

8)  m∠BOC = 150. Thus;

m∠AOC = 180 - 150

m∠AOC = 30° because they are supplementary angles.

9) m∠EOA = 37. Thus;

m∠FOA = 180 - 37

m∠FOA = 143° because they are supplementary angles.

10) ∠EGH is adjacent to ∠OGH

This is from definition of adjacent angles

11) ∠EGH ≅ ∠DOB

m∠HGO = 128°, m∠DOB = 180° - 128° = 52° because they are supplementary angles.

12) m∠EOA = 67°, m∠DOB = 29°. Thus;

m∠EOD = 180 - (67 + 29)

m∠EOD = 84° because sum of angles on a line is 180°

13) m∠AOD + m∠DOB = 180 means that ∠AOD is supplementary to ∠DOB.

14) ∠COF ≅ ∠DOF and so we can say that;

FO is perpendicular to CD.

15) m∠COP = 72° and m∠POF = 31°. Thus;

m∠EOD = 72 + 31

m∠EOD = 103°

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Answer:

3. Linear: f(x) = 1320(1.20)^2

Step-by-step explanation:

Exponential Growth Formula: f(x) = [tex]x_{0}[/tex] × (1 + r)^x

f(x) is the value at time t.

x0 is the initial value at time t=0.

x0 = 1320

r = 20% = 0.2

Solve:

f(x) = [tex]x_{0}[/tex] × (1 + r)^x

f(x) = 1320 × (1 + 0.2)^2

f(x) = 1320(1.2)^2

Answer: 3rd answer

Step-by-step explanation:

Because Purdue starts with 1320 employees, and then multiplies that by 1.2 each year. If x represents 3 years, Purdue has:

 1320(1.2)^3

=1320(1.728)

=2280.96

The geometric mean is 6833.049

The value of fund in 1999 is 5,700

value of fund in 2009 is 8,064

We need to find the geometric mean annual percent increase in the number of funds.

The geometric mean is the average of a set of products,  it is defined as the compounding effect of the numbers in the series in which the numbers are multiplied by taking nth root of the multiplication.

The calculation of which is commonly used to determine the performance results of an investment or portfolio.

We know, The Geometric mean is = [tex]\sqrt[n]{x_1*x_2*...*x_n}[/tex]

substituting values:

[tex]\\ GM = (5790*8064)^{0.5} = 6833.049[/tex]

Geometric mean is = [tex]\sqrt[n]{x_1*x_2*...*x_n}[/tex]

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Using a decaying exponential function, it is found that the maximum height reached after the 10th bounce is of 20.62 cm.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

In this problem, the parameters are:

A(0) = 192, r = 0.2.

Hence the maximum height after the nth bounce is:

[tex]A[n] = 192(0.8)^n[/tex]

After the 10th bounce, the maximum height in cm is of:

[tex]A[10] = 192(0.8)^10 = 20.62[/tex]

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Answers:

=====================================================

Explanation:

A function has any given input lead to exactly one output.

Relation 1 has the input "paper" lead to more than one output, which are the values 9 and -3. Therefore, relation 1 is not a function.

Relations 2 and 4 are similar stories.

---------

In contrast, relation 3 has each input lead to exactly one output, which is why we have a function here.

Put another way: a function cannot have the x coordinates repeat, but the y coordinates can repeat.