Determine whether you would use the Law of Sines or the Law of Cosines to solve each triangle. Do not solve the triangle.

The formula to find the nth term of the AP is 8 + 3(n - 1).

a = first term = 8

d = common difference = 3

The nth term will be:

= a + (n - 1)d

= 8 + (n - 1)3

= 8 + 3(n - 1)

The age of the 4th student will be:

= a + (n - 1)d

= 8 + (4 - 1)3

= 8 + 9

= 17 years

The sum of total ages if there are 20 students in a row will be:

= n/2[2a + (n - 1)d]

= 20/2 [2×8 + (20 - 1)3]

= 10 [16 + (19 × 3)]

= 10(16 + 57)

= 10(73)

= 730

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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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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 area of the region defined by the inequality 2|x| + 3|y-1| ≤ 6 is 12 square units

The inequality is given as:

2|x| + 3|y-1| ≤ 6

Next, we plot the inequality

From the graph of the inequality (see attachment), we have the following highlights:

The area of a rhombus is:

A = 0.5 * d1 * d1

This gives

A = 0.5 * 6 * 4

Evaluate

A = 12

Hence, the area of the region is 12 square units

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I'm not sure

this app is the wrst don't trust it

The value of the variable x will be 44 cm.

Let L be the length and W be the width of the rectangle.

Then the area of the rectangle will be

Area of the rectangle = L × W square units

Kevin built a wooden flower box for his garden. The area of the base of the box is 264 square centimeters.

If the rectangular base has the dimensions shown below.

Then the value of the variable x will be

A = L × W

264 = 6x

x = 264 / 6

x = 44 cm

The value of the variable x will be 44 cm.

The top view of the wooden flower box is given below.

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x = 4

Step-by-step explanation:

2x² - 1 > 6x

2(4)²-1 > 6(4)

2(16)-1 > 24

32-1 > 24

31 > 24

The rate of change of the linear function represented by the table is 3

An equation is an expression that shows the relationship between two or more variables and numbers.

The standard linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the y intercept.

From the table, using the point (0, -7) and (2, -1):

m = [-1 - (-7)] / (2 - 0) = 3

The rate of change of the linear function represented by the table is 3

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Answer:

you need to save $21

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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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

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:

Answer:

Hence the expression [tex]$$(q-5)(q+8)=q^2+3q-40$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\frac{\begin{matrix}{} & {} & q & - & 5 \\ \times & {} & q & + & 8 \\ \end{matrix}}[/tex]

_____________

[tex]{\frac{\begin{matrix}{} & {} & 8q & - & 40 \\ {{q}^2} & - & 5q & {} & {} \\ \end{matrix}}{\begin{matrix}{{q}^2} & + & 3q & - & 40 \\ \end{matrix}}}$$[/tex]

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.

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 pair of lines are parallel.

A line is a one-dimensional figure, which has length but no width.

Given:

lines passes through (-3, -5) and (1, 3)

and, line passes through (0, 1) and (2, 0)

equation of line

y + 5 = -1/2 (x + 3)

-2y - 10 = x + 3

x + 2y + 13 = 0

and, equation of line

y - 1  = -1/2 (x - 0)

-2y + 2 = x

x + 2y -2 = 0

m1= -1/2 and m2 = -1/2

Hence, the lines are parallel.

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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:

Im guessing you want it as a equation

80-3.50x+70-3x

x being the ammount of time

Step-by-step explanation:

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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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

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 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:

18484.3

Step-by-step explanation:

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

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

18484.3

The difference in speed is 41 km /hr.

Average speed is the total distance travelled per time.

Average speed = total distance / total time

The first step is to determine the distance that Mr. Suksod drives.

Distance = average speed x time

82 x (15/60) = 20.50 km

The second step is to determine the average speed of Mr Taylor = 20.50 ÷ (10/60) = 123 km /hr

Difference in speed = 123 - 82 = 41 km /hr

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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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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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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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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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The equation that represents the total number of apples that Sally has will be the equations x + y = 8 and 8x + 14y = 58

System of equations are equations that consists of two or more equations.

Let the number of small fruits basket be y

Large fruit basket be y

If Sally buys a total of 5 fruit baskets, then;

x + y = 8

If there are 8 apples in a small fruit basket and 14 apples in a large fruit basket with a combined total of 58 apples, then;

8x + 14y = 58

The equation that represents the total number of apples that Sally has will be the equations x + y = 8 and 8x + 14y = 58

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