10. Find the measure of each missing angle.m_1 =m22=127mZ3 =2.m24 =595/43m25 =

Answer:

AB and GH

Step-by-step explanation:

they never intersect

Hope this helps

Answer:

c) AB and GH

Explanation:

Parallel lines are any two (or more) lines that have the same slope and would not intersect if the line is continued in either direction.

(a) Since u = cos(x) gives du = -sin(x) dx, we have

∫ sin(x) cos(x) dx = - ∫ (-sin(x)) cos(x) dx

= - ∫ cos(x) d(cos(x))

= - ∫ u du

= - 1/2 u² + C

= -1/2 cos²(x) + C

(b) Now u = sin(x) gives du = cos(x) dx, so

∫ sin(x) cos(x) dx = ∫ sin(x) d(sin(x))

= ∫ u du

= 1/2 u² + C

= 1/2 sin²(x) + C

(c) Since sin(2x) = 2 sin(x) cos(x), we have

∫ sin(x) cos(x) dx = 1/2 ∫ sin(2x) dx

Substitute u = 2x, so that du = 2 dx, and

∫ sin(x) cos(x) dx = 1/2 ∫ sin(2x) dx

= 1/4 ∫ 2 sin(2x) dx

= 1/4 ∫ sin(u) du

= -1/4 cos(u) + C

= -1/4 cos(2x) + C

(d) Integrate by parts, setting

u = sin(x)          ==>  du = cos(x) dx

dv = cos(x) dx  ==>  v = sin(x)

Then

∫ sin(x) cos(x) dx = sin²(x) - ∫ sin(x) cos(x) dx

2 ∫ sin(x) cos(x) dx = sin²(x) + C

∫ sin(x) cos(x) dx = 1/2 sin²(x) + C

The solutions in (b) and (d) are identical, but all 4 are equivalent, and this follows from the identities,

sin²(x) + cos²(x) = 1

cos(2x) = cos²(x) - sin²(x)

"Let x be any vector in \(C^n\), let q = \(x^T\)Ax, and let A be an n-by-n real matrix with the characteristic that \(A^T\) = A. By confirming that q = q, the equalities below demonstrate that q is a real number.

Let A be n x n real matrix with the property that. \(A^T = A\).

if Ax = λx.

(Ax) = λx

\(xA^T=\) λx

xA = λx( and therefore dλ are real, A =\(A^{T}\) = and dλ = λ).

x(A-λL) = 0

Therefore, A-λL is a real matrix.

Assume that A is a n by n matrix with a characteristic polynomial defined by det(λI−A). The number of times an eigenvalue of A appears as a root of that distinctive polynomial is known as its multiplicity.

and x (λI-A) = 0

Therefore, x(λL-A) is also real.

X1 is real.

Therefore, since is one of A's eigenvalues, there exists a nonzero vector X\(C^n\) such that AX=X

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Answer:

30.9717685346

Step-by-step explanation:

The probability that the sum of the numbers on your dice is 9 or 8 is 1/4.

It should be noted that to calculate the probability of rolling a 9 or 8, we can first list all the possible outcomes of rolling two six-sided dice:

1 + 1 = 2

1 + 2 = 3

1 + 3 = 4

1 + 4 = 5

1 + 5 = 6

1 + 6 = 7

2 + 1 = 3

2 + 2 = 4

2 + 3 = 5

2 + 4 = 6

2 + 5 = 7

2 + 6 = 8

3 + 1 = 4

3 + 2 = 5

3 + 3 = 6

3 + 4 = 7

3 + 5 = 8

3 + 6 = 9

4 + 1 = 5

4 + 2 = 6

4 + 3 = 7

4 + 4 = 8

4 + 5 = 9

4 + 6 = 10

5 + 1 = 6

5 + 2 = 7

5 + 3 = 8

5 + 4 = 9

5 + 5 = 10

5 + 6 = 11

6 + 1 = 7

6 + 2 = 8

6 + 3 = 9

6 + 4 = 10

6 + 5 = 11

6 + 6 = 12

There are a total of 36 possible outcomes, and we need to find the probability of rolling a 9 or 8, which corresponds 9 outcomes.

This will be;

= 9 / 36

= 1/4

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Answer: $125

Step-by-step explanation:

$55 per tire (2)

$30 per hour of labor (0.5)

$55(2)+30(0.5)=$125

Answer:

$125

Step-by-step explanation:

2 tires =$110 ($55 each tire)

half an hour of labor=$15

the data classification (categorical or quantitative) and type of data (Nominal or Ordinal or Continuous or Discrete)

A. Height of sunflowers in a field.

1.Quantitative

2.Continuous

B. Jersey color of all the NCAA football teams.

1.Categorical

2.Nominal

A. Height of sunflowers in a field.

1.Quantitative

2.Continuous

B. Jersey color of all the NCAA football teams.

1.Categorical

2.Nominal

Data classification is a process of organizing data into categories based on their characteristics, attributes, or features. There are two main types of data classification:

Categorical Data: Data that can be divided into categories or classes. For example, color, gender, and type of cuisine are all examples of categorical data. Categorical data can be further classified into two types:

a. Nominal Data: Data that does not have an inherent order or ranking. For example, hair color, eye color, and favorite movie are all examples of nominal data.

b. Ordinal Data: Data that has a natural order or ranking. For example, education level (high school, college, postgraduate), star rating (1 star, 2 stars, 3 stars), and satisfaction level (very unsatisfied, unsatisfied, neutral, satisfied, very satisfied) are all examples of ordinal data.

Quantitative Data: Data that can be measured and expressed as a number. For example, height, weight, and time are all examples of quantitative data. Quantitative data can be further classified into two types:

a. Continuous Data: Data that can take on any value within a specified range. For example, height, weight, and temperature are all examples of continuous data.

b. Discrete Data: Data that can only take on specific values. For example, number of children in a family, number of pets, and number of rooms in a house are all examples of discrete data

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Answer:

5000

Step-by-step explanation:

Assuming they both work 365days

roughly 52 weeks

number of time sherry is paid per year = \(\frac{52}{2} = 26\)

because she is paid every two weeks

number of time donna is paid per year = \(4\)

because she is paid 4 times a year (quarterly)

let s =  amount sherry is paid biweekly

let d = amount donna is paid quarterly

\(s = \frac{26000}{26} = 1000\\\\d = \frac{26000}{4} = 6500\\\\difference = 65000 - 1000 = 5000\\\)

Answer:

5500

Step-by-step explanation:

\( x - 7 = 10 \\ \\ x = 10 - 7 \\ \\ x = 3\)

Answer:

\(\cos G=\dfrac{2}{3}\)

\(\csc E=\dfrac{3}{2}\)

\(\cot G=\dfrac{2}{\sqrt{5}}\)

Step-by-step explanation:

If the right angle of right triangle EFG is ∠F, then EG is the hypotenuse, and EF and FG are the legs of the triangle. (Refer to attached diagram).

Given ΔEFG is a right triangle, and EG = 6 and FG = 4, we can use Pythagoras Theorem to calculate the length of EF.

\(\begin{aligned}EF^2+FG^2&=EG^2\\EF^2+4^2&=6^2\\EF^2+16&=36\\EF^2&=20\\\sqrt{EF^2}&=\sqrt{20}\\EF&=2\sqrt{5}\end{aligned}\)

Therefore:

\(\hrulefill\)

To find cos G, use the cosine trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the hypotenuse is EG.

Therefore:

\(\cos G=\dfrac{FG}{EG}=\dfrac{4}{6}=\dfrac{2}{3}\)

\(\hrulefill\)

To find csc E, use the cosecant trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosecant trigonometric ratio} \\\\$\sf \csc(\theta)=\dfrac{H}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle E, the hypotenuse is EG and the opposite side is FG.

Therefore:

\(\csc E=\dfrac{EG}{FG}=\dfrac{6}{4}=\dfrac{3}{2}\)

\(\hrulefill\)

To find cot G, use the cotangent trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cotangent trigonometric ratio} \\\\$\sf \cot(\theta)=\dfrac{A}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the opposite side is EF.

Therefore:

\(\cot G=\dfrac{FG}{EF}=\dfrac{4}{2\sqrt{5}}=\dfrac{2}{\sqrt{5}}\)

The unit rate of computers per day using the graph is that 12 computers are made per day.

The unit rate is how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. Unit rates is said to be the amount of something in each unit or per unit.

To obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x

So, it is given by:

\(\text{Slope} = \dfrac{\text{change in y}}{\text{change in x}}\)

\(\text{Slope} = \dfrac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}\)

\(\text{y}_2 = 60 , \ \text{y}_1 = 36 , \ \text{x}_2 = 5, \ \text{x}_1 = 3.\)

\(\text{Slope} = \dfrac{(60 - 36)}{(5 - 3)} = \dfrac{24}{2} = 12\)

\(\bold{Slope = 12}\)

Unit rate = 12 computers per day.

The attachment of the graph is given below.

Therefore, the unit rate of computers per day is 12.

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The amount of the investment after 8 years will be, $4,357.64

Given, $500 is invested in an account earning 7% interest compounded quarterly.

We have to find the value of the invested amount after 8 years,

as, Amount = P(1 + r/100)^t

where, P is the amount of money invested, r is the rate of interest and t is the amount of time

Amount = 500(1 + 7/100)^(8×4)

Amount = 500(1.07)^32

Amount = 500×8.715

Amount = 4,357.635

So, the amount of the investment after 8 years will be, $4,357.64

Hence, the amount of the investment after 8 years will be, $4,357.64

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The rate that is equivalent to the rate at which John drove to San Antonio is 60 miles per hour

From the question, we have the following parameters that can be used in our computation:

John drove from here to San Antonio which is 180 miles away in 3 hours.

This means that

Distance = 180 miles

Time = 3 hours

Using the above as a guide, we have the following:

Speed = Distance/Time

Substitute the known values in the above equation, so, we have the following representation

Speed = 180/3

Evaluate

Speed = 60

Hence. the rate that is equivalent to the rate at which John drove to San Antonio is 60 miles per hour

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Answer:

Thus, the equation of line for point (-1, 2)  is y = x + 3.

Step-by-step explanation:

Answer:

The equation of the line is y = x + 3.

Step-by-step explanation:

A line that is parallel to y=x+4 and passes through the point (-1,2) will have the same slope as y=x+4. The slope of y=x+4 is 1, so the equation of the line will be in the form y = mx + b, where m=1. To find b, we can plug in x = -1 and y = 2 into the equation and solve for b.

y = mx + b

y = 1 * -1 + b

y = -1 + b

b = y + 1

b = 2 + 1

b = 3

Answer:

You didn't show the options but the correct equation should be y=5x+12

Step-by-step explanation:

Hope this helps!

Answer:

Step-by-step explanation:

You want points A(-4, 0), B(0, -1) and C(-3, -3) reflected across the y-axis and translated left 5 and up 2.

The reflection across the y-axis changes the sign of the x-coordinate:

  (x, y) ⇒ (-x, y)

The translation adds the translation vector to the reflected coordinates.

  (x, y) ⇒ (x -5, y +2) . . . . . . translation (by itself)

Then the result of both transformations is ...

  (x, y) ⇒ (-x -5, y +2)

For a number of points, this arithmetic is conveniently accomplished by a calculator. The result is ...

The minimum amount of fencing she can use is 126.5 ft.

An equation is an expression used to show the relationship between two or more variables and numbers.

Let x represent the length of the long side of pen and y represent the length of the small side of pen. Hence:

xy = 2000

x = 2000/y

The perimeter (P) is:

P = x + 2y

P = 2000/y + 2y

The minimum amount is at dP/dy = 0, hence:

dP / dy = 2 - 2000/y²

2 - 2000/y² = 0

2 = 2000/y²

y = 31.6 ft.

Also:

x(31.6) = 2000

x = 63.3

P = 63.3 + 2(31.6) = 126.5 ft.

The minimum amount of fencing she can use is 126.5 ft.

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Answer:

Step-by-step explanation:

\(1c-0.25c=0.75c\)

Answer:

a) Kat's equation is 10 + 12x = Amount

b) Carter's equation is 85 + 7x = Amount

c)

Explanation:

Kat has $10 saved up in her account and charges $12 for each car she washes, the equation representing this is:

10 + 12x

Where x is the number of cars she washes.

Carter's equation is:

85 + 7x

I

Answer: Length 132cm, Breadth 48cm

Explanation:

Perimeter = 360cm

Let the length and breadth be x

ATQ

2(11x + 4x) = 360

22x + 8x = 360

30x = 360

x = 360/30

x = 12

Length = 11×12

= 132 cm

Breadth = 4×12

= 48cm

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Answer:

9

Step-by-step explanation:

12 minutes long it will take her to complete the triathlon.

A division is a process of splitting a specific amount into equal parts.

Given that The race consists of a 2.4-mile swim

Tiffany can swim at an average pace of 1.8mph.

d=rt

t=d/r

time=2.4/1.8=1.33

Tiffany can ride  a 112-mile bike.

She rides her bike at an average of 18.8mph

t=112/18.2=6.15

tiffany runs 26.2 mile at an  average of 6.2 mph

t=26.2/6.2=4.23

We total the sum of the times to complete each of the three legs of the triathlon

1.33+6.15+4.23

12 minutes

Hence, 12 minutes long it will take her to complete the triathlon.

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Answer:

0.63

Step-by-step explanation:

Given that:

\(C \ = \ Californians \ (registered \ voters) \ preferrin g \ life \ in \ prison \ without \ parole \ over \ the \ death \\ penalty \ for \ a \ person \ convicted \ of \ first \ degree \ murder.\)P(C) = 0.48

L = Latino Californians

P(L) = 0.364

∴

P(C/L) = 0.63

Answer:

option c

y = -1

Step-by-step explanation:

2x - y = 3 -----------------(1)

x - 3y = 4 ------------------(2)

from equation (2)

x = 4 + 3y-------------------(3)

substituting the value of x in equation (1)

2(4+3y) - y = 3

8 + 6y - y = 3

5y = 3-8

5y = -5

y = -1

substituting the value of y in equation (3)

x = 4 - 3

x = 1

We are given two coupons A and B. Coupon A gives a 60% discount on a $87 item. Let's calculate the amount to pay by subtracting 60% of 87. We do that by multiplying 87 by 60/100, like this:

Now we subtract this from the initial price, like this:

therefore, using coupon A she must pay $34.8

For coupon B there's a rebate of $55. We calculate the amount to pay by subtracting 55 to the total price of 87, like this:

Therefore, using coupon B she must pay $32.

Coupon B gives the lowest price, the price of coupon B compared to coupon A is calculated by subtracting both prices:

Therefore, with coupon B she pays $2.8 less than the price with coupon A.

Answer:

x is 21. dccxpxpdpdpdpdp

Answer:

Mutual

Step-by-step explanation:

33° +2x-15 =90

2x =90+15-33

2x=72

X=36

Answer:

4005

Step-by-step explanation:

3,998 - (-7) = ?

Two negative signs will make a positive sign.

3,998 - (-7) = 3998 + 7 = 4005

So, the answer is 4005