In the given quadrilateral, ∠ A= 110 and ∠ B= 52. Find the measure of ∠ D.

Answer:

\([d(A, B)]^2=\boxed{85}\)

\([d(A,C)]^2+[d(B,C)]^2=\boxed{85}\)

\(\sf Area=\boxed{17}\; units^2\)

Step-by-step explanation:

From inspection of the given diagram, the vertices of the triangle are:

If ΔABC is a right triangle, the sum of the squares of the two shorter sides will equal the square of the longest side.  This is the definition of Pythagoras Theorem.

Use the distance formula to find the side lengths of the triangle.

\(\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}\)

\(\begin{aligned}d[(A,B)]&=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\&=\sqrt{(1-(-5))^2+(-2-5)^2}\\&=\sqrt{(6)^2+(-7)^2}\\&=\sqrt{36+49}\\&=\sqrt{85}\end{aligned}\)

\(\begin{aligned}d[(A, C)]&=\sqrt{(x_C-x_A)^2+(y_C-y_A)^2}\\&=\sqrt{(-1-(-5))^2+(6-5)^2}\\&=\sqrt{(-4)^2+(1)^2}\\&=\sqrt{16+1}\\&=\sqrt{17}\end{aligned}\)

\(\begin{aligned}d[(B, C)]&=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\&=\sqrt{(-1-1)^2+(6-(-2))^2}\\&=\sqrt{(-2)^2+(8)^2}\\&=\sqrt{4+64}\\&=\sqrt{68}\end{aligned}\)

Therefore:

\(\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}\)

The triangle is a right triangle if:

\([d(A,C)]^2+[d(B,C)]^2=[d(A,B)]^2\)

Substitute the found side lengths into the formula:

\(\implies [\sqrt{17}]^2+[\sqrt{68}]^2=[\sqrt{85}]^2\)

\(\implies 17+68=85\)

\(\implies 85=85\)

Therefore, this proves that ΔABC is a right triangle.

To find the area of a right triangle, half the product of the two shorter sides:

\(\begin{aligned}\implies \sf Area &= \dfrac{1}{2}bh\\&=\dfrac{1}{2} \cdot [d(A,C)] \cdot [d(B,C)]\\&=\dfrac{1}{2} \cdot \sqrt{17} \cdot \sqrt{68}\\&=\dfrac{1}{2} \cdot \sqrt{17 \cdot 68}\\&=\dfrac{1}{2} \cdot \sqrt{1156}\\&=\dfrac{1}{2} \cdot \sqrt{34^2}\\&=\dfrac{1}{2} \cdot 34\\&=17 \sf \; units^2\end{aligned}\)

Therefore, the area of the given triangle is 17 units².

Answer:

a = 3x - 6/x

................

Answer:

0.108

Step-by-step explanation:

Given that:

Number of flights reached early = 65

Number of flights reached on time = 273

Number of flights reached late = 218

Number of flights canceled = 44

To find:

The probability that a flight is early.

Solution:

First of all, let us have a look at the formula for probability of an event E.

Formula for probability of an event E can be observed as:

\(P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}\)

Here, Event E is that the flight is early.

Number of favorable cases is equal to the number of a flights which reached early i.e. 65

Total number of cases is the total number of flights.

i.e. 65 + 273 + 218 + 44 = 600

So, the required probability is:

\(P(E) = \dfrac{65}{600} = \bold{0.108}\)

Answer:

  SAS Postulate

Step-by-step explanation:

The contributors to the proof are listed in the left column. They consist of a congruent Side, a congruent Angle, and a congruent Side. The SAS Postulate is an appropriate choice.

To simplify the expression (2x-3)(5x^2-2x+7), we can use the distributive property.

First, multiply 2x by each term inside the second parentheses:

2x * 5x^2 = 10x^3

2x * -2x = -4x^2

2x * 7 = 14x

Next, multiply -3 by each term inside the second parentheses:

-3 * 5x^2 = -15x^2

-3 * -2x = 6x

-3 * 7 = -21

Combine all the resulting terms:

10x^3 - 4x^2 + 14x - 15x^2 + 6x - 21

Now, combine like terms:

10x^3 - 19x^2 + 20x - 21

So, the simplified expression is 10x^3 - 19x^2 + 20x - 21.

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Answer:10

Step-by-step explanation:

Answer:

200

Step-by-step explanation:

\(a^{2}\) + \(b^{2}\) = \(c^{2}\)

\(120^{2}\) + \(160^{2}\) = \(c^{2}\)

14400 + 25600 = \(c^{2}\)

40000 = \(c^{2}\)

\(\sqrt{40000}\) = \(\sqrt{c^{2} }\)

200 = c

Jesus love you.

Answer:

For acute angles, remember what sine means: opposite over hypotenuse. If we increase the angle, then the opposite side gets larger. That means "opposite/hypotenuse" gets larger or increases.

Step by Step:

Keep this in mind >>

Consider the unit circle > The sine and cosine ratios are the only ratios that have 1 (the radius or hypotenuse) as the denominator. The numerators (sides) vary between 0 and 1, thus determining that the sine and cosine do the same.

All of the other ratios (tangent, cotangent, secant, cosecant) have a side as the denominator, varying between 0 and 1. As any denominator approaches 0, the value of the ratio approaches infinity.

a.) The value of pulses exported by US in billion would be=30 billion.

b.) The ratio of wheat export of UK to maize export of IND would be= 6:5

For question a.)

To calculate the pulses, the following steps should be taken as follows:

From the bar chart, the value of pulses in billions = 30 billions.

For question b.)

The ratio of wheat export at UK and maize export at IND would be calculated as follows:

The quantity of wheat export at UK = 24

The quantity of maize export at IND = 20

Therefore, the ratio of wheat to maize = 24:20= 6:5

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Answer:

Step-by-step explanation:

Slope of the line:

\(m = \frac{y-y1}{x-x1} \\\)

Given:

slope = -3/4

point (x1,y1) = (2, -1)

Substitute and solve

\(m = \frac{y-y1}{x-x1} \\-\frac{3}{4} = \frac{y-(-1))}{x-2} \\-3(x-2) = 4(y+1)\\-3x + 6 = 4y + 4 \\Transpose\\4y = -3x + 6 - 4\\4y = -3x + 2 \\y = -3/4x + 2/4\\y = -3/4x + 1/2\\OR\\4y +3x - 2 = 0\)

1/2 is the y-intercept

(0,1/2)

Since we have 2 points already, we can then graph the line.

(2, -1) and (0, 1/2)

Expanding the polynomial, (7x + 5)(2x³ − 4x² + 9x − 3), we have: A. 14x^4 - 18x³ + 43x² + 24x - 15.

By applying the distribution property, we can expand a given polynomial expression like the one given above.

Given, (7x + 5)(2x³ − 4x² + 9x − 3), distribute to eliminate the parentheses:

7x(2x³ − 4x² + 9x − 3) + 5(2x³ − 4x² + 9x − 3)

14x^4 - 28x³ + 63x² - 21x + 10x³ - 20x² + 45x - 15

Combine like terms:

14x^4 - 18x³ + 43x² + 24x - 15

The correct solution is option A.

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Answer:

76.665

Step-by-step explanation:

Given that,

cos α = 0.93, Sin θ =0.26 and tanβ = 0.84

We need to find the value of α, β and θ

\(\alpha =\cos^{-1}(0.93)\\\\=21.565\\\\\beta =\tan^{-1}(0.84)\\\\=40.030\\\\\theta=\sin^{-1}(0.26)\\\\=15.07\)

So,

\(\alpha +\beta +\theta=21.565+40.03+15.07\\\\=76.665\)

Hence, the final answer is 76.665.

Step-by-step explanation:

Area of a kite = D1 × D2/2

D1 = 6.9 + 13.8 = 20.7m

D2 = 9.2 + 9.2 = 18.4m

Area =. 20.7 × 18.4

------------------

2

= 190.44m²

Answer:

the first one is 5/12 and the second one is 6/28. Hope this helps and have a nice day:)

Answer: 5/12, 3/14

Step-by-step explanation:

first problem:

first, we just reduce the numbers.

5/4 x 1/3

then, we simply multiply.

5/12

second problem:

again, we just reduce the numbers.

3/2 x 1/7

and then multiply.

3/14

Answer:

y=2x-6

Step-by-step explanation:

y+4=-2(x-1)

Since the slope intercept form is in the form of:

y=mx+c

Making above equation in this form.

y+4=-2(x-1)

opening bracket

y+4=2x-2

subtracting both side by 4.

y+4-4=2x-2-4

y=2x-6

This equation is the slope intercept form.

The five-number summary for this data set is 29, 32, 43.5, 50.5, and 53, and the interquartile range is 18.5.

Measures of statistical dispersion, or the spread of the data, include the interquartile range. In addition to the IQR, other names for it include the midspread, middle 50%, fourth spread, and H-spread.

To find the five-number summary and interquartile range for this data set, we first need to find the quartiles.

Step 1: Find the median (Q2)

When a data collection is sorted from least to largest, the median is the midway value. Since there are 12 values in this data set, the median is the average of the sixth and seventh values:

Median (Q2) = (41 + 46)/2 = 43.5

Step 2: Find the lower quartile (Q1)

The lower quartile is the median of the lower half of the data set. Since there are 6 values below the median, we take the median of those values:

Q1 = (32 + 32)/2 = 32

Step 3: Find the upper quartile (Q3)

The upper quartile is the median of the upper half of the data set. Since there are 6 values above the median, we take the median of those values:

Q3 = (50 + 51)/2 = 50.5

Now we have all the information we need to construct the five-number summary and interquartile range:

Minimum: 29

Lower quartile (Q1): 32

Median (Q2): 43.5

Upper quartile (Q3): 50.5

Maximum: 53

Interquartile range (IQR) = Q3 - Q1 = 50.5 - 32 = 18.5

the five-number summary for this data set is 29, 32, 43.5, 50.5, and 53, and the interquartile range is 18.5.

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Answer:

100%hajsmsmwkwkkqjwjnwnw

The graph of y=-3x-1 is given in the attachment.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The given equation is  y=-3x-1

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

In the given equation slope is -3.

Let us find few values of x and y.

x    0    1    2     3    4

y    -1   -4   -7    -10  -13

Hence, the graph of y=-3x-1 is given in the attachment.

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Answer:

36

Step-by-step explanation:

The angles of the triangle are equal.

Hence, the sides of the triangle must also be equal.

It is an equilateral triangle.

Equating JK and KL :

Finding KL :

All angles are equal means all sides are equal

KL

Answer:

Equation 2: y=750-100x

Step-by-step explanation:

The equations that are true for x = -2 and x = 2 are x² + 4 = 0 and 4x² = 16. So, the correct option is A) and D).

To determine which equations are true for x = -2 and x = 2, we simply substitute these values into each equation and check if the equation is true or not. Here are the results

x² - 4 = 0

Substituting x = -2 gives (-2)² - 4 = 0, which is true. Substituting x = 2 gives 2² - 4 = 0, which is also true. Therefore, this equation is true for both x = -2 and x = 2.

x² = -4

Substituting x = -2 gives (-2)² = -4, which is not true. Substituting x = 2 gives 2² = -4, which is also not true. Therefore, this equation is not true for either x = -2 or x = 2.

3x² + 12 = 0

Substituting x = -2 gives 3(-2)² + 12 = 0, which is true. Substituting x = 2 gives 3(2)² + 12 = 24, which is not equal to zero. Therefore, this equation is true for x = -2 but not for x = 2.

4x² = 16

Substituting x = -2 gives 4(-2)² = 16, which is true. Substituting x = 2 gives 4(2)² = 16, which is also true. Therefore, this equation is true for both x = -2 and x = 2.

2(x - 2)² = 0

Substituting x = -2 gives 2(-2 - 2)² = 0, which is true. Substituting x = 2 gives 2(2 - 2)² = 0, which is also true. Therefore, this equation is true for both x = -2 and x = 2.

Therefore, the two equations that are true for both x = -2 and x = 2 are x² - 4 = 0 and 4x² = 16. So, the correct answer is A) and D).

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Answer:

the answer is 70

Step-by-step explanation:

Answer:

Z

Step-by-step explanation:

Answer:

The total capacity of the container is 30 gallons in volume.

Step-by-step explanation:

Assume that the container total capacity is [x] gallons. Then, according to the question -

7x/10 - 6 = x/2

7x/10 - x/2 = 6

x(0.7 - 0.5) = 6

0.2x = 6

x = 6/0.2

x = 6/(1/5)

x = 30 gallons

After making all the necessary adjustments, the reconciled bank balance for ABC Company's ledger at the end of July is Br. 4,164.42.

To reconcile the bank statement balance with the company's ledger balance for ABC Company, we need to go through the provided information step by step and make the necessary adjustments. Let's calculate the adjusted bank balance:

Starting with the bank statement balance: Br. 4,964.47

Add the deposit made after banking hours: + Br. 410.90

New bank balance: Br. 5,375.37

Now let's make adjustments for the outstanding checks and other transactions:

Deduct the erroneously charged check: - Br. 973

New bank balance: Br. 4,402.37

Deduct the outstanding checks:

Check No. 801: Br. 100.00

Check No. 888: Br. 10.25

Check No. 890: Br. 294.50

Check No. 891: Br. 205.00

Total deduction: Br. 609.75

New bank balance: Br. 3,792.62

Correct the incorrectly charged check: + Br. 90

New bank balance: Br. 3,882.62

Add the proceeds from the collection of the interest-bearing note: + Br. 500.00

New bank balance: Br. 4,382.62

Add the interest earned on the average account balance: + Br. 24.75

New bank balance: Br. 4,407.37

Deduct the incorrectly recorded check: - Br. 90

New bank balance: Br. 4,317.37

Deduct the fee charged for handling the collection of the note: - Br. 5.00

New bank balance: Br. 4,312.37

Deduct the check returned due to insufficient funds: - Br. 50.25

New bank balance: Br. 4,262.12

Deduct the service charge for the month of July: - Br. 12.70

New bank balance: Br. 4,249.42

Deduct the erroneously recorded check: - Br. 85.00

New bank balance: Br. 4,164.42

Now, we compare the adjusted bank balance (Br. 4,164.42) with the ledger balance provided (Br. 4,173.83).

Adjusted bank balance: Br. 4,164.42

Ledger balance: Br. 4,173.83

The difference between the adjusted bank balance and the ledger balance is Br. 9.41. This difference is likely due to some unrecorded transactions or errors in recording. To reconcile the balances fully, further investigation is required to identify the specific cause of the discrepancy and make the necessary adjustments in the company's ledger.

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Answer:

3.33

Step-by-step explanation:

Independent events:

If two events, A and B, are independent, we have that:

\(P(A \cap B) = P(A)*P(B)\)

In this question, we have that:

The question are independent of each other.

Event A: Correct guess on the first question.

Event B: Correct guess on the second question.

A quick quiz consists of a multiple-choice question with 6 possible answers followed by a multiple-choice question with 5 possible answers.

This means that \(P(A) = \frac{1}{6}, P(B) = \frac{1}{5}\)

Probability that both responses are correct.

\(P(A \cap B) = \frac{1}{6}*\frac{1}{5} = \frac{1}{30} = 0.333\)

The answer is 3.33%. Since it asks without the "%" symbol, 3.33

The value of the expression \(2(cos^4 60 + sin^4 30) -(tan^2 60 + cot^2 45) + 3\times sec^2 30 is 33/4.\)

Let's simplify the expression step by step:

Recall the values of trigonometric functions for common angles:

cos(60°) = 1/2

sin(30°) = 1/2

tan(60°) = √(3)

cot(45°) = 1

sec(30°) = 2

Substitute the values into the expression:

\(2(cos^4 60 + sin^4 30) - (tan^2 60 + cot^2 45) + 3sec^2 30\)

= \(2((1/2)^4 + (1/2)^4) - (\sqrt{(3)^2 + 1^2} ) + 3(2^2)\)

= 2(1/16 + 1/16) - (3 + 1) + 3*4

= 2(1/8) - 4 + 12

= 1/4 - 4 + 12

= -15/4 + 12

= -15/4 + 48/4

= 33/4

Therefore, the value of the expression \(2(cos^4 60 + sin^4 30) -(tan^2 60 + cot^2 45) + 3\times sec^2 30 is 33/4.\)

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The probability that a 42 person shift will put together between 193.2 and 201.6 computers per hour is given as follows:

0.0006 = 0.06%.

The z-score of a measure X of a normally distributed variable that has mean represented by \(\mu\) and standard deviation represented by \(\sigma\) is obtained by the equation presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The parameters for this problem are given as follows:

\(\mu = 4.2, \sigma = 0.8, n = 42, s = \frac{0.8}{\sqrt{42}} = 0.1234\)

The probability that a 42 person shift will put together between 193.2 and 201.6 computers per hour is equivalent to the probability of a sample mean between 193.2/42 = 4.6 and 201.6/42 = 4.8.

The probability is the p-value of Z when X = 4.8 subtracted by the p-value of Z when X = 4.6, hence:

Z = (4.8 - 4.2)/0.1234

Z = 4.86

Z = 4.86 has a p-value of 1.

Z = (4.6 - 4.2)/0.1234

Z = 3.24

Z = 3.24 has a p-value of 0.9994.

Hence:

1 - 0.9994 = 0.0006 = 0.06%.

The missing section is given by the image presented at the end of the answer.

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We have the following conjecture: "The square of an odd number is always odd".

4.1) We select the odd numbers 1, 3, 5 and check the conjecture:

We notice that the results of the squares are odd numbers, so the conjecture is true for these numbers.

4.2) We can't find an example where the conjecture is false. In point 4.4, we will prove that the conjecture is true.

4.3) We agree with the conjecture. We believe that it is TRUE.

4.4) We prove that the conjecture is true for all odd numbers.

By definition, an odd number can be written as:

Where:

• n is an integer,

• 2n is an even number because 2n is divisible by 2.

Now, we compute the square of m:

We see that the result is the sum of an even number 2*(2n²+2n) plus 1, so the result is an odd number for every odd number m = 2n + 1. This result proves the conjecture.

The conjecture is TRUE for all odd numbers.