1
Three times the measure of a supplement of an angle is eight times the measure of a complement of the angle. What is the measure of the angle?
Type in the number only
The measure of the angle is

Answer:

\(y = 36\)

Step-by-step explanation:

Given; the triangle above

Required

Find y

This question falls under the topic/subtopic similar triangles where we need to make comparison between similar sides'

But first, it should be noted that triangle MOP is similar to triangle MLN

This implies that

Side MP is similar to MN

Side MO is similar to  ML

Mathematically; This can be represented as follows;

\(\frac{MP}{MN} = \frac{MO}{ML}\)

Where MP =y; MN = y + 18; MO = 28; ML = 28 + 14

Substitute these values in the above expression

\(\frac{y}{y+18} = \frac{28}{28+14}\)

\(\frac{y}{y+18} = \frac{28}{42}\)

Multiply both sides by 42

\(42 * \frac{y}{y+18} = \frac{28}{42} * 42\)

\(\frac{42y}{y+18} = \frac{28*42}{42}\)

\(\frac{42y}{y+18} = 28\)

Multiply both sides by y + 18

\((y+18)*\frac{42y}{y+18} = 28 * (y+18)\)

\(42y = 28 * (y+18)\)

Open Bracket

\(42y = 28 * y+28 * 18\)

\(42y = 28y+504\)

Subtract 28y from both sides

\(42y - 28y = 28y - 28y +504\)

\(14y = 504\)

Divide both sides by 14

\(\frac{14y}{14} = \frac{504}{14}\)

\(y = \frac{504}{14}\)

\(y = 36\)

Answer:

y= 36

Step-by-step explanation:

also ily, no homo

Answer:

5.06

Step-by-step explanation:

Given that the remaining credit after 38 minutes of calls is 19.68, and the remaining credit after 60 minutes of calls is 12.20.

As the credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes), so let the linear equation be

\(y=ax+b\cdots(i)\)

where y is the credit remaining on a phone card (in dollars) and x is the total calling time made with the card (in minutes).

Now, as the remaining credit after 38 minutes of calls is 19.68, so, put x=38 and y=19.68 in equation (i), we have

\(19.68=38a+b \\\\\Rightarrow b= 19.68-38a\cdots(ii)\)

Similarly, the remaining credit after 60 minutes of calls is 12.20, so, put x=60 and y=12.20 in equation (i), we have

\(12.20=60a+b \\\\\)

\(\Rightarrow 12.20=60a+(19.68-38a)\) [ by using (ii)]

\(\Rightarrow 12.20=60a+19.68-38a \\\\\Rightarrow 22a=12.20-19.68=-7.48 \\\\\Rightarrow a=-7.48/22=-0.34\)

From equation (ii),

\(b=19.68-38\times(-0.34)=32.6\)

Putting the value od a and b in equation (i), we have

\(y=-0.34x+32.6\)

So, the remaining credit after 81 minutes can be determined by putting x=81 in the above equation.

\(y=-0.34\times 81 +32.6 \\\\ \Rightarrow y=5.06\)

Hence, the remaining credit after 81 minutes of calls is $5.06.

1) The pairs \((x, y) = (2 + \sqrt{7}, 2 - \sqrt{7})\) and \((x, y) = (2 - \sqrt{7}, 2 + \sqrt{7})\) are solutions of the system.

2) The quadratic formula has conjugated complex roots for \(k \in (-36, 36)\).

3) The pairs \((x, y) = (5 + \sqrt{47}, 5 - \sqrt{47})\) and \((x, y) = (5 - \sqrt{47}, 5 + \sqrt{47})\) are solutions of the system.

4) The complex number \(z = \frac{1-i}{2+3\cdot i}\) is equal to the complex number \(-\frac{1}{13}-\frac{5}{13}\cdot i\).

5) \(1.25\) is the smallest value that satisfies the quadratic equation \(8\cdot x^{2}-38\cdot x + 35 = 0\).

We need to solve the following system of equations to determine at least one pair of real numbers that are its solution:

\(x+y = 4\) (1)

\(x^{3} + y^{3} = 100\) (2)

By (1) in (2) we have the following expression.

\((4-y)^{3} + y^{3} = 100\)

\(y^{2}-48\cdot y -36 = 0\) (3)

Whose solutions are: \(y_{1} = 2 + \sqrt{7}\), \(y_{2} = 2 - \sqrt{7}\)

And by (1) we find the respective solutions for \(x\): \(x_{1} = 2-\sqrt{7}\), \(x_{2} = 2 +\sqrt{7}\).

In a nutshell, the pairs \((x, y) = (2 + \sqrt{7}, 2 - \sqrt{7})\) and \((x, y) = (2 - \sqrt{7}, 2 + \sqrt{7})\) are solutions of the system. \(\blacksquare\)

By the Quadratic Formula we understand that roots of

\(12\cdot x^{2}+k\cdot x + 27 = 0\) are conjugated complex if and only if the following condition is observed:

\(d^{2} = k^{2}-1296 < 0\) (4)

Where \(d\) is the discriminant of the quadratic formula.

After some mathematical handling we have the following result:

\(k^{2} < 1296\)

\(-36 < k < 36\)

Hence, the quadratic formula has conjugated complex roots for \(k \in (-36, 36)\). \(\blacksquare\)

By using the approach used in part 1), we find that the resulting polynomial is \(2\cdot y^{2} -20\cdot y -44 = 0\) for \(x = 10-y\), whose solutions are \((x,y) = (5 + \sqrt{47}, 5 - \sqrt{47})\) and \((x,y) = (5-\sqrt{47}, 5+\sqrt{47})\).

In a nutshell, the pairs \((x, y) = (5 + \sqrt{47}, 5 - \sqrt{47})\) and \((x, y) = (5 - \sqrt{47}, 5 + \sqrt{47})\) are solutions of the system. \(\blacksquare\)

Let be \(z = \frac{1-i}{2+3\cdot i}\), we proceed to simplify the expression by means of complex algebra:

\(\frac{1-i}{2+3\cdot i} = \frac{(1-i)\cdot (2-3\cdot i)}{(2+3\cdot i)\cdot (2-3\cdot i)} = \frac{2-5\cdot i + 3\cdot i^{2}}{2^{2}+3^{2}} = -\frac{1}{13} -\frac{5}{13} \cdot i\)

The complex number \(z = \frac{1-i}{2+3\cdot i}\) is equal to the complex number \(-\frac{1}{13}-\frac{5}{13}\cdot i\). \(\blacksquare\)

Let be \(8\cdot x^{2}-38\cdot x + 35 = 0\), whose roots are contained in the following quadratic formula:

\(x = \frac{38\pm \sqrt{(-38)^{2}-4\cdot (8)\cdot (35)}}{2\cdot (8)}\)

Whose solutions are: \(x_{1} = 3.5\) and \(x_{2} = 1.25\). We notice that the latter root is the smallest value of \(x\). In consequence, we conclude that \(1.25\) is the smallest value that satisfies the quadratic equation \(8\cdot x^{2}-38\cdot x + 35 = 0\). \(\blacksquare\)

The statement is poorly formatted. Correct form is presented below:

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Answer: We on da same question i do not know

Step-by-step explanation:

The function f(x) = \(x^2 e^{(-x^2)}\) has a maximum value at x = 0, which is a relative maximum point.

To find the relative maximum of the function f(x) =\(x^2 e^{(-x^2)}\), we can take its first derivative, set it to zero, and solve for x.

f(x) = \(x^2 e^{(-x^2)}\)

f'(x) = \(2x e^{(-x^2)} - 2x^3 e^{(-x^2)}\)

Setting f'(x) = 0, we get:

\(2x e^{(-x^2)} - 2x^3 e^{(-x^2)} = 0\)

\(2x e^{(-x^2)} (1 - x^2) = 0\)

This equation is true when either \(2x e^{(-x^2)} = 0\) or \(1 - x^2 = 0\).

Solving \(2x e^{(-x^2)} = 0\), we get x = 0.

Solving \(1 - x^2 = 0\), we get x = 1 or x = -1.

Now, we need to determine whether these values of x correspond to relative maximum, minimum, or inflection points.

To do this, we can use the second derivative test. The second derivative of f(x) is:

f''(x) = \(2e^{(-x^2)} - 4xe^{(-x^2)} - 4x^2e^{(-x^2)}\)

At x = 0, f''(0) = 2, which is positive. This means that f(x) has a relative minimum at x = 0.

At x = 1, f''(1) = \(-6e^{(-1)}\), which is negative. This means that f(x) has a relative maximum at x = 1.

At x = -1, f''(-1) = \(-6e^{(-1)}\), which is negative. This means that f(x) has a relative maximum at x = -1.

Therefore, the answer is (D) -1 and 1 only, as these are the only values of x at which f(x) has a relative maximum.

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Answer:

34 Deg

Step-by-step explanation:

Since the Triangle is isoceles, each of the internal base angle = 180-107=73

Sum of internal angles =180,  Angle4= 180-(73+73)= 180-146=34

Answer:

8/4 or 2/1 simplified

Step-by-step explanation:

The following are deductive reasoning for each statement in the algebraic proof given:

1. CD + DE = CE (Segment Addition Postulate)

2. 8 + (3x + 7) = 6x (Substitution)

3. 3x + 15 = 6x (Combining like terms)

4. 15 = 3x (Subtraction Property of Equality)

5. x = 5 (Division Property of Equality)

6. CE = 6(5) (Substitution)

Recall:

Thus, the following are deductive reasoning for each statement in the algebraic proof given:

1. CD + DE = CE (Segment Addition Postulate)

2. 8 + (3x + 7) = 6x (Substitution)

3. 3x + 15 = 6x (Combining like terms)

4. 15 = 3x (Subtraction Property of Equality)

5. x = 5 (Division Property of Equality)

6. CE = 6(5) (Substitution)

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Answer:

2/11

Step-by-step explanation:

5-3/7--4 = 2/11

In this case, we cannot find the limit as (x, y) approaches (0, 0) using standard techniques. This suggests that the limit may not exist at (0, 0) for the given expression.

I'm happy to help you with your question. As (x, y) approaches (0, 0), we want to find the limit of the following expression:
(sin(2x) - 2x + y) / (x^3 + y)
To find the limit, we can use L'Hopital's Rule for the indeterminate forms 0/0 or ∞/∞. However, we first need to check if we can apply L'Hopital's Rule in this case. Since this expression involves two variables (x and y), we should attempt to rewrite the expression in terms of one variable or determine if the limit exists.
After analyzing the given expression, it is difficult to rewrite it in terms of a single variable or directly apply L'Hopital's Rule. In this case, we cannot find the limit as (x, y) approaches (0, 0) using standard techniques. This suggests that the limit may not exist at (0, 0) for the given expression.

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Answer:

d:1

Step-by-step explanation:

the answers will always be negative and the other side will always be positive

The vertex of y=|2x+4|+5 is (-2, 5) and Range of the y=|2x+4|+5 is 5≤y<∞

A relation is a function if it has only one y-value for each x-value.

We need to find the vertex and range of y=|2x+4|+5

f(x)=2x+4

f of x is equal to zero

2x+4=0

Subtract 4 from both sides

2x=-4

Divide both sides by 2

x=-2

y=|2x+4|+5

=|2(-2)+4|+5=|-4+4|+5=5

Hence vertex is (-2, 5)

The range of the y=|2x+4|+5 is 5≤y<∞

Hence vertex is (-2, 5) and Range of the y=|2x+4|+5 is 5≤y<∞

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Answer:

1/2

Step-by-step explanation:

Pick two points on the line

I picked (0, 2) and (2, 3)

m = (3-2)/(2 -0) = 1/2

Answer:

11m + 2

Step-by-step explanation:

Combine like-terms.

5m + 6m = 11m

-7 + 9 = 2

Answer:

m= 16

Step-by-step explanation:

first you would rewrite the statement

then you would subtract 5m -6m =M

then you subtract 7 from 9 =16

so your answer is M=16

can I get the brainliest?

D: "\(c_{1} = 10\) and \(c_{2} = 2\)" are programmer-defined constants for quadratic probing that cannot be used in a quadratic probing equation. Option D is correct answer.

The quadratic probing equation is defined as:

h (k, i) = (h′(k) + \(c_{1}\) * i + \(c_{2}\) * i^2) mod m,

where h′(k) is the hash value of key

k and m is the size of the hash table.

The constants \(c_{1}\) and \(c_{2}\) are programmer-defined constants that are used to compute the new hash index when a collision occurs in the hash table.

The given hash function is h(k) = k % 10.

Therefore, the hash value of any key will be between `0` and `9`.Now, let's check which of the given programmer-defined constants for quadratic probing cannot be used in a quadratic probing equation:

Option A: `c1 = 1 and c2 = 0`This option can be used in the quadratic probing equation. It means that linear probing is being used.

Option B: \(c_1 = 5\) and \(c_2 = 1\) This option can be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + 5i + i^2) mod m`.

Option C: \(c_1 = 1\) and \(c_2 = 5\) This option can be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + i + 5i^2) mod m`.

Option D: \(c_1 = 10\) and \(c_2 = 2\) This option cannot be used in the quadratic probing equation. It means that the new index is being computed as `h(k, i) = (h′(k) + 10i + 2i^2) mod m`.

Since \(c_{1}\) is greater than or equal to `m`, this equation will always result in a hash index that is greater than or equal to `m`. Therefore, it is not possible to use `\(c_{1}\)= 10` in the quadratic probing equation. Hence, the correct option is D.

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The correct Area of extended portion will be 28 square feet

A rectangle in the Euclidean plane is a quadrilateral with four right angles. Other names for it include a parallelogram with a right angle and an equiangular quadrilateral, where equiangular means that all of its angles are equal. Four equally long sides make to a square, which is a rectangle.

Area of original garden=length*breadth=4 × x=4x square feet

Area of extended garden=4 × 7=28 sq. feet

Total area (including the extended portion)=4x+28=

4(x+7) square feet

The mistake made by gardener is that he added 4+7=11 square feet

But correct area of extended portion= length*breadth=4 × 7=28 square feet.

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Part 1: Triangles are similar by Side-Side-Side similarity.

Part 2: Triangles are similar angle-Angle (AA) similarity.

Part 1: Ratios must be equal for triangle similarity.

Taking the ratios of the sides:

17/37.4  = 20/44 = 25/55

On solving

0.4545 = 0.4545 = 0.4545

As the ratios are equal, triangles are similar.by Side-Side-Side similarity.

Part 2:

∠F = ∠H (given)

∠EGF = ∠JGH (vertically opposite)

By Angle-Angle (AA) similarity.

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The correct question is 1 and 2.

Answer:

\(3 \times |x| = 0 \\ 3 \times |x| \div 3 = 0 \div 3 \\ |x | = 0 \\ x = 0\)

Answer:

C. I and II

Step-by-step explanation:

In q1, all trig functions are positive. q2, sin and csc is positve. hope this helps!!

The question gives,

We would start by converting this into feet. The conversion rate is

Therefore, the conversion would be;

Also, to convert feet into miles, the conversion rate is;

ANSWER:

The correct answer is option C: 2 miles

Answer:−

3c+2

Step-by-step explanation:

Answer:

−3c +2

Step-by-step explanation:

Combine Like Terms

Constructing a confidence interval for the mean of a distribution based on one sample is Confidence level = 1 - significance level.

The definition of the confidence level is (1-α). Zα is the number of standard deviations from the mean at which X with a certain probability lies. If Z = 1.96 is selected, the likelihood that the real mean falls inside the range is set at 0.95, hence we are asking for the 95% confidence interval.

Let us consider,

Confidence level = c

significance level \(= \alpha\)

\(c = 1 - \alpha\)

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Answer:

The probability of being dealt a spade is 13/52.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:                                                      

15 yards

Step-by-step explanation:

the pitcher is in the middle of the diamond square thingy,the length is 30, so half of 30 is 15

The probability of getting at least 2 1's in 4 spins is:

1 - 0.7383 = 0.2617 or approximately 26.17%.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

To calculate the probability that at least 2 of the spins result in a 1, we can use the complement rule and subtract the probability that fewer than 2 of the spins result in a 1 from 1.

The probability of getting exactly 0 1's in 4 spins is:

(3/4)⁴ = 0.3164

The probability of getting exactly 1 1 in 4 spins is:

4 * (1/4) * (3/4)³ = 0.4219

So the probability of getting 0 or 1 1's in 4 spins is:

0.3164 + 0.4219 = 0.7383

Therefore, the probability of getting at least 2 1's in 4 spins is:

1 - 0.7383 = 0.2617 or approximately 26.17%.

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It will take 15/2 hours for Mitch to run 1 mile. Cancelling out the common factors from numerator and denominator, the ratio reduces to 15/2.

Mitch ran 5/2 of a mile in 1/3 of an hour. To calculate how many hours it will take Mitch to run 1 mile, we need to use a ratio. The ratio is (5/2)/(1/3). To solve this, we need to multiply the numerator and denominator of the first fraction with the denominator of the second fraction, and then multiply the numerator and denominator of the second fraction with the denominator of the first fraction. So, the ratio becomes (5/2)*(3/1)/(1/3)*(2/1). Cancelling out the common factors from numerator and denominator, the ratio reduces to 15/2. This means that it will take 15/2 hours for Mitch to run 1 mile.

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

Work Shown:

P( (A u B u C)' ) = 0.33

P(A u B u C) = 1 - P( (A u B u C)' )

P(A u B u C) = 1 - 0.33

P(A u B u C) = 0.67

--------

P(AuBuC) = P(A)+P(B)+P(C)-P(AnB)-P(AnC)-P(BnC)+P(AnBnC)

0.67 = 0.24 + 0.26 + P(C) - 0.05 - 0.05 - 0.05 + 0.02

0.67 = P(C) + 0.37

P(C) = 0.67 - 0.37

P(C) = 0.30

For more information, search out "inclusion-exclusion principle". Also feel free to ask me if you have any questions.

Answer:

z comes after y in the alphabet

In this scenario, we are considering an investment that will pay $3,000 in 34 years. We are given an appropriate discount rate of 8 percent. To determine the present value of this investment, we can use the present value formula. Additionally, we are provided with the information that the investment is being sold for $773, and we need to calculate the rate of return investors will earn on this investment.

a. Present value of the investment:

To calculate the present value of the investment, we use the present value formula:

Present Value = Future Value / (1 + Discount Rate)^n,

where Future Value is $3,000, the Discount Rate is 8 percent (0.08), and n is the number of years, which is 34 in this case.

Present Value = $3,000 / (1 + 0.08)^34 = $219.13

Therefore, the present value of the investment, considering an 8 percent discount rate, is $219.13.

b. Rate of return on the investment:

The rate of return on an investment is calculated using the formula:

Rate of Return = (Future Value - Purchase Price) / Purchase Price * 100,

where Future Value is $3,000 and the Purchase Price is $773.

Rate of Return = ($3,000 - $773) / $773 * 100 ≈ 288.46%

Therefore, the rate of return investors can earn on this investment, if they buy it for $773, is approximately 288.46%.

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