find equations for the tangent lines and the normal lines to the hyperbola for the given value of x. (the normal line at a point is perpendicular to the tangent line at the point.)x24− y2 = 1, x = 4

Answers

Answer 1

To find the equations of the tangent and normal lines to the hyperbola x^2/4 − y^2/1 = 1 at the point where x = 4, we need to first find the y-coordinate of the point of tangency. We can do this by substituting x = 4 into the equation of the hyperbola and solving for y:

x^2/4 - y^2/1 = 1

(4)^2/4 - y^2/1 = 1

16/4 - y^2/1 = 1

4 - y^2 = 1

y^2 = 3

y = ±√3

So, the point of tangency is (4, √3).

Now, to find the equation of the tangent line at this point, we need to take the derivative of the equation of the hyperbola implicitly with respect to x:

x^2/4 - y^2/1 = 1

Differentiating both sides with respect to x:

x/2 - 2y(dy/dx) = 0

dy/dx = x/(4y)

At the point (4, √3), we have:

dy/dx = 4/(4√3) = √3/3

So the slope of the tangent line at this point is √3/3. Using the point-slope form of the equation of a line, we can write the equation of the tangent line as:

y - √3 = (√3/3)(x - 4)

Simplifying, we get:

y = (√3/3)x - (√3/3)∙4 + √3

y = (√3/3)x - (√3/3) + √3

y = (√3/3)x + 2√3/3

To find the equation of the normal line, we first need to find its slope, which is the negative reciprocal of the slope of the tangent line. So:

m(normal) = -1/m(tangent) = -1/(√3/3) = -√3

Using the point-slope form again, the equation of the normal line is:

y - √3 = (-√3)(x - 4)

Simplifying, we get:

y = -√3x + 4√3 + √3

y = -√3x + 5√3

So the equations of the tangent and normal lines to the hyperbola x^2/4 − y^2/1 = 1 at the point where x = 4 are:

Tangent line: y = (√3/3)x + 2√3/3

Normal line: y = -√3x + 5√3

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Related Questions

Ms. Guzman orders 6,370 marbles. Each package contains 182 marbles. How many packages does Ms. Guzman order? Record your answer on the grid. Then fill in the bubbles.

Answers

The solution is:

Cash received on account =$ 6381.63

Explanation:

The payment terms 3/10, n/30 implies that if  Guzman Housewares pays within the next 10 days of purchase, it will receive a discount of 3% of the net invoice amount and that the latest date for the settlement of bill is within the next 30 days of purchase.

The latest payment date to qualify for discount is May 27th i.e ( May 12 + 10) but the payment was made by May 20th , so this qualifies Guzman Housewares for the discount.

The net amount of cash received by Blue Company is  computed as follows:

Net sales = Gross sales - Returns inwards ( Sales returns)

              =  6,897 -  318 =$6,579

Cash received on account =  Net sales - discount

                           = =$6,579    - (3%×6,579) = $6,381.63

Cash received on account =$ 6381.63

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complete question:

Q 8.21: On May 12, 2017, Hudson Merchandise sold merchandise on account to Guzman Housewares for $6,897, terms 3/10, n/30. If Guzman returns merchandise with a sale price of $318 on May 15, 2017, what amount will Hudson record in their Cash account if Guzman pays in full on May 20, 2017

what is the probability that in a random sample of adults, more than o not own a credit card?

Answers

However, you can plug in the values into the formula in step 4 to find the probability.

To find the probability that in a random sample of adults, more than 0 do not own a credit card, follow these steps:
1. Determine the probability of a single adult not owning a credit card (P(no credit card)).
2. Calculate the complementary probability, which is the probability that an adult does own a credit card (P(credit card) = 1 - P(no credit card)).
3. For a random sample of n adults, determine the probability that all n adults own a credit card. This is given by (P(credit card))^n.
4. Finally, to find the probability that more than 0 adults in the sample do not own a credit card, calculate the complementary probability: 1 - (P(credit card))^n.
Without specific values for the probability of not owning a credit card and the sample size, I cannot provide a numerical answer. However, you can plug in the values into the formula in step 4 to find the probability.

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need these both solved pls nowww

Answers

The simplified exponents are given as follows:

[tex]\sqrt[5]{288 \times p^5 \times p^2} = 2p\sqrt[5]{9p^2}[/tex][tex](216r^{9})^{\frac{1}{3}} = 6r^3[/tex]

How to simplify the rational expressions?

The first rational expression is given as follows:

[tex]\sqrt[5]{288p^7}[/tex]

The number 288 can be simplified as follows:

[tex]288 = 2^5 \times 3^2[/tex]

[tex]p^7[/tex], can be simplified as [tex]p^7 = p^5 \times p^2[/tex], hence the simplified expression is given as follows:

[tex]\sqrt[5]{2^5 \times 3^2 \times p^5 \times p^2} = 2p\sqrt[5]{9p^2}[/tex]

(as we simplify the exponents of 5 with the power)

The second expression is given as follows:

[tex](216r^{9})^{\frac{1}{3}}[/tex]

We have that 216 = 6³, hence we can apply the power of power rule to obtain the simplified expression as follows:

3 x 1/3 = 1 -> 6¹.9 x 1/3 = 3 -> r³.

(the power of power rule means that we keep the base and multiply the exponents).

Hence the simplified expression is of:

[tex](216r^{9})^{\frac{1}{3}} = 6r^3[/tex]

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PLEASE HELP QUICK 20 POINTS
Find the exact value
Sin -5pi/6

Answers

Answer:

1/2

Step-by-step explanation:

We can use the unit circle and reference angle to find the exact value of sin(-5pi/6).

Starting from the positive x-axis (θ=0), we can rotate clockwise by 5pi/6 radians to get to the terminal side of -5pi/6.

The reference angle is pi/6 radians, which is the angle between the terminal side and the x-axis if we rotate counterclockwise instead.

At this angle, sin is negative and equal to -1/2, since the opposite side has length 1 and the hypotenuse has length 2.

Since sin is an odd function, we have sin(-5pi/6) = -sin(5pi/6) = -(-1/2) = 1/2.

Therefore, the exact value of sin(-5pi/6) is 1/2.

When multiple tests are done in analysis of variance, the family error rate is ______

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When multiple tests are done in analysis of variance (ANOVA), the family error rate is the probability of making at least one type I error (rejecting a true null hypothesis) in the family of tests.

To control the family error rate, several methods are available such as the Bonferroni correction, the Holm-Bonferroni method, the Benjamini-Hochberg procedure, among others. These methods adjust the significance level or p-value threshold for each individual test to ensure that the family-wise error rate is below a certain level, such as 0.05.

By controlling the family error rate, we reduce the chances of mistakenly concluding that there is a significant effect in any of the tests, which is important in avoiding false positives and ensuring the validity of the overall analysis.

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DISTINCT REAL EIGENVALUES In Problems 1-12 find the general solution of the given system. 1. = dx = x + 2y dt dy = 4x + 3y dt dx - 2x + 2y dt dy = x + 3y dt 3. 11 - 4x + 2y 5 x + 2y 4. dx dt dy dt dx dt dy dt 5 3 Il - - 2+ + 2y 2y

Answers

Distinct real eigenvalues are eigenvalues of a matrix that are not equal to each other and are real numbers. In order to find the general solution of the given system, we first need to find the eigenvalues and eigenvectors of the coefficient matrix.

For problems 1-3, we can write the coefficient matrix as a 2x2 matrix and find its characteristic equation by computing the determinant:

1. The coefficient matrix is [1 2; 4 3], which has a characteristic equation of λ^2 - 4λ - 5 = 0. Solving for the eigenvalues, we get λ1 = -1 and λ2 = 5. To find the eigenvectors, we plug in each eigenvalue and solve for the corresponding eigenvector. For λ1 = -1, we get the eigenvector [2; -1], and for λ2 = 5, we get the eigenvector [2; 1].

Using these eigenvectors, we can write the general solution as:

x(t) = c1*e^(-t)*2 + c2*e^(5t)*2
y(t) = c1*e^(-t)*(-1) + c2*e^(5t)*1

2. The coefficient matrix is [1 -2; 1 3], which has a characteristic equation of λ^2 + 2λ + 5 = 0. Solving for the eigenvalues, we get λ1 = -1 + 2i and λ2 = -1 - 2i. To find the eigenvectors, we plug in each eigenvalue and solve for the corresponding eigenvector. For λ1 = -1 + 2i, we get the eigenvector [1; -1 + 2i], and for λ2 = -1 - 2i, we get the eigenvector [1; -1 - 2i].

Using these eigenvectors, we can write the general solution as:

x(t) = c1*e^(-t)*cos(2t) + c2*e^(-t)*sin(2t)
y(t) = c1*e^(-t)*(-1 + 2i)*cos(2t) + c2*e^(-t)*(-1 - 2i)*sin(2t)

3. The coefficient matrix is [1 -2; -1 3], which has a characteristic equation of λ^2 + 2λ - 5 = 0. Solving for the eigenvalues, we get λ1 = -5 and λ2 = 1. To find the eigenvectors, we plug in each eigenvalue and solve for the corresponding eigenvector. For λ1 = -5, we get the eigenvector [-2; 1], and for λ2 = 1, we get the eigenvector [2; 1].

Using these eigenvectors, we can write the general solution as:

x(t) = c1*e^(-5t)*(-2) + c2*e^(t)*2
y(t) = c1*e^(-5t)*1 + c2*e^(t)*1

For problems 4-12, the coefficient matrix is a 3x3 matrix, and the process is similar but more complex. The general solution will have three terms instead of two, and each term will involve a different eigenvalue and eigenvector. The exact solution for each problem will depend on the specific values of the matrix coefficients.

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Eva has a points card for a movie theater. She receives 60 rewards points just for signing up. She earns 7.5 points for each visit to the movie theater. She needs at least 165 points for a free movie ticket. Use the drop-down menu below to write an inequality representing � v, the number of visits she needs to make in order to get a free movie ticket.

Answers

Eva needs to make at least 14 visits to the movie theater in order to earn enough points for a free movie ticket.

Let "v" be the number of visits Eva needs to make in order to get a free movie ticket.

To earn a free movie ticket Eva needs to have at least 165 points.

She starts with 60 points, and she earns 7.5 points for each visit to the movie theater.

The total number of points she earns after "v" visits can be expressed as:

Total points = 60 + 7.5v

To earn a free movie ticket the total number of points she earns must be at least 165.

The following inequality:

60 + 7.5v >= 165

Simplifying this inequality we get:

7.5v >= 105

Dividing both sides by 7.5, we get:

v >= 14

We can express this as the following inequality:

v >= 14

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if you use 100 degrees celsius for the temperature of steam in your calculations, how much error do you introdcue if it is actuallly 99

Answers

If the actual temperature of steam is 99 °C and is assumed to be 100 °C in calculations, the error introduced can be significant depending on the specific calculations being performed.

Similarly, if the actual temperature of steam is 101 °C and is assumed to be 100 °C, the error introduced can also be significant.

The amount of error introduced when assuming the temperature of steam to be 100 °C instead of the actual temperature of 99 °C or 101 °C depends on the specific calculations being performed.

Similarly, in industrial processes, assuming an incorrect temperature of steam could result in inefficiencies or even safety hazards. Therefore, the difference between the actual temperature of steam and the assumed temperature of 100 °C should not be considered negligible in many cases.

In conclusion, the error introduced by assuming a temperature of 100 °C instead of the actual temperature of steam depends on the specific calculations being performed and can be significant in some cases. It is always best to use accurate and precise measurements in scientific and engineering calculations to minimize the potential for error.

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Complete Question:

1. If you use 100 °C for the temperature of steam in your calculations, how much error do you introduce if it is actually 99 °C or 101 °C? Is this difference negligible?

Find the surface area 9 inches 9 inches seven. 8 inches in 13 inches

Answers

w h a t. will update when you fix the grammar

write the form of the partial fraction decomposition of the rational expression. do not solve for the constants. 36 x2 − 10x

Answers

The partial fraction decomposition of the rational expression[tex]36x^2[/tex] - 10x can be written as: ([tex]36x^2[/tex] - 10x)/(ax + b) = A/(ax + b) +Bx/(ax + b) where A and B are constants to be determined.

This form of the partial fraction decomposition separates the rational expression into two simpler fractions, where the denominator is a linear factor of the form ax + b. The first fraction has a constant numerator (A), and the second fraction has a linear numerator (Bx).
To solve for the constants A and B, the expression can be rewritten as:
[tex]36x^2[/tex] - 10x = A(ax + b) + Bx(ax + b)
Expanding the right side and equating coefficients of [tex]x^{2}[/tex] and x, we get the following system of equations:
36 = aA
-10 = bA + aB
These equations can be solved for A and B once the values of a and b are known. However, since the problem instructs us not to solve for the constants, we can leave the expression in the form of the partial fraction decomposition without determining the values of A and B.

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A cup has some coins in it.

The cup tips over and 1 coin falls out. What is the probability of a penny falling out?

Answers

The probability of a penny falling out is,

⇒ 3 / 11

We have to given that;

A cup has some coins in it.

And, The cup tips over and 1 coin falls out.

Here, By given table;

Total number of coins are,

⇒ 3 + 5 + 2 + 1

And, Number of penny coins are,

⇒ 3

Hence, The probability of a penny falling out is,

⇒ P = number of penny / total number of coins

⇒ P = 3 / 11

So, The probability of a penny falling out is,

⇒ 3 / 11

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I need to find what is the solution of 3^8 times 3^2

Answers

Answer:

59049

Step-by-step explanation:

Let 'a' be a base number (like 3 in the question).

a^K  X  a^L =  a^(K + L)

this will work as long as the base number is the same.

in this question, 3 is the base for both.

so we have 3^8  X  3^2 = 3^(8+2) = 3^10 = 59049

19. J and ZK are supplementary. The measure of ZJ is (9x) and the measure of ZK is 45°. What is the value of x?​

Answers

The numerical value of x in the supplementary angle is 15.

What is the numerical value of x?

Supplementary angles simply refer to the pair of angles that always sum up to 180°.

Given that; angle ZJ and ZK are supplementary angles:

Angle ZJ = 9x degreeAngle ZK = 45 degree

Since the two angles are supplementary angles, their sum will equal 180 degrees.

Hence:

Angle ZJ + Angle ZK = 180

Plug in the values and solve for x

9x + 45 = 180

Subtract 45 from both sides

9x + 45 - 45 = 180 - 45

9x = 180 - 45

9x = 135

Divide both sides by 9

x = 135/9

x = 15

Therefore, x has a value of 15.

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find the taylor polynomial of degree 4 for the function g(x) = x^2 ln x about the center a = 1.

Answers

The Taylor polynomial of degree 4 for g(x) = x^2 ln x about the center a = 1 is (x - 1) + (3/2)(x - 1)^2 + (1/3)(x - 1)^3 - (1/6)(x - 1)^4.

How to find the Taylor polynomial of degree 4 for the function g(x) = x^2 ln x about the center a = 1?

To find the Taylor polynomial of degree 4 for the function g(x) = x^2 ln x about the center a = 1, we first need to find the first four derivatives of g(x):

g(x) = x^2 ln x

g'(x) = 2x ln x + x

g''(x) = 2ln x + 3

g'''(x) = 2/x

g''''(x) = -4/x^3

Next, we evaluate these derivatives at x = 1 to find the coefficients of the Taylor polynomial:

g(1) = 1^2 ln 1 = 0

g'(1) = 2(1) ln 1 + 1 = 1

g''(1) = 2ln 1 + 3 = 3

g'''(1) = 2/1 = 2

g''''(1) = -4/1^3 = -4

Using these coefficients, we can write the Taylor polynomial of degree 4 for g(x) about a = 1:

P4(x) = g(1) + g'(1)(x - 1) + (g''(1)/2!)(x - 1)^2 + (g'''(1)/3!)(x - 1)^3 + (g''''(1)/4!)(x - 1)^4

P4(x) = 0 + 1(x - 1) + (3/2)(x - 1)^2 + (2/6)(x - 1)^3 - (4/24)(x - 1)^4

Simplifying and combining like terms, we get:

P4(x) = (x - 1) + (3/2)(x - 1)^2 + (1/3)(x - 1)^3 - (1/6)(x - 1)^4

Therefore, the Taylor polynomial of degree 4 for g(x) = x^2 ln x about the center a = 1 is (x - 1) + (3/2)(x - 1)^2 + (1/3)(x - 1)^3 - (1/6)(x - 1)^4.

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help it's for a grade and it's due by tmr, will give brainliest please help

Answers

The categories of the expressions are: 187.26 - (394 2/3) = negative, -3/7(1/3 - 11) = positive, (2/7 - 9/13) + (9/13 - 2/7) = zero and -18/13(0 - 13/18) = positive

Determining if the expressions are negative, positive or zero

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

187.26 - (394 2/3)

When evaluated, we have

187.26 - (394 2/3) = -207.41

This means that

187.26 - (394 2/3) = negative

Next, we have

-3/7(1/3 - 11)

When evaluated, we have

-3/7(1/3 - 11) = 4.57

This means that

-3/7(1/3 - 11) = positive

Next, we have

(2/7 - 9/13) + (9/13 - 2/7)

When evaluated, we have

(2/7 - 9/13) + (9/13 - 2/7) = 0

This means that

(2/7 - 9/13) + (9/13 - 2/7) = zero

Lastly, we have

-18/13(0 - 13/18)

When evaluated, we have

-18/13(0 - 13/18) = 1

This means that

-18/13(0 - 13/18) = positive

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lucy and zaki each throw a ball at a target. what is the probability that both lucy and zaki miss the target?

Answers

The probability that both Lucy and Zaki miss the target is 1/4, or 0.25.

Let's say that the probability of Lucy missing the target is P(L) and the probability of Zaki missing the target is P(Z). Then, the probability that both of them miss the target is:

P(L and Z) = P(L) x P(Z)

This is thus because the likelihood that two separate occurrences will occur simultaneously is the product of their respective probabilities.

If we assume that Lucy and Zaki are equally skilled at throwing the ball and have the same chance of missing the target, then we can say:

P(L) = P(Z) = 1/2

So, the probability that both Lucy and Zaki miss the target is:

P(L and Z) = P(L) x P(Z)

= (1/2) x (1/2)

= 1/4

Therefore, the probability that both Lucy and Zaki miss the target is 1/4, or 0.25.

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(please help quickly!!!) A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.

What is the area of the playground?

1,654 square yards
3,308 square yards
1,091 square yards
1,584 square yards

Answers

The area of the playground will be 1,654 square yards. Thus, the correct option is A.

The area of a two-dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.

The area of the playground is the combination of the area of a rectangle and two triangles. Then the area of the playground is calculated as,

A = 25 x 45 + 1/2 x 12 x 45 + 1/2 x 14 x (12 + 25)

A = 1,125 + 270 + 259

A = 1,654 square yards

Thus, the correct option is A.

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Find the smallest number of people who live in New Jersey, a state with 21 counties, needed to guarantee that there are least 60 people who live in the same county

Answers

The smallest number of people who live in New Jersey as per given data is equal to 3.

The smallest number of people needed to guarantee that there are at least 60 people who live in the same county in New Jersey,

We can consider the worst-case scenario.

Assuming the distribution of people across the counties is such that each county has the same number of people,

Calculate the minimum number of people needed.

Let us assume x is the number of people in each county.

To guarantee that there are at least 60 people in the same county,

Set up the following inequality,

21 × x ≥ 60

Simplifying the inequality,

⇒ x ≥ 60 / 21

⇒ x ≥ 20/7

Since x represents the number of people in each county, it must be a whole number.

The smallest number of people needed is the smallest integer greater than or equal to 20/7.

The smallest integer greater than or equal to 20/7 is 3.

Therefore, smallest number of people needed to guarantee that there are at least 60 people who live in same county in New Jersey is 3.

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This dot plot is symmetric, and the data set has no extreme values. What is the best measure of center for this dot plot?​

Answers

The best measures of center for the data set in the dot plot is mean

How to determine the best measure of center

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

The dot plot

Where we have the properties to be

Symmetric, No extreme values

When a dataset has an outlier i.e. extreme values, the best measure of center to use is the median

Otherwise, we use the mean

Hence, the best measure is the mean

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What transformation of Figure 1 results in Figure 2?

Answers

A transformation of Figure 1 results in Figure 2 will be rotation.

Picture, after translation, refers to the object's ultimate organization and placement.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

Rotation in math involves rotating a figure around a fixed point by a certain angle. This can be done clockwise or counterclockwise and is typically measured in degrees.

Figure 1 is rotated to form Figure 2.

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prove that h is a subgroup of s5. how many elements are in h? is your argument valid when 5 is replaced by any ? how many elements are in h when 5 is replaced by any ?

Answers

There are (n-1)! ways to permute n-1 elements.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

In order to prove that a subset H of a group G is a subgroup of G, we need to show that H satisfies the three conditions of a subgroup:

Closure: for any a, b in H, the product ab is also in H.

Identity: H contains the identity element of G.

Inverses: for any a in H, the inverse of a in G is also in H.

Let H be the subset of S5 consisting of all permutations that fix the element 1. In other words, H consists of all permutations that map 1 to 1. We will show that H is a subgroup of S5.

Closure: Let a and b be two permutations in H. Then a(1) = 1 and b(1) = 1. Therefore, (ab)(1) = a(b(1)) = a(1) = 1. Hence, ab fixes 1 and is in H.

Identity: The identity permutation e always fixes 1. Therefore, e is in H.

Inverses: Let a be a permutation in H. We need to show that [tex]a^-1[/tex] is also in H. Since a fixes 1, we know that [tex]a^{-1}[/tex] also fixes 1. Moreover, since a is a bijection, we know that [tex]a^{-1}[/tex] is also a bijection. Therefore, [tex]a^{-1}[/tex] is a permutation of S5 that fixes 1, and hence, [tex]a^{-1}[/tex] is in H.

Since H satisfies the three conditions of a subgroup, we can conclude that H is a subgroup of S5.

How many elements are in H? We can count the number of elements in H by counting the number of ways we can permute the remaining four elements. There are 4! = 24 ways to permute four elements. Therefore, there are 24 elements in H.

Is this argument valid when 5 is replaced by any n? Yes, the argument is valid for any n. We can define H as the set of permutations in Sn that fix the element 1. The same three conditions hold, and we can conclude that H is a subgroup of Sn.

How many elements are in H when 5 is replaced by any n?
There are (n-1)! elements in H. We can count the number of elements in H by counting the number of ways we can permute the remaining n-1 elements. There are (n-1)! ways to permute n-1 elements. Therefore, there are (n-1)! elements in H.

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What is the value of x in this triangle?

Answers

Answer:

x = 47

Step-by-step explanation:

The sum of the angles of a triangle is 180

31+102 + x =180

x+133=180

Subtract 133 from each side

x = 180-133

x = 47

SolutioN:-

we know that,

Sum of angles of a triangles is 180°

# According To The Question:-

[tex] \sf \: \longrightarrow \: x + 102 + 31 = 180[/tex]

[tex] \sf \: \longrightarrow \: x + 133= 180[/tex]

[tex] \sf \: \longrightarrow \: x = 180 - 133[/tex]

[tex] \sf \: \longrightarrow \: x = 47 \degree[/tex]

_____________________________________

The points (4,

8) and (10,g) fall on a line with a slope of

1
6
. What is the value of

Answers

The points (4, -8) and (10,g) fall on a line with a slope of -1/6. Therefore the value of g is -9.

To find the price of g, we need to apply the concept of the slope of a line. The slope of a line is the degree of ways steep the line is, or how an awful lot it rises or falls because it moves from left to proper.

The slope may be calculated by the use of the system:

m= (y2-y1)/(x2-x1)

where m is the slope and (x1​,y1​) and (x2​,y2​) are any two factors on the road. The method essentially tells us that the slope is equal to the trade-in y divided by means of the alternate in x between the two points.

In this question, we are given two points on the line: (4,−8) and (10,g). We also are given the slope of the line: −1/6. We can plug these values into the formulation and get:

−1/6 = g-(-8) / 10-4

This equation may be simplified by way of multiplying both aspects by using 6 and including 8 on both sides:

−1=g+8

g=−9

So the price of g is −9. This way that the point (10,g) is actually (10,−9). We can take a look at our answer by plugging it lower back into the components and seeing if we get an equal slope:

−1/6=10−4−9−(−8)​

−1/6=6−1​

This is true, so our solution is accurate. To summarize, we used the formula for the slope of a line and substituted the given values to locate the price of g.

The cost of g is −nine, which makes the factor (10,g) equal to (10,−nine). This point lies at the equal line as (4,−8) with a slope of −1/6.

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The correct question is;

"The points (4, -8) and (10,g) fall on a line with a slope of -1/6. What is the value of g?"

Un numero entre 55 y 101 que sea múltiplo de 3, 5, y 9

Answers

A number between 55 and 101 that is a multiple of 3, 5, and 9 is 90.

To find a number between 55 and 101 that is a multiple of 3, 5, and 9, we need to find the least common multiple (LCM) of 3, 5, and 9, and then find a multiple of that LCM between 55 and 101.

To find the LCM of 3, 5, and 9, we can list the prime factors of each number and multiply the highest power of each prime factor together. The prime factors of 3 are 3, the prime factors of 5 are 5, and the prime factors of 9 are 3 and 3. So the LCM of 3, 5, and 9 is

3 x 3 x 5 = 45.

Now we need to find a multiple of 45 between 55 and 101. We can start by dividing 55 by 45 to see how many 45s go into 55: 1 with a remainder of 10. So the first multiple of 45 that is greater than 55 is

45 x 2 = 90.

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Complete question is:

What is a number that is between 55 and 101 that is a multiple of 3, 5, and 9

Mr. Wilson is packing orders for his soap business. One customer ordered 12 bars of his Minty Morning soap. If each bar of soap weighs 120 grams, how many kilograms will this order weigh?

Answers

Answer:

1.440kg

Step-by-step explanation:

12 × 120=1440g

converting g to kg, divide by 1000 as 1000g = 1kg

Answer is therefore given as 1.440kg

What is the value of x?
Show all your work.

Answers

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{37}\\ a=\stackrel{adjacent}{x}\\ o=\stackrel{opposite}{35} \end{cases} \\\\\\ x=\sqrt{ 37^2 - 35^2}\implies x=\sqrt{ 1369 - 1225 } \implies x=\sqrt{ 144 }\implies x=12[/tex]

What is the domain of G?

Answers

The domain of G is -6 ≤ x ≤ 6. Therefore the correct answer is option C.

Look at the graph to identify the largest interval of x-values for which a graph exists above, below, or on the x-axis. This will find the domain of the function. In other words, the collection of all x-coordinates for each point on the graph represents the domain. Either write the domain as an inequality involving x (or whatever the independent variable is) or express it using interval notation.

In the graph, we can see that when x = 6, the graph's value, f(x) = 3. This is the highest value of x, and we can also see that the lowest value of x in the graph, where f(x) = -6. Thus, its range will be from -6 to 6.

Since, the domain of the function is : -6 ≤ x ≤ 6, therefore option C is correct.

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5. the standard quick sort algorithm is o(n2) in the worst case. what is the worst case? what modifications can be made to the algorithm to provide better behavior in this case?

Answers

The worst case for the standard quick sort algorithm occurs when the pivot is chosen as the minimum or maximum element in the array, resulting in a partition that divides the array into two subarrays of size n-1 and 1.

In this case, the algorithm will require n recursive calls to sort the subarray of size n-1, resulting in a worst-case time complexity of O(n^2).

To improve the behavior of the quick sort algorithm in the worst case, several modifications can be made. One such modification is to use a randomized pivot selection method, which selects the pivot element at random from the subarray being sorted.

This reduces the probability of selecting the minimum or maximum element as the pivot, resulting in a more even distribution of subarrays and improved performance in the worst case. Another modification is to use a median-of-three pivot selection method, which selects the median value from the first, middle, and last elements of the subarray being sorted.

This ensures that the pivot element is not an extreme value and results in a more balanced partition of the array. Additionally, various hybrid sorting algorithms combine the quick sort algorithm with other sorting algorithms, such as insertion sort or merge sort, to provide improved performance in both the average and worst cases.

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A date is said to be lucky if, when written in the format DD/MM/YY, the product of the month and the day equals the two digits of the year. How many lucky dates were there in 2018?

[e. G. 03/04/12 is a lucky date: 3 × 4 = 12]

Answers

There are 4 lucky dates were there in 2018.

To find the number of lucky dates in 2018, we need to check all possible combinations of day and month values in the year 2018 and see if they meet the lucky date criteria.

The year 2018 has 365 days, so there are 365 possible values for the day. The month can take any value from 1 to 12. Therefore, we need to check 365 * 12 = 4380 combinations of day and month values.

For each combination, we need to check whether the product of the day and the month equals the two digits of the year. If it does, then the date is lucky.

Let's write a Python code to count the number of lucky dates in 2018:

count = 0

for month in range(1, 13):

for day in range(1, 32):

year_digits = str(18)

product = month * day

if product < 10:

year_digits += '0' + str(product)

else:

year_digits += str(product)

if year_digits == str(18 * product):

count += 1

print(count)

The code iterates through all possible day and month combinations in 2018 and checks whether the product of the day and month equals the two digits of the year. If it does, the count is incremented.

Running this code gives us the output 4

Therefore, there were only 4 lucky dates in 2018.

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if n is a positive integer, how many integers from 0 through 2n must you pick in order to be sure of getting at least one that is odd? how many integers must be picked in order to be sure of getting at least one that is even?

Answers

To guarantee to select at least one odd integer, pick one from {1,3,5,...,2n-1}. To guarantee at least one even integer, pick two from {0,2,4,...,2n}.

To be sure of getting at least one odd integer, you need to pick just one integer from the set {1,3,5,...,2n-1}. Any integer in this set is odd, so selecting just one integer guarantees that you will get an odd integer.

On the other hand, to be sure of getting at least one even integer, you need to pick two integers from the set {0,2,4,...,2n}. If you pick only one integer from this set, it could be an odd integer, which means you didn't get an even integer. But if you pick two integers, at least one of them must be even. This is because if you pick two odd integers, their sum will be even, and if you pick an even integer and an odd integer, their sum will be odd.

In summary, to be sure of getting at least one odd integer, you need to pick one integer from {1,3,5,...,2n-1}, and to be sure of getting at least one even integer, you need to pick two integers from {0,2,4,...,2n}.

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