I need help with this Quadratic equation-standard form

The circle has center C. Suppose that m∠EDF = 38 and that DF is tangent to the circle at D.

a) mDE = 52°

b) m∠DCE =  14°

A line that touches the circle at a single point is known as a tangent to a circle. The point where tangent meets the circle is called the point of tangency. The tangent is perpendicular to the radius of the circle, with which it intersects.

Since DF is tangent to the circle at D, we know that ∠DFC = 90 degrees (tangent and radius are perpendicular).

a) Since ∠EDF is an external angle to triangle CDF, we have:

m∠EDF = m∠CDF + m∠DFC

Substituting the given values, we get:

38 = m∠CDF + 90

m∠CDF = 38 - 90 = -52

However, angles cannot have negative measures, so we need to add 180 degrees to get a positive angle that is coterminal with -52 degrees:

m∠CDF = -52 + 180 = 128 degrees

Now, using the fact that the angles in a triangle add up to 180 degrees, we can find m∠CDE:

m∠CDE = 180 - m∠CDF - m∠EDF

m∠CDE = 180 - 128 - 38

m∠CDE = 14 degrees

Finally, since CD is a radius of the circle, we know that m∠CDE = m∠DCE, so:

m∠DCE = 14 degrees

Therefore, the answers are:

a) mDE = 180 - m∠CDF = 180 - 128 = 52°

b) m∠DCE = 14°

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Answer: The plane traveled 15838.5 feet from point A to point B.

The sum of the interior angles of a polygon with \( n \) sides is \( (n-2) \pi \) radians.

When \( n \) is a positive integer, we can use mathematical induction to prove that \( \left(n^{3}+6 n^{2}+2 n\right) / 3 \) is also a positive integer.

Base case: \( n = 1 \), then \( \left(1^{3}+6 \cdot 1^{2}+2 \cdot 1\right) / 3 = \frac{9}{3} = 3 \) which is a positive integer.

Induction step: Assume \( \left(k^{3}+6 k^{2}+2 k\right) / 3 \) is a positive integer for some positive integer \( k \). Then:

\[ \left( \left(k+1\right)^{3}+6 \left(k+1\right)^{2}+2 \left(k+1\right)\right) / 3 = \frac{k^{3}+18 k^{2}+22 k+9}{3} \]

\[ = \frac{k^{3}+6 k^{2}+2 k + 6 k^{2}+16 k + 9}{3} \]

\[ = \frac{k^{3}+6 k^{2}+2 k}{3} + \frac{6 k^{2}+16 k + 9}{3} \]

\[ = \frac{\left(k^{3}+6 k^{2}+2 k\right)}{3} + \frac{\left(6 k^{2}+16 k + 9\right)}{3} \]

\[ = \frac{\left(k^{3}+6 k^{2}+2 k\right)}{3} + \left(2 k + 3\right) \]

Since the first term is a positive integer and the second term is a positive integer, it follows that \( \left(\left(k+1\right)^{3}+6 \left(k+1\right)^{2}+2 \left(k+1\right)\right) / 3 \) is a positive integer as well.

Therefore, it has been shown that when \( n \) is a positive integer, so also is \( \left(n^{3}+6 n^{2}+2 n\right) / 3 \).

To verify that the sum of the interior angles of a polygon with \( n \) sides is \( (n-2) \pi \) radians, consider the following: the sum of the interior angles of any polygon is equal to \( (n-2) \pi \) radians, where \( n \) is the number of sides in the polygon. This is true for any type of polygon, whether it is a triangle, quadrilateral, pentagon, etc.

Therefore, the sum of the interior angles of a polygon with \( n \) sides is \( (n-2) \pi \) radians.

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The required measure of the angle S in the isosceles trapezoid is ∠S = 115°.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

For isosceles trapezoid,
The sum of the opposite angle is equal to 180°.
∠Q + ∠S = 180

Substitute the value in the above expression,
65 + ∠S = 180
∠S = 180 - 65
∠S = 115°

Thus, the required measure of the angle S in the isosceles trapezoid is ∠S = 115°.

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Answer:

100%

Step-by-step explanation:

If all 32 the beads were plastic it would be 100%

The solution for u-(3)/(4)=5(1)/(3) u is 2(5)/(12).

The additive property of equality states that if the same amount is added to both sides of an equation, the equation remains true. In this case, we can use the additive property of equality to solve for u by isolating the variable on one side of the equation.

Step 1: Add (3)/(4) to both sides of the equation to cancel out the subtraction on the left side of the equation.
u-(3)/(4)+(3)/(4)=5(1)/(3)+(3)/(4)

Step 2: Simplify the left side of the equation.
u=5(1)/(3)+(3)/(4)

Step 3: Find a common denominator for the fractions on the right side of the equation and combine them.
u=20(1)/(12)+(9)/(12)

Step 4: Simplify the right side of the equation.
u=29/(12)

Step 5: Convert the improper fraction to a mixed number.
u=2(5)/(12)

Therefore, the solution for u is 2(5)/(12).

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1). 15 days

2). 115.2 pounds.

3). 500 meters

1. To find out when the couple will have another day off together, we need to find the least common multiple (LCM) of their work schedules. The LCM of 3 and 5 is 15, so the couple will have another day off together after 15 days.

2. The weight W of an object above the earth varies inversely as the square of the distance D from the center of the earth.

This means that W = k/D^2, where k is a constant.

To find k, we can plug in the values given in the question: 180 = k/4000^2.

Solving for k gives us k = 180*4000^2 = 2880000000. Now we can plug in the new distance, 4000 + 1000 = 5000 miles, to

find the new weight: W = 2880000000/5000^2 = 115.2 pounds.

3. To find the total distance traveled by the fly, we need to find out how long it takes for the turtles to meet.

The combined rate of the turtles is 10 + 20 = 30 m/s, so it will take them 150/30 = 5 seconds to meet.

The fly travels at a constant rate of 100 m/s, so in 5 seconds it will have traveled 100*5 = 500 meters.

Therefore, the total distance traveled by the fly is 500 meters.

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The quadratic function written in vertex form is:

y = -1*(x - 1)^2

We know that the vertex of the parabola is (1, 0), so if the leading coefficient is a, we can write the vertex form:

y = a*(x - 1)^2 + 0

y = a*(x - 1)^2

In this case we know two points on the parabola, the vertex which is at(1, 0) and the y-intercept which is (0, -1).

Using the vertex (1, 0) we can write the parabola as:

y = a*(x - 1)^2 + 0

y = a*(x - 1)^2

Now we can use the values of the other point and replace this in the formula above so we get:

-1 = a*(0 - 1)^2

-1 = a

Then the quadratic function is:

y = -1*(x - 1)^2

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The result of the formula "20 - 4.65" is 15.35, which corresponds to the amount of change the customer gets.

Expressions are separated by mathematical sign i.e positive or negative.

The expression "20 - 4.65" represents the amount of change a customer would receive after ordering from the menu board.

The first part of the expression, "20", represents the amount of money the customer paid for their order. This is the total cost of the items they purchased from the menu board.

The second part of the expression, "4.65", represents the amount of money that the customer spent on their order. This is the subtotal of the items they purchased before tax and any other fees that may be added to the bill.

To calculate the change the customer receives, you subtract the amount the customer spent from the amount they paid. So in this case, the expression "20 - 4.65" gives us the answer of 15.35, which represents the amount of change the customer receives.

As for what the customer ordered, we cannot know for sure based on this expression alone. It's possible that the customer ordered a single item that cost exactly $4.65, or they may have ordered multiple items that added up to that subtotal. Without more information about the menu board and the prices of the items, it's impossible to determine exactly what the customer ordered.

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Margin of error = 1.4

Sample mean = 13.4

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

Explanation:

To find the margin of error, we subtract the endpoints and divide by 2.

(b-a)/2 = (14.8-12.0)/2 = 1.4 is the margin of error

The b-a portion calculates the width of the confidence interval. It's the distance from one endpoint to the other. Splitting that in half gives the "radius" so to speak of this interval.

----------

The sample mean is at the midpoint of those given confidence interval endpoints.

The midpoint formula will have us add up the values and divide by 2

(a+b)/2 = (12.0+14.8)/2 = 13.4 is the sample mean

The a+b portion is the same as b+a, meaning we could have written that formula as (b+a)/2 as indicated in the next section.

-----------

Take note how similar each formula is:

The only difference is one has a minus sign and the other has a plus sign.

Answer:

3 Miles

Step-by-step explanation:

3 mi = 15,840ft.

15,840 is greater than 10,000, so 3 miles is more

The function is decreasing in the interval (3, ∞).

f(x) = -x² + 6x - 4

Differentiate the equation with respect to 'x'.

f'(x) = -2x + 6

Put f'(x) = 0

-2x + 6 = 0

x = 6/2

x = 3 (critical point)

Now, write the function as:

f(x) = -x² + 6x - 4

-(x² - 6x + 4) (negative form)

Thus, the function is decreasing in the interval (3, ∞)

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Answer:

1/4

Step-by-step explanation:

you can plug it into a calculator

1/4

First rewrite the - as 1/2^2 , then 2^2=4 so answer is 1/4

Answer:(A) Show your work.

Step-by-step explanation:(A) Show your work.

Answer: holy math sucks but check the explanation i gotchu

Step-by-step explanation: A) -2x^6 + 3x^5 - 2x^4 - 15x^3 + 4x^2 -20x - 20

B) No, the product is not equal to (x^3-3x-4)*(-2x^3+x-5). This is because the order of the terms in the product is different than the order of the terms in the expression. The product takes the form of -2x^6 + 3x^5 - 2x^4 - 15x^3 + 4x^2 -20x - 20, whereas the expression has the form of (-2x^3+x-5)*(x^3-3x-4).

If z varies jointly as x and y, then the value of z when x = 20 and y = 8 is 24.

When a variable varies jointly as two other variables, it means that the variable is directly proportional to the product of the two other variables.

In this case, we can use the formula:

z = kxy

where k is a constant of proportionality.

We can find the value of k by using the given values of z, x, and y:

6 = k(4)(10)

6 = 40k

k = 6/40

k = 3/20

Now that we know the value of k, we can use the formula to find z when x = 20 and y = 8:

z = (3/20)xy

z = (3/20)(20)(8)

z = (3)(8)

z = 24

Therefore, the value of z when x = 20 and y = 8 is 24.

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Answer:

Option three

Step-by-step explanation:

The first two are incorrect reasonings so they are not even options to consider. The bottom two are correct reasonings. But, the third option would be best because it is most specific. With it being an isosceles trapizoid.

Answer: Yes, you are correct.

Step-by-step explanation:

The relationship between the number of flowers and the number of bouquets is an example of a unit rate.

Answer:

yes

Step-by-step explanation:

it is a unit rate

Answer:

B. 6

Step-by-step explanation:

3/4 can be added to itsef to be 6/8

6/8

----      6/1   = 6

1/8

Answer:

Step-by-step explanation:

tbh i don't know how to explain it but i feel like its D i multiply and add

Answer:

y= -1/3x+3

Step-by-step explanation:

we only need to look at the gradient as the gradient of both equations is not the same.

gradient= -1-0/12-9

= -1/3

hence, the answer is y= -1/3x+3

The time needed for Chad to drive the 672 miles is given as follows:

t = 672/v.

In which v is his current rate.

Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:

v = d/t.

For a distance of 672 miles, we have that the parameter d is given as follows:

d = 672.

Hence the time is obtained as follows:

v = 672/t

t = 672/v.

(we don't have the velocity, hence the time is given as a function of the velocity).

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The values of x if the distance between the points (x, 4) & (3, x) be 131/2 are approximately 9.39 and -4.39.

To find the values of x if the distance between the points (x, 4) & (3, x) be 131/2, we can use the distance formula:

D = √((x2 - x1)² + (y2 - y1)²)

Where D is the distance, (x1, y1) and (x2, y2) are the coordinates of the two points.

Plugging in the given values, we get:

131/2 = √((3 - x)² + (x - 4)²)

Squaring both sides and simplifying, we get:

169 = (3 - x)² + (x - 4)²

Expanding and rearranging, we get:

2x² - 14x - 110 = 0

Using the quadratic formula, we can find the values of x:

x = (-(-14) ± √((-14)² - 4(2)(-110))) / (2(2))

x = (14 ± √(196 + 880)) / 4

x = (14 ± √1076) / 4

x ≈ 9.39 or x ≈ -4.39

So the values of x are approximately 9.39 and -4.39.

Therefore, the values of x if the distance between the points (x, 4) & (3, x) be 131/2 are approximately 9.39 and -4.39.

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The percentage change of the depth from 1846 to 1847 is 28%.

The percentage change of the depth from 1846 to 1848 is 14%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Percentage change formula:

= [ (Final percentage - Initial percentage) / Initial percentage ] x 100

Percentage change of the depth from 1846 to 1847.

= [ (3.6 - 5) / 5 ] x 100

= 1.4/5 x 100

= 1.4 x 20

= 28

Percentage change of the depth from 1846 to 1848.

= [ (5.1 - 5) / 5 ] x 100

= 0.7/5 x 100

= 0.7 x 20

= 14

Now,

Year                              1847        1848

Depth                          3.6 feet   5.7 feet

Percentage change     28%           14%          

Thus,

The percentage change of the depth from 1846 to 1847 and 1846 to 1848 is 28% and 14%

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The answer of the given question based on the graph shows  number of birdhouses Penn and his father can build, if they have enough time to build not more than 10 birdhouses, the correct option is A).

What is Graph?

In mathematics, a graph is a collection of points (called vertices or nodes) and the lines or arcs (called edges) that connect them. Graphs are used to model and analyze a variety of real-world situations, such as social networks, transportation systems, and electrical circuits.

Based on the given graph, the horizontal axis represents the number of birdhouses Penn's father can build and the vertical axis represents the number of birdhouses Penn can build. The graph is bounded by the line x + y = 10, which means that the sum of  number of the birdhouses Penn and his father can build cannot be exceed more than10.

Therefore, the domain of this graph is the set of possible values for the number of birdhouses Penn's father can build, subject to the constraint that the sum of the number of the birdhouses Penn and his father can build cannot be exceed more than 10. This domain is the set of non-negative integers less than or equal to 10, inclusive. In interval notation, this can be written as [0, 10].

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Complete question:-The graph shows the number of birdhouses Penn and his father can build if they have enough time to build no more than 10 birdhouses. What is the domain of this graph?

The solution to the system of equations 2x + 3y = 18 and x + y = 7 is (x,y) = (3,4).

What is the linear equations?

A linear equation can have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on.

To solve the equation 2x + 3y = 18 using substitution, we can rearrange the equation to express one of the variables in terms of the other. For example, we can solve for x as follows:

2x + 3y = 18

2x = 18 - 3y

x = (18 - 3y)/2

Now we have an expression for x in terms of y. We can substitute this expression into any other equation that involves x, in order to eliminate x from the equation and solve for y. For example, if we have the equation:

x + y = 7

We can substitute (18 - 3y)/2 for x, to get:

(18 - 3y)/2 + y = 7

Now we can solve for y:

18 - 3y + 2y = 14

-y = -4

y = 4

Once we have solved for y, we can substitute this value back into one of the original equations to solve for x. For example, using the equation 2x + 3y = 18:

2x + 3(4) = 18

2x + 12 = 18

2x = 6

x = 3

Therefore, the solution to the system of equations 2x + 3y = 18 and x + y = 7 is (x,y) = (3,4).

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The smallest positive integer value of m is 676.

To find the smallest positive integer value of m, we need to factor 52m into its prime factors and find the smallest value of m that makes 52m a perfect cube.

First, let's factor 52m into its prime factors:

52m = 2 * 2 * 13 * m

A perfect cube has all of its prime factors raised to the power of 3. So, in order for 52m to be a perfect cube, we need to have two more 2's, two more 13's, and two more m's.

This means that m must be equal to 2 * 2 * 13 * 13 = 676.

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Q3) The correct answer is 0.30.

Q2) (a) The sample space for three True or False questions is:
TTT, TTF, TFT, TFF, FTT, FTF, FFT, FFF

Q2) The outcomes corresponding to the event "The student answered True at least two times" are:
TTT, TTF, TFT, FTT

Q2) The probability of the student answering True at least two times is:
P(X >= 2) = 4/8 = 0.50

The probability of an item being exceptionally good is 0.20, and the probability of an item not being exceptionally good is 0.80. We can use the binomial probability formula to find the probability of exactly 2 of the 10 inspected items being exceptionally good:

P(X = 2) = (10 choose 2) * (0.20)^2 * (0.80)^8 = 45 * 0.04 * 0.16777 = 0.30

Therefore, the correct answer is 0.30.

(a) The sample space for three True or False questions is:
TTT, TTF, TFT, TFF, FTT, FTF, FFT, FFF

(b) The outcomes corresponding to the event "The student answered True at least two times" are:
TTT, TTF, TFT, FTT

(c) The probability of the student answering True at least two times is:
P(X >= 2) = 4/8 = 0.50

Therefore, the correct answer is 0.50.

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Answer:

Step-by-step explanation:

ISSA PARADE INSIDE MY CITY YEAHHHHH

The final answer of Jane is 13(9)/(30) years old.

To find out how old Jane is, we need to first calculate Bill's age and then add 1(1)/(3) years to it.

Here are the steps:

1. Calculate Bill's age:

- Start with Lisa's age: 12(4)/(5) years

- Add 1(1)/(6) years to it: 12(4)/(5) + 1(1)/(6) = 12(24)/(30) + 1(5)/(30) = 12(29)/(30) = 12 + 29/30 = 12(29)/(30) years

2. Calculate Jane's age:

- Start with Bill's age: 12(29)/(30) years

- Add 1(1)/(3) years to it: 12(29)/(30) + 1(1)/(3) = 12(29)/(30) + 1(10)/(30) = 12(39)/(30) = 12 + 39/30 = 12 + 1(9)/(30) = 13(9)/(30) years

So, Jane is 13(9)/(30) years old.

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The area is 893/15.

The area can be calculated by evaluating the given expression at the limits of integration and subtracting the two values.

we will evaluate the expression at the upper limit of integration, t = 7:
[(7)/(3)(7)^((3)/(2))-(1)/(5)(7)^((5)/(2))] = [(7)/(3)(7^(3/2))-(1)/(5)(7^(5/2))] = [(7)/(3)(49)-(1)/(5)(16807/49)] = [(343/3)-(33614/245)] = [(343/3)-(274/5)] = [(1715/15)-(822/15)] = 893/15

we will evaluate the expression at the lower limit of integration, t = 0:
[(7)/(3)(0)^((3)/(2))-(1)/(5)(0)^((5)/(2))] = [(7)/(3)(0)-(1)/(5)(0)] = 0

we will subtract the two values to find the area:
893/15 - 0 = 893/15

Therefore, the area is 893/15.

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The factorization of the polynomial is (x-10)² (x² + 13x + 42).

To factor the given polynomial, we can use the fact that it has a zero at 10 with multiplicity 2. This means that (x-10)² is a factor of the polynomial. We can divide the polynomial by (x-10)² using long division to find the other factor.

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