Ð


B


1) This shape is a Regular Hexagon. Line


BE is a line of symmetry.


F


Ñ


a) Calculate the size of Angle ABE


b) Work out the size of Angle DCE


c) Calculate the size of Angle BEC


E


D


2) A regular polygon has an exterior angle which is 20°.


a) Calculate the size of its interior angle


b) How many sides must the polygon have? Explain why!

Answer: $0.65

Step-by-step explanation:

Amount for the magazine in a regular newsstand for one year:

1.95*12=$23.4

Amount saved per issue with subscription:

(23.4-15.60) ÷ 12 = $0.65 per issue is saved with a subscription

Answer:

f(-1)=3

Step-by-step explanation:

plug in -1 for x

-(-1)+2

negative and negative make a positive 1+2=3

The original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

To show that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves, we need to take the derivative of the equation and set it equal to -1/b^2, the slope of the orthogonal line.

First, we take the derivative of the equation with respect to x:

2x/a^2 = -2y/b^2 * dy/dx

Simplifying, we get:

dy/dx = -b^2*x/a^2*y

Now, we set this equal to -1/b^2:

-b^2*x/a^2*y = -1/b^2

Cross-multiplying and simplifying, we get:

x/a^2*y = 1/b^2

Finally, we can rearrange this equation to get:

y = b^2*x/a^2

This equation represents the orthogonal family of curves to the original family of conics. Since the original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

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Answer:

{5, 15, 19}

Step-by-step explanation:

According to the triangle inequality theorem, the sum of the lengths of any two sides of a ∆ must be greater than the length of the third side.

Thus, any of the given sets of numbers will represent the 3 sides of a ∆, if the following condition is satisfied:

a + b > c

b + c > a

a + c > b

Where a and b are the smaller side lengths, and c is the length of the longest side.

Let's check each set of numbers given to see if any satisfies this condition.

✍️Option 1: {6, 20, 28}

6 + 20 is not greater than 28

20 + 28 > 6

6 + 28 > 20

❌This set of numbers does not represent the sides of a ∆.

✍️Option 2: {4, 11, 15}

4 + 11 = 15

11 + 15 > 4

4 + 15 > 11

❌This set of numbers does not represent the sides of a ∆.

Option 3: {9, 19, 30}

9 + 19 is not greater than 30

19 + 30 > 9

9 + 30 > 19

❌This set of numbers does not represent the sides of a ∆

Option 4: {5, 15, 19}

5 + 15 > 19

15 + 19 > 5

5 + 19 > 15

✅This set of numbers does not represent the sides of a ∆

Only option 4, satisfied the condition stated earlier, therefore, based on the triangle inequality theorem, {5, 15, 19}, is the set of numbers that represents the 3 sides of a triangle.

Answer:57

Step-by-step explanation:

The Lewis family used their sprinkler for 30 hours, while the Pham family used theirs for 25 hours.

Let's assume x represents the number of hours the Lewis family used their sprinkler, and y represents the number of hours the Pham family used their sprinkler. We can set up a system of equations based on the given information.

Equation 1: x + y = 55 (The combined total of hours)

Equation 2: 30x + 25y = 1475 (The total water output in liters)

To solve this system of equations, we can use substitution or elimination methods. By solving Equation 1 for x and substituting it into Equation 2, we get:

30(55 - y) + 25y = 1475

1650 - 30y + 25y = 1475

-5y = -175

y = 35

Substituting the value of y into Equation 1, we find:

x + 35 = 55

x = 20

Therefore, the Lewis family used their sprinkler for 20 hours, while the Pham family used theirs for 35 hours.

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Answer: c) $109.88

Step-by-step explanation: divide 750 by 21.5 to figure out how many gallons he would need and than multiply that by $3.15 to find out how much it would cost and you get $109.88

Answer:

109.88

Step-by-step explanation:

Divide 750 by 21.5. Then multiply the result by 3.15.

(a) The height after t years is given by: h(t) = 0.75t^2 + 5t + 12

(b) The shrubs are 54 centimeters tall when they are sold.

To solve this problem, we need to integrate the given differential equation dh/dt = 1.5t + 5 with respect to t to obtain an expression for h in terms of t. Then we can use this expression to answer the questions asked.

Integrating both sides of the equation with respect to t, we get

∫dh = ∫(1.5t + 5) dt

h = 0.75t^2 + 5t + C

where C is the constant of integration. To find C, we use the initial condition that the seedlings are 12 centimeters tall when planted, i.e., h(0) = 12. Substituting t = 0 and h = 12 in the above equation, we get

12 = 0.75(0)^2 + 5(0) + C

C = 12

Therefore, the expression for h in terms of t is

h = 0.75t^2 + 5t + 12

(a) To find the height after t years, we simply substitute the value of t in the above equation

h(t) = 0.75t^2 + 5t + 12

(b) The shrubs are sold after 6 years of growth and shaping. Therefore, we need to find h(6) to determine their height at the time of sale

h(6) = 0.75(6)^2 + 5(6) + 12

= 54 cm

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The given question is incomplete, the complete question is:

Tree growth an evergreen nursery usually sells a certain shrub after 6 years of growth and shaping. the growth rate during those 6 years is approximated by dh/dt = 1.5t + 5 where t is the time in years and h is the height in centimeters. the seedlings are 12 centimeters tall when planted (a) find the height after years. (b) how tall are the shrubs when they are sold?

\(\sqrt{3} - \frac{2}{\sqrt{3} } = \frac{3}{\sqrt{3} } - \frac{2}{\sqrt{3} } = \frac{1}{\sqrt{3} } = \frac{\sqrt{3} }{3}\)

ok done. thank to me :>

Answer:1 2/3 per day

Step-by-step explanation:

The weaker inequality 1/2 · 3/4 ··· 2n-1/2n < 1/√(3n) holds for all positive integers n, but using mathematical induction, the basis step works, although the inductive step fails.

a) If we try to prove the inequality 1/2 · 3/4 ··· 2n-1/2n < 1/√(3n) using mathematical induction, we can see that the basis step works. When n = 1, we have 1/2 < 1/√3, which is true.

Now, let's consider the inductive step. Assuming that the inequality holds for some positive integer k, we need to show that it also holds for k+1, i.e., we assume 1/2 · 3/4 ··· 2k-1/2k < 1/√(3k) and we want to prove 1/2 · 3/4 ··· 2k-1/2k · (2k+1)/(2k+2) < 1/√(3k+3).

If we attempt to manipulate the expression, we can simplify it to (2k+1)/(2k+2) < 1/√(3k+3). However, we cannot proceed further to prove this inequality, as it is not necessarily true. Therefore, the inductive step fails, and we cannot establish the original inequality using mathematical induction.

b) However, mathematical induction can still be used to prove the stronger inequality 1/2 · 3/4 ··· 2n-1/2n < 1/√(3n+1) for all integers greater than 1. We can start by verifying the case where n = 1, which gives us 1/2 < 1/√4, which is true.

Now, assuming the inequality holds for some integer k, we can multiply both sides of the inequality by (2k+3)/(2k+2) to get:

(1/2 · 3/4 ··· 2k-1/2k) · (2k+3)/(2k+2) < 1/√(3k+1) · (2k+3)/(2k+2).

Simplifying the expression on both sides, we have:

(2k+3)/(2k+2) < 1/√(3k+1) · (2k+3)/(2k+2).

We can observe that the right side of the inequality is less than 1/√(3k+3) by multiplying the denominator of the right side by (2k+3)/(2k+3). Hence, we obtain:

(2k+3)/(2k+2) < 1/√(3k+3).

This establishes the inequality for k+1, and thus, we have proven the stronger inequality using mathematical induction.

By verifying the case where n = 1 separately, we can conclude that the weaker inequality 1/2 · 3/4 ··· 2n-1/2n < 1/√(3n) holds for all positive integers n, as it follows from the proven stronger inequality using mathematical induction.

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The correct statements regarding the dilation are given as follows:

a. Rectangle S is similar to rectangle S'.

d. The side lengths of rectangle S are not equal to the corresponding side lengths of rectangle S'.

e. The angle measurements of rectangle S are equal to the corresponding angle measurements of rectangle S'

A dilation occurs when each of the vertices of a polygon is multiplied by a constant, which is called scale factor, hence the side lengths of the dilated figure are different than of the original figure.

Hence the effects of the dilation are presented as follows:

Hence statements a, d and e are correct, as:

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Answer:

29.1°

Step-by-step explanation:

Given that :

Riser, AB, Opposite = 10 cm

Thread, = AC, Adjacent = 18 cm

Angle of inclination, θ

Using trigonometry :

Tan θ = opposite / Adjacent = AB / AC

Tan θ = 10 / 18

θ = tan^-1(10/18)

θ = 29.055

Hence, angle of inclination is 29.1° (1 decimal place)

Answer:

consider the < as = signs

and take -5 to the other side making it a +

x<0+5

x<5

The value of x is 65. Please note that this solution is based on the assumption that the angles QRP and PSQ are supplementary. If this assumption doesn't hold, feel free to let me know.

We need to find the value of x in the equation ZQRP = (2x + 20)° given that ZPSQ = 30°. Since the question doesn't provide enough information about the relationship between angles QRP and PSQ, I'll assume that they are supplementary angles (angles that add up to 180°). This assumption is based on the possibility that the angles form a straight line or a linear pair.

If angles QRP and PSQ are supplementary, their sum is 180°:

(2x + 20)° + 30° = 180°

Now, we can solve for x:

2x + 50 = 180

Subtract 50 from both sides:

2x = 130

Divide by 2:

x = 65

Answer:

\(5.3\times 10^{-11}\ m\)

Step-by-step explanation:

In this problem, we need to express 53 pm in which is the size of a hydrogen atom, in scientific notation.

Any number can be expressed in scientific notation as follows :

\(N=a\times 10^b\)

a is any real no and b is any integer

We know that, 1 pm = \(10^{-12}\ m\)

It means, \(53\ pm=53\times 10^{-12}\ m\)

or

\(53\times 10^{-12}\ m=\dfrac{53}{10}\times 10^{-12}\times 10\\\\=5.3\times 10^{-12+1}\\\\=5.3\times 10^{-11}\ m\)

Therefore, the above is the scientific notation for the size of a hydrogen atom.

To rewrite Newton's formula for solving f(x) = 0 using the given function f(x) = x^2 - 8, first, let's recall the general Newton's formula:
x_{n+1} = x_n - f(x_n) / f'(x_n)

In this case, f(x) = x^2 - 8. To apply the formula, we need the derivative of f(x), f'(x):
f'(x) = 2x

Now, plug f(x) and f'(x) into the Newton's formula:
x_{n+1} = x_n - (x_n^2 - 8) / (2x_n)
This equation represents Newton's method for solving f(x) = x^2 - 8, with f(x_n) = x_n^2 - 8.

Newton's formula for solving equations of form f(x) = 0 is given by the recurrence relation:
xn+1 = xn - f(xn)/f'(xn)
where xn is the nth approximation of the root of f(x) = 0, and f'(xn) is the derivative of f(x) evaluated at xn.

To write this formula as xn+1 = f(xn), we need to first rearrange the original formula to solve for xn+1:
xn+1 = xn - f(xn)/f'(xn)

Multiplying both sides by f'(xn) and adding f(xn) to both sides, we get:
xn+1*f'(xn) + f(xn) = xn*f'(xn)

Rearranging terms and dividing both sides by f'(xn), we get:
xn+1 = xn - f(xn)/f'(xn)

which is the same as:
xn+1 = f(xn) - xn*f'(xn)/f(xn)

Substituting f(x) = x^2 - 8 into this formula, we get:
xn+1 = (xn^2 - 8) - xn*(2*xn)/((xn^2 - 8))

Simplifying, we get:
xn+1 = xn - (xn^2 - 8)/(2*xn)

This is Newton's formula in form xn+1 = f(xn) for solving f(x) = 0, where f(x) = x^2 - 8.

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Answer:

27°

Step-by-step explanation:

The two lines are parallel, causing them to be equal

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

x = 0

Step-by-step explanation:

Calculate the product

Any expression multiplied by 0 equales 0

Solution

X = 0

Hope this helps!

Answer:

f. 85

Step-by-step explanation:

All triangles add up to 180 degrees

BCE=25

then you need to find DBC, you can do that since ABD is isocilies that means all sides are equal in length and angle so 180 divided by 3 (number of side) is 60

isoceles triangle have 2 sides that are equiangular, cince we know BCA is 25 we also know BAC is 25, leaving angle ABC to be 130 (180-50=130)

we subtract angle ABD from angle ABC to get angle DBC, leaving angle DBC to equal 70 degrees

since 70 (angle DBC) + 25 (Angel BCA)= 95

we just subtrract 95 from 180 to get the answer 85 (:

Answer:

85 degrees

Step-by-step explanation:

if Δ ABD is equilateral  then the 3 sides and three angles are equal

sum of angles of Δ=180

180/3=60 degrees (∠A,∠B,∠D)

ΔBCA is isosceles then the two angles A and C are equal = 25

∠B=180-50=130

∠B in Δ BEC=130-60=70

∠E+∠B+∠C in Δ BEC=180

∠E= 180-70-25=85 degrees

Answer:

$18 :)

Step-by-step explanation:

10% of 180 is 18

Answer:
The 3 examples undefined terms and illustration are 1)line 2)point 3)set.

What is geometry ?
Geometry is a branch of mathematics that focuses on the study of shapes, sizes, positions, and relationships of objects in space. It is concerned with understanding the properties and characteristics of various geometric figures, such as points, lines, angles, circles, triangles, polygons, and three-dimensional objects like spheres, pyramids, and cubes.

According to Question:

In mathematics, undefined terms are terms that are not formally defined, but are instead assumed to be understood based on their common usage or intuitive meaning. Here are three examples of undefined terms:

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The locations of A' and B' are A' (0, 6) and B' (6, 0); lines f and f' are parallel.

To explain this using a formula, we can use the dilation formula. This formula states that for any point (x,y) on the original line (f), when dilated with a scale factor of k and the center of dilation is the origin (0,0), the coordinates of the point on the new line (f') would be (kx, ky).

For point A, which has coordinates (2,0) on line f, when dilated with a scale factor of 3 and the center of dilation being the origin, the coordinates of point A' on line f' would be (3 * 2, 3 * 0) = (6, 0).

Similarly, for point B, which has coordinates (0,2) on line f, when dilated with a scale factor of 3 and the center of dilation being the origin, the coordinates of point B' on line f' would be (3 * 0, 3 * 2) = (0, 6).

Since the two lines have the same slope, line f and line f' are parallel.

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Using a significance level of 0.05 a. z approximately equals 2.00 for a P-value of 0.02275 (d) z approximately equals 2.00 for a P-value of 0.02275. Since the P-value is less than 0.05, reject the null hypothesis that there is no difference in the number of sunny days between City A and City B.

To determine if City B is significantly sunnier than City A, we can use a z-test for two proportions. Using the given data, we calculate a z-value of 2.00 and a corresponding P-value of 0.02275.

Since the P-value is less than the significance level of 0.05, we reject the null hypothesis that there is no difference in the number of sunny days between City A and City B. This means that we have evidence to suggest that City B is significantly sunnier than City A based on the sample data.

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A function must have one y-value for any given x-value.

Usually, if you see the same x-value in the x-column more than once, that's not going to be a function, because that usuall makes a single x-value pair with more than one y-value.

This would be NOT be a function, because x-value of 3 is paired with two different y-values.

x  |  y

3    7

4    8

3    9

6    7

Can you identify the function?

Answer:

  15 kg

Step-by-step explanation:

We can multiply the given ratio units by 6 to make them be integers:

  (1/2) : (1/3) = 3 : 2

Then we can see that the second man has 2/3 the weight of the first man.

  (2/3)(22.5 kg) = 15 kg

The second person weighs 15 kg.

Answer:

y = 8.7

Step-by-step explanation:

Assuming we can use decimal places, y is equal to 8.7.

In programming, += is often used as a substitute for y = y + x (example)

Therefore, y = y + 3.7, and since y = 5, y = 5 + 3.7, y = 8.7

A and B have the same elements, the measure of AUB will be equal to the measure of B.

To show that if m*(A) = 0, then m*(AUB) = m*(B), we need to prove the following:
1. If m*(A) = 0, then A is a null set.
2. If A is a null set, then AUB = B.
3. If AUB = B, then m*(AUB) = m*(B).
Let's break down each step:
1. If m*(A) = 0, then A is a null set:
  - By definition, a null set has a measure of 0.
  - Since m*(A) = 0, it implies that A has no elements or its measure is 0.
  - Therefore, A is a null set.
2. If A is a null set, then AUB = B:
  - Since A is a null set, it means that it has no elements or its measure is 0.
  - In set theory, the union of a null set (A) with any set (B) results in B.
  - Therefore, AUB = B.
3. If AUB = B, then m*(AUB) = m*(B):
  - Since AUB = B, it implies that both sets have the same elements.
  - The measure of a set is defined as the sum of the measures of its individual elements.
  - Since A and B have the same elements, the measure of AUB will be equal to the measure of B.
  - Therefore, m*(AUB) = m*(B).
By proving these three steps, we have shown that if m*(A) = 0, then m*(AUB) = m*(B).

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The simplification of the expression (-3/4x - 8) - (-17 + 2/8x) is (-1/2x) + 9.

To write the given expression in simplest form we have to solve the necessary operations, in the correct order, in other words, we need to combine like terms and simplify. Here are the steps:

1. Distribute the negative sign in front of the second set of parentheses:

(-3/4x - 8) + (17 - 2/8x)

2. Combine like terms:

(-3/4x + 2/8x) + (17 - 8)

3. Simplify the fractions:

(-6/8x + 2/8x) + 9

4. Combine like terms again:

(-4/8x) + 9

5. Simplify the fraction:

(-1/2x) + 9

So the expression in simplest form is (-1/2x) + 9.

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