Jordy tried to prove that △ A B E ≅ △ B C D △ABE≅△BCDtriangle, A, B, E, \cong, triangle, B, C, D. A A B B C C D D E E Statement Reason 1 ∠ B C D ≅ ∠ A B E ∠BCD≅∠ABEangle, B, C, D, \cong, angle, A, B, E Given 2 ∠ C D B ≅ ∠ B E A ∠CDB≅∠BEAangle, C, D, B, \cong, angle, B, E, A Given 3 B D ↔ ∥ A E ↔ BD ∥ AE B, D, with, \overleftrightarrow, on top, \parallel, A, E, with, \overleftrightarrow, on top Given 4 ∠ C B D ≅ ∠ B A E ∠CBD≅∠BAEangle, C, B, D, \cong, angle, B, A, E Corresponding angles on parallel lines are congruent. 5 △ A B E ≅ △ B C D △ABE≅△BCDtriangle, A, B, E, \cong, triangle, B, C, D Angle-angle-angle congruence What is the first error Jordy made in his proof? Choose 1 answer: Choose 1 answer: (Choice A) A Jordy used an invalid reason to justify the congruence of a pair of sides or angles. (Choice B) B Jordy only established some of the necessary conditions for a congruence criterion. (Choice C) C Jordy establish

Answer:

Step-by-step explanation:

tan x= opp./adj.

tan x = 12/5 so

     x = tan^-1 (12/5)

second choice

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

See the steps below, one ratio - one pair of numbers changes at a time.

      spiders    webs      days

9514 1404 393

Answer:

  3/2

Step-by-step explanation:

The scale factor is the ratio of corresponding side lengths.

  larger/smaller = (21/2)/7 = 21/14 = 3/2

The scale factor is 3/2.

Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

\(\boxed{I = \frac{P \times R \times T}{100}}\),

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

\(6180 = \frac{P \times 6.12 \times 28}{100}\)

⇒ \(6180 \times 100 = P \times 171.36\)     [Multiplying both sides by 100]

⇒ \(P = \frac{6180 \times 100}{171.36}\)    [Dividing both sides of the equation by 171.36]

⇒ \(P = \bf 3606.44\)

Therefore, James needs to invest $3606.44.

Answer:

The word name of a number is how it sounds when we say its name the long way.

Step-by-step explanation:

Astronomers can use geometry to measure the distance of objects in space and describe ttheir relationship.

It should be noted that astronomers study stars, planets, and other celestial bodies. It should be noted that they use ground-based equipment, like optical telescopes, and space-based equipment. Some astronomers study distant galaxies and phenomena such as black holes and neutron stars.

In this case, astronomers can use geometry to measure the distance of objects in space and describe ttheir relationship.

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Answer:

distance between, motion

Step-by-step explanation:

plato, I got it right

The conjectures can be the product of two odd numbers is always an odd number and product of two odd numbers is always greater than either of them.

It is given that a number is product of two odd numbers.

We have to make a conjecture about it.

What do you mean by a conjecture ?

A conjecture is a conclusion which is believed to be true but hasn't been proved or disproved yet.

As per the question ;

We need to make a conjecture about product of two odd numbers.

The two conjectures can be ;

(1) The product of two odd numbers is always an odd number.

i.e.,

Let's assume the numbers are 21 and 27.

The product of these two numbers will be ;

= 21 × 27

= 567

So , 567 is an odd number.

2) The product of two odd numbers is always greater than either of them.

i.e.,

Let's assume numbers are 13 and 15.

The product will be ;

= 13 × 15

= 195

is greater than both of 13 and 15.

Thus , the conjectures can be the product of two odd numbers is always an odd number and product of two odd numbers is always greater than either of them.

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Answer:

The graph of the parent function y = 2^x can be transformed to create the graph of y = 2^(3x) by horizontally compressing by a factor of 3. Therefore, the correct answer is C.

Answer:

Advantages:

● Bar charts are pretty easy to interpret, and there's a very clear relationship between size and value that allows easy comparison.

● They're simple to make and most people have experience creating and understanding them from school.

● They can help in presenting very large or very small values more emphatically.

Disadvantages:

● Bar charts that attempt to represent wide ranges of numbers will struggle to efficiently communicate their message. For example, a bar chart for the numbers 5, 6, 10 and 378 will lend extreme visual weight to the highest value and make the relative values of the other measurements appear irrelevant. An alternative to this would be creating an adjusting scale for the bars, but this complicates the visual aspect of the presentation and breaks the intuitive sense that size correlates directly to value.

● Bar graphs tend to be locked into a particular data set, making it hard to show multiple values or changes over time unless the chart is modified, such as by making the bars layered and three-dimensional.

I hope it's helpful!

Answer:

Advantages:

Disadvantages:

By using the concept of number line, it can be calculated that

a) g is a function

b) g(5) = 3 means after 5 flips, the person is at '3' on the number line

c) Probability that g(3) = 0 is zero

What is a number line?

All the real numbers, integers, fractions can be pictorially represented with the help of a line. The line is known as number line.

a) Here, g represents the position after the nth flip

After n flips, a person stands at only one position on the number line, not more than one. So every point on the domain has unique image. So g is a function.

b) g(5) = 3 means after 5 flips, the person is at '3' on the number line

c) The person is initially standing at zero. To move to zero position, even number of flips have to be made. But 3 is not an even number. So probability that g(3) = 0 is zero

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Hello!

∠AED and ∠BEC are opposite angles

so ∠AED = ∠BEC = 36°.

Answer:

y = |x+5|-7

Step-by-step explanation:

y = |x| is the parent function with vertex (0,0) so to get to (-5,-7) you need to move left 5 and move down 7

Answer:

C

Step-by-step explanation:

You can’t multiply anything to make A work

Nor B

C you can multiply by 3

D you can’t do anything.

The first three terms of the arithmetic sequence are -97, -63, and -29.

The value of x = -14.

To find the value of x and the first three terms of the arithmetic sequence, we can equate the differences between consecutive terms:

The common difference (d) is the same between all consecutive terms.

So, we have:

(5x + 7) - (7x + 1) = (2x - 1) - (5x + 7)

Simplifying the equation:

5x + 7 - 7x - 1 = 2x - 1 - 5x - 7

-2x + 6 = -3x - 8

Now, let's solve for X:

-2x + 3x = -8 - 6

x = -14

Substituting the value of X back into the expressions, we can find the first three terms:

First term: 7x + 1 = 7(-14) + 1 = -97

Second term: 5x + 7 = 5(-14) + 7 = -63

Third term: 2x - 1 = 2(-14) - 1 = -29

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It will take 15 days for the hair to grow from 12mm to 16.5mm

By "average rate" in this context, we mean the typical or usual amount of hair growth per unit of time, which is often measured in millimeters per day. This rate can vary slightly depending on factors such as age, gender, genetics, diet, and overall health.

Let's first find out how much the hair needs to grow by subtracting its initial length (12mm) from its target length (16.5mm):

16.5mm - 12mm = 4.5mm

Now we can divide this growth by the average rate of hair growth to find the number of days it will take to grow this much:

4.5mm ÷ 0.3mm/day = 15 days

Therefore, it will take 15 days for the hair to grow from 12mm to 16.5mm.

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Two stockpots are similar cylinders. The smaller stockpot has a height of 10 inches and a radius of 2.5 inches, the volume of larger one is 628.32 cubic inches.

We know that, to find volume:

Volume = π * \(r^2\) * h

For the smaller stockpot:

Radius (r) = 2.5 inches

Height (h) = 10 inches

Volume = π * (2.5)² * 10 ≈ 196.35 cubic inches

For the larger stockpot:

Radius (r) = 2.5 inches

Height (h) = 16 inches

Volume = π * (2.5)² * 16

             ≈ 628.32 cubic inches

Thus, the volume of larger one is 628.32 cubic inches.

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To find the number of temperatures in the set, we can divide the sum of the temperatures by the mean temperature.

Number of temperatures = Sum of temperatures / Mean temperature

In this case, the sum of temperatures is given as 2,516 and the mean temperature is given as 74 degrees Fahrenheit.

Number of temperatures = 2,516 / 74

Calculating the division:

Number of temperatures ≈ 34.05

Since we cannot have a fraction of a temperature, we need to round the result to the nearest whole number. Therefore, there are approximately 34 temperatures in the set.

Answer:

14.13

Step-by-step explanation:

(7 + 5) +4.13 - 2

PEMDAS says parentheses first

(12) +4.13 - 2

Then add and subtract from left to right

16.13 -2

14.13

I am guessing you are talking about Option 3. They start with $125. So they times it by 1.25 as we are using the multiplier method. So in the First month, it will be 156.25. Second it will be 195.3125. So in August it will be $476.837157. Of couse round it and you will get $476.84.

I believe there is a more efficent way of doing this but I have forgotten.

The number of listeners is given from the total number of listeners and

the ratio of the listeners between the two stations.

Required:

Given:

The daily listening audience of the AM station = 4 × The audience of the FM sister station

The number of people that listen to the two stations = 105,000

Required:

The number of listeners of the FM station

Solution:

The ratio of the listeners is 1:4

Let x represent the number of listeners of the FM sister station, we have;

The number of listeners of AM radio station = 4·x

Which gives;

4·x + x = 105,000

5·x = 105,000

\(x = \dfrac{105,000}{5} = \mathbf{21,000}\)

The number of listeners of he radio station = 21,000 × 4 = 84,000

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Answer:

The shape cannot be determined since we don't know the shape of either population distribution.

Step-by-step explanation:

Answer on Khan

1. The velocity at time t , v(t) = (18t² + 3 ) m/s

2. The velocity at time t = 3 seconds = 165 m/s

3. The acceleration at time t, a(t) =( 36t )m/s²

4. The acceleration at time t = 3 seconds = 108 m/s²

The quantity that tells us how fast an object is moving anywhere along its path is the instantaneous velocity.

Instantaneous acceleration is defined as the ratio of change in velocity during a given time interval such that the time interval goes to zero.

1. s(t) = 6t³ + 3t +9

to find the velocity at time t, we differentiate s(t)

= 18t² + 3

2. at t = 3s

= 18(3)² +3

= 165 m/s²

3. v(t) = 18t² + 3

to get the acceleration at time t, we differentiate v(t)

= 36t

4. when t = 3

a = 36 × 3

= 108 m/s²

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Winston's economic profit based on the forgone salary of $60,000, and the revenue of $150,000 is $78,000. The correct option is therefore;

$78,000

An economic profit is a profit that accounts for both the explicit and implicit costs of a business. The economic profit is obtained from the difference between the total revenue and the costs including the opportunity costs.

The annual salary of Winston as an accountant = $60,000

The amount Winston's financial asset generates = $4,000 per year

The cost of running the business = $8,000

The amount Winston earns as revenue = $150,000

Therefore;

Winston's opportunity cost which is the forgone alternative, is the amount he earns as an accountant = $60,000

The interest of $4,000, earned from the financial asset = The cost of using the financial asset for the business

The cost of running the business = $8,000

The total cost = Opportunity cost + Cost of making use of the financial asset + The business running cost

The total cost = $60,000 + $4,000 + $8,000 = $72,000

The economic profit = The total revenue - The total cost

Therefore;

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The probability that the mean battery life would be greater than 526.4 minutes if in a sample of 81 batteries having a variance of, 2916 and a mean life of 518 minutes is 0.0808.

The ratio of good outcomes to all possible outcomes of an event is known as probability. A lot of successful results for an experimental with 'n' results can be represented by the symbol x.

Given:

The variance = 2916,

The mean life of a battery, m = 518 min,

The total number of samples, n = 81

Calculate the probability of a mean battery life of lower than 526.4 minutes by the following formula,

z = x - m / (σ / √ n)

Here, x is the expected value, σ is the deviation, and z is the probability.

Substitute the values,

z = 526.4 - 518 / (54 / √81)         [σ = √ variance = √2916  = 54]

z = 1.4

Consult the cumulative standard normal table

P (z < 526.4) = 0.9192,

But we know that

P (z > 526.4) = 1 - P (z < 526.4)

P (z > 526.4) = 1 - 0.9192 = 0.0808

Therefore, The probability that the mean battery life would be greater than 526.4 minutes if in a sample of 81 batteries having a variance of, 2916 and a mean life of 518 minutes is 0.0808.

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Using functions,

Domain:

[−7,7], {x|−7≤x≤7}

Range:

[−7,7], {y|−7≤y≤7}

Graph is attached.

A function is a procedure or a connection that links each element of a non-empty set A, at least, to one element of a different non-empty set B. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain. f = {(a,b)| for all a ∈ A, b ∈ B}

Subtract x2 from both sides of the equation.

y2=49−x2

Take the square root of both sides of the equation to eliminate the exponent on the left side.

y=±√49−x2

Simplify

±√49−x2

y=±√(7+x) (7−x)

The complete solution is the result of both the positive and negative portions of the solution.

y=√(7+x) (7−x)

y=−√(7+x) (7−x)

Set the radicand in

√(7+x) (7−x)

greater than or equal to 0 to find where the expression is defined.

(7+x) (7−x) ≥0

7≤x≤7

The domain is all values of x that make the expression defined.

Interval Notation:

[−7,7]

Set-Builder Notation:

{x|−7≤x≤7}

The range is the set of all valid y values.

Use the graph to find the range.

Interval Notation:

[−7,7]

Set-Builder Notation:

{y|−7≤y≤7}

Now, determining the domain and range.

Domain:

[−7,7], {x|−7≤x≤7}

Range:

[−7,7], {y|−7≤y≤7}

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The domain and range are:

Domain: [−7,7], {x|−7 ≤ x ≤ 7}

Range: [−7,7], {y|−7 ≤ y ≤ 7}

Determine the value of the independent variable x for which the function is specified to determine the domain and range of an equation y = f(x).

Simply solve the equation x = g(y) and then identify the domain of g to ascertain the function's range(y).

Graphs can also be used to determine the scope and range of functions. Because the domain refers to the set of potential input values, the domain of a graph includes all of the input values displayed on the x axis. The range represents the collection of possible output values shown on the y axis.

For all values of a and b, f = {(a,b)| for all a ∈ A, b ∈ B}

Subtract x² from both parts of the equation.

y² = 49−x²

Take the square roots of both parts of the equation to remove the exponent on the left side.

y = ±√49−x²

Simplify the above equation,

±√49−x²

y=±√(7+x) (7−x)

The solution's positive and negative halves combine to create the entire solution.

y=√(7+x) (7−x)

y=−√(7+x) (7−x)

Set the radicand in

√(7+x) (7−x)

Greater than or equal to 0 to locate the expression's definition.

(7+x) (7−x) ≥0

7≤x≤7

The domain is the set of x values that determine the expression.

Interval Notation: m[−7,7]

Set-Builder Notation: {x|−7≤x≤7}

The range is the gathering of all legal y values.

Use the graph to find the range.

Interval Notation: [−7,7]

Set-Builder Notation: {y|−7≤y≤7}

Following that, determine the scope and range.

Domain: [−7,7], {x|−7≤x≤7}

Range: [−7,7], {y|−7≤y≤7}

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to find the interest you simply just multiply the amount by the percentage, so:

$3000 × 3.5%

= $3000÷100×3.5

=$105

There are 9,000 numbers that have 7 in the thousands of places and are less than 54,000.

Consider the possible digits in the hundreds, tens, and one's places.

Thousands of places: There is only one possibility, which is 7.

Hundreds place: Any digit from 0 to 9 is possible.

Tens place: Any digit from 0 to 9 is possible.

One place: Any digit from 0 to 9 is possible.

Since the number is less than 54,000, the digit in the hundreds place cannot be 5.

So, there are 9 possible digits (0 to 9, except 5) for the hundreds place, and 10 possible digits (0 to 9) for the tens and one's places.

So, the total number of such numbers is:

9 x 10 x 10 x 10 = 9,000

Therefore, there are 9,000 numbers that satisfy the given condition.

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The volume of the cuboid, obtained using the specified area of the rectangular face and the square thickness surface, indicates that the possible volume of the cuboid are;

2,646 cm³ or 756 cm³, depending on the thickness of the cuboid

A cuboid is a hexahedron consisting of six quadrilateral faces.

The area of the rectangular face of the cuboid, A = 126 cm²

The ratio of the length to the height of the rectangular face = 7 : 2

Let L represent the length of the rectangular face, and let H represent the height of the face, we get;

A = L × H = 126

L/H = 7/2

Therefore; L = (7/2) × H

Plugging in the value of L, in the equation for the area, we get;

A = (7/2) × H × H = (7/2) × H² = 126

H² = 126 × (2/7) = 36

H = √(36) = 6

The height of the rectangular face, H = 6 cm

L = (7/2) × H

Therefore, L = (7/2) × 6 = 21

The length, L, of the rectangular face, L = 21 cm

Whereby the cuboid consists of two square faces, we get;

The possible volume, V, of the cuboid are V = H×L² or V = L×H²

Therefore, the possible volume of the cuboid are;

V = 6 × 21² = 2646 cm³

V = 21 × 6² = 756 cm³

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Answer:

35

Step-by-step explanation:

75% of 40 is 30

40+30=70

70/2=35