Using SSS, SAS, ASA, & AAS WITH CONGRUENT TRIANGLES For each problem below, state each of the following: a ) state the congruent parts b )state how the triangles are congruent c ) state the congruence

The equation of the line with coordinate (0, -2) that goes through y = -²/₃x + 5 is; y = -²/₃x - 2

We know that the general formula for an equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Now, from the given equation of y = -²/₃x + 5, we can say that;

Slope; m = -²/₃

y-intercept = 5

Thus, equation of the new line would be;

y - (-2) = -²/₃(x - 0)

y + 2 = -²/₃x

y = -²/₃x - 2

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Answer:

[tex]f(x) = $\begin{cases}3x-4 & -2\le x < 1\\x + 3 & 1 \le x \le 5\\8 & 5 \le x \le 8 \end{cases}$[/tex]

Step-by-step explanation:

The permissible values of x for a function is called the domain of the function. Permissible values mean that the function is real and defined.

The range of a function is the set of all y values for the domain

If a point on a graph is a filled circle, that point is included in the domain(x-value) and represents a ≤ or a ≥ inequality

If a point on a graph is an unfilled or hollow circle, that point is not included in the domain(x-value) and represents a < or a >inequality

Let's look at the three parts of the given piecewise graph

Piecewise part A

We see that the minimum and maximum values of x for this function are x = -2 and x = 1 respectively. The point corresponding to x= 1 is a hollow circle so it is not included in the domain whereas the point corresponding to x = -2 is included

Let's find the equation of this line:
Take 2 points on the line. We choose points (0, -4) and (1, -1)

Slope of this line is -1 -(-4)/(1-0) = (-1 + 4)/1 = 3
The y-intercept is -4

So equation of the line is y = 3x -4  for -2 ≤ x < 1

Proceeding in a similar manner we can determine the domain and function equation for the other two pieces, B and C

Piecewise part B

Domain of x : 1 ≤ x ≤5
Slope = (8-4)/(5-1) = 4/4 = 1

Equation is of the form y = 1x + b
To calculate b, plug in values of x = 1, y = 4 to get
4 = 1(1) + b

b = 3

Equation of this piecewise function is
y = x + 3    for 1 ≤ x ≤ 5

Piecewise Part C

This is a flat horizontal line at y = 8
So that is the equation of the line
The domain of this piece is 5 ≤ x ≤ 8  
So we get y = 8 for [tex]$\begin{cases}3x-4 & -2\le x < 1\\x + 3 & 1 \le x \le 5\\8 & 5 \le x \le 8 \end{cases}$[/tex]

Normally, instead of using y we use f(x)

Putting all this together we get the piecewise function defined as

[tex]f(x) = $\begin{cases}3x-4 & -2\le x < 1\\x + 3 & 1 \le x \le 5\\8 & 5 \le x \le 8 \end{cases}$[/tex]

The cosine relation is defined by the length of the adjacent side over the length of the hypotenuse.

So, for triangle ABC, the cosine of B is defined as:

And for triangle DEF, since the triangles are similar, the cosine of B is equal the cosine of its corresponding angle E:

So the correct options are the first and fifth ones.

For the given condition when B is 5% more than A and B is 15% less than C then ratio of A to C is equal to 17 : 21.

As given in the question,

Let value of A is equal to 100

As per given condition we have,

B is 5% more than A

5% of 100

= (5/100) × 100

= 5

So B is equal to

= 100 +5

= 105

A:B = 100/105

       = 20/21

B is 15% less than C

let C= 100

15 % of 100

= (15/100) × 100

= 15

Value of B is equal to

= 100 - 15

= 85

B:C = 85 : 100

      = 17 : 20

Ratio A : B : C

= 340 : 357 : 420

Ratio A : C = 340 : 420

                 = 17 :21

Therefore, for the given condition when B is 5% more than A and B is 15% less than C then ratio of A to C is equal to 17 : 21.

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Given data:

The numbers given are 12 and 3.

The 12 and 3 are both positive integers in which 12 is greater than 3.

The 12 and 3 both lie on the right side of the number line in which 12 comes after 3, so 12 is bigger number than 3.

The 12 and 3 are both natural as well as rational number, 12 is nine more than 3.

The value of the mutual fund of Tom after 15 deposits will be $5197.320   .

In the question ,

it is given that , Tom invested $2500 in mutual fund for 15 years ,

So,

the investment amount(P) = $2500 .

time for investment(x) = 15 years

rate of increase(r) = 5% = 0.05

The amount of fund  after 15 deposits can be calculated using the formula

amount = P*(1+r)ˣ

Substituting the values of  P, x and r , we get

amount = 2500*(1 + 0.05)¹⁵

= 2500*(1.05)¹⁵

= 5197.320

Therefore , The value of the mutual fund of Tom after 15 deposits will be $5197.320   .

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A graph of what the proportional relationship would look like is: C. a coordinate plane with the x-axis labeled Blueberries (in pints) and the y-axis labeled Cost (in dollars) shows a line going through (0, 0) and (5, 17).

In Mathematics, a graph is commonly used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).

Generally speaking, the graph of a proportional relationship between two variables is always characterized by a straight line with its data points passing through the origin (0, 0).

In this context, the x-axis of this graph would be labeled Blueberries (in pints) while the y-axis would be labeled Cost (in dollars), with the data points starting from the origin (0, 0) and passes through (5, 17) as shown in the image attached below.

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Answer:

C. a coordinate plane with the x-axis labeled Blueberries (in pints) and the y-axis labeled Cost (in dollars) shows a line going through (0, 0) and (5, 17).

Step-by-step explanation:

Answer: t = 820

Step-by-step explanation:

1) Set up the equation

369 + 55%t = t

2) Simplify the percentage

369+ 0.55t = t

3) Minus 0.55 t on both sides

369 = 0.45t

4) Set t by itself.

t = 820

Answer:

40 R 1.

Step-by-step explanation:

Answer:

600

Step-by-step explanation:

[tex]R(1)=400 \\ \\ R(2)=1000 \\ \\ R(2)-R(1)=600[/tex]

describe the transformation from f to g where f(x)=x² and g(x)=(1/3)x²​

In this problem we have a dilation of the y-coordinate

so

the rule is

(x,y) -------> (x,ay)

where

the scale factor a=1/3

Answer:

21.9

Step-by-step explanation:

it rounds up

First, we need to graph the lines:

In the solution of the first inequality, the points on the line are not included, then this line must be dashed. On the other hand, in the solution of the second inequality, the points on the line are included, then this line must be solid.

In both cases, the solution to each inequality is the area below each line.

Combining this information we get the next graph:

where the solution is the orange area.

From the above graph, one point in the solution set is (1, -7). We can check if this point is part of the solution by replacing it into the inequalities, as follows:

Given that the point satisfies both inequalities, then it is part of the solution set.

A golf lesson lasts from 10:00 am - 11:15 am and includes a 15 minutes break with equal lengths of time before and after the break is at 10:30 am.

Total lesson time is 1 hour and 15 minutes (10:00 - 11:15)

There is 15 minutes break with equal lengths of time before and after break.

The lesson before the break is from 10 - 10:30

Therefore , break is at 10:30 am

Lesson resumes at 10:45 when break is over then lesson runs another 30 minutes until 11:15 am (10:45 - 11:15).

Therefore, the break is at 10:30 am in mid of 10:00 am - 11:15 am.

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Answer:

r=32

Step-by-step explanation:

when DM=35

then. 35=r+3

35-3=r

r=32 therefore, substitute into

second equation to solve GM

GM=4r-28

GM=128-28

GM=100

Answer:

Explanation:

a)

The formula for calculating the length of an arc is expressed as

Length of arc = θ/360 x 2πr

where

θ is the angle subtended at the center of the circle.

r is the radius of the circle

From the information given,

diameter = 5(length of each metal spoke)

r =diameter/2 = 5/2 = 2.5

Recall, the total angle in the circle is 360 degrees. There are 8 partitions. Angle between consecutive spokes is

360/8 = 45. Thus,

θ = 45

Length of are between consecutive spokes = 45//360 x 2 x π x 2.5

Length of are between consecutive spokes = 5π/8

b) The formula for calculating the area of a sector is expressed as

area of a sector = θ/360 x πr^2

By substituting the values,

area of a sector = 45/360 x π x 2.5^2

Area of sector = 25π/32 square inches

The most appropriate choice for binomial distribution will be given by-

Mean of binomial distribution= 20

Standard deviation of binomial distribution = 16

What is binomial distribution?

Let there are n number of success or failure experiment called Bernouli trial and let p be the probability of success. Binomial distribution with parameters n and p is the probability distribution of p successes in n number of Bernouli trials.

Probability mass function of Binomial distribution

P(x = k) = [tex]n \choose k[/tex][tex]p^k(1-p)^k[/tex]

Here,

n = 100,

p = [tex]\frac{1}{5}\\[/tex]

1 - p = [tex]1 - \frac{1}{5}[/tex]

       = [tex]\frac{5-1}{5}[/tex]

       = [tex]\frac{4}{5}[/tex]

Mean of binomial distribution = np

                                                 = [tex]100 \times \frac{1}{5}\\[/tex]

                                                 =20

Standard deviation of binomial distribution  =

                                                                          [tex]100 \times \frac{1}{5}(1- \frac{1}{5})\\100 \times \frac{1}{5} \times \frac{4}{5}\\16[/tex]

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When going to the movies and we pay the ticket, most of the times (if we pay in cash) we will receive change for the bill we use.

For example, if the ticket costs $7 and we pay with $10, we will receive 10-7 = $3 as change.

We then have used math to know that the change we receive is correct.

Given the expression :

so, the result will be as following:

the term 16.2 is a constant

Hey there!

Whenever, you hear or see the word “constant” think of the definition ‘a specific number or value that never changes in a particular equation’

16.2 - 3(4) + 14/2

= 16.2 - 12 + 14/2

= 16.2 - 12 + 7

= 4.2 + 7

= 11.2

Now, that we have that information out the way, we can answer your equation

Your CONSTANTS aren’t:

• -3(4) because we had to simplify it and convert it to: -12

• 14/2 because we had to simplify that as well and it converted it to: 7

(That’s how we figured out to make the equation much easier to breakdown)

(By the way, you can use PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, & Subtraction) to solve for the overall problem, like how I did for you :))

This leaves the constant to: 16.2 because we didn’t have to anything to it.

Therefore, your answer should be:

16.2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

You have the following trinomial given in the exercise:

Notice that is is a trinomial because it is a polynomial that has three terms.

In order to factor it (as the product ot two binomials) you can find two numbers whose sum is -8 and whose sum is 7. These numbers would be -1 and -7, because:

Then, you can factor it

The answer is:

Answer:

es 1 1/4 + 2/4 +3 2/4 = 5 1/4

5 1/4

1. Calculating the marginal cost per day yields the following results:

Air conditioners  Total cost    Marginal cost

    per day          ($ per day)      ($ per day)

      1                          100                  100

      2                         150                   50

      3                        220                   70

      4                         310                   90

      5                        405                   95

      6                         510                  105

      7                        650                  140

      8                       800                   150

2. To maximize profits, the price-taking firm should produce 6 air conditioners per day.

The profit-maximizing point or units is the output and price interaction that ensures that the marginal revenue equals the marginal cost.

The marginal revenue (MR) is the revenue earned from an additional unit. The marginal cost (MC) is the production cost per additional unit.

For price-taking firms, the maximum profit is achieved at the level of output where MC equals MR.

Market Price for one unit = $125

Air conditioners  Total cost    Marginal cost

    per day          ($ per day)      ($ per day)

      1                          100              100 (100 - 0)

      2                         150               50 (150 - 100)

      3                        220               70 (220 - 150)

      4                         310              90 (310 - 220)

      5                        405              95 (405 - 310)

      6                         510            105 (510 - 405)

      7                        650             140 (650 - 510)

      8                       800              150 (800 - 650)

Thus, profit is not maximized where the MC exceeds the MR. Instead producing at that unit reduces profit.

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Total Cost Information

Air conditioners  Total cost

    per day          ($ per day)

      1                          100

      2                         150

      3                        220

      4                         310

      5                        405

      6                         510

      7                        650

      8                       800

1. Calculate marginal cost per day, and enter your responses as whole numbers.

2. How many air conditioners should the firm produce per day if its goal is to maximize its profit? air conditioners per day.

y = x(x + 1)

Yes, it's a valid equation, there are 2 values for x and two values for y.

In my opinion it's a continuous function because if we graph it there would not be gaps on it.

The answer is d. 82.1

Explanation:

Tan 75 = x/22

For a right-angled triangle, Pythagoras theorems hold

Pythagoras theorem states that the square of the hypotenus is equal to the sum of the square of the other two sides

The hypotenuse is 250 feet

We are given the following information:

• 174 paving stones total (examined)

• 16, paving stones ,cracked

• 21, paving stones ,discolored

• 3, paving stones ,both cracked and discolored

We are trying to find the probability of paving stones that are not cracked.

Since we know from our given that 16 paving stones were cracked plus an additional 3 paving stones were both cracked and discolored, the total amount of cracked stones out of the 174 paving stones is equal to 19.

Therefore, we know that there will be 155 paving stones that aren't cracked. In order to find the probability, we will need to divide this number over the total amount of stones present:

If we evaluate this fraction, we should obtain our answer.

The probability that a paving stone isn't cracked is equal to 0.890805.

Answer:

a.

b. The standard deviation is at an acceptable level

Explanation:

The confidence interval for the variance can be calculated as:

Where n is the size of the sample, s² is the variance of the sample, (1-∝) is the level of confidence, and χ² is the value of chi-square with n-1 degrees of freedom.

In this case, we get that n is 14 tablets, s² is 0.000071, and 1-∝ = 90%, so ∝ is 10%.

Then, the values of chi-square with 13 (14 -1) degrees of freedom is:

Therefore, the interval of confidence for the population variance is:

Then, the standard deviation is the square root of the variance, so the interval of confidence for the population standard deviation is:

Finally, since the upper limit of the interval for the standard deviation is less than 0.15 milligrams, we can say that the population standard deviation is at an acceptable level with a confidence level of 90%

Applying the two-tangent theorem, the length of LM is: A. 18.

The two-tangent theorem states that if two tangents are drawn from a circle to meet at a point outside the circle, then the tangent segments are congruent to each other, that is they have equal lengths.

Segments LK and LM are tangent segments drawn to meet at the external point L. This means, the length of Lk and the length of LM would be equal to each other.

LK = 4x - 2

LM = 3x + 3

LK = LM

Substitute

4x - 2 = 3x + 3

Combine like terms

4x - 3x = 2 + 3

x = 5

LM = 3x + 3

Plug in the value of x

LM = 3(5) + 3

LM = 15 + 3

LM = 18

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Answer:

Concept:

To figure out the measure of angle A, we will use the sine rule below

By substituting the values, we will have

Cross multiply, we will have

Hence,

The measure of angle A to the nearest whole number is

Given -

(2s - 1)² = 225

To Find -

s =?

Step-by-Step Explanation -

(2s - 1)² = 225

Now, on removing square =

(2s - 1) = √225

2s - 1 = 15

2s = 15 + 1

2s = 16

s = 16/2

s = 8

Final Answer -

s = 8