Proving Triangle Similarity

Proving Triangle Similarity

Answers

Answer 1

The proof is completed using two column proof as follows

Statement                               Reason

QT ⊥ PT                                   Given

∠ QRP ≅ ∠ SRT = 90              definition of perpendicularity

∠ QPR ≅ ∠ STR                       Given

Δ PQR is similar to Δ TSR       AA similarity theorem

What is AA similarity theorem?

The AA similarity theorem, also known as the Angle-Angle Similarity Theorem, states that if two triangles have two corresponding angles that are congruent, then the triangles are similar.

In the given triangle, the two angles given to be equal are

∠ QRP ≅ ∠ SRT = 90 and ∠ QPR ≅ ∠ STR

Hence the triangles are similar

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Answer 2

Answer:

:)

Hopefully this helps you guys :)

good luck :D

Proving Triangle Similarity

Related Questions

Kendall will find the total surface area of the prism below. Assuming the base is the shaded surface (the bottom), drag an
drop the correct values for the variables P, h, B that she should use in her formula.
1.2 ft
P.⠀
h:
B:
feet
feet
8.8 ft
square feet
nwore mangslugnsits arts to come sostua eri bait of absan y
So
2 ft

Answers

Answer:

Step-by-step explanation:

is 8,15,24

suppose a jar contains 6 red marbles and 13 blue marbles. if you reach in the jar and pull out 2 marbles at random, find the probability that both are red. write your answer as a reduced fraction.

Answers

From the given jar, the probability that both are red marbles is 15/171.

What is the probability?

Suppose a jar contains 6 red marbles and 13 blue marbles.

If you reach in the jar and pull out 2 marbles at random, find the probability that both are red. Write your answer as a reduced fraction.

Let's first find out the total number of marbles in the jar:

Total number of marbles in the jar = 6 + 13 = 19

Since we need to find the probability of picking out two red marbles, we need to calculate the total number of ways we can pick 2 marbles from 19:

n(S) = (¹⁹C₂)

we need to calculate the total number of ways to pick out two red marbles from 6:

n(E) = (⁶C₂)

We can use the formula for probability:

[tex]P(picking two red marbles) = \frac{n(E) }{n(S)} \\ = \frac{6C2 }{19C2} \\= \frac{15}{171}[/tex]

So, the probability of both marbles being red is 15/171. This fraction cannot be reduced any further.

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Suppose X and Y are independent N(0; 1) random variables.
(a) Find P(X^2 < 1).
(b) Find P(X^2 + Y^2 < 1)

Answers

The required probability is obtained as:

(a) P(X^2 < 1) = 0.8413.

(b) P(X^2 + Y^2 < 1) = 0.7854.

(a) We know that X^2 follows a chi-squared distribution with 1 degree of freedom, which can be written as X^2 ~ chi-squared(1). Therefore, we can find P(X^2 < 1) as:

P(X^2 < 1) = P(Z < √1) (where Z ~ chi-squared(1))

Since the square of a standard normal distribution is a chi-squared distribution with 1 degree of freedom, we can rewrite the above equation as:

P(X^2 < 1) = P(Z < 1) (where Z ~ N(0,1))

Using a standard normal distribution table or calculator, we can find that P(Z < 1) = 0.8413. Therefore, P(X^2 < 1) = 0.8413.

(b) We can rewrite X^2 + Y^2 < 1 as the inequality r^2 < 1, where r is the distance from the origin to the point (X,Y) in the xy-plane. Therefore, we need to find the probability that the point (X,Y) falls within the unit circle centered at the origin.

We can use polar coordinates to express X and Y as:

X = Rcosθ

Y = Rsinθ

where R is the distance from the origin to (X,Y), and θ is the angle between the positive x-axis and the line connecting the origin and (X,Y). Since X and Y are independent N(0,1) random variables, R^2 = X^2 + Y^2 follows a chi-squared distribution with 2 degrees of freedom, which can be written as R^2 ~ chi-squared(2).

Therefore, we can find P(X^2 + Y^2 < 1) as:

P(X^2 + Y^2 < 1) = P(R^2 < 1) (where R^2 ~ chi-squared(2))

Using the cumulative distribution function (CDF) of the chi-squared distribution with 2 degrees of freedom, we can find that:

P(R^2 < 1) = 0.7854

Therefore, P(X^2 + Y^2 < 1) = 0.7854.

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this isnt making any sense i need help please!

Answers

The value οf sin F is 5/6.

What is meant by trigοnοmetry?

The branch οf Mathematics which helps in dealing with measure οf three sides οf a right-angled triangle is called Trigοnοmetry.

What are the different Trigοnοmetric Ratiο?

sin θ  = Perpendicular/Hypοtenuse

cοs θ = Base/Hypοtenuse

tan θ = Perpendicular/Base

cοsec θ = Hypοtenuse/Perpendicular

sec θ = Hypοtenuse/Base

cοt θ = Base/Perpendicular

Cοs D = 5/6 (given)

We knοw, cοs θ =Base / Hypοtenuse

Thus, base = 5  and hypοtenuse = 6

Therefοre, DE = 5 and DF = 6

Sin  θ = Perpendicular / Hypοtenuse

Sin F = DE / DF

Sin F = 5/6

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Here is a hanger that is in balance. We don't know how much any of its shapes weigh. How

could you change the number of shapes on it, but keep it in balance? Describe in a couple

sentences

Answers

We can change the number of shapes on it by putting one rectangle to the right and put two triangles to the left.

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

Let's say the circle is A, Triangle is B, and Rectangle is C.

2A + 4C = 2A + 4B + 2C

So, C = 2B    ( 4C = 4B + 2C, 2C = 4B, C = 2B)

That one rectangle and two triangles are equally weighed. So, put one rectangle to the right and put two triangles to the left. The hanger is still in the balance.

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Bethany wants to build a wooden deck on her patio, which is in the shape of a parallelogram. The area of the patio is 580 ft2. Find the base. Round your answer to the nearest foot.

Answers

The base of the parallelogram is 18. 3 feet

How to determine the base of the parallelogram

From the information given, we have that;

Area = 280ft^2

height = 5x

Base = 6x

Note that he formula that is used for calculating the area of the parallelogram is represented with the equation;

Area = bh

Given that the parameters are;

b is the base of the parallelogramh is the height of the parallelogram

Substituting the values of area, base and height.

280 = 5x × 6x

280 = 30x^2

Divide both sides by 30

x^2 = 280/30

Find the square root of both sides

x = √(280/30)

We have that the base = 6x

Substitute the value of x, we get;

Base = 6x = 6(√(280/30))

Base = 18.3ft

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A diagonal of rectangle is inclined to one side of the rectangle at 25 degree the acute angle between diagonal is

Answers

Answer:

A diagonal of a rectangle is inclined to one side of the rectangle at 25º Angle between a side of the rectangle and its diagonal = 25º Consider x as the acute angle between diagonals

Step-by-step explanation:

Evaluate
(
3
7
)

2
Give your answer as an improper fraction in its simplest form

Answers

The value of (37)-2 is 1/1369, in its simplest form as an improper fraction.

An improper fraction is a fraction where the numerator is greater than or equal to the denominator. In other words, it is a fraction that is larger than a whole number.

When an expression is written in the form of [tex]x^{(-n)[/tex], it means the reciprocal of [tex]x^n.[/tex] In this case, we have the expression[tex](37)^{(-2)[/tex] which means the reciprocal of 37².

The expression (37)-2 means 37 raised to the power of -2, or 1/(37²). To simplify this fraction, we can multiply the numerator and denominator by 1,296 (37²):

1/(37²) = 1 * 1 / (37 * 37)

= 1/1369

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Find the amount of the following ordinary annuities rounded to the nearest cent. Find the tot
Amount of Deposited
Interest
Rate Time (Years) Amount of an
Annuity
Earned
each deposit
$1050
annually
5%
14

Answers

Answer:I=(PxRxT)/100

I=(10000x20x1)/100x2

I=200000/200

I=1000I=(

Step-by-step explanation:

the population of a community is known to increase at a rate proportional to the number of people present at time t. if an initial population p0 has doubled in 5 years, how long will it take to triple? (round your answer to one decimal place.) yr how long will it take to quadruple? (round your answer to one decimal place.) yr

Answers

It will take approximately 8.5 years to triple the population and approximately 10 years to quadruple the population.

Given that the population of a community is known to increase at a rate proportional to the number of people present at time t, and an initial population p0 has doubled in 5 years.

To calculate:

How long will it take to triple?

How long will it take to quadruple?

Let p be the population of a community at any time t. According to the given information, the population p is proportional to the number of people present at time t. Therefore, we have p ∝ p_0 …… (1)

where p_0 is the initial population of the community. It is given that the initial population p_0 has doubled in 5 years.

So, we have 2p_0 = p_0e^(rt) 2 = e^(5r)

Taking natural logarithm on both sides, ln 2 = ln e^(5r) = 5rln 2/5 = r …… (2)

Using equation (1) and (2), we can write population p asp = p_0e^(rt) = p_0e^(ln2/5 t) = p_0 2^(t/5)

Now, we have to find for how many years (t) we need to wait until the population of the community triples, i.e.

3p_0 = p_0 2^(t/5) 3 = 2^(t/5)

Taking logarithm (with base 2) on both sides,

log_2 3 = log_2 2^(t/5)log_2 3 = (t/5)log_2 2t = 5 log_2 3t ≈ 8.5 (Rounded to one decimal place)

Therefore, it will take approximately 8.5 years to triple the population.

Now, we need to find for how many years (t) we need to wait until the population of the community quadruples, i.e. 4p_0 = p_0 2^(t/5) 4 = 2^(t/5)

Taking logarithm (with base 2) on both sides,

log_2 4 = log_2 2^(t/5)

log_2 4 = (t/5)log_2 2t = 5 log_2 4t ≈ 10 (Rounded to one decimal place)Therefore, it will take approximately 10 years to quadruple the population.

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Which angles would the Alternate Exterior Angles Theorem state are congruent?
Which angles would the Alternate Exterior Angles Theorem state are congruent?

Answers

Answer:

Choice 2
∠1 and ∠7, ∠2 and ∠8

Step-by-step explanation:

This is a good example of a problem that can be solved by POE(process of elimination)

First choice: ∠2 and ∠3 are on the same straight line so they cannot be congruent. They are supplementary in that they add up to 180°

The same applies for ∠3 and ∠4 (third choice)

The same applies for ∠1 and ∠4 (fourth choice)

That leaves choice 2

We can prove ∠1 ≅ ∠7 as follows:

∠1 ≅ ∠3 since they are vertically opposite angles

∠3 ≅ ∠7 since they are exterior angles

So ∠1 ≅ ∠7

By similar reasoning,
∠2 ≅ ∠8

So correct choice is Choice 2

one hundred students were asked whether they liked certain candy flavors. it was found that liked cherry, liked coconut, and liked both flavors. what's the probability that a randomly selected student...

Answers

The probability that a randomly selected student likes coconut is 0.6.

Step-by-step explanation:

Given that,

The number of students = 100 The number of students who liked cherry = 30 The number of students who liked coconut = 60 The number of students who liked both flavors = 10

Now we have to find the probability that a randomly selected student likes coconut.

P (student likes coconut) = the number of students who liked coconut / total number of students

= 60/100

= 0.6

Therefore, the probability that a randomly selected student likes coconut is 0.6.

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Amy, Beth, and Cassandra were carpeting 4 identically sized rooms. It would take Amy 6 hours to carpet one of the rooms; it would take Beth 4 hours to carpet one room; and it would take Cassandra 8 hours to carpet one room. Together, how long would it take them to carpet the 4 rooms (round to the nearest thousandth of an hour;

Answers

It would take the three of them about 6 hours to paint the four rooms.

How to solve an equation?

Let t represent the time that it would take all three of them to paint one room.

It would take Amy 6 hours to carpet one of the rooms; it would take Beth 4 hours to carpet one room; and it would take Cassandra 8 hours to carpet one room.

Therefore:

(1/6 + 1/4 + 1/8)t = 1

(2/3)t = 1

t = 1.5 hours

It would take all of them 1.5 hours each to paint one room.

For 4 rooms:

Total time = 1.5 hours * 4 = 6 hours

It would take the three of them about 6 hours to paint the four rooms.

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A certain computer loses half of its value every four years. If the value of the computer after 6 years is $835, what was the initial value of the computer?

Answers

The PC is initially worth $3,340.

Given that a computer loses half of its worth after six years, and assuming that value is $835, we must determine the device's original value.

What does the term "starting value" mean?

The starting output value is the initial value.

Let's say that computer's starting value is x.

As a result, after four years,

It is X/2 for the fourth year.

It is X/2 for the fifth year.

It's X/4 in the sixth year.

We stated that the PC will be worth $835 after six years. Hence, we may express it as,

X/4 = $835

X=4( $835)

X= $3,340

Hence, the initial value of the computer is $3,340.

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0
2
Given the function f(x) = x-2, draw a line from the value of
to the corresponding value of f(x).
16
undefined

Answers

The graph of the function f(x) = x - 2 is a straight line that passes through the origin and has a slope of 1.

What is function in math?

Function is a mathematical concept which refers to a rule or set of rules that takes an input and produces an output. Its purpose is to map out a relationship between two distinct sets of data. The input is called the argument, and the output is called the value. Functions are used to model real-world situations, to discover patterns, and to solve problems. Functions help to organize data and make it easier to interpret and analyze. They are also used to predict the effects of changes in the input.

This means that for every unit increase in x, the value of f(x) increases by 1 unit. Therefore, when x is equal to 0, the value of f(x) is equal to -2. When x is equal to 1, the value of f(x) is equal to -1. When x is equal to 2, the value of f(x) is equal to 0. When x is equal to 16, the value of f(x) is equal to 14. As you can see, for every increase in x, the value of f(x) increases by 2 units.  This is the reason why the line drawn from the value of x to the corresponding value of f(x) increases by 2 units when x is increased by 1 unit.

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In this case, there is no corresponding point on the line, so the line does not extend from (2, 4) to (4, 2).

What is function ?

Function is a mathematical concept which refers to a rule or set of rules that takes an input and produces an output. Its purpose is to map out a relationship between two distinct sets of data. The input is called the argument, and the output is called the value. Functions are used to model real-world situations, to discover patterns, and to solve problems. Functions help to organize data and make it easier to interpret and analyze. They are also used to predict the effects of changes in the input.
In this example, the function f(x) = x-2 is being represented by a line that connects each value of x to the corresponding value of f(x).

When x = 4,

then f(x) = 4-2

f(x) = 2,

so the line extends from (4, 2) to the origin (0, 0).

Similarly, when x = 0,

then f(x) = 0-2

f(x) = -2,

so the line extends from (0, -2) to (4, 2).

When x = 1,

then f(x) = 1-2

f(x) = -1,

so the line extends from (1, -1) to (4, 2).

Finally,

when x = 2,

then f(x) is undefined.

In this case, there is no corresponding point on the line, so the line does not extend from (2, 4) to (4, 2).

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the life of light bulbs is distributed normally. the variance of the lifetime is 225 and the mean lifetime of a bulb is 530 hours. find the probability of a bulb lasting for at most 540 hours. round your answer to four decimal places.

Answers

The probability of a bulb lasting for at most 540 hours is 0.7521, rounded to four decimal places.

The life of light bulbs is distributed normally. The variance of the lifetime is 225 and the mean lifetime of a bulb is 530 hours. Find the probability of a bulb lasting for at most 540 hours. Round your answer to four decimal places.

Using the z-score formula z = (x - μ) / σ, where x is the value in question (540 hours in this case), μ is the mean (530 hours in this case) and σ is the standard deviation (15 hours in this case), we can calculate the z-score:
z = (540 - 530) / 15
z = 10 / 15
z = 0.67
Using a z-table, we can look up the probability of a value being less than or equal to 0.67, which is 0.7521.
Therefore, the probability of a bulb lasting for at most 540 hours is 0.7521, rounded to four decimal places.

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Which mathematical term is best defined as two lines that intersect each other at 90 ° angles?

Answers

Answer:

Perpendicular

Step-by-step explanation:

Part A Which solution do you get when you use the quadratic formula to solve the equation –4x2 – 12x – 9 = 0?

Answers

Answer:

A: -3/2

Step-by-step explanation:

-4x²-12x-9=0 First split the b value so that it equals a×c, or -4×-9

-4x²-6x-6x-9=0 Factor by grouping

(-2x-3)(2x+3)=0 Solve for x

x= -3/2

Write an equation for the line on a graph below.

Answers

Check the picture below.

Answer:

x=-3

Step-by-step explanation:

In Drosophila, the allele for normal-length wings is dominant over the allele for vestigial wings. In a population of 1,000 individuals, 360 show the recessive phenotype. How many individuals would you expect to be homozygous dominant and heterozygous for this trait?1:2:1 :1:2:1 is the expected genotypic ratio in the progeny derived from a cross involving two heterozygotes of the same gene. The first "1" represents the proportion of dominant homozygotes, the second class, or class "2", the heterozygotes, and the second "1" the recessive homozygotes. This also means that the phenotypic ratio should be 3 dominant phenotype:1 recessive phenotype. From the phenotypic class "3", 2/3 are represented by the heterozygotes, while the remaining 1/3 by the dominant homozygotes.

Answers

The number of individuals who are homozygous dominant (VV) is 160 individuals, and the number of individuals who are heterozygous (Vv) is 320 individuals.

The population of Drosophila has 1000 individuals, 360 of which display the recessive phenotype. Homozygous dominant and heterozygous for this trait in Drosophila would be expected to be found in how many individuals?

In Drosophila, the dominant allele for normal-length wings is denoted as 'V' and the recessive allele for vestigial wings is denoted as 'v.'To determine the number of individuals who are homozygous dominant or heterozygous for this trait, we'll first determine the number of individuals who are homozygous recessive:

Homozygous recessive individuals in the population = number of individuals displaying the recessive phenotype = 360

This indicate that there are 360 individuals with the genotype vv (homozygous recessive), which will be used to determine the remaining genotypes via the Punnett square. To get the number of individuals who are heterozygous (Vv), we first need to identify the number of individuals with the dominant V allele (VV and Vv). The sum of these two genotypes equals the total number of individuals minus the homozygous recessive individuals, as follows:

Total number of individuals - homozygous recessive individuals = (VV + Vv) individuals+ (vv) individuals = 1000 individuals

Hence, VV + Vv = 1000 - 360 = 640 individuals.Now that we know VV + Vv = 640, we can use the expected genotypic ratio of 1:2:1 to calculate the number of homozygous dominant (VV) and heterozygous (Vv) individuals.1:2:1 represents the expected genotypic ratio in the progeny derived from a cross involving two heterozygotes of the same gene. The first "1" represents the proportion of dominant homozygotes, the second class, or class "2", the heterozygotes, and the second "1" the recessive homozygotes.

Therefore, homozygous dominant (VV) and heterozygous (Vv) individuals in the population would be expected in the following ratio:VV:Vv:vv = 1:2:1. Therefore, the number of individuals who are homozygous dominant (VV) is 1/4 of the total individuals (VV + Vv + vv):

Number of individuals who are homozygous dominant (VV) = 1/4 (VV + Vv + vv)= 1/4 (640) = 160 individuals

And the number of individuals who are heterozygous (Vv) is 2/4 of the total individuals (VV + Vv + vv):

Number of individuals who are heterozygous (Vv) = 2/4 (VV + Vv + vv)= 2/4 (640) = 320 individuals

Therefore, the number of individuals who are homozygous dominant (VV) is 160 individuals, and the number of individuals who are heterozygous (Vv) is 320 individuals.

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What is 6x+2y=-4 in slope-intercept form

Answers

Answer:

y = -3x - 2

Step-by-step explanation:

To write the equation 6x + 2y = -4 in slope-intercept form, we need to solve for y.

First, we can isolate the y-term by subtracting 6x from both sides:

6x + 2y = -4

2y = -6x - 4

Next, we can divide both sides by 2 to isolate y:

2y/2 = (-6x - 4)/2

y = -3x - 2

So the slope-intercept form of the equation 6x + 2y = -4 is y = -3x - 2.

Stock sold at 23 7/8 at the start of
trading. It was up 3 1/2 points at the
end of trading. What was the price
at the end of trading?

Answers

Answer:

To solve the problem, we need to add 23 7/8 and 3 1/2 to find the final price.

First, we need to convert 3 1/2 to an improper fraction:

3 1/2 = (2 x 3) + 1/2 = 7/2

Next, we need to find a common denominator between 8 and 2:

8 = 8/1

2 = 2/1 x 4/4 = 8/4

Now we can add the two fractions:

23 7/8 + 3 1/2

= 23 14/16 + 3 8/16 (using 16 as the common denominator)

= 27 6/16

= 27 3/8

Therefore, the stock was priced at $27 3/8 at the end of trading.

A gardener wants to divide a square piece of lawn in half diagonally. What is the length of the diagonal if the side of the square is 8 ft? Leave your answer in simplest radical form.A. 16B. 2C. 8D. 4

Answers

The length of the diagonal is 8√2 ft.

How to find the length of the diagonal if the side of the square is 8 ft?

If the side of the square is 8 ft, then the diagonal will form a right triangle with legs of length 8 ft. We can use the Pythagorean theorem to find the length of the diagonal (hypotenuse).

Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

In this case, we have:

a = 8 ft (one leg)

b = 8 ft (the other leg)

c = ? (the hypotenuse)

Using the Pythagorean theorem, we have:

c² = a² + b²

c² = 8² + 8²

c² =  64 + 64

c² = 128

c = √128

c = 8√2 ft

Therefore, the length of the diagonal is 8√2 ft.

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2 HCl + CaCO3 → CaCl2 + H2O + CO2

If 1.8392 moles of HCl are reacted, how many grams of CaCO3 will also be reacted?

Answers

Hope this helps

It is converting moles to grams. The amount of reactants is always equal to the amount of products so we use the mole ratio. The number that balances each compound is the number of moles of the ratio.
When converting moles to grams, we multiply the given moles by a fraction; (the numerator being the mole ratio of the compound we want and the denomin being the mole ratio of the compound we have) and multiply it by the molar mass of the compound we want.
By substituting all the units of each compound, we are left with the grams of CaCO3.

The newspaper in Haventown had a circulation of 80,000 papers in the year 2000. In 2010, the circulation was 50,000. With x=0 representing the year 2000, the graph below models this scenario.
What number will complete the point-slope equation that models this scenario?

Answers

Answer:

The answer to your problem is, -3000

Step-by-step explanation:

:Write down the points through which the line passes through

:The line is passing through a point at (0, 80000) and (10, 50000)

Next, ( important )

Find the slope of the line

Since the line is passing through the point (0, 80000) and (10, 50000)

So the slope of the line:

= m

[tex]\frac{80,000 - 50,000}{0 - 10}[/tex]

= [tex]\frac{30,000 }{-10}[/tex]

= -3,000

Techniquelly the answer is, 30,000 but for more explanation here it is :)

Find the number that will complete the point-slope equation that models this scenario

The required point-slope equation that models this scenario is

[tex]y - y_{1} - m( x - x_{1} )[/tex]

y - 50,000 = -30,000 ( x - 10 )

Thus the answer to your problem is, - 3,000

Any questions? Write them down below \/

I dont know the answer helpppo

Answers

For all values of x the function is decreasing function because as x increases the value of the function decreases.

What is derivative?

One of the core ideas of calculus is the derivative, which shows how quickly a function is changing at any given moment. It offers a means of determining the slope of a curve at a certain location, which may be used to address a variety of issues in physics, engineering, economics, and social sciences. The derivative may be used to predict the behaviour of physical systems, discover the maximum and lowest values of a function, and improve a process or system.

From the given table we observe that as x increases the value of the function decreases.

That is for all values of x the function is decreasing function.

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X^2+9x+20/x+3 • x^2-x-12/x^2+3x-4
What is the product in simplest form? State any restrictions on the variable

Answers

To find the product, we need to first factor the numerators and denominators of both fractions:

x^2 + 9x + 20 = (x + 5)(x + 4)

x^2 - x - 12 = (x - 4)(x + 3)

x^2 + 3x - 4 = (x + 4)(x - 1)

Substituting these into the expression, we get:

[(x + 5)(x + 4)/(x + 3)] * [(x - 4)(x + 3)/(x + 4)(x - 1)]

Now, we can simplify the product by cancelling out common factors:

[(x + 5) * 1/(x - 1)] * [(x - 4) * 1/1]

= (x + 5)(x - 4)/(x - 1)

So the product in simplest form is (x + 5)(x - 4)/(x - 1).

However, there is a restriction on the variable because the expression involves division by (x + 3), (x - 1), and (x - 4). Therefore, x cannot be equal to -3, 1, or 4, since these values would make the denominators zero and the expression undefined.

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A garden is shaped like a right-angled triangle.
Work out the perimeter of the garden.
Give your answer in metres (m) to 1 d.p.

Answers

Answer:

Step-by-step explanation:

First , we would add 10 + 4 = 14 then ,

using Pythagoras Theorem , a^2 + b^2 = c^2 to find out the hypotenuse so

10^2+4^2= 116

Finally , add the square root of 116 to 14 to get  

24.8 metres rounded to 1 decimal place.

The population of a city increases by 5% per year. What should we multiply the current population by to find the next year's population in one step? Answer:

Answers

Answer:

Step-by-step explanation:

Tο find the pοpulatiοn οf the city after οne year, we shοuld multiply the current pοpulatiοn by 1.05.

What is the percentage?

A percentage that represents a tenth οf a quantity. One percent, denοted by the symbοl 1%, is equal tο οne-hundredth οf sοmething; hence, 100 percent denοtes the full thing, and 200 percent designates twice the amοunt specified. A pοrtiοn per hundred is what the percentage denοtes. The percentage refers tο οne in a hundred. The % sign is used tο denοte it.

We can express a 5% increase as a decimal by dividing 5 by 100, which gives 0.05. This means that the pοpulatiοn after οne year will be the current pοpulatiοn plus 5% οf the current pοpulatiοn. Mathematically, we can write:

Next year's pοpulatiοn = Current pοpulatiοn + 0.05 * Current pοpulatiοn

We can simplify this expressiοn by factοring οut the current pοpulatiοn:

Next year's pοpulatiοn = Current pοpulatiοn * (1 + 0.05)

Simplifying further, we can add 1 tο the decimal tο get:

Next year's pοpulatiοn = Current pοpulatiοn * 1.05

Therefοre, tο find the pοpulatiοn οf the city after οne year, we shοuld multiply the current pοpulatiοn by 1.05.

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ADEF-AABC. What is the sequence of transformations that maps AABC to ADEF?

A reflection across the y-axis and a translation 4 units down

A rotation of 180* about the origin and a dilation with center (0,0) and scale factor 2

A reflection across the y-axis and a translation 2 units down.

A rotation of 90° about the origin and a translation 2 units down

Answers

The series of transformations consists of a translation down two units and a reflection across the y-axis. Thus, option C is correct.

What is transformation?

The points A and C will be replaced with D and F, respectively, by a reflection across the y-axis, leaving B in the same location. As a result, the image of AABC is given, A'D'BCF.

The final image, denoted by the letters ADEF, is produced by translating all the points of the image A'D'BCF' down by two units.

ADEF and AABC are not in the same location, even if they are the same height and shape.

The first thing we notice is that ADEF and AABC are oriented the same way, so we don't need to rotate them. Instead, by utilising a reflection over the y-axis, we may swap out the places where A and B were for D and E, respectively.

A'B'C' is still not in the appropriate place even though it is 2 units to the left of ADEF. Hence, we must translate 2 units down in order to position A'B'C' where ADEF is.

Therefore, A reflection across the y-axis and a translation 2 units down.

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