Find the 3 ×3 matrix that produces the described composite 2D transformation​ below, using homogeneous coordinates. Translate by ​( −6​, 3​), and then scale the​ x-coordinate by 0.3 and the​ y-coordinate by 1.3.

The zeros with each multiplicity are given as follows:

The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

Considering the linear factors of the function in this problem, the zeros are given as follows:

More can be learned about the Factor Theorem at brainly.com/question/24729294

#SPJ1

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

For similar question on probability.

https://brainly.com/question/7965468  

#SPJ8

Answer:

314 m²

Step-by-step explanation:

the surface area of a sphere (As) = 4×pi×r²

our radius r (half the diameter) here is 5m.

=>

As = 4×pi×5² = 4×3.14×25 = 100×3.14 = 314 m²

1. The trigonometric ratios are given as follows:

2. The equation to solve for x is given as follows: sin(52º) = x/13.

3. Two equations to solve for m are given as follows:

4. The length of the hypotenuse of the triangle is given as follows: 7.9 inches.

5. The lengths are given as follows:

The three trigonometric ratios are given as follows:

In the second problem, we have that the side x is opposite to the angle of 52º, while the hypotenuse is of 13, hence the equation to solve for x is given as follows:

sin(52º) = x/13.

In item 3, the Pythagorean Theorem is used to solve for m, as follows:

n² + m² = l².

m² = l² - n²

m = square root (l² - n²).

In item 4, we have that the angle opposite to the leg of length 7 inches is of 62º, hence the hypotenuse is given as follows:

sin(62º) = 7/h

h = 7/sin(62º)

h = 7.9 inches.

The length BD in item 5 is obtained as follows:

cos(30º) = BD/5

BD = 5 x cos (30º)

BD = 4.3 cm.

Then the length BC is calculated as follows:

sin(22º) = 4.3/BC

BC = 4.3/sin(22º)

BC = 11.5 cm.

More can be learned about trigonometric ratios at brainly.com/question/24349828

#SPJ1

The amount of money needed to mortgage is $1,11,600.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

You bought a house priced at $139,500.

Assuming you put 20% down payment,

= 139,500 x 0.2

= $27900

Now, 139500 - 27900 = $1,11,600

Hence, the mortgage amount is $1,11,600.

To learn more about the percentage;

https://brainly.com/question/24159063

#SPJ1

The measure of arc angle QTP is 204 degrees.

When a tangent and a secant intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

Therefore, let's find the measure of arc angle QTP as follows:

90 = 0.5(x - 68)

90 = 0.5x - 34

0.5x = 124

x = 124 / 0.5

x = 248 degrees

Where

x = arc angle TSQ

Therefore,

arc QP = 44 degrees

Therefore,

arc QTP = 248 - 44

arc QTP = 204 degrees

learn more on arc angle here: https://brainly.com/question/22826189

#SPJ1

The Back-end ratio based on the information is 18.14% and the Santiago's can buy their house.

Monthly debt payments = $1230 + $389 + $600 + ($121 x 12 / 12) (converting annual premium to monthly payment)

Monthly debt payments = $2239

Gross monthly income = $148,000 / 12

Gross monthly income = $12,333.33

Back-end ratio = (Monthly debt payments / Gross monthly income) x 100%

Back-end ratio = ($2239 / $12,333.33) x 100%

Back-end ratio = 18.14%

Total monthly housing expenses = $1230 + ($2,850 / 12) + $121

Total monthly housing expenses = $1230 + $237.50 + $121

Total monthly housing expenses = $1588.50

Their total monthly housing expenses are well within their budget, given their back-end ratio and gross income. Therefore, the Santiago's can buy their house.

Learn more about back end ratio on

https://brainly.com/question/30098606

#SPJ1

Answer:

2/3

Step-by-step explanation:

The months whose names end in 'y' include Jan, Feb, May, Jul.  The probability of randomly selecting a month whose name ends in 'y' is 4/12 (remember that there are 12 months in a year), or 1/3.

Thus, the probability of selecting a month whose name does NOT end in 'y' is 8/12, or 2/3.  Note that this event is the 'complement' of the first event:  

P(name does not end in 'y') = 1 - P(name does not end in 'y') = 1 - 1/3 = 2/3

Answer:

25

Step-by-step explanation:

\(1^2=1\\\\2^2=4\\\\3^2 = 9\\\\4^2=16\\\\\text{So the next number should be}~ 5^2=25\)

The amount invested at each rate is $30,000 at 4%, and $2000 at 6%.

Given that;

Larry Mitchell invested part of his $32,000 advance at 4% annual simple interest and the rest at 6% annual simple interest.

If his total yearly interest from both accounts was $1,340.

To find;

The amount invested at each rate.

Let x is the amount at 4%, therefore the amount at 6% is 32000 - x.

The total interest is:

0.04x + 0.06(32000 - x) = 1320

0.04x - 0.06x + 1920 = 1320

0.02x = 1920 - 1320

0.02x = 600

x = 600/0.02

x = 30,000

The amount at 6% is:

$32,000 - $30,000 = $2000

To learn more about Simple interest, please click the link;

https://brainly.com/question/25845758

#SPJ1

The answer of the given question based on Statistics to find minimum monthly premium payments is option D) Plan 2, since it has lower monthly premium payments.

Probability is  measure of  likelihood or chance of an event occurring. It is expressed as  number between 0 and 1, where 0 indicates an impossible event and 1 indicates  certain event

Assuming that the coverage details are similar, we can compare the monthly premium payments for each plan based on the different categories of coverage:

Individual: Plan 1 has a monthly premium of $87.32, while Plan 2 has a monthly premium of $11.77. Therefore, Plan 2 has the lower monthly premium for this category of coverage.

Individual+Spouse: Plan 2 has a monthly premium of $735.00, while Plan 1 has a monthly premium of $890.00. Therefore, Plan 2 has the lower monthly premium for this category of coverage.

Individual+Child: Plan 2 has a monthly premium of $606.00, while Plan 1 has a monthly premium of $750.00. Therefore, Plan 2 has the lower monthly premium for this category of coverage.

Individual+Family: Plan 2 has a monthly premium of $1,400.00, while Plan 1 has a monthly premium of $1,600.00. Therefore, Plan 2 has the lower monthly premium for this category of coverage.

Based on these comparisons, we can see that Plan 2 has a lower monthly premium for all categories of coverage. Therefore, the answer is option D: Plan 2, since it has lower monthly premium payments.

To know more about Event visit:

https://brainly.com/question/2505843

#SPJ1

Answer:

45

Step-by-step explanation:

Answer:

5²=25

25+20= 45

hope it helps

Answer:

x-int:(-2,0)(-4,0) . y-int:(0,8)

Step-by-step explanation:

y = x2+6x+8 and y = (x+2)(x+4)

x-int:

x+2=0

x= -2

(-2,0)

x-int:

x+4=0

x=-4

(-4,0)

y-int: plug 0 for x

y=(0+2)(0+4)

y=8

(0,8)

The intercepts of a graph are the points where the graph crosses the x or y axes.

Given that:

\(y = x^2 + 6x + 8\)

\(y = (x + 2)(x + 4)\)

The x-intercepts

This is when \(y = 0\)

So, we have:

\(y = (x + 2)(x + 4)\)

\((x + 2)(x + 4) = 0\)

Split

\((x + 2) = 0\) or \((x + 4) = 0\)

Solve for x

\(x = -2\) or \(x = -4\)

Hence, the x-intercepts are: (-2,0) and (-4,0)

The y-intercepts

This is when \(x = 0\)

So, we have:

\(y = x^2 + 6x + 8\)

Substitute 0 for x

\(y = 0^2 + 6 \times 0 + 8\)

\(y = 8\)

Hence, the y intercept is (0,8)

Read more about intercepts at:

https://brainly.com/question/1354826

The inequality representing the given situation is -

300x + 700y ≤ 7500

Advertising is the practice and techniques employed to bring attention to a product or service. Advertising aims to put a product or service in the spotlight in hopes of drawing it attention from consumers.

Given is that Bobby Flay is deciding how to advertise a new gourmet restaurant that he is opening. An online ad costs $300, and a TV ad costs $700. He has $7,500 to spend on the ads.

We can write the inequality as -

300x + 700y ≤ 7500

where -

{x} - number of online ads posted

{y} - number of TV ads poste

Plot the inequality on the graph. The shaded region represents the possible number of advertisements of each category Bobby can use to advertise.

Therefore, the inequality representing the given situation is -

300x + 700y ≤ 7500

To solve more questions on inequalities, visit the link below -

https://brainly.com/question/16872672

#SPJ1

Answer:

59049 ways

Step-by-step explanation:

Given

\(Colors = 9\)

\(Dogs = 5\)

Required

Determine number of selection (repetition is allowed)

The number of collars is not given.

So, we'll assume that there are enough collars to go round.

If no repetition is allowed, each of the 5 dogs have 9 colours to select from.

i.e.

\(Dog\ 1 = 9\)

\(Dog\ 2 = 9\)

\(Dog\ 3 = 9\)

\(Dog\ 4 = 9\)

\(Dog\ 5 = 9\)

So, the number of selection is:

\(Selection = 9 * 9 * 9 * 9 * 9\)

\(Selection = 59049\)

Answer: C

Step-by-step explanation:

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

Learn more about integrations here:

https://brainly.com/question/30217024

#SPJ1

The equivalent expressions are (b) (7 * 7)^x , (c) 7^x * 7^x and (e) 7^(2x)

The expression is given as:

49^x

Express 49 as 7 * 7

(7 * 7)^x ---- option (b)

Express 7 * 7 as an exponent

7^(2x) ---- option (e)

Express 2x as x + x

7^(x +x)

Expand

7^x * 7^x --- option (c)

Hence, the equivalent expressions are (b), (c) and (e)

Read more about equivalent expressions at:

https://brainly.com/question/27911936

#SPJ1

The insurance company has 4 doctor visits y=35x is lower rate and Rate 35 $ per doctor visit for more than 4 doctor visits y=100+10x.

A system of equations is a collection of two or more equations with a same set of unknowns.

In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system.

Aaron is considering two health insurance plans. The Get Well Soon Company charges an annual fee of 100 plus 10 per doctor visit, given y=100+10x

The Mega Coverage Company charges $35 per doctor, with no annual fee, represented by the equation: y=35x.

On solving both the equations

\(\rm 35x=100+10x\\\\35x-10x=100\\\\25x=100\\\\x=\dfrac{100}{25}\\\\x=4\)

For 4 doctor visits charges are same and Rate 35 $ per doctor visit.

For less than 4 doctor visits y=35x is lower rate and Rate 35 $ per doctor visit for more than 4 doctor visits y=100+10x.  

Hence, The insurance company has 4 doctor visits y=35x is lower rate and Rate 35 $ per doctor visit for more than 4 doctor visits y=100+10x.

Learn more about system of equation here;

brainly.in/question/21918540

.

#SPJ2

To calculate the circumference of a circle, you can use the formula:

\(\displaystyle C=2\pi r\)

Where \(\displaystyle C\) represents the circumference and \(\displaystyle r\) represents the radius of the circle.

Given that the radius \(\displaystyle r\) is 8 inches, we can substitute this value into the formula:

\(\displaystyle C=2\pi (8)\)

Simplifying the expression:

\(\displaystyle C=16\pi \)

Thus, the circumference of a circle with a radius of 8 inches is \(\displaystyle 16\pi \) inches.

Note: \(\displaystyle \pi \) represents the mathematical constant pi, which is approximately equal to 3.14159.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

2.833

Step-by-step explanation:

Answer:19/6/16

Step-by-step explanation:

The easiest way to find the slope is to find 2 points that are at an exact point. (-3,1) and (2,-3) are exact points. Start at (-3,1) and count to the right 5 and go down four. The slope would be \(\frac{5}{-4}\) or \(\frac{-5}{4}\).

I hope my explanation makes sense! :) If it doesn't make sense I can try to explain it better!

The monthly cell phone bill when shared data equals zero is given as follows:

$26.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The intercept of the line in this problem is given as follows:

b = 26.

Hence $26 is the monthly cell phone bill when shared data equals zero.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

By comparism using the given scale ratio, the weight of Ellie at birth is 7.7pounds.

Ratio simply compares values, it shows how much of one thing is related or compared to another thing.

Given the data in the question;

To determine the weight of Ellie, we simply say;

0.75pounds : 0.9pounds = 6.4pounds : X

0.75pounds / 0.9pounds = 6.4pounds / X

Cross multiply

0.75pounds × X = 0.9pounds × 6.4pounds

0.75pounds × X = 5.76pounds²

X = 5.76pounds² / 0.75pounds

X = 7.68pounds

X = 7.7pounds

Therefore, by comparism using the given scale ratio, the weight of Ellie at birth is 7.7pounds.

Learn more about ratio here: https://brainly.com/question/13419413

Answer:

We can use the formula for continuous compound interest to find the balance in Joseph and Deb's savings account after 1 year:

A = Pe^(rt)

where A is the balance, P is the principal (initial deposit), e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate as a decimal, and t is the time in years.

Substituting the given values, we get:

A = $600.00e^(0.05*1)

Using a calculator, we get:

A ≈ $632.57

Therefore, Joseph and Deb will have approximately $632.57 in their savings account after 1 year. They can spend up to this amount on their trip. Rounded to the nearest cent, the answer is $632.57.

Answer:

circumference=2πr=2×22/7×6.5=40.8571428571

option

A.

A.40.82 in

is your answer.

Step-by-step explanation:

the formula for the circumference of a circle for just the radius is

2r(pie)

so just insert 6.5 for r

2(6.5)(pie)

40.82

Hope that helps :)

The height of the trapezium prism is calculated as: 17.3 ft.

Surface area of trapezium prism = (b1+b2)h + PH.

Given the following:

Substitute the values into (b1+b2)h + PH:

1508 = (35 + 11)14 + (50)H

1508 = 644 + 50H

1508 - 644 = 50H

864 = 50H

H = 17.3 ft

Learn more about Surface area of trapezium on:

https://brainly.com/question/15476307

Answer: 9

Step-by-step explanation:

that one person was right they help me pass my test

proof with other answers

Answer:

8

Step-by-step explanation:

line of symmetry indicates equal measurements between both sides, 4 from eye not nose and another 4 from the nose to eye