what is an equation of the image of the line after dilation

Thus, the dimensions of the rectangle are - length 22 inches and width 13 inches.

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). The opposite sides of a rectangular are equal and parallel. A rectangle has two dimensions—length and width—because it is a two-dimensional form. The rectangle's longer side is its length, while its shorter side is its breadth.

Let the length of rectangle be 'l'

Let the width be 'w'.

Then,

Perimeter = 2(l + w)

70 = 2(l + w)

35 = l + w

l = 35 - w ...eq 1

Now,

Area = length * width

286 = l*w ...eq 2

Put eq 1 in eq 2

286 = (35 - w)*w

286 = 35w - w²

w² - 35w + 286 = 0

Solving the quadratic equation:

w² - 22w - 13w + 22*13 = 0

w(w - 22) - 13(w - 22)= 0

(w - 22)(w - 13) = 0

w = 22 and w = 13

As, length is greater than width-

width w = 13 inch

Length l = 35 - 13 = 22 inches.

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The cost per kilogram of cheese is found by dividing the cost per pound by the conversion factor 0.45359237 kilograms per pound. The result is $9.68 per kilogram.

Start with the given cost of cheese per pound: $4.40.

To convert from pounds to kilograms, we need to divide by the conversion factor 2.2 (since 1 kilogram is approximately equal to 2.2 pounds). So, we have

1 pound / 2.2 = 0.45359237 kilograms / 1 pound

Note that we can write this as a conversion factor with the pound unit cancelling out, leaving us with kilograms as the desired unit.

Now, we can multiply the cost per pound by the conversion factor to get the cost per kilogram

Cost per kilogram = Cost per pound * (1 pound / 0.45359237 kilograms)

            = $4.40 * (1 / 0.45359237)            

Evaluating this expression using a calculator gives us

Cost per kilogram = $9.68

So the cost of cheese per kilogram is approximately $9.68.

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The values closest to these middle elements are 60 and 61 inches.

To construct a stemplot for the given data, we need to separate each observation into a stem and a leaf. The stem is the digit(s) on the left-hand side of the decimal point, while the leaf is the digit on the right-hand side. The stemplot for the given data is:

3 | 2

4 | 0 9 9

5 | 0 0 0 4 4 9

6 | 1 2 3

7 | 0 0 3 0

8 | 0 8

9 | 0

To find the two values that are closest to the middle, we need to sort the data in order from lowest to highest:

We have 19 observations, so the middle two observations are the 10th and 11th values, which are 60 inches and 61 inches, respectively. Therefore, the two values closest to the middle are 60 inches and 61 inches.

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The values closest to these middle elements are 60 and 61 inches.

To construct a stemplot for the given data, we need to separate each observation into a stem and a leaf. The stem is the digit(s) on the left-hand side of the decimal point, while the leaf is the digit on the right-hand side. The stemplot for the given data is:

3 | 2

4 | 0 9 9

5 | 0 0 0 4 4 9

6 | 1 2 3

7 | 0 0 3 0

8 | 0 8

9 | 0

To find the two values that are closest to the middle, we need to sort the data in order from lowest to highest:

We have 19 observations, so the middle two observations are the 10th and 11th values, which are 60 inches and 61 inches, respectively. Therefore, the two values closest to the middle are 60 inches and 61 inches.

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The missing sides of the triangle are

10). ∠ ABD = 60 degrees

11). ∠ ADB = 90 degrees

12). ∠ BAD = 30 degrees

13). ∠ CAD = 30 degrees

14. BD is half of the length = BC / 2 = 6/2 = 3

15. AD is the height this is solved using Pythagoras theorem as below

AD^2 = AB^2 - BD^2

AD^2 = 6^2 - 3^2

AD^2 = 36 - 9

AD = sqrt (27)

16. Area of Δ ABC

= 1/2 * base * height

= 1/2 * 6 * sqrt (27)

= 9 sqrt (3)

= 15.59 square units

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Answer:

12%

Step-by-step explanation:

Let the rate of interest be R%
r = R% as decimal =R/100

Simple interest earned for 3 years at rate r on ₹15,000 = ₹5,400

The formula for interest earned is given by
I = Prt
where P is the principal amount (15,000)

r = annual interest rate as a decimal (to be determined)

t = number of years

Plugging in known values we get

5400 = 15000 x r x 3

         = 45000 x r

r = 5400/45000

r = 0.12

Rate of interest as a percentage = r x 100 = 0.12 x 100 = 12%

Interest charge for the month = 51.69 rounded to the nearest penny.

Here, we have,

The particular month in question is 30 days long.

Your balance at the start of the month is 3,000.

Annual interest rate = 21%.

Payment = 150.00.

When the payment is made in the month, it reflects on the tax amount you pay on both the average day balance.

YOU SEND THE PAYMENT IN ON THE FIRST DAY OF THE MONTH.

YOUR ACCOUNT IS CREDITED ON THE 11TH DAY OF THE MONTH.

Average daily balance is 3000 from day 1 until day 10 (10 days)

Average daily balance is 2850 from day 11 until day 30 (20 days)

Average daily balance for the month = 10 * 3000 + 20 * 2850

                                                            = 87000 / 30

                                                            = 2900

Interest charge for the month = 0.21 * 2900 * 30 / 365

Interest charge for the month = 50.05 rounded to the nearest penny

YOU SEND THE PAYMENT IN ON THE TWENTIETH DAY OF THE MONTH.

YOUR ACCOUNT IS CREDITED ON THE 30TH DAY OF THE MONTH.

Average daily balance is 3000 from day 1 until day 29 (29 days)

Average daily balance is 2850 from day 30 until day 30 (1 day)

Average daily balance for the month = 3000 * 29 + 1 * 2850

                                                            = 89850 / 30

                                                            = 2995

Interest charge for the month = 0.21 * 2995 * 30 / 365

Interest charge for the month = 51.69 rounded to the nearest penny

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Complete Question:

Calculate the monthly finance charge for the following credit card transaction. Assume that it takes 10 days for a payment to be received and recorded and that the month is 30 days long. Round your answer to the nearest cent.

3,000 balance, 21% rate, 150 payment, average daily method

If 100 different students were chosen from this population, we would expect approximately 27 of them to read more than 94 words per minute. Therefore, the correct choice is (A).

The probability that a randomly selected student in the city will read more than 94 words per minute is 0.2743.

z-score = (x - μ) / σ = (94 - 88) / 10 = 0.6

Therefore, the probability of a z-score being greater than 0.6 is:

P(Z > 0.6) = 1 - P(Z < 0.6) = 1 - 0.7257 = 0.2743

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your aanswer is 9 ⚡

The value of numbers are,

⇒ 9 and 16

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

The product of two numbers is 1296.

And, one number is 16 times the other,

Let first number = x

Hence, Second number is, 16x

So, We get;

⇒ 16x × x = 1296

⇒ 16x² = 1296

⇒ x² = 81

⇒ x = 9

Hence, first number = 9

And, Second number is,

= 16x

= 16 x 9

= 144

Thus, The value of numbers are,

⇒ 9 and 16

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The missing sides of the triangle have been identified here.

Trigonometric ratios relate the angles of a right triangle to the lengths of its sides. The three primary trigonometric ratios are sine, cosine, and tangent. If you know the measure of one of the acute angles in the triangle and the length of one of the sides, you can use trigonometric ratios to solve for the length of another side.

1) Sin x = 5/14

x = Sin-1 (5/14)

x = 21°

2) Tan x = 8/5

x = Tan-1 (8/5)

x = 58°

3) Cos x = 9/13

x = Cos-1 (9/13)

x = 46°

4) Cos x = 3/5.8

x = Cos-(3/5.8)

x = 59°

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The missing sides of the triangle have been identified here.

Trigonometric ratios relate the angles of a right triangle to the lengths of its sides. The three primary trigonometric ratios are sine, cosine, and tangent. If you know the measure of one of the acute angles in the triangle and the length of one of the sides, you can use trigonometric ratios to solve for the length of another side.

1) Sin x = 5/14

x = Sin-1 (5/14)

x = 21°

2) Tan x = 8/5

x = Tan-1 (8/5)

x = 58°

3) Cos x = 9/13

x = Cos-1 (9/13)

x = 46°

4) Cos x = 3/5.8

x = Cos-(3/5.8)

x = 59°

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This method can be used to quickly obtain the product of two polynomials.A-6k²+25k²-16k-15.

Expression in math is a combination of numbers, symbols and operators that represent a mathematical quantity or operation. It can be a single number, a single variable, or a combination of numbers, variables and symbols combined together to form a mathematical statement. An expression can also include functions, such as polynomials, exponential functions, or logarithmic functions.


The vertical method involves writing the terms of the two factors side by side and multiplying them together to get the product.

(3k+5)  (2k²-5k-3)

6k³  +   0k²  +   0k   +  -15
0k³  +  10k²  + -15k   +   0
0k³  +   5k²   + -15k   +   0
0k³ +   0k²  +  15k   +   0

Adding the terms in each column yields the product:

A-6k³+25k²-16k-15

Therefore, the correct answer is A-6k³+25k²-16k-15.

In conclusion, using the vertical method can simplify algebraic multiplication problems by breaking them down into columns and adding the terms in each column. This method can be used to quickly obtain the product of two polynomials.

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The length of the two unknown sides of the triangle are: 12√2

There are different methods of finding the missing sides of triangles such as:

Pythagoras Theorem

Law of sines or sine rule

Law of cosines or cosine rule

Now, we are given an Isosceles triangle with a base length and two equal base angles.

Thus, the two unknown sides will have equal side lengths.

∠D = 90°

Thus, using sine rule:

12/sin 90 = QR/sin 45

QR = 12 * 1/√2

Rationalizing the denominator gives:

QR = 12√2

Since the two unknown sides of the triangle are equal, then we say that:

PQ = 12√2

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To solve this equation by combining terms, the answer will be: (c) -4a + 22b.

To solve the equation, we need to combine like terms together. This means that the figures with the suffix, a will come together, while those with the suffix, b will also align themselves. Going by this rule, we will have:

12a -16a + 26b -4b.

= -4a + 22b

When a higher number is to be subtracted from a smaller number, the result will be a negative number as is the case with the terms that have the 'a' initials.

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Answer: if the first angle is 61° then the angle x is 119°

               but if the first angle is 67 then the angle x is 113°

Step-by-step explanation:

Line is 180° that means our formula will look like that 67 or 61 + x = 180 in that case we have to calculate x ⇒ 180 - 61 or 67 = x

Answer:

The mean of a binomial distribution is μ = np, where n is the sample size and p is the probability of success (having blue eyes).

μ = 20 x 0.08

μ = 1.6

Rounded to one decimal place, μ is 1.6.

Answer:

12[tex]x^{2}[/tex]+4x

Step-by-step explanation:

area = width * height

substitution: area = (3x+1)*4x

distributive property: area = (4x*3x)+(4x*1)

simplify: area = 12[tex]x^{2}[/tex]+4x

The maximum pressure differential in a stairwell is 58,860 Pa.

The atmospheric pressure difference between the top of the building and the street level is 2,943,000 Pa.

The difference in static water pressure between consecutive floors is 29,430 Pa.

We have,

Assuming a standard atmospheric pressure of 101.3 kPa.

Maximum pressure differential in a stairwell:

Since each stairwell is no more than 20 stories high and each story is approximately 3 m high, the maximum height difference between two floors in a stairwell is:

= 20 x 3

= 60 m

Using the formula for hydrostatic pressure, the maximum pressure differential in a stairwell is:

ΔP = ρgh

= (1000 kg/m³)(9.81 m/s²)(60 m)

= 58,860 Pa

The atmospheric pressure difference between the top of the building and street level:

The atmospheric pressure decreases with increasing altitude.

Using the formula for hydrostatic pressure, the pressure difference between the top of the building and the street level is:

ΔP = ρgh

= (1000 kg/m³)(9.81 m/s²)(300 m)

= 2,943,000 Pa

The difference in static water pressure between consecutive floors:

Assuming a standard density of water of 1000 kg/m³, the difference in static water pressure between consecutive floors is:

ΔP = ρgh = (1000 kg/m³)(9.81 m/s²)(3 m) = 29,430 Pa

Therefore,

The maximum pressure differential in a stairwell is 58,860 Pa.

The atmospheric pressure difference between the top of the building and the street level is 2,943,000 Pa.

The difference in static water pressure between consecutive floors is 29,430 Pa.

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The exponential growth functions are,

[tex]y=\frac{9}{11}(4)^t[/tex]

[tex]V=0.8(9)^t[/tex]

[tex]P=0.9(8.3)^t[/tex]

[tex]P=\frac{7}{9}(\frac{5}{4})^t[/tex]

The exponential decay functions are,

[tex]A= (0.97)^t[/tex]

[tex]y= 3.7 (0.2)^t[/tex]

The function which is neither exponential growth nor exponential decay is,

g(x)=2.1(x).

What is exponential function?

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.

If the base is larger than 1, it will be an exponential growth.

For example, [tex]3^2=9[/tex]

If the base is smaller than 1, it will be an exponential decay.

For example, [tex]0.5^2=0.25[/tex]

If the function does not have an exponent, that means there will be no exponential growth or decay.

Therefore the exponential growth functions are,

[tex]y=\frac{9}{11}(4)^t[/tex]

[tex]V=0.8(9)^t[/tex]

[tex]P=0.9(8.3)^t[/tex]

[tex]P=\frac{7}{9}(\frac{5}{4})^t[/tex]

The exponential decay functions are,

[tex]A= (0.97)^t[/tex]

[tex]y= 3.7 (0.2)^t[/tex]

The function which is neither exponential growth nor exponential decay is,

g(x)=2.1(x).

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The price of the wheelbarrow is $86, and Pedro will need to pay an additional 30% of the price for shipping and handling.

To calculate the shipping and handling cost, we can first find 30% of the price of the wheelbarrow:

30% of $86 = 0.3 x $86 = $25.80

Therefore, Pedro will need to pay $25.80 for shipping and handling.

The equation of line perpendicular to the tangent is found to be -

y = -2x + 7.

The equation for a line should be written in the slope-intercept form so that the y-intercept (where its line crosses a vertical y-axis) and slope (steepness) are immediately visible. The y = mx + b form is a common name for this form.

Given condition of digression line:

Comparing with the standard form: y = 1/2 x + 7 y = mx + c

m is the slant and c is the y block:

m = 1/2

Let the incline of the line opposite to the digression be M.

Then, at that point, connection between the inclines of opposite lines:

m. M = -1 equation of line perpendicular to the tangent.

y - 3 = M(x - 2)

y - 3 = -2(x - 2)

y = -2x + 4 + 3

y = -2x + 7

Thus, the equation of line perpendicular to the tangent is found to be -

y = -2x + 7.

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The circle has the centre at (2,3). The equation of the tangent of the line on the circle : y = 1/2 x + 7. What is equation of line perpendicular to the tangent.

1.) m<A = 51°

AB = 17.5

BC = 13.6

To calculate the missing part of the triangle, m <A ;

The sum of the interior triangle = 180°

That is , 180° = 90°+ 39° + m

make m the subject of formula;

m = 180 - 129

m <A = 51°

Using the formula from SOHCAHTOA;

Sin 39° = 11/AB

make AB the subject of formula;

AB = 11/0.629320391

= 17.5

Using the Pythagorean formula;

C² = a² + b²

C² = 17.5

a² = 11

b² = BC = ?

17.5² = 11² + b²

make b² the subject of formula;

b² = 17.5²-11²

b² = 306.25 - 121

b² = 185.25

b = √185.25

b = 13.60

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Answer:

Formula for finding the surface area of a cone is shown below

[tex]\pi \: r {}^{2} + \pi \: rl \\ or \\ \pi(r + l)r[/tex]

The formula for finding the surface area of a cone is:

Surface area = πr² + πrl

Where:

The measure of the smaller angle of the  co-interior angles is 69°

Co-interior angles are simply angles that occur in between two parallel lines when they are intersected by a transversal.

The two angles add up to 180º as they occur on the same side of the transversal always.

From the image, the two co-interior angles are:

x + 114

x + 72

Since the two angles add up to 180º.

x + 114 + x + 72 = 180

Solve for x

2x + 186 = 180

2x = 180 - 186

2x = -6

x = -6/2

x = -3

Hence, the measure of the two angles are:

x + 114 = -3 + 114 = 111°

x + 72 = -3 + 72 = 69°

Therefore, the smallest angle is 69 degree.

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Answer:

38.part A) 3p = 25.47

partB) $8.49

Step-by-step explanation:

38) to get the price of a game ,$25.47 will be divided by

 25.47÷3=$8.49

the price of 1 game =&8.49

 to get the price of 1 game , the equation will be

 3p=25.47

 p=25.47÷3

 p=$8.49

The number line where we plotting -2 1/6 and 11/6 is attached

From the question, we have the following parameters that can be used in our computation:

-2 1/6 and 11/6

To start with, we convert both numbers to the same form

i.e. decimal or fraction

When converted to fractions, we have

-13/6 and 11/6

This means that we can plot -13/6 at -13 and 11/6 at point 11 where the difference in each interval is 1/6

Using the above as a guide, we have the following:

The number line is attached

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Answer: yes, the hex of the number 1,000,000 would be 40.

Answer:

[tex]Triangle\: 1: } \dfrac{opposite}{adjacent} = \dfrac{16}{39.6} = \boxed{0.40404\cdots}[/tex]

[tex]Triangle\: 2: } \dfrac{opposite}{adjacent} = \dfrac{48}{118.8} = \boxed{0.40404\cdots}[/tex]

Choice C: The ratio is the same for both triangles

Step-by-step explanation:

[tex]Triangle\: 1: } \dfrac{opposite}{adjacent} = \dfrac{16}{39.6} = \boxed{0.40404\cdots}[/tex]

[tex]Triangle\: 2: } \dfrac{opposite}{adjacent} = \dfrac{48}{118.8} = \boxed{0.40404\cdots}[/tex]

So both ratios are the same. This is also because the ratios represent the tan of the angle that the adjacent side makes with the hypotenuse and this angle of 22° is same in both triangles

The relative maximum and minimum point as well as the absolute maximum and minimum points based on labeled points on the graph are;

Points 1, 3, and 5 are relative maximum points

Points 2 and 4 are relative minimum points

Point 5 is an absolute maximum point

Point 2 is an absolute minimum point

A relative maximum is a point in which the maximum with regards to the immediate surrounding points.

Therefore, the relative maximum points are;

The points 1, 3, and 5

The relative minimum points are points that are the minimum points, when compared with the surrounding points

The relative minimum are the points 2 and 4

The absolute maximum is the point which is at the highest point on the graph

The absolute maximum on the graph is therefore, the [oint 5

The absolute minimum on the graph is the point which is the minimum point compared to all other points

Therefore, the absolute minimum point is the point 2

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Answer:

Step-by-step explanation:

a. The number of red roses left t hours before the store opens can be represented by the formula:

N(t) = 400 * (1/2)^(t/2)

Here, we're dividing the number of available roses by 2 every 2 hours, so the exponent t/2 represents the number of 2-hour intervals that have passed since the store opened.

b. The number of box chocolates left t hours after the store opens can be represented by the formula:

M(t) = 200 * (0.85)^t

Here, we're multiplying the number of available boxes by 0.85 every hour, so the exponent t represents the number of hours that have passed since the store opened.

c. We need to find the time t when the number of roses is equal to the number of boxes of chocolates:

400 * (1/2)^(t/2) = 200 * (0.85)^t

Dividing both sides by 200:

2 * (1/2)^(t/2) = 0.85^t

Taking the logarithm of both sides:

log(2) - (t/2) * log(2) = t * log(0.85)

Simplifying:

t * (log(0.85) + (log(2)/2)) = log(2)

t = log(2) / (log(0.85) + (log(2)/2))

Using a calculator, we get:

t ≈ 11.9 hours

Therefore, the number of roses will be equal to the number of boxes of chocolates approximately 11.9 hours before the store opens, or around 9 p.m. on the day before Valentine's Day.

d. To find the number of boxes of chocolate left at 12:30 p.m. (3.5 hours after the store opens), we can use the formula:

M(3.5) = 200 * (0.85)^3.5

M(3.5) ≈ 97.4

Therefore, there are approximately 97 boxes of chocolate left at 12:30 p.m.

e. To buy 36 red roses, we need to find the latest time we can arrive before the store runs out of roses. We can set N(t) equal to 36 and solve for t:

400 * (1/2)^(t/2) = 36

Dividing both sides by 400:

(1/2)^(t/2) = 0.09

Taking the logarithm of both sides:

t/2 * log(1/2) = log(0.09)

Simplifying:

t ≈ 5.2 hours

Therefore, the latest time we can arrive to successfully buy 36 red roses is approximately 5.2 hours before the store opens, or around 3:50 a.m. on the day before Valentine's Day.