Not drawn to scale
: Find the value of x in the figure at the right. Round your answer to the nearest tenth.
MUST SHOW WORK.

The rule that describes the transformation is (x, y) → (y, -x)

We are given that;

The points (-2,5),(2,5),(2,1).

Now,

To rotate a point 90° clockwise with the origin as the center of rotation, we can use the following rule:

(x, y) → (y, -x)

This means that the x-coordinate of the original point becomes the y-coordinate of the new point, and the y-coordinate of the original point becomes the opposite of the x-coordinate of the new point.

For example, applying this rule to the point (-2, 5), we get:

(-2, 5) → (5, 2)

Therefore, by the transformation the answer will be(x, y) → (y, -x)

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Answer:

Elena

Step-by-step explanation:

Sorry we have to see the complement first because it is of 90° jjust let the second w go we will do that later we can find the value of w by choosing elena

To complete the job in 12 days, they need 100 workers.

We know that 30 workes can complete 1 job in 40 days, then if each worker works at a rate R, then we can write:

30*R*40 days = 1 job

R = (1/1200) job/day

Then if they need to complete the job in 12 days, the number N of workers needed is:

N*(1/1200)*12 = 1

N = (1200/12) = 100

100 workers are needed.

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The composite function f(f(x)) has a solution of - (1 - x)/x

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

f(x) = 1/1 - x

To calculate f(f(x)), we replace the occurence of x in the function f(x) = 1/1 - x with f(x)

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

f(f(x)) = 1/1 - f(x)

Substitute the known values in the above equation, so, we have the following representation

f(f(x)) = 1/(1 - 1/(1 - x))

Evaluate

f(f(x)) = - (1 - x)/x

Hence, the solution is f(f(x)) = - (1 - x)/x

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The solution is:

The equations are;

4(2x + 5) = 3(2x + 8)

x = 2

Perimeter of each shape is 36

Here, we have,

Mathematically;

The perimeter of a square is 4L

while the perimeter of an equilateral triangle is 3L

where L represents the lengths of the sides

Mathematically, from what we have in the question, since the perimeter are equal;

4(2x + 5) = 3(2x + 8)

8x + 20 = 6x + 24

8x-6x = 24-20

2x = 4

x = 4/2

x = 2

The side of the square will measure;

2(2) + 5 = 9

Its perimeter is 4(9) = 36

The side of the triangle will measure

2(2) + 8 = 12

Its perimeter will be 3(12) = 36

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In the rhombus PQRS, if angle ∠ SPQ = 120° then ∠SPO is 30°

∠POS is 90° and ∠PSO is 60 degrees, ∠PO is 90° and ∠SO  is 150°

PQRS is a rhombus.

∠ SPQ = 120° and SP = 8.

We have to find angles,∠SPO = (180° - ∠SPQ) / 2

= (180° - 120°) / 2

= 30°

∠POS = 90°

Now we have to find angle PSO

∠PSO+∠SPO+∠POS =180

30+90+∠PSO=180

120+∠PSO=180

∠PSO=180-120

∠PSO=60 degrees

∠PO = 360° / 4 = 90°

∠SO = 180° - ∠POS = 180° - 30°

= 150°

The area we find by using formula diagonal 1 × diagonal 2/2

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The surface area of the prism is 112 in²

A prism is a solid shape that is bound on all its sides by plane faces.

The surface area of a prism is expressed as;

SA = 2B +pH

where h is the height and B is the base area and p is the perimeter of the base

The perimeter of the base = 2(l+b)

= 2(3+4) = 2×7 =14 in

The area of the base = l× b

= 4× 3 = 12 in²

height = 7

Therefore the surface area = 2 × 12 + 14 × 7

= 14+98

= 112 in²

therefore the surface area of the prism is 112 in²

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The interest is $293.88 in interest

The remaining balance is approximately $2793.88.

Monthly Interest Rate = 0.2 / 12

Monthly Interest Rate ≈ 0.01667 (rounded)

Month 1:

Interest: $4000 * 0.01667 ≈ $66.68 (rounded)

New Balance: $4000 + $66.68 = $4066.68

Payment: $300

Remaining Balance: $4066.68 - $300 = $3766.68

Month 2:

Interest: $3766.68 * 0.01667 ≈ $62.82 (rounded)

New Balance: $3766.68 + $62.82 = $3829.50

Payment: $300

Remaining Balance: $3829.50 - $300 = $3529.50

Month 3:

Interest: $3529.50 * 0.01667 ≈ $58.86 (rounded)

New Balance: $3529.50 + $58.86 = $3588.36

Payment: $300

Remaining Balance: $3588.36 - $300 = $3288.36

Month 4:

Interest: $3288.36 * 0.01667 ≈ $54.80 (rounded)

New Balance: $3288.36 + $54.80 = $3343.16

Payment: $300

Remaining Balance: $3343.16 - $300 = $3043.16

Interest: $3043.16 * 0.01667 ≈ $50.72 (rounded)

New Balance: $3043.16 + $50.72 = $3093.88

Payment: $300

Remaining Balance: $3093.88 - $300 = $2793.88

Total = $66.68 + $62.82 + $58.86 + $54.80 + $50.72

≈ $293.88 in interest

The remaining balance is approximately $2793.88.

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If in a triangle ABC, right angle is at C, BA is hypotenuse, the length of side BC is 5√7 units.

In a right triangle, the hypotenuse is the longest side and is opposite the right angle. Therefore, in triangle ABC, side BA is the longest side, and it is also the hypotenuse.

Using the Pythagorean theorem, we can find the length of the third side BC. The theorem states that the square of the hypotenuse (BA²) is equal to the sum of the squares of the other two sides (BC² + CA²).

BA² = BC² + CA²

16² = BC² + 9²

256 = BC² + 81

BC² = 256 - 81

BC² = 175

BC = √175

BC = 5√7

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The value of Y is givan as y = 2 * 3^x

The general form is of

y = ab^x

where we have to define the terms as

'a' is the initial value, 'b' is the base, and 'x' is the exponent

Point (0, 2):

y = ab^x

2 = a * b^0

Since any non-zero number raised to the power of 0 is 1, we have:

2 = a * 1

a = 2

Point (1, 6):

y = ab^x

6 = 2 * b^1

6 = 2 * b

b = 6 / 2

b = 3

From the values that we have solve we would have

y = 2 * 3^x

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The approximate shortest distance between the treasure chest and driftwood is 3.2 yards

The correct answer is an option (C)

From the attached figure of the coordinate plane,

the coordinates of the palm tree = (1, 2),

the coordinates of the  treasure chest = (5, 8)

and the coordinates of the driftwood = (8, 7)

We know that the distance formula between two points (x₁, y₁) and (x₂, y₂) is:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

We need to find the distance between the treasure chest and driftwood.

Let (x₁, y₁) = (5, 8)

and (x₂, y₂) = (8, 7)

Using distance formula, the approximate shortest distance between the treasure chest and driftwood would be,

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

d = √[(7 - 8 )² + (8 - 5)²]

d = √[(-1)² + (3)²]

d = √[1 + 9]

d = √(10)

d = 3.1622

d ≈ 3.2 yards

This is the required distance between the treasure chest and the driftwood.

Therefore, the correct answer is an option (C)

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Find the complete question below.

Answer:

To write the number 0.000089 in scientific notation, we need to move the decimal point to the right until there is only one non-zero digit to the left of the decimal point, and count the number of places we moved the decimal point. In this case, we need to move the decimal point 5 places to the right:

0.000089 = 8.9 × 10^(-5)

Therefore, the number 0.000089 in scientific notation is 8.9 × 10^(-5).

The calculated range of the amount of rainfall in mm is 20.5 mm

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

Data values in mm

0.0, 12.2, 2.1, 0.0, 20.5, 5.5 and 1.0

The range of the rainfall  is the difference between the least and the highest amount of rainfalls

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

Range = 20.5 - 0.00

Evaluate

Range = 20.5

Hence, the range of rainfall is 20.5 mm

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Asked equations are written below with the explanation.

Here are three equations that involve adding negative numbers:

-5 + (-3) = -8

This equation involves adding the negative numbers -5 and -3.

-10 + (-2) + (-3) = -15

This equation involves adding the negative numbers -10, -2, and -3.

-7 + (-1) + (-4) + (-2) = -14

This equation involves adding the negative numbers -7, -1, -4, and -2.

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The probability that it weighs more than 51 pounds exactly 53 pounds.

Given that, mean weight of 50 pounds and a standard deviation of 0.5 pounds.

We need to find the probability that it weighs more than 51 pounds,

P(X = 53) = 0

z = (51 - 50) / 0.5 = 2.00

P(X > 51) = P(z > 2.00) = 0.0228

z1 = (49 - 50) / 0.5 = -2.00

z2 = (51 - 50) / 0.5 = 2.00

P(49 < X < 51) = P(-2.00 < z < 2.00) = P(z < 2.00) - P(z < -2.00) = 0.9772 - 0.0228 = 0.9544

Hence, the probability that it weighs more than 51 pounds exactly 53 pounds.

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The measure of arc and angle in the given circle are as follow,

Measure of arc CA = 144°

Measure of arc AD  = 98°

Measure of ∠C = 90°

In the circle ,

Center of the circle = Q

m∠ABC = 72°

Measure of arc CD = 46°

Measure of arc CA

Measure of ∠ABC = 72°

In a circle angle at the center is double of angle at the circumference of the circle in the same arc.

Measure of ∠CQA = 2 ×∠ABC

                               =  2× 72°

                               = 144°

measure of arc CA = measure of ∠CQA

                                = 144°

Measure of arc AD ,

m ∠AQD + m ∠CQD = m ∠CQA

⇒m ∠AQD  = 144° - 46°

⇒m ∠AQD  =  98°

⇒ Measure of arc AD  = 98°

Measure of angle C = ( 1/2) times of measure of BQD

                                 = ( 1/2) × 180°

                                 = 90°

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Answer:

  (b)  0.083

Step-by-step explanation:

You want the probability that a part is New and Passed the test, given the distribution of parts as shown in the table.

"This group" consists of all the parts described by the table. That is a total of ...

  5 + 23 + 2 + 30 = 60

parts.

Of those 60 parts, the number that is found in the table cell (New, Passed) is 5. This means 5/60 = 1/12 ≈ 0.083 of the total number of parts shown were New and Passed the test.

The probability of choosing one of those parts at random is 0.083.

__

Additional comment

This is not "coordinate algebra". It is probability.

The perimeter of the composite figure that is given above would be = 96.6m.

To calculate the perimeter of the given shape, it has to be divided into two.

First shape is a rectangle. Therefore the perimeter of a rectangle is calculated with the formula = 2(l+w)

Where ;

length = 16m

width = 11m

perimeter = 2(16+11)

= 2×27

= 54m

The second shape:

Perimeter of triangle = l+w+h

where;

length = 18-11 = 7m

width = 16m

height = 19.5m

perimeter = 7+16+19.5 = 42.5m

Therefore, the perimeter of the shape = 54+42.5 = 96.6m

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Answer: The width of the garden/fence will be 15 m.

Step-by-step explanation: First, we have to understand that there will be two wide sides and two long sides, and in a rectangle, the long sides always equal each other and the wide sides equal each other as well. This means that one width and one length will equal 120/2=60.

In other words:

one length of the garden + one width of the garden = 60

Now that we know this, we move on to the "3 times" part of the question. For this step, it is easiest to imagine quarters of something, because 3/4 of something will always be 3 x 1/4 of something; The proportion for 3/4:1/4 will always be 3:1.

60 x 3/4 is equal to 45 and 60 x 1/4 is equal to 15.

To check our answer, L+W+L+W = 45+15+45+15 = 120.

This means each wide side is equal to 15.

Answer:

65.8

Step-by-step explanation:

to solve such equations u should use (PEMDAS)

parenthesis, exponents, multiplication, division, addition, subtraction

note that multiplication doesn't become always before division if the division is before in the equation we divide then multiply

same with addition and subtraction we add or subtract depnding on what first

other than that we follow the steps i mentioned before

parenthesis, exponents, multiplication, division, addition, subtraction

so solve the parantheses first

then the exponents (you may have not learned this yet)

then multiplication and division together start with the one that comes first

the addition and subtraction start with the one that comes first

so for example :5×5÷5×5

=25÷5×5

=5×5

=25

i started with the first multiplication cuz it came first then division cuz it was before the other multiplication

and then the other multiplication

now here is the answer for your equation 93+48÷(12-42)x17

using PEMDAS(don't write this it's just for explaining)

parantheses first

93+48÷-30×17

we don't have exponents so just skip it

now division and multiplication

93+(-1.6)×17

finally addition amd subtraction

because we don't have subtraction we won't use it too

93 +(-27.2)

=65.8

Answer:1,000

Step-by-step explanation:

So we add 25 million to 5 million which is 30 million. Then we divide 30 million to 30 thousand and get 1 thousand.

The bond price at 12% maturity is $435.42, at 10% maturity is $500.00, at 8% maturity is $607.28, and at 6% maturity is $748.65. The balance at the end of 28 months is approximately $41,097,019.67.

To determine the price of the bond at different yield to maturity rates, we need to use the bond pricing formula

Bond price = (Coupon payment / (1 + YTM)¹) + (Coupon payment / (1 + YTM)²) + ... + (Coupon payment + Face value) / (1 + YTM)ⁿ

Where Coupon payment = Annual coupon rate x Face value

YTM = Yield to maturity

n = Number of years to maturity x Number of coupon payments per year

Using $1,000 as the face value and an annual coupon rate of 10%, we have

At 12% yield to maturity

Coupon payment = 0.10 x $1,000 = $100

n = 20 x 2 = 40

Bond price = ($100 / (1 + 0.12)¹) + ($100 / (1 + 0.12)²) + ... + ($100 + $1,000) / (1 + 0.12)⁴⁰

Bond price = $435.42

At 10% yield to maturity

Coupon payment = 0.10 x $1,000 = $100

n = 20 x 2 = 40

Bond price = ($100 / (1 + 0.10)¹) + ($100 / (1 + 0.10)²) + ... + ($100 + $1,000) / (1 + 0.10)⁴⁰

Bond price = $500.00

At 8% yield to maturity

Coupon payment = 0.10 x $1,000 = $100

n = 20 x 2 = 40

Bond price = ($100 / (1 + 0.08)¹) + ($100 / (1 + 0.08)²) + ... + ($100 + $1,000) / (1 + 0.08)⁴⁰

Bond price = $607.28

At 6% yield to maturity

Coupon payment = 0.10 x $1,000 = $100

n = 20 x 2 = 40

Bond price = ($100 / (1 + 0.06)¹) + ($100 / (1 + 0.06)²) + ... + ($100 + $1,000) / (1 + 0.06)⁴⁰

Bond price = $748.65

To calculate the monthly payment and balance of the loan from the bank, we can use the formula for the monthly payment of an amortizing loan

P = (r × A) / (1 - (1 + r)⁻ⁿ)

where P is the monthly payment, r is the monthly interest rate (which is the annual interest rate divided by 12), A is the loan amount, and n is the total number of months in the loan.

First, we need to calculate the values of r, A, and n

r = 0.08 / 12 = 0.00667 (monthly interest rate)

A = $50,000,000 (loan amount)

n = 5 years × 12 months/year = 60 months (total number of months in the loan)

Now, we can plug these values into the formula to calculate the monthly payment

P = (0.00667 × $50,000,000) / (1 - (1 + 0.00667)⁻⁶⁰)

P ≈ $1,029,299.29

Therefore, the monthly payment on the loan is approximately $1,029,299.29.

To find the balance at the end of 28 months, we can use the formula for the remaining balance of an amortizing loan

B = (P * (1 - (1 + r)⁻ⁿ')) / r

where B is the remaining balance, r is the monthly interest rate, P is the monthly payment, and n' is the number of months remaining in the loan (which is equal to the total number of months minus the number of months already paid).

After 28 months, the number of months remaining in the loan is

n' = 60 - 28 = 32

We can now plug the values of P, r, and n' into the formula to find the balance

B = ($1,029,299.29 × (1 - (1 + 0.00667)⁻³²)) / 0.00667

B ≈ $41,097,019.67

Therefore, the balance at the end of 28 months is approximately $41,097,019.67.

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The wheel will make one complete revolution around the circle after travelling a distance of 62.8 inches.

The distance that the wheel travels around the circle once is equal to the circumference of the circle.

The formula for circumference of a circle is given as;

D = 2πr

where;

The radius of the circle = 10 inches

The circumference of the circle is calculated as follows;

D = 2 x 3.14 x 10

D = 62.8 inches

Thus, the circumference of the circle is determined as 62.8 inches.

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Answer:

Step-by-step explanation:

(4 – 5) – (13 – 18 + 2).

= -1-(13+2-18).

= -1-(15-18).

= -1-(-3).

= -1+3.

= 2.

Answer:

Step-by-step explanation:

To combine the terms 12a + 26b - 4b - 16a, you first simplify the like terms. Add the coefficients of a terms and add the coefficients of b terms separately. You get 12a - 16a + 26b - 4b which results in -4a + 22b. Therefore, the correct answer is (c) -4a + 22b.

The correct equation to find that can be used to find the width of the feed  trough is (b) 4620 = 8w×w×6, and the width of the "feed-trough"  is 9.8 inches wide.

The "Volume" of "rectangular-prism" can be found using formula V = l×w×h, where V is = volume, l is = length, w is = width, and h is = height.

We know that the volume of the "feed-trough" is 4,620 cubic inches, and

The height is = 6 inches. Let us denote the width as "w" and the length as "8w" (because trough's length is 8 times the width),

So, the equation for the volume of the feed trough is:

⇒ 4620 = (8w) × (w) × (6),

So, the correct equation to find the width is Option (b) 4620 = (8w) × (w) × (6).

Simplifying further,

We get,

⇒ w² = 96.25,

⇒ w ≈ 9.8 inches (rounded to the nearest tenth)

Therefore, the width of the feed trough will be approximately 9.8 inches.

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The number of coupon codes that can be generated is given as follows:

247,808 coupon codes.

The Fundamental Counting Theorem states that if there are m ways to do one thing and n ways to do another, then there are m x n ways to do both.

This can be extended to more than two events, where the number of ways to do all the events is the product of the number of ways to do each individual event, according to the equation presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

The codes are composed as follows:

Thus the total number of codes is obtained as follows:

N = 22² x 8³

N = 247,808 coupon codes.

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Yes, this collection is a set because it has a well-defined and finite number of elements, namely {2, 3, 5, 7}.

(ii) The method of describing this collection is the roster method or tabular method, where the elements of the set are listed within curly braces and separated by commas.

(iii) {2, 3, 5, 7}

In mathematics, a set is a collection of conspicuous objects or elements, taken as an object in its own right. These elements can either be numbers, letters, symbols, or even other sets. A set is defined by listing its elements or by specifying a property that its elements satisfy.

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