Marta simplified this expression.
4 logs x+logs 2x log, 3x
In which step did she incorrectly apply a property of logarithms?

The image vertices of P' if the preimage is rotated 90° counter clockwise is P'(-5,1)

An image vertex refers to a point in the plane that results from applying a transformation to a given vertex. A transformation is a mathematical operation that changes the position, size, or shape of a figure.

The image vertices of P' when the preimage polygon PSRT is rotated 90° counter clockwise can be found by applying a transformation to each vertex of the polygon. This transformation involves switching the x- and y-coordinates of each vertex and negating the new y-coordinate.

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

For the vertex P(1, 5), we can apply this transformation to get the image vertex P':

P' = (-5, 1)

Similarly, we can apply the transformation to the other vertices of the polygon:

S(1, 0) -> S'(0, 1)

R(−2, −3) -> R'(3, -2)

T(−4, 2) -> T'(2, 4)

Therefore, the image vertices of P' are P'(-5, 1), S'(0, 1), R'(3, -2), and T'(2, 4).

This means that the rotated polygon has the vertices P', S', R', and T', which form a new polygon that is 90° counter clockwise rotated from the original polygon PSRT.

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Answer: 10.95

Step-by-step explanation:

To identify the pattern, we need to look at the differences between the given numbers.

The difference between 10.21 and 9.47 is 0.74.

The difference between 10.57 and 10.21 is 0.36.

The difference between 12.15 and 10.57 is 1.58.

We can see that the differences between the numbers are not constant. However, the differences themselves follow a pattern: they are increasing by 0.38 each time.

So, to find the missing number, we can add 0.38 to 10.57:

10.57 + 0.38 = 10.95

Therefore, the missing number is 10.95.

Answer:

378

Step-by-step explanation:

[tex]\frac{14}{x}[/tex] = [tex]\frac{1}{27}[/tex]  Cross multiply and solve for x

x = (14)(27)

x = 378

Helping in the name of Jesus.

the length of AC is 5. we can get the answer with the help of  Pythagorean theorem in triangle ABC.

what is Pythagorean theorem ?

The Pythagorean theorem is a fundamental concept in geometry that relates to the relationship between the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).

In the given question,

In triangle ABC, we have:

angle ABC = 90 degrees (given)

AB = 4 (given)

AD = 3 (given)

Let's call the length of AC "x". We want to find the value of x.

From the given information, we know that BD is the altitude of triangle ABC from vertex B to the side AC. Therefore, the length of BD is equal to the length of AD, which is 3.

Using the Pythagorean theorem in triangle ABD, we can find the length of the hypotenuse AB:

AB² = AD² + BD²

AB² = 3² + 4²

AB² = 9 + 16

AB² = 25

AB = 5

Now, we can use the Pythagorean theorem in triangle ABC to find the length of AC:

AC² = AB² + BC²

AC² = 5² + BC²

But we don't know the length of BC. However, we can use the fact that triangle ABD and triangle ABC are similar. This is because angle ABD is a right angle (from the definition of altitude BD), and angle ABC is a right angle (given), so angle ABD and angle ABC are both right angles. Therefore, the two triangles share angle A and are similar by the AA (angle-angle) similarity criterion.

Since triangles ABD and ABC are similar, we have:

AB/AD = AC/BD

Substituting the known values, we get:

5/3 = x/3

Solving for x, we get:

x = 5

Therefore, the length of AC is 5.

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The measure of the angle x is 41.41° in the given triangle.

Triangle is a clοsed twο-dimensiοnal shape. It is a three-sided pοlygοn. All sides are made οf straight lines. The pοint where twο straight lines jοin is the vertex. Hence, the triangle has three vertices. Each vertex fοrms an angle.

Given that cos θ = side adjacent to angle x/hypotensive

Here, side adjacent to angle x = 6

hypotensive = 8

cos x = 6/8

x = arccos 6/8

x = 41.41°

Thus, the measure of the angle x is 41.41° in the given triangle.

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To estimate the number of square feet of carpeting needed for a room with dimensions x, y, w, z, and n, we can use the formula A = xy + w[z(2n - 1) + 2n].

What are the dimensions?

The given formula for estimating the number of square feet, A, of carpeting needed for a room x feet by y feet containing a stairway w feet by z feet with n stairs is:

A = xy + w[z(2n - 1) + 2n]

Let's break down this formula to understand the different parts:

The term w[z(2n - 1) + 2n] represents the additional area needed to cover the stairway. We add this to the area of the main part of the room, xy, to get the total area of carpeting needed, A.

So to estimate the number of square feet of carpeting needed for a room with dimensions x, y, w, z, and n, we can use the formula A = xy + w[z(2n - 1) + 2n].

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Step-by-step explanation:

See image.....as these are definitions, it is self-explanatory:

Answer:

7x = 126 is the equation

She sold 18 t-shirts.

Step-by-step explanation:

Since she sold t-shirts for 7 each, we need to find how many T-shirts she sold. 126 dollars is how much she made, so we need to divide.

126/7 = 18.

The equation would be:

7x = 126.

The loan's simple interest rate is 5.232% per quarter.

What is the formula for the future value of a loan with simple interest?

A = P(1 + rt)

where A is the future value, P is the principal, r is the simple interest rate per period, and t is the number of periods.

In this case, we have:

P = 4500

A = 4561.88

t = 3 months = 3/12 year =0.25 year

Substituting these values into the formula,

[tex]4561.88 = 4500(1 + 0.25r)[/tex]

Dividing both sides by 4500,

[tex]1.01308 = 1 + 0.25r[/tex]

Subtracting 1 from both sides,

[tex]0.01308 = 0.25r[/tex]

Dividing both sides by 0.25,

[tex]r = 0.05232 \: or \: 5.232\%[/tex]

Therefore, the loan's simple interest rate is 5.232% per quarter.

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Answer:

68.01

Step-by-step explanation:

let the unknown be y

opposite is 45

adjacent is 51

hypotenuse is ?

=y^2=45^2+51^2

y^2=2025+2601

y^2=4626

y=68.01

The number of books that each kid in Mr. Johnson's sixth-grade class read during the summer was recorded. 5 books have been read on average by Mr. Johnson's students.

There are six students in Mr. Johnson's sixth-grade class, and their number of books read is 0, 2, 4, 6, 8, and 10.

To find the median, we need to find the middle value in the list of numbers. If there is an odd number of values, then the median is the middle number. If there is an even number of values, then the median is the average of the two middle numbers.

In this case, there are six numbers, which is an even number, so we need to find the average of the two middle numbers, which are 4 and 6.

The average of 4 and 6 is (4 + 6)/2 = 5.

Therefore, the median number of books read by Mr. Johnson's students is 5.

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Answer:

There are 26 letters in the alphabet, and 9 digits from 1 to 9.

The probability of choosing X as the letter is 1/26, since there is only one X in the alphabet.

The probability of choosing a prime number digit is 4/9, since there are 4 prime numbers among the digits 1-9 (2, 3, 5, and 7) and 9 total digits.

Therefore, the probability of choosing X followed by a prime number digit is:

P(X and prime) = P(X) × P(prime) = (1/26) × (4/9) = 4/234

So the probability of getting X followed by a prime number is 4/234, or approximately 0.017 or 1.7%.

Using calculations based on a perpetual inventory system, the inventory balance that Altira Corporation would report in its August 31, 2024, balance sheet and the cost of goods sold it would report in the income statement, using the Average Cost Method are as follows:

The average cost method or the weighted-average cost method under the perpetual inventory system adds up all the cost of goods available for sale at each sales point and divides by the number of units available for sale in determining the average cost to be applied to the cost of goods sold.

Principally, the perpetual inventory system ensures that each inventory movement is separately recognized and the cost of goods sold determined, unlike the periodic inventory system.

August 14 for Sales of 6,000 units:

Average cost per unit = $5.46 ($54,600 ÷ 10,000)

Cost of goods sold  = $32,760 ($5.46 x 6,000)

August 25 for Sales of 7,000 units:

Average cost per unit = $5.54 ($21,840 + $33,600 ÷ 10,000)

Cost of goods sold  = $38,780 ($5.54 x 7,000)

Total cost of goods sold = $71,540 ($32,760 + $38,780)

Total cost of goods available for sale = $111,400 ($10,600 + $44,000 + $33,600 + $23,200)

Ending Inventory = $39,860 ($111,400 - $71,540)

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The selling price of the DVD player after a 15% discount is applied can be found as follows:

Discount = 15% of the marked price = (15/100)*$320 = $48

Selling price = Marked price - Discount = $320 - $48 = $272

Therefore, the actual selling price of the DVD player after a 15% discount is $272.

Answer:

$272

Step-by-step explanation:

Formula:
Selling price = Marked price - Discount

We first find the discount by taking 15% off of $320 which is $48

We then insert the Maked price and the Discount into the formula which is:

Selling price = $320 - $48
Selling price = $272

We can use the formula for the monthly payment of a loan to calculate the amount we need to pay each month:

M = (P * r * (1+r)^n) / ((1+r)^n - 1)

Where:

M = the monthly payment

P = the principal (the amount borrowed)

r = the monthly interest rate (which is the annual interest rate divided by 12)

n = the total number of months in the loan term (which is the number of years multiplied by 12)

Plugging in the given values, we get:

P = $3825

r = 15% / 12 = 0.0125

n = 4 years * 12 = 48 months

M = ($3825 * 0.0125 * (1+0.0125)^48) / ((1+0.0125)^48 - 1)

M ≈ $94.87

Therefore, the monthly payment will be approximately $94.87.

The intersection (2,2) (2,4) (8,4) (8,2) is  (5,3).

On the coordinate plane, the four points that are given together form a rectangle. We must first locate the midway of both diagonals in order to determine where the diagonals will connect.

The midpoint of the diagonal that passes through the points (2,2) and (8,4) is ((2+8)/2, (2+4)/2). (5,3).

The midpoint of the diagonal that passes through the points (2,4) and (8,2) is ((2+8)/2, (4+2)/2). (5,3).

Consequently, the diagonals' point of intersection is (5,3).

Due to the fact that a rectangle's two diagonals meet here in the middle, this location also serves as the rectangle's centre.

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Answer:

The equation that represents the situation is: A = 200(1-0.025)^5 where A is the amount remaining after 5 years, 200 is the starting value, 0.025 is the decimal equivalent of the decay rate of 2.5%, and 5 is the number of years.

Answer:

Step-by-step explanation:

slope of a=3

slope of b=(4-2)/(1-0)=2/1=2

slope of c is negative

1. a has the steepest slope.

2. a has the largest y-intercept.

3. c is decreasing.

4.b after 3 weeks,you have 8 as a solution.

The answer is failed to estimate number of rock songs on his MP3 player.

What is a MP3 player and how does it work?

It's a compressed digital audio file. A player stores these files on a memory chip so that you can play it back at your leisure. Contains a miniature hard disk drive, which can store huge quantities of data. MP3s usually contain music, but the format is also used for general audio files such as audiobooks and podcasts.

The statements that are true about Josiah's solution are:

He set up a proportion correctly using the information given.

He correctly solved for x, the number of rock songs on his MP3 player.

Therefore, he did not find the average of the number of rock songs in the sample to estimate the number of rock songs on his MP3 player.

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Answer:

1, the mid point

The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) can be found using the midpoint formula:

midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Substituting the given endpoints (4, -4) and (0, 9), we get:

midpoint = ((4 + 0) / 2, (-4 + 9) / 2) = (2, 2.5)

Therefore, the midpoint of the line segment with endpoints (4, -4) and (0, 9) is (2, 2.5).

2,  the slope

The slope of the line passing through the points (4, -4) and (0, 9) can be found using the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Substituting the given coordinates, we get:

slope = (9 - (-4)) / (0 - 4) = 13 / (-4) = -3.25

Therefore, the slope of the line is -3.25.

3, the length

The length of the line passing through the points (4, -4) and (0, 9) can be found using the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the given coordinates, we get:

distance = sqrt((0 - 4)^2 + (9 - (-4))^2) = sqrt(16 + 169) = sqrt(185)

Therefore, the length of the line is sqrt(185).

4,  the equation

The equation of the line passing through the points (4, -4) and (0, 9) can be found using the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is one of the points.

Substituting the given slope and one of the points, we get:

y - (-4) = -3.25(x - 4)

Simplifying, we get:

y + 4 = -3.25x + 13

y = -3.25x + 9

Therefore, the equation of the line passing through the points (4, -4) and (0, 9) is y = -3.25x + 9.

A)  64π inches² B) 94.15π inches² C) the pizza from Tallahassee is larger. D)  The scale factor relationship between the pizzas is:  1.462

Part A: The diameter of the pizza from Tallahassee is 16 inches, so the radius is 8 inches. The area of the pizza is:

A = πr²

= π(8)²

= 64π inches²

Part B: The diameter of the pizza from Jaco, Costa Rica is 27.8 centimeters. Converting this to inches, we get:

27.8 cm ÷ 2.54 cm/inch = 10.94 inches

The radius is 5.47 inches, so the area of the pizza is:

A = πr²

= π(5.47)²

= 94.15π inches²

Part C: Converting the area of the pizza from Tallahassee to square centimeters, we get:

64π inches² × (2.54 cm/inch)² = 1648.89 centimeters²

The area of the pizza from Jaco, Costa Rica is 94.15π inches² × (2.54 cm/inch)² = 594.85π centimeters². Therefore, the pizza from Tallahassee is larger.

Part D: The scale factor relationship between the pizzas is:

16 inches ÷ 27.8 cm × 2.54 cm/inch = 1.462

This means that the diameter of the pizza from Tallahassee is 1.462 times larger than the diameter of the pizza from Jaco, Costa Rica. Since area is proportional to the square of the diameter (or radius), the area of the pizza from Tallahassee is (1.462)² = 2.14 times larger than the area of the pizza from Jaco, Costa Rica.

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The circumference οf the οbject is apprοximately 37.68mm οr 37.71mm, depending οn whether we use 3.14 οr {22}/{7} fοr π.

The measurement οf the circle's bοundaries is called as the circumference οr perimeter οf the circle. whereas the circumference οf a circle determines the space it οccupies. The circumference οf a circle is its length when it is οpened up and drawn as a straight line.

Units like cm οr unit m are typically used tο measure it. The circle's radius is cοnsidered while calculating the circumference οf the circle using the fοrmula. As a result, in οrder tο calculate the circle's perimeter, we must knοw the radius οr diameter value.

The fοrmula fοr the circumference οf a circle is:

C = 2πr

where C is the circumference, π is pi (apprοximately equal tο 3.14 οr {22}/{7}), and r is the radius οf the circle.

In this case, the radius οf the οbject is 6mm. Therefοre, we can plug this value intο the fοrmula and use either 3.14 οr {22}/{7} fοr π:

C = 2 × 3.14 × 6mm

C = 37.68mm (rοunded tο twο decimal places)

C = 2 × ({22}/{7}) × 6mm

C = 37.71mm (rοunded tο twο decimal places)

Therefοre, the circumference οf the οbject is apprοximately 37.68mm οr 37.71mm, depending οn whether we use 3.14 οr {22}/{7} fοr π.

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The circumference οf the οbject is apprοximately 37.68mm οr 37.71mm, depending οn whether we use 3.14 οr {22}/{7} fοr π.

The measurement οf the circle's bοundaries is called as the circumference οr perimeter οf the circle. whereas the circumference οf a circle determines the space it οccupies. The circumference οf a circle is its length when it is οpened up and drawn as a straight line.

Units like cm οr unit m are typically used tο measure it. The circle's radius is cοnsidered while calculating the circumference οf the circle using the fοrmula. As a result, in οrder tο calculate the circle's perimeter, we must knοw the radius οr diameter value.

The fοrmula fοr the circumference οf a circle is:

C = 2πr

where C is the circumference, π is pi (apprοximately equal tο 3.14 οr {22}/{7}), and r is the radius οf the circle.

In this case, the radius οf the οbject is 6mm. Therefοre, we can plug this value intο the fοrmula and use either 3.14 οr {22}/{7} fοr π:

C = 2 × 3.14 × 6mm

C = 37.68mm (rοunded tο twο decimal places)

C = 2 × ({22}/{7}) × 6mm

C = 37.71mm (rοunded tο twο decimal places)

Therefοre, the circumference οf the οbject is apprοximately 37.68mm οr 37.71mm, depending οn whether we use 3.14 οr {22}/{7} fοr π.

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Complete question:

Find the circumference of the object which has a radius 6mm. Use 3.14 or {22}{7}.

Answer:

d= 90 Degrees

e= 97 Degrees

f = 83

Answer:

Step-by-step explanation:

To find:-

Answer:-

We can see that angles e and 97° are vertically opposite angles. So they will be equal as vertically opposite angles are equal .

Hence here ,

→ e = 97°

Secondly e and f form linear pair , and the sum of linear pair is 180° . Hence here ,

→ e + f = 180°

→ 97° + f = 180°

→ f = (180-97)°

→ f = 83°

Same goes with d and 90° . They both form linear pair. So that ,

→ 90° + d = 180°

→ d = 180°-90°

→ d = 90°

These are the required values of the unknown angles.

Answer:

the final factored form of the function is:

f(x) = 6(x+1)^2(x-3)(x-1)

Step-by-step explanation:

To write the function in factored form, we need to use the zeros and their multiplicities.

From the given zeros, we can write:

x = -1 (multiplicity 2) means (x+1)(x+1) = (x+1)^2 = 0

x = 3 (multiplicity 1) means (x-3) = 0

x = 1 (multiplicity 1) means (x-1) = 0

So the factored form of the function is:

f(x) = a(x+1)^2(x-3)(x-1)

To find the value of "a" and satisfy the condition that the function goes through the point (2,-18), we can substitute the given point into the function:

-18 = a(2+1)^2(2-3)(2-1)

-18 = a(-3)

Solving for "a", we get:

a = 6

So the final factored form of the function is:

f(x) = 6(x+1)^2(x-3)(x-1)

Answer: 8c3 = 56

the rest of the equation;
P(3) = 56 * (0.45)^3 * (0.55)^5

P(3) = 56 * 0.091125 * 0.05031737

P(3) = 0.257

To express this probability as a percentage, we multiply by 100:

P(3) = 25.7%

25.7% is the final answer (not 8c3)

The measure of angle D is 100°

A triangle is a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees. It means that the sum of the interior angles of a triangle is equal to 180°.

Since the the sum of angle in a triangle is 180°, then to get the value of angle D will subtract the sum of the known angles from 180.

Therefore,

angle D = 180-( 40+40)

= 180-80

= 100°

therefore the measure of angle D Is 180°

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Answer:

∠A=125° and ∠B=35°

Step-by-step explanation:

We know that, by angle sum property of triangles,

∠A +∠B+∠C=180°

⇒​ (6x−1)° ​+20°  +(x + 14)°=180°

⇒​ 6x−1 ​+20 +x + 14=180 [Open parenthesis]

⇒7x+33=180

⇒7x=180-33  [Subtracting 33  from both sides]

⇒7x=147  

⇒x=21  [Divide 7 from both sides]

Now substitute value of x in the expressions of ∠A and ∠B.

Therefore, ∠A=(6(21)-1)°=(126-1)°=125°

∠B=(21+14)°=35°

Step-by-step explanation:

let the third vertex=C

180-86.2=93.8°

angle near the satellite=180-(83.9+93.8)=180-177.7°=2.3°

angles of triangle are 83.9°,93.8°,2.3°

by sine formula

[tex]\frac{AC}{Sin~93.8} =\frac{AB}{Sin 2.3} \\\frac{AC}{Sin(180-93.8)} =\frac{68}{Sin~2.3} \\\frac{AC}{Sin~86.2} =\frac{68}{Sin~2.3} \\AC=\frac{Sin~86.2}{Sin~2.3} \times~68\\AC \approx 1690.69\\AC\approx1691~mile[/tex]

The building is 89 m tall.

What is proportional?

A comparison of two numbers  is called a proportion. Two sets of supplied numbers are said to be directly proportional to one another in terms of proportion if they increase or decrease in the same ratio between them.

height of pole : 3.2 m

shadow of pole : 1.59 m

shadow of building : 44.25 m

let the height of building : x m

Now, according to the question:

height of pole/shadow of pole =  height of building/shadow of building

Putting values into the equation.

we get, 3.2 / 1.59 = x / 44.25

3.2 × 44.25 = 1.59x

141.6 = 1.59x

∴ x = 141.6/1.59

     = 89 m

hence, height of the building is 89 m.

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