Triangle UVW is drawn with vertices at U(−1, 1), V(0, −4), W(−4, −1). Determine the coordinates of the vertices for the image, triangle U′V′W′, if the preimage is rotated 90° clockwise.

U′(1, −1), V′(0, 4), W′(4, 1)
U′(−1, −1), V′(−4, 0), W′(1, 4)
U′(1, 1), V′(−4, 0), W′(−1, 4)
U′(−1, 1), V′(0, −4), W′(−4, −1)

Answer: 40

Step-by-step explanation:

The sides of the rectangle should be in improper fractions, to calculate the area.

When a side has a measurement that is a mixed number, it's recommended to convert it to an improper fraction before using it in the formula for area.

To convert a mixed number to an improper fraction, you multiply the whole number by the denominator of the fraction part and add the numerator.

Then, you put the result over the original denominator.

Once you have the sides of the rectangle as improper fractions, you can proceed to calculate the area using the formula: area = length x width.

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The value of each angle 6x + 7 and 4x + 3 will be 55° and 35°, respectively.

Given that:

Angles, ∠1 = 6x + 7 and ∠2 = 4x + 3

Two angles are said to be complementary angles if their sum is 90 degrees.

The equation is given as,

∠1 + ∠2 = 90°

6x + 7 + 4x + 3 = 90°

10x + 10 = 90°

10x = 80°

x = 8

The value of each angle is calculated as,

∠1 = 6 * 8 + 7

∠1 = 55°

∠2 = 4 * 8 + 3

∠2 = 35°

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The remainder when dividing

[tex](10m^8 + 4m^6 + 10m^5) by (2m^2 + 5m^6 + 4m^4 + 10m^3)[/tex] is

[tex]-25m^{12} - 20m^{10} - 50m^9 + 4m^6 + 10m^5.[/tex]

To find the remainder when dividing

[tex](10m^8 + 4m^6 + 10m^5) by (2m^2 + 5m^6 + 4m^4 + 10m^3),[/tex] we can use polynomial long division.

The dividend is[tex](10m^8 + 4m^6 + 10m^5)[/tex] and the divisor is [tex](2m^2 + 5m^6 + 4m^4 + 10m^3).[/tex]

Starting with the highest degree term, we divide ([tex]10m^8[/tex]) by ([tex]2m^2[/tex]) which gives us [tex]5m^6[/tex].

Next, we multiply the entire divisor [tex](2m^2 + 5m^6 + 4m^4 + 10m^3)[/tex] by [tex]5m^6[/tex], which gives us ([tex]10m^8 + 25m^{12} + 20m^{10} + 50m^9[/tex]).

We then subtract this product from the original dividend:

[tex](10m^8 + 4m^6 + 10m^5) - (10m^8 + 25m^{12} + 20m^{10} + 50m^9)[/tex] =[tex]-25m^{12} - 20m^{10} - 50m^9 + 4m^6 + 10m^5.[/tex]

We repeat the process with the new dividend ([tex]-25m^{12} - 20m^{10} - 50m^9 + 4m^6 + 10m^5[/tex]) and the divisor ([tex]2m^2 + 5m^6 + 4m^4 + 10m^3[/tex]).

Continuing the long division process, we eventually find the remainder to be: [tex]-25m^{12} - 20m^{10} - 50m^9 + 4m^6 + 10m^5.[/tex]

Therefore, the remainder when dividing ([tex]10m^8 + 4m^6 + 10m^5[/tex]) by ([tex]2m^2 + 5m^6 + 4m^4 + 10m^3[/tex]) is [tex]-25m^{12} - 20m^{10} - 50m^9 + 4m^6 + 10m^5[/tex].

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Note the full question is:

Divide. (10m8 + 4m6 + 10m5) ÷ 2m2 5m6 + 4m4 + 10m3 5m6 + 2m4 + 10m5 5m6 + 2m4 + 5m3 5m8 + 2m6 + 5m5

What is the reminder

After using Gauss-Jordon elimination method, the solution for the system of equation is as follows;

[tex]\left[\begin{array}{cccc}1&0&0&-1\\0&1&0&-3\\0&0&1&-2\end{array}\right][/tex]

To solve the system of equation, its needs us to use the Gauss-Jordon elimination method. Therefore, the matrix

- 5  7  7  -30

1  -4   4    3

2   -4   6   -2  will be reduced to its echelon form as follows;

 R₁ ÷ 5                                   R₂ - R₁                       R₃ - 2× R₁

1  −1.4 −1.4   6                   1  −1.4 −1.4   6                1  −1.4 −1.4   6        

1   −4    4    3                    0  2.6  5.4  -3                0  2.6  5.4  -3

2 −4    6  −2                     2 −4    6  −2                  0  −1.2  8.8 −14

   R₂  ÷ -2.6                          R₃ - 1.2 R₂

1    −1.4    −1.4     6                1    −1.4    −1.4     6

0     1    -2.077  1.154            0     1    -2.077  1.154

0  −1.2     8.8    −14              0    0      1         -2

  R₁ - 1.4R₃                                 R₂ - 2.077R₃                 R₁ - 1.4R₂

1  -1.4  0  3.2                              1  -1.4  0  3.2               1   0    0   -1

0   1  -2.077  1.154                     0   1     0   -3               0   1     0   -3

0  0   1  -2                                  0   0    1    -2               0   0    1    -2          

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The solution to the equation is x = 28/9

Given data ,

To solve the equation 3x/4 = 7/3, you can follow these algebraic steps:

Step 1 :
Multiply both sides of the equation by 4 to eliminate the fraction in the denominator of the left side:

(4) (3x/4) = (4) (7/3)

3x = (4/1) (7/3)

Step 2:
Simplify the right side of the equation:

3x = 28/3

Step 3 :
Divide both sides of the equation by 3 to isolate x:

(1/3) (3x) = (1/3)(28/3)

x = (28/3) / 3

Step 4 :

Simplify the right side of the equation:

x = 28/9

Hence , the solution to the equation 3x/4 = 7/3 is x = 28/9

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The solution to all parts are shown below.

a) For a rectangle with a perimeter of 12 units, the dimensions that give the greatest area are 3 units by 3 units.

For a perimeter of 13 units, the dimensions are 3 units by 3.5 units.

For a perimeter of 14 units, the dimensions are 3.5 units by 3.5 units.

For a perimeter of 15 units, the dimensions are 3.5 units by 4 units.

For a perimeter of 16 units, the dimensions are 4 units by 4 units.

b) For a rectangle with a perimeter of 12 units, the dimensions that give the least area are 1 unit by 5 units.

For a perimeter of 13 units, the dimensions are 1 unit by 6 units.

For a perimeter of 14 units, the dimensions are 2 units by 5 units.

For a perimeter of 15 units, the dimensions are 2 units by 6 units.

For a perimeter of 16 units, the dimensions are 2 units by 7 units.

6. One possible figure made from square tiles where adding an additional tile decreases the perimeter is a "U" shape.

If you arrange 9 square tiles in the shape of a "U", the perimeter is 12 units. If you add another tile to the middle of the "U", the perimeter will decrease to 10 units.

7. Perimeter is a 1-dimensional measure because it only involves adding up the lengths of the sides of a shape. The student's claim that perimeter is a 2-dimensional measure is incorrect.

8. For a square, equilateral triangle, and circle each with a perimeter of 12 cm, the circle has the greatest area and the equilateral triangle has the least area.

To see this, we can use the formulas for the perimeter and area of each shape:

Its area is (3 cm)² = 9 cm².

Its area can be calculated using the formula A = (√(3)/4) x s², where s is the side length of the triangle.

Thus, the area is (√(3)/4) x (4 cm)² = 4sqrt(3) cm², which is approximately 6.9 cm².

Its radius can be calculated using the formula C = 2πr, where C is the circumference and r is the radius of the circle.

Thus, r = 6/(2π) cm, which is approximately 0.955 cm.

The area of the circle is πr², which is approximately 2.87 cm².

Therefore, the circle has the greatest area, followed by the square, and the equilateral triangle has the least area.

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Answer:

The total cost of the two toys before the discount is VND 45,000 + VND 25,000 = VND 70,000.

Step-by-step explanation:

The discount is 10% of the total cost, which is 0.1 x VND 70,000 = VND 7,000.

Therefore, the final cost after the discount is VND 70,000 - VND 7,000 = VND 63,000.

Nam will have to pay VND 63,000 to buy the two toys after the discount.

Answer:

To calculate the length of BC in the triangle ABC, we can use the trigonometric functions sine and cosine.

Given that ∠CAB = 90° and ∠ABC = 58°, we can determine that ∠BCA = 180° - 90° - 58° = 32°.

Using the sine function, we can find the length of BC:

sin(∠BCA) = BC / AB

Rearranging the formula, we have:

BC = AB * sin(∠BCA)

Substituting the given values:

BC = 9.3 * sin(32°)

Using a calculator or trigonometric table, we find:

BC ≈ 9.3 * 0.529 = 4.917

Rounding to three significant figures (SF), the length of BC is approximately 4.92 units.

Step-by-step explanation:

Step-by-step explanation:

If side 1 and side 2 are LEGS of the triangle, then hypotenuse is found by

hyp^2 = 9^2 + 3^2     using pythagorean theorem

hyp^2 = 90

hyp = sqrt 90  = 3 sqt 10 =9.5 units

If hyp is 9   and  3 is one leg:

9^2 = 3^2 + L^2

L = 6 sqrt 2 =8.5 units

Answer:

Step-by-step explanation:

If we know that 2/5 of the number is 14, 5/5 must be the answer Paul is thinking of.

= (14/2) x 5 <---- This is 1/5 of the number

= 35

∴, the number Paul is thinking of if 35

Answer:

14

Step-by-step explanation:

used a calculator to check the answer

The matrices after the row operations are given as follows:

a) [tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\4&10&-12&-8\end{array}\right][/tex]

b) [tex]\left[\begin{array}{cccc}2&5&-6&-4\\6&5&-1&-3\\-6&-5&-2&-3\end{array}\right][/tex]

The matrix in the context of this problem is defined as follows:

[tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\2&5&-6&-4\end{array}\right][/tex]

When we multiply a matrix row by a constant, each element of the row is multiplied by the constant.

Hence the resulting matrix after we multiply row 3 by 2 is given as follows:

[tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\4&10&-12&-8\end{array}\right][/tex]

We can also exchange rows of the matrix, hence the resulting matrix after rows 1 and 3 are exchanged is given as follows:

[tex]\left[\begin{array}{cccc}2&5&-6&-4\\6&5&-1&-3\\-6&-5&-2&-3\end{array}\right][/tex]

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Answer:

can you be more clear

Step-by-step explanation:

what exactly does question need

Answer:36000

Step-by-step explanation:

He saves 36000 dollars

Answer:

I’m sorry but I don’t see any sentence below. Could you please provide me with the sentence?

Answer:

50%.

Step-by-step explanation:

If the die is perfectly balanced, the probability of rolling an odd number is 3 out of 6, or 50%.

The amount of fluid ounces of water the water bottle can hold is 48 fluid ounces.

Annabel's water bottle holds 6 cups of water.  Therefore, the amount in fluid ounces the bottle water can hold can be calculated as follows:

Therefore,

1 cup = 8 fluid ounces

6 cups = ?

cross multiply

Hence,

number of fluid ounces of water the water bottle can hold = 8 × 6

number of fluid ounces of water the water bottle can hold = 48 fluid ounces.

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The requried, predicted percentage of U.S. households with an Internet subscription in 2020 is approximately 88.3%.

To find the number of subscriptions in the year 2020, we need to find the value of y when x = 10 (since x is the number of years after 2010).

Substituting x = 10 into the equation y = 1.56x + 72.7, we get:

y = 1.56(10) + 72.7

y = 15.6 + 72.7

y = 88.3

Therefore, the predicted percentage of U.S. households with an Internet subscription in 2020 is approximately 88.3%.

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Answer: 0.68

Step-by-step explanation:

Answer: what subject, and i got you.

Step-by-step explanation:

The volume of the cylinder, when expressed as a function of the height of same cylinder, is V ( h ) = 40 h ft ³.

The volume V of a cylinder is given by the formula:

V = Area of the base of the cylinder x height of the cylinder

Given that the area of the base A is 40 ft², you can substitute this into the formula to express the volume as a function of height:

V ( h )  = 40 ft ² x h

V ( h ) = 40h ft ³

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The value of w is 9.

We can use the slope formula to find the value of w.

The slope formula is:

m =[tex](y_2 - y_1) / (x_2 - x_1)[/tex]

where m is the slope of the line and [tex](x_1, y_1)[/tex]and [tex](x_2, y_2)[/tex] are two points on the line.

We know that the slope of the line is 7, and the two points on the line are (-5, -5) and (-3, w). So we can plug in these values into the slope formula and solve for w:

7 = (w - (-5)) / (-3 - (-5))

Simplifying the right-hand side, we get:

7 = (w + 5) / 2

Multiplying both sides by 2, we get:

14 = w + 5

Subtracting 5 from both sides, we get:

w = 9

Therefore, the value of w is 9.

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Answer:

12) x = 6. 13) not tangent

Step-by-step explanation:

12) x² - 5 = 31 (since they are both tangents)

x²  = 31 + 5 = 36

x = ±6

x = +6 (has to be positive since it's a length).

13) if it was tangent, angle BAC would be 90°.

that would also mean AB²  = BC² - AC²

                                            =  15² - 5²

                                            = 225 - 25

                                           = 200

AB = √200 ≠ 14.

Since the values are different, AB is not a tangent to the circle

Answer:

9180 (cm³)

Step-by-step explanation:

area of cross-section (trapezium) = 0.5 X (12 + 22) X 9

= 0.5 X 34 X 9 = 153 cm²

then multiply that by the length (60)

153 X 60 = 9180 (cm³)

(a) The leading coefficient is 4

(b) The degree is 8

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

4xy⁸

Consider an expression ax where the variable is x

The leading coefficient of the variable in the expression is a

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

The leading coefficient is 4

Consider an expression axⁿ where the variable is x

The degree of the variable in the expression is n

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

The degree is 8

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Answer:

The total number of possible outcomes for the math quiz is 16

Step-by-step explanation: