Use Pythagoras' theorem to work out the length of AD in this triangular prism. Give your answer in centimetres (cm) to 1 d. P

The distance from the point (15,-21) to the line is 5.39 units.

The equation of a line in point-slope form is:

y - y1 = m(x - x1) (x - x1)

where (x1, y1) is a point on the line and m is the slope of the line. When we are unsure of the y-intercept but are aware of the line's slope and a point on the line, we can utilise this form of the equation.

To calculate the equation of a line using the point-slope method, we must first determine the slope of the line using the following formula:

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

where the two points on the line are (x1, y1) and (x2, y2). We may enter the slope, along with one of the line's points, into the point-slope form to obtain the equation of the line.

Given that, the line has the following values f(4)=-8 and f(8)=-18.

The coordinates of the line are (4, -8) and (8, -18)

Thus, the slope of the line is:

m = y2 - y1/ x2 - x1

m = -18 + 8 / 8 - 4

m = -10/4 = -5/2

Now the slope intercept form is given as:

y - y1 = m (x - x1)

Substitute the values:

y + 8 = -5/2(x - 4)

2y + 16 = -5x + 20

2y = -5x + 20 - 16

2y = -5x + 4

The distance from the line to point is given as:

Distance = |ax + by + c| / √(a² + b²)

Substituting the values:

Distance = |-5(15) + -2(-21) + 4| √(-5² + -2²)

Distance = |-29|/ 5.38

Distance = 5.39

Hence, the distance from the point (15,-21) to the line is 5.39 units.

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Answer:

[tex]\bf a^2* (a - 0.4)(a^2 + 0.4a + 0.16)[/tex]

Step-by-step explanation:

Factorize:

 First take out the common term a².

[tex]a^5 - 0.064a^2= a^2*(a^3 - 0.064)\\\\[/tex]

Now, factorize using the identity a³ - b³

a³ - b³ = (a - b) (a²  + ab + b²)

[tex]a^2 * (a^2 - 0.064) = a^2 * (a^3 - 0.4^3)[/tex]

                          [tex]= a^2 * (a - 0.4) * (a^2 + a*0.4 + 0.4^2)\\\\=a^2 * (a - 0.4)(a^2 + 0.4a + 0.16)[/tex]

a 12 cm tall and radius of 10 cm cylinder is filled with 10 cm of water.

a) Rotational speed at which the water just touches the bottom of the cylinder:

                  We will use the formula for centripetal force for a liquid with the volume of a cylinder to obtain the rotational speed at which the water just touches the bottom of the cylinder.

         The formula for centripetal force for a liquid with the volume of a cylinder is as follows:

                   F = (ρr²πh)ω²WhereF:

   Centripetal forceρ: Densityr: Radiush : Heightω: Rotational speed Substituting the given values,

we get: F = (1000 kg/m³ × (0.1m)² × π × 0.12m)ω²F

                = 377 Nω

                = √(F/m)ω

                = √(377 N/ 10 kg)ω

                = √37.7ω = 6.14 rad/sb)

      Pressure at points A and B:

                                We will use the formula for hydrostatic pressure for a liquid to calculate the pressure at points A and B. The formula for hydrostatic pressure for a liquid is as follows:

                         P = ρgh

  Where,

           P: Pressureρ: Densityg: Acceleration due to gravity: DepthSubstituting the given values for point A,

we get P = 1000 kg/m³ × 9.8 m/s² × 0.1 mP

                = 980 Pa

        Substituting the given values for point B,

we get P = 1000 kg/m³ × 9.8 m/s² × 0.22 mP

                = 2156 Pa

      The resulting pressure at point A is 980 Pa and the resulting pressure at point B is 2156 Pa.

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The total value of both bonds is $704,367,500.

Coupon payment = [tex]\frac{Coupon rate * Par value}{2}[/tex]

Coupon payment = [tex]\frac{11 * $1,000}{2}[/tex]

Coupon payment = $55

PV = [tex]55 * [1 - (1 + 0.04)^{^-40} ] / 0.04 + $1,000 / (1 + 0.04)^40[/tex]

[tex]PV = $1,026.45[/tex]

[tex]Total value = PV * Number of bonds * Par value\\Total value = $1,026.45 * 150,000 * $1,000\\Total value = $153,967,500[/tex]

[tex]PV = \frac{Price}{(1 + r)^n}[/tex]

[tex]PV = \frac{16}{(1 +0.03)^60}\\PV = $1.72[/tex]

[tex]Total value = PV * Number of bonds * Par value\\Total value = $1.72 * 320,000 * $1,000\\Total value = $550,400,000[/tex]

Therefore, the total value of both bonds is:

[tex]Total value = Value of coupon bonds + Value of zero coupon bonds\\Total value = $153,967,500 + $550,400,000\\Total value = $704,367,500[/tex]

A coupon rate is the annual interest rate paid by a bond or other fixed-income security to its bondholders or investors. It is typically expressed as a percentage of the bond's face value, also known as its par value. For example, if a bond has a face value of $1,000 and a coupon rate of 5%, the bond will pay $50 in interest each year to its bondholders. The coupon payments are usually made semi-annually or annually, depending on the terms of the bond.

The coupon rate is set when the bond is issued and remains fixed throughout the life of the bond unless the bond issuer chooses to call the bond or the bond defaults. Coupon rates are determined by a variety of factors, including market conditions, the creditworthiness of the issuer, and the length of the bond's maturity.

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Complete Question: -

The IPO Investment Bank has the following financing outstanding,

Debt: 150,000 bonds with a coupon rate of 11 percent and a current price quote of 108; the bonds have 20 years to maturity. 320,000 zero coupon bonds with a price quote of 16 and 30 years until maturity. Both bonds have a par value of $1,000 and semiannual coupons.

Preferred stock: 240,000 shares of 9 percent preferred stock with a current price of $67, and a par value of $100.

Common stock: 3,500,000 shares of common stock; the current price is $53, and the beta of the stock is.9.

Market: The corporate tax rate is 24 percent, the market risk premium is 8 percent, and the risk-free rate is 5 percent.

What is the WACC for the company? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

The maximum possible length of the repeating section of the decimal representation of 727 1,229 is 7.

The maximum possible length of the repeating section of the decimal representation of 727 1,229 is 7. The repeating section is comprised of 729.

To calculate this, first consider the prime factorization of 727 1,229. 727 1,229 = 17 × 43 × 137.

Since 17, 43 and 137 are all prime numbers, the prime factorization will not yield a power of 10 as a factor. Therefore, the repeating section must have a length of 7 in the decimal representation of 727 1,229.  
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Answer:

Step-by-step explanation:

Let h be the height of the trapezoid.

The area of a trapezoid is given by the formula:

Area = (1/2) × (sum of parallel sides) × (height)

In this case, we know that the area is 21 cm², one base length is 5 cm, and the other base length is 9 cm. So we can write:

21 = (1/2) × (5 + 9) × h

Simplifying this equation, we get:

21 = 7h

Dividing both sides by 7, we get:

h = 3

Therefore, the height of the trapezoid is 3 cm.

Answer:

Step-by-step explanation:

Area of Trapezium is 21 cm². Parallel sides are 5 cm and 9 cm .

Shorter parallel side is 5 cm and the Longer Side is 9 cm.

As we know that formula of area of Trapezium is,

Where,

On substituting the values of area and the two parallel sides in the above formula we will get the required Height.

Substituting the values,

21 = ½ (5 + 9)h

21 = ½ × 14 × h

21 = 7 × h

h = 21/7

h = 3 cm

Therefore, Height of the Trapezium will be 3 cm respectively.

(a) The recursive formula for An is: An = (1.015)An-1 - 100.

(b) The explicit formula for An in summation notation is: An = 4000(1.015)^n - 100[1 + (1.015) + (1.015)^2 + ... + (1.015)^(n-1)].

(a) This formula says that to find the balance for month n, we take the balance for month n-1, multiply it by 1.015 (to account for the interest rate), and subtract 100 (to account for the withdrawal). This formula is consistent with the results for n=1,2,3 on the previous page.

(b) The explicit formula for An in summation notation is: An = 4000(1.015)^n - 100[1 + (1.015) + (1.015)^2 + ... + (1.015)^(n-1)].

This formula says that to find the balance for month n, we take the starting balance of 4000 multiplied by the interest rate raised to the power of n, and then subtract the sum of 100 multiplied by the geometric series (1 + r + r^2 + ... + r^(n-1)), where r = 1.015. This formula is consistent with the results for n=1,2,3 on the previous page.

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Step-by-step explanation:

Area of a square = s x s   and this equals  10 x s

 this is :  

     s^2 = 10 s    divide both sides of the equation by 's'

  s = 10   units    ( or zero....but that makes no sense)

The measure of ∠J in ΔJKL is approximately 57.5 degrees.

The measure of ∠J in ΔJKL can be found using the trigonometric function tangent, which is defined as the ratio of the opposite side to the adjacent side.

The straight line that "just touches" the plane curve at a given point is called the tangent line in geometry. It was defined by Leibniz as the line that passes through two infinitely close points on the curve.

tan(∠J) = JK/KL

tan(∠J) = 7.3/4.7

∠J = arctan(7.3/4.7)

∠J = 57.5 degrees (rounded to the nearest tenth of a degree)

Therefore, the measure of ∠J in ΔJKL is approximately 57.5 degrees.

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Answer:

The sum of the first n terms in an arithmetic sequence is (n/2)⋅(a₁+aₙ). It is called the arithmetic series formula.

Step-by-step explanation:

An arithmetic series is the sum of the terms in an arithmetic sequence with a definite number of terms. Following is a simple formula for finding the sum: Formula 1: If S nrepresents the sum of an arithmetic sequence with terms , then. This formula requires the values of the first and last terms and the number of terms.

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Consequently, the area of triangle $AMN$ is equal to $A = \frac{1}{2}bh = \frac{1}{2}(4)(2) = 4$ cm2.

The area of triangle $AMN$ in square $ABCD$ can be calculated using the formula for area of a triangle, $A = \frac{1}{2}bh$, where $b$ is the length of the base and $h$ is the height of the triangle.

Since side $BC$ has a length of 4 cm, we can determine that $N$ is located 2 cm away from point $B$ and 2 cm away from point $C$.

Similarly, we can conclude that $M$ is located 2 cm away from point $C$ and 2 cm away from point $D$.

Therefore, the base of triangle $AMN$ is equal to 4 cm, and the height of triangle $AMN$ is equal to 2 cm.

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Using the t-distribution, the 99% confidence interval for the true average number of alcoholic drinks all UF female students (over 21) have in a one week period is (3.25, 4.85).

First, we find the number of degrees of freedom, which is the sample size subtracted by 1, thus:

df = 170-1 = 169

Using the following formulas the lower and upper limits of the Interval are calculated,

n = 170

x = 4.05

s = 4.66 = 99% = 0.99

Because the population standard deviation is unknown, the Student T-distribution should be used. Yet, because the sample is huge, some books will utilise the normal distribution. I'll provide solutions for both techniques.

Error = z x s/√n

= 1.99 x 4.66/√170

Error margin ≈ 0.8

Lower limit = 4.05 - Error

= 4.05 - 0.8

= 3.25

Upper limit = 4.05 + Error

= 4.05 + 0.8

= 4.85

Therefore, the upper limit and lower limit is 3.25 and 4.85.

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An interval is a set of real numbers that contains all real numbers lying between any two numbers of the set.

For each calculation, the smallest interval in which the result, using true instead of rounded values, must lie is as follows:

(a) 1.1062+0.947 = 2.0532 ≤ true result ≤ 2.053

(b) 23.46 - 12.753 = 10.707 ≤ true result ≤ 10.708

(c) (2.747) (6.83) = 18.6181 ≤ true result ≤ 18.6182

(d) 8.473/0.064 = 132.3906 ≤ true result ≤ 132.3907

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Answer:

The answer to 1 + 1 is 2.

Very complicated problem, please mark brainliest!

Answer:

1+1 = 2

Or, 1=2-1

1=1

we know value of one is one

so,

1+1=11

Answer:

Step-by-step explanation:

I think a calculator is the only way to solve this question:

[tex]\sqrt{7} +\sqrt{3} = 2.96\\\\\sqrt{6} +\sqrt{4} = 2.54\\\\\sqrt{8} +\sqrt{2} =3.07[/tex]

So (c) is the greatest.

The characteristic of a reliable scientific poll is small sampling error. The small sampling error is a characteristic of a reliable scientific poll.

What is a scientific poll?Scientific polls are surveys that gather and evaluate people's opinions or responses to questions. These surveys are done in a scientific way, implying that pollsters use scientifically proven techniques to gather responses and analyze data.A reliable scientific poll must have a small sampling error. A sampling error is the deviation of the sample mean from the population mean due to random error. The smaller the sample size, the more likely it is that the results will be imprecise. As a result, it's essential to conduct a reliable scientific poll with a sample size that is representative of the population as a whole.The option for the correct answer to this question is; (choice a) small sampling error.

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The perimeter of the smaller triangle would be = 28.1

A triangle can be defined as a three sided polygon that has a total internal angle of 180°.

To calculate the perimeter of the triangle is to find out the scale factor that exists between the two triangles.

The formula for scale factor = original object/new object

Scale factor= 8/7 = 1.14

The perimeter of the smaller triangle = 32/1.14

= 28.1.

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Answer:

Step-by-step explanation:

The answer is true

The slope of a linear equation is an important skill to have, as it can be used to identify the rate of change of the equation, and can be used to predict future values of the equation.

An equation is an expression that states the equality of two things. It typically consists of an equal sign (=) and two expressions on either side of the equal sign that represent the same thing. Equations are used to describe relationships between different variables and can be used to solve mathematical problems. They can also be used to show the relationships between different quantities in physics and chemistry.

a)The slope of this linear equation can be determined by using the slope formula, which is rise over run. In this equation, the rise is 6, and the run is 2, so the slope is 3.

b) The slope of this linear equation can be determined by using the slope formula, which is rise over run. In this equation, the rise is 3, and the run is -7, so the slope is -3/7.

c) The slope of this linear equation can be determined by using the slope formula, which is rise over run. In this equation, the rise is 4, and the run is 6, so the slope is 2/3.

Finding slope in tables and graphs is a common mathematical skill that is used to identify the rate of change of a linear equation. This is determined by finding the change in the dependent variable (the y-axis) divided by the change in the independent variable (the x-axis). This is what is referred to as the slope of the equation. To find the slope in tables and graphs, you must look at the differences between the points on the x-axis and y-axis, and divide the change in the y-axis by the change in the x-axis. This will give you the slope of the equation. Finding the slope of a linear equation is an important skill to have, as it can be used to identify the rate of change of the equation, and can be used to predict future values of the equation.

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intersection of A and B events, P(A ∩ B) is 0. So, P(A U B) = P(A) + P(B) = 0.3 + 0.6 = 0.9Hence, P(AUB) = 0.9.

Probability of P(ANC)We know that events A, B and C are mutually exclusive.

Therefore, if A, B, and C are mutually exclusive events, then P(A U B U C) = P(A) + P(B) + P(C). Given, P(A) = 0.3,P(B) = 0.6,P(C) = 0.1

Therefore, P(A U B U C) = P(A) + P(B) + P(C) = 0.3 + 0.6 + 0.1 = 1Now, P(ANC) = 1 - P(A U B U C) = 1 - 1 = 0

Probability the intersection of A and B events, P(A ∩ B) is 0. So, P(A U B) = P(A) + P(B) = 0.3 + 0.6 = 0.9

Hence, P(AUB) = 0.9.ility of P(AUB)We know that events A, B and C are mutually exclusive.

Therefore, if A, B, and C are mutually exclusive events, then P(A U B U C) = P(A) + P(B) + P(C)

Now, we need to find P(AUB). If two events A and B are not mutually exclusive events, then the probability of their union P(A U B) can be found as follows; [tex]P(A U B) = P(A) + P(B) - P(A ∩ B)[/tex]We know that events A, B and C are mutually exclusive.

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Answer:

I'm sorry, your question is not clear. Please provide more information or context so I can better understand what you are asking.

Step-by-step explanation:

Answer:

"9 more than A" is a verbal expression.

By using this value of x in the formula we previously discovered, we can get the patio's area Patio's size is equal to x2 + 4x + 4 = ((1 + 7)/3)2 + 4((1 + 7)/3) + 4 = 4.72 square meters.

A square is a 2D shape with equal-sized sides on each side. The area would be length times width, which is equal to side  side because all the sides are equal. As a result, a square's area is side square.

Let's first find the area of the entire rectangle:

A = lw = (3x + 6)(2x + 4) = 6x² + 30x + 24

Area of patio = (x + 2)² = x² + 4x + 4

Area of herb garden = (2x + 2)(x + 4) = 2x² + 10x + 8

Area of flower garden = (3x + 4)(x + 4) = 3x² + 16x + 16

Sum of areas = x² + 4x + 4 + 2x² + 10x + 8 + 3x² + 16x + 16

= 6x² + 30x + 28

0.25(6x² + 30x + 24) = 6x² + 30x + 28

Simplifying and solving for x, we get:

1.5x² - x - 1 = 0

Using the quadratic formula, we find that:

x = (1 ± √7)/3

x = (1 + √7)/3

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The area in square meters of the patio is 850 square meters.

What is a rectangle?

A rectangle is a geometric shape that has four sides and four right angles (90 degrees) with opposite sides being parallel and equal in length.

Let's start by calculating the total area of the rectangle:

Area of rectangle = length x width = 100m x 40m = 4000 square meters

Now, let's denote the width of the herb garden as x meters. Then, the length of the herb garden would be 10 meters.

The area of the herb garden would be:

Area of herb garden = length x width = 10m x x = 10x square meters

The area of the patio can be calculated as:

Area of patio = (100 - x) x (40 - 2x) square meters

(100 - x) is the length of the patio, and (40 - 2x) is the width of the patio, since the herb garden takes up x meters of the width.

The area of the flower garden can be calculated by subtracting the area of the rectangle, the herb garden, and the patio from each other:

Area of flower garden = 4000 - 10x - (100 - x) x (40 - 2x) square meters

Now, we need to find the value of x so that the sum of the areas of the patio, herb garden, and flower garden is 25% of the area of the entire rectangle. In other words:

Area of herb garden + Area of patio + Area of flower garden = 0.25 x Area of rectangle

10x + (100 - x) x (40 - 2x) + 4000 - 10x = 0.25 x 4000

Simplifying this equation, we get:

-2x^2 + 30x + 1000 = 1000

-2x^2 + 30x = 0

-2x(x - 15) = 0

Therefore, x = 0 or x = 15. Since x cannot be 0 (since the herb garden would have no width), the value of x must be 15 meters.

Now we can calculate the area of the patio:

Area of patio = (100 - x) x (40 - 2x) = (100 - 15) x (40 - 2(15)) = 850 square meters

Therefore, the area in square meters of the patio is 850 square meters.

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Answer:

operaciones vectoriales, Extensión de las leyes del álgebra elemental a los vectores. Incluyen suma, resta y tres tipos de multiplicación. La suma de dos vectores es un tercer vector, representado como la diagonal del paralelogramo construido con los dos vectores originales como lados.

Answer:

operaciones vectoriales, Extensión de las leyes del álgebra elemental a los vectores. Incluyen suma, resta y tres tipos de multiplicación. La suma de dos vectores es un tercer vector, representado como la diagonal del paralelogramo construido con los dos vectores originales como lados.

Step-by-step explanation:

The work required to pump all the water out of the rectangular swimming pool over the top is approximately 2,323,200 ft-lb.

We have,

To find the work required to pump all the water out of the rectangular swimming pool, we can use the concept of work as the force multiplied by the distance.

First, let's calculate the weight of the water in the pool.

The weight of an object is given by the formula:

Weight = mass x gravitational acceleration

Since the density of water is given as 1 lb/ft³, we need to find the volume of water in the pool.

The volume of the pool is given by the formula:

Volume = length x width x depth

Volume = 50 ft x 30 ft x 6 ft = 9000 ft³

Now, let's calculate the weight of the water:

Weight = density x volume x gravitational acceleration

Weight = 1 lb/ft³ x 9000 ft³ x 32.2 ft/s² ≈ 290,400 lb

To pump all the water out over the top, we need to raise it to the height of the pool, which is 8 ft.

The work required to pump the water out is given by the formula:

Work = weight x height

Work = 290,400 lb x 8 ft = 2,323,200 ft-lb

Therefore,

The work required to pump all the water out of the rectangular swimming pool over the top is approximately 2,323,200 ft-lb.

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Answer: 180,000 g

Step-by-step explanation:

1st add all masses together:

80kg + 40kg + 60 kg = 180 kg

then we need to convert kilograms to grams:

1 kg = 1000g

180kg * (1000g / 1kg) = 180,000 g

To calculate the total mass (in grams) of the three boxes, we first need to convert their masses from kilograms to grams and then add them together.

The mass of the first box is 80 kg, which is equivalent to 80,000 grams (because 1 kg = 1000 grams).

The mass of the second box is 40 kilograms, or 40,000 grams.

The mass of the third box is 60 kilograms, or 60,000 grams.

To find the total mass of the three boxes, we add these values:

80,000 grams + 40,000 grams + 60,000 grams = 180,000 grams

Therefore, The total mass of the three boxes in gram is 180,000

The correct answer is D) 180,000

The sum of the geometric series is 3904/3125.

By using the formula for the sum of a geometric series, we'll have to identify the first term, the common ratio, and the number of terms.

Let's identify the first term, the common ratio, and the number of terms in the given series as shown below;

The first term, a = 4³/5³

Common ratio, r = 4/5

The number of terms, n = 3

We have identified the values of a, r, and n, we can now substitute them into the formula for the sum of a geometric series, shown below;

S_n = a(1 - rⁿ) / (1 - r)

S₃ = {(4³/5³) [1 - (4/5)³]} / [1 - (4/5)]

S₃ = {(64/125) [1 - (64/125)]} / [1/5]

S₃ = (64/125) [(125-64)/125] [5/1]

S₃ = (64/125) (61/125) (5)

Therefore, S₃ = 3904/3125.

Thus, the sum of the geometric series (4³/5³) + (4⁴/5⁴) + (4⁵/5⁵) is equal to 3904/3125.

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According to Moore's Law, the number of transistors that can be placed inexpensively on a silicon chip doubles every two years, a typical CPU contained about 1,000,000 transistors in 1990.

Let’s first calculate the number of doublings from 1990 to 2000. Number of years from 1990 to 2000 = 2000 - 1990 = 10 yearsDoublings from 1990 to 2000 = [tex]$\dfrac{10 \text{ years}}{2 \text{ years per doubling}} = 5$[/tex] doublingsNow, we can calculate the number of transistors in a typical CPU in the year 2000:

[tex]$$\begin{aligned} \text{Number of transistors in 2000} &= \text{Number of transistors in 1990} \times 2^{\text{number of doublings}} \\ &= 1,\!000,\!000 \times 2^5 \\ &= 32,\!000,\!000 \end{aligned}$$[/tex]

Therefore, a typical CPU contained about 32,000,000 transistors in the year 2000.

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Answer:

10

Step-by-step explanation:

Based on the given conditions, formulate: 40x16 divided by 64

Cross out the common factor: 40/4

Cross out common factor: 10

Get the result

Answer: 10

Correct Option is Shifted 2 units left and 4 units up

A triangle is a geometric shape that is formed by three straight line segments that connect three non-collinear points. The three points where the segments intersect are called the vertices of the triangle, while the segments themselves are called the sides. The area enclosed by the sides of the triangle is called its interior, while the space outside the triangle is called its exterior.

The vertices of ABC are (4, 6), (7, 6), and (5,9)

The transformed image A'B'C' has vertices as

(2,10) (5,10) (3,13)

We see a pattern when we compare the matching vertices.

The y coordinate is raised by 4, while the x coordinate is shrunk by 2.

This implies the transformation is

Shifted 2 units left and 4 units up

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Answer:

Shifted 2 units left and 4 units up

Step-by-step explanation:

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