Drag the tiles to the correct boxes to complete the pairs *Not all tiles will be used*
Match the correct volume formula with each described figure
1. V = 1/2 * pi * x ^ 3;
2. V = x ^ 3;
3. V = 1/3 * x ^ 3;
4. V = 1/2 * pi * x ^ 3;
5. V = 1/2 * x ^ 3;
6. V = pi * x ^ 3
A. a prism with a height of x cm and a square base with side length of x cm
B. a cylinder with a radius of x and height of cm
C. a pyramid with a height of x cm and a square base with a side length of x cm
D. a cone with a radius of x cm and height of x cm

Answer:

20

Step-by-step explanation:

True, r² is a metric that expresses how much of a variable is accounted for by a basic linear regression model.

Calculate the sum of squares for the regression model (SSR):  SSR = Σ (predicted values - mean of the dependent variable)²

Calculate the sum of the squares of the residuals (SSE): SSE = Σ (observed values - predicted values)²

Calculate the coefficient of determination (r²): r² = SSR/ (SSR + SSE)

The coefficient of determination (r²) is then a percentage measure of the proportion of the variation explained by the simple linear regression model.

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Answer:

Step-by-step explanation:

Evaluate the expression

Divide 18 by 3 = 6

Then add the 6 to the 8

then subtract 7 from 14

answer=7

The chemist should use 3.75 liters of the 4% acid solution and 1.25 liters of the 28% acid solution to make 5 liters of a 10% acid solution.

Let's denote the volume of the 4% acid solution as x and the volume of the 28% acid solution as y, both in liters.

To make a 10% acid solution, we need to mix the two solutions in such a way that the resulting mixture has a total volume of 5 liters, and the concentration of acid in the mixture is 10%.

Since we want 5 liters of the final mixture, we can write the following equation based on the conservation of volume:

x + y = 5

The total amount of acid in the final mixture should be 10% of the total volume of the mixture, so we can write the following equation:

0.04x + 0.28y = 0.1(5)

On simplifying:

0.04x + 0.28y = 0.5

From the first equation:

y = 5 - x

Substituting into second equation:

0.04x + 0.28(5 - x) = 0.5

Simplifying and solving for x:

0.04x + 1.4 - 0.28x = 0.5

-0.24x = -0.9

x = 3.75

Using first equation,

x + y = 5

3.75 + y = 5

y = 1.25

Therefore, she needs to use 3.75 liters of the 4% acid solution and 1.25 liters of the 28% acid solution to make 5 liters of a 10% acid solution.

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If the circumference of the circle is 153.86 units, then the radius of that  circle is 24.5 units.

The "Circum-ference" of circle is defined as "total-length" of boundary of the circle. The formula for circumference is = 2 × π × Radius,

The "Radius" of circle is the distance from center of circle to its outer edge. It is half of "diameter" of circle, and it is a measure of size of circle.

We know that, circumference of circle is 153.86 units,

So, the circumference equation becomes,

⇒ 2 × 3.14 × Radius = 153.86,

⇒ 153.86/(2 × 3.14) = Radius,

⇒ Radius ≈ 24.5

So, the radius of the circle is approximately 24.5 units.

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The given question is incomplete, the complete question is

What is the radius of the circle if it has a circumference of 153.86 units?

The solution to the equation -2/(x - 8) = (x - 1)/(x + 2) is x = 3 after checking for extraneous solutions.

To solve the equation

-2/(x - 8) = (x - 1)/(x + 2)

We can start by cross-multiplying to eliminate the fractions

-2(x + 2) = (x - 1)(x - 8)

Simplifying both sides, we get

-2x - 4 = x² - 9x + 8

Bringing all the terms to one side, we get

x² - 7x + 12 = 0

Now we can factor the quadratic equation to get

(x - 3)(x - 4) = 0

So the solutions are x = 3 and x = 4. However, we need to check for any extraneous solutions that may have been introduced by the original equation.

Plugging in x = 3 to the original equation, we get

-2/(3 - 8) = (3 - 1)/(3 + 2)

Which simplifies to

2/5 = 2/5

Therefore, x = 3 is a valid solution.

Plugging in x = 4 to the original equation, we get

-2/(4 - 8) = (4 - 1)/(4 + 2)

Which simplifies to

1/2 = 3/6

Therefore, x = 4 is not a valid solution.

So the only solution to the equation is x = 3.

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The amount that each of Xavier Yolando, and Zachary has is   $1.48

We know that what we need to do is to convert the problem to an equation. The first step is always to be able to form the equation from the sentence that we have been given and we must have to look out for the key words in the problem.

We are told that each of them; Xavier Yolando, and Zachary have the same amount thus;

3x = 4.44

x = 4.44/3

x = $1.48

Thus they would all have a sum of $1.48

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The value of the given expression is 31/6.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

We can simplify the given expression using the order of operations (PEMDAS):

First, we evaluate the expression inside the parentheses:

9 - 3/4 = 35/4

Next, we simplify the multiplication by 2/3:

2/3 * 35/4 = 35/6

Now we substitute the above values in the expression and simplify:

-1/6 + 35/6 - 1/2 = (-1 + 35 - 3)/6

= 31/6

Therefore, the value of the given expression is 31/6.

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Answer:

a) The scale factor from A to B is 3/5 since (3/5)(5) = 3.

b) r = (3/5)(11) = 33/5 = 6 3/5

The elements of the given relations in the set P = {(x, y) : y = 3x - 1, x ≤ 4, x ∈ N} are: (a) y = x: {(1, 1), (2, 2), (3, 3), (4, 4)}

(b) y = 4x: {(1, 4), (2, 8), (3, 12), (4, 16)}

(c) x + y: {(1, 3), (2, 7), (3, 11), (4, 15)}

(d) x + y ≥ 20: {(3, 8), (4, 11)}

To find the elements of the given relations in the set P = {(x, y) : y = 3x - 1, x ≤ 4, x ∈ N}, we substitute the x-values from the set P into the corresponding equations.

(a) y = x:

In this relation, the y-values will be the same as the x-values.

Substituting the x-values from the set P into the equation, we get:

(1, 2), (2, 5), (3, 8), (4, 11)

So, the elements of the relation y = x in the set P are:

{(1, 1), (2, 2), (3, 3), (4, 4)}

(b) y = 4x:

Substituting the x-values from the set P into the equation, we get:

(1, 4), (2, 8), (3, 12), (4, 16)

So, the elements of the relation y = 4x in the set P are:

{(1, 4), (2, 8), (3, 12), (4, 16)}

(c) x + y:

Substituting the x-values from the set P into the equation, we get:

(1, 2), (2, 5), (3, 8), (4, 11)

So, the elements of the relation x + y in the set P are:

{(1, 3), (2, 7), (3, 11), (4, 15)}

(d) x + y ≥ 20:

Substituting the x-values from the set P into the inequality, we get:

(1, 2), (2, 5), (3, 8), (4, 11)

So, the elements of the relation x + y ≥ 20 in the set P are:

{(3, 8), (4, 11)}

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The probability of drawing a matching pair of socks is 1/5 or 0.2.

The basic principle of probability, states that the probability of an event happening is the number of ways the event can occur divided by the total number of possible outcomes.

In this problem, we first calculated the number of ways to draw a matching pair of socks for each of the three possible colors.

We then added these probabilities together to get the total probability of drawing a matching pair of socks.

Here we have

A box contains two white socks, two blue socks, and two red socks.

To find the probability of drawing a matching pair of socks, consider the different cases of matching pairs of socks that can be drawn.

Case 1: Matching white socks

The probability of drawing one white sock = 2/6

After drawing one white sock,

Remains 5 socks and of which 1 is white

The probability of drawing 2nd white sock =  1/5  

Hence, probability of selecting 2 white socks = (2/6) × (1/5) = 1/15

Similarly, we can calculate probabilities for Red and Blue socks

Case 2: Matching blue socks

The probability of drawing two blue socks is (2/6) × (1/5) = 1/15  

Case 3: Matching red socks

The probability of drawing two red socks is (2/6) × (1/5) = 1/15.

Therefore, the total probability of drawing a matching pair of socks is the sum of the probabilities of each of these cases:

P(matching pair) = P(white) + P(blue) + P(red)

= 1/15 + 1/15 + 1/15 = 3/15 = 1/5

Therefore,

The probability of drawing a matching pair of socks is 1/5 or 0.2.

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Answer:

x= -3.5

Step-by-step explanation:

0.4x+2.9= 1.5

-2.9. -2.9

(0.4/0.4)x= -1.4/0.4

x= -3.5

By solving the given equation 0.4x + 2.9 = 1.5, the value of x is -3.5

In the given equation, we have one variable of 'x' with a constant value of 0.4 and two non-variable values of 2.9 and 1.5.

To solve the given equation, we have to transfer the non-variable values to either the L.H.S (Left Hand Side) or R.H.S (Right Hand Side) of the equation. After transferring the non-variable values, we will solve it by dividing it by the constant value of the given variable as shown below:

0.4x + 2.9 = 1.5

0.4x = 1.5 - 2.9

0.4x = -1.4

     x = [tex]\frac{-1.4}{0.4}[/tex]

     x = -3.5

By solving the above equation, we can conclude that the value of x in equation 0.4x + 2.9 = 1.5 is -3.5

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Answer:

the diameter of the softball is approximately 4.72 inches.

Step-by-step explanation:

The formula to calculate the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius of the sphere.

We can rearrange the formula to find the radius of the softball:

r = cube root of [(3V)/(4π)]

r = cube root of [(3 x 33.5)/(4π)]

r ≈ 2.36 inches

The diameter is twice the radius:

d = 2r

d ≈ 4.72 inches

Therefore, the diameter of the softball is approximately 4.72 inches.

Answer: the diameter of the softball is approximately 4.22 inches.

Step-by-step explanation: The volume of a sphere can be calculated using the formula:

V = (4/3)πr^3

where V is the volume of the sphere, r is the radius of the sphere, and π is the mathematical constant pi.

To find the diameter of the softball, we can use the formula:

d = 2r

where d is the diameter of the sphere.

We know that the volume of the softball is 33.5 in^3. So, we can solve for the radius as follows:

33.5 = (4/3)πr^3

r^3 = (3/4)(33.5/π)

r^3 = 8.9375

r = ∛(8.9375)

r ≈ 2.11 inches

Now, we can find the diameter of the softball:

d = 2r

d = 2(2.11)

d ≈ 4.22 inches

Answer:

x<8

Step-by-step explanation:

...................

Ordinary Least Squares (OLS) is a method used to estimate the parameters of a linear regression model.

In OLS, the objective is to find the line that best fits the observed data by minimizing the sum of squared residuals between the predicted values of the dependent variable and the actual values.

To produce the Best Linear Unbiased Estimators (BLUE) in OLS, the following assumptions must be satisfied:

Linearity: The relationship between the dependent variable and the independent variables must be linear.

Independence: The observations must be independent of each other.

Homoscedasticity: The variance of the residuals should be constant across all levels of the independent variables.

Normality: The residuals should be normally distributed.

No multicollinearity: The independent variables should not be highly correlated with each other.

If these assumptions are met, then OLS produces the BLUE, which means that the estimated coefficients are the best unbiased estimates of the true population parameters, and they have the smallest variance among all unbiased linear estimators.

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Networking is the experience that uses social and professional connections to learn more about jobs from others. So, correct option is D.

It involves building and maintaining relationships with individuals who can offer information, advice, or support related to one's career goals. Networking can be done in various settings such as professional organizations, conferences, social events, and online platforms.

It can also involve exchanging information, sharing experiences, and providing referrals or recommendations. By networking, individuals can learn about job opportunities, industry trends, and insights into different career paths.

Additionally, networking can lead to mentorship and collaboration, which can help individuals develop their skills and expand their professional network further. Networking is an essential aspect of career development, as it can help individuals gain exposure and access to new opportunities that can lead to career advancement.

So, correct option is D.

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The value of the identities are;

1. sin M = 3√39/20

2. sin M = √3/5

3. sin M = 3√19/14

4. sin M = √3/2

The different trigonometric identities and their ratios are written as;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the information given, we have;

1. opposite = 3√39

Hypotenuse = 20

Then, sin M = 3√39/20

2. Opposite = 4√3

Hypotenuse = 20

sin M =  4√3/20

Divide the values

sin M = √3/5

3. The Opposite side = 3√19

Hypotenuse = 14

sin M = 3√19/14

4. Opposite = 6√3

Hypotenuse = 12

sin M =  6√3/12

Divide the values

sin M = √3/2

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a) The passage is a piece of written text that provides information about Makayla's experience during an Easter egg hunt. (option c)

(b) It also highlights how knowledge gained in the classroom can be applied to everyday life.

At the beginning of the passage, Makayla is getting ready to go on an Easter egg hunt. This is evident from the line "Makayla was getting ready for the Easter egg hunt at the park." Easter egg hunts are a popular tradition in many parts of the world, where children search for hidden eggs that are often filled with candy or small toys.

Hence the correct option is (c).

Throughout the story, Makayla remembers information that Mrs. Narula taught in class. Mrs. Narula is Makayla's science teacher, and the information she taught in class is about the process of photosynthesis. Photosynthesis is the process by which plants convert sunlight, water, and carbon dioxide into oxygen and sugar.

Makayla remembers this information as she observes the trees and plants in the park during the Easter egg hunt. She notes that the plants are producing oxygen through photosynthesis and that this process is essential for the survival of all living beings.

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Answer:

To calculate how many standard deviations away from the mean an ACT score of 31 is, we need to use the formula:

z = (x - μ) / σ

Where:

x = ACT score of 31

μ = mean of ACT scores (28)

σ = standard deviation of ACT scores (2)

z = number of standard deviations away from the mean

Substituting the values, we get:

z = (31 - 28) / 2

z = 1.5

Therefore, an ACT score of 31 is 1.5 standard deviations away from the mean.

100% of the number is 100 times X.

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

If 10% of a number is X,

0.1 * number = X

number = X / 0.1

number = 10 * X

As a result, if X represents 10% of a number, the whole number is 10 times X. To get 100% of the answer, simply multiply X by 10 again:

100% of the number = 10 * X * 10 = 100 * X

So, 100% of the number is 100 times X.

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Step-by-step explanation:

16x²-1 = (4x-1)(4x+1)

4x²-9 = (2x+3)(2x-3)

16x²-4 = 4(2x+1)(2x-1)

4x²-1 = (2x+1)(2x-1)

16x²+1 = (4x+i)(4x-i)

Answer:

z > - [tex]\frac{11}{9}[/tex]

Step-by-step explanation:

7z + 7 > - 2z - 4

9z + 7 > - 4

9z > -11

z > - [tex]\frac{11}{9}[/tex]

Answer: Just turn it into an equation! Replace the > with a =.

Step-by-step explanation:

Subtract 7 from both sides (bc you’re doing the opposite of +7) So 7z +7-7 cancels out so you just have 7z. 7z = -2z -4 -7, so 7z = -2z -11

Add 2z to both sides (bc your doing the opposite again) to get 9z = -11

Divide both sides by the number of the of the term with both a number and variable, in this case 9z, the number is 9. So 9z/9= -11/9 so simplified, z= -11/9

Final answer = -11/9

Hope this helps :D

Answer:

999,000,000 bytes

Step-by-step explanation:

if you subtract the total of the gigabytes from the total of the megabytes you get this answer.

The answer to 2 decimal places, we only need to keep two numbers after the decimal point. In this case, there are no numbers after the decimal point, so the answer is simply 5.00.

To find the answer, we need to know the number of robberies in year 3 and year 5. Let's say there were 100 robberies in year 3 and 500 robberies in year 5.

To compare the two numbers, we can divide the number of robberies in year 5 by the number of robberies in year 3:

500/100 = 5

This means that there were 5 times as many robberies in year 5 compared to year 3.

To round the answer to 2 decimal places, we only need to keep two numbers after the decimal point. In this case, there are no numbers after the decimal point, so the answer is simply 5.00.

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Y = 3(-3) + 4 = -5 when x is equal to 3. Hence, the final set of negative x- and y-coordinates is (-3, -5).

A set of numbers known as coordinates describes a point or object's location in a given space or coordinate system. When representing a spot's location in a plane or three-dimensional space, coordinates are frequently expressed as x or triples in mathematics. Depending also on system being utilised, several values can be used to represent coordinates, although often, integers or real numbers are used to express them.

given

We can substitute negative values for x and solve for y to obtain three pairs of negative x and y coordinates that lie on the line y = 3x + 4.

With x = 1, y = 3(-1), plus 4, equals 1. Hence, one set of negative x and y coordinates is (-1, 1).

Y = 3(-2) + 4 = -2 when x is equal to 2. In light of this, another set of negative x- and y-coordinates is (-2, -2).

Y = 3(-3) + 4 = -5 when x is equal to 3. Hence, the final set of negative x- and y-coordinates is (-3, -5).

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we get the coordinates of Q' as (2,3) after rotation of the triangle.

What is rotation of axis?

Rotation of axes is a transformation in which the coordinate axes are rotated by a certain angle with respect to the original axes. This transformation can be used to simplify the equations of curves and to make it easier to solve problems involving them. The rotation is usually done by finding the angle of rotation, which is the angle between the original x-axis and the new x-axis. The formulae for converting coordinates from the old system to the new system can then be applied.

In the given problem, we are given that triangle PQR is located in the xy-plane with coordinates of Q being (2,-3). The task is to find the coordinates of Q' when triangle PQR is rotated 180 degrees clockwise about the origin and then reflected across the y-axis to produce triangle P'Q'R'.

To start, we apply the 180 degree clockwise rotation about the origin transformation rule to the coordinates of Q (2,-3) which gives us (-2,3).

Next, we reflect the point (-2,3) across the y-axis. Reflecting across the y-axis involves changing the sign of the x-coordinate while leaving the y-coordinate unchanged. Applying this rule,

Hence, we get the coordinates of Q' as (2,3) after rotation of the triangle.

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The center will be on the line segment CA because, as we already know, a circle's diameter is a chord that passes through its center.

Therefore, the answers are CA and diameter.

we have that in the question, a circle with center 'O' is passing through three A, B and C, where ∠B is a right angle.

In the circumscribed circle, we have the converse of the Thales' theorem, which states that -

if A, B, and C are distinct points on a circle where angle ∠ABC is a right-angle, then the line AC will be a diameter of the circle.

The given information is drawn in the attached figure.

Applying the converse of Thales' Theorem, we have AC will be a diameter of the circle.

As the longest side (hypotenuse) of a right-angled triangle is the opposite side of the right-angle, CA is the longest side of ABC.

The longest side of the triangle equals the diameter of the circle because CA is likewise a diameter of the circle.

Thus, the center will lie on the line segment CA and the longest side of the triangle is equal to the diameter of the circle.

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#complete question:

Point O is the center of a circle passing through points A, B, and C. ∠B is a right angle.

The center of the circumscribed circle lies on line segment, (options: AB,BC, or CA) and the longest side of the triangle is equal to the (options: radius, diameter, or circumference) of the circle.

From the cyclic quadrilateral, If ∠ADC=120° and AB is a diameter, then ∠BAC=30°

Correct option is A

Given that:  ∠ADC=120

                  ∠ACB=90° (Diameter of the circle subtends an angle of 90°)

Consider  cyclic quadrilateral ABCD:

                  ∠ADC+∠ABC=180°   (sum of opposite angles of a cyclic quadrilateral is 180°)

        Thus, ∠ABC=180°−120°=60°

In △ABC:

                  ∠BAC=180°−∠ACB−∠ABC .....(Sum of three angles of a triangle is 180°)

                  ∠BAC=180°−90°−60°=30°

Answer:     ∠BAC=30°

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Point Q is the centre of a circle passing through the points A, B, C and D taken in order. If ∠ADC=120° and AB is a diameter, then ∠BAC=

A 30°

B 40°

C 45°

D50°

The value of | a b c 7d + a 7e + b 7f + c g h i| is given by -35 + b(ch - di) + c(gi - eh) + a(hk - fg).

Expanding the determinant using the first row, we get:

| a b c 7d + a 7e + b 7f + c g h i|

= a | b c 7d + 7e b 7f + g h i| - b |a c 7d + 7e c 7f + g h i| + c |a b 7d + 7e 7f + g h i|

= a | b c 7d + 7e b 7f + g h i| + b |a c 7d + 7e c 7f + g h i| - c |a b 7d + 7e 7f + g h i|

Now, we can expand each of the three determinants on the right-hand side using the first row and simplify:

| b c 7d + 7e b 7f + g h i| = b | c 7f h i| - 7e |b 7f h i| + g |b c h i|

= -7e b |7f h i| + g |b c h i| - h |b c 7f i| + i |b c 7f h|

= -7e bi + gh - bhf + chi

|a c 7d + 7e c 7f + g h i| = a |c 7f h i| - 7e |c 7d h i| + g |c 7d 7f i|

= 7e ac - gci + chd - ahf

|a b 7d + 7e 7f + g h i| = a |b 7f h i| - 7e |b 7d h i| + g |b 7d 7f i|

= -7e ab + ghi - bgd + aef

Substituting these expressions back into the expanded determinant and simplifying, we get:

| a b c 7d + a 7e + b 7f + c g h i|

= a(-7e bi + gh - bhf + chi) + b(7e ac - gci + chd - ahf) + c(-7e ab + ghi - bgd + aef)

= -7abe - 7bdf - 7cfg + 7aef + bch + cgi + ahk - ceh - afg - bdi

= -7(abe + bdf + cfg - aef) + (bch + cgi + ahk - ceh - afg - bdi)

Since |a b c d e f g h i| = 5, we have:

abe + bdf + cfg - aef = 5

Therefore, we can simplify the expression further:

| a b c 7d + a 7e + b 7f + c g h i|

= -7(5) + (bch + cgi + ahk - ceh - afg - bdi)

= -35 + b(ch - di) + c(gi - eh) + a(hk - fg)

Hence, the value of | a b c 7d + a 7e + b 7f + c g h i| is given by -35 + b(ch - di) + c(gi - eh) + a(hk - fg).

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The simplified expression for | a b c 7d + a 7e + b 7f + c g h i| is 7| a b c d g h i| + 7| a b c e g h i| - 35.

First, factor out the 7 from the second row:

| a b c 7(d + e + f) g h i| = 7| a b c d + e + f g h i|

Expand the second row using the property of determinants that allows us to break up a row sum:

7(| a b c d g h i| + | a b c e g h i| + | a b c f g h i|)

Now, use the property of determinants that allows us to switch rows and multiply by -1:

7(| a b c d g h i| + | a b c e g h i| - | d e f a b c g h i|)

Recognize that the third determinant is equivalent to the given determinant, but with rows 1 and 3 switched, which

gives us:

7(| a b c d g h i| + | a b c e g h i| - 5)

Finally, multiply 7 by the expression inside the parentheses:

7| a b c d g h i| + 7| a b c e g h i| - 35

So, the simplified expression for | a b c 7d + a 7e + b 7f + c g h i| is 7| a b c d g h i| + 7| a b c e g h i| - 35.

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Answer:

24 meters

Step-by-step explanation:

We can use Pythagoras' theorem to solve this problem. Let's call the width of the field "w". We know that Ken ran from one corner of the field to the opposite corner, a distance of 85 meters. This distance is equal to the hypotenuse of a right triangle whose legs are the length and width of the field. We also know that Ken ran along its length, a distance of 77 meters. This length is one of the legs of the right triangle.

Using Pythagoras' theorem, we can write:

w^2 + 77^2 = 85^2

Simplifying this equation gives:

w^2 = 85^2 - 77^2

w^2 = 576

Taking the square root of both sides gives:

w = sqrt(576)

w = 24

Therefore, the width of the field is 24 meters 1.

I hope this helps!

You are being asked to provide the minimum amount of information necessary to build a triangle that is congruence to the triangle shown in the image. All that is needed are the sides and angles.

What are the congruent triangle's five rules?

If two triangles satisfy all conditions for congruence, then they are congruent. They are right angle-hypotenuse-side (RHS), side-side-side (SSS), angle-side-angle (ASA), and angle-angle-side (AAS).

In order to form a triangle , two sides must be long and there must be an angle between them. A triangle's angle total is 180 degrees, and an acute angle is one with a measure of fewer than 90 degrees, among other triangle-related properties.

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Hence , the least amount of additional information that Andre needs to construct a triangle congruent to the given triangle is either the length of  one side or the lengths of two angles other than angle LKJ.

If two triangles satisfy all conditions for congruence, then they are congruent. They are right angle-hypotenuse-side (RHS), side-side-side (SSS), angle-side-angle (ASA), and angle-angle-side (AAS).

To construct a triangle  congruent to the given triangle, Andre needs to know the length of at least one side or the length of two angles other than angle LKJ.

If Andre knows the length of one side, say LJ, he can construct a line segment of the same length, say MN, and then construct two angles at each end of the line segment congruent to angles LJK and LKJ. The triangle formed by  the three line segments LJ, JK, and KM will be congruent to the given triangle.

If Andre knows the lengths of two angles other than angle LKJ, he can use the  Law of Sines or Law of   Cosines to find the lengths of two sides, and then proceed as described above.

Therefore, the least amount of additional information that Andre needs to construct a triangle congruent to the given triangle is either the length of  one side or the lengths of two angles other than angle LKJ.

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