Each of the s swimmers on the relay team swam an equal number of the 8 laps in a race. Write an expression that shows how many laps each swimmer swam.

True -  the statement says that a basic variable corresponds to a pivot column in the coefficient matrix. From the definition of basic variables, basic variables correspond to the columns that have a leading 1's (pivot columns).

A mathematical system model based on the use of a linear operator is known as a "linear system" in systems theory. In contrast to nonlinear cases, linear systems often display considerably simpler traits and attributes.

In linear systems, the variables are really only multiplied with constants and then added together; they are never multiplied by each other. In order to express both static and dynamic relationships between variables, linear systems are used.

Something relating to a line is linear. To build a line, all of the linear equations are used. Any equation that doesn't result in a straight line is considered as non. It has a variable slope value and appears as a curve on a graph.

A linear system is one in which both the superposition and homogeneity principles hold true.

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The required length of of the third side of isosceles triangle is 9 units.

An Isosceles triangle is a triangle that has two equal sides. Also, the two angles opposite the two equal sides are equal. In other words, we can say that “An isosceles triangle is a triangle which has two congruent sides“.

Let the length of Equal two sides is x.

Third side = 2x - 5

Then, perimeter is 23 cm

x + x + 2x - 5 = 23

4x - 5 = 23

4x = 28

x = 7

Then, third side is 2x - 5

= 2(7) - 5

= 14 - 5

= 9 units

Thus, required length of third side is 9 units.

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Answer: We can start by using algebra to represent the given information. Let's call the number we're trying to find "x".

We know that:

quotient = (3x)/5

quotient + 4 <= 34

We can simplify the first equation:

(3x)/5 + 4 <= 34

We can then solve this inequality for x:

(3x)/5 + 4 <= 34

3x/5 <= 30

3x <= 150

x <= 50

So the quotient of three times a number and five is no more than 34 if that number is less than or equal to 50.

Step-by-step explanation:

An artist connects stained glass pieces with lead strips and cut the strips so that FH = 28 in and JG = 14 in.  

Now, According to the question:

A plane shape, as opposed to a square, with four straight sides and four right angles, particularly one with uneven neighboring sides.

Here, we have

FH ≅ GH

FH = EG = 28in

If diagonals bisect each other then, an artist connects stained glass pieces with lead strips

1/2(EG) = JG

1/2 (28) = JG

14 = JG

Hence, an artist connects stained glass pieces with lead strips and cut the strips so that FH = 28 in and JG = 14 in.  

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Marlon's height is 42.52 inches.

Since the heights of four-year-old's are normally distributed with a mean of 40 inches and a standard deviation of 3 inches, we can use the z-score formula to find Marlon's height.

z = (x - mean) / standard deviation

where x is Marlon's height, mean is the population mean of 40 inches, and standard deviation is the population standard deviation of 3 inches.

We know that Marlon's height is taller than 70% of boys his age, so we can find his z-score using the cumulative standard normal distribution table, which tells us the proportion of the population that is less than a given value.

A z-score of 0.84 corresponds to a cumulative probability of 0.70.

So we can substitute this value into the z-score formula:

0.84 = (x - 40) / 3

Solving for x, we get:

x = 40 + (3 * 0.84) = 40 + 2.52 = 42.52 inches

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The lateral area for the prism is equal to 54 square inches. (Correct choice: B)

Herein we have the case of a prism with five faces, two triangles and three rectangles. The lateral area for the prism is the sume of the areas of the three rectangular faces, whose formula is described below:

Rectangle

A = w · l

Where:

Finally, we proceed to determine the lateral area of the prism:

A = 3 · (3 in) · (6 in)

A = 54 in²

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Used the distributive property a(b+c)=ab+ac, the value of x is x>1/2

Solving inequality using distribution property includes change of inequality signs when multiplied or divided by negative number but, not in the equation.

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

Curran:

-4(x-6)< 22

Used the distributive property a(b+c)=ab+ac

-4x+24<22

Then subtracted 24 from bot the sides

-4x<22-24

-4x< -2

Divide both sides by -4 ( inequality changes because of dividing by negative number)

x>1/2

Anjani:

-4(x-6)< 22

Divide both sides by -4

x-6> -22/4

add 6 on both sides

x> -22/4 + 6

x> -11/2 + 6

x> 1/2

Solving inequality using distribution property includes change of inequality signs when multiplied or divided by negative number but, not in the equation.

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The triangle types is impossible to draw is

A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees. The other two angles sum up to 90 degrees. The sides that include the right angle are perpendicular and the base of the triangle.

Given:

First, a scalene with right-angled triangle is possible to make.

Now, an isosceles with acute-angled triangle is possible to make such triangle in which all three angles are less than 90°, and at least two of its angles are equal in measurement.

Now, an isosceles with obtuse-angled triangle is not possible to make because if two angles are greater than 90 then sum of angles exceed 180.

and, an equilateral with right-angled triangle is not possible to make because in Equilateral triangle are angles are of equal measurement 60.

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Answer:

is try ur hardest

Step-by-step explanation:

Answer: 50g steel, 30g gold and 70g brass

Step-by-step explanation:

     This means for every 5g of steel there is 3g of gold and 7g of brass. We will find how many g there are total for every 5g of steel.

           5 + 3 + 7 = 15

     Next, we will divide 150g by 15g to see how many times the ratio will "repeat" to create the 150g of alloy.

           150g / 15g = 10g

     Next, we will multiply each amount of metal in one ratio by 10.

5g * 10 = 50g steel

3g * 10 = 30g gold

7g * 10 = 70g brass

Answer:

Step-by-step explanation

                                          to get 50g of steel.

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Some of the other types of the separation process are used in every house and company. The process of segregating undesirable particles from necessary components is the essence of the separation method. We will study in-depth information about several physical separation techniques in this particular article. The discussion's conclusion would allow students to recognize various techniques and their importance.

The blind man could use one hand to separate the pills by color, for example by holding one group of pills in one hand and the other group of pills in the other hand. Then, he could reach into one hand and take one pill, and reach into the other hand and take one pill, ensuring that he has taken one red pill and one blue pill. Another way could be to put each color pill in a different pocket, so he can feel the different pockets and take one pill of each color.

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A. We can see that the intersection made by lines C and D classifies ∠7 and ∠8 as vertically opposite angles.

B. The special angles created by intersection of lines C and D can be used to solve for y by equating the expressions, 5y-29 and  3y+19 as they are vertically opposite angles.

C. Solving for y, we have: y = -5

Intersection, in mathematics, refers to the common elements or overlap between two sets. For example, if set A contains the elements 1, 2, and 3, and set B contains the elements 2, 3, and 4, then the intersection of set A and set B would be the set containing the element 2 and 3. In general, intersection is represented by the symbol ∩. Lines can also intersect to form angles.

Vertically opposite angles are actually known to be equal. It then means that:

∠7 = ∠8 (Vertically opposite angles)

Also, 5y-29 = 3y+19 (Vertically opposite angles)

Thus, solving for y, we have:

5y-29 = 3y+19

5y - 29 -29 = 3y + 19 - 29

5y -3y = - 10

2y = -10

y = -10/2 = -5

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Answer: -15x - 9

Step-by-step explanation:

(2x ×2 −6x−5)+(−9x ×2 +5x−4)

(4x-6x-5)+(-18x+5x-4)

(-2x-5)+(-13x-4)

-2x-5-13x-4

-15x -

The value of the given equation is −7x2−x−9.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

The equation (2x 2 −6x−5)+(−9x 2 +5x−4)

Now,

We need to add the two polynomials by combining like terms. Like terms are terms that have the same variable and exponent. For example, 2x2 and −9x2 are like terms because they both have x2

To add like terms, we just add their coefficients. For example, 2x2+(−9x2)=(−7x2)

We can apply this rule to each pair of like terms in the problem and get:

(2x2−6x−5)+(−9x2+5x−4)

=(2x2+(−9x2))+(−6x+5x)+(−5+(−4))

=(−7x2)+(−x)+(−9)

=−7x2−x−9

Therefore, by algebra the answer will be −7x2−x−9.

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People celebrate Pi Day on March 14th at 1:59 because this date and time is an easy way to remember the mathematical constant pi (π).

Pi, which is represented by the Greek letter π, is an irrational number that starts with 3.14 and continues for an infinite amount of digits. The numerical value of pi is the ratio of a circle's circumference to its diameter, and is approximately equal to 3.1415926535897932384626433832795. The date and time of March 14th, 1:59 is a way to represent the first four digits of pi (3.14). People celebrate Pi Day by eating pie, making pi-related crafts, and sharing facts about pi. People celebrate Pi Day on March 14th at 1:59 because this date and time is an easy way to remember the mathematical constant pi (π).

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The ball has both kinetic energy and potential energy.

The values of each type of energy the object has are KE = 37.5 J and GPE = 2205 J

Energy is the ability to do work. It can take many forms, such as kinetic energy (energy of motion), potential energy (stored energy) etc.

If a  3-kg bowling ball rolls at a speed of 5 m/s on the roof of the building that is 75 m tall.

Then ball has kinetic energy due to his motion and also has potential energy due to his height.

Thus, M = 3-kg, h = 75 m and V = 5 m/s

KE = 1/2(M)(V)² = 1/2 × 3 × 5² = 37.5 J

GPE = mgh = 3 × 9.8 × 75 = 2205 J

KE + PE = 37.5 + 2205 = 2242.5 J

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The three (3) true statements about the quadratic function, f(x) = x^2 – 5x + 12 and its graph include the following:

A. The value of f(–10) = 82

B. The graph of the function is a parabola.

D. The graph contains the point (20, –8).

Generally speaking, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. For this quadratic function, the graph is a upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero.

Next, we would determine the other true statements about the graph of this quadratic function:

At data point (-10, 82), we have the following:

Quadratic function, f(x) = 1/5 x² – 5x + 12

Quadratic function, f(x) = x²/5 – 5x + 12

Quadratic function, f(-10) = -10²/5 – 5(-10) + 12

Quadratic function, f(-10) = 82

At data point (20, -8), we have the following:

Quadratic function, f(x) = 1/5 x² – 5x + 12

Quadratic function, f(x) = x²/5 – 5x + 12

Quadratic function, f(20) = 20²/5 – 5(20) + 12

Quadratic function, f(20) = -8

In conclusion, the graph of this quadratic function, f(x) = x^2 – 5x + 12 does not contain the data point (0, 0) as shown in the image attached below.

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The measurement of indicated angle is 20 degree.

Here opposite angles are congruent .

Therefore the indicated angle is 20 degree.

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Required equation to represent the translation 6 units left and reflected over x-axis is y = - (x + 6 ).

Let us consider the original equation be  y = x.

Translation to the left by k unit is f(x) = f ( x + k )

Now the equation gets translated 6 units to the left represents as

y = ( x + 6 )

Now the reflected over the x-axis is represented by :

Here y -coordinates change the sign.

If ( x, y ) after reflection over x -axis it is  ( x , -y ).

y = - ( x + 6 )

Equation to represents the reflected over x-axis and translated 6 units left of the original function y = x is written as y = - ( x + 6 ).

Therefore, the equation to represent the required translation and reflection is given by y = - ( x + 6 ).

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Answer:

cotθ=√21/2

Step-by-step explanation:

we have,

sinθ= 2/5= perpendicular/hypotenuse

here,

perpendicular=2

hypotenuse = 5

Now using Pythagorean theorem,

h^2 = p^2+ b^2

(5)^2 = 2^2 +b^2

b= √21

so,

cotθ= base/perpendicular = √21 /2

Hope you like the explanation.

Based on the information, it can be concluded Isabella bought  2 paintbrushes and 3 jars of paint.

The average of buying a product is 0.97, which means Isabella can buy a total of 5 items (0.97 x 5 = 4.85)

Based on this different combinations of products are possible, for example, 1 paintbrush and 4 jars or 3 jars and 2 paintbrushes. However, the one that fits the final price is:

2 paintbrushes x 0.95 = $1.9

3 jars of paint x 0.99 = $2.97

$2.97 + 1.9 = $4.87

Note: This question is incomplete, here is the missing information

The paintbrushes cost $0.95 and the jar of paint cost $.099

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The price paid by school district for each typewriter after applying 18% quantify discount is equal to  $106.56.

Regular selling price of each typewriter = $129.95

Number of typewriter required by school district  = 50

Total cost of 50 type writers = $129.95 × 50

                                               = $6497.5

Discount percent on whole quantity = 18%

18% of $6497.5

= ( 18 / 100 ) × $6497.5

= $1169.55

Total price paid by school district for 50 typewriters

= $6497.5 - $1169.55

= $5327.95

Price paid by school district for 1 typewriters

= $5327.95 / 50

= $106.559

= $106.56

Therefore, the price paid school district for each typewriter is equal to

$106.56.

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The side length of AC is 6 units for the shown triangle. The correct answer would be an option (C).

Similar Triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.

The right triangle is given in the question, as shown.

AD = 4 cm and BD = 5

In ΔACD and ΔABC

∠ACD = ∠ABC

∠ACD = ∠BAC = 90°

∠CAD = ∠ACD (remaining)

So ΔACD and ΔABC are similar

Hence

AD / AC = AC/ BC

Apply the cross-multiplication operation, and we get

AC² = AD × BC

AC² = 4 × 9

AC² = 36

AC = 6 cm

So, the side length of AC is 6 units.

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Answer:

A ratio in words compares a whole to a part. For example, the ratio of apples to oranges in a basket is "three to one." This can also be written as "3:1" or "3/1."

Another example: is the ratio of students to teachers in a class is "twenty to one." This can also be written as "20:1" or "20/1."

Step-by-step explanation:

Answer:

3 x (5 + 2)

Step-by-step explanation:

Just use the distributive property, it's very simple.

Answer:

9

Step-by-step explanation:

9x9=81

Answer:

Step-by-step explanation:

So the rectangle is 9 units wide.

becuase given that the area of the rectangle is 81m'n' square units and the length of the rectangle is 9mn', we can set up the equation as:

81 = 9 x width

To solve for width, we can divide both sides of the equation by 9:

width = 81/9

width = 9

The value of the missing angle x of the triangle is; x = 18.67°

The sum of angles on a straight line is 180 degrees. Thus, the supplementary angle to 130 degrees is;

180 - 130 = 50°

Now, the alternate angle to 80 degrees which will be located inside the triangle is 80°.

The sum of angles in a triangle is 180 degrees. Thus;

3x - 6 + 80 + 50 = 180

3x + 124 = 180

3x = 180 - 124

3x = 56

x = 56/3

x = 18.67°

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