there are 208 students going on the school field trip each bus can carry 32 students how many buses will be needed

The area of each triangle is given as follows:

The area of a triangle is given by half the multiplication of the base and the height, as follows:

Area = 0.5 x base x height.

The dimensions for each triangle are given as follows:

Hence the areas are:

The triangles are given by the image presented at the end of the answer.

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Case 1: The linear equations has infinite solutions.

Case 2: The linear equations has no solution.

In this problem we find two cases of systems of two linear equations with two variables, which are described by a system of the form:

a · x + b · y = c

d · x + e · y = f

Where:

The solution of this kind of systems can be found graphically on Cartesian plane, whose procedure is described briefly:

Now we proceed to find the solution for each case:

Case 1

Line 1: y = 0.5 · x + 1

y-Intercept

y = 0.5 · 0 + 1

y = 1

(x, y) = (0, 1)

x-Intercept

0 = 0.5 · x + 1

0.5 · x = - 1

x = - 2

(x, y) = (- 2, 0)

Line 2: - 2 · x + 4 · y =  4

y-Intercept

- 2 · 0 + 4 · y = 4

4 · y = 4

y = 1

(x, y) = (0, 1)

x-Intercept

- 2 · x + 4 · 0 = 4

- 2 · x = 4

x = - 2

(x, y) = (- 2, 0)

Since the two lines have the same intercepts, then there are infinite solutions.

Case 2

Line 1: y = - x - 3

y-Intercept

y = - 0 - 3

y = - 3

(x, y) = (0, - 3)

x-Intercept

0 = - x - 3

x = - 3

(x, y) = (- 3, 0)

Line 2: y + x = 2

y-Intercept

y + 0 = 2

y = 2

(x, y) = (0, 2)

x-Intercept

0 + x = 2

x = 2

(x, y) = (2, 0)

The system of linear equations has no solution as both lines are parallel.

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The coordinate of the point reflection across the x-axis will be (3, -6). Then the correct option is A.

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

The reflection does not change the shape and size of the geometry. But flipped the image.

The quadrilateral ABCD is shown. The coordinate of point B is (3, 6).

If the quadrilateral ABCD is reflected across the x-axis. Then the coordinates of B' will be given as,

B' = (3, -6)

The coordinate of the point reflection across the x-axis will be (3, -6). Then the correct option is A.

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The solution to the given system of equations y = 1/3x - 10 and 2x + y = 4 is (6, -8).

y = 1/3x - 10 … (1)

2x + y = 4 … (2)

We can use the substitution method to determine the solution of the given system of linear equations.

Substituting (1) in (2), we get

⇒2x + (1/3 x - 10) = 4

⇒2x + 1/3 x - 10 = 4

⇒(6 + 1)/3 x = 14

⇒7/3 x = 14

⇒7x = 14 × 3

⇒7x = 42

Dividing both sides by 7

x = 6

Place the value of x in equation (1)

⇒y = 1/3 (6) - 10

⇒y = 2 - 10

⇒y = -8

--The given question is incomplete, the complete question is

"What is the solution to the system of equations y = 1/3x - 10 and 2x + y = 4?"--

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Christine has 262 pieces of bread, 336 lice of patrami, and 302 lice of cheese, so she can make a maximum of 131 hero sandwiches if each sandwich consist of two pieces of bread, two slices of patrami, and two slices of cheese.

Therefore the answer is 131.

Christine is making hero sandwiches, each of which consist of two pieces of bread, two slices of patrami, and two slices of cheese. To find the greatest number of heroes he can make, we need to divide the total number of each ingredient by the number of that ingredient used in each sandwich.

The number of heroes Christine can make with the bread is:

262 pieces of bread / 2 pieces of bread per hero = 131 heroes

The number of heroes Christine can make with the patrami is:

336 slices of patrami / 2 slices of patrami per hero = 168 heroes

The number of heroes Christine can make with the cheese is:

302 slices of cheese / 2 slices of cheese per hero = 151 heroes

To find the greatest number of heroes Christine can make, we need to take the smallest of these three values, which is 131 heroes. This means that Christine can make a maximum of 131 heroes with the ingredients he has on hand.

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Option B is the correct answer. The best approximation of the relative maximum of the polynomial function  graphed below is (-3.6,17)

The relative maximum is in the peak on the left side.

A function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, or cubic equation.

The general Polynomial Formula is

[tex]P(x)=a_{n} x^n+a_{n-1} x^n^-1+..........+a_{2} x^2+a_{1} x^1+a_{0}[/tex]

where all the powers are non-negative integers.

And, a0,a1,………,an ∈ R

The graph of function depends upon its degree, and having one variable which has the largest exponent is called a degree of the polynomial.

There are some Graphs of Higher Degree Polynomial Functions:

The Standard form is:

P(x) = an xn + an-1 xn-1+.……….…+ a0

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The section formula provides a way to check if three points in 3D space are collinear by verifying that the equation (x2 - x1)(y3 - y1) - (x3 - x1)(y2 - y1) = 0 is satisfied when their coordinates are substituted.

To prove three points are collinear in 3D using the section formula, first determine the coordinates of the three points. Then, substitute the coordinates into the section formula equation, (x2 - x1)(y3 - y1) - (x3 - x1)(y2 - y1) = 0. Finally, calculate the equation and if it is equal to 0, the three points are collinear.

For example, if the coordinates of three points are (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3), then the three points are collinear if the following equation is satisfied:

(x2 - x1)(y3 - y1) - (x3 - x1)(y2 - y1) = 0

If the equation is not equal to 0, the points are not collinear. To illustrate, if the coordinates of three points are

(x1, y1, z1), (x2, y2, z2) and (x3, y3, z3),

then the three points are collinear if the following equation is satisfied: (x2 - x1)(y3 - y1) - (x3 - x1)(y2 - y1) = 0.

If this equation is not equal to 0, then the three points are not collinear. To check if the points are collinear, one must calculate the equation and determine if the equation is equal to 0. If so, the three points are collinear.

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The type of dilation and scale factor in the figure shown is

Scale factors are used to increase or decrease image. The situation of increment is usually called magnifying or enlargement.

The given problem is enlargement since the preimage is smaller than the image. Also the scale factor will be greater than 1

Taking a point of reference say side 6 in the preimage and side 15 in the image and solve for the factor, assuming the factor is k

6k = 15

k = 15/6

k = 2.5

hence we say that the scale factor is 2.5

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Answer: Enlargement with scale factor of 2.5

Step-by-step explanation: I took the quiz so you don't have too!

Answer:

400 m³

Step-by-step explanation:

The tent consists of a cylinder at the bottom and the roof of the tent is a cone

The height of the cone = 2h - h = h which is the same as the height of the cylindrical part

Volume of a cylinder = πr²h where r = radius, h- height

We are given this volume = 300 m³

The volume of a cone is (1/3)πr²h

If the heights and radius are the same, the volume of the cone is 1/3 the volume of the cylinder

Volume of conical part of tent = 1/3 x volume of cylindrical part

= 1/3 x 300 = 100 m³

Total volume of the tent and therefore the volume of air

= 300 + 100 = 400 m³

The law of cosines serves as a generalization of the Pythagorean formula, which is applicable to all triangles.

Compare the total of the squares on the two smaller sides to the square on the largest side to determine if the triangle is acute, right, or obtuse. Because of the larger sum, the triangle is sharp.

The Pythagorean formula applies to all triangles and is generalised by the law of cosines. The square of one side of the triangle, c², is said to be equal to a² + b², the sum of the squares of the other two sides, minus 2ab cos C, which is the product of the two squares times the cosine of the opposite angle.

Three closed sides make up a triangle. The Pythagoras theorem and the Heron's formula are two significant formulas that pertain to triangles.

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The number line represents an inequality. The inequality is x  ≥ -3.

What is a number line?

A number line is a picture of a graduated straight line that serves as a visual representation of real numbers in primary mathematics. Every number line point is considered to correspond to a real number and every real number to a number line point.

If a number line contains a close circle, then the number includes in the inequality.

If a number line contains an open circle, then the number does not include in the inequality.

In the graph, there is a close circle on -3.

The line represents all real numbers greater than -3.

Since there is a close circle on -3, thus -3 include in the inequality.

The given variable is x.

The graph represents all real numbers greater than or equal to -3.

The inequality is x  ≥ -3.

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Then the two solutions are: x = (4 + 5.66) / 8 = 11.2075  and x = (4 - 5.66) / 8 = -0.2075

The sine approximation formula of Bhaskara I is a rational equation in one variable for computing the approximations of the trigonometric sines found by Bhaskara I (c. 600–c. 680), an Indian mathematician of the seventh century.

Indian astronomer and mathematician Bhaskara II lived in the 12th century. He created a number of the same foundations and findings that are entirely attributable to Europeans and are still very helpful in modern science and forecasts, such as a basic form of calculus.

Here we have the equation:

y = 4 × x² - 4 × x - 1

And the graph should be available (you can see it below this answer)

Now, we're seeking answers to:

4 × x²- 4 × x - 1 = 0

The two x values at which the graph of our function intersects the y = 0 line, or the x-axis, will be these solutions.

The next step is to identify the two x values where our graph crosses the x-axis.

We can estimate the solutions in the graph as follows:

x = -0.2

x = 1.2

The Bhaskara's equation can be used to determine the precise solutions, and we will discover that the solutions are provided by:

[tex]$x=\frac{-(-4)+-\sqrt{(-4)^2-4 * 4 *(-1)}}{2 * 4}=\frac{4+-\sqrt{32}}{8}=\frac{4+-5.66}{8}[/tex]

Then the two solutions are:

x = (4 + 5.66) / 8 = 11.2075

x = (4 - 5.66) / 8 = -0.2075

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The correlation coefficient r = +0.9 indicates a strong positive correlation as a strong positive (negative) linear relationship is shown by values between 0.7 and 1.0 (or -0.7 and -1.0).

What is corelation coefficient?

A statistical concept known as the correlation coefficient aids in establishing a relationship between expected and actual values gained through statistical experimentation. The estimated correlation coefficient's value explains how well the expected and actual values match.

The following points are the accepted guidelines for interpreting the correlation coefficient  -

1. Zero means there is no linear relationship.

2. A perfect positive linear relationship, or one with a value of 1, means that as one variable rises in value, the other variable rises in value according to an exact linear law.

3. A perfect negative linear relationship is represented by a value of 1; as one variable's values rise, the other variable's values fall according to an exact linear law.

4. Values between 0 and 0.3 (0 and -0.3) denote a wobbly linear rule with a weak positive (negative) linear relationship.

5. A fuzzy-firm linear rule indicates a somewhat positive (negative) linear relationship for values between 0.3 and 0.7 (-0.3 and -0.7).

6. A strong positive (negative) linear relationship is shown by values between 0.7 and 1.0 (or 0.7 and 1.0) by a strict linear rule.

Therefore,  r = +0.9 indicates a strong positive correlation.

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Volume of a cube = a3

here a = 4

  then = a3 = 4^3 =64

The rectangular prism shows 12 cubes: 3 rows and 4 columns.

The volume of a prism is the area of the base times the height,

The volume of a rectangular prism is the length times width times height,

The volume of a cube is the length of one side cubed,

Volume of a rectangular prism = (length x width x height) cubic units.

V = (l x w x h) cubic units

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Answer:

y = 15.4

Step-by-step explanation:

the outer and inner triangles are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{y}{11}[/tex] = [tex]\frac{8+3.2}{8}[/tex] = [tex]\frac{11.2}{8}[/tex] ( cross- multiply )

8y = 11 × 11.2 = 123.2 ( divide both sides by 8 )

y = 15.4

There are 180 degrees of longitude, which is divided into 360 lines of longitude (meridians).

Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is measured in degrees, with a full circle consisting of 360 degrees. The Prime Meridian is located at 0 degrees longitude, and each degree is further divided into 60 minutes and each minute is divided into 60 seconds. Therefore, there are 180 degrees of longitude east of the Prime Meridian and 180 degrees of longitude west of the Prime Meridian.

There are 180 degrees of longitude, which is divided into 360 lines of longitude (meridians).

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Provided the given distance and the angle of elevation, Using the trigonometry in the right angled triangle formed, The answer is 74.89 feet.

Trigonometry is the branch of mathematics that deals with the relationships between the angles and sides of triangles, particularly right triangles. Trigonometry is used to study properties such as lengths, angles, and areas of triangles and the relationships between them. It is also used in many fields, including physics, engineering, and navigation. Trigonometry is based on the study of the ratios of the sides of a right triangle. The three main ratios are sine, cosine, and tangent. These ratios are defined using the right triangle's angles and are often abbreviated as sin, cos, and tan. In addition to these three main ratios, there are also several other trigonometric functions, including cosecant, secant, and cotangent. These functions are the reciprocals of the sine, cosine, and tangent functions, respectively.

A right triangle is a type of triangle that has one angle that measures exactly 90 degrees. This angle is called the right angle and the two sides that form the angle are called the legs of the triangle. The side opposite the right angle is called the hypotenuse. A right triangle can also be defined as a triangle that has a 90-degree angle and two acute angles. The legs of the triangle are the sides that are opposite the acute angles, and the hypotenuse is the side that is opposite the right angle.

tan(A) = rise/run

tan(59) = height/45

height = tan(59)*45

=74.89 feet

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By addition, $1,850 is the right response. Mrs. Jones' company spent $1,850 on business expenditures in March, including $480 on raw materials, $1,200 on labour, and $170 on other expenses.

The other three fundamental operations are subtraction, multiplication, and division. Addition is one of the four basic operations. The sum or total of these combined values is obtained by adding two integers. The process of merging two or more numbers is known as addition in mathematics. Numbers are added together to form addends, and the outcome of this operation, or the final response, is referred to as the sum. This is one of the crucial mathematical operations we employ on a regular basis. You would add numbers in a variety of circumstances. Combining two or more numbers is the foundation of addition. You can learn the fundamentals of addition if you can count.

Mrs. Jones's business spent $480 on raw materials

Mrs. Jones' company spent $1,850 on business expenditures in March,

$1,200 on labour

$170 on other expenses.

by addition

Total = 1200+480+170 = $1850

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Answer:

x = -4

Step-by-step explanation:

4^(3x) = 16^(x-2)

First, we create equivalent expressions in the equation that all have equal bases.

4^3x = 4^2(x-2)

Since the bases are the same, two expressions are only equal if the exponents are also equal.

3x = 2(x − 2)

3x = 2x -4

x = -4

So, the answer is x = -4

So, 175 children's tickets were sold, and 100 adult tickets were sold.

We can start solving the problem by using a system of equations. Let x be the number of children's tickets and y be the number of adult tickets. We know that:

x + y = 275 (the total number of tickets sold)

3x + 5y = 1025 (the total value of the tickets sold)

To find the number of each type of ticket sold, we can use the first equation to express one of the variables in terms of the other, and then substitute that into the second equation. For example, we can express y in terms of x:

y = 275 - x

Now we can substitute this into the second equation and solve for x:

3x + 5(275 - x) = 1025

3x + 1375 - 5x = 1025

-2x = -350

x = 175

So, 175 children's tickets were sold, and 275 - 175 = 100 adult tickets were sold.

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The equation of the temperature at midnight is written as 3y + 5 = -7

The temperature at the midnight is calculated to be -4 degrees

The equation for the temperature at midnight is following the information given in the problem tripled and increased by 5

Assuming the temperature at midnight is y. For the temperature to triple we have

3y

For the temperature to rise 5 degrees will result to

3y + 5 = -7

solving for y

3y + 5 = -7

3y = -7 - 5

3y = -12

y = -4

At midnight the temperature was -4 degrees

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Answer:

Which of the following is a solution of the equation 2x + 3y = 6 ? * *1 pointa. (1 , 2 )b. ( 1 , 1 )c. ( -3 , 4 )d. ( 3 , 1 ). the answer is question b

Value of f[g(x-1)] is 2x^2-4x+9. The solution has been obtained by applying the multiplication operation on functions and substituting the functions.

Just like we add, subtract, multiply and divide the terms in a function, the functions can also be added, subtracted, multiplied or divided in a similar way.

Suppose there are two functions f(x) and g(x). The notations are as follows:

For Addition: (f+g)(x) = f(x) + g(x)

For Subtraction: (f-g)(x) = f(x) - g(x)

For Multiplication: (f×g)(x) = f(x) × g(x)

For Division: (f/g)(x) = (f(x))/(g(x))

When we substitute one function into another, a function is generated in which one function is considered to be a part of another function.

Now, f(g) = 2g-3

We are given g = x^2+5

So, g(x-1) = (x-1)^2+5

Substituting the value of g(x-1) in f(g), we get

f(g(x-1)) = 2((x-1)^2+5)-3

= 2x^2-4x+9

Hence, the value of f[g(x-1)] is 2x^2-4x+9.

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Answer:

this question has 3 answers, according to improper fraction your answer can be 50 over 11(50/11).

According to decimal point your answer can be 4.55.

Step-by-step explanation:

According to mixed numbers your answer can be 4 as a whole number 6as numerator and 11 as denominator

Answer:

100÷(22+3)

Step-by-Step:

you cant leave it as 100÷22+3 because pemdas states that division would be first but according to the problem it needs to be the last part. parenthesis comes before any other operation so the only way to do addition first is to put it in parenthesis.

Answer:  The discriminant of a quadratic equation ax² + bx + c = 0 is given by the formula:

b² - 4ac

Given the equation x^2 - 4x - 4 = 0, we can find the discriminant by substituting the values of a, b, and c into the formula:

b² - 4ac = (-4)² - 4(1)(-4) = 16 + 16 = 32

So, the discriminant of the equation x^2 - 4x - 4 = 0 is 32.

Step-by-step explanation:

Answer:I don’t know I just need points

Step-by-step explanation:

The missing values from Ariel’s bank account are;

3. -$155.15

4. -$223.75

5. -$1.40

6. -$7.2

Week 1:

Account balance = $360.00

Change from previous week = nil (this is because the previous week account balance is not given)

Week 2:

Account balance = $337.50

Change from previous week = $337.50 - $337.50

= -$22.50

Week 3:

Account balance = $182.35

Change from previous week = $182.35 - $337.50

= -$155.15

Week 4:

Account balance = -$41.40

Change from previous week = -$41.40 - $182.35

= -$223.75

Week 5:

Account balance = -$1.40

Change from previous week = -$1.40 - (-$41.40)

= $40.00

Week 6:

Account balance = -$5.80

Change from previous week = -$5.80 - (-$1.40)

= -$7.2

Therefore, the change in Ariel's bank account from previous week can be calculated by finding the difference between the present and previous week account balance.

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Answer:

Step-by-step explanation:

(3^1)^4

By using the numbers 3, 1, and 4, you are able to get the answer 81