what is the purpose of the dx in the integral ∫2x dx?

Using substitution method to solve the system of linear equation, the number of children is 90 and adults is 93.

In mathematics, a system of linear equations is the collection of two or more linear equations that share the same variables. The maximum power of the variable in the linear equations in this situation is 1, making them first-order equations. A linear equation may have one, two, or three variables. We can therefore create linear equations with n variables.

To solve this problem, we have to define our variables and then write the equations.

Let;

x + y = 183 ...eq(i)

1.75x + 2.5y = 390 ...eq(ii)

solving both equations

From equation (i)

x + y = 183

x = 183 - y ...eq(iii)

Put equation (iii) into equation (ii)

1.75(183 - y) + 2.5y = 390

y = 93

Put y = 93 into equation (i)

x + 93 = 183

x = 90

The number of child is 90 and adult is 93

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The given linear relationship slope of the line is D) 6.

What is slope?

An indication of how steep a line is is its slope. When calculating slope mathematically, "rise over run" is used (change in y divided by change in x). The ratio of how much y grows as x grows by a certain amount is known as the slope of a line. A line's slope, or the amount by which y rises as x rises, indicates how steep a line is. The slope is constant (the same) along the line.

Here from given tables lets take any two points to find slope, then

[tex](x_1,y_1)=(0,-6) and (x_2,y_2)=(1,0)[/tex]

Now using slope formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] then

=> m = [tex]\frac{0-(-6)}{1-0}[/tex]

=> m =[tex]\frac{6}{1}[/tex]

=> m = 6.

Hence the slope of the given table is D)6.

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The theoretical probability of landing on pink is 3/10, and the experimental probability is 30%. Therefore, option D is the correct answer.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Given that, a spinner with 4 equal sections is spun 20 times.

The frequency of spinning each color is recorded in the table below.

Outcome         Frequency

   Pink                    6

   White                  3

   Blue                    7

   Orange               4

Probability of landing on color pink is 6/20

= 3/10

= 3/10 ×100

= 30%

Therefore, option D is the correct answer.

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Answer: C

Step-by-step explanation:

The equation of the line with a slope of 2/3 passing through (-4, 1) is y = (2/3)x + 11/3

An equation is an expression relating two or more numbers and variables.

The slope - intercept form of a linear equation is:

y = mx + b

Where m is the rate of change(slope) and b is the y intercept.

The equation of a line passing through (x₁, y₁) with a slope of m is given by:

y - y₁ = m(x - x₁)

The line has a slope of 2/3 and pass through point (-4, 1). Hence:

y - 1 = (2/3)(x - (-4))

y - 1 = (2/3)(x + 4)

y = (2/3)x + 11/3

The equation of the line is y = (2/3)x + 11/3

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Answer:

TQN

Step-by-step explanation:

Equations now take the shape:

  [1]    3x - 4y = 24

  [2]    3x + 4y = 6

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So on solving the provided question, we can say that  y= |x| makes a starlight line, this equation is a linear function.

Two distinct but related concepts are referred to as linear functions in mathematics. A polynomial function of degree 0 or 1 is a linear function in calculus and related subjects if its graph is a straight line. Any function that depicts a straight line on a coordinate plane is said to be linear. For instance, y = 3x - 2 is a linear function since it depicts a straight line on the coordinate plane. f(x) = 3x - 2 can be used to represent the function since f(x) can be linked to y.

equation represents a linear function is that polynomial function of degree 0 or 1 is a linear function in calculus and related subjects if its graph is a straight line.

so, here  y= |x| makes a starlight line, this equation is a linear function.

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Answer:

C. 21.35 inches

Step-by-step explanation:

circumference = πd

circumference = 3.14 × 6.8 inches

circumference = 21.35 inches

The probability of selecting a student from the class who is a pet owner or prefers cats to dogs is; 0.4

In probability, If events A and B are not mutually exclusive, then the probability of A or B is expressed as;

p(A or B) = p(A) * p(B).

Total number of students = 26

Total number of students that are pet owners = 18

Total number of students that prefers cats to dogs = 26 - (8 + 3) = 15

Thus;

P(pet owner) = 18/26

P(prefers cats to dogs) = 15/26

P(Pet owner or prefers cats to dogs) = (18/26) * (15/26)

= 0.4

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The answer for y + 6 = -2 (x + 1) the equation in the general form is y - 2x = -8.

What is equation?

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.

The equation is represented in the general form Ax+By=C.

The given equation is -

y + 6 = -2 (x + 1)

Simplify further -

y + 6 = -2 (x + 1)

y + 6 = -2x -2

y - 2x = -2 - 6

y - 2x = -8

Therefore, the equation is y - 2x = -8.

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Therefore , the solution of the given problem of expression comes out to be as a result, we can minimize the radical statement by doing the actions listed below.

the value of an object  variable is represented by collections of numbers, signs, and procedures (like + and).Examples: The equation is 5+7. 3 x/2 is an alternative formula. An expression lacks the equals symbol.

Here,

To simplify a radical expression, use the Product Property.

1) Determine the radical's largest factor, which is also the index's precise power. Use that factor to rewrite the radicand as the intersection of two factors.

2) Apply the product rule to the radicals to rewrite them as the outcomes of two additional radicals.

3. Decompose the root of the ideal power.

Therefore, by taking the methods outlined above, we may simplify the radical expression.

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The zeroes of the equation x² + 3x - 40 is -8 or 5.

A quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0 .

It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem.

Given:

F(x) = x² + 3x - 40

Now, solving the quadratic Equation

x² + 3x - 40 = 0

x² + 8x - 5x - 40 = 0

x(x + 8) - 5(x + 8)=0

(x+8) (x-5)= 0

So, x+8 = 0 or x-5=0

x=-8 or x= 5

Hence, the zeroes are -8 and 5.

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Since the midsegment of each trapezoid is parallel to each base and is half, it has a GH value of 0.85.

Having at least one pair of parallel sides, a trapezoid is a quadrilateral in American and Canadian English. In the UK and other nations that speak English, it is referred as as the Trapezium. A trapezoid is a convex quadrilateral according to Euclidean geometry. Its parallel sides make up the trapezoid's base. The trapezoid, a convex quadrilateral, is defined by an identical pair of opposite sides that are parallel to one another. On paper, the two-dimensional trapezoid shape seems like a table. The term "quadrilateral" in Euclidean geometry refers to a polygon with four sides and four vertices.

given

A trapezoid's midsegment runs parallel to each base and is half as long as all of the bases combined.

1/2 * 3x - 6 = 2x

3x - 6 = 4x

= -6 = 7x

x = 0.85

Since the midsegment of each trapezoid is parallel to each base and is half, it has a GH value of 0.85.

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The trapezoid is a form of quadrilateral that has at least one parallel sides. The trapezoid here is given by the mentioned coordinates.

A point is a dot on a sheet of paper or in a plane. There are no lengths, widths, or heights in a point. It establishes a plane's position or location.

It is possible to find any point in a 2D plane or 3D space using coordinates, which are ordered pairs of points. You may have observed the use of grids in mathematics.

Select a point on the graph according to the given coordinates. Connect all the points on the graph using a line segment. The shape formed by joining all the points together is knows as a trapezoid.

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Answer:

Height = 557.1 to 1dp.

Step-by-step explanation:

Surface area of the given prism

= 2(12*3 + 12*10 + 10*3)

= 7272

The new prism must have surface are 2*7272 = 14544.

Let the new height be h, then:

2(3h + 10h + 30) = 14544

6h + 20h = 14544 - 60

26h = 14484

h = 14484/26

  = 557.1 cm.

1.125 cups of frozen mango is needed to serve one

A smoothie recipe contains 2 1/4 cups of frozen mango

This recipe can serve a total number of two people

The first step is to change the mixed fraction to an improper fraction

2 1/4

9/4

The number of cups of frozen mango needed to serve one person is

9/4 ÷ 2

9/4 × 1/2

= 9/8

= 1.125

Hence the number of cups of frozen mango required to serve one person is 1.125

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Answer:

x-intercept = -2; y-intercept = -7

Step-by-step explanation:

Answer: (0,10) and (3,1)

Step-by-step explanation:

Before I solve the system, I am going to rewrite it to make it easier for me to understand it.

[tex]y=(x-3)^2+1\\y=-3x+10[/tex]

Notice that f(x) and g(x) have been changed into y. The reason is because f(x) and g(x) are the same and stand for y, but we only use f and g to distinguish between the 2 equations. We can use equal values to solve.

[tex](x-3)^2+1=-3x+10[/tex]              [exponent]

[tex]x^2-6x+9+1=-3x+10[/tex]        [add both sides by 3x]

[tex]x^2-3x+10=10[/tex]                        [subtract both sides by 10]

[tex]x^2-3x=0[/tex]                                  [factor]

[tex]x(x-3)=0[/tex]

Notice that x=0 and x-3=0. This means the solutions are x=0 and x=3.

To find the actual full solution, we have to plug those points back into the original equations.

[tex]-3(0)+10=0+10=10\\-3(3)+10=-9+10=1[/tex]

Therefore, the solutions to this system are (0,10) and (3,1).

Answer:A

Step-by-step explanation:

The tortoise travelled the maximum distance of 9 m estimated from the time graph journey of a tortoise.

Distance-time graphs demonstrate how a moving object's distance travelled varies over time.

For the stated time graph of the journey of tortoise.

On x axis - time taken.

On y axis - distance covered by the tortoise.

Thus, the maximum distance is covered by the tortoise is 9 m at the time of 3 minutes.

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Answer:113.1 square feet

Step-by-step explanation:

Answer: B

Step-by-step explanation:

2/3 = 1/3 and 1/4 is already there

Hope this helps !

Answer:

Step-by-step explanati

Your answer would be A.

Answer:

22,256

Step-by-step explanation:

If the speedometer reading is 60, your actual speed is miles. miles per hour. Since the value of k = 1.1128 for the two tires in comparison, 1.1128 (20,000) = 22,256 miles (actual) and 1.1128 (60) = 66.768 miles per hour (actual). The percent error is 11.28% for both readings.

Answer:

10:15

Step-by-step explanation:

fsd

The slope of the line that goes through the points (0, 2) and (1, -1) is -3.

What is the slope of the line?

The slope of a line is a number that describes the steepness of a line and the direction it is heading. It is also known as the "rise over run" or the "rate of change" of a line. The slope of a line is typically represented by the letter "m" and is found using the formula:

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

To find the slope of a line, you need two points on the line (x1, y1) and (x2, y2) and substitute their coordinates into the slope formula.

To find the slope of a line, we use the formula:

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

In this case, we have two points: (0, 2) and (1, -1). To find the slope between these two points, we can substitute their coordinates into the slope formula:

slope = (-1 - 2) / (1 - 0)

slope = -3

Hence, the slope of the line that goes through the points (0, 2) and (1, -1) is -3.

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Question 23

Using the alternate interior angles theorem, [tex]m\angle BCA=20^{\circ}[/tex].

Question 24

[tex]\overline{AD} \cong \overline{DC}[/tex] by the definition of a rhombus. This means that [tex]\triangle ADC[/tex] is isosceles. It follows that [tex]m\angle ACD=20^{\circ}[/tex]. Using the angle sum of a triangle, [tex]m\angle CDA=140^{\circ}[/tex].

Question 25

All rhombi are parallelograms, and diagonals of parallelograms bisect each other. This means that [tex]AC=2(4)=8[/tex].

A system of linear inequalities represented by the graph are;

Inequality 1: y ≤ 3x - 3

Inequality 2: y ≥ ¹/₂x - 3

Inequalities that use < or > symbols are usually plotted with a dashed line that shows us that the line is not included in the region. Meanwhile, Inequalities that use ≤ or ≥ symbols are normally plotted with a solid line that shows us that the line is included in the region.

The general formula of equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Thus, the graph that rises to the right side in the first quadrant has;

Slope = (3 - 1)/(3 - 2)

Slope = 3

the y-intercept is at y = -3

Thus, equation is;

y ≤ 3x - 3

Thus, the graph that rises to the left side in the second quadrant has;

Slope = (1 - 0)/(2 - 0)

Slope = 1/2

the y-intercept is at y = 1

Thus, equation is;

y ≥ ¹/₂x - 3

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