In the sketchpad, solve 27 x 7 with an area model.

For the given equations 7x+6y=16 and 4x-2y=1 the value of x is 1 and y is 3 / 2.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the two equations are 7x+6y=16 and 4x-2y=1. The solution of the equations by elimination method is calculated as,

7x + 6y = 16

4x -2y = 1

Cross-multiply the two equations by the coefficients of variable y.

-14x -12y = -32

-24x + 12y = -6

____________

-38x = -38

x =1

The value of y will be calculated as,

4x - 2y = 1

4 -2 y = 1

y = 3 / 2

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As a result, the East Pacific Rise rate of change extends by around 6 to 16 centimeters annually, compared to the Mid-Atlantic Ridge's 2 to 5 cm.

The relation of one quantity's changes to someone else's change is known as the rate of change. The rate of change in linear relationships is constant. Here are a few instances with varying rates: Every week, forty rats are added to the rat population. When an automobile is moving at 68 km, its distance traveled grows by 68 mph over time. When calculating the change in distance for a car employing 27 miles per gallon, the duration is multiplied x 27 mile for each gallon.

Here,

Using the data in the inquiry

Conclusion: As a result, we may say also that East Pacific Rise is expanding more quickly than the Mid-Atlantic Ridge.

The East Pacific Rise expands roughly 6 to 16 centimeters year, whereas the Mid-Atlantic Ridge distributes about 2 to 5 centimeters annually.

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To find the mass of the lamina, we need to integrate the density function over region D. The density function is given by? (x, y) = 7ky, where k is a constant. The region D is bounded by y = [tex](1 ? x^2)[/tex]  and y = 0, and the limits of integration are [tex]0 < = y < = (1 - x^2)[/tex] .

So, the mass of the lamina is:

[tex]m = ∫∫?(x, y) dx dy = ∫∫ 7ky dx dy\\= 7k ∫∫ y dx dy = 7k * ∫ (1 - x^2) dy dx\\= 7k * ∫(0 to 1 - x^2) y dy\\= 7k * (1/2 * ∫(0 to 1 - x^2) y^2 dy)\\= 7k * (1/2 * [y^3/3] evaluated at y = (1-x^2) and y=0)\\= 7k * (1/2 * [((1-x^2)^3/3] - 0))= 7k * (1/2 * (1/3 - x^6))[/tex]

To find the center of mass (x bar, y bar) of the lamina, we need to find the x and y coordinates of the center of mass.

The x-coordinate is given by

[tex](x bar) = 1/m * ∫∫ x ?(x, y) dx dy = 1/m * ∫∫ x * 7ky dx dy \\= 7k * ∫ (x * y) dx dy\\= 7k * (x * 1/2 * ∫(0 to 1 - x^2) y^2 dy)\\= 7k * (x * 1/2 * [y^3/3] evaluated at y = (1-x^2) and y=0)\\= 7k * (x * (1/2 * (1/3 - x^6))\\The y-coordinate is given by\\(y bar) = 1/m * ∫∫ y ?(x, y) dx dy = 1/m * ∫∫ y * 7ky dx dy= 7k * ∫ (y^2) dx dy\\= 7k * (1/3 * ∫(0 to 1 - x^2) y^3 dy)\\= 7k * (1/3 * [y^4/4] evaluated at y = (1-x^2) and y=0)\\= 7k * (1/3 * (1/4 - x^6/2))[/tex]

It's worth noting that the mass and center of mass of the lamina depend on the constant k, which is not specified in the problem.

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Therefore, We can use the Gaussian elimination method to find the basis of H.

In linear and multilinear algebra, the procedure of Gauss elimination involves first solving one of the simultaneous linear equations for one variable (in terms of all the others) and then substituting this expression into the other equations to discover the answers.

A linear equation is an algebraic equation in which each term has an exponent of 1, which, when plotted on a graph, always yields a straight line. One example with one variable is where ax+b = 0, where a and b are fundamental values and x is the variable.

Selecting the polynomials Pi(t) = 1 + t and P2(t) = 1 - t from the set S. These are linearly independent since they cannot be written as a linear combination of the other polynomials in the set and checking if the span of Pi(t) and P2(t) is equal to H. Then expressing the remaining

polynomials P3(t), P4(t), and Ps(t) in terms of Pi(t) and P2(t) and checking if they can be written as a linear combination of Pi(t) and P2(t) or not.

P3(t) = 4 can be written as 4 * Pi(t) - 4 * P2(t)

P4(t) = 1 + 7t can be written as Pi(t) + 7 * P2(t)

Ps(t) = 1 + 2t + 7t^2 can be written as Pi(t) + 2t * P2(t) + 7 * P2(t)^2

From this, we can see that all the polynomials in S can be written as a linear combination of Pi(t) and P2(t). So, the span of Pi(t) and P2(t) equals H. Hence, { Pi(t), P2(t) } is a basis for the subspace H.

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In the question given, only option a, c and e are correct because the bars in a histogram do not touch, the bars also represent the frequency and the histogram can have a horizontal axis with different intervals

A histogram is a graphical representation of data that uses bars of different heights to show the frequency of a particular variable. It is used to show the distribution of numerical data.

In the given question, we can simply select the right choices and eliminate the wrong ones.

In option A, the bars in a histogram don't touch. This is true because in histogram, the bars do not touch.

In option B, this is false because we can't find the exact value of the median with only the histogram.

In option C, this is true because the bars represents the frequency of the data.

In option d, this is false as the histogram must not go up the same interval along the horizontal axis.

In option e, this is true because the histogram can have a horizontal axis with different intervals.

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The complement of A∪B is A′∩B ′.

A set of components in the universal set that are not a part of the initial set is known as the complement of a set in mathematics. Discover what a subset and its complement are, how to calculate a subset's complement, and the proper notation to use when writing a subset and its complement.

Given, universal set, U={1,2,3,4,5,6,7}

A={1,2,5,7}

B={3,4,5,6}

(A∪B) ′=U−(A∪B)

={1,2,3,4,5,6,7}−{1,2,3,4,5,6,7}=ϕ

A′∩B′=(U−A)n(U−B)

={3,4,6}n{1,2,7}=ϕ

Hence ( A∪B)′=A′∩B ′.

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The terms in given expression like variables, coefficient, constant are respectively, y, 1, -9

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

An expression,

⇒ y-9

In given expression, y is term which is variable

And coefficient of y is 1

constant term is -9

Therefore, we can write our terms are,  y, 1, -9

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Answer:

c=2a/h-b

Step-by-step explanation:

Therefore , the solution of the given problem of expression comes out to be 589418163090.78.

Multiplying, dividing, adding, and subtracting are necessary math operations. When combined, the following expression would appear: A mathematical operator, some data, and an equation Values, variables, and functions make up a statement of fact's constituent parts, such as additions, deductions, multiplications, divisions, etc. It is possible to contrast and compare words and phrases.

Here,

Given :

=> 2 x/y [tex]3^{z}[/tex]

At x = 72 , y=23 , z=23

So,

Putting values

=> 2*72/23 * 3²³

=> 589418163090.78

Therefore , the solution of the given problem of expression comes out to be 589418163090.78.

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The tip was $7.77 in total, and it is a 18.5% of the bill cost.

Here we know that the bill was $42, while the family spend a total of $49.77

Then the amount for the tip is equal to the difference between the bill and the amount that the family spends.

Tip = $49.77 - $42  = $7.77

Now we want to see which percentage of the bill this is, to check that, we need to take the quotient between the tip and the bill, and multiply that by 100%, we will get:

percentage = ($7.77/$42)*100%

percentage = (0.185)*100% = 18.5%

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On solving the provided question we can say that the expression of the emaily number will be as =[tex]\frac{1}{4}n - 3[/tex]

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.

here,

the expression of the emaily number will be as =[tex]\frac{1}{4}n - 3[/tex]

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Answer:

28.71

I looked it up.

Answer:

28.71

Step-by-step explanation:

To be honest with you, I looked it up

Answer:

(0,5) and (3,320)

Step-by-step explanation:

Plug in the ordered pair into the function and see if it makes sense.

Plug in 5 for y and 0 for x:

5= 5(4)^0
4^0 = 1 (anything to the power of 0 except 0 is one)
5x1 = 5
5=5
(0,5) works

320 = 5(4)^3

4^3 = 64

64x5 = 320

320=320

320=320 (3,320) works

(0,5) and (3,320) both work.

The correct answer is (option A)

We are trying to find the greatest common factor of 6 and 10 so we need to divide 10 and 6:

→ 10/6

→ = 1.6

→ = 2

Now we are rounding the number 1.6. 6 is close to 10 so it would equal 10 = 2

Therefore, the correct answer is (option A)

The first digit to the right of the decimal point indicates the number of tenths. For example, the decimal 0.3 is the same as the fraction 3/10. 

The radius of the globe with a volume of 904.78 in³ is 6 in.

The amount of space occupied within a sphere is referred to as its volume. Every point on the surface of the sphere is equally spaced from its centre, making it a three-dimensional round solid figure.

The fixed point and fixed distance are referred to as the sphere's centre and radius, respectively.

Given that the volume of the sphere is 904.78 in³. The radius of the sphere is calculated as,

Volume = ( 4 / 3 )πr³

r³ = ( 3 x volume ) / 4π

r³ = ( 3 x 904.78 ) / 4π

r³ = 2714.34 / 4π

r³ = 216

r = 6 in

Hence, the radius of the globe is 6 in.

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We can use the formula:

[tex]m = (y2 - y1) / (x2 - x1) = (5 - 3) / (-4 - 1) = 2/5[/tex]

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

20) The point-slope form of a line is[tex]y - y1 = m(x - x1)[/tex], where [tex](x1, y1)[/tex] is a point on the line and m is the slope. The slope of the line can be found by using the coordinates of two points on the line. To find the slope between the points [tex](1, 3)[/tex] and [tex](-4, 5)[/tex], we can use the formula:

[tex]m = (y2 - y1) / (x2 - x1) = (5 - 3) / (-4 - 1) = 2/5[/tex]

The point-slope form of the line is then:

[tex]y - 3 = (2/5)(x - 1)[/tex]

To convert this to slope-intercept form (y = mx + b), we can solve for y:

[tex]y = (2/5)x + (3 - (2/5)) = (2/5)x + (12/5)[/tex]

21) The line is parallel to [tex]y = -2x - 5[/tex], so we know that the slope of the line is -2. We can use the point [tex](4, -7)[/tex]and the slope -2 to write the equation in point-slope form:

[tex]y - (-7) = -2(x - 4)[/tex]

or

[tex]y + 7 = -2x + 8[/tex]

To convert this to slope-intercept form [tex](y = mx + b)[/tex], we can solve for y:

[tex]y = -2x + 1[/tex]

22) The line is perpendicular to [tex]y = -3/2x + 1[/tex], so we know that the slope of the line is the negative reciprocal of [tex]-3/2[/tex]. The slope of the line is [tex]2/3[/tex]. We can use the point [tex](3, 5)[/tex] and the slope [tex]2/3[/tex] to write the equation in point-slope form:

[tex]y - 5 = (2/3)(x - 3)[/tex]

or

[tex]y = (2/3)x + (5 - (2/3)3) = (2/3)x + (5 - 2) = (2/3)x + 3[/tex]

To convert this to slope-intercept form [tex](y = mx + b)[/tex], we can solve for y:

[tex]y = (2/3)x + 3[/tex]

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Answer:  C. the domain is 2 to 5 because it's the x axis

Step-by-step explanation:

Answer:

Answer is in attached photo.

Step-by-step explanation:

The solution is in the attached photo. Do note that since this is a right-angled triangle, Pythagoras' Theorem can be used to find the length of one side：

[tex]c^{2} = a^{2} + b^{2}[/tex]

A right Riemann sum has the formula  A=∑ni=1Δxf(xi) A = ∑ i = 1 n Δ x f ( x i ) where x is the width of each of the n rectangles and f(xi) is the height.

A specific method of approximating an integral with a finite sum in mathematics is known as a Riemann sum. Riemann is the name of a German mathematician who lived in the 19th century. Approximating the area of functions or lines in graphs, as well as the length of curves and other approximations, is a highly typical application. The picked points in each subinterval of the partition are all in the upper Riemann sum, given an interval partition. The interval is often separated into subintervals of equal size.

Riemann  sum formula is A=∑f(xi)Δx A = ∑ f ( x i ) Δ x ,

where A is the curve's area under the evaluable interval,

f(xi) f ( x i ) is each rectangle's height (or the average of the two heights in the case of a trapezoid)

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On solving the provided question, we can say that By addition, people could be at a game = 42,500 - 275 = 42225

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.

By addition,

Stadium capacity = 42,500

General admission seating = 31,750

Reserved seating = 10,475

42,500-( 31,750 + 10,475 ) =42,500- 42225 = 275

people could be at a game = 42,500 - 275 = 42225

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Therefore ,the mean of given data is 36, Simply dividing the total number of values by the sum of all the values in the data set yields it.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

Here,

Given :

=> Mean=summation of fxi

=> Mean = 3600 /100 = 36

Therefore , the solution of the given problem of mean is comes out to be

Mean  = 36.

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The Fencing Mrs. Jones will need in centimeters is 1220 cm

The fencing is a measure of the perimeter of the region to be covered

With the dimensions in meters deduced form the problem as 3.4 m by 2.7 m. the perimeter is calculated using the formula

= 2( length * width)

= 2(3.4 + 2.7)

= 2(6.1)

= 12.2 m

To convert 12.2 m to cm we use the factor, 1 m i= 100 cm, therefore

= 12.2 * 100

= 1220 cm

the perimeter is 1220 cm

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The difference in the monthly payments for a 20-year mortgage and a 30-year mortgage on a $135,000 loan at 3.32% APR is $430.

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The sine of an angle is the ratio of height to the hypotenuse. The value of sin 50° = 0.7660.

What is an angle?

An angle is a figure in Plane Geometry generated by two rays or lines that share a common endpoint. The term "angle" is derived from the Latin word "angulus," which meaning "corner". The two rays are referred to as the sides of an angle, while the common terminus is referred to as the vertex.

The sine of an angle is the ratio of height to the hypotenuse of a right triangle.

The reference angle is 50.

Now sin 50 = 0.766044.

The 5 digits after the decimal point is 4. 4 is less than 5 thus the 4 digits after the decimal point remain the same.

sin 50 = 0.7660

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The asymptote of the graph is given as 3

As one or both of the x or y coordinates go to infinity, a line is said to be an asymptote of a curve in analytic geometry when the distance between the curve and the line approaches zero.

The value of x from the graph here is given as 3. The curve cuts across the x axis at 3. This is the value as x moves towards positive infinity

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a) The polygon has 11 sides

b) The Sum of the Interior Angles of the 11 sided Polygon = 1620 degrees

What is a polygon ?

The definition of a polygon is a closed, two-dimensional, plane shape created by connecting three or more line segments. During our study of geometry, polygons are a common sight.

A polygon's sides are constructed from segments of straight lines joined end to end. The sides or edges of a polygon are the line segments that make up its shape. The vertex or corners formed by two line segments are where an angle is created. A triangle with three sides is an illustration of a polygon.

There are 11  sides, So, n=11

Sum of the Interior Angles of a Polygon = 180 (n-2) degrees

So,

The Sum of the Interior Angles of the 11 sided Polygon
= 180 (11-2) degrees

= 180 ( 9)

= 1620 degrees

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Answer:

Let a, b and c be integers with a≠0 and b≠0, and let d=gcd(a,b). If d does not divide c, then the linear Diophantine equation ax+by=c has no solution.