Ue the given condition to write an equation for the line in​ point-lope form and in​ lope-intercept form. Slope​ = 1/2​, paing through the origin

In most cases, the area of the shaded zone is obtained by deducting the area of a smaller inner form from the area of a larger outer shape.The expression for the area of the shaded region is x² - 23x - 49.

In most cases, the area of the shaded zone is obtained by deducting the area of a smaller inner form from the area of a larger outer shape.The area of the shaded region is the difference between the total area of the polygon and the area of its unobscured interior.

There are two ways for polygons to have the area of the shaded region.

Depending on the shape of the polygon, the shaded area may be on one or both of its sides.

Area of a rectangle

area = lw

where

l = length

w = width

Therefore,

The area of the shaded region  = area of the big rectangle - area of the small rectangle

Therefore,

area of the big rectangle = (x+10)(2x+5) = 2x² + 5x + 20x + 50 = 2x² + 25x + 50

area of the small rectangle = (x+1)(x+1) = x² + x + x + 1 = x² + 2x + 1

area of the shaded region = 2x² + 25x + 50 - ( x² + 2x + 1)

area of the shaded region =  2x² + 25x + 50 - x² - 2x - 1

area of the shaded region = x² - 23x - 49

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If a calculator displays an angle measure in radians instead of degrees, it would make you question whether the calculator is in the right mode. Radians and degrees are two different units of measuring angles, with radians being the standard unit in mathematics and degrees being more commonly used in everyday life and geography.

Because the range of values for angles in radians is between 0 and 2π, while the range for angles in degrees is between 0 and 360. So, if a calculator gives an angle measure in radians that is outside the range of 0 to 2π or gives an angle measure in degrees that is outside the range of 0 to 360, it would indicate that the calculator is not in the correct mode for the desired unit of measurement.

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The value of x determined from the area of parallelogram is 6 units.

A parallelogram's area is the area that it occupies in a two-dimensional plane. A parallelogram is a four-sided, two-dimensional form in geometry. This particular quadrilateral example has equal and parallel opposing sides. The space bounded by a parallelogram's four sides is known as its area. A parallelogram's area is determined by multiplying its length by its height.

Given that the area of the parallelogram is 24 square units.

The area of the parallelogram is given by the formula:

A = (b)(h)

Substitute the value of A = 24, and b = 8 as given in the figure:

24 = 8(h)

h = 3

The measure of the height is 3 units.

For the triangle, we can observe that it is a right-angled triangle and the angle given is 30 degrees.

Using trigonometric functions, we have:

sin 30 = h / x

Substitute the values:

0.5 = 3 / x

x = 6

Hence, the value of x determined from the area of parallelogram is 6 units.

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In order for a function to be continuous at a point, then,

The limit of f(x) as x approaches the x coordinate of the point from the left and the right equals the value of the function at that point.

What does the term "continuous function" mean?

A continuous function in mathematics is a function that causes the value of the function to continuously vary as a result of a continuous variation of the argument, or a change without a leap.

                            This indicates that there aren't any discontinuities, or sharp shifts in value.

What does it mean when a function is continuous or discontinuous?

If one can sketch a function without picking up a pencil, one can say that it is continuous. A function is considered discontinuous if it is not.

                          If there is no break in the graph of the given function at the point, then a function f(x) in calculus is continuous at x = c.

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Answer:

IF you do A + B you will get P, p is = to enis which is AB.

Step-by-step explanation:

The matrix's entry of 1.00 on the diagonal denotes that it is an identity matrix, which means that all values besides 1 along the diagonal are 0.

The matrix is an identity matrix, as evidenced by the entry of 1.00 on its diagonal. A square matrix called an identity matrix is one in which the primary diagonal's elements are all ones and the other components are all zeros. The letter "I" stands for this particular sort of matrix. In several branches of mathematics, such as matrix theory and linear algebra, identity matrices are employed. Calculations and equations can also be made simpler by using identity matrices. An identity matrix, for instance, is created by multiplying it by any other matrix. This characteristic can be used for matrix inversion or to solve a set of linear equations. In group theory and abstract algebra, the identity element is also represented by identity matrices.

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The positive value of the parameter t corresponding to a point on the parametric curve x = t^2 + 7, y = t^2 + t for which the tangent line passes through the origin is t = 7 + √56.

Given the parametric curve {x = t^2 + 7, y = t^2 + t}, we want to find the positive value of t corresponding to a point on the curve for which the tangent line passes through the origin (0, 0).

First, we find the derivative of the x and y equations to obtain the slope of the tangent line at the point (t^2 + 7, t^2 + t). The derivative of x = t^2 + 7 is

dx/ dt = 2t

and the derivative of y = t^2 + t is

dy/dt = 2t + 1

So, the slope of the tangent line at the point (t^2 + 7, t^2 + t) is

dy/dx = (dy/dt) / (dx/dt)

dy/dx = (2t + 1)/ 2t

dy/dx = 1 + 1/(2t)

Next, we use the fact that the slope of the tangent line is equal to the ratio of the change in y to the change in x between the point and the origin (0, 0). Since the origin is located at x = 0 and y = 0, we have:

(t^2 + t - 0) / (t^2 + 7 - 0) = 2t + 1)/ (2t)

2t(t^2 + t) = (2t + 1) (t^2 + 7)

2t^3 + 2t^2 = 2t^3 + t^2 + 14t + 7

t^2 - 14t = 7

t^2 - 14t + 49 = 7 + 49

(t - 7)^2 = 56

t - 7 = ±√56

t = 7 ± √56

As we require only positive value t = 7 + √56

--The question is incomplete, answering to the question below--

"find the positive value of the parameter t corresponding to a point on the parametric curve { x = t^2 + 7, y = t^2 + t for which the tangent line passes through the origin. answer exactly."

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Answer:

kaoajaoàwkwk2k2kwkw

Step-by-step explanation:

[tex] \boxed{ \sf \: \\ \\ \\ \\ \\ \\ \\ } \: \: \: \: \: \: \: \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \boxed{ \colorbox{blue}{ \: }}[/tex]

Para completar la piramide hay que ir sumando los polynomios que  hay en cada bloque.

Para construir las piramides, solo debes sumar los polinomios de los bloques inferiores para obtener los superiores.

La primer piramide tiene los valores en los dos bloques de la izquierda:

2r - 3s y 5s - r

Si los sumamos, obtendremos:

(2r - 3s) + (5s - r) = (2r - r) + (-3s + 5s) = r + 2s

Entonces eso es lo que colocamos en el bloque que esta justo arriba.

Si vemos el segundo y el tercero son:

5s - r y 7r - 6s

Sumandolos obtenemos:

5s - r + 7r - 6s = 6r - s

Y eso va en el bloque que esta justo arriba, y asi de a poco vamos completando la piramide.

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The average complexity of linear search for a list of size n is O(n).

The average complexity of linear search for a list of size n is calculated by taking the sum of the number of comparisons for each possible position of the search element, and then dividing it by the total number of possible positions.

For example, if we have a list of size n = 10, and the search element is equally likely to be found in any position, then the number of comparisons to find the element in each position is as follows:

Position 1: 1 comparison Position 2: 2 comparisons Position 3: 3 comparisons Position 4: 4 comparisons Position 5: 5 comparisons Position 6: 6 comparisons Position 7: 7 comparisons Position 8: 8 comparisons Position 9: 9 comparisons Position 10: 10 comparisons

Therefore, the average number of comparisons to find the search element in the list is (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) / 10 = 5.5

This means that the average complexity of linear search for a list of size n is O(n).

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Answer:

C

Step-by-step explanation:

15 (-42 x + 40) = 15 (- 8 x + 244)

15 cancelled on each side

-42x+40= -8x+244

move all the x to one side & numbers to the other,

-34x =204

x=6

Answer:

56

The range is calculated by subtracting the lowest value from the highest value.

The highest value of the set is 78.

The lowest value of the set is 22.

78 - 22 = 56

Step-by-step explanation:

Hope it helps! =D

Answer:

56

Step-by-step explanation:

Trapezoid JKLM is shown on the coordinate plane, the coordinates of L should be (8,-6) if the rule is (x + 5, y - 4), because the coordinates are (3, -2), and you have to add 5 to x, and -4 to y.

The origin of the coordinate system is the intersection of the axes, and the first and second coordinates are known as the abscissa and the ordinate of P, respectively. The coordinates are often represented as two integers enclosed in parenthesis and placed in that particular order, all separated by commas. Coordinates are two integers (Cartesian coordinates) or, in certain cases, a letter and a number that point to a specific place on a grid known as a coordinate plane. The x axis (horizontal) and y axis are the two axes of a coordinate plane, which contains four quadrants (vertical).

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The complete question is as follows:

6x² - 31 x + 40, after factorization we get: (2x - 5) (3x - 8).

correct option: a

Expanding brackets is done in reverse when factorising. By eliminating the most common factors, an expression is fully factored when it is enclosed in brackets. The simplest method of factorization is to identify the term in the equation with the largest common factor. The Grouping technique, the Difference in Two Squares, the Sum or Difference in Cubes, and the Greatest Common Factors (GCF) are the four primary methods of factoring.

Similar to this, factoring is a very useful technique in algebra that is utilised at all levels. Additionally to, of course, simplifying complex expressions, it offers a standard way for solving quadratic equations. Graphing functions also makes advantage of it.

= 6x² - 31 x+40

= 6x² - 15 x - 16 x +40

= 3x (2x - 5) - 8 (2x - 5)

= (2x - 5) (3x - 8)

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(a) The probability that there are less than 2 accidents occur between 3-7pm is 0.2465.

(b) The probability that the next accident occurred within 30 minutes on both days is 0.1358.

Suppose that accidents occur at a rate of 1 per hour from 3-5pm and 6-7pm, and 4 per hour from 5-6pm as Poisson process.

(a) We have to determine the probability that there are less than 2 accidents occur between 3-7pm.

We may use the Poisson distribution to determine the likelihood that there would be less than two accidents between 3 and 7 pm.

The total of the rates for each individual hour represents the rate of accidents during this time period, which is

= 1 + 1 + 4 + 1

= 7 accidents per hours

So the Poisson variable λ = 7

So the probability that there are less than 2 accidents occur between 3-7pm is:

P(X < 2) = P(X = 0) + P(X = 1)

P(X < 2) = [tex]e^{-7}[/tex] × (7^0/0!) + [tex]e^{-7}[/tex] × (7^1/1!)

After simplifying

P(X < 2) = 0.2465

(b) Suppose that on day 1, there was an accident at 3pm and on day 2, at 5pm, then we have to determine the probability that the next accident occurred within 30 minutes on both days.

Since accidents occur in a Poisson process, we may use the Poisson distribution to determine the likelihood that an accident will occur within the next 30 minutes.

Since there are 4 accidents every hour between 5 and 6 o'clock, the likelihood that one will happen in the next 30 minutes is:

P(X = 1) = [tex]e^{-1}[/tex] × (1^1 / 1!)

P(X = 1) = 0.3679

The likelihood that the following event will occur within 30 minutes on both days would thus be

= 0.3679 × 0.3679

= 0.1358

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From a position 17 cm from the circle's center, the tangent to it is 8 cm long.

Distance from a circle's center to any point along its perimeter is known as the radius of the circle. R or r are frequently used to indicate it.

Almost every formula involving circles makes use of this amount.

A circle's radius is used to determine both its surface area and circumference.

Give the circle's radius, r.

Given:

PQ=8cm

PO=17cm

OQ=r

Since the radius across the point of contact is perpendicular to any point on a line, it follows that any point on a line must be.

According to Pythagoras' Theorem, in OPQ, OP 2 = PQ 2 + OQ 2.

(17) ²  = (8) ² +r ²

⇒ r=  √289−64  = √225  =15cm

Consequently, the circle has a 15 cm radius.

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The digit in the ones place of 2^90 is 4. The pattern of the digits in the ones place for powers of 2 follows a repeating cycle of 0, 2, 4, 6, 8, 0, 2, 4, 6, 8 and so on.

The digit in the ones place of 2^88 is 6 because the last digit of 2^88 is 6. The pattern of the digits in the ones place for powers of 2 is 0, 2, 4, 6, 8, 0, 2, 4, 6, 8, etc. Therefore, the digit in the ones place of 2^90 is 4 since the pattern starts over again at 0 after 8.

The pattern of the digits in the ones place for powers of 2 follows a repeating cycle of 0, 2, 4, 6, 8, 0, 2, 4, 6, 8 and so on. This pattern is a result of the fact that 2^n is divisible by 10 for all integers n greater than or equal to 0. Since 10 is divisible by 10, the remainder of 2^n divided by 10 will always be the same for certain powers of 2. The remainder for 2^0 is 0, 2^2 is 4, 2^4 is 6, 2^6 is 8 and 2^8 is 0. This pattern then repeats with 2^10 being 2 and so on. Therefore, the digit in the ones place of 2^90 is 4, since the pattern starts over again at 0 after 8.

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Answer:

y=-4x+2

Step-by-step explanation:

y2-y1/x2-x1

= 10-(-2)/-10-5

=12/-15 (divide by 3)

= -4/5x ---(Slope)

y=mx+b

-2=(-4/5)(5)+b

-2=-4+b (Add 4 on both Sides)

2=b

Put it all together

y=mx+b

Therefore,the equation is : y=-4/5x+2

The solution of the differential equation with the given initial condition is[tex]()=⟨7⋅e^2x, 5⋅e^2x, 3⋅e^2x⟩.[/tex]

Let () be a vector-valued function in three-space. Then the solution of the differential equation ′()=2() with the initial condition [tex](0)=⟨7,5,3⟩[/tex] can be found by solving the system of differential equations:

[tex]′1()=2⋅1()\\′2()=2⋅2()\\′3()=2⋅3()[/tex]

where 1(), 2(), and 3() denote the components of ().

Solving for the general solution of each equation yields:

[tex]1()=7⋅e^2x\\2()=5⋅e^2x\\3()=3⋅e^2x[/tex]

Therefore, the solution of the differential equation with the given initial condition is:

[tex]()=⟨7⋅e^2x, 5⋅e^2x, 3⋅e^2x⟩.[/tex]

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There is a ''negative correlation'' in the data set.

Hence, Option B is correct.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, By the graph;

The graph shows points that are grouped together and are decreasing.

And, The gathered data shows that there is a possibility to get correlation between them.

Thus, The group of data is decreasing.

So, the correlation of the data will be negative in nature.

Therefore, It can be said that the "There is a negative correlation in the data set".

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Answer:

Your answer is B

Answer: 60% boys and 40% girls

Step-by-step explanation:

The total amount of kids in the class would be 13 + 9 = 22 kids.

Boys would make up 13 / 22 = 60% of the class,

Girls would make up 9 / 22 = 40% of the class

Answer:

The value of ? is 1004.

Step-by-step explanation:

I'll use x instead of ?:

[tex]9^x+9^x+9^x=3^{2009}\\3\cdot9^x=3^{2009}\\3\cdot(3^2)^x=3^{2009}\\3\cdot3^{2x}=3^{2009}\\3^{2x+1}=3^{2009}\\2x+1=2009\\2x=2008\\x=1004[/tex]

By graphing, the solution to the given system of equations is: (2, 4).

To solve a system of equations by graphing:

The graph of y = 7/2x - 3 is the red line while that of y = –3/2x + 7 is the red line. They intersect at (2, 4).

Therefore, the solution of the system of equations is: .

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The value of the function when evaluated is 1/2

From the question, we have the following parameters that can be used in our computation:

f(x)=2/√10-6

Express properly

So, we have the following representation

f(x)=2/√(10-x)

Substitute the known values in the above equation, so, we have the following representation

f(-6)=2/√10+6

Evaluate the like terms

f(-6)=2/√16

So, we have

f(-6) = 1/2

Hence, the function value is 1/2

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The digits {1,2,...,5} are randomly arranged in a row so total 5 ordered elements are in the sample space.

The digits {1,2,...,5} are randomly arranged in a row.

We have determine how many ordered elements are in the sample space.

The number of possible ways to choose items from a collection when the order of choice is irrelevant is determined using the combination formula. Combination, to put it simply, is the choosing of items or things from a bigger group when the order doesn't important.

So, we use the combination formula

[tex]^nC_{r} = \frac{n!}{r!(n-r)!}[/tex]

Total digits are 5. So,

Sample space = [tex]^5C_{1}[/tex]

Sample space = [tex]\frac{5!}{1!(5-1)!}[/tex]

Sample space = [tex]\frac{5!}{1!4!}[/tex]

Sample space = [tex]\frac{5\times 4!}{1\times 4!}[/tex]

Sample space = 5

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Salut/Hello!

Answer:

Step-by-step explanation:

x = 5 : 6 + (10 - 2x - 20)
x= 0,8(3) + 10 - 2x - 20
2x + x = 0,8(3) + 10 - 20
3x = 0,8(3) + 10 - 20
3x = -10,8(3)
x = -3.6(1)

I hope it was helpful! :]

According to the linear equation, because 8.8 rounds to 9 and 2.7 rounds to 3, division rounds to 3. His solution of 4.14 equals 4. As a result, it is illogical.

A linear equation is an equation having one or more variables, the maximum power of which is one. A linear equation is an algebraic equation with simply a constant and a first-order (linear) component of the form y=mx+b, where m is the slope and b is the y-intercept. The above is sometimes referred to as a "linear equation with two variables," where y and x are the variables.

The following expression is:

Given expression is:

8.8 ÷ 2.7

≈ 9 ÷ 3

= 3

His answer is 4.14 ≈ 4.

According to the linear equation, division rounds to 3 since 8.8 rounds to 9 and 2.7 rounds to 3. His solution of 4.14 equals 4. It is thus irrational.

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Answer:

Since 6/7  rounds to 1 and 4 4/5 rounds to 5, the sum rounds to 6. Her answer of 5 22/23 rounds to 6. So it is reasonable.

Step-by-step explanation:

There are 7.58 ounces of silver are in the bar.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

A metal bar weights 8.15 ounces.

And, 93% of the bar is silver.

Now, Let the amount of silver in the bar = x

So, We can formulate;

⇒ x = 93% of 8.15

⇒ x = 93/100 × 8.15

⇒ x = 7.58

Thus, the amount of silver in the bar = 7.58 ounces

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Answer: 4.761 (Not Rounded)

Step-by-step explanation: Divide 25/5.25 and that will give you each card price.

Answer:

1 card = $0.21
25 cards = $5.25