Write an equation for the graph below.
y = mx + b

Answer: a) Parent function:

f(x) = √x

Domain: x ≥ 0

Range: y ≥ 0

Applying transformations:

shift 2 units left: f(x+2)

shift 1 unit down: f(x+2)-1

Final equation and graph:

y = √(x+2) - 1

Domain: x ≥ -2

Range: y ≥ -1

b) Parent function:

f(x) = 1/x

Domain: x ≠ 0

Range: y ≠ 0

Applying transformations:

multiply by -2: -2f(x)

shift 4 units up: -2f(x)+4

Final equation and graph:

y = -2/x + 4

Domain: x ≠ 0

Range: y ≠ 4

c) Parent function:

f(x) = 1/x

Domain: x ≠ 0

Range: y ≠ 0

Applying transformations:

shift 3 units right: f(-(x-3))

multiply by -2: -2f(-(x-3))

shift 1 unit up: -2f(-(x-3))+1

Final equation and graph:

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

Domain: x ≠ 3

Range: y ≠ 1

Step-by-step explanation:

Answer:

x = +8

x = -8

That's the thing that I only know. Im a seventh grader(turned 13) so I wouldn't know this fully. Ask someone else to get it fully.

Step-by-step explanation:

5x + 6x - 10 + 12 = 90

11x = -88

x = -8

or

x = 8

To find the next two terms of the sequence, we need to first find the common difference between consecutive terms:

52 - 44 = 8

64 - 52 = 12

80 - 64 = 16

We notice that the common difference is increasing by 4 for each term. Therefore, the next two terms of the sequence are:

80 + 20 = 100

100 + 24 = 124

To determine the nth term of the quadratic sequence, we can use the formula:

an = a1 + (n-1)d + bn^2

where a1 is the first term, d is the common difference, b is the coefficient of n^2, and n is the term number.

Using the first four terms of the sequence, we can form a system of equations:

44 = a1 + b

52 = a1 + d + b

64 = a1 + 2d + b

80 = a1 + 3d + b

Solving for a1 and b, we get:

a1 = 20

b = 24

Substituting these values into the formula for an, we get:

an = 20 + (n-1)4 + 24n^2

an = 24n^2 + 4n - 4

To find the 30th term of the sequence, we simply substitute n = 30 into the formula we just derived:

a30 = 24(30)^2 + 4(30) - 4

a30 = 21,596

To prove that the quadratic sequence will always have even terms, we notice that the first term is even (44 = 2 x 22), and the common difference is even (8 = 2 x 4). Therefore, every term of the sequence can be expressed as an even number plus an even multiple of n^2, which is always even. Hence, the quadratic sequence will always have even terms.

Step-by-step explanation:

Sequence is 44;52;64;80;.....44;52;64;80;.....

General formula is Tn=2n2+2n+40

Sec x is the simplified expression cos(−x)+tan(−x)sin(−x) involving a single trigonometric function with no fractions.

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

The Given expression is

cos(−x)+tan(−x)sin(−x)

Now,

cos(−x) + tan(−x)sin(−x)

= cos x + (- tan x) (- sin x)

= cos x + tan x * sin x

= cos x + (sin x / cos x) * sin x

= (cos²x + sin²x) / cos x     ( As sin²x + cos²x = 1)

= 1/ cos x

= sec x       (As sec x = 1/cos x)

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To find the length of side b in triangle ABC, we can use the Law of Sines. The length of side b is approximately 20.058 inches.

To find the length of side b in triangle ABC, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a triangle.

Using the Law of Sines, we have:

sin(A)/a = sin(B)/b

We are given the measure of angle B as 78 degrees and side a as 16 inches. We can substitute these values into the equation:

sin(A)/16 = sin(78)/b

To find sin(A), we can use the fact that the sum of the angles in a triangle is 180 degrees:

A + B + C = 180

A + 78 + 52 = 180

A = 180 - 78 - 52

A = 50 degrees

Now we can substitute the values into the equation again:

sin(50)/16 = sin(78)/b

To solve for b, we can cross-multiply and isolate b:

b = (16 * sin(78))/sin(50)

We can calculate the length of side b by evaluating this expression using a calculator. The measurement will be roughly 20.058 inches.

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Answer:

A

Step-by-step explanation:

The total area under the curve for x ≥ 6 is 449/4500.

The area under the curve y = 2x-3 from x = 6 to x = t and its evaluation at t = 10 and t = 100The area under the curve y = 2x-3 from x = 6 to x = t can be calculated as follows:

We know that the area of the region under the curve f(x) between x = a and x = b is given by [tex]A = ∫abf(x)dx[/tex]

Since the given function is y = 2x-3, we can write it as y = 2x^(-3) by applying the power rule.

Hence,A = [tex]∫62x^(-3)dx = [-2x^(-2)]6t = -2/t^2 + 2/36[/tex]We need to evaluate this area for t = 10 and t = 100, so we get[tex]A = -2/10^2 + 2/36 = -1/25 + 1/18 = 7/450andA = -2/100^2 + 2/36 = -1/5000 + 1/18 = 449/4500[/tex]Total area under this curve for x ≥ 6

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The theoretical probability for the 1 horned, 1 eyed,  flying, people eater purple is found to be 1/120.

Experimental Probability: Based on actual results rather than mathematical calculations, the experimental probability of an occurrence is the likelihood that the event will actually occur.

Theoretical Probability: Considering that the event is ideal, the theoretical chance that it will occur is the theoretically ideal probability of a specific result. The flaws in the system are not taken into consideration by theoretical probability.

Theoretical Probability = Number of favorable outcomes / Number of possible outcomes.

The given probability are;

Let P(E)  be the theoretical probability  1 horned, 1 eyed,  flying, people eater purple.

Then,

P(E) =  3/4 * 1/5* 2/3* 3/8* 1/2

P(E) =  1/120

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Over the range [5, 7], the definite integral of f(x) = 1 / (x² + 10x + 25) is around -1/60.

To find the definite integral of f(x) = 1 / (x² + 10x + 25) over the interval [5, 7], we can use the following formula:

∫[a,b] f(x) dx = F(b) - F(a)

where F(x) is the antiderivative of f(x).

First, we need to find the antiderivative of f(x):

∫ f(x) dx = ∫ 1 / (x² + 10x + 25) dx

To do this, we can use a technique called partial fraction decomposition:

1 / (x² + 10x + 25)

= A / (x + 5) + B / (x + 5)²

Multiplying both sides by the denominator (x² + 10x + 25), we get:

1 = A(x + 5) + B

Setting x = -5, we get:

1 = B

Setting x = 0, we get:

A + B = 1

A + 1 = 1

A = 0

Therefore, the partial fraction decomposition of f(x) is:

1 / (x² + 10x + 25) = 1 / (x + 5)²

Now we can find the antiderivative:

∫ f(x) dx = ∫ 1 / (x² + 10x + 25) dx = ∫ 1 / (x + 5)² dx

Using the substitution u = x + 5, du = dx, we get:

∫ 1 / (x + 5)² dx = -1 / (x + 5) + C

where C is the constant of integration.

Now we can evaluate the definite integral over the interval [5, 7]:

∫[5,7] f(x) dx = F(7) - F(5)

∫[5,7] f(x) dx = [-1 / (7 + 5) + C] - [-1 / (5 + 5) + C]

∫[5,7] f(x) dx = [-1 / 12 + C] - [-1 / 10 + C]

∫[5,7] f(x) dx = -1 / 12 + C + 1 / 10 - C

∫[5,7] f(x) dx = -1 / 60

Therefore, the definite integral of f(x) = 1 / (x² + 10x + 25) over the interval [5, 7] is approximately -1/60.

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Yes, W_2 = {p_2 = a_2t_2 + a_1t + a_0 ∈ ℙ_2 | a_0 = 2} is a subspace of the vector space ℙ_2.

Yes, W_1 = {[a b c; d 0 0] ∈ M_{2x3} | b = a + c} is a subspace of the vector space M_{2x3}.

Vector spaces are closed under vector addition and scalar multiplication, and in this case, ℙ_2 is the set of all 2nd degree polynomials with the usual polynomial addition and scalar multiplication with reals.

Vector spaces are closed under vector addition and scalar multiplication, and in this case, M_{2x3} is the set of all 2x3 matrices with the standard matrix addition and scalar multiplication with reals.

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Using the Unique factorization theorem for the following integers the standard factored form of 504 is 2³ x 3²x 7 , for 819 is 3² ×7×13 and for  5,445 is 3²×5×7².

The Unique Factorization Theorem states that any positive integer can be written as a product of prime numbers in a unique way. To write each of the integers in standard factored form.

Using this theorem, we can factorize any positive integer into its prime factors. Here are the steps to factorize a number:

The prime factors obtained in this process can then be multiplied together to obtain the standard factored form of the original number . Therefore,

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Answer:

hundreth

Step-by-step explanation:

the 2 is in the tenth and the 3 is in the hundreth

In solving the given question, we can say that ∠ZEFI and ∠ZJIK are equal parallel lines  by  co-exterior angles property.

Geometry parallel lines are coplanar infinite lines that do not intersect anywhere. In a given three-dimensional space, parallel faces are faces that never intersect. Curves with a constant minimum distance between them and no tangents or intersections are said to be parallel. Two lines that lie in the same plane, are equally spaced, and never intersect are called parallel lines in geometry. Can be applied horizontally or vertically. Parallel lines are found in everyday objects such as railroad tracks, rows of books, and crosswalks.  

∠ZHIK and ∠ZEFI are equal by alternative angles property.

∠ZGFD and ∠ZEFD are equal by co-interior angles property.

∠ZGFD and ∠ZEFI are equal by interior alt. angles property.

∠ZEFI and ∠ZJIK are equal by  co-exterior angles property.

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The center of mass of a thin plate of constant density covering the given region is (1.8, 3.6).

To find the center of mass, we must calculate the weighted average of all the points in the region. The region is bounded by the parabola y = 3x - x² and the line y = -3x.

We must calculate the integral of the region and divide by the total mass. The mass is equal to the area times the density, .

The integral of the region is calculated using the limits of the two curves, yielding a final integral of 32/15. Dividing this integral by the density gives the total mass, and multiplying by the density gives us the center of mass, (1.8, 3.6).

We can also find the center of mass by calculating the moments of the plate about the x-axis and y-axis.

The moment about the x-axis is calculated by finding the integral of the parabola and line using the x-coordinate, and the moment about the y-axis is calculated by finding the integral of the parabola and line using the y-coordinate. Once the moments are found, we can divide each moment by the total mass to get the center of mass.

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The area of the prism is given by the sum of the areas of all the parts that compose the prism.

The parts that compose the prism are given as follows:

Hence the area of the prism is given as follows:

A = 3 x 5 + 5 x 10 + 2 x 1/2 x 3 x 10

A = 95 m².

The volume is given by the multiplication of the base area by the height, hence:

Thus:

V = 15 x 10 = 150 m³.

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Answer:

10.24

Step-by-step explanation:

i used an online calculator

Answer:

100 minutes

Step-by-step explanation:

We know

It takes 3 hrs to run a distance of 180 km.

180 / 3 = 60 km / h

60 minutes = 60 km

40 minutes = 40 km

What time it will take to run 100 km?

60 + 40 = 100 minutes

So, it takes 100 minutes to run 100 km.

Mei Mei utilized wrapping paper that was 337.212 square inches in size.

The formula V = 1/3AH, where H is the height of the pyramid or the distance from its base to its apex, may be used to calculate the volume of a triangular pyramid.

To find the amount of wrapping paper Mei Mei used

we need to find the surface area of the triangular pyramid.

The formula for an equilateral triangle's area is as follows:

[tex]A = (\sqrt{(3)/4}) \times s^2[/tex]

where s is a side of the triangle's length.

The base of the triangular base is 13 inches, so the sides of the triangles are also 13 inches.

The slant height of the pyramid is given as 11.26 inches.

Using the formula, we find that the area of each triangular face is:

[tex]A = (\sqrt{(3)/4)} \times s^2 = (\sqrt{(3)/4)} \times 13^2 = 84.303[/tex]

To find the total surface area of the pyramid, we add up the areas of all four triangular faces. There are four triangles, so:

total surface area =[tex]4 \times A = 4 \times 84.303 = 337.212[/tex]

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Complete question -

Mei Mei wraps a gift box in the shape of a triangular pyramid. The figure below shows a net for the gift box.

the sale price of the cell phone after the 35% discount is $315.25.

How to solve and what is sale?

To find the sale price of the cell phone, we need to apply the discount of 35% to the regular price of $485. We can do this by multiplying the regular price by 0.35 and then subtracting the result from the regular price:

Sale price = Regular price - Discount amount

Sale price = $485 - (0.35 x $485)

Sale price = $485 - $169.75

Sale price = $315.25

Therefore, the sale price of the cell phone after the 35% discount is $315.25.

A sale is a temporary reduction in the price of a product or service. Sales are often used by businesses to attract customers and increase sales volume. Sales can be offered for many reasons, such as to clear out inventory, promote a new product, or attract customers during a slow period.

In a sale, the price of a product or service is discounted, either by a fixed amount or by a percentage of the regular price. For example, a store might offer a 20% discount on all clothing items, or a car dealership might offer a $5,000 discount on a particular model of car.

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Answer: Let x be the number of hamburgers sold.

Then, the number of cheeseburgers sold is 3x.

The total number of burgers sold is x + 3x = 4x.

Given that the total number of burgers sold is 416, we have:

4x = 416

x = 416/4

x = 104

Therefore, 104 hamburgers were sold.

Step-by-step explanation:

The volume of the sphere which is equivalent to the lung capacity is approximately =2,571 cm³

To calculate the volume of a sphere the formula used = V = 4/3 πr³

Radius = 8.5 cm

First cube the radius = 8.5³ = 614.125

The, multiply r³ by π = r³×π = 614.125× 3.14= 1928.3525

Take this answer and multiply it by 4 = 4×1928.3525= 7713.41

Last, divide this answer by 3 = 7713.41/3 = 2571.136666

Therefore the volume of the balloon = 2,571 cm³(approximately)

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Answer:

In the picture.

34 ft.

Answer: 844344.55555

The number of papers xavier have remaining after working for 12 hours is 18

Xavier can grade 6 papers per hour, so in 12 hours he can grade:

6 papers/hour x 12 hours = 72 papers

Therefore, after working for 12 hours, Xavier would have

90 - 72 = 18 papers remaining to grade.

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Answer:

Y=x^2+7x-3

complete the square to re-write the quadratic function in vertex form.

pls help

Step-by-step explanation:

To complete the square, we need to add and subtract a constant term inside the parentheses, which when combined with the quadratic term will give us a perfect square trinomial.

y = x^2 + 7x - 3

y = (x^2 + 7x + ?) - ? - 3 (adding and subtracting the same constant)

y = (x^2 + 7x + (7/2)^2) - (7/2)^2 - 3 (the constant we need to add is half of the coefficient of the x-term squared)

y = (x + 7/2)^2 - 49/4 - 3

y = (x + 7/2)^2 - 61/4

So the quadratic function in vertex form is y = (x + 7/2)^2 - 61/4, which has a vertex at (-7/2, -61/4).

As Masons backyard deck is rectangular, the length of the deck is 22 feet.

Let's start by using algebra to solve for the length of the rectangular deck.

Let L be the length of the deck.

Then, the width of the deck is L - 12.

The perimeter is the sum of all four sides, so we have:

Perimeter = 2L + 2(L - 12) = 64

Simplifying the equation, we get:

2L + 2L - 24 = 64

Combining like terms, we get:

4L - 24 = 64

Adding 24 to both sides, we get:

4L = 88

Dividing both sides by 4, we get:

L = 22

Therefore, the length of the deck is 22 feet.

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According to the given information, the solution to H(x) = 3 is x = 2.

What is equation?

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation typically consists of two parts: the left-hand side (LHS) and the right-hand side (RHS). The LHS and RHS are separated by an equals sign (=), indicating that they have the same value. The general form of an equation is: LHS = RHS

To solve for x when H(x) = 3, we substitute 3 for H(x) in the equation and solve for x:

H(x) = -x + 5

3 = -x + 5

Subtracting 5 from both sides, we get:

-2 = -x

Multiplying both sides by -1, we get:

2 = x

Therefore, the solution to H(x) = 3 is x = 2.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathtt{h(x) = -x + 5}\\\\\mathtt{3 = -x + 5}\\\\\mathtt{-x + 5 = 3}\\\\\textsf{SUBTRACT 5 to BOTH SIDES}\\\\\mathtt{-x + 5 - 5 = 3 - 5}\\\\\textsf{SIMPLIFY it}\\\\\mathtt{-x = 3 - 5}\\\\\mathtt{-x = -2}\\\\\mathtt{-1x = -2}\\\\\textsf{DIVIDE }\mathsf{-1}\textsf{ to BOTH SIDES}\\\\\mathtt{\dfrac{-1x}{-1} = \dfrac{-2}{-1}}\\\\\textsf{SIMPLIFY it}\\\\\mathtt{x = \dfrac{-2}{-1}}\\\\\mathtt{x = 2}[/tex]

[tex]\huge\text{Therefore your answer should be:}\\\\\huge\boxed{\mathtt{x = 2}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The system of inequalities that represents the number of quarters, x, and the number of dimes, y, that Mai could have is given by:

x + y ≥ 10 and 0.25x + 0.1y < 2

These are the two systems of inequalities that represent the number of quarters, x, and the number of dimes, y, that Mai could have.

Let x be the number of quarters and y be the number of dimes that Mai has. Then, the system of inequalities can be represented as:

Thus, the first inequality is x + y ≥ 10.

Also, Mai has less than $2.00, therefore, the second inequality is 0.25x + 0.1y < 2. The value of x and y are assumed to be non-negative integers.+

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The area of the square base = x².

we have:l = w = x ... (2) ... And, h = V/lw = V/x² ... (3) ...

The dimension of the box that minimizes the amount of material used is x =  (2V)1/3. A(x) = x² + 4V/x, A'(x) = 2x - 4V/x², x =  (2V)1/3

The given volume of the box is 62500 cm³. We wish to find the dimensions of the box that minimize the amount of material used.

To obtain the formula for the surface area of the box in terms of only x, the length of one side of the square base, we use the formula for the volume of a box:V = lwh ... (1) ... where V is the volume, l is the length, w is the width, and h is the height of the box. Here, the base of the box is a square with side length x.

Hence, the area of the square base = x². Therefore, we have:l = w = x ... (2) ... And, h = V/lw = V/x² ... (3) ... We can substitute (2) and (3) in (1) to get the formula for V in terms of x as follows:V = x² V/x² A(x) = A(x) = x² + 4xhA(x) = x² + 4x(V/x²) = x² + 4V/x

Now, to find the derivative A'(x) of A(x), we differentiate A(x) with respect to x:A'(x) = 2x - 4V/x²  A'(x) = 0 when x =  (2V)1/3. Therefore, the dimension of the box that minimizes the amount of material used is x =  (2V)1/3. A(x) = x² + 4V/x, A'(x) = 2x - 4V/x², x =  (2V)1/3

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