Sketch the graph, showing one complete cycle. State the period and amplitude, and the greatest and least values of yy=3sin(θ−π/2)

Step-by-step explanation:

the area of a triangle is always

baseline × height / 2

where baseline and height are perpendicular (at a 90° angle) to each other.

so, in our case the area is

7 × 2 / 2 = 7 × 1 = 7 units²

Answer:

16x² + 64x + 64

Step-by-step explanation:

Given

A = 16x²

Increasing the sides by 2, substitute x = x + 2 into A

A = 16(x + 2)² ← expand factor using FOIL

   = 16(x² + 4x + 4 ) ← distribute

   = 16x² + 64x + 64

Answer:

30,000

Step-by-step explanation:

Answer:

your answer is 114

I hope it's helps you

Answer:

C

Step-by-step explanation:

You can divide the hexagon into a rectangle and two triangles. Using the area formulas for all shapes, the area of each can be calculated and added together.

\(x^2 -4x +1 = 0\)

According to the Zero-Product Property, if you have the Quadratic Equation, \((x +a)(x +b) =0\), it's roots will be \(x = -h\) and \(x = -k\).

If we want our roots to be \(2 -\sqrt 3\) and \(\frac{1}{2 -\sqrt 3}\\\), then \(-h = 2 -\sqrt 3\) and \(-k = \frac{1}{2 -\sqrt 3}\\\).

Solving for \(h\):

\(-h = 2 -\sqrt 3 \\ -h \cdot -1 = (2 -\sqrt 3) \cdot -1 \\ h = \sqrt 3 -2\)

Solving for \(k\):

\(-k = \frac{1}{2 -\sqrt 3} \\ -k \cdot -1 = \frac{1}{2 -\sqrt 3} \cdot -1 \\ k = \frac{1}{\sqrt 3 -2}\)

Writing the equation:

\((x +h)(x +k) = 0 \\ (x +(\sqrt 3 -2))(x +\frac{1}{\sqrt 3 -2}) = 0\)

Unsurprisingly, the answer shouldn't be that because it shouldn't be that easy. By that, we have to apply the distributive property.

\((x +(\sqrt 3 -2))(x +\frac{1}{\sqrt 3 -2}) = 0 \\ x(x +(\sqrt 3 -2)) +\frac{1}{\sqrt 3 -2}(x +(\sqrt 3 -2)) = 0 \\ x^2 +(\sqrt 3 -2)x +\frac{1}{\sqrt 3 -2}x +\frac{1}{\sqrt 3 -2}(\sqrt 3 -2) = 0 \\ x^2 +((\sqrt 3 -2) +\frac{1}{\sqrt 3 -2})x +1 = 0 \\ x^2 + (\frac{(\sqrt 3 -2)^2}{\sqrt 3 -2} +\frac{1}{\sqrt 3 -2})x +1 = 0 \\ x^2 +\frac{3 -4\sqrt 3 +4 +1}{\sqrt 3 -2}x +1 = 0 \\ x^2 +\frac{8 -4\sqrt 3}{\sqrt 3 -2}x +1 = 0 \\ x^2 +\frac{-4(\sqrt 3 -2)}{\sqrt 3 -2}x +1 = 0 \\ x^2 -4x +1 = 0\)

The quadratic equation will be y = (x - 2 - √3)[x - 1/(2-√3)].

Let b, c, d, and e be the zeroes of the polynomial. And 'a' be the leading coefficient.

Then the polynomial is given as,

⇒ a(x - b)(x - c)(x - d)(x - e)

The degree of the polynomial will be greater than or equal to the number of zeroes.

Write a quadratic equation if its roots are: 2-√3, and 1/(2-√3) assuming that the leading coefficient a = 1.

Then the equation of the quadratic equation will be

y = 1(x - 2 - √3)[x - 1/(2-√3)]

y = (x - 2 - √3)[x - 1/(2-√3)]

The quadratic equation will be y = (x - 2 - √3)[x - 1/(2-√3)].

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The R= {y | y is an integer and -5 ≤ y ≤ -4} is null set because there is no integers between -5 and -4.

The set is

R= {y | y is an integer and -5 ≤ y ≤ -4}

An integer is a combination of number zero, all the positive numbers and negative numbers without any fraction.

Any set that does not contains any numbers or elements is called null set, which is also called empty set or void set. Null set can be denoted as {} or ∅.

The set is R= {y | y is an integer and -5 ≤ y ≤ -4}

There is no integers between -5 and -4, therefore it is a null set

Hence, The R= {y | y is an integer and -5 ≤ y ≤ -4} is null set because there is no integers between -5 and -4.

The complete question is :

Write the set in roaster form R= {y | y is an integer and -5 ≤ y ≤ -4}

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The area of the composite figure whose vertices have the  (2,-2), (2,1), (4,2), (6,2), (4,-1) coordinates is 6 square units

We first need to plot all the given points A  (2,-2), B (2,1), C (4,2), D (6,2)and E (4,-1) which is coordinate geometry

After joining the Points which is a pentagon and it can be divided in two shapes one is triangle CDE and a quadrilateral ABCE

Using the distance formula

BC = \(\sqrt{(y2-y1)^{2}+(x2-x1)^{2} }\) = \(\sqrt{(2-1)^{2} + (4-2^{2} }\) = √5

Since BC = AE and BC ll AE , we can say ABCE is a parallelogram

area of a parallelogram = base × Altitude

                                      = 2 × 2= 4

Area of triangle CDE where CD is perpendicular and CE is the base

                        = 1/2 ( 2×2)

                        = 1/2 (4)

                         = 2 square units

So the area of ABCDE = Area of ABCE + area of CDE

                                     = 4 square units + 2 square units

                                      = 6 square units

Hence, the area of the composite figure whose vertices have the  (2,-2), (2,1), (4,2), (6,2), (4,-1)coordinates is 6 square units

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In triangle ABC

a) The value of x = 29⁰

b) The angle c equal to 93⁰

A triangle is a closed plane figure that is formed by connecting three line segments, also known as sides, at their endpoints. The three endpoints, or vertices, where the sides of the triangle meet are not collinear. Triangles are important in mathematics and geometry because they are the simplest polygon that can exist in two-dimensional space.

In a triangle, the sum of all interior angles is always 180 degrees. Therefore, we can use this fact to find the value of x and angle c.

We know that:

angle a = 35⁰

angle b = 52⁰

angle c = 3(x+2)⁰

Using the fact that the sum of all interior angles in a triangle is 180 degrees, we can write:

angle a + angle b + angle c = 180

Substituting the values we know, we get:

35 + 52 + 3(x+2) = 180

Simplifying the equation, we get:

87 + 3x + 6 = 180

3x + 93 = 180

3x = 87

x = 29

Therefore, x = 29⁰

To find angle c, we can substitute the value of x into the equation we were given for angle c:

angle c = 3(x+2)

angle c = 3(29+2)

angle c = 3(31)

angle c = 93

Therefore, angle c is equal to 93⁰.

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Answer:

BODMAS RULE

(c-3)²=100

c²-6c+9=100

c²-6c=100-9

c²-6c=91

c²-6c-91=0

then factories

Answer:

9

Step-by-step explanation:

1-log (x+1) = log(x-8)

<=> log 10 -log (x+1) = log(x-8)

10/(x+1)=(x-8)

=> (x+1) (x-8)= 10

x²-7x-8=10

x²-7x-18=0

(x-9) (x+2)=0

x=9 or x=-2

so, x=9 is the possible value

One angle measure provided (27 degrees), to determine the lengths of the sides or the measures of the other Angles.

The triangle, we need more information about the triangle, such as the lengths of the sides or the measures of other angles. The given information, "27 degrees," only specifies one angle of the triangle, but it is not sufficient to solve the triangle completely.

To solve a triangle, we typically need at least three pieces of information, which can include side lengths, angle measures, or a combination of both. With only one angle measure provided (27 degrees), we are unable to determine the lengths of the sides or the measures of the other angles.

To fully solve the triangle, we would need additional information such as the lengths of the sides or measures of at least two more angles. Without this additional information, it is not possible to provide a complete solution or determine the lengths of the sides or the measures of the other angles in the triangle.

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Check the picture below.

Answer:

10

Step-by-step explanation:

The amount Siya will spend on tiles is given by the expression (1.1 x T / 6) x R234, where T represents the required number of tiles. To calculate the amount Siya will spend on tiles, we need to determine the number of boxes of tiles he needs to purchase and then multiply it by the price per box.

First, we need to determine the number of tiles required. Let's assume the required number of tiles is represented by the variable "T."

Since the builder recommends buying 10% more tiles in case of breakages, Siya needs to purchase 110 percentage of the required number of tiles. This can be calculated as:

110% of T = 1.1 x T

Next, we need to convert the number of tiles into the number of boxes required. We know that one box contains 6 tiles, so the number of boxes Siya needs to purchase is:

Number of boxes = (1.1 x T) / 6

Finally, we can calculate the total cost by multiplying the number of boxes by the price per box:

Total cost = (1.1 x T / 6) x R234

Please note that without knowing the specific number of tiles required (T), we cannot provide an exact amount Siya will spend.

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The straight-line distance between Akira's house and Cooper's house is 6.13 kilometers (rounded to the nearest tenth)

Given that,To get from home to his friend Akira's house, Jaden would have to walk 2.8 kilometers due east.The straight-line distance between Akira's house and Cooper's house is given by the distance between two points in a coordinate plane. Let the home be the origin (0, 0) of the coordinate plane and Akira's house be represented by the point (2.8, 4.7). Similarly, let Cooper's house be represented by the point (8.3, 7.4).The distance formula between the two points (2.8, 4.7) and (8.3, 7.4) is given by:distance = √[(8.3 - 2.8)² + (7.4 - 4.7)²]= √[5.5² + 2.7²]= √(30.25 + 7.29)= √37.54= 6.13 km (rounded to the nearest tenth)

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Answer:

The permeter will be 26 units

Step-by-step explanation:

First to find this you need to know what the value of x is to do this I will use the equation 3x - 7 = x + 2

1. add seven to both sides leaving 3x = x + 9

2. Then subtract the 1x from both sides leaving 2x = 9

3. Then divide 9 by 2 which will be 4.5, x = 4.5

Then just plug 4.5 into each x value 4.5 + 2 and 3(4.5) - 7

1. 4.5 + 2 = 6.5

2. 3(4.5) - 7              13.5 - 7 = 6.5

The perimeter of the rectangle below in simplest form will be 4(x - 3).

Length of the rectangle = 3x - 7

Width of the rectangle = x+2

The perimeter of a rectangle is given as 2(length + width). The perimeter of the rectangle given will then be:

= 2(length + width)

= 2(3x - 7) + 2(x + 2)

= 6x - 14 + 2x + 4

= 4x - 12 = 4(x - 3)

Therefore, the perimeter of the rectangle in simplest form will be 4(x - 3).

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Answer: 7 Per Plain wrapping paper, and 8 Per Shiny wrapping paper

Hope this helps :)

Answer:

in total for both would be 19

Step-by-step explanation:

I'm not good at math but trying to help

Answer: 6/14 and 42/99

Step-by-step explanation:

The standard quadratic equation is (c) y = x² + 5x - 66

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

Zeros  -11 and 6

This means that

x = -11 and x = 6

The quadratic equation can then be calculated as

y = (x - 6) * (x + 11)

Evaluate the products

y = x² - 6x + 11x - 66

Evaluae the like terms

y = x² + 5x - 66

Hence, the equation is y = x² + 5x - 66

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The Interpretatiom of the equation is that;

w represents number of weeks she will have saved for the remaining items

$25 represents the amount she saves per week

$65 represents the amount she has already saved

The algebra word problem can be solved by using variables to denote certain parameters I'm the question.

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

y = mx + c

Where;

m is slope

c is y-intercept

We are given the equation:

$25w + $65

This equation represents the amount of money Kelly will have saved after some amount of weeks.

Thus;

w represents number of weeks she will have saved for the remaining items

$25 represents the amount she saves per week

$65 represents the amount she has already saved

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Answer:

No..

Step-by-step explanation:

Because 34-2=32 and if u still had one left it would be 31. So No

Answer:

(x + i) (x - i)

Step-by-step explanation:

The expression x^2 + 1 is a sum of squares, which means that it cannot be factored using real numbers. However, it can be factored using complex numbers.

To factor x^2 + 1, we can use the fact that i^2 = -1, where i is the imaginary unit.

We can rewrite x^2 + 1 as:

x^2 + 1 = x^2 - (-1)

Now, we can use the difference of squares formula to factor x^2 - (-1):

x^2 - (-1) = (x + i)(x - i)

Therefore, the factored form of x^2 + 1 is:

(x + i)(x - i)

Answer:

Emma types at a rate of 45 words per minute.

Step-by-step explanation:

I know this because if you divide 90/2 you can get 45 because as you see on the graph, every two minutes is 90 words, so just divide 90/2.

To find how many shares Jerry owns we can use the rule of three:

then:

Therefore he owns 960 shares.

(i)  The partial fraction decomposition of\(100/(x^7 * (10 - x))\) is\(100/(x^7 * (10 - x)) = 10/x^7 + (1/10^5)/(10 - x).\) (ii) The expression for t in terms of x is t = 10 ± √(100 + 200/x).

(i) To express the rational function 100/(\(x^7\) * (10 - x)) in partial fractions, we need to decompose it into simpler fractions. The general form of partial fractions for a rational function with distinct linear factors in the denominator is:

A/(factor 1) + B/(factor 2) + C/(factor 3) + ...

In this case, we have two factors: \(x^7\) and (10 - x). Therefore, we can express the given rational function as:

100/(\(x^7\) * (10 - x)) = A/\(x^7\) + B/(10 - x)

To determine the values of A and B, we need to find a common denominator for the right-hand side and combine the fractions:

100/(x^7 * (10 - x)) = (A * (10 - x) + B * \(x^7\))/(\(x^7\) * (10 - x))

Now, we can equate the numerators:

100 = (A * (10 - x) + B * \(x^7\))

To solve for A and B, we can substitute appropriate values of x. Let's choose x = 0 and x = 10:

For x = 0:

100 = (A * (10 - 0) + B * \(0^7\))

100 = 10A

A = 10

For x = 10:

100 = (A * (10 - 10) + B *\(10^7\))

100 = B * 10^7

B = 100 / 10^7

B = 1/10^5

Therefore, the partial fraction decomposition of 100/(\(x^7\) * (10 - x)) is:

100/(\(x^7\) * (10 - x)) = 10/\(x^7\) + (1/10^5)/(10 - x)

(ii) Given the differential equation: dx/dt = (1/100) *\(x^2\) * (10 - x)

We are also given x = 1 when t = 0.

To solve this equation and obtain an expression for t in terms of x, we can separate the variables and integrate both sides:

∫(1/\(x^2\)) dx = ∫((1/100) * (10 - x)) dt

Integrating both sides:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) + C

Where C is the constant of integration.

Now, we can substitute the initial condition x = 1 and t = 0 into the equation to find the value of C:

-1/1 = (1/100) * (10*0 - (1/2)*\(0^2\)) + C

-1 = 0 + C

C = -1

Plugging in the value of C, we have:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) - 1

To solve for t in terms of x, we can rearrange the equation:

1/x = -(1/100) * (10t - (1/2)\(t^2\)) + 1

Multiplying both sides by -1, we get:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) - 1

Simplifying further:

1/x = -(1/100) * (10t - (1/2)\(t^2\)) + 1

Now, we can isolate t on one side of the equation:

(1/100) * (10t - (1/2)t^2) = 1 - 1/x

10t - (1/2)t^2 = 100 - 100/x

Simplifying the equation:

(1/2)\(t^2\) - 10t + (100 - 100/x) = 0

At this point, we have a quadratic equation in terms of t. To solve for t, we can use the quadratic formula:

t = (-(-10) ± √((-10)^2 - 4*(1/2)(100 - 100/x))) / (2(1/2))

Simplifying further:

t = (10 ± √(100 + 200/x)) / 1

t = 10 ± √(100 + 200/x)

Therefore, the expression for t in terms of x is t = 10 ± √(100 + 200/x).

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The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

we have that

variables" because the numbers they represent can vary—that is, we can substitute one or more numbers for the letters in the expression. Coefficients are the number part of the terms with variables

example

5x

In the term 5x

x is the variable

5 is a coefficient