Please help with these two equations, and please show work as well, thank you!

An equation that models the trigonometric graph is:

y = 4 sin 4x

The general form for an equation that models a wave is this:

±a (sin/cos) (2π(x - p)/T)

where:

a is the amplitude

p is the phase shift

T is the period.

The ±ve will turn into +ve if the graph tends to start from the positive direction, and then turns -ve if it the graph tends to start from the negative direction.

The (sin/cos) will definitely become sine if the graph starts at 0 before it is being shifted. Then, it becomes cosine if the graph begins at the amplitude.

In this problem, we see that the graph begins as positive, and then at the amplitude with no phase shift, we see that the ±ve becomes +ve, (sin/cos) becomes sin, and p becomes zero. Plugging in the given values  in the problem, we see that a = 4 and T = π/2.

We see that this equation becomes:

y = 4sin(2πx/(π/2)).

y = 4 sin 4x

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13.) The simplified polynomials that can represent the area and perimeter of the large rectangle =40x + 5x² and

12X + 16 respectively.

14.)The simplified polynomials that can represent the area and perimeter of the large rectangle =21+10x + x² and 20+4x respectively.

To determine the simplified polynomials, the formula for the area and perimeter of the rectangule should be used. That is:

Area of rectangle = length×width

where;

length = 5x

width = 8+X

Area = 5x * 8+X

= 40x + 5x²

Perimeter of rectangle = 2(length+width)

= 2(5x + 8+X)

= 10x + 16 + 2x

= 12X + 16

For question 14.)

Area of rectangle = length× width

where;

length = 7+X

width = 3+X

Area = 7+X × 3+X

= 21+7x+3x +x²

= 21+10x + x²

Perimeter = 2(length+width)

= 2(7+X+3 + X)

= 2(10+2x)

= 20+4x

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Answer: 0.

Step-by-step explanation:

        y-(1/2*x+5)=0 STEP 1:              

simplify 1/2

Equation at the end of step 1:         1        

 y -  ((— • x) +  5)  = 0

Answer: 25%

Step-by-step explanation:

51/204=0.25

0.25 x 100 = 25

Answer:25%

Step-by-step explanation:

Answer:

[tex]=\left(x-2\right)\left(x-3\right)\\[/tex]

Step-by-step explanation:

Given:

[tex]x^2-5x\:+6[/tex]

To find:

Equivalent to x^2-5x+6

Explanation:

[tex]x^2-5x+6\\=\left(x^2-2x\right)+\left(-3x+6\right)\\=x\left(x-2\right)-3\left(x-2\right)\\\mathrm{Factor\:out\:common\:term\:}x-2\\=\left(x-2\right)\left(x-3\right)[/tex]

Final Answer:

(x-2)(x-3)

The solution for x is -48, the answer is D) -48.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It represents a value that can change based on the values assigned to the variables.

Starting with:

x:4 = 12

Multiplying both sides by -1 gives:

(-x÷4) = -12

Simplifying the left side:

x÷4 = -12

Multiplying both sides by 4 gives:

x = -48

Therefore, the solution for x is -48, the answer is D) -48.

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a) Yes, the function is in standard form.

  Degree = 2

  Exponent = 2

  Constant term = -1

b) No, the function is not in standard form.

   And it doesn't have the degree, exponent and constant term.

Firstly, let's consider the function f(x) = x(x-1). To determine if it is a polynomial function, we need to check if all of its terms have non-negative integer exponents. In this case, we see that f(x) can be written as x² - x, which has only two terms, and each term has a non-negative integer exponent. Therefore, f(x) is a polynomial function.

In this case, the degree of f(x) is 2 because the highest exponent of x is 2.

In this case, the leading term of f(x) is x², and its leading coefficient is 1.

Finally, the constant term is the term that does not have the variable in it. Here, the constant term of f(x) is -1.

Next, let's consider the function f(x) = 3 - 1/2 x. We can see that f(x) is not a polynomial function because it has a term with a negative exponent.

Polynomial functions must have non-negative integer exponents on all terms.

Therefore, the answer to the first question is 'no.'

Since f(x) is not a polynomial function, it does not have a degree, leading term, or constant term.

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1) Line AB

2) Ray AB

3) Line segment AB

4)Ray BA

The first drawing is a line AB because a line passing through two different points A and B

The second drawing is ray AB because it started at A

The third drawing is a line segment AB because it is part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints

The fourth drawing is ray BA

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Note that equation of a parabola with a vertical axis, vertex (h, k), and directrix y = k – p, where p is a nonzero real number is (y-k)² = 4p(x-h).

The equation of a parabola with a vertical axis, vertex (h, k), and directrix y = k – p, where p is a nonzero real number, is:

(y - k)²   = 4p( x -  h)

If the vertex is at the origin (h = 0, k = 0 ), the equation an be simplified to....

y² = 4px

where p is still a nonzero real number.

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The solution for the variable x is x = 8.4

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

The right triangle

Using the proportion of similar triagles, we have

x/7 = 10/x

This gives

x * x = 7 * 10

So, we have

x² = 70

Next, we have

x = √70

Evaluate

x = 8.4

Hence, the solution for the variable x is x = 8.4

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x = -6.

[tex]\sf \dfrac{3x+4}{3} -\dfrac{2x}{x-3} =x[/tex]

Applying the distributive property of multiplication on the left hand side:

[tex]\sf (3)(\dfrac{3x+4}{3} -\dfrac{2x}{x-3}) =x(3)\\ \\ \\{3x+4} -\dfrac{(3)2x}{x-3}=3x\\ \\ \\{3x+4} -\dfrac{6x}{x-3}=3x[/tex]

Applying the distributive property of multiplication:

[tex]\sf (x-3)({3x+4} -\dfrac{6x}{x-3})=3x(x-3)\\ \\ \\(x-3)({3x+4}) -6x=3x(x-3)\\ \\ \\(x)(3x)+(x)(4)+(-3)(3x)+(-3)(4) -[6x]=3x(x-3)\\ \\ \\[/tex]

Check the image below to see an illustration of this process.

[tex]\sf 3x^{2} +4x-9x-12 -[6x]=3x(x-3)\\ \\ \\3x^{2} +4x-9x-12 -6x=3x(x-3)\\ \\ \\3x^{2} -11x-12 =3x(x-3)[/tex]

Now simplifying on the right hand side (applying the same logic as last step).

[tex]\sf 3x^{2} -11x-12 =3x(x-3)\\ \\ \\3x^{2} -11x-12 =(3x)(x)+(3x)(-3)\\ \\ \\3x^{2} -11x-12 =3x^{2}-9x[/tex]

[tex]\sf 3x^{2} -11x-12+9x =3x^{2}-9x+9x\\ \\ \\3x^{2} -2x-12 =3x^{2}[/tex]

[tex]\sf 3x^{2} -2x-12-3x^{2} =3x^{2}-3x^{2}\\ \\ \\-2x-12 =0[/tex]

[tex]\sf -2x-12+12=0+12\\ \\ \\-2x=12[/tex]

[tex]\sf \dfrac{-2x}{-2} =\dfrac{12}{-2} \\ \\ \\x =-6[/tex]

If "x= -6" is the correct answer, substituting "x" by "-6" on the original equation should return the same value on both sides of the equal (=) symbol. Let's test!

[tex]\sf \dfrac{3(-6)+4}{3} -\dfrac{2(-6)}{(-6)-3} =(-6)\\ \\-6=-6[/tex]

That's correct!

x = -6 is the corect answer.

Probability that event A or B takes place is, P(A or B) = 16/21.

Here from the Venn diagram we can obtain that,

Probability of occurring event A = 2/21 + 4/21 = (2 + 4)/21 = 6/21

Probability of occurring event B = 10/21 + 4/21 = (10 + 4)/21 = 14/21

Probability of occurring event A and event B both = 4/21

So, P(A) = 6/21

P(B) = 14/21

P(A and B) = 4/21

We know that the union of events formula,  

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 6/21 + 14/21 - 4/21

P(A or B) = (6 + 14 - 4)/21

P(A or B) = 16/21

Hence the value of P(A or B) = 16/21.

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The surface area of the given composite solid is calculated as: 200.24 square units.

Surface area of the composite solid = surface area of rectangular prism + surface area of cylinder - 2(area of the base of the cylinder)

Surface area of rectangular prism = length * width * height = 10 * 3 * 5

= 150 square units.

Surface area of cylinder = 2πr(h + r)

height (h) = 4

Radius (r) = 2

Plug in the values:

Surface area of cylinder = 2 * 3.14 * 2(4 + 2) = 75.36 square units

Area of the base of the cylinder = πr² = 3.14 * 2²

= 12.56 square units

Thus, we have:

Surface area of the composite solid = 150 + 75.36 - 2(12.56) = 200.24 square units.

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As a result, the prism's volume is given by V = lwh = 3 x 5 x 5.5 = 82.5 cubic yards. Thus, option C—eighty two and a half yards—is the correct response.

The quantity of room an object takes up in three dimensions is measured by its volume. It is frequently expressed in cubic units like cubic metres, cubic feet, and cubic centimetres. Mathematics formulas that are particular to the shape of the object can be used to calculate its volume, such as V = l w h for a rectangular shape or V = (4/3)r3 for a sphere.

given

V = lwh is the formula for calculating the volume of a rectangular prism, where l, w, and h stand for the prism's length, width, and height, respectively.

Here, the dimensions are 3 yards in length, 5 yards in breadth, and 5.5 yards in height.

As a result, the prism's volume is given by V = lwh = 3 x 5 x 5.5 = 82.5 cubic yards.

Thus, option C—eighty two and a half yards—is the correct response.

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Answer:

the car's angular speed is 72,000π radians per hour.

the car's linear speed is approximately 100.53 miles per hour.

Step-by-step explanation:

To find the car's angular speed in radians per hour, we can start by finding the angular speed in radians per second.

The formula for angular speed is:

ω = 2πf

where ω is the angular speed in radians per second, and f is the frequency or rate of rotation in revolutions per second.

In this case, the wheel is spinning at a rate of 10 revolutions per second, so:

ω = 2π(10) = 20π radians per second

To convert this to radians per hour, we can multiply by the number of seconds per hour:

20π radians per second × 3600 seconds per hour = 72,000π radians per hour

To find the car's linear speed in miles per hour, we can use the formula:

v = rω

where v is the linear speed, r is the radius of the wheel, and ω is the angular speed in radians per second.

The radius of the wheel is half the diameter, or 9 inches. To convert this to miles, we can divide by 12 and then by 5280:

9 inches ÷ 12 inches per foot ÷ 5280 feet per mile = 0.000142045 miles

Now we can substitute the values we have found:

v = (0.000142045 miles) × (18/2 inches) × (20π radians per second)

v ≈ 100.53 miles per hour

Answer:

(i) 10 revolutions = 10(2π) = 20π radians

10 revolutions/sec =

(20π radians/sec)(3,600 sec/hr) =

72,000π radians/hr

(ii) C = 18π inches

10 revolutions × 18π inches =

180π inches

(180π in./sec)(3,600 sec/hr) =

(648,000π in./hr)(1 mi./63,360 in.)

= 225π/22 miles/hour

= about 32.13 miles/hour

Step-by-step explanation:

The equation of the line (by inspection) is y = 1/2 x

Answer:

[tex]5 {}^{3} \times 10 {}^{ - 2} \\ = 5 {}^{3} \times \frac{1}{10 {}^{2} } \\ = 5 {}^{3} \times \frac{1}{2 {}^{2} 5 {}^{2} } \\ = 5 \times \frac{1}{4 \\ } \\ = \frac{5}{4} [/tex]

hope it helps

Answer:

Step-by-step explanation:

15.) [tex]\sqrt{12}[/tex]

      [tex]\sqrt{4}[/tex] * [tex]\sqrt{3}[/tex]

      Answer: 2[tex]\sqrt{3}[/tex]

17.) Distribute 3[tex]\sqrt{3}[/tex] into both sides of the parentheses

     3[tex]\sqrt{3}[/tex] * 4 = 12[tex]\sqrt{3}[/tex]

     3[tex]\sqrt{3}[/tex] * -3[tex]\sqrt{5}[/tex] = -9[tex]\sqrt{15}[/tex]

     Answer: 12[tex]\sqrt{3}[/tex] - 9[tex]\sqrt{15}[/tex]

19.) Distribute 4[tex]\sqrt{15}[/tex] into both sides of the parentheses

      4[tex]\sqrt{90}[/tex] + 4[tex]\sqrt{75}[/tex]

      4*[tex]\sqrt{9}[/tex]*[tex]\sqrt{10}[/tex] + 4*[tex]\sqrt{25}[/tex]*[tex]\sqrt{3}[/tex]

      4*3*[tex]\sqrt{10}[/tex] + 4*5*[tex]\sqrt{3}[/tex]

      12[tex]\sqrt{10}[/tex] + 20[tex]\sqrt{3}[/tex]

21.) Distribute [tex]\sqrt{15}[/tex] into both sides of the parentheses

      2[tex]\sqrt{150}[/tex] - 4[tex]\sqrt{90}[/tex]

      2*[tex]\sqrt{25}[/tex]*[tex]\sqrt{6}[/tex] - 4*[tex]\sqrt{9}[/tex]*[tex]\sqrt{10}[/tex]

      2*5*[tex]\sqrt{6}[/tex] - 4*3*[tex]\sqrt{10}[/tex]

      10[tex]\sqrt{6}[/tex] - 12[tex]\sqrt{10}[/tex]

The sum of any matrix with the identity matrix of the same size, with respect to addition, will give the matrix itself. Therefore, the sum of matrix A and B, where B is the identity matrix, will give the matrix A.

globe meaning a sphere, and since it has a diameter of 25.8, that means its radius is half that, or 12.9

[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=12.9 \end{cases}\implies V=\cfrac{4\pi (12.9)^3}{3}\implies \stackrel{ using~\pi =3.14 }{V\approx 8987.47}[/tex]

If an avocado costs $1 per pound, the cost of 9 pounds, using multiplication, is $9.

Multiplication is one of the four basic mathematical operations, including addition, subtraction, and division.

Multiplication involves the multiplicand, the multiplier, and the product.

The cost per pound of an avocado = $1

The total quantity considered = 9 pounds

Proportionately, the total cost of 9 pounds = $9 ($1 x 9)

Thus, based on multiplication operation, the total cost of 9 pounds is $9.00.

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The interval-notation for "all real-numbers" greater than 2 is (2, ∞).

The "Interval-Notation" is a way of expressing a set of real numbers using brackets to show which numbers are included in the set. In the case of all real numbers greater than 2, we can write this as:

(2, ∞)

The open-bracket "(" indicate that the number 2 is not included in the set, while the symbol "∞" represents all real numbers greater than 2.

This notation is used to express an open interval, meaning that the endpoints (in this case, 2 and infinity) are not included in the set.

Therefore, the required interval-notation is (2, ∞).

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The solution to the given quadratic equation is [tex]=-1\pm \sqrt{6}[/tex]

A quadratic equation is an equation whose highest power is raised to the power of 2. Mathematically it is written in the form ax² + bx + c. There are many ways in which we can solve a quadratic equation such as:

From the given information, we have:

x² + 2x - 5 = 0

Using the quadratic formula method;

[tex]=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

here;

[tex]=\dfrac{-2\pm \sqrt{2^2-4(1)(-5)}}{2(1)}[/tex]

[tex]=\dfrac{-2\pm \sqrt{4+20}}{2}[/tex]

[tex]=\dfrac{-2\pm \sqrt{24}}{2}[/tex]

[tex]=\dfrac{-2\pm 2\sqrt{6}}{2}[/tex]

[tex]=-1\pm \sqrt{6}[/tex]

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Answer:

Step-by-step explanation:

Using the equations given, only equation 2 has a proportional relationship.

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other.

The difference between proportional and non-proportional linear relationships is that, although both have constant rates of change the proportional relationship has constant output to input ratios, and the non-proportional relationship does not.

In this problem, to determine the proportional relationship, we can also check for both values of x and y.

1. y = -0.75x + 5

When x = 1

y = -0.75(1) + 5

y = 4.25

when x = 2

y = -0.75(2) + 5

y = 3.5

The relationship is not proportional since as one variable increase, the other decreases.

2. y = 4x - 1

When x = 1

y = 4(1) - 1

y = 4 - 1

y = 3

when x = 2

y = 4(2) - 1

y = 8 - 1

y = 7

This relationship is proportional since the variables increases or decreases with one another.

3. y = (3/4)x

When x = 1

y = (3/4)(1)

y = 3/4

when x = 2

y = (3/4)(2)

y = 2/3

This relationship is not proportional

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Answer:

12 / min

720 / hr

17,280 / day

6,307,200 / yr

Now divide 1,000,000,000 by 6,307,200 (darn close to your 158!)