Over a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. The tide measures 5.15 ft at midnight, rises to a
high of 10.2 ft falls to a low of 0.1 ft, and then rises to 5.15 ft by the next midnight
What is the equation for the sine function f(x), where x represents time in hours since the beginning of the 24-hour period, that models the
situation?
Enter your answer in the box

Answer:

2x - 3

Step-by-step explanation:

3x-1 - (x+2)

3x-1 -x -2

2x - 3

Consider that we need to find [tex](a+b)(x), (a-b)(x), (ab)(x),\left(\dfrac{a}{b}\right)(x)[/tex].

Given:

The functions are:

[tex]a(x)=4x+9[/tex]

[tex]b(x)=3x-5[/tex]

To find:

The function operations [tex](a+b)(x), (a-b)(x), (ab)(x),\left(\dfrac{a}{b}\right)(x)[/tex].

Solution:

We have,

[tex]a(x)=4x+9[/tex]

[tex]b(x)=3x-5[/tex]

Now,

[tex](a+b)(x)=a(x)+b(x)[/tex]

[tex](a+b)(x)=4x+9+3x-5[/tex]

[tex](a+b)(x)=7x+4[/tex]

Similarly,

[tex](a-b)(x)=a(x)-b(x)[/tex]

[tex](a-b)(x)=4x+9-(3x-5)[/tex]

[tex](a-b)(x)=4x+9-3x+5[/tex]

[tex](a-b)(x)=x+14[/tex]

And,

[tex](ab)(x)=a(x)b(x)[/tex]

[tex](ab)(x)=(4x+9)(3x-5)[/tex]

[tex](ab)(x)=12x^2-20x+27x-45[/tex]

[tex](ab)(x)=12x^2+7x-45[/tex]

And,

[tex]\left(\dfrac{a}{b}\right)(x)=\dfrac{a(x)}{b(x)}[/tex]

[tex]\left(\dfrac{a}{b}\right)(x)=\dfrac{4x+9}{3x-5}[/tex]

Therefore, the required functions are [tex](a+b)(x)=7x+4[/tex], [tex](a-b)(x)=x+14[/tex], [tex](ab)(x)=12x^2+7x-45[/tex] and [tex]\left(\dfrac{a}{b}\right)(x)=\dfrac{4x+9}{3x-5}[/tex].

Answer:

[tex]18 + 18 + 18 = 18 \times 3 = 54[/tex]

Step-by-step explanation:

I ain't sure but it might help you out:D

Answer:

140.3 cm²

Step-by-step explanation:

area of an equilateral triangle

[tex] = \frac{\sqrt{3} }{4} {a}^{2} [/tex]

where a is the side of the triangle

[tex] = \frac{ \sqrt{3} }{4} \times {18}^{2} \\ = 140.3 \: cm {}^{2} [/tex]

Answer:

Two solutions

Step-by-step explanation:

The number of points of intersections represents the number of solutions to the system of equations. Since the parabola intersects the circle at two points, there are two solutions to the circle.

Furthermore, these two points of intersection are exactly the solutions to the system of equations. Finding the coordinates of the points of intersection will give you the solutions to the system of equations.

Answer:

0.2992 = 29.92% probability of obtaining at least 8 failures.

Step-by-step explanation:

For each dice, there are only two possible outcomes. Either a failure is obtained, or a success is obtained. Trials are independent, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

A success is 5 or 6.

A dice has 6 sides, numbered 1 to 6. Since a success is 5 or 6, the other 4 numbers are failures, and the probability of failure is:

[tex]p = \frac{4}{6} = 0.6667[/tex]

10 normal six sided dice are thrown.

This means that [tex]n = 10[/tex]

Find the probability of obtaining at least 8 failures.

This is:

[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)[/tex]

So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 8) = C_{10,8}.(0.6667)^{8}.(0.3333)^{2} = 0.1951[/tex]

[tex]P(X = 9) = C_{10,9}.(0.6667)^{9}.(0.3333)^{1} = 0.0867[/tex]

[tex]P(X = 10) = C_{10,10}.(0.6667)^{10}.(0.3333)^{0} = 0.0174[/tex]

Then

[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.1951 + 0.0867 + 0.0174 = 0.2992[/tex]

0.2992 = 29.92% probability of obtaining at least 8 failures.

Answer:

20

Step-by-step explanation:

The numbers whose product are to be obtained :

(–24.98)(–1.29)

To use front end approximation, numbers are rounded to the greatest place value :

For :

(-24.98) is rounded to - 20 (4 is rounded here to 0)

(-1.29) is rounder to - 1 (2 is rounded to 0)

Then, the product of the two numbers will be :

-20 * - 1 = 20

Answer:

55 mph

Step-by-step explanation:

Answer:

it's B

Step-by-step explanation:

I'm quite sure it is. Hope it helps u

Answer:

x = 32 and BEC = 43

Step-by-step explanation:

3X + 41 = 137

3X = 96

X = 32

FOR BEC:

137 + 137 = 274

360-274=86 ( ANGLES AROUND A POINT ADD UP TO 360)

86/2 = 43

BEC/AED = 43 ( VERTICALLY OPPOSITE ANGLES ARE EQUAL)

hope this helps good luck!

Answer:

Para el CO₂ sabemos que:

densidad = 0,001976 g/cm³

Sabemos que:

densidad = masa/volumen

Entonces, si tenemos una masa de 28 g, podemos escribir:

volumen = masa/densidad

volumen = (28g)/(0,001976 g/cm³) = 14,170 cm^3

Para obtener la masa molar (es decir, la masa de un mol de esta sustancia) simplemente sumamos la masa de un mol de cada componente.

Carbono: tiene una masa molar de 12 g/mol

Oxígeno: tiene una masa molar de 16 g/mol (y tenemos dos oxígenos)

entonces la masa molar va a ser:

masa molar = 12g/mol + 2*16g/mol = 44 g/mol

Es decir, un mol de CO₂, pesa 44 gramos.

f(x)/g(x) = (x2-16)/(x+4)

The domain is all real numbers except x = -4 (because the denominator is zero at x = -4 and division by zero is undefined.)

We can simplify by factoring the numerator:

(x2-16)/(x+4) = (x-4)(x+4)/(x+4) = (x-4)

The domain is the same as the original expression: all real numbers except x = -4

Answer:

[tex]Area = 52\sqrt3 \ ft^2[/tex]

Step-by-step explanation:

Area of trapezoid

                         [tex](\frac{a+ b}{2}) \times h[/tex]      -----------( 1 )

We will split the trapezoid into Triangle and rectangle. To find the height and full length of base.

[tex]sin 60 = \frac{opposite}{hypotenuse}[/tex]   [tex][ opposite \ in \ the \ equation \ \ is \ the \ height \ of \ the \ trapezoid ][/tex]

[tex]\frac{\sqrt3}{2} = \frac{opposite }{ 8}\\\\\frac{\sqrt3}{2} \times 8 = opposite\\\\4\sqrt3 = opposite[/tex]

Therefore, h = 4√3 ft

[tex]cos 60 = \frac{adjacent}{hypotenuse}[/tex]    [tex]adjacent \ in \ the\ equation \ is \ the\ base \ of \ the \ triangle ][/tex]

[tex]\frac{1}{2} = \frac{adjacent}{hypotenuse}\\\\\frac{1}{2} \times 8 = adjacent\\\\4 = adjacent[/tex]

Therefore, a = 11 feet, b = 11 + 4 = 15 feet

Substitute the values in the Area equation :

                                                [tex]Area = \frac{11 + 15}{2} \times 4 \sqrt3 = \frac{26}{2} \times 4\sqrt3 = 13 \times 4\sqrt3=52\sqrt3 \ ft^2[/tex]

Answer:

c)  y = 8[tex]\sqrt{3}[/tex]

Step-by-step explanation:

in a 30-60-90° Δ the ratio of the sides, respectively, is 1: [tex]\sqrt{3}[/tex] : 2

if the side opposite the 30°∡ is 8 then 'y' is 8[tex]\sqrt{3}[/tex] and 'x' is 16

Answer:

[tex] \sqrt[5]{96x {}^{7} y {}^{11} } = 2xy {}^{2} \sqrt[5]{3x {}^{2}y } [/tex]

Answer:

y = 2*(x - 3)^2 - 2

Step-by-step explanation:

Remember that a quadratic equation of vertex (h, k) is written as:

y = a*(x - h)^2 + k

Where a is the leading coefficient.

So, if we know that the vertex is at (3, - 2)

we have:

y = a*(x - 3)^2 + (-2)

And we want the y-intercept to be (0, 16)

This means that, when we take x = 0, we must have y = 16

if we replace these in the above equation we get:

16 = a*(0 - 3)^2 - 2

now we can solve this for a

16 = a*(-3)^2 - 2

16 = a*9 - 2

16 + 2 = a*9

18 = a*9

18/9 = a

2 = a

Then the quadratic equation is:

y = 2*(x - 3)^2 - 2

Step-by-step explanation:

answers I the above photo

some of the questions are not clear

Answer:

1. C(13inches)

2. A(40°)

3. B(126°)

4. C(50°)

5. 7cm

Step-by-step explanation:

According To the Question,

1. Given, The sum of all the sides of a STOP sign is 104 inches. A STOP sign is Octagon  with all sides equal.

Thus, Octagon has 8 equal side

So, Each Side Measure = 104/8 ⇔ 13inches

2. Given, In Triangle ABC, ∠A & ∠B each measure 70°

And, We Know Sum of all angles of a triangle is 180°.

Thus, ∠C = 180° - (∠A + ∠B)  ⇔  180°-140° ⇒ 40°

3. Given, The measures of the three angles of a quadrilateral are ∠A=49° ,∠B=58° & ∠C=127° .

And, We know sum of all angles of quadrilateral is 360°.

Thus, ∠D=360° - (∠A+∠B+∠C)  ⇔ 360°-234° ⇒ 126°

4. Given, The measure of all the Four angles of a quadrilateral are ∠A=(x+40)°, ∠B=130°, ∠C=x° & ∠D=(2x-10)° .

And, We know sum of all the angles of quadrilateral is 360°.

Thus, ∠A+∠B+∠C+∠D = 360°

Put all the Values, we get

x+40+130+x+2x-10 = 360

4x+160 = 360

4x = 200 ⇔ 200/4 ⇒ 50°

5. Given, the length of the two sides of an isosceles triangle are 3cm and 7cm .

Now, in order to form a triangle the sum of any two side of a triangle is always greater than the third side of a triangle.

So, We have an isosceles triangle in which two sides is always equal & we have given two sides of 3cm & 7cm .

Assume, if third side be 3cm (First Side+Third side > Second side)

3+3 ⇒6cm which is not greater than 7cm(thus, the Triangle not possible if we assume 3cm as triangle's third side)

Hence, The other Side of Triangle Surely be 7 cm.  

Answer:

7√10 / 10.

Step-by-step explanation:

7/√10

Multiply top and bottom by √10:

= 7√10 / 10

Answer:

solution,

x+41+59=180⁰ ( the sum of total angle of triangle is 180⁰)

or, x+ 100=180

or, X=180-100

so , X=80

Step-by-step explanation:

let us check

59+41+80=180

Answer:

it is b

Step-by-step explanation:

Answer:

it is b

Step-by-step explanation:

Step-by-step explanation:

[tex]1) \\ - 2 \leqslant x \leqslant 1 \\ 2) \\ - 3 > x \geqslant 2 \\ 3) \\ x> 0[/tex]

[tex]4) \\ x \leqslant - 3 \\ 5) \\ - 4 \leqslant x \geqslant 1[/tex]

[tex]6) \\ - 2< x \leqslant 0[/tex]

Answer:

(4, -4)

Step-by-step explanation:

Using the midpoint formula;

M(X,Y) = {(ax1+bx2)/a+b, (ay1+by2)/a+b}

X = (ax1+bx2)/a+b

Y = (ay1+by2)/a+b

Substitute

X = 4(2)+2(8)/4+2

X = 8+16/6

X = 24/6

X = 4

Also

Y = 4(-3)+2(-6)/6

Y = -12-12/6

Y = -24/6

Y = -4

Hence the required partition is (4, -4)

Answer:

The given relation is presented as follows;

[tex]\dfrac{1}{a} + \dfrac{1}{b} +\dfrac{1}{c} = \dfrac{1}{a + b + c}[/tex]

Where 'a', 'b', and 'c' are member of real numbers, we have;

a⁹, b⁹, and c⁹ are also member of real numbers

When a⁹ = x, b⁹ = y, and c⁹ = z

By the above relationship, we have;

[tex]\dfrac{1}{x} + \dfrac{1}{y} +\dfrac{1}{z} = \dfrac{1}{x + y + z}[/tex]

Substituting x = a⁹, y = b⁹, and z = c⁹, we get;

[tex]\dfrac{1}{a^9} + \dfrac{1}{b^9} +\dfrac{1}{c^9} = \dfrac{1}{a^9 + b^9 + c^9}[/tex]

Step-by-step explanation:

Answer:

? = 10

Step-by-step explanation:

13 - (10) = 7-4 ....... 2×2 =4

3 = 3

Answer:

x = + 5/4 or x = - 5/4

Step-by-step explanation:

[tex]4 x^2 = 6\frac{1}{4}\\\\4 x^2 = \frac{25}{4}\\\\x^2 =\frac{25}{16}\\\\x = \pm \frac{5}{4}[/tex]

Answer:

y-acis

Step-by-step explanation:

the function graph is symmetric about

- y-axis when it is an even function

-the origin ehen it is an even function

A symmetrical graph about the x-axis is not a function graph

f(×) is a even if and only if f(×) =f(×)

f(×) is a odd if and only f(×)=f(×)

We have the function r(0) = 4cos (50)

(only symmetry about the y-acis or about the origin)

Check r(-0)

r(-0) = 4cos (5-0) = 4cos (-50 = 4 cos (50)

Used cos (-× = cos ×

We have r(0). Therefore the graph of r(0) is symmectric about the y-axis.

Answer:

(a - b)^2 = 49 - 4b^2 +2ab

Step-by-step explanation:

Given: a^2 + b^2 = 7b (assuming A is really “a”)

b^2 + (2b - a)^2 = 7^2

Find; (a - b)^2

Plan: Use Algebraic Manipulation

Start with b^2 + (2b - a)^2 = 7^2 =>

b^2 + 4b^2 - 4ab + a^2 = 49 by expanding the binomial.

a^2 + b^2 + 4b^2 - 4ab = 49 rearranging terms

a^2 + b^2 -2ab - 2ab + 4b^2 = 49 =>

a^2 - 2ab + b^2 = 49 - 4b^2 +2ab rearranging and subtracting 4b^2 and adding 2ab to both sides of the equation and by factoring a^2 - 2ab + b^2

(a - b)^2 = 49 - 4b^2 +2ab

Double Check: recalculated ✅ ✅

(a - b)^2 = 49 - 4b^2 +2ab