Graph the linear equation. Find three points that solve the equation, then plot on the graph.
-3x + 2y = 2

Answer:

16.15

Step-by-step explanation:

sin(30) = a / c

a = c * sin(30)

a = 32.3 * 0.5

a = 16.15

The equation of the function is  F(x) = -3(x-4)² +4 , the correct answer is Option D

The missing graph is attached with the answer

A function is a law that relate the independent variable and the dependent variable.

It is given that

The graph of F(x), shown below, resembles the graph of G(x)= x², but it has been changed

From the graph, it is seen that,

G(x) when shifted by -4 on the negative x axis.

and graph shifted by +4 on the positive y axis.

F(x) is scaled by a factor of -⅓ of G(x)

it is reflected across the x-axis.

So the equation of the function is

F(x) = -3(x-4)² +4

Therefore ,  the correct answer is Option D.

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Answer:

7x² + 5x - 9

Step-by-step explanation:

(9x + 1) - (- 7x² + 4x + 10) ← distribute parenthesis by - 1

= 9x + 1 + 7x² - 4x - 10 ← collect like terms

= 7x² + 5x - 9

Step-by-step explanation:

Let simplify the identity

[tex] \frac{ \csc {}^{2} (x) - \sec {}^{2} (x) }{ \csc {}^{2} (x) + \sec {}^{2} (x) } [/tex]

[tex] \frac{ \frac{1}{ \sin {}^{2} (x) } - \frac{1}{ \cos {}^{2} (x) } }{ \frac{1}{ \sin {}^{2} (x) } + \frac{1}{ \cos {}^{2} (x) } } [/tex]

Combine Like Fractions

[tex] \frac{ \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{ \sin {}^{2} (x) \cos {}^{2} (x) } }{ \frac{ \sin {}^{2} (x) + \cos {}^{2} (x) }{ \cos {}^{2} (x) \sin {}^{2} (x) } } [/tex]

Multiply by reciprocals.

[tex] \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{ \sin {}^{2} (x) \cos {}^{2} (x) } \times \frac{ \cos {}^{2} (x) \sin {}^{2} (x) }{ \sin {}^{2} (x) + \cos {}^{2} (x) } [/tex]

Pythagorean Identity

[tex] \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{1} [/tex]

Double Angle Identity

[tex] \frac{ \cos(2x) }{1} [/tex]

[tex] \cos(2x) [/tex]

Now, we need to find cos 2x. Given that we have tan x.

Note that

[tex] \cos {}^{2} (x) - \sin {}^{2} (x) = \cos(2x) [/tex]

So let find cos x and tan x.

We know that

[tex] \tan(x) = \frac{ \sin(x) }{ \cos(x) } [/tex]

We know that

[tex] \tan(x) = \frac{o}{a} [/tex]

[tex] \sin(x) = \frac{o}{h} [/tex]

[tex] \cos(x) = \frac{a}{h} [/tex]

So naturally,

[tex] \tan(x) = \frac{ \frac{o}{h} }{ \frac{a}{h} } = \frac{o}{a} [/tex]

So we need to find the hypotenuse,

remember Pythagorean theorem.

[tex]h {}^{2} = {o}^{2} + {a}^{2} [/tex]

Here o is 1

h is root of 5.

So

[tex] {h}^{2} = {1}^{2} + ( \sqrt{5} ) {}^{2} [/tex]

[tex] {h}^{2} = 1 + 5[/tex]

[tex] {h}^{2} = 6[/tex]

[tex]h = \sqrt{6} [/tex]

Now, we know h, let plug in to find sin x and cos x.

[tex] \sin(x) = \frac{1}{ \sqrt{6} } [/tex]

[tex] \cos(x) = \frac{ \sqrt{5} }{ \sqrt{6} } [/tex]

Let's find these values squared

[tex] \sin {}^{2} (x) = \frac{1}{6} [/tex]

[tex] \cos {}^{2} (x) = \frac{5}{6} [/tex]

Finally, use the trig identity

[tex] \frac{5}{6} - \frac{1}{6} = \frac{2}{3} [/tex]

So part I.= 2/3

ii. Use the definition of sine and cosine and Pythagorean theorem

Let sin x= o/h

Let cos x= a/h.

So

sin x squared is

[tex] \sin {}^{2} (x) = \frac{o {}^{2} }{h {}^{2} } [/tex]

[tex] \cos {}^{2} (x) = \frac{ {a}^{2} }{h {}^{2} } [/tex]

By definition,

[tex] \frac{ {o}^{2} }{ {h}^{2} } + \frac{ {a}^{2} }{h {}^{2} } = 1[/tex]

[tex] \frac{ {o}^{2} + a {}^{2} }{h {}^{2} } = 1[/tex]

Remember that

[tex]{ {o}^{2} + {a}^{2} } = {h}^{2} [/tex]

So

[tex] \frac{ {h}^{2} }{h {}^{2} } = 1[/tex]

[tex]1 = 1[/tex]

Answer:

10

Step-by-step explanation:

BX=2/3 (BP)

2/3 of 15 = 10

Answer:

A1 = 18

A(n) = A (n-1) -2

Step-by-step explanation:

N represents the number in a sequence and the difference in the sequence is -2 since each time the number is listed in the sequence it is divide by 2.

Answer: 49

Step-by-step explanation:

If R is the midpoint of QS, QS=2(QR)=2(RS).

[tex]15x-7=2(7x)\\15x-7=14x\\-7=-x\\\\x=7\\\\QR=7(7)=\boxed{49}[/tex]

Answer:

x2

Step-by-step explanation:

x2

Answer: sqrt 3 / 2

Step-by-step explanation: cos20°sin80°-cos80°sin20° is about 0.66 and sqrt(3)/2 is about 0.66.

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Considering the directrix and vertex given in the graph, the equation of the parabola is:

B. [tex]x = -\frac{1}{4}(y + 2)^2 - 2[/tex]

The equation of a quadratic function, of vertex (h,k), is given by:

(y - k)² = 4p(x - h).

In which the directrix is the line x = h - p.

Looking at the graph, we have that:

Thus the equation is:

(y + 2)² = -4(x + 2).

Writing x as a function of y:

B. [tex]x = -\frac{1}{4}(y + 2)^2 - 2[/tex]

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Answer:

10 years old

Step-by-step explanation:

let his age be x , then in 20 years

x + 20 = 3x ( subtract x from both sides )

20 = 2x ( divide both sides by 2 )

10 = x

Charlie is 10 years old

The side length of the original cube is 1.95 inch.

Let each side length of each cube be 'x' inch.

Given : New side = (x+4 ) inch

Another new side = 2x inch

Since the sides are not equal, so it forms a cuboid in the case of new sides as given.

Also, according to question,

The volume of new rectangular prism is 450 cubic inches

= (x+4)*2x*x = 450

⇒ 2x cubed 8x squared =450

=16x5=450= 1.95 inch ( by taking out the cubic root of x3=7.5)

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Answer:

The answer is -4×3 or -3×4 or -6×2 or -2×6 or -1×12 or -12×1

Step-by-step explanation:

Answer:

point A is the intersection point between XA and AC

Answer:

no solutions

Step-by-step explanation:

[tex]4x + 2(-2x+1) = -3\\4x-4x+2 = -3\\2 = -3\\[/tex]

this means there are no solutions.

The value of the car is January 2003 is  $199,148.54.

Depreciation is the rate of decline in the value of an asset with the passage of time.

The exponential equation that can be used to determine the value of the car is:

Value of the car = purchase value(1 - rate of decline)^time

400,000 x (1 - 0.16)^(2003 - 1999)

400,000 x (0.84^4) = $199,148.54

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Answer:

y - 1 = -2(x + 2)  

Step-by-step explanation:

The general structure of an equation in point-slope form is:

y - y₁ = m(x - x₁)

In this form, "x" and "y" stand for the values of one point and "x₁" and "y₁" stand for the values of another point. The variable "m" represents the value of the slope. You have been given the values of one point and the slope. When you plug them into the general form, you get this answer:

Point: (-2, 1)

m = -2

y - y₁ = m(x - x₁)                    <----- Point-slope form

y - y₁ = -2(x - x₁)                    <----- Plug -2 in "m"

y - 1 = -2(x - (-2))                   <----- Plug in values from point

y - 1 = -2(x + 2)                    <----- Simplify

Answer:

 (x-1)^4    +  (y-4)^2  = 25

Step-by-step explanation:

Center at 1,4 means the circle is of the form:

   (x-1)^4    +  (y-4)^2  = r^2

Find r^2 using distance formula from center to the given point

 r ^2 = ( 8-4)^2 + (4-1)^2

 r^2 = 16 +9 = 25

so you answer is      (x-4)^4    +  (y-8)^2  = 25

If ÐABC and ÐCBD are a linear pair, then it means that their sum is 180°.

Linear pair of angles are angles formed when two lines intersect each other at a single point.

Now, the angles are also said to be linear if they are adjacent to each other after the intersection of the two lines and the sum of the linear pair of angles is always equal to 180°.

Looking at the definition above we can say that if ÐABC and ÐCBD are a linear pair, then it means that their sum is 180°.

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Answer: 21 sqrt(43)/43

Step-by-step explanation: The tangent identity states that tanx = sinx/cosx. Thus, we get 21/22 / sqrt(43)/22. We can simplify this to 21 sqrt(43)/43

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Using a calculator, we have that:

To find the equation, we need to insert the points (x,y) in the calculator.

In this problem, we have that:

Hence the regression equation is:

y = -4.75x + 88.57143.

Also using a calculator, the correlation coefficient is of -0.906.

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Answer:

volume of cone = 1/3 volume of cylinder

according to the question, volume of cylinder =

V =

[tex]\pi \times (r) {}^{2} h[/tex]

diameter = 3 inches

radius = 3/2 inches

height = 8 inches

V = 22.7 * (3/2)²* 8

V = 22.7 * 9/4 * 8

V = 22.7 * 18

maximum volume a cone can have = 1/3 of cylinder

Volume of cone = 1/3 * 22.7 * 18

= 22.7 * 6

= 132.6

Answer:

[tex]\fbox {1) A}\\\fbox {2) A}[/tex]

Step-by-step explanation:

Q1

⇒ Graph A is most accurate as the situation is linear and the dots indicate per cup as you can't have any rational part (such as 0.5 cups, etc.)

Q2

⇒ A

⇒ The graph is discrete because the sellers have limited the purchaser to buy a distinct whole number of cups

Answer:

36.7075 Hz is the answer

Bearing is a topic that deals with the distance and location of a given object with respect to a reference point. Thus in the given question, the ship is 57.23 km to the yacht.

Bearing is a topic that considers the distance and position of a given object with respect to a reference point. Thus the angles are usually measured with reference to the north pole.

Thus to solve the given question, let the required distance be represented by x.

Applying the cosine rule, we have;

[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2ab Cos C

The angle C between the line from ship to tugboat and from tugboat to yacht can be determined as;

C = [tex]10^{o}[/tex] + [tex]40^{o}[/tex]

C = [tex]50^{o}[/tex]

Thus,

[tex]c^{2}[/tex] = [tex]36^{2}[/tex] + [tex]27^{2}[/tex] + 2(36 x 27) Cos [tex]50^{o}[/tex]

  = 1296 + 729 + 1944(0.6429)

  = 2025 + 1249.8

[tex]c^{2}[/tex] = 3274.8

c = [tex]\sqrt{3274.8}[/tex]

  = 57.2259

c = 57.23

Therefore, the distance from the ship to the yacht is 57.23 km.

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Kindly contact a 1-on-1 tutor if more explanations are needed.

Answer:

On a coordinate plane, an absolute value graph has a vertex at (0, 0.5).

Step-by-step explanation:

properties of the given function

Answer: it's the second option

Step-by-step explanation:

The perimeter of the given isosceles triangle is; 725.77 units

We are given;

Area of Isosceles Triangle = 56 units squared

Base of Isosceles Triangle = ¹/₃h where h is height

Formula for area of triangle is;

A = ¹/₂bh

A = ¹/₂ * ¹/₃h * h

A = ¹/₆h²

Thus;

¹/₆h² = 56

h² = 56 * 6

h = √336 = 18.33

Thus, base =  ¹/₃√336

Length of hypotenuse = √((√336)² + (¹/₃√336)²)

Length of hypotenuse = √(336 + (336/9))

Length of hypotenuse = 373.33

Thus, Perimeter of Triangle = 2(373.33) + ¹/₃(√336)

Perimeter = 725.77 units

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Answer:

x = 5.81

Step-by-step explanation:

3(12x-7) = 4(5x+18)

36x-21 = 20x +72

16x = 93

x = 5.81

Answer:

y=23.6

Step-by-step explanation:

20+0.45×8

20+3.6

23.6