determine the general solution of -4sinx = 5cosx​

The function in vertex form is equivalent to [tex]\rm y = (x + 2/4)^2 + \frac{3}{4}[/tex].

A quadratic equation is an equation of degree 2 in other words.Quadratic equations have the form ax² + bx + c = 0 and are second-degree algebraic expressions.

The standard quadratic function with vertex (h, k) is ;

[tex]\rm y = a(x - h)^2 + k[/tex]

The general quadratic equation is found as;

[tex]\rm y = ax^2 + bx + c[/tex]

The value of h is given as;

[tex]\rm h = \frac{-b}{2a}[/tex]

For the given equation in the problem;

[tex]\rm y = x^2 + x + 1[/tex]

The value of the k is found by;

[tex]\rm y =( \frac{-1}{2}) ^2 - \frac{1}{2} + 1 \\\\ y= \frac{1}{4} - \frac{1}{2}+ 1 \\\\ y= \frac{1}{4}- \frac{2}{4}+ \frac{4}{4}\\\\ y= \frac{3}{4}[/tex]

So the vertex is at [tex]\frac{-2}{4}[/tex] and [tex]\frac{1}{4}[/tex]  then the vertex form is:

[tex]y = (x +\frac{2}{4} )^2 + \frac{3}{4}[/tex]

Hence the functions in vertex form are equivalent [tex]\rm y = (x + 2/4)^2 + \frac{3}{4}[/tex].

To learn more about the quadratic functions refer to the link;

brainly.com/question/1214333

Answer: OPTION 3

Step-by-step explanation:

Answer:

3 faces

A cylinder has 3 faces - 2 circle ones and a rectangle (if you take the top and bottom off a tin can then cut the cylinder part on the seam and flatten it out you would get a rectangle). It has 2 edges and no vertices (no corners).

Step-by-step explanation:

[tex] \huge\fbox\blue{ANSWER} [/tex]

A cylinder has 3 faces - 2 circle ones and a rectangle

Step-by-step explanation:

since the equation is v = 1.225 × sqrt(a)

we can plug in the known values to find the altitude.

so:

(67.1/1.225)^2 = a

a = 3000

Base on the visibility formula v = 1.225√a, the altitude at which Dereck is hang gliding is 7.4 miles

The visibility formula is given as follows:

v = 1.225√a

where

Therefore,

v = 67.1 miles

v = 1.225√a

67.1 = 1.225√a

divide both sides by 1.225

√a = 67.1 / 1.225

√a = 54.7755102041

square both sides

√a² = √54.7755102041

a = 7.40104789878

a = 7.4 miles

learn more on visibility here: https://brainly.com/question/16166215

Answer:

C: 12^12/12^6

Step-by-step explanation:

it is equal to 12^6

Answer:

Step-by-step explanation:

In rectangle, the diagonals are equal  bisect each other.

⇒ OA = OB

⇒ΔAOB is an isosceles triangle.

In ΔAOB,

x + x + 120 = 180°

  2x + 120 = 180

           2x = 180 -120

           2x = 60

             x = 30°

In ΔABD

∠A + ∠ABD ∠BDA = 180

90  + 30 + ∠BDA  = 180

                 ∠BDA = 180 - 90 -30 = 60°

ΔABD is 30 - 60 - 90 triangle.

The ratio of sides of 30-60-90 triangle is x : x√3 : 2x

x →shortest leg which is opposite ot 30°

∵ x = AD =  20

x√3 → longest leg which is opposite to 60°

x√3 ( AB) = 20*1.732

            AB   = 34.64

Area of rectangle = length * width

                              = 34.64 *20

                             = 692.8

                             ≈ 693 square units

Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

[tex]\frac{3}{5} = \frac{36}{x}[/tex]

3x = 36 x 5

3x = 180

x = 60

Michael has 60 marbles.

Nick recieves 9 more marbles so he has 36 + 9 = 45 marbles

The new ratio will be:

[tex]\frac{45}{60}[/tex]  = [tex]\frac{3}{4}[/tex]

Answer:

Third option

Step-by-step explanation:

The y-intercepts are -2 and 3 so first option is wrong

One is dashed line and other is solid so one needs to have equal and other one shouldn't, so second option is wrong as both are less than but not also equal

Third option the -2 intercept one is less than or equal to And the slope is positive while the 3 intercept one is greater with negative slope.

The given graph represents the system of inequalities in the third option y ≤ 2x - 2 and y > -x + 3.

It is clear from the graph that one of the inequality has a solid graph line while other has a dotted graph line.

So one of the inequality must be of the form ≤ or ≥ and the other one is of the form < or >.

The only inequalities of this form in the options are,

y ≤ 2x - 2

y > -x + 3

Consider y = 2x - 2.

The points through the line are (0, -2), (1, 0), (2, 2), ...

At origin, (0, 0), 0 ≤ -2 is false. So (0, 0) does not include in the solution region.

So the solution region of y ≤ 2x - 2 is on the part of the line of y = 2x - 2 where (0, 0) is not included.

Consider y = -x + 3

Line passes through (0, 3), (1, 2), (2, 1), (3, 0),....

At (0, 0), 0 > 3, which is false.

So the solution region of y > -x + 3 does not contain the part where (0, 0) is included.

So the resulting graph is correct for this system of inequalities.

Learn more about System of Inequalities here :

https://brainly.com/question/19526736

#SPJ7

Answer: look at the attached image

Step-by-step explanation:

Answer:

x = y = 64° , z = 20°

Step-by-step explanation:

x = y = [tex]\frac{180-52}{2}[/tex] = 64 °

m∠ADC = 52° + x

m∠ADC = 52° + 64° = 116°

z = 180° - 116° - 44° = 20 °

Answer:

$7.30

Step-by-step explanation:

All you have to do is 9 x 5= 45

Then 45 - 37.70= 7.30

HGD

-ghost

Tristan would have paid $7.3 more, if he had purchased the books online.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, Tristan paid $37.70 for 5 books by his favorite author.

Each book would have cost $9 if he had purchased it online instead.

Total money paid to purchase books online = 5×9

= $45

Difference in cost = 45-37.70

= $7.3

Therefore, Tristan would have paid $7.3 more, if he had purchased the books online.

To learn more about the unitary method visit:

brainly.com/question/22056199.

#SPJ2

Answer:

6

Step-by-step explanation:

24/4 = 6

30/5 = 6

Dividing the values of the larger print by the corresponding values of the smaller print results in a scale factor of 6

Using the binomial distribution, it is found that the expected score of the game is of 21.

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected number of trials until q successes is:

[tex]E_s(X) = \frac{q}{p}[/tex]

In this problem, a die has a p = 1/6 probability of resulting in a 1, hence the expected number of trials is:

[tex]E_s(X) = \frac{1}{\frac{1}{6}} = 6[/tex]

In each trial, each outcome from 1 to 6 is equally as likely, hence the expected score of a single trial is given by:

[tex]E = \frac{1 + 6}{2} = 3.5[/tex]

Then, the expected score of the six trials is:

6 x 3.5 = 21.

More can be learned about the binomial distribution at https://brainly.com/question/24863377

Answer:

false

Step-by-step explanation:

Answer:

234mm

Step-by-step explanation:

0.18

Percentages and decimals are closely related. As a matter of fact, we don't need to use any actual math to solve this question because there is a shortcut.

Answer by Dividing

One way to solve the question is by dividing. Percentages are numbers that represent a portion of 100. So, to find the decimal form we can divide the percentage by 100.

Shortcut

While dividing by 100 can work, there is an easier way to find the decimal form. Dividing by 100 will always be equivalent to moving the decimal point 2 digits to the left.

Answer:

The mean of the data is 3 inches, is false

Step-by-step explanation:

3, 3, 4, 4, and 6 inches.

To find the mean, add the numbers together and divide by the number of data points

( 3+3+4+4+6)/5 = 20/5 = 4

The median is the middle number

3, 3,    4,      4, and 6 inches.

The median is 4

The range is the largest number minus the smallest number

6-3 =3

two pipes= $1.20

Selling price of the first pipe = $1.20

Profit = 20%

Let’s try to find the cost price of the first pipe

CP = Selling price - Profit

CP = 1.20 - 20% of CP

CP = 1.20 - 0.20CP

CP + 0.20CP = 1.20

1.20CP = 1.20

CP = 1.20/1.20

CP = $ 1

Selling price of the Second pipe = $1.20

Loss = 20%

Let’s try to find the cost price of the second pipe

CP = Selling price + Loss

CP = 1.20 + 20% of CP

CP = 1.20 + 0.20CP

CP - 0.20CP = 1.20

0.80CP = 1.20

CP = 1.20/0.80

CP = $1.50

Therefore, total cost price of the two pipes

= $1.00 + $1.50

= $2.50

And total selling price of the two pipes

= $1.20 + $1.20

= $2.40

Loss = $2.50 – $2.40 = $0.10

Therefore, Mr. Jones loss 10 cents.

answer= option d.

Answer:

Step-by-step explanation:

Remark

All triangles are made up of 3 angles totally 180 degrees.

In addition a right triangle has a measurement of 90 degrees.

The other two angles must add to 90 degrees as will. That is the definition of complementary. (2 angles add to 90 degrees).

Formula

x + 28 = 90

Solution

x + 28 = 90              Subtract 28 from both sides.

x+28 -28=90 - 28

x = 62

The measure of the second angle is 62

Answer:

[tex] - 8x {}^{2} - 6x + 35 [/tex]

Step-by-step explanation:

(2x+5)(7-4x)

expanding

2x(7-4x)+5(8-4x)

removing brackets

2x×7+2x×-4x+5×7+5×-4x

14x-8x^2+35-20x

arranging properly

-8x^2-6x+35

Answer:

-------------------

Step-by-step explanation:

as I see it, A is the full 180° angle.

and so, there are 3 more 180° angles:

below A in the other side of the blue line the whole 180° arc.

above and below the blue line at the intersection point with the second, parallel red line (again, the whole 180° arcs).

Answer:

  f(x) = 6·sin(8(x -π/2))

Step-by-step explanation:

A transformed sine function with amplitude A, period P, and horizontal shift S can be written as ...

  f(x) = A·sin(2π/P(x -S))

__

The equation for A=6, P=π/4, and S=π/2 is then ...

  f(x) = 6·sin(8(x -π/2))

_____

Additional comment

The horizontal shift is equal to two full periods, so the shifted function is indistinguishable from the unshifted function.

Answer:

its B

Step-by-step explanation:

Answer:

the answer is B 1/50. I think

Answer:

Circumference = 23.23600 (using 3.14 instead of whole PI)

Step-by-step explanation:

Answer:

the slope u find by looking for where the line hits an exact + and the y-int is where the line touches the y-axis