Express this number in standard form.

3

.

6

4

3

×

1

0

−

1

=

?

3.643×10

−1

=?3, point, 643, times, 10, start superscript, minus, 1, end superscript, equals, question mark

Answer:

2π/3 cm

Step-by-step explanation:

The formula for arc length is s = rФ, where Ф is the central angle in radians.

Thus, we must convert 30° into radians:  that'd be π/6 rad.

Then the arc length here is s = rФ = (4 cm)(π/6 rad) = 2π/3 cm

[tex]\bf 2sin(\theta )cos(\theta )+\sqrt{3}cos(\theta )=0\implies \stackrel{\textit{common factor}}{cos(\theta )[2sin(\theta )+\sqrt{3}]=0} \\\\[-0.35em] ~\dotfill\\\\ cos(\theta )=0\implies \theta =cos^{-1}(0)\implies \theta = \begin{cases} \frac{\pi }{2}\\\\ \frac{3\pi }{2} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf 2sin(\theta )+\sqrt{3}=\implies 2sin(\theta )=-\sqrt{3}\implies sin(\theta )=-\cfrac{\sqrt{3}}{2} \\\\\\ \theta =sin^{-1}\left( -\cfrac{\sqrt{3}}{2} \right)\implies \theta= \begin{cases} \frac{4\pi }{3}\\\\ \frac{5\pi }{3} \end{cases}[/tex]

Step-by-step answer:

Given equation:

2sin(theta)cos(theta) + sqrt(3)*cos(theta) = 0  ...........................(1)

Solve for theta for 0<=theta<=2pi.

Factor out cos(theta), we get

cos(theta) * ( 2sin(theta) + sqrt(3) ) = 0

By the zero product theorem, we can conclude

cos(theta) = 0   ...................................(2)

OR  

2sin(theta) + sqrt(3) = 0  ................. (3)

Solving (2)

cos(theta) = 0 has solutions pi/2 or 3pi/2  from the cosing curve.

Solving (3)

2sin(theta) + sqrt(3) = 0  =>

sin(theta) = -sqrt(3)/2

which has solutions  4pi/3 or 5pi/3.

So the solutions to equation (1) are

S={pi/2,  4pi/3, 3pi/2, 5pi/3}

you have to calculate the SID number and then take it upon yourself and divided X it's actual number and then there's a chance and the answer would be c.72

Answer:

54°

Step-by-step explanation:

y is an inscribed angle.  That means that it is half the measure of the arc it intercepts.  The arc it intercepts is 108, so the angle is 54°

Check the picture below.

The travel of the barnacle would be the circumference of the circle.

Circumference formula is 2 x PI x r

Circumference  = 2 x PI x 1m

= 2 x PI

If you use 3.14 for PI the circumference is 2 x 3.14 = 6.28 m.

Round the answer as needed.

System A --> B

Equation A1 and B1 the same, but B2 changes. The change is that the whole equation is multiplied by 4. So, the answer is B and 4 goes in the blank

System B --> C

Equation B1 and C1 are the same, but C2 changes. This change is not multiplication, so our only option now is C. In C2, the x-factor is removed, which means that elimination occurred. -12/-3 = 4, so in the blank, 4 goes in.

Answer: Option D

D. [tex]\frac{3n^{3}}{5m^{2}}[/tex]

Step-by-step explanation:

Use the following property of the exponents to simplify the expression.

We know that:

[tex]a^{-x}=\frac{1}{a^x}[/tex]

So for the expression

[tex]\frac{3m^{-2}}{5n^{-3}}[/tex]

Using the aforementioned property we have that:

[tex]\frac{3m^{-2}}{5n^{-3}}= \frac{3*\frac{1}{m^2}}{5*\frac{1}{n^3}}\\\\\\\frac{3*\frac{1}{m^2}}{5*\frac{1}{n^3}}=\frac{3n^{3}}{5m^{2}}[/tex]

Finally the answer is the option D

Answer:

The correct answer is option D

3n³/5m²

Step-by-step explanation:

Points to remember

Identities

Xᵃ * Xᵇ = X⁽ᵃ ⁺ ᵇ⁾

X⁻ᵃ = 1/Xᵃ

Xᵃ/Xᵇ = X⁽ᵃ ⁻ ᵇ⁾

To find the correct answer  

It is given that,

3m⁻²/5n⁻³

By using identities we can write,

m⁻² = 1/m²  and 1/n⁻³ = n³

3m⁻²/5n⁻³ = 3n³/5m²

Therefore the correct answer is option D.  3n³/5m²

2x - 3 = -8

    +3     + 3

2x = -5

/2    /2

x = -2.5 (Answer)

Prove.

2(-2.5) - 3 = -8

-5 - 3 = -8

-8 = -8

True.

Answer:

Answer -2.5

Step-by-step explanation:

Simple:

2x-3=-8

   +3  +3,  Add 3  on both sides of the equal sign.

2x = -5, Bring the 2x down and add the -8 + 3

2        2,  Divide by 2

x= -2.5

Hope my answer has helped you!

Answer:

1/3

Step-by-step explanation:

This question is an application of binomial distribution model. If we consider each question as an independent trial, then for each trial there are two possible outcomes, success or failure. Success in the sense that she guesses the question correctly, and failure if the guess is wrong. Now, for each trial or question the probability of success is;

1/3

This is because each question has 3 possible answers and only 1 of them is correct.

Now if Shelly guesses on 5 multiple choice test questions in a row, the probability that she will guess the 6th question correctly is still 1/3. This is because the questions represent independent trials and the probability of success is constant in each trial just like in tossing a coin.

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

The probability isn't affected by what she guesses on the previous questions.

So basically the question is "what is the probability that Shelly will answer correctly on any one question?"

There are 3 answer choices and 1 is correct, so the probability of getting a correct answer is 1 out of 3, or, 1/3.

Answer:

$108

Step-by-step explanation:

Step 1: Find the interest. You do this by multiplying the amount borrowed by the interest rate. In this case, you multiply 1,200 by 9% (0.09). 1,200 * 0.09 is $108. That's the amount she paid on the loan in her first year.

The answer is B)13

The rest of these words are to reach the minimum 20 words of an answer lol

Answer:

If you need any further help, feel free to let me know

Step-by-step explanation:

The answers are

(8-9)-(9+3)*5=-61

5+(5+5+6)+9=30

(5/3-3)= -4 over 3 or -4/3 or -1.3 or -1 1/3 depends on what your choices are but all those are correct

2*3+(4*2)/2=10

ANSWER

A. 15 units^2

EXPLANATION

The area of kite is half the product of the diagonals.

The first diagonal has vertices at,

T(0,0) and R(5,5).

The length of this diagonal is

[tex]TR = \sqrt{ {5}^{2} + {5}^{2} } [/tex]

[tex]TR = \sqrt{25 + 25} [/tex]

[tex]TR = \sqrt{50} =5 \sqrt{2} [/tex]

The other diagonal has vertices at;

Q(0,3) and S(3,0).

The length of this diagonal is

[tex]QS = \sqrt{ {3}^{2} + {3}^{2} } [/tex]

[tex]QS = \sqrt{ 9+ 9 } [/tex]

[tex]QS = \sqrt{18} = 3 \sqrt{2} [/tex]

The area of the kite is

[tex] = \frac{1}{2} \times 3 \sqrt{2} \times 5 \sqrt{2} [/tex]

[tex] = 15 \: {units}^{2} [/tex]

This is a problem of projectile motion. A projectile is an object you throw with an initial velocity and whose trajectory is determined by the effect of gravitational acceleration. The general equation in this case is described as:

[tex]h(t)=-\frac{1}{2}gt^2+v_{0}t+h_{0}[/tex]

Where:

[tex]h(t): \ height \ at \ any \ time \\ \\ g: \ acceleration \ due \ to \ gravity \ 9.8m/s^2 \ or \ 32.16ft/s^2 \\ \\ v_{0}= \ Initial \ velocity[/tex]

So:

[tex]v_{0}=64ft/s \\ \\ h_{0}=3ft[/tex]

Finally, the equation is:

[tex]h(t)=-\frac{1}{2}(32.16)t^2+(64)t+3 \\ \\ \boxed{h(t)=-16.08t^2+64t+3}[/tex]

The rocket will reach the maximum height at the vertex of the parabola described by the equation [tex]h(t)=-16.08t^2+64t+3[/tex]. Therefore, our goal is to find [tex]t[/tex] at this point. In math, a parabola is described by the quadratic function:

[tex]f(x)=ax^2+bx+c[/tex]

So the x-coordinate of the vertex can be calculated as:

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

From our equation:

[tex]a=-16.08 \\ \\ b=64 \\ \\ c=3[/tex]

So:

[tex]t=-\frac{64}{2(-16.08)} \\ \\ \boxed{t=1.99s}[/tex]

So the rocket will take its maximum value after 1.99 seconds.

From the previous solution, we know that after 1.99 seconds, the rocket will reach its maximum, so it is obvious that the maximum height is given by [tex]h(1.99)[/tex]. Thus, we can find this as follows:

[tex]H_{max}=h(1.99)=-16.08(1.99)^2+64(1.99)+3 \\ \\ \boxed{H_{max}=66.68ft}[/tex]

So the maximum height the rocket will reach is 66.68ft

The rocket is in the air until it hits the ground. This can be found setting [tex]h(t)=0[/tex], so:

[tex]0=-16.08t^2+64t+3 \\ \\ Applying \ quadratic \ formula: \\ \\ t_{12}=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ a=-16.08 \\ \\ b=64 \\ \\ c=3 \\ \\ t_{12}=\frac{-64 \pm \sqrt{64^2-4(-16.08)(3)}}{2(-16.08)} \\ \\ t_{1}=4.0264 \\ \\ t_{2}=-0.046[/tex]

We can't have negative value of time, so the only correct option is [tex]t_{1}=4.0264[/tex] and rounding to the nearest hundredth we have definitively:

[tex]\boxed{t=4.03s}[/tex]

Answer:

36π cubic inches

Step-by-step explanation:

The formula for the volume of a sphere is ...

V = (4/3)πr^3

Fill in the given value and simplify:

V = (4/3)π(3 in)^3 = 36π in^3

The graph of f(x) = [tex]2^{x+3}[/tex] is option "B" .

An exponential function is a mathematical function of the following form:

f ( x ) = [tex]a^{x}[/tex]. where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e , which is equal to approximately 2.71828.

According to the question

Represents the graph of f(x) = [tex]2^{x+3}[/tex]

f(x) = [tex]2^{x+3}[/tex] is a  exponential function

To draw the graph of f(x) = [tex]2^{x+3}[/tex]

The values will be

x                  f(x)

0                   8

1                   16

-1                   4

-2                  2

-3                  0

Hence, the graph of f(x) = [tex]2^{x+3}[/tex] is option "B" .

To know more about exponential function here:

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The graph of the function represented by the equation f(x) = 2ˣ + 3 is (c)

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

The function

Where, we have

f(x) = 2ˣ + 3

The above function is an exponential function that has been transformed as follows

Using the above as a guide, we have the following:

The graph of the function is (c)

Read more about functions at

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Answer:

f(x) = (x - 1)(x + 2)(x - 3)

Step-by-step explanation:

We are given the following function and we are to factorize it completely:

[tex] f ( x ) = x ^ 3 - 2 x ^ 2 - 5 x + 6 [/tex]

To factorize this completely, we will use the rational roots theorem.

[tex] x ^ 3 - 2 x ^ 2 - 5 x + 6 [/tex]

P = ± multiples of constant term [tex]6 = \pm1, \pm2, \pm3, \pm6[/tex]

Q = ± multiples of the coefficient of highest degree term  [tex] = \pm1[/tex]

So the factors will be [tex]\frac{P}{Q}[/tex].

The possible rational roots are [tex] 1, \pm2, \pm3, \pm6[/tex].

1 is a confirmed root and now we will use synthetic division to find the other rational roots:

1 | 1  -2  -5   6

        1   -1   -6

___________

   1   -1   -6   0    

So the polynomial will be [tex](x^2 - x - 6)[/tex] which can we factorize now.

[tex]x^2 - x - 6 = x^2 - 3x + 2x - 6[/tex]

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

Therefore, the completely factorized form of the given function is f(x) = (x - 1)(x + 2)(x - 3).

Answer:

Logically, the answer is the sphere, as it is the figure which gives maximum volume for the same total surface area. But I'll just solve them like you want it.

I'm just writing the numerical values without the units.Please resolve

Solid 1: Square Prism with each side of the base equal to 8 in. and a height of 8 in.

Volume = 8^3 = 512

Area = 8^2 * 6 = 384

V/A Ratio = 1.33 (We need the highest ratio, that's why they hired us)

Cost = $7.68

Solid 2: Square Pyramid with each side of the base equal to 10 in. and a height of 15 in.

Volume = 1/3 * 10^2 * 15 = 500

Slant height = [(10/2)^2 + 15^2]^(1/2) = root of 250 = 15.81

Area = 2*10*15.81 + 10^2 = 416.23

V/A Ratio = 1.20

Cost = $8.34

Solid 3: Cylinder with a radius of 4 in. and a height of 10 in.

Volume = pi*4*4*10 = 502.65

Area = 2*pi*4*4 + 2*pi*4*10 = 351.86

V/A Ratio = 1.43

Cost = $7.04

Solid 4: Cone with a radius of 7 in. and a height of 10 in.

Volume = (1/3)*pi*7*7*10 = 513.13

Slant height = [(7^2)+(10^2)]^(1/2) = 12.21

Area = pi*7*12.21 + pi*7*7 = 422.37

V/A Ratio = 1.21

Cost = $8.45

Solid 5: Sphere with a radius of 5 in.

Volume = (4/3)*pi*(5^3) = 523.60

Area = 4*pi*(r^2) = 314.16

V/A Ratio = 1.67

Cost = $6.28

Hence, Solid 5 must be the packaging model opted for

Step-by-step explanation:

Logically, the answer is the sphere, as it is the figure which gives maximum volume for the same total surface area. But I'll just solve them like you want it.

I'm just writing the numerical values without the units.Please resolve

Solid 1: Square Prism with each side of the base equal to 8 in. and a height of 8 in.

Volume = 8^3 = 512

Area = 8^2 * 6 = 384

V/A Ratio = 1.33 (We need the highest ratio, that's why they hired us)

Cost = $7.68

Solid 2: Square Pyramid with each side of the base equal to 10 in. and a height of 15 in.

Volume = 1/3 * 10^2 * 15 = 500

Slant height = [(10/2)^2 + 15^2]^(1/2) = root of 250 = 15.81

Area = 2*10*15.81 + 10^2 = 416.23

V/A Ratio = 1.20

Cost = $8.34

Solid 3: Cylinder with a radius of 4 in. and a height of 10 in.

Volume = pi*4*4*10 = 502.65

Area = 2*pi*4*4 + 2*pi*4*10 = 351.86

V/A Ratio = 1.43

Cost = $7.04

Solid 4: Cone with a radius of 7 in. and a height of 10 in.

Volume = (1/3)*pi*7*7*10 = 513.13

Slant height = [(7^2)+(10^2)]^(1/2) = 12.21

Area = pi*7*12.21 + pi*7*7 = 422.37

V/A Ratio = 1.21

Cost = $8.45

Solid 5: Sphere with a radius of 5 in.

Volume = (4/3)*pi*(5^3) = 523.60

Area = 4*pi*(r^2) = 314.16

V/A Ratio = 1.67

Cost = $6.28

Hence, Solid 5 must be the packaging model opted for

25-17=8

8÷2=4

4 apples per friend.

Answer:

7√2 / 2

Step-by-step explanation:

An isosceles right triangle is also known as a 45-45-90 triangle.  For such a triangle, the hypotenuse (long side) is √2 the legs.

s√2 = 7

s = 7/√2

s = 7√2 / 2

You can also show this with Pythagorean theorem.

Answer:

46

Step-by-step explanation:

You need to replace i with 2,3,4,5.

i=2, 6+1

3, 9+1

4, 12+1

5, 15+1

sum=46

Answer:  B) 46

Step-by-step explanation:

The summation of 3i + 1 from i = 2 to i = 5 can be calculated by finding the value of each term and then adding them up ... or.... using the formula:

i = 2: 3(2) + 1 = 7

i = 3: 3(3) + 1 = 10

i = 4: 3(4) + 1 = 13

i = 5: 3(5) + 1 = 16

       TOTAL = 46

[tex]\text{Equation: }\dfrac{a_1+a_5}{2}\times n\\\\.\qquad =\dfrac{7+16}{2}\times 4\\\\.\qquad =23\times 2\\\\.\qquad =46[/tex]

Answer:

not safe

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationship between an angle and the ratio of side opposite to hypotenuse:

Sin = Opposite/Hypotenuse

You have the ratio of lengths and you want to find the angle. You use the inverse sine function (arcsin, or sin⁻¹) for this purpose.

sin(angle with ground) = (16.5 ft)/(17 ft) = 33/34

angle with ground = arcsin(33/34) ≈ 76.1°

This angle is greater than the angle of 70° recommended as a maximum. The ladder will not be safe at this height.

_____

A calculator does all the work. You just need to make sure it is in degrees mode.

Answer:

D

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 3, 1) and (x₂, y₂ ) = (1, - 2)

m = [tex]\frac{-2-1}{1+3}[/tex] = [tex]\frac{-3}{4}[/tex] = - [tex]\frac{3}{4}[/tex]

The slope of the line containing points  (-3, 1) and (1 ,-2) is Option (D) -3/4

The slope of a straight line gives the measure of its steepness and direction. It represents how steep a line can be.

The slope (m) of a straight line from two given points can be found by the formula,

Slope = m = (y2 - y1)/(x2 - x1)

where x1,x2 are the respective x-coordinates of the given points.

and y1,y2 are the respective y-coordinates of the given points .

By the problem, x1 = -3 , x2 = 1 , y1 = 1 , y2 = -2

Slope, m = (-2 -1)/(1 - (-3)) = -3/4

To learn more about  slope of a straight line , refer -

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The expression x + 7 will determine how many cats Staci has.

Since Staci has 7 more cats than Taylor (x), we know the expression uses addition.

Answer:

Step-by-step explanation:

There are various guidelines that one is supposed to follow when estimating affordable rent.  For example, "rent must not exceed 40%" of one's monthly salary.  You don't mention a percentage (do that next time, please), but I will use 40% as an example.

If Gavin's gross biweekly salary is $1,120, 40% of that is

0.40($1,120) = $448 biweekly.

In this example, Gavin can afford to spend no more than $448 biweekly on rent.

Answer:

12

Step-by-step explanation:

I find it convenient to use the following relation:

JL -KL +5 = JM

(x +7) -(2x -4) +5 = 3x . . . . . substituting values shown

16 -x = 3x . . . . . . . . . . . . . . . collect terms

16 = 4x . . . . . add x

4 = x . . . . . . . divide by 4

JM = 3x = 3·4 . . . . . . find the length of JM

JM = 12

The slope is 5/3.hope this helps

Answer:

slope = [tex]\frac{5}{3}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (0, 5)

m = [tex]\frac{5-0}{0+3}[/tex] = [tex]\frac{5}{3}[/tex]

Answer:

  see below

Step-by-step explanation:

The equation is in point-slope form, so you know the line goes through the point (x, y) = (-3, 2) and it has a slope of -3. The slope tells you the line goes down 3 units for each 2 units to the right.

4x-3(x-2)=21

4x-3x+6=21

4x-3x=21-6

x=15

is this right? let's check

4(15)-3(15-2) = 21? yes

For this case we have the following expression, we must find the value of the variable "x":

[tex]4x-3 (x-2) = 21[/tex]

We apply distributive property to the terms of the parenthesis taking into account that:

[tex]- * + = -\\- * - = +\\4x-3x + 6 = 21[/tex]

We add similar terms:

[tex]x + 6 = 21[/tex]

We subtract 6 on both sides of the equation:

[tex]x = 21-6\\x = 15[/tex]

Now, the value of x is 15

Answer:

[tex]x = 15[/tex]

For this case we have the following system of equations:

[tex]4x + 5y = -4\\4x + 3y = 12[/tex]

We multiply the second equation by -1:

[tex]-4x-3y = -12[/tex]

We add the equations:

[tex]4x-4x + 5y-3y = -4-12\\5y-3y = -4-12\\2y = -16\\y = \frac {-16} {2}\\y = -8[/tex]

We find the value of "x":

[tex]4x = 12-3y\\x = \frac {12-3y} {4}\\x = \frac {12-3 (-8)} {4}\\x = \frac {12 + 24} {4}\\x = \frac {36} {4}\\x = 9[/tex]

Thus, the solution of the system is given by:

[tex](x, y) :( 9, -8)[/tex]

ANswer:

(9, -8)

Answer:

x = 9 and y = -8

Step-by-step explanation:

It is given that,

4x + 5y = -4     ----(1)

4x + 3y = 12    -----(2)

To find the value of x and y

eq (1) - eq (2) ⇒

4x + 5y = -4     ----(1)

4x + 3y = 12    -----(2)

  0 + 2y = -16

y = -16/2 = -8

Substitute the value of y in eq (1)

4x + 5y = -4     ----(1)

4x + 5*-8 = -4

4x - 40 = -4

4x = -4 + 40 = 36

x = 36/4 = 9

x = 9 and y = -8