Using the unit circle, determine the value of sin(-240°).
A) -1/2
B) √3/2
C) 1/2
D) -√3/2

Answer:

The value of the mutual force between them is 3.6 x 10⁶ N

Step-by-step explanation:

Given;

distance between the two-point charges, r = 2000 m

the value of the two-point charges, q₁ and q₂ = 40 C and -40 C

Coulomb's constant, k = 9 x 10⁹ Nm²/C²

The value of the mutual force between them is calculated by applying Coulomb's law;

[tex]F = \frac{K|q_1|q_2|}{r^2} \\\\F = \frac{(9 \times 10^9)(40\times 40)}{(2000)^2} \\\\F = 3.6 \times 10^6 \ N[/tex]

Therefore, the value of the mutual force between them is 3.6 x 10⁶ N.

(B)

.....................

Answer:

No

Step-by-step explanation:

[tex]7x-4y>-4[/tex]

[tex]7(-9)-4(7)>-4[/tex]

[tex](-63)-(28)>-4[/tex]

[tex](-91)>-4[/tex]

[tex](-9,7)[/tex] is not a solution to the system of inequality

Answer:

I believe 90

Step-by-step explanation:

because if you take away 25 (40 pounds) from 100, you divide 100 by 2 to see how many pounds that are 2 $ fit in 100

100/2=50 (pounds)

so 50pounds + the 40pounds (which was the 25$ i took off to make it easier) =90 pounds

hope I helped and feel free to ask questions :)

We should multiply the expression by (9+√14) fraction.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers.

To rationalize the terms, we multiply both the denominator and denominator by the conjugate of the denominator.

The denominator is 9-√14 and its conjugate is; (9+√14).

(5-√7)/(9-√14) = (5-√7)(9+√14)/(9-√14)(9+√14)

                       =  (5-√7)(9+√14)/(9²-14)

                      = (45 + 5√14 - 9√7 - √98)/(81-14)

                       =  (45 + 5√14 - 9√7 - √98)/67

                       = (45 + 5√14 - 9√7 - 7√2)67

This is the rationalized expression.  

The denominator is (9-√14) and its conjugate is (9+√14).

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Answer: 72.78% of the drivers are traveling between 70 and 80 miles per hour based on this distribution.

Step-by-step explanation:

Let X be a random variable that represents the speed of the drivers.

Given: population mean : M = 72 miles ,

Standard deviation: s= 3.2 miles

The probability that the drivers are traveling between 70 and 80 miles per hour based on this distribution:

[tex]P(70\leq X\leq 80)=P(\frac{70-72}{3.2}\leq \frac{X-M}{s}\leq\frac{80-72}{3.2})\\\\= P(-0.625\leq Z\leq 2.5)\ \ \ \ \ [Z=\frac{X-M}{s}]\\\\=P(Z\leq2.5)-P(Z\leq -0.625)\\\\\\ =0.9938-0.2660\ \ \ [\text{Using p-value calculator}]\\\\=0.7278[/tex]

Hence, 72.78% of the drivers are traveling between 70 and 80 miles per hour based on this distribution.

Answer:

13Y

Step-by-step explanation:

7+6 = 13

Answer:

Step-by-step explanation:

7y+6y

y(7+6)

y*13

13y

Or

since they are like term u simply add them

7y+6y

13y

The value of x that makes ABCD a parallelogram is C. x = 70°.

Parallelogram is a type of polygon with four sides, four angles and four vertices. It is a type of Quadrilateral.

Opposite sides are parallel, and the opposite sides and opposite angles are equal.

Given that ABCD is a parallelogram.

We know that opposite angles of a parallelogram are equal.

It is already given.

Also, adjacent angles of a parallelogram is equal to 180°.

So,

x + 40 + 70 = 180

x + 110 = 180

x = 180 - 110

x = 70

Hence the correct option is C. x = 70°.

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Answer:

6 cm

Step-by-step explanation:

Given :

base is 9cm, Height is 4cm, and Length is 12cm.

Volume of triangular prism :

V = 1/2 * base * height * length

V = 1/2 * 9 * 4 * 12

V = 9 * 2 * 12

V = 216 cm³

Volume of a cube = a³

Where , a = side length

If 216cm³ is melted to form a cube

Then ;

a = 216^1/3

a = 6 cm

Answer:

Step-by-step explanation:

Here,

3x - 5

There is 3 as coefficient of x and -5 constant.

Hence,

Option D is correct

Answer:

  a) 9^2

  b) 9^(1/2)

  c) 9^(3/2)

Step-by-step explanation:

It is perhaps easier to start by using 3^n.

  3 = 3^1

  27 = 3^3

  81 = 3^4

Recognize that 3 = 9^(1/2) and replace 3 in each of the above. The applicable rule of exponents is (a^b)^c = a^(bc).

a) 81 = (9^(1/2))^4 = 9^2

b) 3 = 9^(1/2)

c) 27 = (9^(1/2))^3 = 9^(3/2)

Answer:

(a) 9^2

(b) 9^0.5

(c) 9^1.5

Step-by-step explanation:

We need to find n such that 9^n = value indicated.

Recall that n=2 is a square, so

(a) 9^2=9*9=81

Recall that n=0.5 (or 1/2) is a square root, because 9^0.5 * 9^0.5 = 9^1 = 9, so

(b) 9^0.5 = 3, because 3*3 = 9

Recall that multiplication of two powers with the same base is the sum of the exponents, e.g. 9^a * 9^b = 9^(a+b).

Therefore,

(c) 27 = 9*3 = 9^1 * 9^0.5 = 9^(1+0.5) = 9^1.5

Answer:

110degrees

Step-by-step explanation:

Complete question

Q4: If x and y are two supplementary angles whereas m<x=70 then find the m<y.

The sum of two supplementary angles is 180degrees, hence;

m<x + m<y = 180

70 + m<y = 180

m<y = 180 - 70

m<y = 110degrees

Hence the measure of ,=m<y is 110degrees

Answer:

[tex](a)\ t^2 - 20t + 75= 0[/tex]

[tex](b)[/tex] [tex]t = 5; t -=15[/tex]

Step-by-step explanation:

Given

[tex]p(t) = t^2 - 20t + 175[/tex]

Solving (a): Equation when profit = 100.

This implies that:

[tex]p(t) =100[/tex]

So, we have:

[tex]100 = t^2 - 20t + 175[/tex]

Rewrite as:

[tex]t^2 - 20t + 175 - 100 = 0[/tex]

[tex]t^2 - 20t + 75= 0[/tex]

Solving (b): Calculate t, in (a)

In a, we have:

[tex]t^2 - 20t + 75= 0[/tex]

Expand

[tex]t^2 - 15t -5t + 75= 0[/tex]

Factorize

[tex]t(t - 15) -5(t - 15)= 0[/tex]

Factor out t - 15

[tex](t - 5)(t - 15)= 0[/tex]

Split

[tex]t - 5 = 0; t - 15 =0[/tex]

Solve

[tex]t = 5; t -=15[/tex]

The prices are $5 and $15, respectively

Step-by-step explanation:

[tex] \frac{1}{3} ( \frac{22}{7} ) {(3)}^{2} (14) \\ \frac{1}{3} ( \frac{22}{7})(9)(14) \\ \frac{1}{3}( \frac{22}{7}) (126) \\ 42( \frac{22}{7}) \\ \frac{924}{7} \\ 132{cm}^{3} [/tex]

Answer:

$13.50

Step-by-step explanation:

2 bags of cat food = $4.50

1 bag of cat food = 2/4.50

= 2.25

6 bags of cat food = 2.25*6

=13.50

Answer:

400 miles per hour

Step-by-step explanation:

8000 miles         ÷  20   =        400   Miles

20 hours            ÷  20     =         1     hour

Answer:

Diameter

Step-by-step explanation:

The diameter is a straight line through the centre of a circle.

Hope this helps :)

Answer

27^0.5+0.25 or 3^0.5+0.25

3^2t + 1/4 expression is equivalent to 81^0.5t+0.25​.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression  81^0.5t+0.25​

Simplifying the given expression:

=> 81^0.5t+0.25​

Simplify using the exponent power rule: (a^m)^n = (a)^mn

Convert decimal to fraction:

=> (3⁴ )^0.5t + 25/100

Cross out the common factor:

=> 3^2t + 1/4

therefore, 3^2t + 1/4 expression is equivalent to 81^0.5t+0.25​.

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Answer:

subject

Step-by-step explanation:

subject is a noun (person, place or thing)

verb is doing something *example: running

object is a thing *example: apple

conjunction is a word used to connect sentences *example: but

Answer:

36:45

Step-by-step explanation:

$81. u add the ratios 4+5=9

$81/9=9

9*4=36

9*5=45

Answer:

13.5

Step-by-step explanation:

Answer:

Total surface area=728cm^2

Volume of pyramid=1241.33 cm^3

Step-by-step explanation:

Given data

Square base= 14cm

Height= 19cm

Slant height = 21cm

Area of all four triangular surfaces= 1/2B*H*4

Area of all four triangular surfaces= 1/2*14*19*4

Area of all four triangular surfaces= 1/2*1064

Area of all four triangular surfaces=532 cm^2

Area of square base= 14^2

Area of square base=196cm^2

Total surface area= Area of all four triangular surfaces+Area of square base

Total surface area=532+196

Total surface area=728cm^2

Volume of pyramid= a^2h/3

Volume of pyramid= 14^2*19/3

Volume of pyramid= 196*19/3

Volume of pyramid=3724/3

Volume of pyramid=1241.33 cm^3

Answer:

2h3-r5

Step-by-step explanation:

first 3-2=5

then 2h3-r=2h3-r5

finally 2h3-r5

Answer:

3.28653¯V7h

Step-by-step explanation:

Given:

The graph of an inequality.

To find:

The inequality in slope intercept form.

Solution:

The slope intercept form is:

[tex]y=mx+b[/tex]

Where, m is slope and b is y-intercept.

From the given graph it is clear that the boundary line passes through the points (-3,0) and (0,-3).

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-0=\dfrac{-3-0}{0-(-3)}(x-(-3))[/tex]

[tex]y=\dfrac{-3}{3}(x+3)[/tex]

[tex]y=-1(x+3)[/tex]

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

From the given graph it is clear that the boundary line is a solid line and the shaded region lies above the line, so the sign of inequality must be "≥".

[tex]y\geq -x-3[/tex]

Therefore, the required inequality is [tex]y\geq -x-3[/tex].