Need help with factoring the trinomial and simplifying

Answer:

Below.

Step-by-step explanation:

(sine) [tex]sin=30=1/2[/tex]

[tex]=cos [90-30][/tex]

Which means cos=60

Same as:

(cosine) [tex]cos=60=1/2[/tex] or [tex]Sin30=Cos 60=1/2[/tex]

Hence, the answer is...

cos 60° = ½....

By:✨ RobloxYt ✨

The value of the trigonometric ratio cos60 is  1 / 2.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that the value of sin 30° is 1 over 2. The value of cos(90-30) will be calculated as:-

sin(30) = cos(90-30) = cos60
sin(30) = cos(90-30) = 1 / 2

Hence, the value of the cos60 is 1 / 2.

To know more about Trigonometry follow

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Answer:

10

Step-by-step explanation:

Anything greater than 9.49 would be rounded to 10, if it were 9.49, it would be rounded to 9. But only look at the numbers after the decimal.

i.e. ;

7.23 = 7

3.33 = 3

8.89 = 9

14.56 = 15

26.91 = 27

Answer:

512

Step-by-step explanation:

In a geometric sequence, the ratio between the second term and the first term is equal to the ratio between the third term and the second term.

(m² + 4) / m = 16m / (m² + 4)

Solve:

(m² + 4)² = 16m²

m² + 4 = 4m

m² − 4m + 4 = 0

(m − 2)² = 0

m = 2

The first three terms of the geometric sequence are therefore 2, 8, 32.

The common ratio is 4, and the first term is 2.  So the 5th term is:

a = 2 (4)⁵⁻¹

a = 512

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{29 \: mm}}}}}[/tex]

Step-by-step explanation:

Let the width of a rectangle be 'w'

Length of a rectangle be 4w - 5

Perimeter of a rectangle = 75 mm

First, finding the width of the rectangle ( w )

[tex] \boxed{ \sf{perimeter \: of \: a \: rectangle = 2(length + width)}}[/tex]

[tex] \dashrightarrow{ \sf{75 = 2(4w - 5 + w)}}[/tex]

[tex] \dashrightarrow{ \sf{75 = 2(5w - 5)}}[/tex]

[tex] \dashrightarrow{ \sf{75 = 10w - 10}}[/tex]

[tex] \dashrightarrow{ \sf{10w - 10 = 75}}[/tex]

[tex] \dashrightarrow{ \sf{10w = 75 + 10}}[/tex]

[tex] \dashrightarrow{ \sf{10w = 85}}[/tex]

[tex] \dashrightarrow{ \sf{ \frac{10w}{10} = \frac{85}{10} }}[/tex]

[tex] \dashrightarrow{ \sf{w = 8 .5 \: mm}}[/tex]

Replacing / substituting the value of width of a rectangle in order to find the length of a rectangle

[tex] \sf{length \: of \: a \: rectangle = 4w - 5}[/tex]

[tex] \dashrightarrow{ \sf{4 \times 8.5 - 5}}[/tex]

[tex] \dashrightarrow{ \sf{34 - 5}}[/tex]

[tex] \dashrightarrow{ \sf{29 \: mm}}[/tex]

Length of a rectangle = 29 mm

Hope I helped!

Best regards! :D

Answer:

y = -45

Step-by-step explanation:

Y/9 + 5 = 0

y/9 = -5

y = -45

Answer:

x = 16.08

Step-by-step explanation:

x - 8.9 = 7.18

Add 8.9 to each side

x - 8.9+8.9 = 7.18+8.9

x = 16.08

Answer:

THE ANSWER IS :

-(1/10)

Answer:

Lower quartile - (20+32) divided by 2 = 26

Median - (43+46) divided by 2 = 44.5

Upper quartile - 51

Step-by-step explanation:

64

Complete question:

The growth of a city is described by the population function p(t) = P0e^kt where P0 is the initial population of the city, t is the time in years, and k is a constant. If the population of the city atis 19,000 and the population of the city atis 23,000, which is the nearest approximation to the population of the city at

Answer:

27,800

Step-by-step explanation:

We need to obtain the initial population(P0) and constant value (k)

Population function : p(t) = P0e^kt

At t = 0, population = 19,000

19,000 = P0e^(k*0)

19,000 = P0 * e^0

19000 = P0 * 1

19000 = P0

Hence, initial population = 19,000

At t = 3; population = 23,000

23,000 = 19000e^(k*3)

23000 = 19000 * e^3k

e^3k = 23000/ 19000

e^3k = 1.2105263

Take the ln

3k = ln(1.2105263)

k = 0.1910552 / 3

k = 0.0636850

At t = 6

p(t) = P0e^kt

p(6) = 19000 * e^(0.0636850 * 6)

P(6) = 19000 * e^0.3821104

P(6) = 19000 * 1.4653739

P(6) = 27842.104

27,800 ( nearest whole number)

Answer:

Answer: {4,5}. 13) ∪ . Put the sets together in one large set. {1,2,3,5} ... {2,3,1,5}. There are no duplicates to remove, but I can write this in a nicer order.

Step-by-step explanation:

Answer:

[tex]-4.2=q[/tex]

Step-by-step explanation:

To do this you would just add 4.8 to both sides to get rid of the -4.8 so then the equation would look like [tex]-4.2=q[/tex] and that would be our answer.

Answer:

q=-4.2

Step-by-step explanation:

-9 = q - 4.8

Add 4.8 to each side

-9+4.8 = q - 4.8+4.8

-4.2 = q

q=-4.2

Answer:

Yes

Step-by-step explanation:

The sine rule works on all triangles (not just right-angled triangles) where a side and it's opposit angles are known.

Answer:  -2

Step-by-step explanation:

We know that the slope of a secant line over a interval [a,b] is given by :-

[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]

Given f(x) =[tex]-2x^2 + 4[/tex]

Then, the slope of the secant line over the interval [-1, 2] is given by :-

[tex]m=\dfrac{f(2)-f(-1)}{2-(-1)}\\\\=\dfrac{(-2(2)^2+4)-(-2(-1)^2+4)}{2+1}\\\\=\dfrac{(-2(4)+4)-(-2(1)+4)}{3}\\\\=\dfrac{(-8+4)-(-2+4)}{3}\\\\=\dfrac{-4-2}{3}\\\\=\dfrac{-6}{3}\\\\=-1[/tex]

Hence, the slope of the secant line over the interval [-1, 2] is -2.

Answer: y = 4

Step-by-step explanation: If y = x + 2, then the value of y will correspond

to the values that are located in the x-column.

In other words, for the first column, we know that 2 = x.

So if y = x + 2, then y = 2 + 2 or y = 4.

Looks like the equation is

[tex]x^7y+y^7x=7[/tex]

Differentiate both sides with respect to [tex]x[/tex], taking [tex]y[/tex] to be a function of [tex]x[/tex].

[tex]\dfrac{\mathrm d[x^7y+y^7x]}{\mathrm dx}=\dfrac{\mathrm d[7]}{\mathrm dx}[/tex]

[tex]\dfrac{\mathrm d[x^7]}{\mathrm dx}y+x^7\dfrac{\mathrm dy}{\mathrm dx}+\dfrac{\mathrm d[y^7]}{\mathrm dx}x+y^7\dfrac{\mathrm dx}{\mathrm dx}=0[/tex]

[tex]7x^6y+x^7\dfrac{\mathrm dy}{\mathrm dx}+7y^6x\dfrac{\mathrm dy}{\mathrm dx}+y^7=0[/tex]

Solve for [tex]\frac{\mathrm dy}{\mathrm dx}[/tex]:

[tex](x^7+7y^6)\dfrac{\mathrm dy}{\mathrm dx}=-(7x^6y+y^7)[/tex]

[tex]\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{7x^6y+y^7}{x^7+7y^6}[/tex]

Answer:

x = 9.0

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj/ hyp

cos 39 = 7/x

x cos 39 = 7

x = 7/cos 39

x =9.007316961

x = 9.0

Answer:

[tex] \purple{ \boxed{\frac{d^{2} y}{dx ^{2} } = \frac{132}{ {x}^{13} } }}[/tex]

Step-by-step explanation:

[tex]y = \frac{1}{ {x}^{11} } \\ y = {x}^{ - 11} \\ \frac{dy}{dx} = \frac{d}{dx} {x}^{ - 11} \\ \frac{dy}{dx} = - 11{x}^{ - 11 - 1} \\ \frac{dy}{dx} = - 11{x}^{ - 12} \\ \\ \frac{d}{dx} \bigg(\frac{dy}{dx} \bigg) = \frac{d}{dx} ( - 11 {x}^{ - 12} ) \\ \\ \frac{d^{2} y}{dx ^{2} } = - 11\frac{d}{dx} ( {x}^{ - 12} ) \\ \\ \frac{d^{2} y}{dx ^{2} } = - 11( - 12{x}^{ - 13} ) \\ \\ \frac{d^{2} y}{dx ^{2} } = 132{x}^{ - 13} \\ \\ \huge \red{ \boxed{\frac{d^{2} y}{dx ^{2} } = \frac{132}{ {x}^{13} } }}[/tex]

Answer:

1. There are a total of 19 marbles in the bag. The probability of picking a green marble out of them is 4/19 since there are only 4 green ones. The probability of picking a brown marble after replacing what has been initially picked is 1/19. The final probability is the product of the two probabilities and that is 4/361.

2. ?

3. 60%

Step-by-step explanation:

Answer:

2 - [tex]\sqrt{3}[/tex]

Step-by-step explanation:

Using the addition formula for tangent

tan(A - B) = [tex]\frac{tanA-tanB}{1+tanAtanB}[/tex] and the exact values

tan45° = 1 , tan60° = [tex]\sqrt{3}[/tex] , then

tan15° = tan(60 - 45)°

tan(60 - 45)°

= [tex]\frac{tan60-tan45}{1+tan60tan45}[/tex]

= [tex]\frac{\sqrt{3}-1 }{1+\sqrt{3} }[/tex]

Rationalise the denominator by multiplying numerator/ denominator by the conjugate of the denominator.

The conjugate of 1 + [tex]\sqrt{3}[/tex] is 1 - [tex]\sqrt{3}[/tex]

= [tex]\frac{(\sqrt{3}-1)(1-\sqrt{3}) }{(1+\sqrt{3})(1-\sqrt{3}) }[/tex] ← expand numerator/denominator using FOIL

= [tex]\frac{\sqrt{3}-3-1+\sqrt{3} }{1-3}[/tex]

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

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

= 2 - [tex]\sqrt{3}[/tex]

Answer:

4

Step-by-step explanation:

When you convert 160 inches to meters you get 4 meters

Answer:

4.064 Meters

Step-by-step explanation:

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

  [tex]P(X > 66) = P(Z> 1 ) = 0.15866[/tex]

b

[tex]P(\= X > 66) = P(Z> 2 ) = 0.02275[/tex]

c

[tex]P(\= X > 66) = P(Z> 10 ) = 0[/tex]

Step-by-step explanation:

From the question we are told that

   The  population mean is  [tex]\mu = 64 \ inches[/tex]

    The standard deviation is  [tex]\sigma = 2 \ inches[/tex]

The probability that a randomly selected woman is taller than 66 inches   is mathematically represented as

    [tex]P(X > 66) = P(\frac{X - \mu }{\sigma } > \frac{ 66 - \mu }{\sigma} )[/tex]

Generally [tex]\frac{ X - \mu }{\sigma } = Z(The \ standardized \ value \ of \ X )[/tex]

So  

      [tex]P(X > 66) = P(Z> \frac{ 66 - 64 }{ 2} )[/tex]

     [tex]P(X > 66) = P(Z> 1 )[/tex]

From the z-table  the value of  [tex]P(Z > 1 ) = 0.15866[/tex]

 So  

       [tex]P(X > 66) = P(Z> 1 ) = 0.15866[/tex]

Considering b

 sample mean is  n  =  4  

Generally the standard error of mean is mathematically represented as

        [tex]\sigma _{\= x} = \frac{\sigma }{\sqrt{4} }[/tex]

=>    [tex]\sigma _{\= x} = \frac{2 }{\sqrt{4} }[/tex]

=>    [tex]\sigma _{\= x} = 1[/tex]

The probability that the sample mean height is greater than 66 inches    

     [tex]P(\= X > 66) = P(\frac{X - \mu }{\sigma_{\= x } } > \frac{ 66 - \mu }{\sigma_{\= x }} )[/tex]

=>   [tex]P(\= X > 66) = P(Z > \frac{ 66 - 64 }{1} )[/tex]

=>  [tex]P(\= X > 66) = P(Z> 2 )[/tex]

From the z-table  the value of  [tex]P(Z > 2 ) = 0.02275[/tex]

=> [tex]P(\= X > 66) = P(Z> 2 ) = 0.02275[/tex]

Considering b

 sample mean is  n  =  100

Generally the standard error of mean is mathematically represented as

        [tex]\sigma _{\= x} = \frac{2 }{\sqrt{100} }[/tex]

=>    [tex]\sigma _{\= x} = 0.2[/tex]

The probability that the sample mean height is greater than 66 inches

   [tex]P(\= X > 66) = P(Z > \frac{ 66 - 64 }{0.2} )[/tex]

=>  [tex]P(\= X > 66) = P(Z> 10 )[/tex]

From the z-table  the value of  [tex]P(Z > 10 ) = 0[/tex]

[tex]P(\= X > 66) = P(Z> 10 ) = 0[/tex]

Answer:

62.32%

Step-by-step explanation:

172/276 * 100%

= 62.32%

Answer:

standard form means that the terms are ordered from biggest exponent to

lowest exponent. The leading coefficient is the coefficient of the first term in a

polynomial in standard form . For example, 3x^4 + x^3 - 2x^2 + 7x.

Answer:

Angle of elevation from Kim to the satellite launch = 6.654°

Step-by-step explanation:

The distance from Kim to the satellite launch

= 6 miles

Height of the satellite launch

= 0.7 miles

Angle of elevation from Kim to the satellite launch = b

Tan b = height of satellite/distance from Kim

Tan b= 0.7/6

Tan b= 0.1166667

b = tan^-1 (0.1166667)

b= 6.654°

Angle of elevation from Kim to the satellite launch = 6.654°

Answer: x = ⅓ or 5

Step-by-step explanation:

From the quadratic equation, we are asked to find the root of the equation. Therefore, we may use any of the methods.

Here I am using grouping method.

3x² - 16x + 15 = 0

3x² - 15x -x + 15 = 0, we now factorize

3x( x - 5 ) - ( x - 5 ) = 0, we now collect like terms.

( 3x - 1 )( x - 5 ) = 0

Now to find x, we equate each in brackets to zero and then solve.

3x - 1 = 0

x = ⅓ , and if

x - 5 = 0

x = 5, .

Now , the solution of the equation will be

x = ⅓ or 5

Answer:

x^2+y

Step-by-step explanation:

simply because you have x squared and a variable y that needs to be added.

Answer:

Exponent

Step-by-step explanation:

The base tells what number is being repeatedly multiplied, and the exponent tells how many times the base is used in the multiplication. Exponents and have special names. Raising a base to a power of is called “squaring” a number. Raising a base to a power of is called “cubing” a number.

Answer:

90°

Step-by-step explanation:

Through point O draw a ray on left side of O which is || to AB & CD and take any point P on it.

Therefore,

∠ABO + ∠BOP = 180° (by interior angle Postulate)

118° + ∠BOP = 180°

∠BOP = 180° - 118°

∠BOP = 62°.... (1)

Since, ∠BOP + ∠POD = ∠BOD

Therefore, 62° + ∠POD = 152°

∠POD = 152° - 62°

∠POD = 90°.....(2)

∠POD + ∠ODC = 180° (by interior angle Postulate)

90° + ∠ODC = 180°

∠ODC = 180° - 90°

[tex] \huge\red {\boxed {m\angle ODC = 90°}} [/tex]

Answer:

[tex] d = \sqrt{113} = 10.63014 [/tex]

Step-by-step explanation:

Distance between the endpoints of the graph, (-3, 3) and (5, -4), can be calculated using distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex].

Where,

[tex] (-3, 3) = (x_1, y_1) [/tex]

[tex] (5, -4) = (x_2, y_2) [/tex]

Thus,

[tex] d = \sqrt{(5 - (-3))^2 + (-4 - 3)^2} [/tex]

[tex] d = \sqrt{(8)^2 + (-7)^2} [/tex]

[tex] d = \sqrt{64 + 49} = \sqrt{113} [/tex]

[tex] d = \sqrt{113} = 10.63014 [/tex]