the relationship between the zeroes and coefficients of the quadratic polynomial ax2+bx+c is

Answer:

here is a formulae

cos2A= 2cos square a -1

Step-by-step explanation:

as given cos A= 1/2 (a+1/a)

by simplifying

cosA =a²+1/2a

now by following the formulae

cos2A = 2cos²A-1

=2(a²+1/2a)² -1

=2(a⁴+2a²+1/4a²)-1

=a⁴+2a²+1/2a² -1

=a⁴+2a²+1-2a²/2a²

=a⁴+1/2a²

=1/2 (a⁴+1/a²)

=1/2(a⁴/a²+1/a²)

=1/2(a²+1/a²)

{proved}

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thank uuu

Answer:  see proof below

Step-by-step explanation:

Use the Double Angle Identity: cos 2A = 2cos²A - 1

Proof  LHS → RHS

Given:                                [tex]\cos A=\dfrac{1}{2}\bigg(a+\dfrac{1}{a}\bigg)[/tex]

LHS:                                   cos 2A

Double Angle Identity:      2(cos²A) - 1

                                     [tex]=2\bigg(\dfrac{1}{2}\bigg(a+\dfrac{1}{a}\bigg)^2\bigg)-1[/tex]

Simplify:                           [tex]2\bigg(\dfrac{1}{4}\bigg(a^2+2+\dfrac{1}{a^2}\bigg)\bigg)-1[/tex]

                                     [tex]=\dfrac{1}{2}\bigg(a^2+2+\dfrac{1}{a^2}\bigg)-1[/tex]

                                    [tex]=\dfrac{1}{2}a^2+1+\dfrac{1}{2a^2}-1[/tex]

                                    [tex]=\dfrac{1}{2}a^2+\dfrac{1}{2a^2}[/tex]

Factor:                         [tex]=\dfrac{1}{2}\bigg(a^2+\dfrac{1}{a^2}\bigg)[/tex]

[tex]\dfrac{1}{2}\bigg(a^2+\dfrac{1}{a^2}\bigg)=\dfrac{1}{2}\bigg(a^2+\dfrac{1}{a^2}\bigg)\quad \checkmark[/tex]

Answer:

Complement​t angle = 44°

Step-by-step explanation:

Given:

One angle = 46°

Find:

Complement​t angle

Computation:

In complement​ angle

∠A + ∠B = 90°

46° + ∠B = 90°

∠B = 90° - 46°

∠B = 44°

Complement​t angle = 44°

Answer:

length: 30 meters

width: 12 meters

Step-by-step explanation:

2(a+b) = 84

a = 2b + 6

a = length

b = width

then:

2((2b+6)+b) = 84

2b + 6 + b = 84/2

3b + 6 = 42

3b = 42 - 6

3b = 36

b = 36/3

b = 12

a = 2b + 6

a = 2*12 + 6

a = 24 + 6

a = 30

Check:

84 = 2(12+30)

84 = 2*42

Answer:

$24

Step-by-step explanation:

1/4x + 1/3x + 8 = 22

1/4x + 1/3x = 7/12x

7/12x + 8 = 22

22 - 8 = 14

7/12x = 14

14/ 7/12

x = 24

Answer

6 kg/m

Step-by-step explanation:

The linear density is said to give the way the mass is changing it's position and it's a derivatives of mass m here which is differenciated with respect to x position

Given

mass m = 3x^2.

Density ρ= dm/dx =6x

Then if we substitute x=1 into above expresion we have

ρ(1) =6 Kg/m

ρ= 6Kg/m

Hence this is how fast is the mass changing at that position.

Answer:

i think this is the answer

Answer:

the answer is [tex]\frac{3}{2}[/tex] or 1.5 or 1[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Answer:

5a + 5b

Step-by-step explanation:

13a - 8a + 9b - 4b =

Combine like terms. 13a and -8a are like terms and can be combined.

9b and -4b are like terms and can be combined.

= 5a + 5b

Answer:

Step-by-step explanation:

[tex]13a-8a+9b-4b\\\mathrm{Add\:similar\:elements:}\:13a-8a=5a\\=5a+9b-4b\\\mathrm{Add\:similar\:elements:}\:9b-4b=5b\\=5a+5b[/tex]

Answer:

Step-by-step explanation:

Given , value of b = -4

To find : ( - b )²

plug the value of b

⇒[tex] \sf{( - {( - 4))}^{2} }[/tex]

we know that ,

[tex] \sf{( - ) \times ( - ) = ( + )}[/tex]

⇒[tex] \sf{ {4}^{2} }[/tex]

Evaluate the power

⇒[tex] \sf{16}[/tex]

Hope I helped!

Best regards!!

Answer:

C

Step-by-step explanation:

Given

f(x) = 3x - 40 and f(x) = 8 , then equate the right sides, that is

3x - 40 = 8 ( add 40 to both sides )

3x = 48 ( divide both sides by 3 )

x = 16 → C

Answer:79°

Step-by-step explanation:

Given the 124° angle, the other angle formed by that line and the top side of the square must be 56°, as they are supplementary angles (they must add up to 180°). This means that the angle formed by that same line and the bottom side of the square is also 56° since it is a corresponding angle and the top and bottom sides of a square are parallel. The angle that a diagonal of a square forms with the sides of a square is always 45°.

So now we have a triangle (in red in my diagram) with angles of 45°, 56°, and x°. The sum of the angles of a triangle must always equal 180°, so we solve for x:

56 + 45 + x = 180

x = 180 - 56 - 45 = 79

So angle x must be 79°.

Answer:

The minimum sample size needed for each city  = 922

Step-by-step explanation:

From the information given:

the objective is to find the minimum sample size needed for each city so that the margin of error not to exceed 6%.

If we take a look at the question very well:

we are only given the confidence interval of 99% and the margin of error of 6%

we were not informed or given the value or estimate of any proportions>

so we assume that:

[tex]p_1 =q_ 1= p_2 = q_2 = 0.5[/tex]

At confidence interval of 0.99 , the level of significance = 1 - 0.99 = 0.01

The critical value for [tex]z_{\alpha/2} = z_{0.01 /2}[/tex]

= [tex]z_{0.005}[/tex] = 2.576

The minimum sample size needed can be calculated by using the formula :

[tex]n = \dfrac{z^2_{\alpha/2}}{E^2}(p_1q_1+p_2q_2)[/tex]

[tex]n = \dfrac{2.576^2}{0.06^2}((0.5 \times 0.5)+(0.5 \times 0.5))[/tex]

[tex]n = \dfrac{6.635776}{0.0036}(0.25+0.25)[/tex]

[tex]n =1843.271 \times (0.5)[/tex]

n = 921.63

n [tex]\simeq[/tex] 922

∴ The minimum sample size needed for each city  = 922

Answer:

w = -1

Step-by-step explanation:

Answer:

[tex]\Huge \boxed{w=-1}[/tex]

Step-by-step explanation:

[tex]w-5-4= -8-6w+8w[/tex]

Combining like terms.

[tex]w-9= -8+2w[/tex]

Adding -w and 8 to both sides.

[tex]-9+8=2w-w[/tex]

[tex]-1=w[/tex]

Answer:

sue = 18  

tony = 18

sue = 18 - x  

tony = 18 + x  

sue = 18 - x - 5  

tony = (18 + x) / 2  

sue = 13 - x  

tony = (18 + x) / 2

Step-by-step explanation:

You Simplify The Equation by using PEMDAS

P: Parentheses

E: Exponents

M: Multiplication

D: Division

A: Addition

S: Subtraction

Answer:

SU = 70

Step-by-step explanation:

First, we need to find the value of x. Since M is the midpoint of SU, that means that SM = MU, therefore:

x + 15 = 4x - 45

15 = 3x - 45

60 = 3x

x = 20

We know that SU = SM + MU = (x + 15) + (4x - 45) = 5x - 30 and that x = 20 so SU = 5x - 30 = 5 * 20 - 30 = 100 - 30 = 70.

The evaluation of the numeric expression is:

5(−6) = -30

A numeric expression is a mathematical statement that involves only numbers and one or more operation symbols.

Examples of operation symbols are addition, subtraction, multiplication and division. It can also be expressed in the radical symbol (the square root symbol) or the absolute value symbol.

We can evaluate 5(−6) as follow:

5(−6) = 5 * (-6)

        = -30

Learn more about numeric expression on:

https://brainly.com/question/4344214

#SPJ6  

Answer:

-6

Step-by-step explanation:

(-17+4+1-6)=-18

-18/-3=6

6*-1=-6

Answer:

-6

Step-by-step explanation:

(-17+4+1-6)÷(-3)×(-1)

PEMDAS

Parentheses first

(-17+4+1-6)÷(-3)×(-1)

Add and subtract inside the left parentheses

(-18)÷(-3)×(-1)

Multiply and divide from left to right

6 * -1

-6

Answer:

Zero is an integer which is indicated by the symbol 0 in numbers and it is used to indicate that the count of an item when there are non of the item present which is one of the reasons zero along with the fact that it is the number between positive and negative numbers, why it is not associated with a positive or negative sign.

Step-by-step explanation:

A number which is not zero is said to be a non-zero number and the roots of a function is known as the zeros of the function.

Answer:

A,C, and D I believe.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the exponential growth formula expressed as [tex]P = Ae^{kt}[/tex] where P is the countrys population and t is the time.

Initially in 1991, at t= 0, P = 147 million

[tex]P = Ae^{kt}\\147 = Ae^{k(0)}\\147 = Ae^0\\147 = A(1)\\A = 147[/tex]

If by 1998 it was 153 million, this means that the population is 153 million 7 years later i.e when t = 7, P = 153. On substituting into the formula to get the constant 'k';

[tex]P = Ae^{kt}\\153 = 147e^{k(7)}\\153 = 147e^{7k}\\153/147 = e^{7k}\\e^{7k} = 1.041\\Taking \ ln \ of \ both \ sides\\lne^{7k} = ln 1.041\\7k = 0.04018\\k = 0.04018/7\\k = 0.00574[/tex]

To estimate the population in 2017, to number of years from 1991 to 2017 is 26 years. Hence we are to find the value of P given t = 27, A = 147 and k = 0.00574

[tex]P = Ae^{kt}\\P = 147e^{0.00574*26}\\P = 147e^0.14924\\P = 147*1.16095\\P = 170.659[/tex]

Hence the population in 2017 using exponential growth formula to the nearest million is 171 million.

Answer:

x = 9

Step-by-step explanation:

Take the angle of LOJ (3x) and JOK (2x+12).

LOJ + JOK = LOK.

LOK = 57.

So, 3x + 2x + 12 = 57

3x + 2x = 5x

5x + 12 = 57

57 - 12 = 45

5x = 45

x= 9

Answer:

1 + 1 · 7 + 1 · 72 + . . . 1 · 76

Step-by-step explanation:

bc

Answer:

1 + 1 · 7 + 1 · 72 + . . . 1 · 76

Step-by-step explanation:

Hope this helps!

Answer:

1723

Step-by-step explanation:

10 x 70=700

Answer:

1723

Step-by-step explanation:

Answer:

When both the conditions hold true, F is prime.

Step-by-step explanation:

AB, CD, and EF are two-digit numbers, where A, B, C, D, E and F represent distinct digits from 1 to 9.

  AB

+ CD

--------

  EF

1st condition, B and D are consecutive.

Adding B and D gives us F.

Possible values can be (F being the unit value after adding not considering the carry over):

B + D = F

1+2=3

2+3=5

3+4=7

4+5=9

5+6=1

6+7=3

7+8=5

8+9=7

Here F is not prime (because 9 is not prime).

Now, let us consider the 2nd condition as well.

i.e. C = 8

For the following

  AB

+ CD

--------

  EF

C is 8 then A must be 1 because any value other than 1 for A will make the sum of A and C greater than 9 and there will be a carry which is not the case here.

So, E = 8 + 1 = 9

Now, B  and D are consecutive and can not be 1, 8 or 9.

So, possible values are:

B + D = F

2 + 3 = 5

3 + 4 = 7

Here F is prime.

So, when both the conditions hold true, F is prime.

Answer:

The multiplicative inverse of -0.7 is -1/0.7

hope it helps

Answer:

Hey there!

3 x 5/4 = 3 x 5 ÷ 4 = 5 x 3 ÷ 4

5 x 4/3 = 5 x 4 ÷ 3 = 4 x 5 ÷ 3

4 x 3/5 = 4 x 3 ÷ 5 = 4 x 3 ÷ 5

Hope this helps :)

Answer:

13) The planes ABF and FHG are  perpendicular

14)  Segments Ab and CD are parallel.

Step-by-step explanation:

13)

Planes ABF and FHG are perpendicular (they intersect along side EF)

14)

In order to find out about the segments AB and CD, let's use the formula for the slope that joins any two points [tex](x_1,y_1)\,\,\&\,\,(x_2,y_2)[/tex] on the plane:

[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

Therefore, given:

A = (-3, 2)

B = (1, 4)

C = (-3, -1)

D = (1, 1)

we have for segment AB the following slope:

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

and for segment CD the following slope:

[tex]slope_{CD}=\frac{1+1}{1+3} =\frac{2}{4} =\frac{1}{2}[/tex]

Since they show the same slope, these two segments are parallel.

Answer:

A

Step-by-step explanation:

x - 7 = 18

Adding 7 to both sides (to get rid of the -7 on the left side) gives us:

x - 7 + 7 = 18 + 7

x = 25

Answer:

25 is the correct answer

Step-by-step explanation:

i got it right on the test

Step-by-step explanation: the answers are a and d

Answer:

a d

Step-by-step explanation:

got it right

Answer:

x = ln9

Step-by-step explanation:

Using the rule of logarithms

log [tex]x^{n}[/tex] = nlogx , lne = 1

Given

[tex]e^{x}[/tex] = 9 ( take the ln of both sides )

ln[tex]e^{x}[/tex] = ln9, thus

xlne = ln9, that is

x = ln9