P = e f e = 4.8 correct to 2 significant figures. f = 0.26 correct to 2 significant figures. Work out the lower bound for the value of P . Give your answer correct to 3 significant figures. (2 marks)

Answer:

[tex]x^4 + 4x^3 + 6x^2 + 7x + 2[/tex]

Step-by-step explanation:

We are asked to multiply the given polynomials.

[tex](x^ 2 + 3x + 1) \times (x^2 + x + 2)[/tex]

Multiply each term of the first polynomial to each term of the second polynomial.

[tex]x^ 2 \times (x^2 + x + 2) = x^4 + x^3 + 2x^2[/tex]

[tex]3x \times (x^2 + x + 2) = 3x^3 + 3x^2 + 6x[/tex]

[tex]1 \times (x^2 + x + 2) = x^2 + x + 2[/tex]

Add the results

[tex](x^4 + x^3 + 2x^2) + (3x^3 + 3x^2 + 6x) + ( x^2 + x + 2)[/tex]

Combine the like terms

[tex]x^4 + 4x^3 + 6x^2 + 7x + 2[/tex]

The answer is written in descending powers of x.

Answer:

x² - 20 = 0

Using the quadratic formula

[tex]x = \frac{ - b± \sqrt{( {b})^{2} - 4ac } }{2a} [/tex]

a = 1 b = 0 c = -20

So we have

[tex]x = \frac{ - 0 ± \sqrt{ {0}^{2} - 4(1)( -20)} }{2(1)} \\ \\ x = \frac{± \sqrt{80} }{2} \\ \\ x = \frac{±4 \sqrt{5} }{2} \\ \\ \\ x = ±2 \sqrt{5} \\ \\ \\ x = 2 \sqrt{5} \: \: \: or \: \: \: x = - 2 \sqrt{5} [/tex]

Hope this helps you.

Answer:

I think positive

Step-by-step explanation:

Answer:

zero, D

Step-by-step explanation:

a horizontal line (left to right) would be zero

a verticle line (up and down) would be undifined

Answer:

Step-by-step explanation:

(0+2)/(0-10)= 2/-10 = -1/5

y - 0 = -1/5(x - 0)

y = -1/5x

solution is D

Step-by-step explanation:

We will use the Thales theorem since ED and CB are parallel and A,D and B are in the same lign wich is the same for C,E and A

since we have two similar sides and one similar angle between them it will be SAS similarity

Answer:

50

Step-by-step explanation:

Answer:

a). x = 12

b). m∠H = 90°

    m∠I = 58°

    m∠J = 62°

Step-by-step explanation:

a). Use the property of a triangle,

  " Sum of all the angles in a triangle is 180°"

  (2x + 34)° + (4x + 14)° = 180°

  (2x + 4x) + (34 + 14) = 180

  6x + 48 = 180

  6x = 180 - 48

  6x = 132

   x = [tex]\frac{132}{6}[/tex]

   x = 12

b). m∠H = 90° [Given]

   m∠I = (2x + 34)° = [(2 × 12) + 34]°

   m∠I = 58°

   m∠J = (4x + 14)° = [(4 × 12) + 14]°

  m∠J = 62°

Answer:

44°

Step-by-step explanation:

The secant- secant angle y is half the difference of the measure of its intercepted arcs, that is

[tex]\frac{1}{2}[/tex](BHF - CGJ ) = y , that is

[tex]\frac{1}{2}[/tex](156 - CGH) = 56° ( multiply both sides by 2 )

156 - CGH = 112° , thus

CGH = 156° - 112° = 44°

Answer:

Remember to round!

Answer:

Step-by-step explanation:

You're given a coordinate in the form of (x, y) and you're also given the vertex in the form of (h, k). We will use those in the vertex form of the equation

[tex]y=a(x-h)^2+k[/tex] and solve for a. Filling in:

[tex]-11=a(4-2)^2-3[/tex] which simplifies a bit to

[tex]-11=a(2)^2-3[/tex] and a bit more to

[tex]-11=4a-3[/tex]. Add 3 to both sides to get

-8 = 4a so

a = -2

The equation, then, is

[tex]y=-2(x-2)^2-3[/tex]

Answer:

f(x) = -2x + 1

Step-by-step explanation:

The given expression is [tex]\frac{64^x}{4^{5x-1}}[/tex]

By solving the given expression further,

[tex]\frac{64^x}{4^{5x-1}}[/tex] = [tex]\frac{[(4)^{3}]^x}{(4)^{5x-1}}[/tex] [Since 64 = 4³]

        = [tex]\frac{4^{3x}}{4^{5x-1}}[/tex]

        = [tex]4^{3x}\times 4^{-(5x-1)}[/tex] [Since [tex]\frac{1}{a}=a^{-1}[/tex]]

        = [tex]4^{3x-5x+1}[/tex] [Since [tex]a^x\times a^y=a^{(x+y)}[/tex]]

        = [tex]4^{(-2x+1)}[/tex]

By comparing the result with [tex]4^{\text{f(x)}}[/tex]

f(x) = -2x + 1

Therefore, f(x) = (-2x + 1) will be the answer.

Answer:

The number of students that would have a test score between 61 and 71 are 154 students

Step-by-step explanation:

The given information are;

The mean test score, μ = 61

The standard deviation, σ = 10

The sample size, n = 450

The z score is given as follows;

[tex]Z=\dfrac{x-\mu }{\sigma }[/tex]

We therefore have at x = 61,

[tex]Z=\dfrac{61-61 }{10 } = 0[/tex]

P(x > 61) = P(Z > 0) = 1 - 0.5 = 0.5

For x = 71, we  have;

[tex]Z=\dfrac{71-61 }{10 } = 1[/tex]

P(x < 71) = P(Z < 1) = 0.84134

The probability that the score will be between 61 and 71 is the difference between the two probabilities, which is 0.84134 - 0.5 = 0.34134

Given that the probability is equivalent to  the proportion of the students that would have a test score between 61 and 71, we have;

The number of students that would have a test score between 61 and 71 = 0.34134 × 450 = 153.6 ≈ 154 to the nearest whole number.

Answer:

[tex]\large \boxed{\sf \ \ g(x)=3|x| \ \ }[/tex]

Step-by-step explanation:

Hello,

Let's follow the instructions !

Step 1

g(x)=k*f(x)=k*|x|

We know that the point (2,6) is on the graph so 6=g(2) meaning:

6=k*|2|=k*2

*** divide by 2 both sides ***

k = 6/2 = 3

Step 2

g(x)=3*|x|

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

a proper fraction

Answer:

5[tex]\sqrt{2}[/tex]

Step-by-step explanation:

The diagonal divides the square into 2 right triangles.

let s be the side of the square with the diagonal being the hypotenuse.

Applying Pythagoras' identity to one right triangle, gives

s² + s² = 10² , that is

2s² = 100 ( divide both sides by 2 )

s² = 50 ( take the square root of both sides )

s = [tex]\sqrt{50}[/tex] = [tex]\sqrt{25(2)}[/tex] = [tex]\sqrt{25}[/tex] × [tex]\sqrt{2}[/tex] = 5[tex]\sqrt{2}[/tex]

Answer:

The range consists of all real numbers where y ≠ 0

Step-by-step explanation:

reciprocal parent function is y = 1/x

If y = 0, then 1 would have to be divided by a number to equal 0. This would require x to equal a number that can divide 1 to equal 0. Because this is not possible, y cannot be 0.  

Answer:

64

Step-by-step explanation:

Supplementary angles add up to 180. Since you are given one, just subtract 116 from 180 to get 180 - 116 = 64.

Answer:

x= -1 or x= 2

Step-by-step explanation:

Answer:

25,217,091

Step-by-step explanation:

4551 * 5541 = 25,217,091

Answer:

4551*5541=25217091

Step-by-step explanation:

Answer:

498 m

Step-by-step explanation:

The AAA theorem states that triangles are similar if all three corresponding angles are equal.

1. Compare triangles FHS and ILS

(a) Reason for similarity

∠F = ∠I = 90°

∠S is common.

∴ ∠H = ∠L

(b) Calculate SL

[tex]\begin{array}{rcl}\dfrac{SF}{SH} & = & \dfrac{SI}{SL}\\\\\dfrac{225}{380} & = & \dfrac{225 + 475}{SL}\\\\225SL & = & 380 \times 700\\& = & 266000\\SL & = & \textbf{1182 m}\\\end{array}[/tex]

2. Compare triangles ILS and GLE

(a) Reason for similarity

∠I = ∠G = 90°

∠L is common.

∴ ∠S = ∠E

(b) Calculate LE

[tex]\begin{array}{rcl}\dfrac{IS}{GE} & = & \dfrac{LS}{LE}\\\\\dfrac{700}{180} & = & \dfrac{1182}{LE}\\\\700LE & = & 180 \times 1182\\& = & 212800\\LE & = & \textbf{304.0 m}\\\end{array}[/tex]

3. Calculate EH

               LE + EH + HS = LS

304.0 m + EH + 380 m = 1182 m

                  EH + 684 m = 1182 m

                                 EH = 498 m

The distance from E to H is 498 m.

Answer:

84 squared units.

Step-by-step explanation:

In order to find the surface area of the pyramid, you use the following formula:

[tex]S=b^2+\frac{1}{2}ps[/tex]           (1)

b: base of the pyramid = 6

p: perimeter of the base = 6*4 = 24

s: slant height

Then, you first calculate the slant height, by using the Pythagoras' theorem:

[tex]s=\sqrt{(5)^2-(\frac{6}{2})^2}=4[/tex]

Thus, you replace the values of b, p and s in the equation (1):

[tex]S=(6)^2+\frac{1}{2}(24)(4)=84[/tex]

The surface area of the pyramid is 84 squared units.

Answer:

Step-by-step explanation:

wrong

Answer:

x < 7

Step-by-step explanation:

-6x > -42

Divide each side by -6, remembering to flip the inequality

-6x/-6 < -42/-6

x < 7

Answer:

[tex]\boxed{x<7}[/tex]

Step-by-step explanation:

[tex]-6x > -42[/tex]

Divide both sides by -6 (flip sign).

[tex]\displaystyle \frac{-6x}{-6} < \frac{-42}{-6}[/tex]

[tex]x<7[/tex]

Answer:

a) x° = 108°

b) vertically opposite angles (C) justifies my answer.

Answer:

The answer is option c.

Its an vertically opposite angle because when two lines intersect eachother then theangles formed opposite to it is called v.o.a (vertically opposite angle)

Hope it helps...

Answer:

The answer is b

Step-by-step explanation:

since 2*9=18 and (x)(2x+3)=2x^2+3x

Answer: B

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]Using\: A \: as\: a\: refernce\: angle ;\\Hypotenuse = 29\\Opposite =21\\Adjacent = 20\\\\Using \: SOHCAHTOA\\Sin A = \frac{Opposite}{Hypotenuse} \\\\Sin A = \frac{21}{29}[/tex]

Answer:

The answer is:

[tex]\bold{c\approx 20.2\ units}[/tex]

Step-by-step explanation:

Given:

In △ABC:

m∠A=15°

a=10 and

b=11

To find:

c = ?

Solution:

We can use cosine rule here to find the value of third side c.

Formula for cosine rule:

[tex]cos A = \dfrac{b^{2}+c^{2}-a^{2}}{2bc}[/tex]

Where  

a is the side opposite to [tex]\angle A[/tex]

b is the side opposite to [tex]\angle B[/tex]

c is the side opposite to [tex]\angle C[/tex]

Putting all the values.

[tex]cos 15^\circ = \dfrac{11^{2}+c^{2}-10^{2}}{2\times 11 \times c}\\\Rightarrow 0.96 = \dfrac{121+c^{2}-100}{22c}\\\Rightarrow 0.96 \times 22c= 121+c^{2}-100\\\Rightarrow 21.25 c= 21+c^{2}\\\Rightarrow c^{2}-21.25c+21=0\\\\\text{solving the quadratic equation:}\\\\c = \dfrac{21.25+\sqrt{21.25^2-4 \times 1 \times 21}}{2}\\c = \dfrac{21.25+\sqrt{367.56}}{2}\\c = \dfrac{21.25+19.17}{2}\\c \approx 20.2\ units[/tex]

The answer is:

[tex]\bold{c\approx 20.2\ units}[/tex]

Answer:

The correct option is;

(2·x - y = -2 and 22·x + 10·y = 7)

2 x minus y = negative 2 and 22 x + 10 y = 7

Step-by-step explanation:

2x - y = -2.........(1)

3x + 2y = 5.......(2)

4x - y = 2..........(3)

22x + 10y = 7...(4)

Given that the solution of the system of equation is (-0.3, 1.4), we have;

The system of equations consist of those equations that pass through the point (-0.3, 1.4)

We check as follows;

Equation (1)

2×(-0.3) - 1.4 = -2

Therefore, equation (1) passes through the point (-0.3, 1.4) and is one of the equations

Equation (2)

3×(-0.3) + 2×1.4 = 1.9 ≠ 5

Equation (2) is not part of the system of equations

Equation (3)

4×(-0.3) - 1.4 = -2.6 ≠2

Equation (3) is not part of the system of equations

Equation (4)

22×(-0.3) + 10×1.4 = 7.4 ≈ 7

Therefore, equation (4) approximately passes through the point (-0.3, 1.4) and is one of the equations

The correct option is A. [tex]2x - y = -2\ and 22x + 10y = 7.[/tex]

Given equations,

[tex]2x - y = -2.........(1)[/tex]

[tex]3x + 2y = 5.......(2)[/tex]

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

[tex]22x + 10y = 7...(4)[/tex]

Since the solution of the system of equation is [tex](-0.3, 1.4),[/tex]  Hence the system of equation satisfy the above point.

Now check all the equations,

Equation (1),

[tex]2\times(-0.3) - 1.4 = -2\\-0.6-1.4=-2\\-2.0=-2[/tex]

Hence, equation (1) passes through the point[tex](-0.3, 1.4)[/tex]  and is one of the equations.

Similarly, Equation (2)

[tex]3\times (-0.3) + 2\times1.4 = 5\\-0.9+2.8=5\\1.9=5\\[/tex]

Hence the above equation does not satisfy the solution, so it is not the other system of equation.

Now, Equation (3)

[tex]4\times(-0.3) - 1.4 = -2.6 \neq 2[/tex]

Hence Equation (3) is not part of the system of equations.

Now, Equation (4)

[tex]22\times (-0.3) + 10\times1.4 = 7.4[/tex]

Hence the above equation approximately passes through the solution[tex].(-0.3, 1.4)[/tex] and is one of the equations.

Hence the required system of equation is  [tex]2x - y = -2[/tex] and [tex]22x + 10y = 7[/tex].

Therefore the correct option is A.

For more details follow the link:

https://brainly.com/question/2263981