PLEASE HELP ME QUICKKK, FIRST CORRECT PERSON GETS BRAINLIEST​

Answer:

768

Step-by-step explanation:

because 2 to the 3rd power is 8 then 8 times 8 is 64 times 64 times 12 is 768!

please mark brainliest i rlly need one last one

Answer:

$ 3750  = truck rental;   $125 per ton of sugar transported

C is cost;  S is number of tons transported

Equation relating C to S would be a linear equation like y = mx + b

C = 125S + $3750

This equation would be graphed in the first quadrant only

you would start with your y-intercept at (0, 3750)

As x increases by 1, your y increases by 125 yielding these points:

(1, 3875)  (2, 4000)  (3, 4125)  etc.  

This shows that for each increase by one ton of sugar, the cost goes up $125

Step-by-step explanation:

[tex]\Large{\underline{\underline{{\mathfrak{{\bigstar}\:Answer}}}}}\\\\[/tex]

[tex]\bf{1.\:\:x^{2}+4x+1=0}[/tex]

[tex]\longrightarrow\:\:\sf{x=\dfrac{-4{\underline{+}}\sqrt{4^{2}-4\times1\times1}}{2\times1}}[/tex]

[tex]\longrightarrow\:\:\sf{x=\dfrac{-4{\underline{+}}\sqrt{16-4}}{2}}[/tex]

[tex]\longrightarrow\:\:\sf{x=\dfrac{-4{\underline{+}}\sqrt{12}}{2}}[/tex]

[tex]\longrightarrow\:\:\sf{x=\dfrac{4{\underline{+}}2\sqrt{3}}{2}}[/tex]

[tex]\longrightarrow\:\:\sf{x_{1}=-2-\sqrt{3}\:,\:x_{2}= -2+\sqrt{3}}\\\\\\[/tex]

[tex]\bf{2.\:\:x^{2}-9x+14=0}[/tex]

[tex]\longrightarrow\:\:\sf{x^{2}-2x-7x+14=0}[/tex]

[tex]\longrightarrow\:\:\sf{x\times (x-2)-7(x-2)=0}[/tex]

[tex]\longrightarrow\:\:\sf{x_{1}=2\:,\:x_{2}=7}\\\\\\[/tex]

[tex]\bf{3.\:\:x^{2}+8x+2=22}[/tex]

[tex]\longrightarrow\:\:\sf{x^{2}+8x+2-22=0}[/tex]

[tex]\longrightarrow\:\:\sf{x(x+10)-2(x+10)=0}[/tex]

[tex]\longrightarrow\:\:\sf{(x+10)(x-2)=0}[/tex]

[tex]\longrightarrow\:\:\sf{x_{1}=-10\:,\:x_{2}=2}\\\\\\[/tex]

[tex]\bf{4.\:\:x^{2}+8x+7=0}[/tex]

[tex]\longrightarrow\:\:\sf{x^{2}+7x+x+7=0}[/tex]

[tex]\longrightarrow\:\:\sf{x(x+7)+x+7=0}[/tex]

[tex]\longrightarrow\:\:\sf{(x+7)(x+1)=0}[/tex]

[tex]\longrightarrow\:\:\sf{x_{1}=-7\:,\:x_{2}=1}\\\\\\[/tex]

[tex]\bf{5.\:\:x^{2}-10x+25=9}[/tex]

[tex]\longrightarrow\:\:\sf{(x-5)^{2}=9}[/tex]

[tex]\longrightarrow\:\:\sf{x-5={\underline{+}}3}[/tex]

[tex]\longrightarrow\:\:\sf{x-5=-3 \: ; \:x-5=3}[/tex]

[tex]\longrightarrow\:\:\sf{x_{1}=2\:,\:x_{2}=8}\\\\\\[/tex]

[tex]\bf{6.\:\:x^{2}-10x+16=0}[/tex]

[tex]\longrightarrow\:\:\sf{x^{2}-2x-8x+16=0}[/tex]

[tex]\longrightarrow\:\:\sf{(x-2)(x-8)=0}[/tex]

[tex]\longrightarrow\:\:\sf{x-2=0\:;\:x-8=0}[/tex]

[tex]\longrightarrow\:\:\sf{x_{1}=2\:,\:x_{2}=8}\\\\\\[/tex]

[tex]\bf{7.\:\:2x^{2}+7x-4=0}[/tex]

[tex]\longrightarrow\:\:\sf{2x(x+4)-(x-4)=0}[/tex]

[tex]\longrightarrow\:\:\sf{(x+4)((2x-1)=0}[/tex]

[tex]\longrightarrow\:\:\sf{x+4=0\:;\:2x-1=0}[/tex]

[tex]\longrightarrow\:\:\sf{x_{1}=-4\:,\:x_{2}=\dfrac{1}{2}}\\\\\\[/tex]

[tex]\bf{8.\:\:x^{2}-2x+3=0}[/tex]

[tex]\longrightarrow\:\:\sf{x=\dfrac{-(-2){\underline{+}}\sqrt{(-2)^{2}-4\times 1\times 3}}{2\times1}}[/tex]

[tex]\longrightarrow\:\:\sf{\dfrac{2{\underline{+}}\sqrt{4-12}}{2}}[/tex]

[tex]\longrightarrow\:\:\sf{\dfrac{2{\underline{+}}\sqrt{-8}}{2}}[/tex]

[tex]\longrightarrow\:\:\sf{x \notin {\mathbb{R}}}\\\\\\[/tex]

[tex]\bf{9.\:\:3x^{2}+8x+5=0}[/tex]

[tex]\longrightarrow\:\:\sf{x(3x+5)+3x+5=0}[/tex]

[tex]\longrightarrow\:\:\sf{(3x+5)(x+1)=0}[/tex]

[tex]\longrightarrow\:\:\sf{3x+5=0\:;\:x+1=0}[/tex]

[tex]\longrightarrow\:\:\sf{x_{1}=-\dfrac{5}{3}\:,\:x_{2}=-1}\\\\\\[/tex]

[tex]\bf{10.\:\:{\mathbb{\red{1}}}\:\:}[/tex]:')

The solutions are listed below:

(i) [tex]x = -2\pm \sqrt{3}[/tex], (ii) [tex]x = \frac{9}{2}\pm \frac{5}{2}[/tex], (iii) [tex]x = -4 \pm 6[/tex], (iv) [tex]x = -4\pm 3[/tex], (v) [tex]x = -5\pm 3[/tex], (vi) [tex]x = 5 \pm 3[/tex], (vii) [tex]x = -\frac{7}{4}\pm \frac{9}{4}[/tex], (viii) [tex]x = 1 \pm i\sqrt{2}[/tex], (ix) [tex]x = -\frac{4}{3}\pm \frac{1}{3}[/tex], (x) 1. I do not celebrate Valentine's day at all.

Completing the square consists in applying algebraic operations to transform part of the second order polynomial into a perfect square trinomial and simplify the resulting expression. Now we proceed to present the corresponding solutions:

(i) [tex]x^{2}+4\cdot x + 1 = 0[/tex]

[tex]x^{2}+4\cdot x +4 = 3[/tex]

[tex](x+2)^{2} = 3[/tex]

[tex]x+2 = \pm \sqrt{3}[/tex]

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

(ii) [tex]x^{2}-9\cdot x + 14 = 0[/tex]

[tex]x^{2}-9\cdot x + 14+\frac{25}{4} = \frac{25}{4}[/tex]

[tex]x^{2}-9\cdot x +\frac{81}{4} = \frac{25}{4}[/tex]

[tex]\left(x-\frac{9}{2} \right)^{2} = \frac{25}{4}[/tex]

[tex]x -\frac{9}{2} = \pm \frac{5}{2}[/tex]

[tex]x = \frac{9}{2}\pm \frac{5}{2}[/tex]

(iii) [tex]x^{2}+8\cdot x + 2 = 22[/tex]

[tex]x^{2}+8\cdot x +16 = 36[/tex]

[tex](x+4)^{2} = 36[/tex]

[tex]x+4 = \pm 6[/tex]

[tex]x = -4 \pm 6[/tex]

(iv) [tex]x^{2}+8\cdot x + 7 = 0[/tex]

[tex]x^{2}+8\cdot x + 16 = 9[/tex]

[tex](x+4)^{2} = 9[/tex]

[tex]x+4 = \pm 3[/tex]

[tex]x = -4\pm 3[/tex]

(v) [tex]x^{2}+10\cdot x + 25 = 9[/tex]

[tex](x+5)^{2} = 9[/tex]

[tex]x+5 = \pm 3[/tex]

[tex]x = -5\pm 3[/tex]

(vi) [tex]x^{2}-10\cdot x + 16 = 0[/tex]

[tex]x^{2}-10\cdot x + 25 = 9[/tex]

[tex](x-5)^{2} = 9[/tex]

[tex]x-5 = \pm 3[/tex]

[tex]x = 5 \pm 3[/tex]

(vii) [tex]2\cdot x^{2} + 7\cdot x - 4 = 0[/tex]

[tex]x^{2}+\frac{7}{2}\cdot x -2 = 0[/tex]

[tex]x^{2} + \frac{7}{2}\cdot x -2 +\frac{81}{16} = \frac{81}{16}[/tex]

[tex]x^{2}+\frac{7}{2}\cdot x +\frac{49}{16} = \frac{81}{16}[/tex]

[tex]\left(x+\frac{7}{4} \right)^{2} = \frac{81}{16}[/tex]

[tex]x + \frac{7}{4} = \pm \frac{9}{4}[/tex]

[tex]x = -\frac{7}{4}\pm \frac{9}{4}[/tex]

(viii) [tex]x^{2}-2\cdot x + 3 = 0[/tex]

[tex]x^{2}-2\cdot x + 1 + 2 = 0[/tex]

[tex](x-1)^{2} = -2[/tex]

[tex]x-1 = \pm \sqrt{-2}[/tex]

[tex]x = 1 \pm i\sqrt{2}[/tex]

(ix) [tex]3\cdot x^{2} + 8\cdot x + 5 = 0[/tex]

[tex]x^{2}+\frac{8}{3}\cdot x +\frac{5}{3} = 0[/tex]

[tex]x^{2}+\frac{8}{3}\cdot x +\frac{5}{3}+\frac{1}{9} = \frac{1}{9}[/tex]

[tex]x^{2}+\frac{8}{3}\cdot x + \frac{16}{9} = \frac{1}{9}[/tex]

[tex]\left(x+\frac{4}{3} \right)^{2} = \frac{1}{9}[/tex]

[tex]x + \frac{4}{3} = \pm \frac{1}{3}[/tex]

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

(x) 1. I do not celebrate Valentine's day at all.

To learn more on polynomials, we kindly invite to check this verified question: https://brainly.com/question/17822016

Answer: The Answer would be 61

Step-by-step explanation: You will be focusing on PEMDAS if you know the term. Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction, all in the order shown. Since there is no parenthesis or exponent, we go with multiplication as the first option in this problem. 16 x 3 and 3 x 3. 16 x 3 = 48, and 3 x 3 = 9. Since there is no Division on here, we will go the addition, where you add all the numbers up. 48 + 4 = 52 + 9 = 61

Hope this helps!

Answer:

c = 13j × $0.71

Step-by-step explanation:

give me a minute

If the model remains valid, in the year 2,019 the average monthly bill will be $38.46

The linear equation that models the average monthly bill is:

B(x) = -$1.463*x + $95.514

We now want to know when the average monthly bill will be $38.46, then we need to solve:

B(x) = $38.46 = -$1.463*x + $95.514

Solving this for x, we get:

$38.46 = -$1.463*x + $95.514

$1.463*x = $95.514 - $38.46 = $57.054

x = ($57.054)/($1.463)  = 39

And x is the number of years after 1980, then this will be in the year:

1980 + 39 = 2,019

Then, if the model remains valid, in the year 2,019 the average monthly bill will be $38.46

If you want to learn more about linear functions, you can read:

https://brainly.com/question/4025726

no lol ;0 you should ask your teacher for help ;(

Answer:

6a +6a +3 + 6a

12a +3 +6a

18a +3

Answer:

25

Step-by-step explanation:

To find the mean, sum up the five data points and divide this sum by 5:

125

----- = 25

  5

The mean is 25.

Answer:

[tex]area = \frac{1}{2} (base)(height) \\ area = \frac{1}{2} (35cm)(12cm) \\ area = \frac{1}{2} (420 {cm}^{2} ) \\ area = 210 \: {cm}^{2} [/tex]

The area of the triangle with height 12 cm and base 35 cm is A = 210 cm²

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Now , the base of the triangle is AB = 35 cm

The height of the triangle is BC = 12 cm

And , the area of the triangle = ( 1/2 ) x Length x Base

On simplifying , we get

Area of the triangle A = ( 1/2 ) x 12 x 35

Area of the triangle A = ( 6 x 35 )

Area of the triangle A = 210 cm²

Hence , the area of the triangle is 210 cm²

To learn more about triangle click :

https://brainly.com/question/16739377

#SPJ3

The equation of a line in slope intercept form is given by:

y = mx + c

The equation 15x - 9y = -9 of a line into slope-intercept form after simplifying all fractions is y = (5/3)x + 1

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

y = 2x - 3

y = 3x + 4

We have,

15x - 9y = -9

We will rewrite in the slope-intercept form of y = mx + c.

15x - 9y = -9

Subtract 15x on both sides.

-9y = -9 - 15x

-9y = -15x - 9

Divide both sides by -9.

y = (-15x - 9) / -9

y = (15/9)x + 1

y = (5/3)x + 1

Slope = m = 5/3

y-intercept = 1

This is in the slope-intercept form of y = mx + c.

Thus,

The equation 15x - 9y = -9 of a line into slope-intercept form after simplifying all fractions is

y = (5/3)x + 1

Learn more about equation of a line here:

https://brainly.com/question/23087740

#SPJ2

Answer:

77ft ?

Step-by-step explanation:

Answer: 2.48

Step-by-step explanation:

2.48+4.02=6.5

Answer:

here's your answer hope it helps.

Step-by-step explanation:

1. decimal:

39/50=0.78

2. percentage:

39/50=78%

9/50 to a decimal is 0.78 and a percent is 78%.

To convert fraction into decimal, divide the top of the fraction by the bottom number (39/50) here 39 is the top of the fraction and 50 is bottom of the fraction.

39/50 = 0.78

To convert fraction into percent, divide the top of the fraction by the bottom number then multiple the result by 100 here 39 is the top of the fraction and 50 is bottom of the fraction then multiple the result(0.78) by 100.

39/50 = 0.78 * 100 = 78.

Therefore, 39/50 to a decimal is  0.78 and a percent is 78%.

Learn more about decimal and percent here:

https://brainly.com/question/306458

#SPJ6

Answer:

Step-by-step explanation:

<A = <E corresponding parts of 2 geometric figures are =

60 + 8x = 108                    Subtract 60 from both sides

8x = 108 - 60                     Combine

8x = 48                              Divide by 8

8x/8 = 48/8                      

x = 6

< C    = <G                corresponding parts of 2 geometric figures are =

8y - 3x = 62              Use x = 6 from the previous problem

8y - 3*6 = 62             Combine

8y - 18 = 62               Add 18 to both sides

8y = 62 + 18               Combine

8y = 80                       Divide by 8

8y/8 = 80/8

y = 10

Answer:

A bell curve is a common type of distribution for a variable, also known as the normal distribution. The term "bell curve" originates from the fact that the graph used to depict a normal distribution consists of a symmetrical bell-shaped curve.

Step-by-step explanation:

My answer is the one above!

Please mark brainliest i need 2 more!

Answer:

It is called the normal distribution. Hope this help.

Answer:

rate 72 mph; current 16 mph

Step-by-step explanation:

to find the rate of the boat and the current we can model the equation like this

let r = rate

let c = current

8(r - c) = 464

6(r + c) = 540

8r - 8c = 464

6r + 6c = 540

r - c = 58

r + c = 90

then you could use elimination to find r

2r = 148

r = 74

the rate is 74 mph

then plug it in

the current is 16 mph

Answer:

Number of visitors on Friday = 173

Number of visitors on Saturday = 346

Number of visitors on Sunday = 580

Step-by-step explanation:

Total number of visitors over 3 days = 1099

Let x = number of visitors on Friday

If there were twice as many visitors on Saturday than on Friday, then

⇒ number of visitors on Saturday = 2x

If there were 234 more visitors on Sunday than on Saturday, then

⇒ number of visitors on Sunday = 2x + 234

Create an expression for the total number of visitors and solve for x:

⇒ x + 2x + 2x + 234 = 1099

⇒ 5x + 234 = 1099

⇒ 5x = 865

⇒ x = 173

Substitute found value of x into the expressions for each day:

⇒ Number of visitors on Friday = 173

⇒ Number of visitors on Saturday = 2 x 173 = 346

⇒ Number of visitors on Sunday = (2 x 173) + 234 = 580

Answer:

There are no solutions to the system because the equations represent parallel lines.

Step-by-step explanation:

Answer:

What does 0 = −12 mean regarding the solution to the system? There are no solutions to the system because the equations represent parallel lines.

Answer: I think the answer b

Step-by-step explanation:

The cost function for Julia's clothing store per month is 14.60n +970

A function is defined as a relation between a set of inputs having one output each.

Given that, Julia is opening a clothing store. She plans to start by selling sweatshirts. It costs her $10.50 for each sweatshirt, $4 per box for the shirts, and $0.10 a bag. Julia also spends $900 on rent, $40 on electricity, and $30 on advertising each month.

There are two types of cost Julia have,

The variable cost that is not fixed and depend on how many shirts she's making, = $10.50+$4 +$0.10 = $14.60

Let she makes n shirts, so cost = $14.60n

And the second one is fixed cost that is cost she is spending on rent, electricity and advertising, = $900+$40+$30 = $970

Therefore, cost = 14.60n +970

Hence, the cost function for Julia's clothing store per month is 14.60n +970

For more references on functions, click;

https://brainly.com/question/21145944

#SPJ1

Answer:

hi and hello and welcome to the internet

Answer:

AOS: -4

Vertex: (-4,2)

X-intercepts: (-6,0) , (-2,0)

Y-intercept: (0,6)

Step-by-step explanation:

The Parabola opens upwards (as can be seen in the image.) To find the AOS (Axis of Symmetry) first identify the vertex (-4,2) and take the X value of it.

So the AOS is x = -4

Vertex is (-4,2)

The x-intercepts are seen in the graph, (-6,0) and (-2,0)

The y-intercept is where the parabola first touches the Y-axis, which as can be seen is, (0,6).

Hope this helped.

Answer:

100 + 10u

Step-by-step explanation:

apply distributive law: a(b+c) = ab + ac

remove parenthesis

Answer:

Step-by-step explanation:

There's no image, so can't answer it.  If you upload an image, I will help :)

Answer:

Step-by-step explanation:

Need a picture or we can't solve so yes please post another one.

Answer:

w=4

Step-by-step explanation:

First, we can simplify the equation.

28=14w-7w

28=7w

Then, we can divide by 7 on both sides of the equation.

28/7=7w/7

4=w

Finally, we know that x equals 4.

Answer:

w =4

Step-by-step explanation:

28 = 14w - 7w

Combine like terms

28 = 7w

Divide both sides of the equation by the same term

28/7 = 7w/7

Simplify

w = 4

[RevyBreeze]

Answer:

area = 6.5 square units

Step-by-step explanation:

Use the area of a triangle in coordinate geometry formula:

[tex]\triangle GHI =\frac{1}{2} |x_1(y_2- y_3) + x_2(y_3 -y_1) + x_3(y_1 -y_2)|[/tex]

where [tex](x_1,y_1)=(-8,-8) \ \ \ \ (x_2,y_2)=(-6,-7) \ \ \ \ (x_3,y_3)=(-9,-2)[/tex]

      [tex]\triangle GHI =\frac{1}{2} |x_1(y_2- y_3) + x_2(y_3 -y_1) + x_3(y_1 -y_2)|[/tex]

[tex]\implies \triangle GHI =\frac{1}{2} |-8(-7+2) -6(-2 +8) -9(-8 +7)|[/tex]

[tex]\implies \triangle GHI =\frac{1}{2} |40 -36 +9|[/tex]

[tex]\implies \triangle GHI =6.5[/tex]

I don't know what table you have as reference, but I suspect it includes the following transforms:

[tex]1 \leftrightarrow \dfrac1s[/tex]

[tex]e^{at} \leftrightarrow \dfrac{1}{s-a}[/tex]

[tex]\cos(at) \leftrightarrow \dfrac{s}{s^2+a^2}[/tex]

[tex]\sin(at) \leftrightarrow \dfrac{a}{s^2+a^2}[/tex]

[tex]\cosh(at) \leftrigharrow \dfrac{s}{s^2-a^2}[/tex]

[tex]\sinh(at) \leftrigharrow \dfrac{a}{s^2-a^2}[/tex]

It probably also includes some more general properties, like

[tex]t f(t) \leftrightarrow -F'(s)[/tex]

[tex]e^{at} f(t) \leftrightarrow F(s-a)[/tex]

where F(s) is the Laplace transform of f(t).

Beyond these, you should also know the following identities:

[tex]\cosh(t) = \dfrac{e^t + e^{-t}}2[/tex]

[tex]\cosh^2(t) = \dfrac{1 + \cosh(2t)}2[/tex]

[tex]\cos^2(t) = \dfrac{1 + \cos(2t)}2[/tex]

[tex]\sin^2(t) = \dfrac{1 - \cos(2t)}2[/tex]

[tex]\sin(2t) = 2 \sin(t) \cos(t)[/tex]

[tex]\sin(t \pm T) = \sin(t) \cos(T) \pm \cos(t) \sin(T)[/tex]

Putting everything together, we have

• (a)

[tex]\cosh(t) \sin(t) = \dfrac{e^t + e^{-t}}2 \times \sin(t) = \dfrac12 e^t \sin(t) + \dfrac12 e^{-t} \sin(t)[/tex]

and the Laplace transform is

[tex]\dfrac12 F(s - 1) + \dfrac12 F(s + 1)[/tex]

where F(s) is the transform of sin(t),

[tex]F(s) = \dfrac{1}{s^2 + 1}[/tex]

Then

[tex]\cosh(t) \sin(t) \leftrightarrow \dfrac{\frac1{(s-1)^2+1} + \frac1{(s+1)^2+1}}2 = \boxed{\dfrac{s^2+2}{s^4+4}}[/tex]

• (b)

[tex]\sin^2(t) = \dfrac12 \left(1 - \cos(2t)\right)[/tex]

and the transform is

[tex]F(s) = \dfrac12 \left(\dfrac1s - \dfrac{s}{s^2+4}\right) = \boxed{\dfrac{2}{s^3+4s}}[/tex]

• (c)

[tex]\cos^2(2t) = \dfrac12 \left(1 + \cos(4t)\right)[/tex]

with transform

[tex]F(s) = \dfrac12 \left(\dfrac1s + \dfrac{s}{s^2+16}\right) = \boxed{\dfrac{s^2+8}{s^3+16s}}[/tex]

• (d)

[tex]\cosh^2(t) = \dfrac12 \left(1 + \cosh(2t)\right)[/tex]

with transform

[tex]F(s) = \dfrac12 \left(\dfrac1s + \dfrac{s}{s^2-4}\right) = \boxed{-\dfrac2{s^3-4s}}[/tex]

• (e)

[tex]t\sinh(2t) \leftrightarrow -F'(s)[/tex]

where F(s) is the Laplace transform of sinh(2t),

[tex]F(s) = \dfrac{2}{s^2 - 4} \implies -F'(s) = \boxed{\dfrac{4s}{(s^2-4)^2}}[/tex]

• (f)

[tex]\sin(t) \cos(t) = \dfrac12 \left(2\sin(t) \cos(t)\right) = \dfrac12 \sin(2t)[/tex]

with transform

[tex]F(s) = \dfrac12 \times \dfrac{2}{s^2+4} = \boxed{\dfrac1{s^2+4}}[/tex]

• (g)

[tex]\sin\left(t+\dfrac\pi4\right) = \sin(t) \cos\left(\dfrac\pi4\right) + \cos(t) \sin\left(\dfrac\pi4\right) = \dfrac1{\sqrt2} \left(\sin(t) + \cos(t)\right)[/tex]

with transform

[tex]F(s) = \dfrac1{\sqrt2} \left(\dfrac1{s^2+1} + \dfrac{s}{s^2+1}\right) = \boxed{\dfrac{s+1}{\sqrt2 (s^2+1)}}[/tex]

The last two are trivial and follow directly from the properties listed above.

• (h)

[tex]\cos(2t) - \cos(3t) \leftrightarrow \dfrac{s}{s^2+4} - \dfrac{s}{s^2+9} = \boxed{\dfrac{5s}{s^4 + 13s^2 + 36}}[/tex]

• (i)

[tex]\sin(2t) + \cos(4t) \leftrightarrow \dfrac2{s^2+4} + \dfrac{s}{s^2+16} = \boxed{\dfrac{s^3+2s^2+4s+32}{s^4+20s^2+64}}[/tex]

Answer:

h (-5) = 41/4 or 10.25

h (-2) = -3

h (3) = 25/4 or 6.25

Step-by-step explanation:

h (-5) = 1/4(-5)^2 + 4

h (-5) = 1/4(25) + 4

h (-5) = 41/4 or 10.25

h (-2) = -3 (this is given to you in the function)

h (3) = 1/4 (3)^2 + 4

h (3) = 1/4(9) + 4

h (3) = 25/4 or 6.25

Answer:

[tex]x= 4[/tex]

Step-by-step explanation:

[tex]\frac{\sqrt{2x}}{\sqrt{x-2}\:}=2[/tex]                       [ bring √(x - 2) to the opposite side ]

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

[tex](\sqrt{2x} )^{2} = (2\sqrt{x-2})^2[/tex]      [ square both sides ]

[tex]2x = 4(x-2)[/tex]  

[tex]2x=4x-8[/tex]

[tex]2x - 4x = -8[/tex]

[tex]-2x = -8[/tex]

[tex]x= 4[/tex]

Answer:

x=4

Step-by-step explanation:

[tex]\dfrac{\sqrt{2x} }{\sqrt{x-2}}=2[/tex]

Multiply both sides by [tex]\sqrt{x-2}[/tex] :

[tex]\implies \sqrt{2x}=2\sqrt{x-2}[/tex]

Square both sides:

[tex]\implies 2x=4(x-2)\\\\\implies 2x=4x-8[/tex]

Add 8 to both sides:

[tex]\implies 2x+8=4x[/tex]

Subtract [tex]2x[/tex] from both sides:

[tex]\implies 8=2x[/tex]

Divide both sides by 4:

[tex]\implies x=4[/tex]