What is the standard form equation of the line shown below?

Answer:

[tex]\sf x=2+\sqrt{6},\:x=2-\sqrt{6}[/tex]

Explanation:

[tex]\sf y = x^2 -4x[/tex]

given that y = 2

[tex]\sf x^2 -4x = 2[/tex]

[tex]\sf x^2 -4x -2 = 0[/tex]

using quadratic formula:

[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ \ \ when \ ax^2 + bx + c = 0[/tex]

[tex]\rightarrow \sf x_{1,\:2}=\dfrac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:1\cdot \left(-2\right)}}{2\cdot \:1}[/tex]

[tex]\rightarrow \sf x_1=\dfrac{-\left(-4\right)+2\sqrt{6}}{2\cdot \:1},\:x_2=\dfrac{-\left(-4\right)-2\sqrt{6}}{2\cdot \:1}[/tex]

[tex]\rightarrow \sf x=2+\sqrt{6},\:x=2-\sqrt{6}[/tex]

in decimals:

[tex]\rightarrow \sf x=4.45 , \ -0.45[/tex]

The completely factored form of the Wen's polynomial, which has the four terms initial, is,

[tex](6x^2+7)(x-2)[/tex]

The factor of a polynomial is the terms in linear form, which are when multiplied together, give the original polynomial equation as result.

Wen is factoring the polynomial, which has four terms.

[tex]6x^3 - 12x^2+ 7x - 14[/tex] '

Take out the greatest common factor from the equation and make separate groups as,

[tex]6x^2(x - 2)+ 7(x - 2)\\(x-2)(6x^2+7)[/tex]

Rearrange the above equation as,

[tex](6x^2+7)(x-2)[/tex]

Thus, the completely factored form of the Wen's polynomial, which has the four terms initial, is,

[tex](6x^2+7)(x-2)[/tex]

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Answer:

A

Step-by-step explanation:

Trust me

Answer:

Step-by-step explanation:

1)  the equation would be:

(2x+4)x(5x+1) because if the amount of ballpens are (2x+4) and the ballpens are $(5x+1) each, you would multiply them.

this is the expanded version of (2x+4)(5x+1)
{10x^2 + 2x + 20x + 4

10x^2 + 22x + 4}

2) (x^2 +1)(x+2) are multiplied to find the volume of the box

So when expanded it looks like this:

{x^3 + 2x^2 + x + 2}

3) (15a^2b^3) would be multiplied with (2a). This is because to find the total you would times the numbers.
so when expanded:

(15a^2b^3)(2a)

{(15a^3)(2ab^3)}

4) 5X(x+8)=33

5x+40=33

5x=33-40

5x=-7

X= -7/5

5) x-8=8x

8x-x = -8

7x=-8

X=-8/7

Hope this helps :)

The volume of the cylinder is [tex]\pi r^{2}h[/tex]

Volume = [tex]\pi 3^{2} * 4=113.097[/tex] cubic inches (approximated)

Hope that helped!

Rami's family will pay less if they use savings instead of credit.

Step-by-step explanation:

Took the test 8th grade K12

Answer:

10inxy

Step-by-step explanation:

substitute U = ln x, u= ln y into

in(×2y5) and calculate

Answer:

x = 80

Step-by-step explanation:

Because of the parallel lines and the transversal to the left,

x + 67 = 147

x = 80

Answer:

80°

Step-by-step explanation:

I have added some letters for ease.

wyzu is an interior angle. Therefore ∡wyz + ∡yzu = 180°

∡yzu + 147° = 180°

∡yzu = 180°-147

∡yzu = 33°

∡yzu + x° + 67° = 180° ( Supplementary Angle )

33° + x° + 67° = 180°

x° + 100° = 180°

x° = 180° - 100°

x° = 80°

By breaking the front yard into two rectangles, we will see that the area of the front yard is 915 ft^2

The front yard is the green part of the map, we can break this into two rectangles.

One of the rectangles measures 35ft by 25ft, then its area is:

A = 35ft*25ft = 875 ft^2

The other rectangle (in the part that goes from H to Q) has a length of 8ft and a width of 5ft, then its area is:

A' = 8ft*5ft = 40ft^2

The total area of the front yard is the sum of the two that we got above:

area = A + A' =  875 ft^2 + 40ft^2 = 915 ft^2

If you want to learn more about areas, you can read:

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Answer:

1/16

Step-by-step explanation:

start with

3/10 times 5/24 and simplify till you get 1/2 times 1/8 which is 1/16

Answer:

0.0625 or 1/16

Step-by-step explanation:

1. Multiply fractions, a x b/c

When you a x b/c , you would do 0.3 x 5 /24, wich would be 1.5/24

0.3 x 5 = 1.5

2. Simplify 1.5/24.

Change 1.5 to 15/10

To get 15/10, you do 1.5 x 10 over 10, witch would be 15/10 , because 1.5 x 10 is 15.

3. Simplify 15/10

15/10, you can divided both by 5, witch would be 15/5 , 3 and 10 divided by 5 witch would gives you 2, hence 15/10 simplfies to 3/2

4. Divided 3/2 by 24 , which would give you 1/16

Answer:

Mode...

7

Step-by-step explanation:

To find the mode, order the numbers lowest to highest and see which number appears the most often.

and in the list...

8,6,7,9,7,0,2,3,5,7,8,9,69

7 is being repeated.

so mode is 7

Answer:

56 drinks

Step-by-step explanation:

7 drinks = 1 coconut

x drinks = 8 coconut

cross multiply

x drinks = 7 × 8

x drinks = 56

so you can make 56 drinks with 8 coconuts

Answer:

One coconut = 7 drinks

Eight coconuts = X drinks

So set up the equation;

________   _________ = _________, solve for x:-

7/1 = x/8

*8     *8

56 = x, 56 drinks can be made with 8 coconuts.

Answer:

Step-by-step explanation:

First of all, you have to set up the equation

2x^2 + x -1 = 2               Subtract 2 from both sides

2x^2 + x - 1 - 2 = -2+2   Combine

2x^2 + x - 3 = 0             This factors.

(2x + 3)(x -1 ) = 0

Either

2x + 3 = 0                       Subtract 3 from both sides

2x = - 3                           Divide by 2

2x/2 = - 3/2                    

x = - 3/2                         which you already know

or

x - 1 = 0                          Add 1

x - 1 + 1 = 1

x = 1

the other answer is x = 1

Step-by-step explanation:

Let b be base and h be height

b = 11+h

Then the area would be hx b = h(11+h) = 11h + h^2

Perimeter = 2h + 2b

= 2h + 2(11+h)

= 2h + 22 + 2h

= 4h + 22

Answer:

42 sq ft

Step-by-step explanation:

L x W x H

3 x 7 x 2

21 x 2

42 sq ft

Answer:

If [tex]sin x = 0[/tex] we get [tex]2 (0) (\pm1) = 0[/tex] which is true. so we have a first set of solutions given by

[tex]x= 0; x = \pi[/tex];

Else, if [tex]sin x \ne 0[/tex] we can divide both sides by it and we get

[tex]2 cos x = \frac 1 {cos x} \rightarrow 2cos^2x =1 \rightarrow cos^2x =\frac12\\cos x= \pm \frac{\sqrt2}2[/tex]

Which gives us a second set of solutions given by [tex]x= \frac{\pi}4;x= \frac{3\pi}4; x= \frac{5\pi}4;x= \frac{7\pi}4[/tex];

We can group all solutions (doesn't matter, but it's more elegant!) by writing

[tex]x= k\frac{\pi}4; k\in \{0,1,3,4,5,7\}[/tex]

Answer:

A linear function is a function whose graph is a straight line. The line can't be vertical, since then we wouldn't have a function, but any other sort of straight line is fine.

Step-by-step explanation:

Pls, choose me as brainliest!

a way to check for the graph of a function is by using the vertical line test, if vertical lines hit the graph only once, then the graph is the graph of a function.  Check the picture below.

Answer:

if it is area of triangle it would be 49

Step-by-step explanation:

Answer:

Step-by-step explanation:

the square root of 12 is 3.4 so the answer is 3.4

Answer:

Income : £270

Expenditure:£204

profit: £66

Answer:x=-1

add 1 to 3 to get 4, add 3 to -7 to get -4, divide both sides by -4

Answer:

[tex] \: [/tex]

Step-by-step explanation:

Given Equation,

[tex] \\ {\longrightarrow \qquad{ \sf{-3x+3=-7x-1}}}\\ \\ [/tex]

Adding 7x to both sides we get,

[tex]{\longrightarrow \qquad{ \sf{-3x+3 + 7x=-7x-1 + 7x}}}\\ \\ [/tex]

[tex]{\longrightarrow \qquad{ \sf{4x+3=-1}}}\\ \\ [/tex]

Subracting -3 from sides we get,

[tex] \\ {\longrightarrow \qquad{ \sf{4x+3 - 3=-1 - 3}}}\\ \\ [/tex]

[tex]{\longrightarrow \qquad{ \sf{4x=-4}}}\\ \\ [/tex]

Dividing both sides by 4 we get,

[tex] \\ {\longrightarrow \qquad{ \sf{ \frac{4x}{4} = \frac{ - 4}{4} }}}\\ \\ [/tex]

[tex]{\longrightarrow \qquad{ \sf{x=-1}}}\\ \\ [/tex]

The angle of refraction is 15.6 deg.

We have given that An incident ray strikes a piece of diamond at an angle of 40. 5 degrees.

When a ray of light passes from medium 1 to medium 2, the refractive index of medium 2 with respect to 1 is the ratio of the absolute refractive index of medium 2 and medium 1

[tex]1n_{2}=\frac{^{n_{1}}}{n_{2}}[/tex]

When light passes from air into diamond, with the given values of refractive indices,

[tex]an_{d}=\frac{^{n_{d}}}{n_{a}}=\frac{2.42}{1.0003} =2.4193[/tex]

According to Snell's law,

[tex]an_{d}=\frac{^{sini}}{sin r}[/tex]

[tex]< br/ > sinr=an_{d}=\frac{^{sini}}{sin r}=\frac{sin(40.5)}{2.41930} =0.2684[/tex]

[tex]< br/ > r=arcsin(0.2684)=15.57 deg[/tex]

The angle of refraction is 15.6 deg

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Step-by-step explanation:

Pythagoras (for right-angled triangles) :

c² = a² + b²

c being the Hypotenuse, the side opposite of the right angle. and that would be here the diagonal.

c = diagonal = 10 ft

therefore, the width of the rectangle is 10/2 = 5 ft

10² = 5² + b²

100 = 25 + b²

b² = 75

b = length = sqrt(75) = 8.660254038... ft

Answer:1) 1/12 2)21/5 3) 9/25.

Step-by-step explanation:

5x1/12x5 is 5/60, which is 1/12. 4 2/3 is 14/3. 14x9/3x10 is 126/30, or 21/5. 36 percent is 36/100. Divide by 2. 18/50. Divide by two again, 9/25.

Answer:

I believe the answer is D. which is $9.06

Step-by-step explanation:

Step-by-step explanation:

formula for trapezoid or trapezium=h/2 × (a+b)

1.5/2 ×(2+7)

0.75 ×9

3.25msquare