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The roots of the given quadratic equation 3x² - 3x + 1 are x = [3 + √(-3)]/6 and x = [3 - √(-3)]/6 thus options (A) and (B) are correct.

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.

As per the given equation,

3x² - 3x + 1

To find the roots of the above quadratic equation,

3x² - 3x + 1 = 0

x = [-(-3) ± √((-3)² - 4×3×1)]/(2×3)

x = [3 ± √(-3)]/6

x = [3 + √(-3)]/6 and x = [3 - √(-3)]/6

Hence "The roots of the given quadratic equation 3x² - 3x + 1 are x = [3 + √(-3)]/6 and x = [3 - √(-3)]/6".

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Answer:

1. The applicable theorem is the midsegment theorem

y = 5 cm

Step-by-step explanation:

The given quadrilateral MATH is an isosceles trapezoid,

The bases of the isosceles trapezoid are

b₁ = [tex]\overline{MA}[/tex] and b₂ = [tex]\overline{HT}[/tex]

The median of the isosceles trapezoid = [tex]\overline{LV}[/tex]

MA = 3·y - 2

HT = 2·y + 4

LV = 8.5 cm

The midsegment theorem states that the median of a trapezoid is parallel to the bases of the trapezoid and is equal to half the length of the sum of the bases of the trapezoid

The median of a trapezoid = (1/2)×(b₁ + b₂)

Therefore, we have;

The median of the isosceles trapezoid, LV, given as follows;

LV = 8.5 = (1/2)×((3·y - 2) + (2·y + 4))

LV = 8.5 = (1/2)×(5·y + 2) =

2 × 8.5 = (5·y + 2)

17 = 5·y + 2

∴ 5·y = 17 - 2 = 15

y = 15/3 = 5

y = 5 cm

Answer: left a units, down b units

Step-by-step explanation:

The phrase which describe g(x) for parents function p(x) is:

" Graph shifts a units in negative x direction and b units in negative y direction"

The shifted origin has the coordinates (h, k). That is, the shifted X and Y axes are at distances h and k from the original X and Y axes respectively.

Here, general equation

y = cos ( x - h ) + k

where, h and k are points which shows the shifting of function on x and y axes.

On comparing general equation with given equation g(x)

so we get h = -a and k = -b.

Thus, the phrase which describe g(x) for parents function p(x) is:

" Graph shifts a units in negative x direction and b units in negative y direction".

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Answer:

yup umm

Step-by-step explanation:

-4

Answer:

there are infinitely many solutions

LEFT SIDE/ LEFT EQUATION: if you multiply 1 and (b + 14) together, the result becomes the numerator of the fraction (with 2 being the denominator).

Once you do that, you will notice that both sides/both equations are exactly the same.

Thus, if you put in ANY number for variable b, the solution of both sides/both equations will always be the same and work.

The answer is: "There are infinetly many solutions"

Answer:

18 3/4

Step-by-step explanation:

Solve {(32)-3/4)3/4}4/5

Expand the inner parenthesis

{(32)-3/4)3/4}4/5

= {3/4(32) - (3/4)(3/4)}*4/5

= {3(8)- 9/16} * 4/5

= {24 - 9/16}* 4/5

= 4/5(24) - 4/5(9/16)

= 96/5 - 36/80

= 96/5 - 9/20

Fine the LCM

= 96(4)-9/20

= (384-9)/20

= 375/20

= 18 15/20

= 18 3/4

Hence the required result is 18 3/4

Answer:

Both S=8x36 and S=36+36+36+36+36+36+36+36 apply

There are 288 seats in section C

Step-by-step explanation:

S=8x36

S=288

Answer:

30/34

Step-by-step explanation:

Answer:

7x+5 pizzas were sold.

Step-by-step explanation:

4x and 3x combine to make 7x. Since we are adding 9 and also subtracting 4, they cancel out to be adding only 5. Combine this to make 7x+5.

Answer:

a: (9x^3y^2)-(9x^2y^3)

Step-by-step explanation:

Step-by-step explanation:

if you are writing it in an expression then

let raju's age be = x

let daughter be = y

x = 2 (5 × y)

x = 2 (5y)

x = 10y

so if daughter is 2 years old, then

x = 10(2)

x = 20 years

Step-by-step explanation:

Multiply: 6 (children) • 2.15 (cost per ticket) = 12.90

Add: 12.90 + 4.90 = £17.80

Answer:

The answer is 75 inches.

Step-by-step explanation:

If Alice is 10 inches, she is 2/3 as tall as the door. At her regular height, to be 2/3 as tall as the door the door would have to be 75 inches high.

The area of a shape is the amount of space on the shape.

The area of the shaded region is 819 inches square

Start by calculating the area of the sector using:

[tex]A = \frac{\theta}{360}*\pi r^2[/tex]

So, we have:

[tex]A = \frac{150}{360}*\frac{22}{7} * 27.8^2[/tex]

[tex]A = 1012.05[/tex]

Next, calculate the area of the isosceles triangle using:

[tex]A = \frac 12 r^2\sin(\theta)[/tex]

So, we have:

[tex]A = \frac 12 * 27.8^2 * \sin(150)[/tex]

[tex]A = 193.21[/tex]

The shaded area is the difference between the areas of the sector and the triangle.

So, we have:

[tex]A = 1012.05 - 193.21[/tex]

Calculate the difference

[tex]A = 818.84[/tex]

Approximate

[tex]A = 819[/tex]

Hence, the area of the shaded region is 819 inches square

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Answer:

A= 818.4

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

you need to start by plugging in -2x+4 every were it says y then solve for x when you have found x plug it into one of the equations and solve for y

Answer:

[tex]Volume = 144in^3[/tex]

Step-by-step explanation:

Given

[tex]Base\ Area = 36in^2[/tex]

[tex]Height =8[/tex]

Shape: Cone

Required

Determine the volume

Volume is calculated using:

[tex]Volume = \frac{1}{3}\pi r^2h[/tex]

Where

[tex]Base\ Area = \pi r^2 = 36[/tex]

[tex]Height = h = 8[/tex]

So:

[tex]Volume = \frac{1}{3} * 36 * 8[/tex]

[tex]Volume = 144in^3[/tex]

Answer:

83.15

Step-by-step explanation:

Joey's current grade can be determined by weighting his scores with the weights given and adding the results

Tests = 0.6 x 82 = 49.2

Quizzes = 0.25 x 77 = 19.25

homework = 0.15 x 98 = 14.7

49.2 + 19.25 + 14.7 = 83.15

Answer:

y = 42x + 2

Step-by-step explanation:

yeah...

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Answer:

so my calculations show that (12.1 / 9.8) - 1 =~ 0.2346938775510204081632653061224 that is about a percentage of 23.469% thank you for asking that question, oh and this answer is also on yahoo

Step-by-step explanation:

Answer:

Step-by-step explanation:

71+42+BAD=180

BAD=67

Answer:

m<BAD = 67

Step-by-step explanation:

The given figure is a parallelogram. Consecutive angles in a parallelogram are supplementary, meaning that their angle measures sum up to 180 degrees. Using this, one can say,

m<D + m<A = 180

Substitute,

m<ADB + m<BDC + m<A = 180

71 + 42 + m<A = 180

113 + m<A = 180

Inverse operations,

113 + m<A = 180

-113              -113

m<A = 67

Answer:

I think it's A

D because 2 has a x next to it so you divide by 2 on both sides

Answer:

i hope this picture help u

Answer:

312cm squared

Step-by-step explanation:

The area of one of the 4 small triangles is 30 cm squared, multiply this by 4 and you get 120cm squared. Then the area of the rectangle is 192cm squared, add these together and you get 312cm squared.

Answer:

$393.60

Step-by-step explanation:

I will set it up for you only.

Let a = adult tickets

Let s = student tickets

Here is your system of equations:

a + s = 800

12a + 8s = 7500