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2 years ago

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Mathematics

1 answer:

Zielflug [23.3K]2 years ago

3 0

The quadratic formula is
$x= \dfrac{-b\pm \sqrt{b^2-4ac} }{2a}$ .

For the equation $4x^2-3x+9=2x+1$ , we must first convert it into standard form $ax^2+bx+c=0$ . We see it is $4x^2-5x+8=0$ . From this, our coefficients are $a=4, b=-5$ and $c=8$ .

We plug these coefficients into the quadratic formula.

$x= \dfrac{-(-5)\pm\sqrt{(-5)^2-4(4)(8)} }{2(4)} \\ \\ \\ \\ x = \dfrac{5\pm\sqrt{-103}}{8} \\ \\ \\ \\ x = \dfrac{5\pm\ i\sqrt{103}}{8}$

The answer is C.

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Write the equation of the line that passes through the points

Marrrta [24]

Answer:

y+2-x=0

Step-by-step explanation:

Here,

(-3,-5)=(x1,y1)

(3,1)=(x2,y2)

Slope(m)=y2-y1/x2-x1

=1-(-5)/3-(-3)

=1+5/3+3

=6/6

Mid point=(x1+x2/2 , y1+y2/2)

=(-3+3/2 , -5+1/2)

=(0/2 , -4/2)

=(0 , -2)

Now, (0,-2)=(x1,y1)

Equation:

y-y1=m(x-x1)

y+2=1(x-0)

y+2=1x

y+2-x=0 is the required equation.

3 0

2 years ago

PLEASE HELP !!!!

Andre45 [30]

Answer:

600ft square

Step-by-step explanation:

Lets multiply all numbers given by 10 beacuse they represent 10 ft

20ft*30ft=600ft square` the area of living room

25ft*20ft=500ft square` the area of bedroom

3 0

3 years ago

For each of the finite geometric series given below, indicate the number of terms in the sum and find the sum. For the value of

kotykmax [81]

Answer:

Number of term N = 9

Value of Sum = 0.186

Step-by-step explanation:

From the given information:

Number of term N = $3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} + \cdots + 3 (0.5)^{13}$

Number of term N = $3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} +3 (0.5)^{8}+3 (0.5)^{9} +3 (0.5)^{10} +3 (0.5)^{11}+3 (0.5)^{12}+ 3 (0.5)^{13}$

Number of term N = 9

The Value of the sum can be determined by using the expression for geometric series:

$\sum \limits ^n_{k=m}ar^k =\dfrac{a(r^m-r^{n+1})}{1-r}$

here;

m = 5

n = 9

r = 0.5

Then:

$\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.5^5-0.5^{9+1})}{1-0.5}$

$\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.03125-0.5^{10})}{0.5}$

$\sum \limits ^n_{k=m}ar^k =\dfrac{(0.09375-9.765625*10^{-4})}{0.5}$

$\sum \limits ^n_{k=m}ar^k =0.186$

6 0

2 years ago

Answer both with STEPS

Amanda [17]

Answer:

7 )

x = $\frac{3\sqrt{2} }{2}$

$y= 3$

8 )

$x=6\sqrt{6}$

$y= 9\sqrt{2}$

Step-by-step explanation:

7 ) 8)

In Δ ABC In Δ XYZ

∠ C = 45° ∠ X = 60°

∠ A = 90° ∠ Y = 90°

$AC= \frac{3\sqrt{2} }{2}$ $XY= 3\sqrt{6}$

To Find :

x = ?

y = ?

Solution:

We Know

In Δ ABC

∠ C = 45°

∠ A = 90°

∴ ∠ B = 45° ......Angle sum property of a triangle i.e 180°

∴ Δ ABC is an Isosceles Triangle

∴ AC = AB = x = $\frac{3\sqrt{2} }{2}$

Now appplying Trignometry identity we get

$\sin C = \frac{\textrm{side opposite to angle C}}{Hypotenuse}\\\\\sin 45 = \frac{AC}{BC}\\\\\frac{1}{\sqrt{2} } =\frac{\frac{3\sqrt{2} }{2}}{y}\\\\y=\frac{3\times \sqrt{2}\times \sqrt{2} }{2}\\\\y= 3$

Now In Δ XYZ

∠ X = 60°

∠ Y = 90°

∴∠ Z = 30° . .....Angle sum property of a triangle i.e 180°

Now appplying Trignometry identity we get

$\tan X = \frac{\textrm{side opposite to angle X}}{\textrm{side adjacent to angle X}}$

$\tan 60 = \frac{YZ}{XY}\\\\\sqrt{3} =\frac{y}{3\sqrt{6} }\\ y= 3\sqrt{3} \sqrt{6} \\y= 9\sqrt{2}$

Now,

$\sin X = \frac{\textrm{side opposite to angle C}}{Hypotenuse}\\\\\\\sin 60 = \frac{YZ}{XZ}\\ \\\frac{\sqrt{3} }{2} =\frac{9\sqrt{2} }{x} \\\\x=\frac{18\sqrt{2} }{\sqrt{3} } \\\textrm{after fationalizing the denominator root 3 we get}\\\\x=6\sqrt{6}$

8 0

2 years ago

who's better Messi or Ronaldo based on these pictures. when there ratio of shots is m= 500 out of 400 and r=700 out of 3000

jolli1 [7]

Ronaldo................

8 0

2 years ago

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