What are the solutions to the quadratic equation below?

Answer:

Parthava had 100 arrows.

Step-by-step explanation:

Let's define N as the number of arrows that Parthava originally has.

He uses one-half of them in defending himself, so he used N/2 arrows

Now he uses four times the square root of the number of arrows, so now he uses:

4*√N

Then he uses 6

Then he uses 3

Then he uses the last one.

If we add all these numbers of arrows that he used, we should get the initial number of arrows that he used, then:

N/2 + 4*√N  + 6 + 3 + 1  = N

Now we have an equation that we can try to solve.

First, let's move all the terms to the same side:

N/2 + 4*√N + 6 + 3 + 1 - N  = 0

now we can simpify it:

(N/2 - N) + 4*√N + (6 + 3 + 1) = 0

-(1/2)*N + 4*√N + 10 = 0

Now we can define a new variable x = √N

Then we have: x^2 = N

now we can replace these new variables in our equation to get:

-(1/2)*x^2 + 4*x + 10 = 0

Now we just have a quadratic equation.

Remember that for a quadratic equation of the form:

0 = a*x^2 + b*x + c

The solutions were given by:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2a}[/tex]

Then in our case, the solutions will be:

[tex]x = \frac{-4 \pm \sqrt{4^2 - 4*(-1/2)*10} }{2*(-1/2)} = \frac{-4 \pm 6 }{-1} = 4 \pm 6[/tex]

So there are two solutions:

x = 4 + 6 = 10

x = 4 - 6 = -2

And remember that x = √N

Then x should be positive, then we take x = 10 as our solution here.

then we can use the equation:

x = 10 = √N

then

10^2 = √N^2 = N

10^2 = 100 = N

Parthava had 100 arrows.

Answer:

The two bottom angles of this triangle are both represented by the same variable, in this case, an x. This means, that both of the bottom angles are equal to each other.

So we have:

32 + x + x = 180 (since the TOTAL angles of a triangle adds up to 180)

32 + 2x = 180 (combine the 2 x's together)

2x = 148 (subtract a 32 from both sides)

x = 74

Let me know if this helps!

Step-by-step explanation:

Hi there!

Given;

= 5(π\6)

We have;

π = 180°

Keeping value of π in the question;

= 5(180°/6)

= 5*30°

= 150°

Therefore, answer is option B.

Hope it helps!

Cost price is Rs600 and marked price is Rs780.

Must click thanks and mark brainliest

Answer:

9 grams of paint

Step-by-step explanation:

6×8=48

48÷4= 12

48-12=36

36÷4=9

first multiply 6 by 8 because a cube has six faces and you cut that cube eight times

second after you cut that you will have 48 faces and for every six faces there are 4 grams of paint so you divide 48 by 4 and you get 12 this means that 12 of the faces are painted

next you subtract 12 from 48 and you get 36 this means that 36 faces are not painted

lastly you divide 36 by 4 and you will get 9 grams of paint

Answer:

D

Step-by-step explanation:

[tex]8x \sqrt{2} - 4 \sqrt{2} [/tex]

Answer:

-1

Step-by-step explanation:

[3-4(-1)^4]^3

=>(3-4)^3

=>(-1)^3

=>-1

Answer From Gauth Math

Answer:

-1

Step-by-step explanation:

[tex][3-4*(3-4)^4]^3[/tex]        

[tex](3-4)^4= 1\\Therefore, [3-4*1]^3= -1^3\\So, -1^3= -1\\\\[/tex]

Cube of any negative integer will be negative, or, a negative integer raised to any odd number will be negative. Likewise, a negative integer raised to an even number will be positive.

Answer:

circumference = 2*PI*radius

circumference = 2 * PI * 5 cm

circumference = 31.4159265358979 cm

50 km = 500,000 centimeters

rotations = 500,000  / 31.4159 cm

15,915.51  rotations

Step-by-step explanation:

Answer:

(1, -13)

Brainliest, please!

Step-by-step explanation:

To find the x coordinate of the vertex, we use the formula, -b / 2a. In this problem, a = 2, and b = -4. c is -5, but we don't need to know it.

- -4 / 2(2) = 4 / 4 = 1

Vertex = (1, y)

Next, we plug 1 back into the parabola equation for x to solve for y.

y = -2(1)^2 - 4(1) -5

y = -2^2 - 4 - 5

y = -4 - 4 - 5

y = -8 - 5

y = - 13

Vertex = (1, -13)

Let's solve

Using Pythagorean theorem

[tex]\\ \sf\longmapsto H^2=P^2+B^2[/tex]

[tex]\\ \sf\longmapsto c^2=8^2+5^2[/tex]

[tex]\\ \sf\longmapsto c^2=64+25[/tex]

[tex]\\ \sf\longmapsto c^2=89[/tex]

[tex]\\ \sf\longmapsto c=\sqrt{89}[/tex]

[tex]\\ \sf\longmapsto c\approx 9.22[/tex]

Answer:

Step-by-step explanation:

[tex]\Large \boldsymbol{}\bf \dfrac{p^{^/is \ an \ integer}}{q^{ / natural}} -irreducible \ \ fraction[/tex]

Answer:

just add a small amount and and square the new number

between 2.82 and 2.83 seems a bit closer

Step-by-step explanation:

x      x^2

2.8         7.84

2.81         7.8961

2.82 7.9524

2.83 8.0089

2.84 8.0656

2.85 8.1225

2.86 8.1796

2.87         8.2369

Outlined sector:

2 πr x 225/360 +2r

=2x3.14x10 x 225/360 +20

=59.25 cm

Hope this helped!

Given:

The temperature on a mountain peak was 7°F at 6:00 p.m.

By 8:00 p.m., the temperature had dropped to 0°F.

To find:

The temperature at 11:00 p.m. if the temperature continued to drop at about the same rate.

Solution:

Time between 6:00 p.m. to 8:00 p.m. is 2 hours.

Change in temperature in 2 hours is -7°F.

Change in temperature in 1 hours is [tex]-\dfrac{7}{2}^\circ[/tex]F.

Time between 8:00 p.m. to 11:00 p.m. is 3 hours.

Change in temperature in 3 hours is [tex]3\times \dfrac{-7}{2}^\circ[/tex]F, i.e., [tex]-\dfrac{21}{2}^\circ[/tex]F.

Now, the temperature at 11:00 p.m is:

[tex]0-\dfrac{21}{2}=-10.5[/tex]

Therefore, the temperature at 11:00 p.m. is -10.5°F.

Note: All options are incorrect.

Answer:

120.40 per payment

Step-by-step explanation:

Subtract the down payment

642 - 160.40

481.60

Divide this by 4

481.60 / 4

120.40

I'm sorry but there's not enough info

Step-by-step explanation:

Answer:

The triangle with vertices A (2 , 0) , B (3 , 2) , C (5 , 1) is isosceles right Δ

The triangle with vertices A (-3 , 1) , B (-3 , 4) , C (-1 , 1) is right Δ

The triangle with vertices A (-5 , 2) , B (-4 , 4) , C (-2 , 2) is acute scalene Δ

The triangle with vertices A (-4 , 2) , B (-2 , 4) , C (-1 , 4) is obtuse scalene Δ

Answer:

SSS

Step-by-step explanation:

We know all three sides of both triangles. The common ratio of DEF to GHI is 2/3.

Answer:

SSS

Step-by-step explanation:

Similar triangles must have congruent corresponding angles and proportional corresponding sides.

Answer:

3.71 yd

Step-by-step explanation:

Heron's formula:

area = 0.25 * √((a + b + c) * (-a + b + c) * (a - b + c) * (a + b - c))

so h = 0.5 * √((a + b + c) * (-a + b + c) * (a - b + c) * (a + b - c)) / c

a = 6

b = 10

c = 14

a+b+c = 30

-a+b+c = 18

a-b+c = 10

a+b-c = 2

x = h = 0.5×sqrt(30×18×10×2)/14 = sqrt(30×18×10×2)/28 =

= sqrt(10800)/28 = sqrt(400×9×3)/28 =

= 20×3×sqrt(3)/28 = 60×sqrt(3)/28 = 15×sqrt(3)/7 =

= 3.711537 yd

Answer:

a

Step-by-step explanation:

all angles of an equilaterall triangle are equal therefore 180÷3 = 60

Answer:

The center is (9,-8) and the diameter is 8

Step-by-step explanation:

(x − 9)^2 + (y + 8)^2 = 16

A circle is in the form

(x − h)^2 + (y -k)^2 = r^2  where (h,k) is the center and r is the radius

(x − 9)^2 + (y -  -8)^2 = 4^2  

The center is (9,-8) and the radius is 4

The diameter is 2 times the radius so the diameter is 8

The center is (9,-8) and the diameter is 8

Answer:

521.25

Step-by-step explanation:

the circle is 78.75 in area and the square is 600 so 600- 78.75 = 521.25

Answer:

x=2

Step-by-step explanation:

We can use the Pythagorean theorem since this makes a right triangle

a^2+b^2 = c^2

The radius is 1.5

1.5^2 + x^2 = (1+1.5)^2

1.5^2 +x^2 = 2.5^2

2.25+x^2=6.25

Subtract 2.25 from each side

x^2 = 4

Taking the square root of each side

x= 2

Answer:A

Step-by-step explanation:Took quiz

Answer:

16+74

Step-by-step explanation:

substitute 16 into the equation

Answer:

-5

Step-by-step explanation:

-5 -(-2)

=-7

Answer:

Probably the first three answers

Step-by-step explanation:

The rest are

4) 3×5=15 (which is not 8)

5) 6×2=12 (≠8)

So it's just the first three

Answer:

A = 49/pi

Step-by-step explanation:

C = 2 * pi *r

14 = 2 * pi *r

Divide each side by 2 pi

14/2pi = r

7/pi = r

The area is given by

A = pi r^2

A = pi ( 7/ pi)^2

A  = pi * 49 / pi^2

A = 49/pi

Answer:

[tex]area = {15.61m}^{2} [/tex]

explanation is attached to the picture

Hope this helps you

Answer:

C

Step-by-step explanation: