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3 years ago

List all the prime numbers from 1 to 50

Mathematics

2 answers:

White raven [17]3 years ago

8 0

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.
c:

Cloud [144]3 years ago

4 0

Prime numbers from 1 to 50:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37,41, 43, 47

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The difference between the two roots of the equation 3x^2+10x+c=0 is 4 2/3 . Find the solutions for the equation.

andrezito [222]

Answer:

Given the equation: $3x^2+10x+c =0$

A quadratic equation is in the form: $ax^2+bx+c = 0$ where a, b ,c are the coefficient and a≠0 then the solution is given by :

$x_{1,2} = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$ ......[1]

On comparing with given equation we get;

a =3 , b = 10

then, substitute these in equation [1] to solve for c;

$x_{1,2} = \frac{-10\pm \sqrt{10^2-4\cdot 3 \cdot c}}{2 \cdot 3}$

Simplify:

$x_{1,2} = \frac{-10\pm \sqrt{100- 12c}}{6}$

Also, it is given that the difference of two roots of the given equation is $4\frac{2}{3} = \frac{14}{3}$

i.e,

$x_1 -x_2 = \frac{14}{3}$

Here,

$x_1 = \frac{-10 + \sqrt{100- 12c}}{6}$ , ......[2]

$x_2= \frac{-10 - \sqrt{100- 12c}}{6}$ .....[3]

then;

$\frac{-10 + \sqrt{100- 12c}}{6} - (\frac{-10 + \sqrt{100- 12c}}{6}) = \frac{14}{3}$

simplify:

$\frac{2 \sqrt{100- 12c} }{6} = \frac{14}{3}$

$\sqrt{100- 12c} = 14$

Squaring both sides we get;

$100-12c = 196$

Subtract 100 from both sides, we get

$100-12c -100= 196-100$

Simplify:

-12c = -96

Divide both sides by -12 we get;

c = 8

Substitute the value of c in equation [2] and [3]; to solve $x_1 , x_2$

$x_1 = \frac{-10 + \sqrt{100- 12\cdot 8}}{6}$

$x_1 = \frac{-10 + \sqrt{100- 96}}{6}$ or

$x_1 = \frac{-10 + \sqrt{4}}{6}$

Simplify:

$x_1 = \frac{-4}{3}$

Now, to solve for $x_2$ ;

$x_2 = \frac{-10 - \sqrt{100- 12\cdot 8}}{6}$

$x_2 = \frac{-10 - \sqrt{100- 96}}{6}$ or

$x_2 = \frac{-10 - \sqrt{4}}{6}$

Simplify:

$x_2 = -2$

therefore, the solution for the given equation is: $-\frac{4}{3}$ and -2.

3 0

2 years ago

A 60-yard long drawbridge has one end at ground level. The other end is initially at an incline of 5°. During one stage of the d

AVprozaik [17]

The drawbridge will be at an incline of 10.56 degrees. That is 5.56 degrees more than it's initial incline of 5 degrees.

If you draw a picture of this situation, you will see that you can write a sine ratio with the 11 and 60 (opposite over hypotenuse)

sin(x) = 11/60 Solve the equation for x

x = 10.56

7 0

3 years ago

Please help! I’ll give brainliest!

Jlenok [28]

Answer:

27 degrees withI think angle sum postulate

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Please help me with my homework I don't understand it

Damm [24]

Answer:

Part A:

0.1111111111111 = 1/9

Part B:

Step-by-step explanation:

Part A:

When I put 0.111111111 into my calculator I get a conversion of 1/9.

Part B:

The fraction 1/9 means that for every 9 kids he surveyed, 1 of them replied "yes."

So covert 1/9 into x/27

27/9 = 3 which means 9 goes into 27, 3 times.

Multiply 1 by 3.

1 x 3 = 3

Put into fraction form

3/27

This means 3 students out of 27 answered "yes."

6 0

3 years ago

Which of the following is an example of direct variation?

LekaFEV [45]

Answer:

Step-by-step explanation:

Direct variation is a special case of first order equations; in both cases, the input is multiplied by a constant which we call the "slope" or "constant of variation." However, no direct variation equation includes a constant ("y-intercept"). So, if a given equation does have a y-intersect, that equation does not represent direct variation; if it does NOT have a y-intercept, that equation represents direct variation.

A) involves a constant term, -2; NOT direct variation

B) involves a constant term, 10; NOT direct variation

C) Here 3y = x, or y = x/3, involves no constant term, so Does represent direct variation

D) involves a constant term -3; NOT direct variation

6 0

3 years ago