What multiple of 67 is between 700 and 800

Find x so that x, X +2, X'+3 are the first three terms of a geometric sequence. Then find the 5" term of the

velikii [3]

Answer:

The fifth term is -1/4.

Step-by-step explanation:

We know that the first three terms of the geometric sequence is x, x + 2, and x + 3.

So, our first term is x.

Then our second term will be our first term multiplied by the common ratio r. So:

$x+2=xr$

And our third term will be our first term multiplied by the common ratio r twice. Therefore:

$x+3=xr^2$

Solve for x. From the second term, we can divide both sides by x:

$\displaystyle r=\frac{x+2}{x}$

Substitute this into the third equation:

$\displaystyle x+3=x\Big(\frac{x+2}{x}\Big)^2$

Square:

$\displaystyle x+3 = x\Big( \frac{(x+2)^2}{x^2} \Big)$

Simplify:

$\displaystyle x+3=\frac{(x+2)^2}{x}$

We can multiply both sides by x:

$x(x+3)=(x+2)^2$

Expand:

$x^2+3x=x^2+4x+4$

Isolate the x:

$-x=4$

Hence, our first term is:

$x=-4$

Then our common ratio r is:

$\displaystyle r=\frac{(-4)+2}{-4}=\frac{-2}{-4}=\frac{1}{2}$

So, our first term is -4 and our common ratio is 1/2.

Then our sequence will be -4, -2, -1, -1/2, -1/4.

You can verify that the first three terms indeed follow the pattern of x, x + 2, and x + 3.

So, our fifth term is -1/4.

4 0

3 years ago

PLEASE HELP FOR A BRAINLIEST!!!! Create your own example and explain how to solve Quadratic Equation using Quadratic Formula. Wh

SVETLANKA909090 [29]

Step-by-step explanation:

1. Create your own example and explain how to solve Quadratic Equation using Quadratic Formula.

The quadratic formula is used to solve quadratic equations. It is shown as $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

A quadratic equation is generally shown in the form of $ax^{2} +bx + c = 0$

For example, if you saw the equation $7x^{2} + 3x + 20 = 0$

7 would be $a$ , 3 would be $b$ , and 20 would be $c$ .

To solve the equation above, you would fill in the quadratic formula as such, $x=\dfrac{-3\pm\sqrt{(3)^2-4(7)(20)}}{2(7)}$

Then you could solve for x.

2. What part in the Quadratic Formula is the discriminant?

The discriminant is the equation under the square root on the quadratic formula, $b^{2} - 4ac$

It is tells us whether there are two solutions, one solutions, or no solutions.

3. How do you know the number of solutions based on the value of the discriminant?

To know the number of solutions based off of the value of the discriminant, you need to plug in your values. Using the example quadratic equation, $7x^{2} + 3x + 20 = 0$

We will plug the values into the discriminant.

$3^{2} - 4(7)(20) = -551$

Now, if the discriminant is positive it has two real solutions. If the discriminant is zero the equation has no real-number solutions. And finally, if the discriminant is negative, the equation has one real solution. Because our discriminant is -551, the example equation has one real solution.

Hope this helps! (Please consider Brainliest)

8 0

3 years ago

Quadrilateral DEFT has vertices D(2, 7), E(-4, 4), F(5, -6), and T(11, -3). What is the best name for quadrilateral DEFT?

Hoochie [10]

Answer:

parallelogram

Step-by-step explanation:

slope of DE = (4-7) / (-4 - 2) = 1/2

slope of FT = (-3 - -6) / (11-5) = 1/2

DE // FT

slope of EF = (-6 - 4) / (5 - -4) = - 10/9

slope of DT = (-3 - 7) / (11 - 2) = - 10/9

EF // DT

7 0

2 years ago

I WILL GIVE YOU BRAINLY PLSS Worth 19 points

Pavel [41]

Answer:

942

Step-by-step explanation :

so your d is 300 so your r = 300/2= 150

a=3.14*r*r= 3.14*150*150= 70650

c= 3.14*d= 3.14*300= 942

_________________________________________________

OR

The curved surface area of solid cylinder is

As we are given that:

Diameter of solid cylinder = 8 cm

Length or Height o solid cylinder = 140 cm

Formula used to calculate the curved surface area of cylinder is:2n x h

Curved surface area of cylinder =2r x h

where,

r = radius of cylinder

h = height or length of cylinder

Radius of cylinder = daimeter

Now putting all the given values in above formula, we get:

Curved surface area of cylinder = 2x 22/7 x 140cm

Curved surface area of cylinder = $3520cm^{2}$

Therefore, the curved surface area of solid cylinder is3520cm^{2}

8 0

3 years ago

Read 2 more answers

Evaluate 3x+6y when x= -3, y=6

sesenic [268]

Hey there!!!

Given equation - 3x+6y

x is given as -3

y is given as 6

Plugin these values to get the final answer

3 ( -3 ) + 6 ( 6 )

-9 + 36

= 27

27 is the final and the required answer

Hope my answer helps!

3 0

3 years ago

Read 2 more answers