Place value of digit 3 in number 60425321

Find the value of x if A, B, and C are collinear points and B is between A and C.

Andrew [12]

Answer:

x = 6

Option A.

Step-by-step explanation:

We know that

If A, B and C are collineal points, they all pass through a common line.

<--------------14-------------->

A-----------B----------------C

<-----x-----><------x+2---->

Based on the problem and the diagram above,

(x) + (x+2) = 14

(2x+2) = 14

(2x) = 12

(x) = 6

7 0

3 years ago

Factor the quadratic equation below to reveal the solutions. X^2+4x-21=-9

a_sh-v [17]

Answer:

x = 3 and x = -7

Step-by-step explanation:

The given quadratic equation is $x^2+4x-21=0$ . We need to find the solution of this equation.

If the equation is in the form of $ax^2+bx+c=0$ , then its solutions are given by :

$x=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}$

Here, a = 1, b = 4 and c = -21

Plugging all the values in the value of x, such that :

$x=\dfrac{-b+ \sqrt{b^2-4ac} }{2a},\dfrac{-b- \sqrt{b^2-4ac} }{2a}\\\\x=\dfrac{-4+ \sqrt{(4)^2-4\times 1\times (-21)} }{2(1)},\dfrac{-4- \sqrt{(4)^2-4\times 1\times (-21)} }{2(1)}\\\\x=3, -7$

So, the solutions of the quadratic equation are 3 and -7.

6 0

3 years ago

What are the vertices of the resulting image A’B’C’D’E after rotating the figure 90 degrees about the origin?

igor_vitrenko [27]

Answer:

45

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Use the Midpoint Rule with n = 5 to estimate the volume V obtained by rotating about the y-axis the region under the curve y = 1

velikii [3]

Using the shell method, the volume is given exactly by the definite integral,

$2\pi\displaystyle\int_0^1x(1+9x^3)\,\mathrm dx$

Splitting up the interval [0, 1] into 5 subintervals gives the partition,

[0, 1/5], [1/5, 2/5], [2/5, 3/5], [3/5, 4/5], [4/5, 5]

with left and right endpoints, respectively, for the $i$ -th subinterval

$\ell_i=\dfrac{i-1}5$

$r_i=\dfrac i5$

where $1\le i\le5$ . The midpoint of each subinterval is

$m_i=\dfrac{\ell_i+r_i}2=\dfrac{2i-1}{10}$

Then the Riemann sum approximating the integral above is

$2\pi\displaystyle\sum_{i=1}^5m_i(1+9{m_i}^3)\frac{1-0}5$

$\dfrac{2\pi}5\displaystyle\sum_{i=1}^5\left(\frac{2i-1}{10}+9\left(\frac{2i-1}{10}\right)^4\right)$

$\dfrac{2\pi}{5\cdot10^4}\displaystyle\sum_{i=1}^5\left(16i^4-32i^3+24i^2+1992i-999\right)=\frac{112,021\pi}{25,000}\approx\boxed{14.08}$

(compare to the actual value of the integral of about 14.45)

3 0

3 years ago

HELP ME PLZZZZZ!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Lady bird [3.3K]

Answer:

The answer is 90 winners.

Step-by-step explanation:

Well, we are given three days. The first day has a rate of 13% winning. The second day has a rate of 13% as well. And the third day has a rate of 11%. You can find this simply by dividing the amount of winners by amount of participants. Now, we must find the mean, or average, of these statistics. We will get 12% as the average rate of winners. How did we get this? By simply adding all three (13+13+11) then dividing by three (37/3), which gives us 12% if we round to a whole number. Now, we can take this number and get 12% of 750. How do we do this? Well, 12% is equal to 0.12. So we will multiply 0.12 by 750. This will give us 90. And there you have your answer.

<em>Alternatively</em>, you could add up the total amount of contestants from the three days. You should end up with 1000. Then add up the total amount of winners from the three days. You should get 120. Divide both of these by 4. The winners will now be 40, and the total contestants will be 250. Now multiply both by 3. The amount of contestants will be 750, and the amount of winners will be 90. This way is a bit easier, but does not always work. <u>Do what is best for you!</u>

Hope this helped!

7 0

3 years ago