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FromTheMoon [43]
3 years ago
9

Simplify: 5mn – 8mn + 13mn

Mathematics
1 answer:
AfilCa [17]3 years ago
5 0

Answer:

10mn

Step-by-step explanation:

5mn - 8mn + 13mn = 10mn

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The sum of three consecutive terms in an arithmetic sequence is 27, and their product is 585. find the three terms.
sammy [17]
\text{the three consecutive terms in an arithmetic sequence}\\a;\ a+d;\ a+2d\\\\\text{system of equals}\\\\ \left\{\begin{array}{ccc}a+a+d+a+2d=27\\a(a+d)(a+2d)=585\end{array}\right\\ \left\{\begin{array}{ccc}3a+3d=27&|:3\\a(a+d)(a+2d)=585\end{array}\right\\ \left\{\begin{array}{ccc}a+d=9&\to d=9-a\\a(a+d)(a+2d)=585\end{array}\right\\
\text{substitute to the second equation}\\\\a(a+9-a)(a+2(9-a))=585\\\\a(9)(a+18-2a)=585\\9a(18-a)=585\ \ \ |:9\\a(18-a)=65\\18a-a^2=65\ \ \ |\text{change the signs}\\a^2-18a=-65\\a^2-2a\cdot9=-65\ \ \ |+9^2\\\underbrace{a^2-2a\cdot9+9^2}_{(a-b)^2=a^2-2ab+b^2}=-65+9^2\\(a-9)^2=16\to a-9\pm\sqrt{16}\\a-9=-4\ \vee\ a-9=4\ \ \ |+9\\a=5\ \vee\ a=13\\\\d=9-5=4\ \vee\ d=9-13=-4
Answer:\ a=5;\ a+d=9; a+2d=13\ vee\ a=13;\ a+d=9;\ a+2d=5

5 0
3 years ago
The first and second terms of a linear sequence (A.p) are 3 and 8 respectively. Please determine the least Number of terms of Ap
Alla [95]

Answer:

To rewrite your question, you are looking for the smallest    that fulfills the inequality:

∑=1>250

First, we must find the sequence    in explicit form. We can think of it as a line we are trying to get the slope-intercept form of. We have the points (1, 3) and (2, 8). Therefore, the slope is  8−32−1=51=5 . Now we just need the y-intercept. We can find it through substitution:

=5+

In order to solve for   , we can plug in one of the points that we were already given. I will choose the point (1, 3). Note that this point just means that when  =1 ,  =3 .

3=5(1)+

3=5+

=−2

Now for the original question.

∑=1(5−2)>250

((5(1)−2)+(5()−2)2)>250

(5+12)>250

522+12>250

2+15>100

2+15+1100>100+1100

(+110)2>100+1100

(+110)2>10001100

+110>±10001100‾‾‾‾‾‾‾√

+110>±11010001‾‾‾‾‾‾√

>−110±11010001‾‾‾‾‾‾√

Since we are looking for the smallest value, we will subtract for the plus or minus sign.

>−110−11010001‾‾‾‾‾‾√≈−10

Since that is negative, we will have to add instead.

>−110+11010001‾‾‾‾‾‾√≈9.9

Therefore, the smallest integer    that makes sense and satisfies the inequality is 10.

So, the first 10 numbers must be added.

Honestly, it would have been quicker just to brute-force this.

Step-by-step explanation:

Have a good day

8 0
3 years ago
Choose the correct written expression for: (9 x 4) 6.
chubhunter [2.5K]

Answer:

D

Step-by-step explanation:

Product means to multiply 2 numbers and for this question its 9x4. The devided by 6 part is just divided from 6. so (9x4)/6

Hope this helped!

8 0
3 years ago
Read 2 more answers
Please include step by step!
Paladinen [302]

Answer:

C=10pi

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
The base diameter and the height of a cone are both
WITCHER [35]

Answer:

11/ 42. *. X^ 2. * X = I/3 X A * h; if E = 1/3 A

Then the answer is EX

Step-by-step explanation:

Volume of cone= 1/3 * base area * height

= 1/3 * pi* (X/2)^2 * X

= 1/3. * 22/ 7 * X^3/4

= 22/ 21 * X^3 / 4

= 11/21 *. X^2/ 2. *. X

= 11/ 42. * X^3

= 11/ 42. *. X^ 2. * X

3 0
3 years ago
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