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damaskus [11]
3 years ago
12

The sum of two numbers is 18 and their difference is 8

Mathematics
2 answers:
Volgvan3 years ago
8 0

Answer:

13 and 5

Step-by-step explanation:

x+y=18

x-y=8

_____

2x=26

x=13

So the first number must be 13

13+y=18

y=5

And the second number must be 5

Diano4ka-milaya [45]3 years ago
7 0

Answer:

13 and 5

Step-by-step explanation:

13 and 5 because 13-5=8 and the difference is 8 so thats your answer

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Complete the square to the problem X^2+6x-16=0
marishachu [46]

Answer:

<h2>x = -8 or x = 2</h2>

Step-by-step explanation:

(a+b)^2=a^2+2ab+b^2\qquad(*)\\\\-------------------------------\\\\x^2+6x-16=0\qquad\text{add 16 to both sides}\\\\x^2+6x=16\\\\x^2+2(x)(3)=16\qquad\text{add}\ 3^2\ \text{to both sides}\\\\\underbrace{x^2+2(x)(3)+3^2}_{(*)}=16+3^2\\\\(x+3)^2=16+9\\\\(x+3)^2=25\Rightarrow x+3=\pm\sqrt{25}\\\\x+3=-5\ \vee\ x+3=5\qquad\text{subtract 3 from both sides}\\\\\boxed{x=-8\ \vee\ x=2}

3 0
3 years ago
Can anyone help me with this pleaseeee :(
vivado [14]

Answer:

x=65

Step-by-step explanation:

x-5=60

Add 5 to both sides

x=65

7 0
2 years ago
Please help asap!! Is this correct? If not can I please have some help.
Leona [35]

Answer:

Yes, that is correct.

Step-by-step explanation:

3 0
3 years ago
How do find the general solution of sin7A=sinA+sin3A
const2013 [10]

Step-by-step answer:

Solve  

sin(7a) = sin(3a) + sin(a) ..................(1)

Let  

F(a)=sin(7a)-sin(3a)-sin(a)..................(2)

the equivalent problem to (1) is  

F(a)=0 ......................................(3)

F(a)

=sin(7a)-sin(3a)-sin(a)....apply trig sum identities

=sin(6a+a) - sin(3a) - sin(a)

=sin(6a)cos(a)+cos(6a)sin(a) -sin(3a) - sin(a)

apply double angle formulas

=(2sin(3a)cos(3a))cos(a) +

(cos^2(3a)-sin^2(3a))sin(a) -sin(3a) - sin(a)

simplify using sin^2(p)+cos^2(p) = 1

= (2sin(3a)cos(3a))cos(a) +

(1-2sin^2(3a))sin(a) - sin(3a) - sin(a)

simplify algebraically, note 1*sin(a) cancels sin(a)

= (2sin(3a)cos(3a))cos(a) -2sin^2(3a)sin(a) - sin(3a)

factor out sin(3a)

= sin(3a)(2cos(3a)cos(a)-2sin(3a)sin(a) - 1)

now use trig sum formula to reduce to cos(4a)

= sin(3a)(2cos(4a)-1)

So

F(a) = 0   if sin(3a) =0 ...................(4)

or

F(a) = 0   if cos(4a) = 1/2 ................(5)

using the zero product theorem

From (4)

sin(3a) = 0  

3a = sin-1(0) = n*pi

a = n*pi/3  ................................(6)

From (5)

cos(4a) = 1/2

4a = cos^-1(1/2) = 2n*pi +/- pi/3

a = (2n+1/3)pi/4 or (2n-1/3)pi/4............(7)

Combine (6) and (7) to give the general solution

a = n*pi/3 or (2n+1/3)pi/4 or (2n-1/3)pi/4 .....(8)

For checking, use your calculator to substitute every solution given in (8) into the function F(a) in equation (1) to confirm that the result is almost equality.  The small difference will be due to rounding errors of the calculators.  On mine, they work out to be of the order of +/- 10^-15.

6 0
3 years ago
Barbara sells iced tea for $1.49 per bottle and water for $1.25 per bottle she wrote an equation to find the number of bottles s
Ann [662]

Answer:

She did a multiplication, i think she should have substracted both numbers to 100 and divide it by 1.25 or 1.49

Step-by-step explanation:

4 0
3 years ago
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