Start by dividing both sides by 2 to get
. Doing the math on the right, keeping in mind that logs have an unwritten base of 10, gives us
. Rewriting this in exponential form is
. That means that x = 8. Not negative, only positive.
14. 1.5, 10 <- Answer
15. 5,1 <- Answer
Proof 14
Solve the following system:
{2 x - y = -7 | (equation 1)
4 x - y = -4 | (equation 2)
Swap equation 1 with equation 2:
{4 x - y = -4 | (equation 1)
2 x - y = -7 | (equation 2)
Subtract 1/2 × (equation 1) from equation 2:
{4 x - y = -4 | (equation 1)
0 x - y/2 = -5 | (equation 2)
Multiply equation 2 by -2:
{4 x - y = -4 | (equation 1)
0 x+y = 10 | (equation 2)
Add equation 2 to equation 1:
{4 x+0 y = 6 | (equation 1)
0 x+y = 10 | (equation 2)
Divide equation 1 by 4:
{x+0 y = 3/2 | (equation 1)
0 x+y = 10 | (equation 2)
Collect results:
Answer: {x = 1.5
y = 10
Proof 15.
Solve the following system:
{5 x + 7 y = 32 | (equation 1)
8 x + 6 y = 46 | (equation 2)
Swap equation 1 with equation 2:
{8 x + 6 y = 46 | (equation 1)
5 x + 7 y = 32 | (equation 2)
Subtract 5/8 × (equation 1) from equation 2:{8 x + 6 y = 46 | (equation 1)
0 x+(13 y)/4 = 13/4 | (equation 2)
Divide equation 1 by 2:
{4 x + 3 y = 23 | (equation 1)
0 x+(13 y)/4 = 13/4 | (equation 2)
Multiply equation 2 by 4/13:
{4 x + 3 y = 23 | (equation 1)
0 x+y = 1 | (equation 2)
Subtract 3 × (equation 2) from equation 1:
{4 x+0 y = 20 | (equation 1)
0 x+y = 1 | (equation 2)
Divide equation 1 by 4:
{x+0 y = 5 | (equation 1)
0 x+y = 1 | (equation 2)
Collect results:
Answer: {x = 5 y = 1
Answer:
x = 7
y = 8
Step-by-step explanation:
Since the shapes are similar then <B = <F and <A = <E
<B = <F so
10x + 65 = 135 subtract 65 from both sides
10x = 70 divide both sides by 10
x = 7
<A = <E so
4y - 4 = 28 add 4 to both sides
4y = 32 divide both sides by 4
y = 8
Slope (y2-y1)/(x2-x1)
(0-4)/(-5-5) = -4/-10 = 2/5
Y = 2/5x + b
Plug in any point
4 = 2/5(5) + b
4 = 2 + b, b= 2
Final equation: y = 2/5x + 2
The two numbers are <u>12 and 51.</u>
<h3>
EXPLANATION</h3>
To solve this, I did 63-15, to get 48.
I then divided this by 4, to get the first number, which is <u>12.</u>
To find the second answer, I multiplied 12 by 3, which is 36, and then added the 15 back on, to get <u>51.</u>
<u>51 + 12 = </u><em><u>63</u></em>
