Answer:
Equation: 7x - 23 = 25 + x
Solution: x = 8
Step-by-step explanation:
7x - 23 = 25 + x
1. Subtract 25 from both sides:
7x - 23 - 25 = 25 - 25 + x
7x - 48 = x
2. Subtract 7x from both sides to get x on one side:
7x - 7x - 48 = x - 7x
- 48 = -6x
3. Divide both sides by -6 to get x by itself:
8 = x
8 is the solution
Given:
A plane is normal to the vector = -2i+5j+k
It contains the point (-10,7,5).
To find:
The component equation of the plane.
Solution:
The equation of plane is

Where,
is the point on the plane and
is normal vector.
Normal vector is -2i+5j+k and plane passes through (-10,7,5). So, the equation of the plane is





Therefore, the equation of the plane is
.
The answer for the 1st bag is option B = 1/3
The answer for the 2nd bag is option C = 5/9
Number of marbles in 1st bag - 15 (6 red, 4 blue & 5 green)
Number of marbles in 2nd bag - 9 (3 red, 1 blue & 5 green)
The formula of probability = Total number of events in the outcome /total number of outcomes.
Now the probability that Aakesh will select a green marble from the 1st bag is 5(green marbles)/15(total number of marbles in 1st bag)
That is 5/15=1/3
Now the probability that Aakesh will select a green marble from the 2nd bag is 5(green marbles)/9(total number of marbles in 1st bag)
That is 5/9
To know more about probability go to - https://brainly.in/question/17157610?msp_poc_exp=6
Answer:
<em>Thus, the dimensions of the metal plate are 10 dm and 8 dm.</em>
Step-by-step explanation:
For a quadratic equation:

The sum of the roots is -b and the product is c. Note the leading coefficient is 1.
We know the perimeter of the rectangular metal plate is 36 dm and its area is 80 dm^2. Being L and W its dimensions, then:
P=2(L+W)=36
A=L.W=80
Note both formulas are closely related to the roots of the quadratic equation, we only need to adjust the data for the perimeter to be exactly the sum of L+W and not double of it.
Thus we use the semi perimeter instead as P/2=L+W=18
The quadratic equation is, then:

Factoring by finding two numbers that add up to 18 and have a product of 80:

The solutions to the equation are:
x=10, x=8
Thus, the dimensions of the metal plate are 10 dm and 8 dm.
Answer:
3/18
Step-by-step explanation: