3x+2(5x-3)=7
3x+10x-6=7
13x-6=7
13x=13
x=1
Area of the square:
A = s²
and s = AB = sqrt ( ( 4 - 1 )² + ( 3 - 1 )² )
s = √ ( 9 + 4 ) = √ 13
A = ( √13 )² = 13
Answer: Area of the square is 13 units².
The value of <u>x</u> that the given point of the function is 11.
<h3>Linear Function</h3>
An equation can be represented by a linear function. The standard form for the linear equation is: y= ax+b , for example, y=5x+3. Where:
a= the slope
b= the constant term that represents the y-intercept.
For the previous example: a=5 and b=3.
The question gives a point (x , -3) of a function f(x)= -x+8. Therefore, you can write
-3=-x+8
x=8+3
x=11
Thus, the x-coordinate is equal to 11.
Read more about the linear equations here:
brainly.com/question/2030026
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First we calculate the volume of the foundation:
Volume (V) = 20 ft * 12 ft * 4 in (1 ft / 12 in)
V = 80 ft^3
Since the cost is in cubic yard (yard^3) so convert:
V = 80 ft^3 * (1 yard^3 / 27 ft^3) = 2.963 yard^3
So the total cost is:
cost = ($125 / yard^3) * 2.963 yard^3
<span>cost = $370.37</span>
Answer with explanation:
→→→Function 1
f(x)= - x²+ 8 x -15
Differentiating once , to obtain Maximum or minimum of the function
f'(x)= - 2 x + 8
Put,f'(x)=0
-2 x+ 8=0
2 x=8
Dividing both sides by , 2, we get
x=4
Double differentiating the function
f"(x)= -2, which is negative.
Showing that function attains maximum at ,x=4.
Now,f(4)=-4²+ 8× 4-15
= -16 +32 -15
= -31 +32
=1
→→→Function 2:
f(x) = −x² + 2 x − 3
Differentiating once , to obtain Maximum or minimum of the function
f'(x)= -2 x +2
Put,f'(x)=0
-2 x +2=0
2 x=2
Dividing both sides by , 2, we get
x=1
Double differentiating the function,gives
f"(x)= -2 ,which is negative.
Showing that function attains maximum at ,x=1.
f(1)= -1²+2 ×1 -3
= -1 +2 -3
= -4 +2
= -2
⇒⇒⇒Function 1 has the larger maximum.
