Answer:
(x+5)²(x²+5)
Step-by-step explanation:
Given two functions x²+5 and x²+10x+25, to get their Lowest common factor, we need to to first factorize x²+10x+25
On factorising we have:
x²+5x+5x+25
= x(x+5) +5(x+5
= (x+5)(x+5)
= (x+5)²
The LCM can be calculated as thus
| x²+5, (x+5)²
x+5| x²+5, (x+5)
x+5| x²+5, 1
x²+5| 1, 1
The factors of both equation are x+5 × x+5 × x²+5
The LCM will be the product of the three functions i.e
(x+5)²(x²+5)
This hives the required expression.
Answer:
d) x = 72°
Step-by-step explanation:
Corresponding Angles: The pair of angles formed on the same side of traversal which crosses two parallel lines is called a pair of corresponding angles.
These angles are EQUAL to each other.
Now, here in the given figure:
The two below lines are parallel to each other.
Also, the line crossing it on the right side forms a traversal.
So angle x and angle with 72 degrees form a pair of Corresponding Angles.
⇒ x = 72°
Hence the measure of angle x = 72°
Answer:
All real numbers greater than or equal to -3
Step-by-step explanation:
we know that
The curved line could be a vertical parabola opening upwards with vertex at (2,-3)
The vertex is a minimum
The y-intercept is the point (0,1)
The x-intercepts are the points (0.25,0) and (3.75,0)
so
The domain is the interval -----> (-∞,∞)
All real numbers
The range is the interval ----> [-3,∞)
All real numbers greater than or equal to -3
Answer:
x=0.996
Step-by-step explanation:

To take natural log ln , we need to get e^2x alone
Subtract 5 on both sides

Now we divide both sides by 3

Now we take 'ln' on both sides

As per log property we can move exponent 2x before ln

The value of ln(e) = 1

Divide both sides by 2

x= 0.996215082
Round to nearest thousandth
x=0.996
We have two widths of the same length plus one length
Let the width be

and the length be

Perimeter = 2×width + 2×length


(equation 1)
The cost is $5 per foot on the width and $25 per foot on the length
Total cost = (5 × 2 × width) + (25 × length)

(equation 2)
We have two variables that we need to solve, so we will need to use the simultaneous equations method (either elimination or substitution)
Since equation 1 is given

, we can rearrange the equation to make

the subject

then substitute this into equation 2








Substitute w = 75 back into 190 = w + l
190 = 75 + l
l = 190 - 75
l = 115
Answer:
Length = 115 feet
Width = 75 feet