Conjectures are conclusions formed from evidences. Steven's conjecture that:
is true because:
or
for ![|x| > 5](https://tex.z-dn.net/?f=%7Cx%7C%20%3E%205)
Given that:
![|x| > 5](https://tex.z-dn.net/?f=%7Cx%7C%20%3E%205)
Split the inequality as follows:
or ![x > -5](https://tex.z-dn.net/?f=x%20%3E%20-5)
Take the cube of both sides
or ![x^3 > -5^3](https://tex.z-dn.net/?f=x%5E3%20%3E%20-5%5E3)
Evaluate all exponents
or ![x^3 > -125](https://tex.z-dn.net/?f=x%5E3%20%3E%20-125)
Steven's conjecture that:
is true because:
or
for ![|x| > 5](https://tex.z-dn.net/?f=%7Cx%7C%20%3E%205)
Read more about absolute inequalities at:
brainly.com/question/4688732
Answer:
85 square inches
Step-by-step explanation:
![5*5=25](https://tex.z-dn.net/?f=5%2A5%3D25)
![5*6=30*2=60](https://tex.z-dn.net/?f=5%2A6%3D30%2A2%3D60)
![25+60=85](https://tex.z-dn.net/?f=25%2B60%3D85)
Hope this is helpful
Answer:
![\large \boxed{\text{Q31, D. 6.00 F; 32. C. N21.75; Q33. A. 168.00 F}}](https://tex.z-dn.net/?f=%5Clarge%20%5Cboxed%7B%5Ctext%7BQ31%2C%20D.%206.00%20F%3B%2032.%20C.%20N21.75%3B%20Q33.%20A.%20168.00%20F%7D%7D)
Step-by-step explanation:
Your graph is hard to read, so I re-drew it as best I could.
You must first develop an equation relating francs and naira.
The line goes through the origin, so the general equation is
y = kx
One of the points is (40,240).
![\begin{array}{rcl}F & = &k \times N\\240 & = &k \times 40\\k & = & \dfrac{240}{40}\\\\k&=&\textbf{6 F/N}\\\end{array}\\\text{The equation is $\large \boxed{\mathtbf{F = 6 N}}$}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7DF%20%26%20%3D%20%26k%20%5Ctimes%20N%5C%5C240%20%26%20%3D%20%26k%20%5Ctimes%2040%5C%5Ck%20%26%20%3D%20%26%20%5Cdfrac%7B240%7D%7B40%7D%5C%5C%5C%5Ck%26%3D%26%5Ctextbf%7B6%20F%2FN%7D%5C%5C%5Cend%7Barray%7D%5C%5C%5Ctext%7BThe%20equation%20is%20%24%5Clarge%20%5Cboxed%7B%5Cmathtbf%7BF%20%3D%206%20N%7D%7D%24%7D)
Q 31.
![\begin{array}{rcl}F & = &6N\\& = & 6 \times 1.00\\& = & \mathbf{6.00}\end{array}\\\text{The equivalent value of N1.00 is $\large \boxed{\textbf{6.00 F}}$}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7DF%20%26%20%3D%20%266N%5C%5C%26%20%3D%20%26%206%20%5Ctimes%201.00%5C%5C%26%20%3D%20%26%20%5Cmathbf%7B6.00%7D%5Cend%7Barray%7D%5C%5C%5Ctext%7BThe%20equivalent%20value%20of%20N1.00%20is%20%24%5Clarge%20%5Cboxed%7B%5Ctextbf%7B6.00%20F%7D%7D%24%7D)
Q 32.
![\begin{array}{rcl}F & = &6N\\130.5& = & 6 N\\N&=& \dfrac{130.5}{6}\\\\& = & \mathbf{21.75}\\\end{array}\\\text{The equivalent value of 130.5 F is $\large \boxed{\textbf{N21.75}}$}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7DF%20%26%20%3D%20%266N%5C%5C130.5%26%20%3D%20%26%206%20N%5C%5CN%26%3D%26%20%5Cdfrac%7B130.5%7D%7B6%7D%5C%5C%5C%5C%26%20%3D%20%26%20%5Cmathbf%7B21.75%7D%5C%5C%5Cend%7Barray%7D%5C%5C%5Ctext%7BThe%20equivalent%20value%20of%20130.5%20F%20is%20%24%5Clarge%20%5Cboxed%7B%5Ctextbf%7BN21.75%7D%7D%24%7D)
Q 33.
![\begin{array}{rcl}F & = &6N\\& = & 6 \times 28.00\\& = & \mathbf{168.00}\end{array}\\\text{An amount of N28.00 is $\large \boxed{\textbf{168.00 F}}$}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7DF%20%26%20%3D%20%266N%5C%5C%26%20%3D%20%26%206%20%5Ctimes%2028.00%5C%5C%26%20%3D%20%26%20%5Cmathbf%7B168.00%7D%5Cend%7Barray%7D%5C%5C%5Ctext%7BAn%20amount%20of%20N28.00%20is%20%24%5Clarge%20%5Cboxed%7B%5Ctextbf%7B168.00%20F%7D%7D%24%7D)
Answer:
1: 233 m
2: 466 m
3: 241.87 m
4: 483.72
Step-by-step explanation:
The Pythagorean Theorem states that a^2 + b^2 = c^2, in which c is the hypotenuse (in this case, PQ and RS).
1: 105^2 + 208^2 = 54289, square root of 54289 = 233
2: Since the area of the triangle makes up half of the rectangle, multiply the area by 2 to get 466
3: 120^2 + 210^2 = 58500, square root of 58500 is 241.87
4: Multiply by 2 to get 483.72
Answer:
6x+25
Step-by-step explanation: