Answer:
<h2>21 feet</h2>
Step-by-step explanation:
The problem bothers on the dimension of a scaled drawing/prototype
The indications on the blueprint actually represent the scale
that is 1 inch: 3.5 feet
Given that a wall is 6 inches on the blueprint, now, in reality, the actual
length will be 3.5*6= 21 feet
<h2>what is a scaled drawing?</h2>
Usually, the scale is given as a ratio. A drawing, which has been reduced or enlarged or a drawing whose dimensions have been changed to a particular size other than its previous or initial size is a scaled drawing.
Step-by-step explanation:
area of the rectangle =161/2
The value of x is 5/6 and y is 8/5.
Step-by-step explanation:
Given,
12x+15y=34 Eqn 1
-6x+5y=3 Eqn 2
Multiplying Eqn 2 by 2
![2(-6x+5y=3)\\-12x+10y=6\ \ \ Eqn 3](https://tex.z-dn.net/?f=2%28-6x%2B5y%3D3%29%5C%5C-12x%2B10y%3D6%5C%20%5C%20%5C%20Eqn%203)
Adding Eqn 1 and 3
![(12x+15y)+(-12x+10y)=34+6\\12x+15y-12x+10y=40\\25y=40](https://tex.z-dn.net/?f=%2812x%2B15y%29%2B%28-12x%2B10y%29%3D34%2B6%5C%5C12x%2B15y-12x%2B10y%3D40%5C%5C25y%3D40)
Dividing both sides by 25
![\frac{25y}{25}=\frac{40}{25}\\y=\frac{8}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B25y%7D%7B25%7D%3D%5Cfrac%7B40%7D%7B25%7D%5C%5Cy%3D%5Cfrac%7B8%7D%7B5%7D)
Putting y= 8/5 in Eqn 1
![12x+15(\frac{8}{5})=34\\12x+3*8=34\\12x+24=34\\12x=34-24\\12x=10](https://tex.z-dn.net/?f=12x%2B15%28%5Cfrac%7B8%7D%7B5%7D%29%3D34%5C%5C12x%2B3%2A8%3D34%5C%5C12x%2B24%3D34%5C%5C12x%3D34-24%5C%5C12x%3D10)
Dividing both sides by 12
![\frac{12x}{12}=\frac{10}{12}\\x=\frac{5}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B12x%7D%7B12%7D%3D%5Cfrac%7B10%7D%7B12%7D%5C%5Cx%3D%5Cfrac%7B5%7D%7B6%7D)
The value of x is 5/6 and y is 8/5.
Keywords: Linear equations, fractions
Learn more about fractions at:
#LearnwithBrainly
Answer:
x = 38
Step-by-step explanation:
x-13 = 25
Add 13 to each side
x-13+13 = 25+13
x = 38
Check
38-13 = 25
25=25
Answer:
x=8.75
Step-by-step explanation:
The price x that maximizes profit is the maximum value of the function, and the maximum value of the function is located at a point where the first derivative of the function is equal to zero. The first derivative is:
![P(x) = - 2x^2+35x-99\\P'(x)=-2(2)x^{(2-1)}+35(1)-0\\P'(x)=-4x+35](https://tex.z-dn.net/?f=P%28x%29%20%3D%20-%202x%5E2%2B35x-99%5C%5CP%27%28x%29%3D-2%282%29x%5E%7B%282-1%29%7D%2B35%281%29-0%5C%5CP%27%28x%29%3D-4x%2B35)
Using P'(x)=0:
![0=-4x+35\\4x=35\\x=35/4\\x=8.75](https://tex.z-dn.net/?f=0%3D-4x%2B35%5C%5C4x%3D35%5C%5Cx%3D35%2F4%5C%5Cx%3D8.75)
The minimum value of the function is also at a point where the first derivative of the function is equal to zero. To differentiate if x=8. is a minimum or a maximum obtain the second derivative and evaluate it at x=8.75 if the value P''(x)>0 x is minimum and if P''(x)<0 x is a maximum.
![P'(x)=-4x+35\\P''(x)=-4(1)\\P''(x)=-4](https://tex.z-dn.net/?f=P%27%28x%29%3D-4x%2B35%5C%5CP%27%27%28x%29%3D-4%281%29%5C%5CP%27%27%28x%29%3D-4)
Evaluating at x=8.75:
![P''(8.75)=-4](https://tex.z-dn.net/?f=P%27%27%288.75%29%3D-4)
Therefore, x=8.75 is the maximum value of the function and it is the price that maximizes profit.