The owner of a store displays a large jar of nickel and dimes and offers the value of the coins to the person who guesses how ma
1 answer:
N = nickels; $0.05
d = dimes; $0.10
n + d = 1130
Subtract n from both sides.
d = -n + 1130
Input d into the other equation.
.05n + .1(-n + 1130) = 100
.05n - .1n + 113 = 100
-.05n + 113 = 100
Subtract 113 from both sides.
-.05n = -13
Divide both sides by -.05.
n = 260
Input n into the equation we changed earlier.
d = -260 + 1130
d = 870
There were 870 dimes and 260 nickels.
d = dimes; $0.10
n + d = 1130
Subtract n from both sides.
d = -n + 1130
Input d into the other equation.
.05n + .1(-n + 1130) = 100
.05n - .1n + 113 = 100
-.05n + 113 = 100
Subtract 113 from both sides.
-.05n = -13
Divide both sides by -.05.
n = 260
Input n into the equation we changed earlier.
d = -260 + 1130
d = 870
There were 870 dimes and 260 nickels.
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Let us assume uniform width = x cm wide.
Length of rectangular portrait = 50cm and width of rectangular portrait = 70cm.
Therefore, length of rectangle made by frame = 50 + x+x = (2x+50) cm.
And width of rectangle made by frame = 70+x+x = (2x+70) cm.
We know, the area of rectangular portrait = 50 × 70 = 3500 cm^2.
Total area of the rectangle made by frame would be = (2x+50) * (2x+70)
We know,
Actual area of frame = Area of rectangle made by frame - area of rectangular portrait.
We also given "the area of the frame is the same as the area of the portrait."
We can setup an equation now,
3500 = (2x+50) * (2x+70) - 3500.
Subtracting 3500 from both sides, we get
3500-3500 = (2x+50) * (2x+70) - 3500-3500.
0 = (2x+50) * (2x+70) -7000.
FOIL (2x+50) * (2x+70), we get
0 = 2x*2x +2x*70 + 50*2x +50*70 - 7000.
0 = 4x^2 +140x +100x +3500 -7000.
4x^2 +240x -3500 = 0.
Dividing whole equation by 4, we get
x^2 +60x - 875 =0
Applying quadratic formula , we get
We cant take negative value.
So,
We could take approximately 12 cm.
Answer:
Option A
Step-by-step explanation:
- f(x) = x³ + x² + x + 1
This is increasing function
The first option is correct
<em>See attached graph for reference</em>
Answer:
20.78feet
Step-by-step explanation:
The question made us to understand that the man is standing and also there is angle of elevation, then we need to draw a right triangle having a base equal to 36 feet with an angle from the base to the top of the pole which is 30 degrees.
tan= opposite side / adjacent side
Let height of the pole =h
Tan(30)= h/36
But tan 30degree= 1/√3
h= 36 × 1/√3
h= 20.78feet
Therefore, the height of the pole= 20.78feet
CHECK THE ATTACHMENT FOR DETAILED FIGURE
