Given the table for f(x), write an equation for the function.

each blade on a windmill is in the shape of a triangle with a base of 7 feet and a height of 4 ft if there are four blades on th

Sunny_sXe [5.5K]

The total area of the blades is the area of a triangle multiplied by 4.

We have then:

$A = (4) * (1/2) * (b) * (h)$

Where,

b: base of the blades

h: height of the blades

Substituting values we have:

$A = (4) * (1/2) * (7) * (4)$

Doing the calculation we have that the area of the blades is given by:

$A = 56 feet ^ 2$

Answer:

The total area of the blades is:

$A = 56 feet ^ 2$

6 0

3 years ago

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Angl is a square. The equation of line NG is Y= 1/2 X - 6. Find the equation of line LG in slope intercept form given that the c

Irina18 [472]

Answer: y=-2x-9

Step-by-step explanation:

If ANGL is a square, then NG and LG are adjacent sides.

Adjacent sides are perpendicular. [Each angle is 90°]

The equation of line NG is $Y=\dfrac12 X-6$ .

By comparing it to equation in slope intercept form y=mx+c ( where , m= slope , c=y-interecpt)

slope = $\dfrac12$

Let slope of LG be <em>n</em>, then

$n\times \dfrac{1}{2}=-1$ [Product of slopes of two perpendicular line =-1]

$\Rightarrow n=-2$

Equation of a line passes through (a,b) and have slope m is given by :-

$(y-b)=m(x-a)$

Equation of LG :

$(y-1)=-2(x-(-5))\\\\\Rightarrow\ y-1=-2x-10\\\\\Rightarrow\ y=-2x-9$ [In intercept form]

3 0

3 years ago

Paul paid $ 25.50 for 3 cups of hot chocolate and cups of tea. The cost of each cup of tea was 2/3 the cost of each cup of hoy c

Allushta [10]

Let the cost of one cup of hot chocolate be = x

Let the cost of one cup of hot tea be = y

Paul paid $ 25.50 for 3 cups of hot chocolate and 4 cups of tea.

Equation becomes = $3x+4y=25.50$ ...(1)

As given, the cost of each cup of tea was 2/3 the cost of each cup of hot chocolate.

$y=\frac{2x}{3}$ .... (2)

Putting the value of y from (2) in (1)

$3x+4(\frac{2x}{3})=25.50$

= $3x+\frac{8x}{3}=25.50$

= $\frac{9x+8x}{3}=25.50$

= $17x=76.5$

x=4.5

$y=\frac{2x}{3}$

= $\frac{2*4.5}{3}$

y =3

Hence each cup of hot chocolate is $4.50

Each cup of tea is $3.

7 0

3 years ago

Tangent line i think please help me find x

Alex

Answer:

x= 6.5 cm

Step-by-step explanation:

When a tangent line touches the circle, it forms a right angle triangle at that point

Apply the Pythagorean relationship in this case

Given that the height is = 20.2 cm = b

The hypotenuse is = c= x+14.7 cm

General formulae is;

a² +b² =c²

x² + 20.2² =( x+ 14.7)²

x² + 408.04= x² +14.7x+14.7x+216.09

x² + 408.04= x² + 29.4 x +216.09.........................collect like terms

x²-x² + 408.04-216.09= 29.4x

191.95= 29.4x-------------------------------divide by 29.4 t0 get x

191.95/29.4 =x

x=6.5 cm

6 0

3 years ago

For a binomial distribution with p = 0.20 and n = 100, what is the probability of obtaining a score less than or equal to x = 12

notsponge [240]

The binomial distribution is given by,
P(X=x) = $(^{n}C_{x})p^{x} q^{n-x}$
q = probability of failure = 1-0.2 = 0.8
n = 100
They have asked to find the probability <span>of obtaining a score less than or equal to 12.
</span>∴ P(X≤12) = $(^{100}C_{x})(0.2)^{x} (0.8)^{100-x}$
where, x = 0,1,2,3,4,5,6,7,8,9,10,11,12
∴ P(X≤12) = $(^{100}C_{0})(0.2)^{0} (0.8)^{100-0} + (^{100}C_{1})(0.2)^{1} (0.8)^{100-1}$ + $(^{100}C_{2})(0.2)^{2} (0.8)^{100-2} + (^{100}C_{3})(0.2)^{3} (0.8)^{100-3}$ + $(^{100}C_{4})(0.2)^{4} (0.8)^{100-4} + (^{100}C_{5})(0.2)^{5} (0.8)^{100-5}$ + $(^{100}C_{6})(0.2)^{6} (0.8)^{100-6} + (^{100}C_{7})(0.2)^{7} (0.8)^{100-7}$ + $(^{100}C_{8})(0.2)^{8} (0.8)^{100-8} + (^{100}C_{9})(0.2)^{9} (0.8)^{100-9}$ + $(^{100}C_{10})(0.2)^{10} (0.8)^{100-10} + (^{100}C_{11})(0.2)^{11} (0.8)^{100-11}$ + $(^{100}C_{12})(0.2)^{12} (0.8)^{100-12}$

Evaluating each term and adding them you will get,
P(X≤12) = 0.02532833572
This is the required probability.

7 0

3 years ago