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Elza [17]
3 years ago
13

The temperature was -3*C on Friday and dropped overnight by 9*C. What was the temperature on Saturday morning

Mathematics
1 answer:
Anastasy [175]3 years ago
3 0
Well it starts at -3 and dropped (subtract) 9 degrees:
-3 -9 = -12 degrees Saturday morning!
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Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(2, −5, 6), C(4, −2, −1), D(3, 4, −4
almond37 [142]

Answer:

Area = 71.3 sq unit

Step-by-step explanation:

a) We will use properties of parallelogram to verify the given vertices.

Property: Have a pair of parallel opposite sides

Hence, vectors AB AD BD BC CD AC. A pair should be parallel:

vectors

AB = A - B = (1, 1 , 3) - ( 2 , -5 , 6 ) = (-1 , 6 , -3)

AD = A - D = (1, 1 , 3) - (3, 4 , -4) = (-2 , -3 , 7)

BC = B - C = (2 , -5 , 6) - (4, -2 , -1) = (-2 ,-3 , 7)

CD = C - D = (4, -2 , -1) - (3, 4 , -4) = (1 , -6 , 3)

Hence we can see  that AB //CD and AD // BC as their unit vector co-efficents are identical/scalar multiple of each other.

b)

Equation of line AB = (1,1,3) + t*(-1 , 6 , -3 )

Point E = (1-t , 1+6t , 3 -3t) ... denotes an position of point E on line AB.

Choose a point on line CD, lets suppose C = ( 4 , -2 , -1 )

Vector EC = ( 1-t , 1+6t , 3-3t ) - (4 , -2 , -1 ) = (-3 -t , 3 +6t , 4 -3t)

For EC to be perpendicular to AB then dot product of AB . EC = 0

Hence,

EC . AB = -1 * (-3-t) -2*(3+6t) -3*(4-3t) = 0

3 + t -6 -12t -12+9t = 0

-2t-3 = 0

t = -3/2

Vector EC = (-3 -t , 3 +6t , 4 -3t) = (-1.5 , -6 , 8.5)

Area = magnitude (AB) * magnitude (EC)

Area = sqrt ((-1)^2 + 6^2 + (-3)^2) * sqrt ((-1.5)^2 + 6^2 + (8.5)^2)

Area = sqrt (46) * sqrt (442) / 2

Area = 71.3 unit^2

6 0
3 years ago
What is the vertex of the graph of the function below? <br><br>y = x2 + 8x + 12
Vera_Pavlovna [14]
Hello, 

The\,\,formula\,\,for\,\,the\,\,vertex\,\,of\,\,a\,\,quadratic\,\,equation\,\,is:  \\  V=( -\frac{b}{2a},f(-\frac{b}{2a}) )

That means that we must first obtain x, then we replace x in the function to get y, so:

x=- \frac{b}{2a}  \\  \\ x=- \frac{8}{2*(1)}  \\  \\ \boxed{x=-4} \\  \\ Reeplacing \,\,x: \\ y=(-4)^{2} +8*(-4)+12 \\ y=16-32+12 \\ \boxed{y=-4}

Answer: V=(-4 , -4)
5 0
3 years ago
What is -10=k+6 please show work thank you
Tresset [83]

Answer:

k=-16

Step-by-step explanation:

-10=k+6

subtract 6 both both sides to isolate the variable

-16=k

Happy Holidays!!

7 0
3 years ago
Read 2 more answers
The probability distribution for the rate of return on an investment is
babymother [125]

Answer:

a)0.7

b) 10.03

c)  0.0801

Step-by-step explanation:

Rate of return   Probability

9.5                           0.1

9.8                           0.2

10                             0.3

10.2                          0.3

10.6                          0.1

a.

P(Rate of return is at least 10%)=P(R=10)+P(R=10.2)+P(R=10.6)

P(Rate of return is at least 10%)=0.3+0.3+0.1

P(Rate of return is at least 10%)=0.7

b)

Expected rate of return=E(x)=sum(x*p(x))

Rate of return(x)   Probability(p(x))    x*p(x)

9.5                           0.1                       0.95

9.8                           0.2                      1.96

10                             0.3                        3

10.2                          0.3                        3.06

10.6                          0.1                       1.06

Expected rate of return=E(x)=sum(x*p(x))

Expected rate of return=0.95+1.96+3+3.06+1.06=10.03

c)

variance of the rate of return=V(x)=sum(x^2p(x))-[sum(x*p(x))]^2

Rate of return(x)   Probability(p(x))    x*p(x)    x²*p(x)

9.5                           0.1                       0.95       9.025

9.8                           0.2                      1.96         19.208

10                             0.3                       3             30

10.2                          0.3                       3.06        31.212

10.6                          0.1                       1.06         11.236

sum[x²*p(x)]=9.025+19.208+30+31.212+11.236=100.681

variance of the rate of return=V(x)=sum(x²*p(x))-[sum(x*p(x))]²

variance of the rate of return=V(x)=100.681-(10.03)²

variance of the rate of return=V(x)=100.681-100.6009

variance of the rate of return=V(x)=0.0801

6 0
3 years ago
Someone help me out my grades are ba d
Natali5045456 [20]

Answer:

Multiply by Four. x4

12/3

16/4

24/6

36/9

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Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
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