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Naily [24]
2 years ago
8

If f(x)=x-6 and g(x)=x^1/2(x+3) , find g(x) x f(x). A. B. C. D.

Mathematics
1 answer:
Snezhnost [94]2 years ago
3 0

Answer:

Step-by-step explanation:

This is (x - 6)*x^1/2(x + 3)

= x^1/2 (x^2 - 3x - 18)

= x^(5/2) - 3x^(3/2) - 18x^(1/2)

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A group of 72 children completed a survey on what kind of sport they like. The choices were: Chess, Swimming, and Football. Ever
Svetach [21]

Answer:

19/72

Step-by-step explanation:

To calculate the probability that a randomly-chosen child from this group likes either Chess or Swimming but not Football?

We already know the number that liked chess only which is 10, we have to solve for those that liked swimming only which is

8+7+16+x = 40

x which represent swimming only is

40-31 = 9

Thus probability = 10/72 + 9/72 = 19/72

3 0
3 years ago
Bianca's bank offers a savings account with a 2.1% APR, compounded monthly. What is the actual annual percentage yield on this a
Elanso [62]
2.1 x 12 = 25.2% is the percentage yield
5 0
3 years ago
Read 2 more answers
What is the difference between Compound Interest and simple interest???
oksian1 [2.3K]

Answer:

Simple interest is calculated using initial principle while compound interest is calculated considering the interest also .

Step-by-step explanation:

Interest is the cost of borrowing money, where the borrower pays a fee to the lender for using his money. The interest, typically expressed as a percentage, can either be compounded or simple .

Simple interest is based on the principal amount , while compound interest is based on the principal amount and the interest that adds onto it in every period and the final principle is used for calculating the interest.

Simple interest is calculated  on the principal amount of a loan and it's easier to find out than compound interest.

4 0
3 years ago
What is the solution to the equation 8 - 2b = -2/3(12b + 6)?
Delvig [45]
<span>8 - 2b = -2/3(12b + 6)
8 - 2b = -8b -4
8 + 4 = -8b + 2b
12 = -6b
b = -12/6
b = -2

So, your final answer is b = -2</span>
8 0
3 years ago
Triangle ABC has vertices A(-5, -2), B(7, -5), and C(3, 1). Find the coordinates of the intersection of the three altitudes
Darina [25.2K]

Answer:

Orthocentre (intersection of altitudes) is at (37/10, 19/5)

Step-by-step explanation:

Given three vertices of a triangle

A(-5, -2)

B(7, -5)

C(3, 1)

Solution A by geometry

Slope AB = (yb-ya) / (xb-xa) = (-5-(-2)) / (7-(-5)) = -3/12 = -1/4

Slope of line normal to AB, nab = -1/(-1/4) = 4

Altitude of AB = line through C normal to AB

(y-yc) = nab(x-xc)

y-1 = (4)(x-3)

y = 4x-11           .........................(1)

Slope BC = (yc-yb) / (xc-yb) = (1-(-5) / (3-7)= 6 / (-4) = -3/2

Slope of line normal to BC, nbc = -1 / (-3/2) = 2/3

Altitude of BC

(y-ya) = nbc(x-xa)

y-(-2) = (2/3)(x-(-5)

y = 2x/3 + 10/3 - 2

y = (2/3)(x+2)    ........................(2)

Orthocentre is at the intersection of (1) & (2)

Equate right-hand sides

4x-11 = (2/3)(x+2)

Cross multiply and simplify

12x-33 = 2x+4

10x = 37

x = 37/10  ...................(3)

substitute (3) in (2)

y = (2/3)(37/10+2)

y=(2/3)(57/10)

y = 19/5  ......................(4)

Therefore the orthocentre is at (37/10, 19/5)

Alternative Solution B using vectors

Let the position vectors of the vertices represented by

a = <-5, -2>

b = <7, -5>

c = <3, 1>

and the position vector of the orthocentre, to be found

d = <x,y>

the line perpendicular to BC through A

(a-d).(b-c) = 0                          "." is the dot product

expanding

<-5-x,-2-y>.<4,-6> = 0

simplifying

6y-4x-8 = 0 ...................(5)

Similarly, line perpendicular to CA through B

<b-d>.<c-a> = 0

<7-x,-5-y>.<8,3> = 0

Expand and simplify

-3y-8x+41 = 0 ..............(6)

Solve for x, (5) + 2(6)

-20x + 74 = 0

x = 37/10  .............(7)

Substitute (7) in (6)

-3y - 8(37/10) + 41 =0

3y = 114/10

y = 19/5  .............(8)

So orthocentre is at (37/10, 19/5)  as in part A.

8 0
3 years ago
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