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4 years ago

Pts

Mathematics

1 answer:

ladessa [460]4 years ago

8 0

Answer:

<u>In week 20, Seth will have 80 cards and Matt will have 60.</u>

Step-by-step explanation:

Let's find out the amount of cards that Math and Seth will have in week 20, using the information shown in the graph and table:

Amount of cards Seth has in week 20 = 20 * 4 = 80

The equation to find out the amount of cards, c, Seth has in week w:

c = 4w

Amount of cards Matt has in week 20 = 20 + (2 * 20) = 20 + 40 = 60

The equation to find out the amount of cards, c, Matt has in week w:

c = 20 + 2w

<u>In week 20, Seth will have 80 cards and Matt will have 60.</u>

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Art [367]

Bundle (31 , 40) has 40 bananas.
So 40 - 28 = 12 bananas
These 12 banana give the consumer negative utility which will be balance one for one apple.
So we have to need 12 apple to balance it.
So the final utility of apples and banana is 28 + (31 - 12) = 28 + 19 = 43
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Which we will get from 43 - 23 = 20 apples.
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4 years ago

2x + 3 + 4x + 8 = 3x - 10

vodomira [7]

$\text {Hello! Let's solve this Equation!}$

$\text {Your First Step is to Simplify the Equation:}$

$\text {(2x+4x)+(8+3)}$

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$\text {6x+11-3x=3x-10-3x}\\\text {3x+11=-10}$

$\text {Next Step is to Subtract 11:}$

$\text {Q: Why Subtract 11?}$

$\text {A: So they cancel out. We cross them out once we subtract.}$

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$\text {The Final Step is to Divide 3:}$

$\text {3x/3=-21/3}$

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3 years ago

The averageCanadianstudentspent18,600 secondsper dayin classes. How many hours/dayis this?

Yuliya22 [10]

Answer:

Step-by-step explanation:

18600/60/60=5.167 hours

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4 years ago

What is the equation of the circle shown?

Mkey [24]

Answer:

(x + 4)² + (y - 2)² = 8

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k ) = (- 4, 2 ) , then

(x - (- 4))² + (y - 2)² = r²

(x + 4)² + (y - 2)² = r²

CA is the radius of the circle

To find r use the distance formula

r = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }$

with (x₁, y₁ ) = C(- 4, 2) and (x₂, y₂ ) = A(- 2, 4)

r = $\sqrt{(-2+4)^2+(4 -2)^2}$

= $\sqrt{2^2+2^2}$

= $\sqrt{8}$ , then r² = ( $\sqrt{8}$ )² = 8

Then

(x + 4)² + (y - 2)² = 8 ← equation of circle

5 0

3 years ago

Find a unit vector orthogonal to the plane containing the points A= 1,0,0 , B= 3,−1,−3 , and C= 1,3,−2 .

zysi [14]

Answer:

unit normal vector n will be n=(a,b,c) = (4/√171,11/√171,6/√171)

Step-by-step explanation:

There are several ways to solve this problem

1) build 2 vectors AB and BC such that the vectorial product ABxBC is the orthogonal vector to the plane , then find unit vector

2) since the 3 points belongs to the plane solve a linear system of 4 equation with 4 variables

for the second solution , the equation of the plane with normal vector n=(a,b,c) and containing the point (x₀,y₀,z₀) is

a*(x-x₀)+b*(y-y₀)+c*(z-z₀) =0

and

a²+b²+c² = 1 (unit vector)

then choosing A=(x₀,y₀,z₀)=(1,0,0)

a*(x-1)+b*(y-0)+c*(z-0) =0

for B

a*(3-1)+b*(-1-0)+c*(-3-0) =0

1) 2*a - b - 3*c =0

for C

a*(1-1)+b*(3-0)+c*(-2-0) =0

2) 3*b - 2*c=0 → b= 2/3*c

replacing in 1)

2*a - 2/3*c - 3*c =0

2*a-11/3*c=0 → a=11/6*c

thus

a²+b²+c² = 1

(11/6*c)²+(2/3*c)²+c² = 1

(121/36+4/9+1)*c² = 1

171/36*c²=1 → c= 6/√171

therefore

a=11/6*c = 11/6*6/√171= 11/√171

b=2/3*c= 2/3*6/√171= 4/√171

then the unit normal vector n will be

n=(a,b,c) = (4/√171,11/√171,6/√171)

5 0

4 years ago