MATHEMATICS HIGH SCHOOL

Dylan started with 10,000 baseball cards to sell. In each subsequent week, Dylan started with approximately 85% of the previous week's starting number of cards. What is the explicit rule for the number of cards Dylan starts with in week n and approximately how many cards will he start with in the 6th week? Round to the nearest card. Drag and drop the answers into the boxes to match the situation. Explicit rule Amount of cards after the 6th week.

Answers

Answer 1

Answer:

Answer:

Number of cards at week n = 10,000(0.85)^(n-1).

At week 6 Dylan has 4437 cards.

Step-by-step explanation:

At the start of week 1 he had 10,000 = 10,000(0.85)^0 cards.

So at the start of week 2 he had 10,000(0.85)^(2-1) cards.

Number of cards for week n = 10,000(0.85)^(n-1).

Number of he will have at the start of the 6th week

= 10,000(0.85)^(6-1)

= 4437 cards (answer).

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True or false? shapes that have no right angles also have no perpendicular segments?

Answers

It's false. Sometimes shapes might not have perpendicular segments but this is false.

Multiply. start fraction k plus 3 over 4 k minus 2 end fraction dot left parenthesis 12 k squared plus 2 k minus 4 right parenthesis

Answers

Answer:

$\therefore ((k+3))/((4k-2)).(12k^2+2k-4)=3k^2+11k+6$

Step-by-step explanation:

Factorization of a Quadratic polynomial:

In order to factorize $ax^2+bx+c$ we have to find out the numbers p and q such that, p+q = b and pq=ac.

Finding the two integers p and q, we rewrite the middle term of the quadratic as px+qx. Then by grouping of the terms we can get desired factors.

Multiplication of two binomial:

(a+b)(c+d)

=a(c+d)+b(c+d)

=(ac+ad)+(bc+bd)

=ac+ad+bc+bd

Given that,

$((k+3))/((4k-2)).(12k^2+2k-4)$

$=((k+3))/(2(2k-1)).2(6k^2+k-2)$ [ taking common 2]

$=((k+3))/((2k-1)).(6k^2+k-2)$ [ cancel 2]

$=((k+3))/((2k-1)).(6k^2+4k-3k-2)$

$=((k+3))/((2k-1)).\{2k(3k+2)-1(3k+2)\}$

$=((k+3))/((2k-1)).(3k+2)(2k-1)$

$=(k+3).(3k+2)$

$=3k^2+9k+2k+6$

$=3k^2+11k+6$

$\therefore ((k+3))/((4k-2)).(12k^2+2k-4)=3k^2+11k+6$

Three vertices of square WXYZ are W(1, 4), X(4, 0), and Y(0, –3). What are the coordinates of the fourth vertex?

Answers

Hello,

Z=(-3,1)
============

DESCRIBE the probability of a woman growing to be 5 metres tall

Answers

Answer:

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Solve the following system of equations using substitution. What is the value of y?2x+3y=105
x+2y=65
I somehow got -1(4/6)x=-5. Can someone provide a clear explanation on how to do this?

Answers

I have no idea how did you get this result but I can show you the method of elimination. I think that it is the easiest way to solve the system of equations.
2 x + 3 y =105
x + 2 y = 6 /*(-2) // We will multiply 2nd equation by -2. That is because we want to cancel out the x`s//
2 x + 3 y = 105
-2 x - 4 y = -12 // Then we will add down these equations/ and x`s will cancel out//
3 y - 4 y = 105 - 12
- y = 93
y = -93
We can also solve x:
x + 2 * (-93)=6
x - 186 = 6
x = 6 + 186
x = 192

A piling for a high-rise building is pushed by two bulldozers at exactly the same time. One bulldozer exerts a force of 1250 pounds in a westerly direction. The other bulldozer pushes the piling with a force of 2650 pounds in a northerly direction. What is the magnitude of the resultant force upon the piling, to the nearest ten pounds?

Answers

The forces result in a right triangle. To obtain the resultant force, one can simply use the Pythagorean theorem. 1250 lbf and 2650 lbf both act as the legs of the triangle. Obtaining the hypotenuse via the theorem would yield the resultant force. This is done below:

c^2 = a^2 + b^2
c^2 = (1250)^2 + (2650)^2
c = 2930.017 lbf

Therefore, the magnitude of the resultant force is approximately equal to 2930 lbf.

The magnitude of the resultant force is 2930 pounds.

What is the resultant force?

The resultant force is the single force that has the same effect as two or more forces acting together. Two forces that act in the same direction produce a resultant force that is larger than either individual force.

If one bulldozer exerts force in west direction of magnitude 1250 pounds and the other exerts a force in north direction of magnitude 2650 pounds .

let F $_1$ = 1250 pounds and F $_2$ = 2650 pounds