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2 years ago

Jeremy opened two savings accounts at the beginning of 2010, each with an initial deposit of

Mathematics

1 answer:

deff fn [24]2 years ago

7 0

account b has 2.6% more interest than account a

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1. Evaluate each expression when x = -2 and y = 3.

borishaifa [10]

a) 3(-2) + 4(3) = -6 + 12 = 6

b) 2(-2) -3(3) +5 = -4 -9 + 5 = -8

c) 4(-2) -(3) = -8 -3 = -11

d) -(-2) -2(3) = 4 -6 = -2

e) (1/2)(-2) +(3) = -1 +3 = 2

f) (2/3)(3) -(1/2)(-2) = 2 + 1 = 3

5 0

2 years ago

Dose Congruent Mean Having The Same Measure

Julli [10]

So Congruent. Two figures are congruent if they have the same shape and size. Two angles are congruent if they have the same measure. Two figures are similar if they have the same shape but not necessarily the same size.

I hope that help u:)

4 0

2 years ago

Solve the following recurrence relation: <br> <img src="https://tex.z-dn.net/?f=A_%7Bn%7D%3Da_%7Bn-1%7D%2Bn%3B%20a_%7B1%7D%20%3D

-Dominant- [34]

By iteratively substituting, we have

$a_n = a_{n-1} + n$

$a_{n-1} = a_{n-2} + (n - 1) \implies a_n = a_{n-2} + n + (n - 1)$

$a_{n-2} = a_{n-3} + (n - 2) \implies a_n = a_{n-3} + n + (n - 1) + (n - 2)$

and the pattern continues down to the first term $a_1=0$ ,

$a_n = a_{n - (n - 1)} + n + (n - 1) + (n - 2) + \cdots + (n - (n - 2))$

$\implies a_n = a_1 + \displaystyle \sum_{k=0}^{n-2} (n - k)$

$\implies a_n = \displaystyle n \sum_{k=0}^{n-2} 1 - \sum_{k=0}^{n-2} k$

Recall the formulas

$\displaystyle \sum_{n=1}^N 1 = N$

$\displaystyle \sum_{n=1}^N n = \frac{N(N+1)}2$

It follows that

$a_n = n (n - 2) - \dfrac{(n-2)(n-1)}2$

$\implies a_n = \dfrac12 n^2 + \dfrac12 n - 1$

$\implies \boxed{a_n = \dfrac{(n+2)(n-1)}2}$

4 0

2 years ago

A chord is 15 cm long. It is 9 cm from the center of the circle. What is the radius of the circle?

irakobra [83]

Answer:

Step-by-step explanation:

Given a chord of distance of 15cm, if it is 9cm from the center of a circle, this means that the 9cm length will be projecting from the centre of the circle perpendicular to the chord and passing through its centre.

Since the radius of a circle is a line that is drawn from the centre of a circle to ts circumference, the set up will form a right angles triangle within the circle with the hypotenuse as the radius and the other two sides as the opposite and adjacent respectively. Using the Pythagoras theorem to get the length of the radius (hypotenuse);

hyp² = opp² + adj²

Let the opposite be the 9cm length

Adjacent will be half of the chord length = 15/2 = 7.5cm

Substituting this values into the formula we will have;

hyp² = 9² + 7.5²

hyp² = 81+56.25

hyp² = 137.25

hyp² = √137.25

hyp = 11.72

<em>Hence the radius of the circle is approximately 11.72 cm long</em>

5 0

2 years ago

Determine the value of x in the diagram

Sidana [21]

Answer:

3x + x + 3x + x = 360

8x = 360

x = 45

3(45)= 135

Step-by-step explanation:

3 0

3 years ago