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3 years ago

8

You are saving for a bicycle that costs $120. You Deposit $75 in an account that earns compounded annually. The Expression 75(1+

r)^2 represents the balance after 2 years the annual interest rate in decimal form.
A. Write a polynomial that represents the balance of your account.
B. What is the balance of your account when the interest rate is 10%.
C. How much more money do you need to buy the bicycle?

1 answer:

dezoksy [38]3 years ago

8 0

A. Expanding the given expression, you have
balance = 75r^2 +150r +75

B. For r=0.10, the balance after 2 years is 75*1.1^2 = 90.75

C. The difference between $120 and 90.75 is $29.25. You need $29.25 more to buy the bicycle.

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Find the missing side length ED Round answe to the nearest tenth please.

GarryVolchara [31]

Answer:

Step-by-step explanation:

Considering the given triangle EDI, to determine ED, we would apply the sine rule. It is expressed as

a/SinA = b/SinB = c/SinC

Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. Likening it to the given triangle, the expression becomes

ED/SinI = DI/SinE = EI/SinD

Therefore

Recall, the sum of the angles in a triangle is 180°. Therefore,

I° = 180 - (36 + 87) = 57°

Therefore,

ED/Sin 57 = 26/Sin 36

Cross multiplying, it becomes

EDSin36 = 26Sin57

0.588ED = 26 × 0.839

0.588ED = 21.814

ED = 21.814/0.588

ED = 37.1 m

8 0

2 years ago

Is the GCF of two even numbers 2

lions [1.4K]

No, GCF means greatest common factor, meaning the largest number than can be divided into the number. 2 would be the lowest common factor or LCF.
EX. 200 & 440. In this case the GCF would be 40, but the LCF would be 2 because they are both even numbers

3 0

3 years ago

Read 2 more answers

In a geometric sequence, if a3 = ‒5 and a6 = 40, determine a1, r, and an. Then write the first three terms of the sequence.

Tresset [83]

$a_4=ra_3$
$a_5=ra_4=r^2a_3$
$a_6=ra_5=r^3a_3$

$40=-5r^3\implies r^3=-8\implies r=-2$

$a_3=ra_2=r^2a_1$

$-5=(-2)^2a_1\implies a_1=-\dfrac54$

You know the first and third terms, $a_1$ and $a_3$ , so you just need to find the second term $a_2$ :

$a_2=ra_1\implies a_2=-2\left(-\dfrac54\right)=\dfrac52$

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3 years ago

Vicki made a fruit tart and cut it into six equal pieces . vicki, silvia,and Elena each took 2 pieces of the tart home. vicki sa

frez [133]

Yes, Vicki's statement is true.
The fruit tart was split into 6 pieces and to find what 1/3 of 6 is, you'd have to divide 6/3 which equals 2. So, 1/3 of 6 is 2 and each girl took home 2 pieces (1/3) of the tart home

4 0

3 years ago

Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices (0,0,0),(5,0,0),(0,9,0),(0,0,4).

Elan Coil [88]

Answer: $\int\limits^a_E {\int\limits^a_E {\int\limits^a_E {xy} } \, dV$ = 1087.5

Step-by-step explanation: To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedon is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.

An equation of a plane is found with a point and a normal vector. <u>Normal</u> <u>vector</u> is a perpendicular vector on the plane.

Given the points, determine the vectors:

P = (5,0,0); Q = (0,9,0); R = (0,0,4)

vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)

vector QR = (0,9,0) - (0,0,4) = (0,9,-4)

Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:

n = PQ × QR = $\left[\begin{array}{ccc}i&j&k\\5&-9&0\\0&9&-4\end{array}\right]$ $\left[\begin{array}{ccc}i&j\\5&-9\\0&9\end{array}\right]$

n = 36i + 0j + 45k - (0k + 0i - 20j)

n = 36i + 20j + 45k

Equation of a plane is generally given by:

$a(x-x_{0}) + b(y-y_{0}) + c(z-z_{0}) = 0$

Then, replacing with point P and normal vector n:

$36(x-5) + 20(y-0) + 45(z-0) = 0$

The equation is: 36x + 20y + 45z - 180 = 0

Second, in evaluating the triple integral, set limits:

In terms of z:

$z = \frac{180-36x-20y}{45}$

When z = 0:

$y = 9 + \frac{-9x}{5}$

When z=0 and y=0:

x = 5

Then, triple integral is:

$\int\limits^5_0 {\int\limits {\int\ {xy} \, dz } \, dy } \, dx$

Calculating:

$\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx$

$\int\limits^5_0 {\int\limits {\int\ {xy(\frac{180-36x-20y}{45} - 0 )} \, dy } \, dx$

$\frac{1}{45} \int\limits^5_0 {\int\ {180xy-36x^{2}y-20xy^{2}} \, dy } \, dx$

$\frac{1}{45} \int\limits^5_0 {90xy^{2}-18x^{2}y^{2}-\frac{20}{3} xy^{3} } \, dx$

$\frac{1}{45} \int\limits^5_0 {2430x-1458x^{2}+\frac{94770}{125} x^{3}-\frac{23490}{375}x^{4} } \, dx$

$\frac{1}{45} [30375-60750+118462.5-39150]$

$\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx$ = 1087.5

<u>The volume of the tetrahedon is 1087.5 cubic units.</u>

3 0

3 years ago