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Serggg [28]
3 years ago
14

The beginning balance in a savings account is $64.98. After a deposit of $73.87, two withdrawals of $51.00 and $23.50, and $1.15

of interest earned, what is the balance? $138.85 $65.50 $64.35 $87.85
Mathematics
1 answer:
AleksandrR [38]3 years ago
5 0
The account has a balance of $64.98 at the start. That means that there is $64.98 in the account.

A deposit of $73.87 is made after which the amount in the account is $64.98 + $73.87 = $138.85.

Next come two withdrawals (this is money that is taken out of the account so we need to subtract the amounts given). $138.85 - $51.00 = $87.85 and $87.85 - $23.50 = $64.35.

Interest is added to the account. So we end by adding $1.15 to the amount we just arrived at. That is, $64.35 + $1.15 = $65.50

The balance after these transactions is $65.50
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[Pre-Calc] Please Help! I don’t know where to start. How do I do this?
sertanlavr [38]

Answer:

See Below.

Step-by-step explanation:

Problem A)

We have:

\displaystyle \csc^2\theta \tan^2\theta -1=\tan^2\theta

When in doubt, convert all reciprocal trig functions and tangent into terms of sine and cosine.

So, let cscθ = 1/sinθ and tanθ = sinθ/cosθ. Hence:

\displaystyle \left(\frac{1}{\sin^2\theta}\right)\left(\frac{\sin^2\theta}{\cos^2\theta}\right)-1=\tan^2\theta

Cancel:

\displaystyle \frac{1}{\cos^2\theta}-1=\tan^2\theta

Let 1/cosθ = secθ:

\sec^2\theta -1=\tan^2\theta

From the Pythagorean Identity, we know that tan²θ + 1 = sec²θ. Hence, sec²θ - 1 = tan²θ:

\tan^2\theta =\tan^2\theta

Problem B)

We have:

\sin^3x=\sin x-\sin x \cos^2 x

Factor out a sine:

\sin x(\sin^2 x)=\sin x-\sin x\cos^2 x

From the Pythagorean Identity, sin²θ + cos²θ = 1. Hence, sin²θ = 1 - cos²θ:

\sin x(1-\cos^2 x)=\sin x-\sin x\cos^2x

Distribute:

\sin x- \sin x \cos^2 x=\sin x-\sin x\cos^2 x

Problem C)

We have:

\displaystyle \frac{\cos 2x+1}{\sin 2x}=\cot x

Recall that cos2θ = cos²θ - sin²θ and that sin2θ = 2sinθcosθ. Hence:

\displaystyle \frac{\cos^2 x-\sin^2 x+1}{2\sin x\cos x}=\cot x

From the Pythagorean Identity, sin²θ + cos²θ = 1 so cos²θ = 1 - sin²θ:

\displaystyle \frac{2\cos^2 x}{2\sin x\cos x}=\cot x

Cancel:

\displaystyle \frac{\cos x}{\sin x}=\cot x

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\cot x = \cot x

3 0
3 years ago
Yanni threw his paper airplane 15 1/2 feet. Adrian threw his paper airplane 3/4 of yanni's distance. What is the distance Adrian
vagabundo [1.1K]

Answer:

19.125

Step-by-step explanation:

multiply 15.5 by 3 and then divide the answer by 4

4 0
3 years ago
Area of circle <br> sector and finding the percentage
mestny [16]

Answer:2592/25

Step-by-step explanation: Big circle is pi*r^2= (4+3+3)^2*pi =314.15 minus 4^2*pi=50.26 equals 263.89. the big circle minus the first 2 layers of the circle = the outer circle. 314.15-(4+3)^2*pi=160.21 263.89-160.21=2592/25

4 0
4 years ago
1) What does the equation x = 4 represent in R^2? a) a circle.b) a plane.c) a line.d) a pointWhat does it represent in R^3? a) a
Sunny_sXe [5.5K]

Answer:

The equation x=4 represents in R^2 c) a line

The equation x=4 represents in R^3 a) a plane

The equation y+3x=2 represents in R^3 a) a plane

The equation z-4y=8 represents d) a plane

The pair of equations y=2,z=8 represents a) a line

Step-by-step explanation:

Let's start by studying each question :

1)

In R^2 , x=a with a ∈ IR is the equation of all vertical lines

In this case, the only free variable is the variable ''y''

R^2 has two dimensions (x and y) so if we set x=4 we will have only one free variable in R^2 (which is a line in R^2). Therefore, x=4 represents a line in R^2

Now, in R^3 we have three dimensions (x, y and z) so if we set x=4 we will have only two free variables (y and z) and x=4 will represent a plane (which have two dimensions) in R^3.

2) The equation y+3x=2 in R^3 has the free variable ''z'' and given that we select a value (for example for ''x'') the another value from the variable ''y'' is determined. Finally, we have the free variables ''z'' and ''x'', and the variable ''y'' restricted for our choice of the variable ''x''.

The equation y+3x=2 in R^3 (given that we have two free variables) represents a plane.

Using the same reasoning, the equation z-4y=8 represents a plane (given that it has two free variables : ''y'' and ''x'')

Finally, the pair of equations y=2,z=8 set values for ''y'' and ''z'' leading us ''x'' as the free variable. With only one free variable we will have a ''one dimensional'' geometric form. The one dimensional forms in R^3 are lines.

The final answer is a) a line.

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Answer:

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3 rectangles have vertices ABCD that lie on grid nodes

Step-by-step explanation:

3 0
2 years ago
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