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3 years ago

Adam had -$76 in his account. He then deposited $322. How much was in his account after his deposit?

Mathematics

1 answer:

ohaa [14]3 years ago

5 0

Answer:

-398

Step-by-step explanation:

-76 - 322

i hope it wroks

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Nuts Berry Farm sells nuts for $60 for 4 pounds. Today, and just for today only,

tino4ka555 [31]

Answer:

$10.50

Step-by-step explanation:

First, find the cost of a pound of nuts.

Divide the price by the number of pounds:

60/4

= 15

Calculate the price with the 30% discount by multiplying this by 0.7:

15(0.7)

= 10.5

So, after the discount, a pound of nuts will cost $10.50

7 0

3 years ago

Harry has decided to give his collection of 24 old coins to his four grandsons. John, the oldest, gets half the collection. Walt

Aleksandr [31]

John gets 12, Walt, Matt, and Richie get 4 each

5 0

3 years ago

Read 2 more answers

Given tan theta =9, use trigonometric identities to find the exact value of each of the following:_______

Ludmilka [50]

Answer:

$(a)\ \sec^2(\theta) = 82$

$(b)\ \cot(\theta) = \frac{1}{9}$

$(c)\ \cot(\frac{\pi}{2} - \theta) = 9$

$(d)\ \csc^2(\theta) = \frac{82}{81}$

Step-by-step explanation:

Given

$\tan(\theta) = 9$

Required

Solve (a) to (d)

Using tan formula, we have:

$\tan(\theta) = \frac{Opposite}{Adjacent}$

This gives:

$\frac{Opposite}{Adjacent} = 9$

Rewrite as:

$\frac{Opposite}{Adjacent} = \frac{9}{1}$

Using a unit ratio;

$Opposite = 9; Adjacent = 1$

Using Pythagoras theorem, we have:

$Hypotenuse^2 = Opposite^2 + Adjacent^2$

$Hypotenuse^2 = 9^2 + 1^2$

$Hypotenuse^2 = 81 + 1$

$Hypotenuse^2 = 82$

Take square roots of both sides

$Hypotenuse =\sqrt{82}$

So, we have:

$Opposite = 9; Adjacent = 1$

$Hypotenuse =\sqrt{82}$

Solving (a):

$\sec^2(\theta)$

This is calculated as:

$\sec^2(\theta) = (\sec(\theta))^2$

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

Where:

$\cos(\theta) = \frac{Adjacent}{Hypotenuse}$

$\cos(\theta) = \frac{1}{\sqrt{82}}$

So:

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

$\sec^2(\theta) = (\frac{1}{\frac{1}{\sqrt{82}}})^2$

$\sec^2(\theta) = (\sqrt{82})^2$

$\sec^2(\theta) = 82$

Solving (b):

$\cot(\theta)$

This is calculated as:

$\cot(\theta) = \frac{1}{\tan(\theta)}$

Where:

$\tan(\theta) = 9$ ---- given

So:

$\cot(\theta) = \frac{1}{\tan(\theta)}$

$\cot(\theta) = \frac{1}{9}$

Solving (c):

$\cot(\frac{\pi}{2} - \theta)$

In trigonometry:

$\cot(\frac{\pi}{2} - \theta) = \tan(\theta)$

Hence:

$\cot(\frac{\pi}{2} - \theta) = 9$

Solving (d):

$\csc^2(\theta)$

This is calculated as:

$\csc^2(\theta) = (\csc(\theta))^2$

$\csc^2(\theta) = (\frac{1}{\sin(\theta)})^2$

Where:

$\sin(\theta) = \frac{Opposite}{Hypotenuse}$

$\sin(\theta) = \frac{9}{\sqrt{82}}$

So:

$\csc^2(\theta) = (\frac{1}{\frac{9}{\sqrt{82}}})^2$

$\csc^2(\theta) = (\frac{\sqrt{82}}{9})^2$

$\csc^2(\theta) = \frac{82}{81}$

4 0

3 years ago

Which equation has the solution x = 3?

arsen [322]

Well, let's first solve each equation:

1.) -4x + 6 - 3x = 12 - 2x - 3x

To start, combine each like-term on each side of the equal sign (The numbers with variables in-common // the numbers alike on the same side of the equal sign):

-7x + 6 = 12 - 5x

Now, we get the two terms with variables attached to them, on the same side, so, we do the opposite of subtraction, which is, addition:

-7x + 6 = 12 - 5x
+5x +5x
_____________
-2x + 6 = 12

Next, you do the opposite of addition, which is, subtraction, and, subtract 6 from both sides:

-2x + 6 = 12
-6 -6
____________
-2x = 6

Finally, divide by -2 on each side, to find out what the value of 'x' is:

-2x = 6
÷-2 ÷-2
________
x = -3

So, the answer is not 'A.'
_________________________________________

Now, we test out the rest of the equations, the exact same way:

2.) 4x + 6 + 3x = 12 + 2x + 3x

Combine your like-terms, on each side of the equal sign:

7x + 6 = 12 + 5x

Now, get both terms, with the variable, 'x,' to the same side, and, to do that, do the opposite of addition, which is, subtraction:

7x + 6 = 12 + 5x
-5x -5x
______________
2x + 6 = 12

Next, subtract 6 from both sides:

2x + 6 = 12
-6 -6
__________
2x = 6

Finally, divide by 2, on both sides:

2x = 6
÷2 ÷2
__________
x = 3

So, the answer is 'B.'
_________________________________________

3.) 4x + 6 - 3x = 12 - 2x - 3x

Again, we combine the like-terms, on both sides of the equal sign:

x + 6 = 12 - 5x

Now, we get both terms with the variable 'x,' to the same side, and, the opposite of subtraction, is addition, so, we're going to add 5x to both sides:

x + 6 = 12 - 5x
+ 5x + 5x
______________
6x + 6 = 12

Now, we subtract 6 from each side, because, the opposite of addition, is subtraction:

6x + 6 = 12
- 6 - 6
_____________
6x = 6

Now, divide by 6, on both sides:

6x = 6
÷ 6 ÷ 6
_____________
x = 1

So, the answer is not 'C.'
_________________________________________

4.) 4x + 6 - 3x = 12x + 2x + 3x

First, we combine the like-terms:

x + 6 = 17x

Next, we get both terms, with the variable, 'x,' to the same side:

x + 6 = 17x
-x -x
_____________
6 = 16x

Now, divide by 16, on both sides:

X = 3/8

So, 'D,' is not the answer.
_______________________

The answer is, 'B.'

I hope this helps!

8 0

3 years ago

HELP ME PLEASE ECPLAIN WHY

stiv31 [10]

Answer:

A≈110.11

using formula 1/4 $\sqrt5(5+2\sqrt5)a2$

Step-by-step explanation:

8 0

3 years ago