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3 years ago

Jose has $2.50 in nickels and dimes in his jar. If he has 11 more nickels than dimes, how many dimes does he have?

1 answer:

5 0

Jose has $2.50 cents in total,
We need an equation to solve this. We will let d=dime.
dime=.10
nickel=.05

.10d + .05 (d + 11)=2.50

.10d + .05d + 0.55= 2.50

.15d + 0.55 = 2.50

.15d= 1.95

d= 13

There is 13 dimes. To get the nickels, you just add the 11 to 13 and you get 24 nickels.

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Verify cot x sec^4x=cotx +2tanx +tan^3x

Tanzania [10]

Answer:

See explanation

Step-by-step explanation:

We want to verify that:

$\cot(x) \: { \sec}^{4} x = \cot(x) + 2 \tan(x) + { \tan}^{3} x$

Verifying from left, we have

$\cot(x) \: { \sec}^{4} x = \cot(x) \: ( 1 + { \tan}^{2} x )^{2}$

Expand the perfect square in the right:

$\cot(x) \: { \sec}^{4} x = \cot(x) \: ( 1 + { 2\tan}^{2} x + { \tan}^{4} x)$

We expand to get:

$\cot(x) \: { \sec}^{4} x = \cot(x) \: + \cot(x){ 2\tan}^{2} x +\cot(x) { \tan}^{4} x$

We simplify to get:

$\cot(x) \: { \sec}^{4} x = \cot(x) \: + 2 \frac{ \cos(x) }{\sin(x) ) } \times \frac{{ \sin}^{2} x}{{ \cos}^{2} x} +\frac{ \cos(x) }{\sin(x) ) } \times \frac{{ \sin}^{4} x}{{ \cos}^{4} x}$

Cancel common factors:

$\cot(x) \: { \sec}^{4} x = \cot(x) \: + 2 \frac{{ \sin}x}{{ \cos}x} +\frac{{ \sin}^{3} x}{{ \cos}^{3} x}$

This finally gives:

$\cot(x) \: { \sec}^{4} x = \cot(x) + 2 \tan(x) + { \tan}^{3} x$

3 0

3 years ago

Tell whether the sequence is arithmetic. Justify your answer. If the sequence is arithmetic, write a recursive

navik [9.2K]

Answer:

The explicit formula

$a_n = 3 +0.25 (n-1)$

The recursive formula

$a_1 = 3$ for $n=1$

$a_n = a_ {(n-1)} +0.25$ if $n>1$

Step-by-step explanation:

If a sequence is arithmetical then the difference between any of its consecutive terms will be constant

3, 3.25, 3.5, 3.75,

$3.25-3 = 0.25\\\\3.5-3.25 = 0.25\\\\3.75 -3.5 = 0.25$

The difference between the consecutive terms remains constant so the sequence is arithmetic.

The explicit formula for an arithmetic sequence is:

$a_n = a_1 + d (n-1)$

Where d is the constant difference between the terms.

$d = 0.25$

$a_1$ is the first term of the sequence.

$a_1 = 3$

$a_n = 3 +0.25 (n-1)$

Finally, the recursive formula is:

$a_1 = 3\\\\a_n = a_ {(n-1)} +0.25$

8 0

2 years ago

3x + 3 − x + (−7) > 6 what is x

WARRIOR [948]

3x+3-x+(-7)>6

combine like terms on left side

2x-4>6

add 4 to both sides 2x>10

x=10/2 = 5

x>5

6 0

3 years ago

The result of subtracting 2 from its opposite is

belka [17]

It’s four because you subtract 2 minus negative 2

4 0

3 years ago

Read 2 more answers

In order to tell if a graph is a function it must

nikitadnepr [17]

You can use the vertical line test (the blue lines on the drawing) and if the other end or if any part of the line touches the blue line, then it isn’t a function.

5 0

2 years ago