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3 years ago

Construct the graph of the equation given by solving for the intercepts. Show all of the steps in finding the

Mathematics

1 answer:

Ivenika [448]3 years ago

3 0

answer

x, y - intercepts are (0, -1) and (-4, 0)

Step-by-step explanation:

put x and y = 0 respectively in given equation to get intercepts

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$1500 is invested at a rate of 3% compounded monthly. Write a compound interest function to model this situation. Then find the

Marianna [84]

Answer:

Equation: $F=1500(1.0025)^{12t}$

The balance after 5 years is: $1742.43

Step-by-step explanation:

This is a compound growth problem . THe formula is:

$F=P(1+\frac{r}{n})^{nt}$

Where

F is future amount

P is present amount

r is rate of interest, annually

n is the number of compounding per year

t is the time in years

Given:

P = 1500

r = 0.03

n = 12 (compounded monthly means 12 times a year)

The compound interest formula modelled by the variables is:

$F=1500(1+\frac{0.03}{12})^{12t}\\F=1500(1.0025)^{12t}$

Now, we want balance after 5 years, so t = 5, substituting, we get:

$F=1500(1.0025)^{12t}\\F=1500(1.0025)^{12*5}\\F=1500(1.0025)^{60}\\F=1742.43$

The balance after 5 years is: $1742.43

3 0

3 years ago

What is 1/8 divided by4

mixer [17]

1/8 ÷ 4 =
1/8 × 1/4 = 1/32

Multiply the reciprocal

6 0

3 years ago

1. What are the first five terms of the sequence given by the formula an = 5n + 1?

Dvinal [7]

The correct answers are:

(1) 6, 11, 16, 21, 26 (Option B)

(2) $~a_1 = 8$ ; $~a_n = a_{n-1} - 2~$ (Option A)

(3) $~a_n = -2 + 3(n-1)~~~~$ (Option D)

Explanations:

(1) Given Sequence:

$a_n = 5n + 1$

Now in order to find the first 5 terms, we need to put n=1,2,3,4,5 in the above sequence and solve.

For n=1: $a_1 = 5(1) + 1 = 6$

For n=2: $a_2 = 5(2) + 1 = 11$

For n=3: $a_3 = 5(3) + 1 = 16$

For n=4: $a_4 = 5(4) + 1 = 21$

For n=5: $a_5 = 5(5) + 1 = 26$

Hence, the first five terms are: 6, 11, 16, 21, 26 (Option B)

(2) Given Sequence:

8, 6, 4, 2, …

Now to find the recursive definition, we need to adopt trial-and-error approach.

As, $a_1 = 8$ (meaning the first element of the sequence is 8), the second or nth value of the sequence can be found by using the following formula:

$a_n = a_{n-1} - d$ --- (1)

Where, n = the index of the number in a sequence

d = difference between two consecutive numbers = 8-6 = 2

Now,

The second number of the sequence has to be 6 by using (1). Put n = 2 and d = 2 in (1):

$a_2 = a_{2-1} - 2$

$a_2 = a_{1} - 2$

Since $a_1 = 8$ , therefore,

$a_2 = 8 - 2 = 6$ (correct)

Hence the correct answer is $a_1 = 8$ ; $~a_n = a_{n-1} - 2~$ (Option A)

(3) Given Sequence:

−2, 1, 4, 7, …

To find the explicit definition, use the following formula:

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

Where,

$a_n = nth~term~of~the~sequence \\a_1 = 1st~term~of~the~sequence = -2 \\d = common~difference = 4-1 = 7-4 = 3 \\n = index~of~a~number~in~a~sequence \\$

Plug in the values in (X):

(X)=> $a_n = -2 + (n-1)*3~~~~$ (Option D)

3 0

3 years ago

Read 2 more answers

Markers are sold in boxes packs or as single markers each box has 10 packs each pack has 10 markers

KatRina [158]

100 markers per box

10x10

10- one pack

10- packs in a box

3 0

3 years ago

Read 2 more answers

Four milliliters of ink A is added to 10 milliliters of ink B, forming a mixture of inks. Ink A contains 10% blue pigment. Ink B

deff fn [24]

The answer is 45%

1. Calculate how many ml of blue pigment are in 4ml of ink A if it contains 10% blue pigment:
4 ml is 100%
a ml = 10%
4 ml : 100% = a : 10%
a = 4 ml * 10% : 100% = 0.4 ml

2. Calculate how many ml of blue pigment are in 10ml of ink A if it contains x% blue pigment:
10 ml is 100%
b ml = x%
10 ml : 100% = b : x%
b = 10 ml * x% : 100% = x/10 ml

3. 2. Calculate how many ml of blue pigment are in 14ml (because Four milliliters of ink A is added to 10 milliliters of ink B) of total mixture if it contains 35% blue pigment:
14 ml is 100%
t ml = 35%
14 ml : 100% = t : 35%
t = 14 ml * 35% : 100% = 4.9 ml

4. What percentage of blue pigment is in the mixture of the two inks:
a + b = t
0.4 + x/10 = 4.9
x/10 = 4.9 - 0.4
x/10 = 4.5
x = 4.5 * 10 = 45

3 0

3 years ago

Read 2 more answers