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3 years ago

Two sets of three consecutive integers have a property that the product of the larger two is

Mathematics

1 answer:

skelet666 [1.2K]3 years ago

5 0

Answer:

{1, 2, 3}, {3, 4, 5}

Step-by-step explanation:

Write expressions for three consecutive integers: n, n + 1, n + 2.

Set up an equation for the verbal description: the product (mulitplication) of the two larger integers (the last two) is one less than 7 times the smallest (the first one).

(n + 1)(n + 2) = 7n - 1

Multiply (FOIL) the left side.

n^2 + 3n + 2 = 7n - 1

Subtract 7n and subtract 1 to make the right side 0.

n^2 - 4n + 3 = 0

Factor.

(n - 1)(n - 3) = 0

Set the two factors equal to 0

n - 1 = 0, n - 3 = 0

Solve for n.

n = 1, n = 3

One set of integers begins with 1, so it's {1, 2, 3}.

The other set begins with 3, so it's {3, 4, 5}

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Answer: 3 7/12 (three and seven twelfths

Step-by-step explanation:

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2 years ago

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Assume that y varies directly with x. If y = -5 when

steposvetlana [31]

Answer:

Thus, the value of x = -36 when y = 15

Step-by-step explanation:

We know that if y varies directly with x, we can express the relationship such as

y ∝ x

y = kx

k = y/x

where 'k' is called constant of variation.

Given

y = -5

x = 12

Using the equation

k = y/x = -5/12

Thus, the value of k = -5/12

Finding x when y = 15

y = 15

k = -5/12

substituting y = 15 and k = -5/12 in the equation

y = kx

15 = -5/12 (x)

15×12 = -5x

180 = -5x

divding both sides by -5

-5x/-5 = 180/-5

x = -36

Thus, the value of x = -36 when y = 15

8 0

3 years ago

John, Sally, and Natalie would all like to save some money. John decides that it

brilliants [131]

Answer:

Part 1) John’s situation is modeled by a linear equation (see the explanation)

Part 2) $y=100x+300$

Part 3) $\$12,300$

Part 4) $\$2,700$

Part 5) Is a exponential growth function

Part 6) $A=6,000(1.07)^{t}$

Part 7) $\$11,802.91$

Part 8) $\$6,869.40$

Part 9) Is a exponential growth function

Part 10) $A=5,000(e)^{0.10t}$ or $A=5,000(1.1052)^{t}$

Part 11) $\$13,591.41$

Part 12) $\$6,107.01$

Part 13) Natalie has the most money after 10 years

Part 14) Sally has the most money after 2 years

Step-by-step explanation:

Part 1) What type of equation models John’s situation?

Let

y ----> the total money saved in a jar

x ---> the time in months

The linear equation in slope intercept form

y=mx+b

The slope is equal to

$m=\$100\ per\ month$

The y-intercept or initial value is

$b=\$300$

$y=100x+300$

therefore

John’s situation is modeled by a linear equation

Part 2) Write the model equation for John’s situation

see part 1)

Part 3) How much money will John have after 10 years?

Remember that

1 year is equal to 12 months

$10\ years=10(12)=120 months$

For x=120 months

substitute in the linear equation

$y=100(120)+300=\$12,300$

Part 4) How much money will John have after 2 years?

Remember that

1 year is equal to 12 months

$2\ years=2(12)=24\ months$

For x=24 months

substitute in the linear equation

$y=100(24)+300=\$2,700$

Part 5) What type of exponential model is Sally’s situation?

we know that

The compound interest formula is equal to

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

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$P=\$6,000\\ r=7\%=0.07\\n=1$

substitute in the formula above

$A=6,000(1+\frac{0.07}{1})^{1*t}\\ A=6,000(1.07)^{t}$

therefore

Is a exponential growth function

Part 6) Write the model equation for Sally’s situation

see the Part 5)

Part 7) How much money will Sally have after 10 years?

For t=10 years

substitute the value of t in the exponential growth function

$A=6,000(1.07)^{10}=\$11,802.91$

Part 8) How much money will Sally have after 2 years?

For t=2 years

substitute the value of t in the exponential growth function

$A=6,000(1.07)^{2}=\$6,869.40$

Part 9) What type of exponential model is Natalie’s situation?

we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$P=\$5,000\\r=10\%=0.10$

substitute in the formula above

$A=5,000(e)^{0.10t}$

Applying property of exponents

$A=5,000(1.1052)^{t}$

therefore

Is a exponential growth function

Part 10) Write the model equation for Natalie’s situation

$A=5,000(e)^{0.10t}$ or $A=5,000(1.1052)^{t}$

see Part 9)

Part 11) How much money will Natalie have after 10 years?

For t=10 years

substitute

$A=5,000(e)^{0.10*10}=\$13,591.41$

Part 12) How much money will Natalie have after 2 years?

For t=2 years

substitute

$A=5,000(e)^{0.10*2}=\$6,107.01$

Part 13) Who will have the most money after 10 years?

Compare the final investment after 10 years of John, Sally, and Natalie

Natalie has the most money after 10 years

Part 14) Who will have the most money after 2 years?

Compare the final investment after 2 years of John, Sally, and Natalie

Sally has the most money after 2 years

3 0

3 years ago

The picture below shows a box sliding down a ramp:

algol [13]

Answer:

11.3 ft

Step-by-step explanation:

sin = opp/hyp

hyp = opp/sin

AC = 10/sin62

Use calculator

AC = 11.325700506890392

11.3 ft

8 0

3 years ago

Please show your work, and have a good day :)

fomenos

Answer:

273x

Step-by-step explanation:

-7x(-8²+25)

8²=64

-7x(-64+25)

-64+25=-39

-7x(-39)

-7×-39=273

273x

7 0

2 years ago

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