Find 3 consecutive numbers where the product of the smaller two numbers in 19 less than the square of the largest number?

Answers

Answer 1

Answer: Answer is 5, 6, & 7

x = smallest number
y = x + 1
z = x + 2

(x)(y) = z^2 - 19
(x)(x+1) = (x + 2)^2 - 19
(x^2 + x) = (x^2 + 4x + 4) - 19
x^2 + x = x^2 + 4x + 4 - 19

x^2 term drops out from both sides

x = 4x + -15
15 = 4x - x
15 = 3x
15/3 = x
x = 5
y = x + 1 = 6
z = x + 2 = 7

Confirm by substituting back in for the variables:
(x)(y) = z^2 - 19
(5)(6) = (7)^2 - 19
30 = 49 - 19
30 = 30 [OK]

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David invested $220 in a savings account that offers a 3% return on the investment. How many years will the value of David's investment will reach at least $400 ?

Answers

FV = PV ( 1 + i ) ^t
FV = $400, PV = $220, i = 3% = 0.03
400 = 220 * ( 1 + 0.03 ) ^t
( 1 + 0.03 ) ^t = 400 : 220 = 1.818181
t = log ( 1.03 ) 1.81818
t = 20
After 20 years his investment will reach at least $400.

Answer:

t=20

Step-by-step explanation:

Which expression is equivalent to 15a^9b^4 over 5a^5b?Assume the denominator does not equal 0.

A. 10a^4b^3
B. 3a^4b^4
C. 10a^4b^4
D. 3a^4b^3

Answers

If you would like to solve 15a^9b^4 / 5a^5b, you can calculate this using the following steps:

15a^9b^4 / 5a^5b = 3a^(9-5)b^(4-1) = 3a^4b^3

The correct result would be D. 3a^4b^3.

A chef cooked seven kilograms of mashed potatoes for a dinnerparty. If the guests only ate three-quarters of the amount he cooked,
how much did they eat?.....................plz hurry up

Answers

Answer:

Hence, the amount of potatoes they ate is:

$(21)/(4)kg=5.25kg$

Step-by-step explanation:

A chef cooked seven kilograms of mashed potatoes for a dinner

party.

Now it is given that:

If the guests only ate three-quarters of the amount he cooked,

We have to find the amount they ate?

( Three-quarters is an amount that is three out of four equal parts of something )

i.e. the guest ate:

3/4 of 7 kg of mashed potatoes.

which is given by:

$(3)/(4)* 7=(21)/(4)kg=5.25kg$

Hence, the amount of potatoes they ate is:

$(21)/(4)kg=5.25kg$

$7* (3)/(4) = (7*3)/(4) = (21)/(4) = (20+1)/(4) = (20)/(4) + (1)/(4) =5+ (1)/(4) =5.25$

The start of an arthmetic sequence is show Below. a) Work out the n term rule for this sequence. b) Work out the 30 term in this sequence. 4,13,22,31

Answers

Step-by-step explanation:

Each term is 9 more than the previous term....the common difference, d = 9

an = a1 + 9(n-1) where a1 is the first term = 4

this reduces to: an = 4 + 9n-9

an = 9n - 5

the 30th term is then a30 = 9(30) - 5 = 265

The sum of two numbers is 55 and the difference is 13 . What are the numbers?

Answers

21 and 34 are the numbers

The numbers are 21 and 34 because when you add them its 55 and subtract them its 13

What is: 3(7.5 + 2) + 4.6

Answers

Answer:

25.6

Step-by-step explanation:

3(7.5+2)+4.6

15+6+4.6

21+4.6

25.6

Not that hard.

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4⋅(tg(π−x)+ctg(π−x)+ctg(3π2−x))/ctg(π−x)

Which expressions have a value of 18? Choose all answers that are correct. A. –3 – 21 B. 7 – (–25) C. 34 – 16 D. –4 – (–22)