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3 years ago

There are 4 consecutive odd integers that sum to 120.

Mathematics

1 answer:

allsm [11]3 years ago

4 0

Answer:

27, 29, 31, 33

Step-by-step explanation:

Let x represent the smallest odd integer then...

x+2 represents the second

x+4 represents the third

x+6 represents the fourth

We can use this to set up an equation:

x+x+2+x+4+x+6=120

Combine like terms

4x+12=120

Subtract 12 from both sides

4x=108

Divide both sides by 2

x=27

The integers are 27, 29, 31, 33

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Which one of these formulas describes the following sequence?<br><br> 1,5,12,22,35

kati45 [8]

We can find a formula for nth term of the given sequence as follows:

1, 5, 12, 22, 35

The 1st differences between terms:

4, 7, 10, 13

The 2nd differences :

3, 3, 3

Since it takes two rounds of differences to arrive at a constant difference between terms, the nth term will be a 2nd degree polynomial of the form: $a n^2 + b n + c$ , where c is a constant. The coefficients a, b, and the constant c can be found.

We can form the following 3 equations with 3 unknowns a, b, c:

$1 = a\cdot1^2 + b\cdot1 + c\\5 = \cdot2^2 + b\cdot2 + c\\12 = a\cdot3^2 + b\cdot3 + c$

Solving for a, b, c, we get:

a = 3/2, b = -1/2, c = 0

Therefore, the nth term of the given sequence is:

$\boxed{ a_n = \dfrac{3}{2}n^2- \dfrac{1}{2} n}$

7 0

3 years ago

I need help asap pls and thank you ;)

olga55 [171]

Answer:

$\text{Length of AB is }\frac{ah}{a+h}$

Step-by-step explanation:

Given △KMN, ABCD is a square where KN=a, MP⊥KN, MP=h.

we have to find the length of AB.

Let the side of square i.e AB is x units.

As ADCB is a square ⇒ ∠CDN=90°⇒∠CDP=90°

⇒ CP||MP||AB

In ΔMNP and ΔCND

∠NCD=∠NMP (∵ corresponding angles)

∠NDC=∠NPM (∵ corresponding angles)

By AA similarity rule, ΔMNP~ΔCND

Also, ΔKAP~ΔKPM by similarity rule as above.

Hence, corresponding sides are in proportion

$\frac{ND}{NP}=\frac{CD}{MP} \thinspace\thinspace and\thinspace\thinspace \frac{KA}{KP}=\frac{AB}{PM} \\\\\frac{ND}{NP}=\frac{x}{h} \thinspace\thinspace and\thinspace\thinspace \frac{KA}{KP}=\frac{x}{h}\\\\\frac{NP}{ND}=\frac{h}{x} \thinspace\thinspace and\thinspace\thinspace \frac{KP}{KA}=\frac{h}{x}\\\\\frac{PD}{ND}=\frac{h}{x}-1 \thinspace\thinspace and\thinspace\thinspace \frac{AP}{KA}=\frac{h}{x}-1\\$