2 years ago

What are two consecutive numbers whose cubes differ by 169

Mathematics

1 answer:

maxonik [38]2 years ago

4 0

8 and 9

9^3-8^3
729-512
=169

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△ACD∼△BED What is the value of x?

slega [8]

Answer:

C. 5

Step-by-step explanation:

Triangle BED is enlarged by scale factor 4.

(25-x)/4 = x

Multiply both sides by 4.

25-x = 4x

Add x on both sides.

25 = 5x

Divide both sides by 5.

5 = x

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2 years ago

The roots of x2 -( ) +34 are 5 -/+3i

asambeis [7]

Answer: 10

Step-by-step explanation:

Vieta's formulas :

5 - 3i + 5 + 3i = b ⇒ b =10

Now, we have the equation:

x² -10x + 34 = 0

Mark me brainliest

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2 years ago

Given triangle ABC with coordinates A(−6, 4), B(−6, 1), and C(−8, 0), and its image A′B′C′ with A′(−2, 0), B′(−5, 0), and C′(−6,

Zinaida [17]

Answer:

The line of reflection is at y = x+6.

Step-by-step explanation:

The perpendicular bisector of AA' is a line with slope 1 through the midpoint of AA', which is (-4, 2). In point-slope form, the equation is ...

y = 1(x +4) +2

y = x + 6 . . . . . . . line of reflection

6 0

3 years ago

18. Determine the common difference, the fifth term, and the sum of the first 100 terms of the following sequence:

Ksenya-84 [330]

$a_1=1,\ a_2=2.5,\ a_3=4,\ a_4=5.5,\ ...\\\\a_2-a_1=2.5-1=1.5\\a_3-a_2=4-2.5=1.5\\a_4-a_3=5.5-4=1.5\\a_{n+1}-a_n=1.5=constans\\\\\text{It's an arithmetic sequence with}\\a_1=1,\ \boxed{d=1.5}\\\\a_n=a_1+(n-1)d\to a_n=1+(n-1)(1.5)=1+1.5n-1.5\\\\a_n=1.5n-0.5\\\\a_5=1.5(5)-0.5=7.5-0.5=7\\\boxed{a_5=7}\\\\\text{The formula of a Sum of the First n Terms of an Arithmetric Sequence:}\\\\S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n\\\\\text{We have:}\\a_1=1,\ d=1.5,\ n=100\\\\\text{Substitute}$

$S_{100}=\dfrac{(2)(1)+(100-1)(1.5)}{2}\cdot100=\dfrac{2+(99)(1.5)}{1}\cdot50\\\\=(2+148.5)\cdot50=150.5\cdot50=7,525\\\\\boxed{S_{100}=7,525}\\\\Answer:\\the\ common\ difference:\ d=1.5\\the\ fifth\ term:\ a_5=7\\the\ sum\ of\ first\ 100\ terms:\ S_{100}=7,525$

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2 years ago

Geraldine is picking a four-digit password by using the digits 0 through 9. She can use each digit only once. How many different

BabaBlast [244]

Answer:

5040 different combinations

Step-by-step explanation:

0-9 = 10 numbers

1st digit can be 1 0f 10

2nd digit can be 1 of 9

3rd digit can be 1 of 8

4th digit can be 1 of 7

10×9×8×7=5040

5 0

2 years ago

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