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3 years ago

QUESTION 4

Mathematics

1 answer:

Fantom [35]3 years ago

5 0

3, x, x+6 are the first 3 terms of G.P

common ratio is x/3=x+6/x

so we cross multiply x×x=3×x+6

×²= 3x+18 so we have x²-3x-18

(x-6)(x+3)=0

the possible value of x are 6 and -3

b) tenth term of the seauence

first of all the possible sequence are 3, 6, 12 and 3, -3, 3

but we need only the positive GP

so the common ratio of.the GP r is 6/3=2

the 10th term of a GP sequence is ar^10-1=ar^9

where a = first time

3×2^9=3×512=1536

the 10th term is 1536

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Help me PLZZZZZZZ!!!!!!

eduard

Answer:

25% decrease

Step-by-step explanation:

Take the original amount of books and subtract the new number of books

20 -15 = 5

Divide by the original amount of books

5/20 = .25

Multiply by 100%

25%

It is a decrease since the amount went down

25% decrease

7 0

3 years ago

Which of the following systems of linear equations has an infinite number of solutions?

arlik [135]

Answer:

{ y = 3x + 3

{ 3x - y = 3

(Just did the assignment 3/23/21)

8 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

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

$KA(\frac{h}{x}-1)=AP$

$ND(\frac{h}{x}-1)=PD$

Adding above two, we get

$(KA+ND)(\frac{h}{x}-1)=(AP+PD)$

⇒ $(KN-AD)=\frac{x}{(\frac{h}{x}-1)}$

⇒ $a-x=\frac{x}{(\frac{h}{x}-1)}$

⇒ $a-x=\frac{x^2}{h-x}$

⇒ $x^2=ah-ax-xh+x^2$

⇒ $x(h+a)=ah$

⇒ $x=\frac{ah}{a+h}$

3 0

3 years ago

Jason decided to look at new trucks. Jason found a used truck for 34,000 dollars. A new truck is 40,000 dollars so what percent

nexus9112 [7]

Answer:

Percent of rise of a new truck on a used truck = 15%

Step-by-step explanation:

Let x be the percentage of saved money if Jason buying a used truck.

Given:

Price of the used truck = $34,000

Price of the new truck = $40,000

We need to find the percent of rise Jason saves on a used truck rather than buying a new truck

Solution:

Using a percentage formula.

$percentage\ cost = \frac{(100-x)}{100}\times Original\ cost$

Substitute Percentage cost = 34,000 and Original cost = 40,000 in above formula.

$34000 = \frac{(100-x)}{100}\times 40000$

$34000 = (100-x)\times 400$ ( $\frac{40000}{100}=400$ )

Using cross multiplication rule.

$(100-x)=\frac{34000}{400}$

$85=100-x$

$x = 100-85$

x = 15%

Therefore, Jason used 15% rise of a new truck for a used truck.

6 0

3 years ago

What is the vertex of the parabola? A. (-1,0) B. (0,-3) C. (1,-4) D. (3,0)

-BARSIC- [3]

The vertex of a parabola is its highest or lowest point. Here, it is the lowest point, which happens right at the bottom of the U-shape—at (1, –4). Therefore, the answer is C.

5 0

3 years ago