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3 years ago

Priyanka and Ethan were asked to find an explicit formula for the sequence -3,-14,-25,-36,...

Mathematics

1 answer:

irga5000 [103]3 years ago

3 0

Answer:

$a_{n}$ = 8 - 11n

Step-by-step explanation:

These are the terms of an arithmetic sequence with n th term

$a_{n}$ = a + (n - 1)d

where a is the first term and d the common difference

here a = - 3 and

d = - 14 - (- 3) = - 14 + 3 = -11, thus

$a_{n}$ = - 3 - 11(n - 1)

= - 3 - 11n + 11

= 8 - 11n

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Since BC is parallel to DE, triangles ABC and ADE are similar. What are the lengths of the unknown sides? It would be a great he

bija089 [108]

Answer: AC= 10 cm and CE= 5 cm

Step-by-step explanation:

In the given picture, Δ ADE is a right triangle

∴ By Pythagoras theorem,

$AD^2+DE^2=AE^2\\\Rightarrow\ (8+4)^2+9^2=AE^2\\\Rightarrow\ AE^2=12^2+9^2\\\Rightarrow\ AE^2=144+81=225\\\Rightarrow\ AE=15\ cm$

Since triangles ABC and ADE are similar and corresponding sides of similar triangles are proportional therefore,

$\frac{AB}{AC}=\frac{AD}{AE}\\\Rightarrow\frac{8}{AC}=\frac{12}{15}\\\Rightarrow\ AC=\frac{8\times15}{12}\\\Rightarrow\ AC=10\ cm$

Now, AE=AC+CE

⇒CE=AE-AC

⇒CE=15-10=5 cm

4 0

3 years ago

triangle QRS is an equilateral triangle. If QR is seventeen more than twice x, RS is 19 less than six times x, and QS is one les

koban [17]

Value of x is 9 and measure of each side is 35 units.

<u>SOLUTION: </u>

Given, Triangle QRS is an equilateral triangle.

QR is seventeen more than twice x, $\rightarrow QR = 17 + 2x$

RS is 19 less than six times x, $\rightarrow RS = 6x-19$

And QS is one less four times x, $\rightarrow QS = 4x-1$

We have to find x and measure of each side.

Now, we know that, sides of equilateral triangle are equal,

Then $QR = QS \rightarrow 17 + 2x = 4x-1 \rightarrow 4x-2x = 17 + 1 \rightarrow 2x = 18 \rightarrow x = 9$

So, value of x is 9.

$\begin{array}{l}{\text { Now, } \mathrm{QR}=17+2(9)=17+18=35} \\\\ {\mathrm{RS}=6(9)-19=54-19=35} \\\\ {\mathrm{QS}=4(9)-1=36-1=35}\end{array}$

Hence, value of x is 9 and measure of each side is 35.

5 0

3 years ago

What are the solutions to (x+3)(x-4)=0?

marishachu [46]

Answer:

-3, 4

Step-by-step explanation:

(x+3)(x-4)=0

Therefore, x + 3 = 0 and x - 4 = 0

so, x = -3 and x = 4

6 0

3 years ago

What is a formula for the nth term of the given sequence?<br> 180, -240,320...

Semmy [17]

Answer:

Tn=T1+(n-1)*d

Step-by-step explanation:

Tn is the nth term

T1 is the first term of the sequence

n is the nth term as well

d is the common difference

8 0

3 years ago

Which ordered pair is the reflection of (5,-8) across the x axis and the y axis?

Lerok [7]

The ordered pair would be (-5,8)

3 0

3 years ago

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