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3 years ago

Which is an equation for the nth term of the sequence?

Mathematics

2 answers:

Crank3 years ago

6 0

Answer: The correct option is (B) $a_n=3n+9.$

Step-by-step explanation: We are given to select the equation that represents the nth term of the following sequence :

12, 15, 18, 21, . . .

We see that

the given sequence is an arithmetic one with first term a = 12 and common difference d given by

d = 15 - 12 = 18 - 15 = 21 - 18 = . . . =3.

We know that

the nth term of an arithmetic sequence with first term a and common difference d is given by

$a_n=a+(n-1)d.$

Therefore, the nth term of the given sequence is

$a_n=a+(n-1)d=12+(n-1)\times3=12+3n-3=3n+9.$

Thus, the required nth term of the given sequence is $a_n=3n+9.$

Option (B) is CORRECT.

bulgar [2K]3 years ago

5 0

The answer is a I think

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The hypotenuse of an isosceles right triangle is centimeters longer than either of its legs. Find the exact length of each side.

Varvara68 [4.7K]

Question

The hypotenuse of an isosceles right triangle is 11 centimeters longer than either of its legs. find the exact length of each side.

Answer:

$Hypotenuse:37.56$

$Other\ Legs: 26.56$

Step-by-step explanation:

Let the hypotenuse be y and the other legs be x.

So:

$y = 11 + x$

Required

Determine the exact dimension of the triangle

Using Pythagoras theorem;

$y^2 = x^2 + x^2$

$y^2 = 2x^2$

This gives:

$(11+x)^2 = 2x^2$

Open bracket

$121 + 22x + x^2= 2x^2$

Collect like terms

$2x^2 - x^2 -22x - 121 = 0$

$x^2 -22x - 121 = 0$

Using quadratic formula:

$x = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}$

$x = \frac{-(-22)\±\sqrt{(-22)^2 - 4*1*-121}}{2*1}$

$x = \frac{-(-22)\±\sqrt{968}}{2*1}$

$x = \frac{22\±31.11}{2}$

Split

$x = \frac{22+31.11}{2}\ or\ x = \frac{22-31.11}{2}\\$

$x = \frac{53.11}{2}\ or\ x = \frac{-9.11}{2}$

x can not be negative.

So:

$x = \frac{53.11}{2}$

$x = 26.56$

Recall that:

$y = 11 + x$

$y = 11 + 26.56$

$y = 37.56$

Hence, the dimensions are:

$Hypotenuse:37.56$

$Other\ Legs: 26.56$

6 0

3 years ago

What is Y=2x+5 y=3x-1 system by substitution

Bad White [126]

Answer:

x=6 , y=17

Step-by-step explanation

3x-1=2x+5

+1 -2x

x=6

plug in 6 for x to solve y

3 0

2 years ago

Solve the equation using the quadratic formula.<br> 4x2 – 12x +33 = 0

mixer [17]

Answer:

4x2–12x+33=0

Resta 4x

en los dos lados. Cualquier valor restado de cero da como resultado su valor negativo.

−12x+33=−4x

Resta 33 en los dos lados.

−12x=−4x

−33

Divide los dos lados por −12.

−12

−12x

−12

−4x

−33

Al dividir por −12, se deshace la multiplicación por −12.

−12

−4x

−33

Divide −4x

−33 por −12.

Resolver para x_2

=3x−

Step-by-step explanation:

8 0

2 years ago

A plane is approaching an aircraft carrier at 25° angle of elevation from 3.2 miles away how far above sea level is the plane

s2008m [1.1K]

Answer:

$Height\approx 1.35\ miles$

Step-by-step explanation:

The angle of elevation $=25\textdegree$

It is $3.2\ miles$ away from the point.

If we imagine a right triangle having an angle $25\textdegree$ .

Hypotenuse $=3.2$ , Opposite=Height from sea level $(h)$

$\sin 25=\frac{opposite}{hypotenuse}\\\\\sin 25=\frac{h}{3.2}\\\\h=3.2\times \sin 25\\\\h=3.2\times 0.4226\\\\h=1.3524\approx 1.35\ miles$

8 0

3 years ago

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Help what do I do do i just write y-3x+5 or solve it

Rina8888 [55]

Answer:

y=-3x+5

Step-by-step explanation: Yes you have it correct. The question is asking for you to put it into an equation that fits the slope and y-intercept which is slope-intercept form. Additional note, when you have a problem like this and it doesn't say what type of equation form to put it in, put it in slope-intercept form for simplicity's sake.

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2 years ago

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