Find the value of 4b for b = 1/2.

Answer:

[tex]\left\lbrace\begin{aligned}& a_{1} = 7 \\ & a_{n+1} = a_{n} - 3 && \text{for $n \ge 1$}\end{aligned}\right.[/tex].

Step-by-step explanation:

An arithmetic sequence could be defined using only two pieces of information:

The arithmetic sequence in this question is given in the explicit form, [tex]a_{n} = 7 - 3\, (n - 1)[/tex], which is equivalent to [tex]a_{n} = 7 + (-3)\, (n - 1)[/tex]. In the explicit form, [tex]a_{1}[/tex] and [tex]d[/tex] are described in the same equation:

[tex]\text{$a_{n} = a_{1} + d\, (n - 1)$ for $n \ge 1$}[/tex].

Compare [tex]a_{n} = a_{1} + d\, (n - 1)[/tex] with [tex]a_{n} = 7 + (-3)\, (n - 1)[/tex]: [tex]a_{1} = 7[/tex] whereas [tex]d = -3[/tex].

When an arithmetic sequence is given in the recursive form, [tex]a_{1}[/tex] and [tex]d[/tex] are specified in two separate equations:

[tex]\left\lbrace\begin{aligned}& a_{1} = a_{1} \\ & a_{n+1} = a_{n} + d && \text{for $n \ge 1$}\end{aligned}\right.[/tex].

In this question, it was found that [tex]a_{1} = 7[/tex] whereas [tex]d = -3[/tex]. Hence, the corresponding recursive formula for this arithmetic sequence would be:

[tex]\left\lbrace\begin{aligned}& a_{1} = 7 \\ & a_{n+1} = a_{n} + (-3) && \text{for $n \ge 1$}\end{aligned}\right.[/tex].

[tex]\\ \sf\longmapsto GI^2=FI(IH)[/tex]

[tex]\\ \sf\longmapsto GI^2=6(12)[/tex]

[tex]\\ \sf\longmapsto GI^2=72[/tex]

[tex]\\ \sf\longmapsto GI=\sqrt{72}[/tex]

[tex]\\ \sf\longmapsto GI=8.22[/tex]

If FI = 6 and IH = 12. The length of GI = 8.22.

Given: FI = 6 and IH = 12

To estimate the length of GI

[tex]$\mathrm{Gl}^{2}[/tex] = FI (IH)

Simplifying the above equation, we get

[tex]$\mathrm{Gl}^{2}[/tex]= 6 (12)

Remove parentheses: (a) = a

Multiply the numbers then, we get

[tex]$6 \cdot 12=72$[/tex]

[tex]$\mathrm{Gl}^{2}[/tex] = 72

GI = [tex]$\sqrt{72}[/tex]

GI  = 8.22

Therefore, the length of GI = 8.22.

To learn more about triangles length

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Answer: 36 and 28

Step-by-step explanation:

x + x+2 = 74

2x = 72

x1 = 36

x2 = 28

Answer:

2 2/5.

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

90-80=10

10*2=20

20-2=18

Answer:

90-80 x 2-2 = 0

Step-by-step explanation:

Firstly. subtract 80 from 90 to get 10.

90-80= 10

Then subtract 2 from 2, to get 0.

2-2=0

Lastly, for your answer multiply 10 by 0 to get 0.

10 x 0 = 0

,  Hope this helps :)

Have a great day!!

Answer:

p^2 - p - 12

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:

[tex](p - 4)(p + 3) = {p}^{2} + 3p - 4p - 12 \\ = {p}^{2} - p - 12[/tex]

The quadratic equation that contains the three points is y = -x² + 3x + 40

A quadratic equation is in the form:

y = ax² + bx + c

At point (-4, 12):

12 = a(-4)² + b(-4) + c

16a - 4b + c = 12      (1)

At point (2, 42):

42 = a(2)² + b(2) + c

4a + 2b + c = 2      (2)

At point (3, 40):

40 = a(3)² + b(3) + c

9a + 3b + c = 40     (3)

Solving equation 1, 2, and 3 gives:

a = -1, b =3, c = 40

y = -x² + 3x + 40

Hence the quadratic equation is y = -x² + 3x + 40

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Answer:

Que?

Step-by-step explanation:

I don't speak Español

Answer:

(4,0)

Step-by-step explanation:

Both lines intersect, or cross, at one point on the graph, which is (4,0). Therefore, that point is a solution to the system of equations.

Hope this helps!

Answer: AB≅EF, ∠B≅∠E, BC≅DE

Step-by-step explanation:

AB and EF are both marked with one line, making them congruent.

The same goes for BC and DE since they are marked with two lines.

Angles B and E are congruent because of the marking that is specified in both figures.

6*1/3=6/3=2 hours

hope it helped

Answer:

Step-by-step explanation:

Prove that 52n − 1 is divisible by 8 for all n ∈ N.

Solution

To prove by induction, we must

1. Show it is true for n = 1

2. Assume true for n and prove it is true for n + 1.

Let P(n) be the statement 52n − 1 is divisible by 8.

When n = 1, 52 − 1 = 24, which is divisible by 8.

This proves P(1).

Suppose that P(n) is true, i.e., 52n − 1 is divisible by 8.

Then 52(n+1) − 1 = 52

· 5

2n − 1 = 52

(52n − 1) + (52 − 1).

Note that 52n −1 is divisible by 8 using P(n) and also 52 −1 = 24 is divisible

by 8. Thus we have proved that P(n + 1) is true.

We conclude that P(n) is true for all n ∈ N.

Answer:

B ≤ 24

Step-by-step explanation:

Answer:

Cube

Step-by-step explanation:

Answer:

360$

Step-by-step explanation:

you multiply I think?

Is there a answer D?

The hight increases 2.5 inches per second.

Answer:

The answer is the height of the water increases 2.5 inches per second.

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

85%

Step-by-step explanation:

68 divided by 80 is equal to 68/80.

Divide top and bottom by 4 to get 17/20.

17 divided by 20 is 85%

Answer:

x is greater than or equal to 0.

Step-by-step explanation:

The domain is just your X value. In contrast, the range is your Y value. Since we start at and include 0 on the X axis, we continue forever from there. Therefore, X is greater than or equal to 0.

Answer:

The dimensions are 18m by 18m

Step-by-step explanation:

Since the problem says the floor is square, we know that all 4 sides are equal. The area for a square is one side squared. Since we do not have the actual length per side, we write the following formula: x^2= 324.

From there, we simply take the square root to figure out that one side is 18 meters. Once we know one side, we know all 4 because a square has equal sides. Therefore, the dimensions of the floor are 18m x 18m. I hope this helps!

[tex]\\ \sf\longmapsto x^2-4x-5=0[/tex]

[tex]\\ \sf\longmapsto x^2-5x+x-5=0[/tex]

[tex]\\ \sf\longmapsto x(x-5)+1(x-5)=0[/tex]

[tex]\\ \sf\longmapsto (x-5)(x+1)=0[/tex]

[tex]\\ \sf\longmapsto x=5\:or\:x=-1[/tex]

Solution is (-1,0) and (5,0)

Graph attached.

Spare way:-

Use quadratic formula .

[tex]\\ \sf\longmapsto x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(1)(-5)}}{2(1)}[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{4\pm \sqrt{16+20}}{2}[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{4\pm 6}{2}[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{10}{2}\:or\:\dfrac{-2}{2}[/tex]

[tex]\\ \sf\longmapsto x=5\:or\:-1[/tex]

[tex]x {}^{2} - 4x - 5 = 0 \\ x {}^{2} + x - 5x - 5 = 0 \\ x(x + 1) - 5(x + 1) = 0 \\ (x + 1)(x - 5) = 0 \\ x + 1 = 0 \\ x - 5 = 0 \\ x = - 1 \\ x = 5[/tex]

Answer: 6

Step-by-step explanation:

Answer: Parallel

Step-by-step explanation:

First find slope.

Line f: [tex]\frac{10-7}{3-8} =-3/5[/tex]

Line g: [tex]\frac{4-7}{10-5}=-3/5[/tex]

Since the slopes are the same, the lines are parallel.

First we need to find the slope of each line

Slope of line f

(8 , 7)  (3 , 10)

[tex]slope = \frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]

[tex]slope = \frac{10-7}{3-8}[/tex]

[tex]slope = \frac{3}{-5}[/tex]

[tex]slope=-\frac{3}{5}[/tex]

Slope of line g

(5 , 7)  (10 , 4)

[tex]slope = \frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]

[tex]slope = \frac{4-7}{10-5}[/tex]

[tex]slope = \frac{-3}{5}[/tex]

[tex]slope=-\frac{3}{5}[/tex]

The two lines have the same slope therefore they are not perpendicular but instead parallel to each other.

Answer:

The answer is 12

Step-by-step explanation

6x2

Just multiply 6 by 12

Answer:   x = 41

Step-by-step explanation:

4x - 68 = 2x + 14         [since alternate interior angles are equal]

4x - 2x = 14 + 68

       2x = 82

         x = 41

Answer:

x=41

Step-by-step explanation:

this problem can be solved using the alternate interior angles converse theorem, which states that if two coplanar lines are cut by a transversal so that a pair of alternate inerior angles are congruent, then the two lines are parallel.

4x-68=2x+14

2x-68=14 <- subtract 2x from both sides

2x=82 <- add 68 to both sides

x=41 <- divide both sides by 2

check:

4(41)-68=96

2(41)+14=96

Answer:

The area of the circle is 3,8550 mm

Step-by-step explanation:

Answer:

no it would be more

Step-by-step explanation:

3+3=6 so not 17 at all

Answer:

x > 17/2 - 3

Step-by-step explanation:

17 < 2(x+3)

17/2 < x+3

17/2 - 3 < x

deu ruim  aqui pq eu não sei

Step-by-step explanation:

Answer:

32 revolutions per minute(rpm)

Step-by-step explanation:

v inversely proportional to t

so if v increases t will decrease and vice versa

inverse equation is xy=k

xy=k

48×20= 960 (revolutions)

then you'll take k(960) and divide it by number of teeth

so..

960/30 = 32 revolutions per minute

Answer:

5(x+y) - 2x

this is the algebraic expression