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3 years ago

Find an explicit function rule for the sequence -3, 3, 9, 15,.... Use the formula a(n) = a(1) + (n-1)d and simplify fully.

1 answer:

6 0

A(1) = - 3 ;
a(2) = a(1) + ( 2 - 1 )d ;
3 = -3 + d ;
d = 6 ;
a(3) = a(1) + ( 3 - 1)d;
9 = - 3 + 2d ;
12 = 2d ;
d = 6 ;
a(4) = a(1) + ( 4 - 1 )d ;
15 = -3 + 3d ;
18 = 3d ;
d = 6 ;
Then, a(n) = - 3 + ( n- 1 )6 ;
a(n) = - 3 + 6n - 6 ;
a(n) = 6n - 9 is an explicit functin rule for the sequence -3, 3, 9, 15, ...

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2 questions 90 points

saw5 [17]

Answer:

1) Volume of prism = $\frac{105}{8}ft^3=13.125ft^3$

2) Option B is the correct answer.

Explanation:

1) Volume of a prism is given by the expression, Volume V = Base area of prism x Height of prism.

Base area = $3\frac{1}{2} *2\frac{1}{2}=\frac{3*2+1}{2} *\frac{2*2+1}{2} =\frac{7}{2} *\frac{5}{2}=\frac{35}{4} ft^2$

Volume = $\frac{35}{4}*1\frac{1}{2} =\frac{35}{4}*\frac{1*2+1}{2}=\frac{35}{4}*\frac{3}{2}=\frac{105}{8}ft^3$

Volume of prism = $\frac{105}{8}ft^3=13.125ft^3$

2) Volume of a prism is given by the expression, Volume V = Base area of prism x Height of prism.

Base area = $4\frac{1}{4} *3in^2$

Volume = $4\frac{1}{4} *3*1\frac{1}{4}in^3$

Option B is the correct answer.

5 0

3 years ago

Can someone help this

Zanzabum

Answer:

Step-by-step explanation:

The common factor is the largest number that goes into both of those numbers evenly. We do this by finding the prime factorization of each:

25: 5,5

35: 5,7

The common number to both is 5, so 5 is the common factor of both the numerator and denominator.

3 0

3 years ago

Solve for all three unknowns

Rina8888 [55]

Answer:

x= 32.3 (3 s.f.)

θ= 21.8° (1 d.p.)

α= 68.2° (1 d.p.)

Step-by-step explanation:

Applying Pythagoras' Theorem,

x²= 12² +30²

x²= 144 +900

x²= 1044

Square root both sides:

$x = \sqrt{1044}$

x= 32.3 (3s.f.)

$\boxed{ \tanθ = \frac{opp}{adj} }$

$\tanθ = \frac{12}{30}$

$θ = \tan^{ - 1} ( \frac{12}{30} )$

θ= 21.801° (3 d.p.)

θ= 21.8° (1 d.p.)

$\tan\alpha = \frac{30}{12}$

$\alpha = \tan ^{ - 1} ( \frac{30}{12} )$

$\alpha$ = 68.2° (1 d.p.)

Alternatively,

α +θ +90°= 180° (∠ sum of triangle)

α +21.801° +90°= 180°

α +111.801°= 180°

α= 180° -111.801°

α= 68.199°

α= 68.2° (1 d.p.)

5 0

3 years ago

The boxes are shaped as right rectangular prisms. The larger box has a length of 24cm a width of 10 cm, and height of 30cm. The

irina1246 [14]

Answer:

900cm^2

Step-by-step explanation:

24, 10, 30 in half= 12, 5, 15 so, 12*5*15=900cm^2

5 0

4 years ago

A line passes through (2,4) and (-2,2). find the value of y if (6,y) lies on the same line

katrin2010 [14]

Answer:

y = 6, rendering the coordinate pair: (6,6)

Step-by-step explanation:

We start by writing the equation of the line that passes through two given points on the plane: $(x_1,y_1)$ and $(x_2,y_2)$ beginning with finding the slope of the segment that joints the points using the slope formula: $slope=\frac{y_2-y_1}{x_2-x_1}$

Let's call $(x_1,y_1)$ = (2,4), and $(x_2,y_2)$ = (-2,2). Then we have the formula for the slope:

$slope=\frac{y_2-y_1}{x_2-x_1}=\frac{2-4}{-2-2} =\frac{-2}{-4} =\frac{1}{2}$

Now that we have the slope of the line, we can find the actual equation of the line by using one of the given points, and the "point-slope" form of a line with slope "m" and going through a point $(x_0,y_0)$ - which in our case we defie as one of our given points, let's say (2, 4):

$y-y_0=m\,(x-x_0)\\y-4=\frac{1}{2} (x-2)\\y-4=\frac{1}{2} x-1\\y=\frac{1}{2} x-1+4\\y=\frac{1}{2} x+3$

now we find what is the "y" value in such line that corresponds to an x-value of "6" to complete the coordinate pair (6, ?). For such we simply evaluate the equation above at x = 6:

$y=\frac{1}{2} x+3\\y=\frac{1}{2} (6)+3\\y=3+3\\y=6$

Therefore, y must be "6".

7 0

3 years ago