All categories

3 years ago

Find the first, fourth, and eighth terms of the sequence.

1 answer:

6 0

$a(n)=-3\cdot2^{n}-1\\\\a_1=-3\cdot2^1-1=-3\cdot2-1=-6-1=-7\\a_4=-3\cdot2^4-1=-3\cdot16-1=-48-1=-49\\a_8=-3\cdot2^8-1=-3\cdot256-1=-768-1=-769\\\\if\ a(n)=-3\cdot2^{n-1}\ then\\\\a_1=-3\cdot2^{1-1}=-3\cdot2^0=-3\cdot1=-3\\a_4=-3\cdot2^{4-1}=-3\cdot2^3=-3\cdot8=-24\\a_8=-3\cdot2^{8-1}=-3\cdot2^7=-3\cdot128=-384$

You might be interested in

When a bakery opened this morning the ratio of pineapple muffins to the number of mango muffins was 3:2. After 144 pineapple muf

Elena L [17]

$3x-\ pineapple\\
2x-\ mango\\\\
after\ selling\ 144\ pineapple:\\
3y-\ pineapple\\
5y-\ mango\\\\
3x-144=3y\ \ | add\ 144\\
2x=5y\\\\
3x=3y+144\ \ \ | divide\ by\ 3\\
2x=5y\\\\
x=y+48\\2x=5y\\\\
2(y+48)=5y\\
2y+96=5y\ \ \ | subtract\ 2y\\
96=3y\ \ \ | divide\ by\ 3\\
32=y\\
x=32+48=80\\\\
There\ were\ 240\ pineapple\ muffins.
$

6 0

3 years ago

Find the area of the shape shown below. I reallly need help and do not put a unbelieable answer.

larisa [96]

Answer:

63/2 or 31.5

Step-by-step explanation:

we can split this shape into 2, a triangle and a rectangle

A triangle = bh/2 = 7*3*1/2 = 21/2

A rectangle = b*h = 3*7 = 21

21/2 + 21 = 63/2

3 0

3 years ago

Which series of transformations will not map figure H onto itself

7nadin3 [17]

Answer:

Step-by-step explanation:

Given a square with vertices at points (2,1), (1,2), (2,3) and (3,2).

Consider option A.

1st transformation $(x+0,y-2)$ will map vertices of the square into points

$(2,1)\rightarrow (2,-1);$
$(1,2)\rightarrow (1,0);$
$(2,3)\rightarrow (2,1);$
$(3,2)\rightarrow (3,0).$

2nd transformation = reflection over y = 1 has the rule (x,2-y). So,

$(2,-1)\rightarrow (2,3);$
$(1,0)\rightarrow (1,2);$
$(2,1)\rightarrow (2,1);$
$(3,0)\rightarrow (3,2)$

These points are exactly the vertices of the initial square.

Consider option B.

1st transformation $(x+2,y-0)$ will map vertices of the square into points

$(2,1)\rightarrow (4,1);$
$(1,2)\rightarrow (3,2);$
$(2,3)\rightarrow (4,3);$
$(3,2)\rightarrow (5,2).$

2nd transformation = reflection over x = 3 has the rule (6-x,y). So,

$(4,1)\rightarrow (2,1);$
$(3,2)\rightarrow (3,2);$
$(4,3)\rightarrow (2,3);$
$(5,2)\rightarrow (1,2)$

These points are exactly the vertices of the initial square.

Consider option C.

1st transformation $(x+3,y+3)$ will map vertices of the square into points

$(2,1)\rightarrow (5,4);$
$(1,2)\rightarrow (4,5);$
$(2,3)\rightarrow (5,6);$
$(3,2)\rightarrow (6,5).$

2nd transformation = reflection over y = -x + 7 will map vertices into points

$(5,4)\rightarrow (3,2);$
$(4,5)\rightarrow (2,3);$
$(5,6)\rightarrow (1,2);$
$(6,5)\rightarrow (2,1)$

These points are exactly the vertices of the initial square.

Consider option D.

1st transformation $(x-3,y-3)$ will map vertices of the square into points

$(2,1)\rightarrow (-1,-2);$
$(1,2)\rightarrow (-2,-1);$
$(2,3)\rightarrow (-1,0);$
$(3,2)\rightarrow (0,-1).$

2nd transformation = reflection over y = -x + 2 will map vertices into points

$(-1,-2)\rightarrow (4,3);$
$(-2,-1)\rightarrow (3,4);$
$(-1,0)\rightarrow (2,3);$
$(0,-1)\rightarrow (3,2)$

These points are not the vertices of the initial square.

5 0

3 years ago

You are gathering data in the store, recording which shirt is tried on the most. The data you gather is... A) bivariate B) categ

borishaifa [10]

Answer:

(D) Quantitative

Step-by-step explanation:

Bivariate data involves two types of variables. Categorical data will have a number of different categories. Continuous data usually includes a range of values so is likely to be in decimals. Quantitative data will be collected in this scenario as it will be calculated the number of times each shirt is tried on.

8 0

3 years ago

What is the length of s?

Serggg [28]

Answer:

Step-by-step explanation:

We will use trigonometry to solve this problem.

We see that the side provided is the hypotenuse and the side we are looking for is opposite to the angle provided. Thus, we will use sin since sin uses opposite/hypotenuse.

Now we solve.

sin45 = x/14

sin45 * 14 = x

x = 9.899494936611665

6 0

3 years ago