State the various transformations applied to the base function to obtain a graph of the function g(x) = |x + 1| − 2.

Jasmine needs to make a bouquet of 24 yellow and orange carnations. The ratio of yellow carnations to all of the carnations must

aleksley [76]

Answer:

3

Step-by-step explanation:

just did it

4 0

3 years ago

The sum of the first n terms of an arithmetic series is n/2(3n-5). If the second and fourth terms of the arithmetic series are t

sergiy2304 [10]

Let a be the first term in the arithmetic sequence. Since it's arithmetic, consecutive terms in the sequence differ by a constant d, so the sequence is

a, a + d, a + 2d, a + 3d, …

with the n-th term, a + (n - 1)d.

The sum of the first n terms of this sequence is given:

$a + (a+d) + (a+2d) + \cdots + (a+(n-1)d) = \dfrac{n(3n-5)}2$

We can simplify the left side as

$\displaystyle \sum_{i=1}^n (a+(i-1)d) = (a-d)\sum_{i=1}^n1 + d\sum_{i=1}^ni = an+\dfrac{dn(n-1)}2$

so that

$an+\dfrac{dn(n-1)}2 = \dfrac{n(3n-5)}2$

or

$a+\dfrac{d(n-1)}2 = \dfrac{3n-5}2$

Let b be the first term in the geometric sequence. Consecutive terms in this sequence are scaled by a fixed factor r, so the sequence is

b, br, br ², br ³, …

with n-th term br ⁿ⁻¹.

The second arithmetic term is equal to the second geometric term, and the fourth arithmetic term is equal to the third geometric term, so

$\begin{cases}a+d = br \\\\ a+3d = br^2\end{cases}$

and it follows that

$\dfrac{br^2}{br} = r = \dfrac{a+3d}{a+d}$

From the earlier result, we then have

$n=7 \implies a+\dfrac{d(7-1)}2 = a+3d = \dfrac{3\cdot7-5}2 = 8$

and

$n=2 \implies a+\dfrac{d(2-1)}2 = a+d = \dfrac{3\cdot2-5}2 = \dfrac12$

so that

$r = \dfrac8{\frac12} = 16$

and since the second arithmetic and geometric terms are both 1/2, this means that

$br=16b=\dfrac12 \implies b = \dfrac1{32}$

The sum of the first 11 terms of the geometric sequence is

S = b + br + br ² + … + br ¹⁰

Multiply both sides by r :

rS = br + br ² + br ³ + … + br ¹¹

Subtract this from S, then solve for S :

S - rS = b - br ¹¹

(1 - r ) S = b (1 - r ¹¹)

S = b (1 - r ¹¹) / (1 - r )

Plug in b = 1/32 and r = 1/2 to get the sum :

$S = \dfrac1{32}\cdot\dfrac{1-\dfrac1{2^{11}}}{1-\dfrac12} = \boxed{\dfrac{2047}{32768}}$

6 0

3 years ago

A parabola opens upward. The parabola goes through the point (3, -1), and the vertex is at (2, -2). What are the values of h and

Korolek [52]

The value of a is 1/4 and the value of h and k is (2,-7/4)

<h3>What is a Parabola ?</h3>

A parabola is a u shaped curve. It is a plane curve whose all points are at a fixed distance form a point called focus.

(x-h)² = 4a(y-k)

It is given that the parabola goes through the point (3, -1), and the vertex is at (2, -2).

Therefore
(x -2)² = 4a(y +2)

The parabola passes through the point (3,-1)

(3-2)² = 4*a(-1+2)

1 = 4 a

a = 1/4

Now to determine the value of focus point , (h,k)

(h = 2)

k = - 2 +1/4 = -7/4

Therefore The value of a is 1/4 and the value of h and k is (2,-7/4)

To know more about Parabola

brainly.com/question/4074088

#SPJ1

7 0

2 years ago

When baking a cake, you have a choice of the following pans: a round cake pan that is 2 inches deep and has a 7 inch diameter a

ruslelena [56]

Round pan volume is:
3.14•r^2•h
D=7 so r=3.5 in
3.14• (3.5^2)•2 = 76.97 in^3

Rec. pan vol. is :
9•6•2= 108 in^3

Rec. Pan is larger because 108 in^3 is > 76.97 in^3 :) .

The icing that will be needed to frost the round cake pan is:
We need to find the surface area:
S.A= 3.14r^2 + 2 • 3.14•r • h .... 3.14 is the value of PI
So, S.A= 3.14• 3.5^2 + 6.28• 3.5• 2= 82.47 in^2 the icing that'll be needed to frost the round cake pan.

Icing that will be needed for the rec. cake pan is:

2•9•2=36 in^2
6•9•2= 108in^2
6•2= 12 in^2
S.A= 156 in^2 the icing needed to frost the rec. cake pan .... the S.A of all sides except the bottom one :).

Good luck ;-)

8 0

3 years ago

Laura tried to shade all the multiples of 12 on the hundred chart.

miskamm [114]

Answer:

D Laura shaded the factors instead of the multipls of 12

Step-by-step explanation:

The factors of 12 are 1, 2, 3, 4, 6, and 12, because each of those divides 12 without leaving a remainder

The multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144

4 0

2 years ago