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3 years ago

Graph the function. g(x)=-1/3(x+2) (x+8)

Mathematics

1 answer:

kolezko [41]3 years ago

4 0

After finding the vertex and axis of symmetry you get this.

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Find the tenth term in the following geometric sequence. 8, 4, 2, 1, . . .

Marrrta [24]

Answer:

c) 0.0156

Step-by-step explanation:

The general term a[n] of a geometric sequence is given in terms of the first term a[1] and common ratio r as ...

a[n] = a[1]r^(n-1)

The given sequence has an initial term of a[1]=8 and a common ratio of 4/8=1/2. Then the general term is ...

a[n] = 8(1/2)^(n-1)

The 10th term is then ...

a[10] = 8(1/2)^(10-1) = 8(1/2)^9 = 8/512

a[10] = 0.015625 ≈ 0.0156

7 0

3 years ago

Step-by-step explanation please<br> (Worth 3 marks)

atroni [7]

Answer:

62°

Step-by-step explanation:

180-118=62

62+62=124

180-124=56

118-56=62

5 0

3 years ago

Read 2 more answers

Determine the number of zeros of the polynomial function <br> F(x) = x^4 - x^7

Tresset [83]

Answer:

Step-by-step explanation:

Using fundamental theorem of algebra, there should be 7 roots, if you count multiplicity.

If you're only counting distinct roots, then there should be 4 roots.

5 0

2 years ago

Three numbers are in an arithmetic progression with a common difference of 6. if 4 is subtracted from the first number, 1 is sub

UkoKoshka [18]

Answer:

either of {-9.5, -3.5, 2.5} or {7, 13, 19}

Step-by-step explanation:

Let x represent the first number of the arithmetic sequence. Then the second number is x+6, and the third number is x+12. The geometric sequence is then ...

(x -4), (x +5), 3(x+9)

The common ratio is then ...

(x +5)/(x -4) = 3(x +9)/(x +5)

Cross-multiplying gives ...

(x +5)² = 3(x -4)(x +9)

x² +10x +25 = 3x² +15x -108 . . . . eliminate parentheses

0 = 2x² +5x -133 . . . . . . . . . . . . . . subtract the left side

0 = (2x +19)(x -7) . . . . . . . . . . . . . . factor

x = -9.5 . . or . . 7

The possible original three numbers are ...

{-9.5, -3.5, 2.5} . . or . . {7, 13, 19}

8 0

3 years ago

A rose garden Is formed by jolning a rectangle and a semicircle, as shown below. The rectangle Is 23 ft long and 14 ft wide.Find

Ratling [72]

Answer:

Area of the garden:

$\begin{equation*} 398.93\text{ ft}^2 \end{equation*}$

Explanation:

Given the below parameters;

Length of the rectangle(l) = 23 ft

Width of the rectangle(w) = 14 ft

Value of pi = 3.14

Since the width of the rectangle is 14 ft, so the diameter(d) of the semicircle is also 14 ft.

The radius(r) of the semicircle will now be;

$r=\frac{d}{2}=\frac{14}{2}=7\text{ ft}$

Let's now go ahead and determine the area of the semicircle using the below formula;

$A_{sc}=\frac{\pi r^2}{2}=\frac{3.14*\left(7\right)^2}{2}=\frac{3.14*49}{2}=\frac{153.86}{2}=76.93\text{ ft}^2$

Let's also determine the area of the rectangle;

$A_r=l*w=23*14=322\text{ ft}^2$

We can now determine the area of the garden by adding the area of the semicircle and that of the rectangle together;

$\begin{gathered} Area\text{ of the garden = Area of semi circle + Area of rectangle } \\ =76.93+322 \\ =398.93\text{ ft}^2 \end{gathered}$

Therefore, the area of the garden is 398.93 ft^2

8 0

1 year ago