Which of the following functions describes the sequence 4, –2, 1, –12, 14, . . .? A. f(1) = 4, f(n + 1) = –2f(n) for n ≥ 1 B. f(1) = 4, f(n + 1) = f(n) – 2 for n ≥ 1 C. f(1) = 4, f(n) = 12f(n + 1) for n > 1 D. f(1) = 4, f(n) = –12f(n – 1) for n > 1

m = 1/4 = slope

b = 3/4 = y intercept

===================================================

Explanation:

The goal is to solve for y.

Divide both sides by 4 and simplify like so

4y = x+3

4y/4 = (x+3)/4

y = (x+3)/4

y = x/4 + 3/4

y = (1/4)x + 3/4

This equation is in slope intercept form y = mx+b

m = 1/4 is the slope

b = 3/4 is the y intercept

The graph is a straight line that goes through (1,1) and (5,2)

A 200-degree angle is between 180 and 270 degrees, so the terminal side is in QIII.

Do the operation indicated for that quadrant. Subtract 180 degrees from the angle, which is 200 degrees.

You find that 200 – 180 = 20, so the reference angle is 20 degrees.

hope this helped!

o(*￣▽￣*)ブ

Answer:

31

Step-by-step explanation:

5---11

12---25

hmmm

isn't that jsut x * 2 + 1?

soooo

15 would be

15*2+1

which is 31

Answer:

31.

Step-by-step explanation:

5+5 = 10 + 1 = 11

12 + 12 = 24 +1 = 25

15 + 15 = 30 + 1 = 31

I don't know I tried to see if that was the pattern. It checks out math wise.

Answer:

You are just as likely to get a 2 as a 6

Step-by-step explanation:

There are six sides on a die 1,2,3,4,5,6

Assuming a fair normal die

P(2) = number of 2's / total = 1/6

P(6) = number of 6's / total = 1/6

You are just as likely to get a 2 as a 6

Answer:

B=45

The sum of the interior angle of a triangle is equal to 180

Therefore equate angle A, B and C to 180

then add them to get 135 + c=180

group like terms,135 crosse the equal sign to be negative

which is c=18p-135

c=45

==============================================

Explanation:

The x coordinates are -1 and -5. They add to -6. Which is then cut in half to -3

The y coordinates are -5 and 9. They add to 4. This is cut in half to 2.

The midpoint is therefore (-3, 2)

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A symbolic way to write this is if you had endpoints (a,b) and (c,d), then the midpoint is [tex]\left(\frac{a+c}{2}, \frac{b+d}{2}\right)[/tex]

Answer:

second option

Step-by-step explanation:

Given the sequence

7, 4, 1, - 2

There is a common difference d between consecutive terms, that is

d = 4 - 7 = 1 - 4 = - 2 - 1 = - 3

Thus to obtain any term in the sequence from the previous term, subtract 3

Thus

f(1) = 7 , f(n + 1) = f(n) - 3 for n ≥ 1

Answer:

45 yards and 176 yards

Step-by-step explanation:

Perimeter of a rectangular playing field = 2(Length + width)

P = 2(L+W)..................... Equation 1

From the question,

Let the width of the rectangular playing field = x yards,

The the Length = 4x-4 yards.

Given: P = 442 yards.

Substitute these values into equation 1

442 = 2(4x-4+x)

442/2 = 5x-4

221 = 5x-4

5x = 221+4

5x = 225

x = 225/5

x = 45 yards.

Width = 45 yards.

Length = (45×4)-4 yards = 176 yards

Hence the dimensions of the playing field are, 45 yards and 176 yards

Answer:

The width and height of the old 35-inch television are 28 inches and 21 inches, respectively.

Step-by-step explanation:

35-inch television is a television whose screen has an hypotenuse ([tex]l[/tex]) of 35 inches and the aspect ratio of 4 : 3 means that 4 inches width per each 3 inches height. And by Pythagorean Theorem:

[tex]r_{l} =\sqrt{r_{w}^{2}+r_{h}^{2}}[/tex]

Where:

[tex]r_{l}[/tex] - Hypotenuse rate, dimensionless.

[tex]r_{w}[/tex] - Width rate, dimensionless.

[tex]r_{h}[/tex] - Height rate, dimensionless.

If [tex]r_{w} = 4\,in[/tex] and [tex]r_{h} = 3\,in[/tex], the hypotenuse rate is:

[tex]r_{l} = \sqrt{4^{2}+3^{2}}[/tex]

[tex]r_{l} = 5[/tex]

The width and height of the old television can be found with the help of trigonometric functions:

Width of 35-inch old television ([tex]w[/tex])

[tex]w = l\cdot \cos \theta[/tex]

[tex]w = l\times\left(\frac{r_{w}}{r_{l}} \right)[/tex]

Height of 35-inch old television ([tex]h[/tex])

[tex]h = l\cdot \sin \theta[/tex]

[tex]h = l\times\left(\frac{r_{h}}{r_{l}} \right)[/tex]

Where [tex]\theta[/tex] is the direction of the hypotenuse with respect to width, measured in sexagesimal degrees.

If [tex]r_{w} = 4[/tex], [tex]r_{h} = 3[/tex] and [tex]r_{l} = 5[/tex] and [tex]l = 35\,in[/tex], the width and height of the old 35-inch television:

[tex]w = (35\,in)\times \left(\frac{4}{5} \right)[/tex]

[tex]w = 28\,in[/tex]

[tex]h =(35\,in)\times \left(\frac{3}{5} \right)[/tex]

[tex]h = 21\,in[/tex]

The width and height of the old 35-inch television are 28 inches and 21 inches, respectively.

Answer:

y = -7

Step-by-step explanation:

the value of -7 is constant at the x coordinates

y = -7

x   |   y

-8   |  -7

-6   |  -7

-4   |  -7

-2   |  -7

0    |  -7

2    |  -7

4    |  -7

6    |  -7

8    |  -7

Answer:

c, e, f, and i

Step-by-step explanation:

a. is bounded above at y = 1 and below at y = 0

b. is unbounded both above and below

c. is bounded below at y = 0 and unbounded above

d. is unbounded both above and below

e. is bounded below at y = 0 and unbounded above

f. is bounded below at y = 0 and unbounded above

g. is bounded below at y = 0 and bounded above at y = 1

h. is unbounded both above and below

i. is bounded below at y = 0 and unbounded above

j. is unbounded both above and below

Answer:

340000000

Step-by-step explanation:

3.4 x 10^8 is in scientific notation.

To change this to standard form you have to multiply 3.4 by 10 to the 8th power. You would be multiplying 3.4 by 10 eight times. It's a positive 8 so you move the decimal point 8 times to the right. If it were a negative then you'd move the decimal to the left.

3.4

Answer:

D. 264°

Step-by-step explanation:

When a tangent and a secant, two secants, or two tangents intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs. Therefore,

60° = 1/2[(18x - 6)° - (5x +17)°]

60° * 2 = (18x - 6 - 5x - 17)°

120° = (13x - 23)°

120 = 13x - 23

120 + 23 = 13x

143 = 13x

143/13 = x

11 = x

x = 11

(18x - 6)° = (18*11-6)°= (198 - 6)° = 192°

(5x +17)° = (5*11 +17)° =(55+17)° = 72°

m (arc KNL) = (18x - 6)° + (5x +17)° = 192° + 72°

m (arc KNL) = 264°

Answer:

I believe the answer is 2x² - 88 - 24, since it is the only one with a number in front of the x²

Step-by-step explanation:

y = x² - 2x - 24

y = 2x² - 88 - 24

y = x² + 5x - 25

y = x² + 3x - 10x - 24

Answer:

$18

Step-by-step explanation:

To find a percent of a number, change the percent to a decimal by dividing it by 100, and multiply the decimal by the number.

4% of $450 = 4% * $450 = 0.04 * $450 = $18

Answer:

[tex]3x^{3} -25x^{2} -44x+10[/tex]

Step-by-step explanation:

Hello!

To solve this we distribute what in one parenthesis into the other

                 3x                  

3x * x^2 = 3x^3

3x * -10x = -30x^2

3x * 2 = 6x

                 5                  

5 * x^2 = 5x^2

5 * -10x = -50x

5 * 2 = 10

Now we put like terms together and simplify

3x^3 + 0 = 3x^3

-30x^2 + 5x^2 = 25x^2

6x - 50x = -44x

0 + 10 = 10

Put it all together

3x^3 + 25x^2 - 44x + 10

Hope this helps!

Answer:

3x^3 + 25x^2 - 44x +10

Step-by-step explanation:

To answer this use FOIL

First Outer Inner Last

In this problem start by distributing the 3x

3x^3-30x^2+6x

Next distribute the 5 in the second parenthesis

5x^2 - 50x + 10

Lastly, add like terms (terms that have the same variable and powers)

3x^3 - 25x^2 +6x +10

Answer:

9

Step-by-step explanation:

Hello!

They want us to find x when x is 5 so we put 5 in for x

3(2(5) - 7)

Now we follow PEMDAS

3(10 - 7)

3(3) = 9

The answer is 9

Hope this helps!

Answer:

Area of a Circle = 254.34 cm²

Step-by-step explanation:

Area of a Circle = π r²

Area of a Circle = 3.14 * 9²

Area of a Circle = 254.34 cm²

The options in this question are missing; here is the complete question:

Which of the following best describes the term constructions in geometry?

A. Combining two or more figures together to create a new figure or shape.

B. A way to draw precise figures using a compass and a straightedge.

C. Creating a figure or shape by hand.

D. Places where things are being built that often slow down traffic.

The answer to this question is B. A way to draw precise figures using a compass and a straightedge.

Explanation:

Geometry is a sub-field of mathematics that studies figures, lines, angles, and related features. In this, the term "construction" describes the creation of figures by using a straight edge such as a ruler, a compass (object to draw circles or arcs and measure distances), and a pen, pencil, or similar instrument to draw. For example to draw or construct a circle a compass is mainly used while the construction of a hexagon requires a straight edge and compass. According to these ideas, the correct answer is B.

Answer:

c is the best answer in my mind

The value of each digit in a number is known as the place value. The time rounded to the nearest tenth is 13.2 seconds.

The value of each digit in a number is known as the place value. The 5 in 350, for example, represents 5 tens, or 50, whereas the 5 in 5,006 represents 5 thousand, or 5,000. It is critical that children that while a digit can be the same, its value is determined by its position in the number.

Identification of the place value of a digit in a number:

Given the time to run is 13.245, now tenth means the value that is after the decimal. Since the value after the tenth is 4, therefore, the tenth value will remain the same but the numbers after that will be erased.

Hence, the time rounded to the nearest tenth is 13.2 seconds.

Learn more about the Place Value here:

https://brainly.com/question/27734142

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Answer:

  $27

Step-by-step explanation:

Assuming this price list, ...

  4 toy cars cost 6 dollars

  6 toy cars cost 9 dollars

  8 toy cars cost 12 dollars

We recognize that 18 cars is 3 times 6 cars, so the cost will be ...

  cost of 18 cars = 3(cost of 6 cars) = 3($9) = $27

The cost of 18 toy cars is $27.

Answer:

Step-by-step explanation:

[tex]\frac{8}{30}\\\\\mathrm{Cancel\:the\:common\:factor:}\:2\\\\=\frac{4}{15}[/tex]

The truck can travel 60 miles before the tank is completely empty

The capacity of the truck is;

Capacity = 40 gallons

When it is 7/8 empty, the amount of gas in the truck is:

Amount  = (1 - 7/8) * 40 gallons

Amount  = 5 gallons

The rate is given as:

Rate = 12 miles per gallon

So, the number of miles it can travel from this point is:

Miles = Amount * Rate

Miles = 5 * 12

Miles = 60

Hence, the truck can travel 60 miles before the tank is completely empty

Read more about rate at:

https://brainly.com/question/14335655

#SPJ9

Answer:

[tex]\Huge \boxed{\mathrm{d}}[/tex]

Step-by-step explanation:

y is equal to $1.67 per pounds of peanuts

pounds of peanuts = x

y is equal to $1.67 per x

per is for each

y = $1.67 × x

The equation that correctly describes this relation is option d.

x = -3 , y = 6 , z = -4

Take Given equation :

⇒-15 + (-x) + y = 0

substitute values of x and y

⇒-15 + [- ( -3)] + 6

⇒-15 + (3) + 6

⇒-15 + 9

⇒-6

Hence, value of -15 + (-x) + y = - 6

Answer:

[tex]x=\frac{(a^2+ab)}{a-b}[/tex]

Step-by-step explanation:

So we want to make x the subject of the formula:

[tex]a(x-b)=a^2+bx[/tex]

First, distribute the left side:

[tex]a(x)-a(b)=a^2+bx\\ax-ab=a^2+bx[/tex]

Combine all the terms with x with it on one side. To do this, first subtract bx from both sides. The right side cancels:

[tex](ax-ab)-bx=(a^2+bx)-bx\\ax-ab-bx=a^2[/tex]

Remove the -ab from the left. Add ab to both sides. The left side cancels:

[tex](ax-ab-bx)+ab=a^2+ab\\ax-bx=a^2+ab[/tex]

Now, distribute out the x from the left side:

[tex]ax-bx=a^2+ab\\x(a-b)=a^2+ab[/tex]

Divide both sides by (a-b). The left side cancels:

[tex]\frac{(x(a-b))}{a-b}=\frac{(a^2+ab)}{a-b} \\x=\frac{(a^2+ab)}{a-b}[/tex]

Therefore:

[tex]x=\frac{(a^2+ab)}{a-b}[/tex]

Answer:

Step-by-step explanation:

ax -ab = + bx

collect like terms

ax-bx= +ab

factorise

x(a-b)=a(a+b)

x=[tex]\frac{a(a+b)}{a-b}[/tex] or [tex]\frac{a^{2} + ab}{a -b}[/tex]

Answer:

x=-1   , y=7

Step-by-step explanation:

y = -3x+4 and y=-7x

substitute y=-7x in the equation y = -3x+4

-7x=-3x+4 ( put variable(x) together)

-7x+3x=4

-4x=4

x=-4/4

x=-1

find y: y=-7x  ⇒ y=-7(-1) ⇒ y=7

check :y = -3x+4

7=-3(-1)+4

7=7  ( correct)

Answer:

width= 3.17

Step-by-step explanation:

Divide 38 (the area) by 12 (the width)