what is the 52nd term for the following sequence ? 14,6,-2,-10,-18

Answer:

C

Step-by-step explanation:

to factor x² - x - 2

consider the factors of the constant term which sum to give the coefficient of the x-term.

the factors are - 2 and + 1 since - 2 × 1 = - 2 and - 2 + 1 = - 1

x² - x - 2 = (x - 2)(x + 1), hence (x + 1) is a factor

The relationship between (x + 1) and the polynomial x² - x - 2 is that            ( x + 1) is a factor of x² - x - 2.

A mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a non negative integral power.

The given polynomial is x² - x - 2.

x² - x - 2

= x² - 2x + x - 2

= x( x - 2) + 1( x - 2)

=( x - 2) ( x + 1)

So we can see that, ( x + 1) is a factor of x² - x - 2.

So, option C is correct.

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Answer:

(1) 0.08x + 16

(2) 0.08x + 16=0.12x + 14

Step-by-step explanation:

Checking account A has a monthly fee of $16 and a per-check fee of $0.08

Per check fee is a constant rate that is 0.08

Let x represents the number of checks Cecily writes per month

1 check fee = 0.08

x checks fee = 0.08x

monthly fee is $16 , we add that as well

So total monthly fee charges for account A  is

0.08x + 16

checking account B has monthly fee of $14 and a per-check fee of $0.12.

1 check fee = 0.12

x checks fee = 0.12x

monthly fee is $14 , we add that as well

So total monthly fee charges for account B  is

0.12x + 14

(2) To find number of checks write per month for the accounts to charge the same in fees

WE set both expression , account A = account B

0.08x + 16=0.12x + 14

Subtract 0.12x on both sides

-0.04x + 16 = 14

Now subtract 16 on both sides

-0.04x = -2

Divide by -0.04 on both sides

So x= 50

Answer:

C = 6 + 7.5 x

Step-by-step explanation:

Given,

The amount is $24.75 for entrance and 2.5 kilograms of strawberries.

⇒ Entrance fee + 2.5 kilograms of strawberries = $24.75

Since, Entrance fee = $ 6,

And,  the price for each kilogram of strawberries is constant.

⇒  $ 6 + 2.5 × 1 kilograms of strawberries = $24.75

⇒ 2.5 × 1 kilograms of strawberries = 18.75

⇒ 1 kilograms of strawberries = $ 7.5.

Thus, the cost of x  strawberries = 7.5 x

Also, the total charge for x strawberries = Entrance fee + the cost of x  strawberries

= 6 + 7.5 x

⇒ C = 6 + 7.5 x

Which is the required function formula.

Answer:

192

Step-by-step explanation:

Answer:

the slope is 0.

Step-by-step explanation:

You can use the slope equation

[tex]\frac{y-y}{x-x}[/tex]

and plug in your points

[tex]\frac{10-10}{4-1}[/tex]

[tex]\frac{0}{3}[/tex]

slope = 0

Answer:

I will help you with question number 2.

48:

12*4

Step-by-step explanation:

12*4=48

Hi There!

Step-by-step explanation:

40% = 0.4

124.46 * 0.4 = $49.784 (Discount)

124.46 - 49.784 = $74.676 (Sale Price)

74.676 = 74.68

Answer:

$74.676 or $74.68

Hope This Helps :)

Answer:

The cost would be $74.68

Step-by-step explanation:

To find this amount, multiply the original price by the percentage you would be paying. Since the mark down is 40%, we know that the amount paid is 60%. So multiply that by the original cost.

$124.46 * 60% = $74.68

Answer:

133° angle

Step-by-step explanation:

Note that "supplement" means 180°.

To find the supplement of the angle given (47°), subtract the given measurement with the total supplementary measurement.

180 - 47 = 133

The supplement of a 47° angle is 133°.

~

The probability for the spinner landing on the dotted region is 1/2.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lies in the close interval of 0 and 1 [0,1].

The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.

The probability for the given case is evaluated as,

P(Spinner lands on dotted region) = Total space for dotted region/100

                                                         = (25 + 12.5 + 12.5)/100

                                                         = 50/100

                                                         = 1/2

Hence, the probability that the spinner will land on a dotted region is 1/2.

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Answer:

1.16 horse power.  Option A.

Step-by-step explanation:

Work done = m g h = 63 * 9.81 * 7 = 4326.21 joules

Power = 4326.21 / 5 = 865.24 Watts

1 Horse power = 746 watts so the answer is 865.24 / 746 = 1.16 HP to nearest hundredth.

Answer:

1.16 hp

Step-by-step explanation:

Answer:

The original equation contains 3 multiplications.

When multiplying numbers, the order that they are in doesn't matter so 3 *2 is the same as 2 * 3.

This would make D, the same.

D) (3 × 2)×(5 × 6)

Answer:

1647.2

Step-by-step explanation:

5.8% times 28,400 = 1647.2

5.8% = 5.8/100 = .058

so .058 times 28,400 = 1647.2

Final answer:

To find the commission, convert the rate to decimal by dividing by 100 then multiply by the sale price. A salesperson earns 5.8% commission, resulting in $1,647.20 for a $28,400 car.

Explanation:

To calculate the commission a car salesperson earns on the sale of a car, you first need to understand that commission is a percentage of the sale price they receive as their payment. In this case, the salesperson earns a 5.8% commission on each car sold. To find out how much commission they would earn on a $28,400 car, the following calculation is performed:

Sale price of car = $28,400
Commission rate = 5.8%

First, convert the commission rate from a percentage to a decimal by dividing by 100:
5.8% / 100 = 0.058

Next, multiply the sale price by the decimal commission rate:
$28,400 x 0.058 = $1,647.20

Therefore, the commission earned on the $28,400 car is $1,647.20.

Answer: First, multiply 5 by x-2 to get 5x-10. We now have 5x-10=2x+16. Subtract 2x on both sides: 3x-10=16. Add 10 to both sides: 3x=26. Lastly, divide by 3x to isolate x: x=8.6666667

Answer:

C

Step-by-step explanation:

The target area is shown in the attached picture.

We want to figure out probability of hitting red region.

The area of the figure is the area of the red square, which is 196.

Area of red region is area of whole square (196) minus area of blue square (64). So we have:

Area of red region =  196 - 64 = 132

Probability of hitting red region is 132 divided by total, which is 196.

[tex]\frac{132}{196}=0.67[/tex]

Answer choice C is right.

To rearrange the equation for a, subtract b/8c from both sides: a = 4x - b/8c.

To rearrange the equation for a, we start with the given equation 4x = a + b/8c. First, we isolate a by subtracting b/8c from both sides, giving 4x - b/8c = a. Therefore, the equation for a in terms of b, c, and x is a = 4x - b/8c.

Answer:

y+9 =-5(x-2)  point slope form

y = -5x-1  slope intercept form

Step-by-step explanation:

If we have a slope and a point, we can use the point slope form of a line

y-y1 = m(x-x1)

y--9 = -5(x-2)

y+9 =-5(x-2)

If you want to write it in slope intercept form, distribute the -5

y+9 = -5x+10

Subtract 9 from each side

y+9-9 = -5x+10-9

y = -5x-1

Answer:

  [tex]\dfrac{10\sqrt{3}}{3}[/tex]

Step-by-step explanation:

You want the length of the hypotenuse in a 30°-60°-90° right triangle with long leg 5.

The ratios of side lengths in a 30°-60°-90° triangle is ...

  1 : √3 : 2

Multiplying these values by 5/√3 gives ...

  5/√3 : 5 : 10/√3

That is, the length of the side marked X is 10/√3.

The denominator can be rationalized by multiplying the fraction by 1 in the form of (√3)/(√3):

  [tex]X = \dfrac{10}{\sqrt{3}}=\dfrac{10}{\sqrt{3}}\times\dfrac{\sqrt{3}}{\sqrt{3}}\\\\\\\boxed{X=\dfrac{10\sqrt{3}}{3}}[/tex]

Answer: 6

The equation given to you is in the form (x-h)^2 + (y-k)^2 = r^2

The right hand side 36 is in the place of r^2, so r^2 = 36 leading to r = 6 after you apply the square root to both sides.

Answer:

D.

Step-by-step explanation:

Function does not have duplication of a number.be

The A choice contains duplicates of both 2 and -2.

The B choice contains a duplicate of 4.

Therefor, it must be D.

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

Which of the sets of ordered pairs represents a function?  

A = {(−5, 5), (−2, 2), (2, −2), (5, −5)}

B = {(4, 2), (3, −2), (9, 4), (11, −3)}

Select one:

a. Only A

b. Only B

c. Both A and B

d. Neither A nor B

Answer:

There are 260 seats in the economy class and 100 seats in the business class. A plane has 360 total seats, which are divided into economy class and business class. For every 13 seats in economy class, there are 55 seats in business class.

Answer:

D) y = -x - 3

Step-by-step explanation:

Step 1. Find the slope (m₁) of the original line

The equation for the original line is

-x + y = 5       Add x to each side

     y = x + 5

slope = m₁ = 1

Step 2. Find the slope (m₂) of the perpendicular line

m₂ = -1/m₁     Substitute the value of m₁

m₂ = -1/1

m₂ = -1

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

Step 3. Find the equation for the perpendicular line

y = mx + b     Substitute the value of m₂

y = -x + b

The line passes through (2, -5).  

-5 = -2 + b     Add 2 to each side

b = -3  

y = -x - 3

In the image, below  the graph of your original equation is the red line.

The blue line passing through (2, -5) is the perpendicular line.

Answer:

Kentucky Avenue is 575 ft between C street and D street

Step-by-step explanation:

x / (460 ft) = (1000 ft) / (800 ft)

Divide the right side:

x / (460 ft) = 1.25

To solve for "x", multiply both sides by 460 ft:

(460 ft) [x/(460)] = (460) (1.25)

x = 575 ft

Hope this helped :)

Answers:

Angle 1 is 40 degrees

Angle 2 is 90 degrees

Angle 3 is 50 degrees

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

Explanations:

Triangle ABC is a reflection of triangle ADC over the line AC. Doing this reflection forms the kite ABCD. Or you can think of it as gluing two congruent triangles together (ABC and ADC). We can prove the two triangles ABC and ADC congruent by the SSS congruence property. Then we use CPCTC (corresponding parts of congruent triangles are congruent) to prove that angle 1 is 40.

Let E be the intersection of the two diagonals. Through similar reasoning as earlier, we can prove that triangle AEB is congruent to triangle AED, so that leads to angle 2 being 90 degrees because this angle adds to its counterpart to get 180. Both unknown angles are x each meaning x+x = 180 leads to x = 90. One property of kites is that the diagonals are perpendicular.

Triangle AED is a right triangle as discussed above. Therefore, the angle 3 and the 40 degree angle are complementary. If angle 3 is y, then y+40 = 90 giving y = 90-40 = 50, which is why angle 3 is 50 degrees.

Using angle theorems, the value of the angles m1 and m3 are 40° and 50° respectively.

Taking the midpoint of DB as O ;

Angle OAD and Angle OAB are equal

OAD = 40° ; OAB = 40°

A right angle is formed at O ;

Hence,

(O + D + A) = 180°

90° + D + 40° = 180° (Sum of interior angles of a triangle)

D = 180 - 130

D = 50°

Hence, m∠3 = 50°.

Therefore, the value of the angles m1 and m3 are 40° and 50° respectively.

Answer:

2*(n-6) = 8

Step-by-step explanation:

Twice the difference of a number and 6 equals 8

Equals means =

Difference means subtract

2*(n-6) = 8

Answer:

Infinite number of solutions.

Step-by-step explanation:

We have the equations,

1. 3x+3y=10

2. -9x-9y= -30

Now, if we multiply equation 1 with -3, we will obtain equation 2.

i.e. -3×(3x+3y)= -3×10

i.e. -9x-9= -30

So, we see that both the equations are same.

The equation 3x+3y=10 will have solution for many values of x and y.

Hence, the system will have infinite number of solutions.

Answer:

Infinite Solution

Step-by-step explanation:

Given :

[tex]3x+3y=10[/tex]  -----(A)

[tex]-9x-9y = -30[/tex]  ------(B)

To Find : Solution of the given system of equations

Solution :

We will solve it by using substitution method

Finding the value of x from equation (B)

⇒[tex]-9x-9y = -30[/tex]

⇒[tex]-9x= -30+9y[/tex]

⇒[tex]x= \frac{-30+9y}{-9}[/tex]

⇒[tex]x= \frac{-10+3y}{-3}[/tex]

Putting this value of x in  equation (B)

⇒ [tex]3( \frac{-10+3y}{-3})+3y=10[/tex]

⇒[tex]10-3y+3y = 10[/tex]

⇒[tex]10= 10[/tex]

Since x and y both gets eliminated from the equation we got 10 = 10

Since the equations represent the same line.

If a consistent dependent system that has an infinite number of solutions

Hence there is infinite solution .

Answer:

b no is the right answer i think

Answer:

.64 <  65 % < 2/3 < 7/10

Step-by-step explanation:

To order all the numbers from least to greatest, but all the numbers in the same form (fraction, decimal, or percent).  I will put them all in decimal form so that I can compare them.

0.64,   .64

2/3 ,   =.666666repeating

65% = 65/100 = .65

7/10 = .7

.64< .65<.6666repeating<.7

but we need to put them in their original form

.64 <  65 % < 2/3 < 7/10

Answer:

-.033557047

Step-by-step explanation:

Slope = (y2-y1)/ (x2-x1)

    = (4.2 - 5.6)/(.86- 40.86)

 = -1.4/ (.86 + 40.86)

= -1.4/41.72

-.033557047

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (-40.86, 5.6) and (0.86, 4.2). Substitute:

[tex]m=\dfrac{4.2-5.6}{0.86-(-40.86)}=\dfrac{-1.4}{0.86+40.86}=-\dfrac{1.4}{41.72}=-\dfrac{140}{4172}\\\\=-\dfrac{140:4}{4172:4}=-\dfrac{35}{1043}=-\dfrac{35:7}{1043:7}=-\dfrac{5}{149}[/tex]

Answer:

¹/₂₄  

Step-by-step explanation:

Debbie used ⅚ of the cord for necklaces.

That left ⅙ of the cord for four bracelets.

Each bracelet used:

Fraction of cord = ⅙ ×¼ = ¹/₂₄

Debbie used ¹/₂₄ of the cord for each bracelet.