3. An arithmetic sequence a begins 11, 7,...
a. Write a recursive definition for this sequence using function notatio
b. Sketch a graph of the first 5 terms of a

The polynomial of degree 3 is given by x³-3x²-40x+84.

The degree of a polynomial is the highest degree of the variables present with non-zero coefficients.

For example the polynomial [tex]{\displaystyle 2x^{2}y^{3}+8x+10}[/tex] has three terms. The first term has a degree of 5 (the sum of the powers 2 and 3), the second term has a degree of 1, and the last term has a degree of 0. Therefore, the polynomial has a degree of 5, which is the highest degree of any term.

A degree 3 polynomial having zeros α,β and γ and the coefficient of x³ equal a is

a(x-α)(x-β)(x-γ)

So the given zeroes of the polynomial are -6,8 and 7 and the coefficient of x³ is 1. So the desired polynomial is given by:

1(x+6)(x-2)(x-7)

=(x²-4x-12)(x-7)

=x³-3x²-40x+84

Hence the polynomial of degree 3 is given by x³-3x²-40x+84.

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The equivalent expression is,

''Negative two over fifteen times x plus two''

What is Mathematical expression?

The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called Mathematical expression.

We have to given the expression as;

''One fifth times the quantity 3 times x plus 10 end quantity minus 11 over 15 times x''

Now, Write in mathematical expression as,

⇒ [tex]\frac{1}{5} (3x + 10 ) - \frac{11}{15} x[/tex]

We can solve it as,

⇒ [tex]\frac{1}{5} (3x + 10 ) - \frac{11}{15} x[/tex]

⇒ [tex]\frac{3}{5} x + \frac{10}{5} - \frac{11}{15} x[/tex]

⇒ [tex]\frac{3}{5} x - \frac{11}{15} x+ 2[/tex]

⇒ [tex]\frac{-2}{15} x + 2[/tex]

Hence, It can be written as;

⇒ Negative two over fifteen times x plus two.

Therefore, The equivalent expression is,

''Negative two over fifteen times x plus two''.

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Answer:

The answer is this sequence has 18 terms

Step-by-step explanation:

As you can see, the term-to-term rule of the sequence is +2

We can use that to calculate the amount of terms.

First, calculate the distance between the first and last terms

53 - 19 = 34

Then, use this and divide the term-to-term rule.

34/ 2 = 17

Remember to add 1 at the end :)

17 + 1 = 18

There are 18 terms in this sequence.

If you don't trust me, you can check it yourself :D

The each bottle of juice cost $ 7.55  before tax .

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

Grayson bought  bag of popcorn (P)= $3.50

Five pack of juice bottles.

The total cost before tax was $11.05.

According to given question we have

Let the cost of the juice bottles be x.

P+ x= $11.05.

$3.50+x=$11.05

x=$11.05-$3.50

x=$ 7.55

Therefore, the each bottle of juice cost $ 7.55  before tax .

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Answer:-5

Step-by-step explanation:

5*5*5=125

-5*-5=25

25*-5= -125

or

3√-125

The shorter section is x inches length, or 44.

What constitutes a length?

A line segment can be drawn on paper and has a set length. the measurement of the separation between the longest or longer side of an object's ends. 2: an exact distance The three miles of the road. 3: How much time something requires The movie lasts for two hours. 4: a lengthy fragment of something She purchased a length of pipe in

accordance with the instruction;

the shorter portion should be x.

It is 4x because the longer portion is 4 times as long as the other.

4x + x = 55

5x = 55

4x = 44

x = 11

The length of the shorter piece is x, which is 44

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Answer:

The probability of both outcomes is equal i.e. 50% or 1/2. So, the probability of an event is Favorable outcomes/Total number of outcomes. It is denoted with the parenthesis i.e. P(Event).

Answer: 8/52

Step-by-step explanation:

there are 4 jacks in a deck of 52 cards, and also 4 tens. The combined probability of picking a 10 or jack is 8 in 52, which is 15.38%.

Answer:

$29.865

Step-by-step explanation:

Because 3.75/2 =1.875 so $1.875 plus $15 Plus the flat $12.99

Using a linear function, it is found that he spent $29.865 for the 4.5 hours he was on the river.

A linear function is modeled by:

y = mx + b

In which:

For this problem, we have that:

Hence the cost of x hours is given by:

C(x) = 12.99 + 3.75x.

For 4.5 hours, the cost is given as follows:

C(4.5) = 12.99 + 3.75(4.5) = $29.865.

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Alex makes 202 cakes with 50 (1/2) cups of sugar.

Given,

Quantity of sugar Alex with him = 50 (1/2) cups

Quantity of sugar needed for making 1 cake = 1/4 cup

We have to find the number of cakes Alex can make with 50 (1/2) cups of sugar.

Number of cakes = Quantity of sugar Alex with him / Quantity of sugar needed for making 1 cake

Number of cakes = 50 (1/2) ÷ 1/4

Number of cakes = 50 ÷ 0.25 + 0.5 ÷ 0.25

Number of cakes = 200 + 2

Number of cakes = 202

That is, Alex can make 202 cakes with 50 (1/2) cups of sugar.

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Answer:

  1:30 pm

Step-by-step explanation:

You want the time when Sahil catches up to Joaquin, who left at 8 am riding 50 mph when Sahil left at 8:30 am, riding at 55 mph.

The relation between time, speed, and distance is ...

  distance = speed × time

  time = distance / speed

Joaquin has a head start of 0.5 hours (30 minutes), during which time he traveled ...

  head start distance = (50 mi/h) × (0.5 h) = 25 mi

Sahil is traveling 55 - 50 = 5 mph faster than Joaquin, so closes that gap at the rate of 5 mi/h. The time it takes to close the gap entirely is ...

  time = distance / speed = 25 mi / (5 mi/h) = 5 h

So, 5 hours after Sahil starts at 8:30, the two riders will be at the same place.

Sahil catches Joaquin at 1:30 pm.

__

Additional comment

By the time the gap is closed at 1:30 pm, both riders will have traveled a distance of ...

  distance = speed × time = 50 mi/h × 5.5 h = 55 mi/h × 5 h = 275 mi

In the attached graph, we have written equations for the total distance traveled by each motorcycle. The x-value used is the clock time on a 24-hour clock. That is, their meeting time of 13.5 hours corresponds to 13:30 hours or 1:30 p.m. on a 12-hour clock.

We get that the value of  (f + g​)(x​) is 3 x² - 2 x - 10 and (f + g​)(6​) is 86.

We are given the two functions:

f(x) = 3 x² - x - 6

g(x) = x - 4

We need to find:

(f + g​)(x​)

= f(x) +g(x)

= 3 x² - x - 6 + x - 4

= 3 x² - 2 x - 10

Now we have to find:

(f + g​)(6​).

Put x = 6, we get that:

= 3 (6)² - 2 (6) - 10

= 108 - 12 - 10

= 108 - 22

= 86

Therefore, we get that the value of  (f + g​)(x​) is 3 x² - 2 x - 10 and (f + g​)(6​) is 86.

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The value of g(h(10)) is 2√2. the correct option is A.

Given that the functions are g(x)=√x-4 and h(x)=2x-8.

A function is defined as the relationship between a set of inputs where each input has an output.

Firstly, we will find the value of h(10) by substituting x=10 in the function h(x)=2x-8.

h(10)=2(10)-8

h(10)=20-8

h(10)=12

Now, we will find g(h(10)) where h(10)=12.

By substituting h(10)=12 in g(h(10)), we get

g(h(10))=g(12).

Further, we will find g(12) by substituting x=12 in the function g(x)=√x-4, we get

g(12)=√(12-4)

g(12)=√8

g(12)=2√2

Hence, the value of function g(h(10)) when g(x)=√x-4 and h(x)=2x-8 is 2√2.

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Answer:$17.75

Step-by-step explanation:

2+1.75m

2+1.75(9)

2+15.75

17.75

Answer:

1.3 m

Step-by-step explanation:

Given dimensions of rectangle ABCD:

[tex]\begin{aligned}\textsf{Area of a rectangle} & = \sf width \times length\\\\\implies \sf Area\:of\:ABCD& = x(x+4)\\& = x^2+4x \end{aligned}[/tex]

Given dimensions of isosceles triangle ADE:

[tex]\begin{aligned}\textsf{Area of a triangle} & = \dfrac{1}{2} \times \sf base \times height\\\\\implies \textsf{Area of $\triangle$ADE}& = \dfrac{1}{2} \cdot x \cdot x\\& = \dfrac{1}{2}x^2\end{aligned}[/tex]

As the area of the portion remaining when ADE is cut off from ABCE is 6 m²:

[tex]\begin{aligned}\sf ABCD-ADE & = 6\\\implies x^2+4x-\dfrac{1}{2}x^2 & = 6\\2x^2+8x-x^2 & = 12\\x^2+8x & = 12\\x^2+8x-12 & = 0\end{aligned}[/tex]

Solve the found quadratic equation by completing the square.

Move the constant to the right side of the equation:

[tex]\implies x^2+8x-12+12=0+12[/tex]

[tex]\implies x^2+8x=12[/tex]

Add the square of half the coefficient of x to both sides:

[tex]\implies x^2+8x+\left(\dfrac{8}{2}\right)^2=12+\left(\dfrac{8}{2}\right)^2[/tex]

Simplify:

[tex]\implies x^2+8x+4^2=12+4^2[/tex]

[tex]\implies x^2+8x+16=12+16[/tex]

[tex]\implies x^2+8x+16=28[/tex]

Factor the perfect square trinomial on the left side:

[tex]\implies (x+4)^2=28[/tex]

Square root both sides:

[tex]\implies \sqrt{(x+4)^2}=\sqrt{28}[/tex]

[tex]\implies x+4=\pm \sqrt{28}[/tex]

[tex]\implies x+4=\pm \sqrt{4 \cdot 7}[/tex]

[tex]\implies x+4=\pm \sqrt{4}\sqrt{7}[/tex]

[tex]\implies x+4=\pm 2\sqrt{7}[/tex]

Subtract 4 from both sides:

[tex]\implies x=-4\pm 2\sqrt{7}[/tex]

As length is positive:

[tex]\implies x=-4+ 2\sqrt{7}\:\:\sf only[/tex]

Taking the value of √7 = 2.65:

[tex]\implies x \approx -4+ 2(2.65)[/tex]

[tex]\implies x \approx -4+5.3[/tex]

[tex]\implies x \approx 1.3[/tex]

Therefore, the width of the sheet is 1.3 m.

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Answer:

y = 1x + 5

Step-by-step explanation:

First, lets calculate the equation of the line passing through (5, 7) and (1, 3) in slope-intercept form

The general equation of a line in slope-intercept form is
y = mx + b

where m = slope and b = y-intercept is rise over run =

[tex]m = \dfrac {(y_{2} - y_{1})} {(x_{2} - x_{1})}[/tex]

where (x₁, y₁) and (x₂, y₂) are any two points on the line

For the line passing through (5, 7) and (1, 3) , the slope
[tex]m = \dfrac{3 - 7}{1 - 5}[/tex]

[tex]m = \dfrac{-4}{-4}[/tex]

[tex]m = 1[/tex]

To compute the y-intercept, plug in any of the two points x and y values and solve for b

Take point 5, 7 ==> when x = 5, y must be 7

We get
7 = 1 x 5 + b
7 = 5 + b
2 = b                (subtract 5 from both sides)
b = 2

So the equation of the line is
y = 1x + 2  

A line parallel to another line will have the same slope and a different y-intercept

Therefore a parallel line will also have slope 1 and its equation will be of the form
y = 1x + b

To calculate this b, plug in the point (4, 9) into the equation and solve for b
9 = 1 x 4 + b
9 = 4 + b
b = 5

So the equation is
y = 1x + 5

Graph attached shows the real picture

a)  cost C of manufacturing 1000 bicycle is $170

b) cost C of manufacturing 7000 bicycle is $110

c)  As more bicycle is manufactured the cost of manufacturing decreases

What is an mathematical expression?

Expression in mathematics is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

given expression of cost of bicycle C in terms of number of number of bicycles x is :  

C = (100x + 70,000)/ x

a)  Now, to get the cost C of manufacturing 1000 bicycle substitute  x as 1000 in above expression :

C = (100x + 70,000)/ x

C = 100 + (70,000/ x)

C = 100 + 70,000/1000

C = 100 + 70

C = 170 bicycle's

b)  Now, to get the cost C for 7000 bicycle substitute  x as 7000 in above expression :

C = (100x + 70,000)/ x

C = 100 + (70,000/ x)

C = 100 + 70,000/7000

C = 100 + 10

C = 110 bicycle's

c) As it is observed from the above analysis as more bicycle is manufactured the cost of manufacturing decreases.

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Answer:

Step-by-step explanation:

D.16

Answer:

Step-by-step explanation:

Answer: 247 miles.

Step-by-step explanation: First, we need to convert the 45 minutes into hours. we know that 1 hour = 60 minutes. Dividing any number of minutes by sixty gives us the number of hours along with the remaining minutes if there are any. so 45/60 simplifies to 3/4. Now for the miles, it's given that the speed is 52 mph. So we can put into the expression 52(4+3/4)= total miles. Once we distribute 52, we get 208 + 39, which equals to 247.

Answer:

247

Step-by-step explanation:

52÷60 mins x 45= 39 miles for 45 mins

45 mins + 4 x 52 =247

The vertical distance of helicopter from the ground is equal to 2000 / 3 m.

Let the distance between the two planes A and B be x.

In △ ADC, we get that:

tan 60° = 2000 / y

√3 = 2000 / y  ...(1)

Now, in △ BCD, we get that:

tan 30° = 2000 - x / y

1 / √3 = (2000 - x) / y    ... (2)

Divide (1) from (2):

3 = 2000 / (2000 - x)

6000 - 3 x = 2000

3 x = 6000 - 2000

3 x = 4000

x = 4000 / 3

(2000 - x) = 2000 - 4000/3 = 2000 / 3

Therefore, the vertical distance of helicopter from the ground is equal to 2000 / 3 m.

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Answer:

6

Step-by-step explanation:

If there are 4 in each tank, that means there are 2 tanks. 4-2 = 2. 8-2 = 6.

Answer:

There 30 fish left at the store

Step-by-step explanation:

There are 8 tanks

If there are 4 fish in each tank, the total would be 32 fish. If Dalia buys 2 fish, you would do 32 - 2 = 30 fish.

Hope this helped!! ( >ᴗ<) xx

Answer:20.4

Step-by-step explanation:

Change the divisor 1.2 to a whole number by moving the decimal point 1 places to the right. Then move the decimal point in the dividend the same, 1 places to the right.

Answer:

did not do order of operations and added first

94/2 remember order of operations

94/2 = 47

47+95 = 142
There you go :)

the maximum number of candy kisses that each person could have received is 4.

We know that each person receives the same number of candy.

Then the quotients between the number of candy and the number of people should give the same value:

20/K = 52/N

Let's find the common factors between 20 and 52, to do so, we need to rewrite the two numbers as a product of prime factors:

20 = 2*10 = 2*2*5

52 = 2*26 = 2*2*13

The greatest common factor between 20 and 52 is (2*2) = 4

Then, if each person receives 4 candy:

The group that receives 20 candy:

20/K = 4

20/4 = k = 5

That group has 5 people.

The group that receives 52 candy:

52/N = 4

52/4 = N = 13

This group has 13 people.

Then the maximum number of candy kisses that each person could have received is 4.

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Answer:

A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius (in feet) of the outer ripple is given by r ( t ) = 0.6 t r(t) = 0.6t r(t)=0.6t, where t is the time in seconds after the pebble strikes the water.

Step-by-step explanation:

Answer:

well dude it's because of the law of gravity

So, we are to solve for x in:

[tex] \frac{x + k}{m} = r[/tex]

Cross multiply the above to solve for x

[tex]x + k = mr[/tex]

Now, collect like terms to find x

Therefore: [tex]x = mr - k[/tex]

Answer:

C.

Step-by-step explanation:

[tex]\frac{3}{5} = 3 \div 5 = 0.6[/tex]

Answer: A

Step-by-step explanation:

0.6 converted to a fraction is 1/6

Answer:

She will need to rise 55.4 feet.

Step-by-step explanation:

-27.2 feet + 2.1 feet = -25.1

-25.1 + -19.6 = 44.6

100- 44.6 = 55.4 feet