In a circle with a radius of 8ft an arc is intercepted by a central angle of 135 degrees. What is the length of the arc?

A: 6.28 ft
B: 9.42 ft
C: 18.84 ft
D: 28.26 ft

Answer:

Taylor sold 42 pizzas

Step-by-step explanation:

Make a system of equations where t represents the number of pizzas Taylor sold and j represents the number that Jeff sold:

t + j = 126

j = 2t

We can solve this system by substitution, since we can substitute 2t as j.

t + j = 126

t + 2t = 126

3t = 126

t = 42

Taylor sold 42 pizzas.

Answer:

Step-by-step explanation:

Let x represent the number of pizzas that Tailor sold.

Let y represent the number of pizzas that Jeff sold.

Together they have sold a total of 126 pizzas. This means that

x + y = 126- - - - - - - - -1

Taylor has sold half as many

pizzas as Jeff. This means that

x = 1/2 × y = y/2

Substituting x = y/2 into equation 1, it becomes

y/2 + y = 126

Multiplying both sides of the equation by 2, it becomes

y + 2y = 252

3y = 252

y = 252/3

y = 84

x = y/2 = 84/2

x = 42

Taylor sold 42 pizzas

(1) I assume "log" on its own refers to the base-10 logarithm.

[tex]\left(e^{-2x}\log(\ln x)^3\right)'=\left(e^{-2x}\right)'\log(\ln x)^3+e^{-2x}\left(\log(\ln x)^3\right)'[/tex]

[tex]=-2e^{-2x}\log(\ln x)^3+\dfrac{e^{-2x}}{\ln10(\ln x)^3}\left((\ln x)^3\right)'[/tex]

[tex]=-2e^{-2x}\log(\ln x)^3+\dfrac{3e^{-2x}(\ln x)^2}{\ln10(\ln x)^3}\left(\ln x\right)'[/tex]

[tex]=-2e^{-2x}\log(\ln x)^3+\dfrac{3e^{-2x}(\ln x)^2}{\ln10\,x(\ln x)^3}[/tex]

[tex]=-2e^{-2x}\log(\ln x)^3+\dfrac{3e^{-2x}}{\ln10\,x\ln x}[/tex]

Note that writing [tex]\log(\ln x)^3=3\log(\ln x)[/tex] is one way to avoid using the power rule.

(2)

[tex]\left(e^{-2x}(\log(\ln x))^3\right)'=(e^{-2x})'(\log(\ln x))^3+e^{-2x}\left(\log(\ln x))^3\right)'[/tex]

[tex]=-2e^{-2x}(\log(\ln x))^3+3e^{-2x}(\log(\ln x))^2(\log(\ln x))'[/tex]

[tex]=-2e^{-2x}(\log(\ln x))^3+3e^{-2x}(\log(\ln x))^2\dfrac{(\ln x)'}{\ln10\,\ln x}[/tex]

[tex]=-2e^{-2x}(\log(\ln x))^3+\dfrac{3e^{-2x}(\log(\ln x))^2}{\ln10\,x\ln x}[/tex]

(3)

[tex]\left(\sin(xe^x)^3\right)'=\left(\sin(x^3e^{3x})\right)'=\cos(x^3e^{3x}(x^3e^{3x})'[/tex]

[tex]=\cos(x^3e^{3x})((x^3)'e^{3x}+x^3(e^{3x})')[/tex]

[tex]=\cos(x^3e^{3x})(3x^2e^{3x}+3x^3e^{3x})[/tex]

[tex]=3x^2e^{3x}(1+x)\cos(x^3e^{3x})[/tex]

(4)

[tex]\left(\sin^3(xe^x)\right)'=3\sin^2(xe^x)\left(\sin(xe^x)\right)'[/tex]

[tex]=3\sin^2(xe^x)\cos(xe^x)(xe^x)'[/tex]

[tex]=3\sin^2(xe^x)\cos(xe^x)(x'e^x+x(e^x)')[/tex]

[tex]=3\sin^2(xe^x)\cos(xe^x)(e^x+xe^x)[/tex]

[tex]=3e^x(1+x)\sin^2(xe^x)\cos(xe^x)[/tex]

(5) Use implicit differentiation here.

[tex](\ln(xy))'=(e^{2y})'[/tex]

[tex]\dfrac{(xy)'}{xy}=2e^{2y}y'[/tex]

[tex]\dfrac{x'y+xy'}{xy}=2e^{2y}y'[/tex]

[tex]y+xy'=2xye^{2y}y'[/tex]

[tex]y=(2xye^{2y}-x)y'[/tex]

[tex]y'=\dfrac y{2xye^{2y}-x}[/tex]

Answer: c(x) = $50*x + $24

Step-by-step explanation:

First, this situation can be modeled with a linear equation like:

c(x) = s*x + b

where c is the cost, s is the slope, x is the number of cubic yards of mulch bought, and b is the y-intercept ( a constant that no depends on the number x)

Then we know that:

The company charges $50 per cubic yard, so the slope is $50

A delivery charge of $24, this delivery charge does not depend on x, so this is the y-intercept.

Then our equation is:

c(x) = $50*x + $24

This is:

"The cost of buying x cubic yards of mulch"

Answer:

(1,1)

Step-by-step explanation:

y = 3x − 2

y = -2x + 3

the point that satisfies the system:

when the two functions are equal

3x-2=-2x+3

3x+2x=3+2

5x=5

x=5/5=1

when x=1

y=-2x+3

y=-2(1)+3

y=1

Answer:

(1,1) or x=1 and y=1

Step-by-step explanation:

Since both equations are equal to y you can use substitution, replacing he y in y=3x-2 with -2x+3, giving you the equation -2x+3=3x-2. We can use this to solve for x. To isolate the variable you first need to add 2 to both sides, giving you -2x+5=3x, then add 2x to both sides. This gives you 5=5x, lastly you need to divide both sides by 5 to get x=1. Now you can plug x(1) into 1 of the 2 given equations to find y, I'll use y=3x-2. When x is plugged in as 1 you get the equation y=3(1)-2, after multiplying you get y=3-2, then you subtract to get y=1. In order to make sure this is the correct solution you can also plug in x as 1 and now y as 1 into the other equation, y=-2x+3. We can plug 1 in for x and solve for -2(1)+3 to get -2+3, or 1, so y is 1 for both equations, therefore the solution we got was correct, x=1 and y=1, or (1,1).

Answer:

a = 16

b = [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Length of the design 16 inches is represented by the point (0, 16) and length of 12 inches by (1, 12).

That means these points lie on the graph of the function 'f' represented by,

f(x) = a(b)ˣ

For the point (0, 16),

f(0) = a(b)⁰

16 = a(1)

a = 16

For another point (1, 12),

f(1) = a(b)¹

12 = ab

12 = 16(b) [Since a = 16]

b = [tex]\frac{12}{16}[/tex]

b = [tex]\frac{3}{4}[/tex]

Therefore, values of a and b are 16 and [tex]\frac{3}{4}[/tex] respectively.

Answer:

31 m

Step-by-step explanation:

v=l*w*h since it is a cube then all sides (a) are equal:

v=(a*a*a)=a^3

v1+v2=1331 for the first two boxes(

a³+a³=∛1331

l=w=h=11*2=22

v=729 ( for the second cube)

a=∛729=9

9+22=31 m

Answer:

A.

Step-by-step explanation:

40x is the number of lawns he can do, less the time to do his grandparents time (added to other law time) and he has 660 mins of less to complete them.

Answer:

a. 40x + 110 ≤ 660

Step-by-step explanation:

Answer:

[tex]\boxed{\sf Option \ D}[/tex]

Step-by-step explanation:

[tex]\sf g(x) = 2x^2-6x-56\\[/tex]

Factorizing using mid term break formula

[tex]\sf g(x) = 2x^2-14x+8x-56\\g(x) = 2x(x-7)+8(x-7)\\g(x) = (2x+8)(x-7)\\g(x) = 2(x+4)(x-7)[/tex]

Answer:

[tex]\boxed{m = -2}[/tex]

Step-by-step explanation:

[tex]0 = 4+4(m+1)[/tex]

Resolving Parenthesis

[tex]0 = 4+4m + 4[/tex]

[tex]0 = 4m+8[/tex]

Subtracting 8 to both sides

[tex]-8 = 4m[/tex]

[tex]4m = -8[/tex]

Dividing both sides by 4

m = -8/4

m = -2

Step-by-step explanation:

4+4m+4= 0

4m+8=0

4m=-8

m= -8/4=-2

Answer:

11 + Mai's Score = 59

Step-by-step explanation:

You need to add 11 and Mai's score together to get 59, so with the values given we can make the equation 11 + Mai's Score = 59.

*depending on the question, Mai's score may need to be said as a letter variable, so:

If m = mai's score,

11 + m = 59

I hope this helped! :)

Answer:

the smaller is 9 while the digger is 18

Answer: 63°

Step-by-step explanation:

Since BD is the diameter, then arc BCD = 180°

Given that arc BC = 54°, then arc CD = 180° - 54° = 126°

∠DBC is an intercepted angle -> DBC = half of arc CD

[tex]\angle DBC=\bigg(\dfrac{1}{2}\bigg)126^o\quad =\large\boxed{63^o}[/tex]

Answer:

63

Step-by-step explanation:

Answer:  4:9

Step-by-step explanation:

The complete question is provide in the attachment below.

Given, Number of females = 125

Number of males = 100

Total people = 120+100=225

Now, the ratio of males to the total number of people present = [tex]\dfrac{\text{Total number of males}}{\text{Total people}}[/tex]

[tex]=\dfrac{100}{225}[/tex]

Divide numerator and denominator by 25 , we get

Ratio of males to the total number of people present =[tex]\dfrac{4}{9}[/tex]

Hence, the ratio of males to the total number of people present =  4:9

Ans   k = 4

Step-by-step explanation:

Here g(x) =[tex]\frac{-1}{3}x + 1[/tex] and

        f(x) = [tex]\frac{-1}{3} x -3[/tex]

Now,  g(x) = f(x) + k

    or,      [tex]\frac{-1}{3}x + 1[/tex]  =  [tex]\frac{-1}{3} x -3 + k[/tex]

    or,      1 + 3 = k

    So,  k = 4   Answer.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

1) List out all distances singly, before rounding off.

i) From London to Paris → 517Km

ii) From Paris to Munich → 837Km

iii) From Munich to Vienna → 399Km

iv) From Vienna to Moscow → 2,088Km

2) Estimating the distances singly on the basis of rounding off to the nearest 100.

i) 517Km ≈ 500Km to the nearest 100

ii) 837Km ≈ 800Km to the nearest 100

iii) 399Km ≈ 400Km to the nearest 100

iv) 2,088Km ≈ 2,100Km to the nearest 100

3) Summing all estimated distances.

500 + 800 + 400 + 2100

= 3,800Km.

NB: when a number is equal or above 50, you are to round it off as 100; when the number is below 50, you are to round off as zero (0).

Answer:

EB = 9

Step-by-step explanation:

CD = AB

The line with the value of five that also forms a right angle with EB is a perpendicular bisector to AB.

So the value of EB is half of AB (AB is equal to CD).

18/2 = 9

Answer:

It is less  than 3000 ft^3 by 450 ft^3

Step-by-step explanation:

The volume of the bin

V = l*w*h

V = 17*15*10

V =2550 ft^3

If it less than 3000 ft^3

V = 3000- 2550 =450 ft^3

If is less by 450 ft^3

Answer:

Let’s first multiply all the numbers given

Since it wants the volume we need to use the formula

LxWxH

17x15x10=2,550

Part A: yes the bin is under 3,000

Part B: by 450 more because if you subtract 3,000 and 2,550 you will get 450

Hope this helps! :)

Answer:

-20

Step-by-step explanation:

Follow the PEDMAS order (from top to bottom):

Parentheses

Exponents

Division and Multiplication

Addition and Subtraction

(-5 × 9 - 1) ÷ 2 + (5)2 - 7

(-45 - 1) ÷ 2 + 10 - 7

-46 ÷ 2 + 10 - 7

-23 + 10 - 7

-13 - 7

-20

Answer:

-20

Step-by-step explanation:

=> [tex](-5 * 9-1)/2+(5)2-7[/tex]

Expanding parenthesis

=> [tex](-45-1)/2+10-7[/tex]

=> [tex]-46/2 + 3[/tex]

=> -23 + 3

=> -20

Answer:

None

Step-by-step explanation:

Let’s graph the points first.

Look at the image below.

And by looking at the image we can tell that none of the points lay on the same horizontal line.

Thus,

none of the points lay on the same horizontal line.

Hope this helps :)

Answer and explanation:

Advantages of open questions:

B. An open question allows for new solutions to be introduced.

D. An open question allows the respondent to go​ in-depth with their answer.

Disadvantages of open questions:

A. It is difficult to compare the results of surveys with open questions.

B. It is difficult to quantify the responses of open questions.

Advantages of closed questions:

- It is easy to compare the results of surveys with closed questions.

- It is easy to quantify the responses of closed questions.

Disadvantages of closed questions:

- A closed question limits the possible responses of the respondent.

-The researcher must spend time to generate a satisfactory list of possible responses from the respondent.

- possible answers may also be insufficient to be useful.

Open questions and closed questions in research questionnaires are two popular methods of getting data from respondents. They both have advantages and disadvantages and can be used interchangeably or together in questionnaires.

Closed Questions have defined answer alternatives or answer categories. Eg: Which is your favourite time of the day? (Morning or Evening etc)

Open Questions have free answers, not clear defined alternatives or categories. Eg : Why do you like morning/ evening time the most ?

Closed Questions give brief concrete answers, Open Questions have more essence of subjective & personal elaboration.

Advantages of Open Questions

Disadvantages of Open Questions

Advantages of Closed Questions

Disadvantages of Closed Questions

To learn more, refer https://brainly.com/question/2855510?referrer=searchResults

Answer:

Total ways = 5×5×5×5×5

Total ways = 5^5

Total ways = 3125

Therefore, the correct option is C) 5^5

Step-by-step explanation:

John has pairs of red, orange, yellow, blue and green socks.

Which means that John has 5 different colors pairs of socks.

We are asked to find out in how many ways can he wear them over 5 days.

1st Day:

On the first day John has 5 ways to choose from.

2nd Day:

On the second day John has 5×5 ways to choose from.

(Since repetition is allowed)

3rd Day:

On the third day John has 5×5×5 ways to choose from.

4th Day:

On the fourth day John has 5×5×5×5 ways to choose from.

5th Day:

On the fifth day John has 5×5×5×5×5 ways to choose from.

Total ways = 5×5×5×5×5

Total ways = 5^5

Total ways = 3125

Therefore, the correct option is C) 5^5

Answer:

x + 2y = 6

2y = -x + 6

y = -1/2x + 3

So, you will have a downward sloping, less steep line with an intercept at (0, 3).

You can use the Math is Fun Function Grapher and Calculator to graph the line.

Hope this helps!

Answer:

The answer is option B

Step-by-step explanation:

To find cos 45° we must first find the adjacent and the hypotenuse

Let the adjacent be x

Let the hypotenuse be h

To find the adjacent we use tan

tan ∅ = opposite / adjacent

From the question

the opposite is 9

So we have

tan 45 = 9 / x

x tan 45 = 9

but tan 45 = 1

x = 9

Since we have the adjacent we use Pythagoras theorem to find the hypotenuse

That's

h² = 9² + 9²

h² = 81 + 81

h² = 162

h = √162

h = 9√2

Now use the formula for cosine

cos∅ = adjacent / hypotenuse

The adjacent is 9

The hypotenuse is 9√2

So we have

cos 45 = 9/9√2

We have the final answer as

Hope this helps you

Answer:

2.8 cm

Step-by-step explanation:

The map scale is 1 cm : 5 km. That means that 1 cm is equal to 5 km.

To find the map distance (in cm), we have to set up a ratio.

[tex]\frac{1 cm}{5 km} = \frac{x}{14 km}[/tex]

X (the map distance in cm) is over the actual distance of 14 km.

Now cross multiply and divide.

[tex]5x = 14[/tex]

[tex]\frac{5x}{5} = \frac{14}{5}[/tex]

[tex]x = 2.8 cm[/tex]

If the actual distance to be represented is 14 km, the map distance (in cm) will be 2.8 cm.

Hope that helps.

Answer:

m<5 == m<1 since alternate interior angles are same value

m<3 == m<6 since alternate interior angles are same value

m<6 + m<5 + m<2 = m<1 + m<2 + m<3 = 180

Step-by-step explanation:

The use of alternate interior angles definition allows for you to make this completion.  You can use this since you have a line intersecting a point on two parallel lines.  From here, you know that the measures of the angles are the same as the measure of the line, thus you have proven the internal sum of angles to be 180 degrees.

Answer:

1. Sometimes

2. Sometimes

3. Always

4. Sometimes

Step-by-step explanation:

1. Quadratic function : in which maximum power of [tex]x[/tex] is two.

The roots of quadratic function can be either equal or different.

For example:

So, sometimes is the correct answer.

2. Cubic function has atleast 1 real root.

Cubic function has maximum power of [tex]x[/tex] as 3.

If the coefficients are real numbers then atleast 1 real root.

If the coefficients are imaginary in nature, then this is not true.

For example:

Cubic equation [tex]x^3 +i = 0[/tex] does not have any real root.

Cubic equation [tex]x^3 +1 = 0[/tex] has a real root x = -1.

So, it is sometimes true.

3. A function with degree 5 i.e. maximum power of [tex]x[/tex] as 5 will have 5 roots.

It is always true that a function will have number of roots equal to its degree.

4. Quadratic function can have only 1 complex solution.

Two complex solutions are also possible for a quadratic function.

For example:

[tex]x^{2} +1=0[/tex] will have two imaginary roots: [tex]x=i, -i[/tex]

It is also possible to have 1 complex solution,

For example:

[tex](x-1)(x-i) = 0[/tex] will have one complex root and one real root.

So, the statement is sometimes true.

Answer:

MY ANSWER IS CORRECT IN PLATO!!!

1. Sometimes

2. Always

3. Always

4. Never

Step-by-step explanation:

1. A quadratic function has 2 distinct roots SOMETIMES

2. A cubic Function has at least 1 root ALWAYS

3. A function with a degree of 5 has 5 roots ALWAYS

4. A quadratic function can have only 1 complex solution NEVER

I JUST GOT 100% on the quiz in PLATO

Answer: 430

Step-by-step explanation:

An average of 5 scores can be found via: (the sum of the scores)*5.  Thus, simply multiply 86*5 to get that the sum of his scores is 430

Hope it helps <3

Answer:

[tex] y'' =12x^2 -72=0[/tex]

And solving we got:

[tex] x=\pm \sqrt{\frac{72}{12}} =\pm \sqrt{6}[/tex]

We can find the sings of the second derivate on the following intervals:

[tex] (-\infty<x< -\sqrt{6}) , y'' = +[/tex] Concave up

[tex]x=-\sqrt{6}, y =-180[/tex] inflection point

[tex] (-\sqrt{6} <x< \sqrt{6}), y'' =-[/tex] Concave down

[tex]x=\sqrt{6}, y=-180[/tex] inflection point

[tex] (\sqrt{6}<x< \infty) , y'' = +[/tex] Concave up

Step-by-step explanation:

For this case we have the following function:

[tex] y= x^4 -36x^2[/tex]

We can find the first derivate and we got:

[tex] y' = 4x^3 -72x[/tex]

In order to find the concavity we can find the second derivate and we got:

[tex] y'' = 12x^2 -72[/tex]

We can set up this derivate equal to 0 and we got:

[tex] y'' =12x^2 -72=0[/tex]

And solving we got:

[tex] x=\pm \sqrt{\frac{72}{12}} =\pm \sqrt{6}[/tex]

We can find the sings of the second derivate on the following intervals:

[tex] (-\infty<x< -\sqrt{6}) , y'' = +[/tex] Concave up

[tex]x=-\sqrt{6}, y =-180[/tex] inflection point

[tex] (-\sqrt{6} <x< \sqrt{6}), y'' =-[/tex] Concave down

[tex]x=\sqrt{6}, y=-180[/tex] inflection point

[tex] (\sqrt{6}<x< \infty) , y'' = +[/tex] Concave up

Answer: 9/7 or -5/2

Step-by-step explanation:

We can only factorise quadratics if they're in the format ax^2 + bx + c

Re-arranging the equation gives 14x^2 + 17x - 45 = 0

Factorising this quadratic gives:

(7x - 9)(2x + 5) = 0

There are numerous ways to factorise quadratics, using a calculator or via alternate methods you may have learnt in class. (E.g. 2 numbers multiply to make (14 * -45) and add up to make (17).

This gives us our solutions.

x = 9/7 or x = -5/2

Answer:

See below.

Step-by-step explanation:

First, move all the terms to one side so we have only a zero on the right:

[tex]6x^2-17x+13=20x^2-32\\-14x^2-17x+45=0\\14x^2+17x-45=0[/tex]

(I divided everything by negative 1 in the third step. This is optional, but I like having the first term positive.)

Now, we just need to factor it. To factor, what you want to do is find two numbers a and b such that:

When a and b is multiplied together, they equal the first coefficient and constant multiplied together.

And when a and b is added together, they equal the second term.

In other words, we want to find two numbers that when multiplied equals 14(-45)=-630 and when added equals 17. Then, we can substitute this into the 17. You do this by guessing and checking. It's useful to have a calculator.

After a bit, you can find that 35 and -18 works. Thus:

[tex]14x^2+17x-45=0\\14x^2+35x-18x-45=0\\7x(2x+5)-9(2x+5)=0\\(7x-9)(2x+5)=0[/tex]

Now, the finish the problem, we just need to use the Zero Product Property and solve for x:

[tex]2x+5=0\\x=-5/2\\\\7x-9=0\\x=9/7[/tex]

Note: This only works for quadratics.

Answer:

50

Step-by-step explanation:

The ratio of marked fish to caught fish is 4:10, we need to solve for x in 20:x, since 4 * 5 = 20, 10 * 5 = x so x = 50 fish.