The Math Club is ordering food to be delivered to their meeting. They have a coupon for $10 off their order, and each member contributes an additional $5 for the food. The expression 5n + 10 represents the total amount they can spend on their order. Why would it not make sense to substitute 12.125 for n in this expression? A n represents the number of members, so it must be a whole number. B 5n represents the number of members, so n must be a whole number. C n represents an amount of money, so it cannot have more than two decimal places. D 5n represents an amount of money, so n cannot have more than two decimal places.

Answer:

a = 94

b = -66√3

Step-by-step explanation:

Given  z = [tex]-1-i\sqrt{3}[/tex]

[tex]z^{6}=(z^{3})^{2}[/tex]

[tex](-1-i\sqrt{3})^6=[(-1-i\sqrt{3})^3]^2[/tex]

                   [tex]=[-(1+i\sqrt{3})^3]^{2}[/tex]

                   [tex]=[(1+i\sqrt{3})^3]^2[/tex]

                   [tex]=[(1)^3+(i\sqrt{3})^3+3(1)^2(i\sqrt{3})+3(1)(i\sqrt{3})^2]^2[/tex] [(a + b)³ = a³ + b³ + 3a²b + 3ab²]

                   = [1 + 3i² + 3i√3 + 9i²]²

                   = [1 - 3 + 3i√3 - 9]²

                   = [-11 + 3i√3]²

                   = (11)² -2(3i√3)(11) + (3i√3)²

                   = 121 - 66i√3 + 27i²

                   = 121 - 66i√3 - 27

                   = (94 - 66i√3)

Comparing it with (a + bi),

a = 94 and  b = -66√3

Answer:

2/3

Step-by-step explanation:

f(x)=g(x)

-3x+4=2

Add 3x

3x+2=4

subtract 2

3x=2

divide by 3

x=2/3

Answer:

x= 2/3

Step-by-step explanation:

The value where f(x) = g(x) is where the two functions intersect

That would be at

f(x) = g(x)

-3x +4 = 2

Subtract 2 from each side

-3x = -2

x = 2/3

We know the y value.  Substitute x into the equation

g(2/3) = 2

y = 2

The point is (2/3,2)

Answer:

Pythagorean Theorem: a² + b² = c²

Step-by-step explanation:

7-24-25

7² + 24² = 25²

49 + 576 = 625

625 = 625

9-40-41

9² + 40² = 41²

81 + 1600 = 1681

1681 = 1681

Answer: See Explanation

Step-by-step explanation:

Pythagoras' theorem is [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex].

So [tex]7^{2}[/tex] (49) + [tex]24^{2}[/tex] (576) = [tex]25^{2}[/tex] (625)

Same goes for the other one. It is always the smallest number squared (smallest side of triangle) + the middle number squared (middle length side of triangle, = the biggest side/number squared.

Answer:

32

Step-by-step explanation:

k

Answer:

hope this helps, take care, stay safe, keep smiling

Step-by-step explanation:

i see 40 squares

Answer:

Step-by-step explanation:

Not liking rock mostly doesn't effect not liking just rap, since half like both rock and rap.

Though, there are 2 more people that like just rock compared to just rap, so you are more likely to like just rock.

Additionally, if you don't like rock, there is a 31.4 % that you don't like rap as well, since 17 people like neither.

Answer:

x=3, y=2

Step-by-step explanation:

since y =2x-4, we name it as equation I

and the second system as equation 2.

we substitute equation 1 into 2 and we have;

4x+3(2x-4)=18

4x+6x-12=18

10x=18+12

x= 30÷10

x=3.

now, substituting x=3 into the y equation , we have

y= 2(3)-4

y=2.

therefore, x=3, y=2.

...if I was to plot this I would use the equation intercepts. Some people might use the slope whichever is okay for you. but I like to use the intercepts...(x,y)

so first, to find the intercept of equation 1;

we have,

y=2x-4

we set x= 0 and we get .y=2(0)-4=-4, we have (0,-4)...x=0, y=-4 for intercept

we set y to 0 to get the intercept for x...

we have, 0=2x-4=2..we get (2,0)...x=2, y=0 for the second intercept.

we do same for the second equation...

4x+3y=18...

so when doing this set x to 0 to get y intercept that is (0,y) and set y= 0 to get the x intercept that is (x,0)... then you can plot the points on your graph...

the intercept of the two system after you've plotted it on your graph should give you the solution we have that is x=3, y=2.

Answer:

A is the answer

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

the best estimate is 25 cm

Step-by-step explanation:

the best estimate is 25 cm

because A would be too small

C too long

D way too much

Answer:

C ) 25 is your answer

Step-by-step explanation:

the other answers are unreasonable and don't make

sense so this is your best estimate.

Answer:

The smaller exterior angle is the exterior angle in the vertex P, and it measures 90°

Step-by-step explanation:

The sum of the internal angles of a triangle needs to be 180 degrees, so we have two equations:

[tex]mP = mQ + mR[/tex]

[tex]mP + mQ + mR = 180\°[/tex]

Substituting [tex]mQ + mR[/tex] by [tex]mP[/tex] in the second equation, we have:

[tex]mP + mP = 180\°[/tex]

[tex]mP = 90\°[/tex]

The other two angles need to be lesser than mP, and the exterior angle is the supplement of the internal angle, so the bigger the internal angle, the smaller the exterior angle.

So if the bigger internal angle in this triangle is mP, the smaller exterior angle is also the angle in the vertex P:

[tex]exteriorP = 180\° - mP[/tex]

[tex]exteriorP = 90\°[/tex]

Answer:

B (10, 5)

Step-by-step explanation:

We simply set the midpoint equal to each of its respective variable equation in [tex]m = (\frac{x1+x2}{2},\frac{y1+y2}{2} )[/tex]

Step 1: Solve x

4 = (-2 + x)/2

8 = -2 + x

x = 10

Step 2: Solve y

3 = (1 + y)/2

6 = 1 + y

y = 5

Put it in coordinates and we have our final answer!

Answer:

B(10,5)

Step-by-step explanation:

You already have A and M so you just find the difference and add it to M.  That is my way of getting the answer.  I am taking the Honors Geometry class in 6th grade.  

Answer:

7

Step-by-step explanation:

CD is congruent to BC by CPCTC.

Answer:

a) 2 -2 -4 -4 -2 2 8

b) graph B

c) x = -2.55 or x=1.55

Step-by-step explanation:

a) just fill in the x values

b) look at x=0, you'll find y=-4. Only graph B goes through (0, -4)

c) estimate where graph B passes through the x axis.

Answer:

rational

Step-by-step explanation:

Answer:

Rational Number

Step-by-step explanation:

A repeating decimal added to a fraction will result in a rational number.

Answer: B) increasing for x < -4/3 and x > 4/3

                   decreasing for -4/3 < x < 4/3

Step-by-step explanation:

Graph the equation and follow the curve from left to right. If you are going up, it is increasing. If you are going down, it is decreasing.

Refer to the image below. Red is increasing. Blue is decreasing.

The vertices are at: x = -4/3 and x = 4/3

Answer:

1. sum of term = 465

2. nth term of the AP = 30n - 10

Step-by-step explanation:

1. The sum of all natural number from 1 to 30 can be computed as follows. The first term a = 1 and the common difference d = 1 . Therefore

sum of term = n/2(a + l)

where

a = 1

l = last term = 30

n = number of term

sum of term = 30/2(1 + 30)

sum of term = 15(31)

sum of term = 465

2.The nth term of the sequence can be gotten below. The sequence is 20, 50, 80 ......

The first term which is a is equals to 20. The common difference is 50 - 20 or 80 - 50 = 30. Therefore;

a = 20

d = 30

nth term of an AP = a + (n - 1)d

nth term of an AP = 20 + (n - 1)30

nth term of an AP = 20 + 30n - 30

nth term of the AP = 30n - 10

The nth term  formula can be used to find the next term progressively.  where n = number of term

The sequence will be 20, 50, 80, 110, 140, 170, 200..............

Answer:

There are 640 pigs after 5 years.

Step-by-step explanation:

if it doubles each year the first year it doubles it is 40 then the second 80 third 160 fourth 320 and fifth 640.

graph it by having the X axis the years and the Y axis do it by 40s

Answer:

the first one is 6^10

the 2nd one is also 6^10

Step-by-step explanation:

Answer:

[tex]6^{10}[/tex]

Step-by-step explanation:

Any number to the power of zero becomes 1. Any number times 1 is itself.

Answer:

A.

Step-by-step explanation:

Diameter = 4.4 cm

Radius = 2.2 cm

Now

Area of the circle = πr²

= (3.14)(2.2)²

= (3.14)(4.84)

= 15.1976 cm²

Answer:

A.

Step-by-step explanation:

D=4.4, therefore, the Radius is equal to 2.2, half of the diameter.

The formula for Area:

A=pir^2.

A=(3.14)(2.2)^2

A=(3.14)(4.84)

A=15.1976

A=15.1976, which is identical to option A.

Answer:

C

Step-by-step explanation:

Δ AQP and Δ ACB are similar triangles, thus the ratios of corresponding sides are equal, that is

[tex]\frac{AQ}{AC}[/tex] = [tex]\frac{PQ}{BC}[/tex] ( note that AC = 3 + 6 = 9 ), substitute values

[tex]\frac{3}{9}[/tex] = [tex]\frac{4.5}{BC}[/tex] ( cross- multiply )

3BC = 40.5 ( divide both sides by 3 )

BC = 13,5 cm → C

Answer:

Area is 113.097

Step-by-step explanation:

Answer:

113.10 ft²

Step-by-step explanation:

Area of the circle is equal to πr².

Where r is the radius. The radius of the circle is 6 feet.

π(6)²

36π = 113.097336

The area of the circle is 113.10 ft² approximately.

Answer:

The slope of the line will be ZERO.

From the question given above, we are told that when the freezer is working perfectly that the temperature will remain constant over time. This means that if the graph of temperature and time is drawn, the slope of the graph will be constant from one point of the graph to the other, which means that the values will cancel each other out and will be zero.

Step-by-step explanation:

Let the numbers be x and y

2 consecutive even nos.

therefore y = x+2

twice of the first (2x) is 46 more than y

2x = y+46

Solving both the equations

x - y + 2 = 0

(-)2x - y - 46 = 0

____________

-x + 0 + 48 = 0

____________

x = 48

y = x+2

= 48 +2

= 50

Therefore the 2 nos. are 48 and 50

Hope this answers helps you

Answer:

a for saturn is 9.55 astronomical units

Step-by-step explanation:

Here, we are interested in calculating the distance from the sun.

Mathematically, from the question;

P = a^3/2

29.5 = a^3/2

a = 29.5^2/3

a = [3√(29.5)]^2

a = 9.55 in astronomical units

Answer:

a) 9.5 AU

Step-by-step explanation:

on edge

Answer:

The answer is option 2.

Step-by-step explanation:

You have to substitute the value of y into the equation :

[tex]8x - 2y = 48[/tex]

[tex]let \: y = 4[/tex]

[tex]8x - 2(4) = 48[/tex]

[tex]8x - 8 = 48[/tex]

[tex]8x = 48 + 8[/tex]

[tex]8x = 56[/tex]

[tex]x = 56 \div 8[/tex]

[tex]x = 7[/tex]

The value of x in the equation 8x - 2y = 48 is 7.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

We have,

8x - 2y = 48

Now, for y=4 put the value of y as 4 in given equation we get

8x- 2(4)= 48

8x -8= 48

8x = 48+ 8

8x = 56

x= 56/8

x= 7

Thus, the value of x is 7.

Learn more about Equation here:https://brainly.com/question/29657983

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Answer:

Step-by-step explanation:

there is no soltion because it is not intersects

Answer:

No solution as it will not intersect.

Answer:

The answer is 7

because 40 times 7 is 280 then we double 7 to 14 because remember it says he paid 2 times his hourly rate after 40 hours so then we multipy 14 times 10 and it will give you 140 so then u add them to get his total of $420

Answer:

45 people prefered coffee, 81 people prefered tea. A total of 126 people were surveyed.

Step-by-step explanation:

Let t be the people who prefer tea, and let c be the people who prefer coffee.

The ratio between tea and coffee is 9:5, thus we have t/c=9/5. Cross products  give us 5t=9c.

Also, we have 36 more people prefer tea than coffee, so we have c+36=t

Thus we have: 5(c+36)=9c

5c+180=9c

180=4c

c=45

c+36=t

45+36=81

Answer: 2.5 hours or 2 hr and 30 min

Step-by-step explanation:

We can set up an equation to find how many hours you can park.

2.5+4x=12.5

The 2.5 comes from the base fee. The 4x is the hourly rate, where x is hours. The 12.5 is the total amount of money you have.

Since we have our equation, we can solve for x.

4x=10

x=2.5

You can park for 2.5 hours, or 2 hours and 30 min.

Answer:

first option

Step-by-step explanation:

I don't know how to explain