Luca's science class is making slime from cornstarch and glue. Luca is helping pass out materials. He gives each student 80 grams of cornstarch from a 2-kilogram bucket. If Luca's class has a total of 21 students, how many grams of cornstarch will he have left?

Answers:

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Explanation:

Think of a hexagonal room with n = 6 walls, i.e. the floor is a hexagon with n = 6 sides. The floor and ceiling are parallel to each other, and congruent hexagons. That's 2 faces so far. Then we have another 6 faces to account for the walls. This gives 2+6 = 8 faces of a hexagonal prism.

In more general terms, a prism with a base of n sides will have 2 parallel and congruent base faces, and n walls or lateral faces. This gives n+2 total faces.

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Let's go back to the hexagonal prism. The floor has 6 sides to it, and so does the ceiling. We have 6+6 = 12 edges so far. Then we have another 6 edges where each of the rectangular walls meet up. That gives 12+6 = 18 edges total of this hexagonal prism room.

For any more general case, each base has n sides. That gives 2n sides so far for just the bases. Then add on another n for the lateral edges and we get 3n total edges.

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Once again lets revisit the room with the hexagonal floor and ceiling. The floor has 6 vertices and the ceiling has the same vertex count. Therefore, this prism has 6+6 = 12 vertices.

For the general case, each base has n vertices. There are 2 such identical bases giving 2n vertices total.

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One way to check the answer:

We could use Euler's Polyhedron Formula which is

F+V-E = 2

where,

For the hexagonal prism we found

Then notice how

F+V-E = 2

8+12-18 = 2

20-18 = 2

2 = 2

This confirms the formula works for a hexagonal prism.

Now let's check it for the more general case

We found earlier that,

So,

F+V-E = 2

n+2+2n-3n = 2

3n-3n+2 = 2

0n+2 = 2

0+2 = 2

2 = 2

This helps confirm the answer for any prism with the base of n sides.

Answer:

12+9r

Step-by-step explanation:

3(4+3r) = 3*4+3*3r = 12+9r

By using the second condition, we conclude that there are 23 white roses in the tray.

First, we know that there are a total of 50 roses in the tray, and we have the conditions:

The second statement means that, always that we take 28 roses, at least one of them is white. So, there are 27 roses in the tray that are not white.

Whit that in mind, if the 28th rose must be white, then all the remaining roses in the tray are white, this means that there are:

50 - 27 = 23 white roses.

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Answer:

C) <AFL

Step-by-step explanation:

The middle angle typically goes in the middle of the three letters. So, the naming should look like <FAL or <LAF. The letter A would have to remain in the middle for the naming to be correct.

Angles can be named in these following ways:

- By three capital letters (vertex (middle point) always in the middle)

- By one capital letter (typically the vertex)

- By a lowercase letter or number that is in the middle of the angle

Therefore, the incorrect naming would be C) <AFL, since the vertex isn't in the middle.

Hope this helps!! If you have questions please let me know in the comments!

Answer:

a line segment

Step-by-step explanation:

Answer:

A line segment is part of a line that has two endpoints and is finite in length. A ray is a line segment that extends indefinitely in one direction.

Step-by-step explanation:

hope this helps

The equivalent equation of the algebraic Equation (4x - 7)² + 16 = 40x - 70 is; p² + 16 - 10p = 0

We want to simplify the algebraic Equation;

(4x - 7)² + 16 = 40x - 70

Factorize right hand side to get;

(4x - 7)² + 16 = 10(4x - 7)

If p = 4x - 7, then we have;

p² + 16 = 10p

Using subtraction property of equality gives;

p² + 16 - 10p = 10p - 10p

p² + 16 - 10p = 0

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Answer:

E. 12.5

Step-by-step explanation:

[tex](12 \times 2) + 1 = 25 \\ \frac{25}{2} [/tex]

Answer:

B

Step-by-step explanation:

25/2  = 12.5

so, 12.5 /100

= 1/8

Therefore b is the correcrt answer

You should plot the total distance traveled from the base camp on the x-coordinate while the elevation should be plotted on the y-coordinate.

A graph simply refers to a type of chart which is commonly used to graphically represent data on both the vertical and horizontal lines of a cartesian coordinate (x-coordinate and y-coordinate).

In this scenario, you would plot the total distance traveled from the base camp on the x-coordinate while the elevation of the camps would be plotted on the y-coordinate as shown in the image attached below.

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Answer:

38.73 cm

Step-by-step explanation:

Given:

Solution:

S² = (R - r)^2xh^2

(40)^2=(30-20)^2+h^2

1600=(10)^2+h^2

1600-100=h^2

h=√1500

h=10√15

h=38.73 (rounded to the nearest tenth)

Answer:

Question 23: 39

Question 24: 10

Question 25: Airline B

Question 26: 20 to 50

Step-by-step explanation:

Decimal 0,22

fraction 22/100

Answer: 11/50 and 0,22

Step-by-step explanation:

*FRACTION* 22/100, then simplify 11/50.

*DECIMAL* 0,22 x 100 22

Answer:

................

Step-by-step explanation:

Answer:

B) $60.00

Explanation:

The cost for pet sitting per day (1 day) is $7.50

Then for 8 days, Cost = per day price × number of days = $7.50 × 8 = $60

∴ Cathy charge $60 to pet sit for 8 days.

Take two points

Slope

Equation

So for 8 days

Answer:

36

Step-by-step explanation:

4 x 9 = 36

36 / 4 = 9

Therefore, 36 is 4 times as much as 9.

[tex]{\sf Hello!}[/tex]

The answer is 36

⇢ 4 × 9 = 36

Answer:

180-108=72   72/2=36 degrees

Step-by-step explanation:

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Seeing as this is a right triangle, we would solve for the unknown angle using a trigonometric function.

Remember! SOH-CAH-TOA

Looking from the unknown angle, we are given the adjacent side and the hypotenuse. Therefore, we should use the cosine function.

cos(?) = 17 / 19

---To find the unknown angle measure, you will need to use the inverse cosine function. This function is generally found by using the "2nd" button on your calculator and then pressing the cosine button. It should look like one of the following options: "cos^-1" or "arccos".

Make sure your calculator is in degrees, not radians!

cos^(-1) [17/`9]

26.52

---Round to the nearest degree per the instructions

Answer: 27 degrees

Hope this helps!

Answer: Ellipse

This cross section is not parallel to the circular base, so we get a stretched out circle of sorts. In other words, we get an ellipse.

Answer:

[tex]2x - 2y = 24 \\ 2(x - y) = 24 \\ x = 12 + y......eq(1) \\ 4x + 7y = - 40......eq(2) \\ substituting \: the \: value \: of \: x \: in \: eq(2) \\ 4(12 + y) + 7y = - 40 \\ 48 + 4y + 7y = - 40 \\ 11y = - 40 - 48 \\ y = \frac{ - 88}{11} \\ y = - 8 \\ putting \: the \: value \: of \: y \: im \: eq(1) \\ x = 12 - 8 \\ = 4[/tex]

Step-by-step explanation:

3x-2y=24......eqi

x+2y=48........eqii

now solving eq i&ii

4x=72

x=72/4

x=18

now putting the value of x in eqii

18+2y=48

2y=48-18

y=30/2

y=15

Answer:

Mary's route = 49.73 miles

Step-by-step explanation:

[tex] {r}^{2} = {x}^{2} + {y}^{2} [/tex]

[tex]r = \sqrt{ {x}^{2} + {y}^{2} } [/tex]

[tex]r = \sqrt{ {48}^{2} + {13}^{2} } [/tex]

[tex]r = \sqrt{2473} [/tex]

[tex]r = 49.73 \: miles[/tex]

[tex] \sqrt{2840} = 53.3 \: miles[/tex]

#1: Mary's route = 49.73 miles

#2: Theo's route = 50 miles

#3: Nancy's route = 53.3 miles

Answer:

first is 49. 73; second Mary, Theo, Nancy

Step-by-step explanation:

I took the assignment on edge so yeah pleasure to help ^^

Answer:

Min = 1 4/6

Max = 3

Sum = min + max

=> sum = 1 4/6 + 3

=> sum = 4 /4/6

Answer:

4 4/6

Step-by-step explanation:

To solve this problem, we must consider all the trigonometric equations:

 ⇒ (see image below)

Let's examine the diagram:

Thus we can use:

 [tex]cos(A)=\frac{35}{53} \\A= cos^{-1}(\frac{35}{53})\\ A = 48.67[/tex]

Answer: 49 degrees (as rounded)

Hope that helps!

The expression (7+ y) ∙9 is described by its factors and terms as; lt is has two factors and the factor (7+ y) has two terms.

(7 + y) × 9

63 + 9y

The factors are 7 and y and the two terms are 63 + 9y.

Therefore, the correct answer is; lt is has two factors and the factor (7+ y) has two terms.

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Answer:

3  1/2

Step-by-step explanation:

So because the fraction in attatched to the whole numbers have the same denominator you can literally just subtract the whole numbers and the fractions. (You do them seperatly) (5-2)=3   (3/4-1/4) = 2/4 or 1/2

The parabola y=x^2 is reflected across the x axis and then scaled vertically by a factor of 1/8 is y = [tex]-\frac{1}{8}[/tex] x².

The general equation of a parabola is: y = a(x-h²2 + k or x = a(y-k)² +h, where (h,k) denotes the vertex.

The standard equation of a regular parabola is y² = 4ax.

The given equation is of parabola : y= x²

Now, we have to reflect across the x- axis and then scaled vertically by a factor 1/8.

When we reflect this parabola in the x-axis and then scaled vertically by a factor of 1/8.

Then, the new equation of parabola be:

  y = [tex]-\frac{1}{8}[/tex] x²

Hence, The parabola y=x² is reflected across the x axis and then scaled vertically by a factor of 1/8 is y = [tex]-\frac{1}{8}[/tex] x².

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The 90 gallons of water is in the fish tank if the fish tank has 240 quarts of water. Levi adds another 120 quarts to the tank.

It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, multiplication by a conversion factor.

We have a fish tank has 240 quarts of water.

Levi adds another, 1201 quarts to the tank.

Total water in the tank = 240 + 120 = 360 quartz

To convert quartz to gallon, divide by 4

Total water in the tank = 360/4 = 90 gallons

Thus, the 90 gallons of water is in the fish tank if the fish tank has 240 quarts of water. Levi adds another 120 quarts to the tank.

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Based on the balance at the start of May and the purchases and payments made by Ruth, the balance at the beginning of April was b. $797.22.

First find the monthly rate:

= 10.91% / 12

= 0.909%

The beginning balance is x:

May balance = (Beginning balance x (1 + monthy rate) + Purchases - Payments

847.64 = x × 1.00909 + 88.34 - 45.17

1.00909x = 847.64 - 88.34 + 45.17

x = $797.22

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Answer:

B on edge

Step-by-step explanation:

Answer:

You infer that mean weight of catfusf in the lake is close to 2.2lbs

Step-by-step explanation:

Because it's a random sample of 50.

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[tex]\diamond\large\textsf{\textbf{\underline{\underline{Question:-}}}}\diamond[/tex]

             What is the equation of the line that passes through the point  (2, 5) and has a slope of 5?

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}\diamond[/tex]

First let's write the equation of the line in point-slope form:-

[tex]\sf{y-y_1=m(x-x_1)}[/tex]

Substitute 5 for y₁, 5 for m and 2 for x₁:-

[tex]\sf{y-5=5(x-2)}[/tex]

That's the equation of the line in Point-slope form.

Now let's convert it into slope-intercept:-

[tex]\sf{y-5=5x-10}[/tex]

Adding 5 to both sides results in our slope intercept equation, which looks like this:-

[tex]\dashrightarrow\bigstar\boxed{\boxed{\bold{\underline{y=5x-5}}}}\bigstar\dashleftarrow[/tex]

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Answer:

  3 1/2 square units

Step-by-step explanation:

For this small triangle whose vertices are on grid points, the use of Pick's theorem will give the area with the least work.

__

Pick's theorem says that the area is ...

  A = i +b/2 -1

where i is the number of grid points inside the boundary, and b is the number of grid points on the boundary.

Here, only the given coordinates are boundary points that are on grid points. (b = 3)

The figure shows us three grid intersections inside the boundary of the triangle. (i = 3)

That means the area is ...

  A = 3 +3/2 -1 = 3 1/2 . . . . square units

_____

Alternate solution

The triangle is bounded by a square 3 units on a side. From that, we can subtract a 2×3 triangle at upper left, a 1×2 triangle at upper right, and a 3×1 triangle at the bottom. That leave a figure area of ...

  A = 3² -1/2(2×3) -1/2(1×2) -1/2(3×1) = 9 -3 -1 -3/2 = 3 1/2 . . . . square units

(The area of a triangle is 1/2bh, where b and h are the base and height of the triangle.)

__

Another alternate solution can be had by using a formula with the vertex coordinates:

  A = 1/2|(x1)(y2 -y3) +(x2)(y3 -y1) +(x3)(y1 -y2)|

  = 1/2|(-8)(3 -5) +(-5)(5 -2) +(-6)(2 -3)| = 1/2|16 -15 +6| = 3 1/2 . . . square units