An open box is to be made out of a 12-inch by 20-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the resulting box that has the largest volume.

Answer:

8.2 * 10^-3 is the greatest and 5.2 * 10^-6 is the smallest.

Step-by-step explanation:

The missing parts of the given table are

∠1 ≅ ∠4                  → Alternate interior angles Theorem

DB ≅ DB                 → Reflexive property

ΔDAB ≅ ΔBCD       → SAS (Side Angle Side)

From the question, we are to complete the table to prove that ABCD is a parallelogram

The missing parts in the table can be completed as shown below

∠1 ≅ ∠4                  → Alternate interior angles Theorem

DB ≅ DB                 → Reflexive property

ΔDAB ≅ ΔBCD       → SAS (Side Angle Side)

Hence, the missing parts of the given table are

∠1 ≅ ∠4                  → Alternate interior angles Theorem

DB ≅ DB                 → Reflexive property

ΔDAB ≅ ΔBCD       → SAS (Side Angle Side)

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.

The surface area of the triangular prism is 330 centimetres cube.

surface area of a triangular prism = (a + b + c) l + 2(base area)

where

Hence,

surface area = (5 + 12 + 13)9 + 5 × 12

surface area = 30(9) + 60

surface area = 270 + 60

surface area = 330 cm³

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Answer:

4,105 yd cubed

Step-by-step explanation:

This can be divided into three rectangular prisms, one of which is constructed from triangular prisms

19*9*10 = 1,170 yd

30*9*7 = 1,890 yd

10*5.5*9 = 1,045 yd

Adding them all together gets

4,105 yd cubed

Answer:

Just add me and let's our journey begins :3

Step-by-step explanation:

Just add me and let's our journey begins :3

Answer:

If they are 28 Oz and a deviation of 2 it will be 26 so 26 times 800 will be 4800. so technically 1 bag is 26oz so the answer is 1 bag.

Answer:2/7

Step-by-step explanation:

TThe solution is in the image

Answer:

The third measurement is 62°

Step-by-step explanation:

Hey there! Please take a look at the explanation for clear understanding to the answer and also let me know in comment if you have any doubts!

The theorem regarding it states that, sum of all 3 interior angles must equal to 180°.

That means, we will have this equation:

[tex]\displaystyle \large{28^{\circ} + 90^{\circ} + x=180^{\circ}}[/tex] because we know two interior angles and one missing angle - sum of them equals to 180 degrees.

Then we solve for x-term to find the third measurement!

[tex]\displaystyle \large{118^{\circ}+x=180^{\circ}}[/tex]

Subtract both sides by 118 degrees.

[tex]\displaystyle \large{118^{\circ}-118^{\circ}+x=180^{\circ}-118^{\circ}}\\\\\displaystyle \large{x=62^{\circ}}[/tex]

Henceforth, the third measurement is 62°

Answer:

53

Step-by-step explanation:

7 * 7 = 49 + 4 = 53

Answer:

A. 53

Step-by-step explanation:

Find number of trophies on shelves:

7 shelves x 7 trophies each = 49 trophies on shelves

Find total number of trophies:

49 trophies on shelves + 4 leftover = 53 trophies overall

So the answer is A. 53

Answer:

Step-by-step explanation:

3y-9x=9

3y-9x+9x=9+9x

3y=9x+9

y=3x+3

If a line is perpendicular to an equation, the slope is flipped.

So, 3x would equal to -3x.

The final equation is y=-3x+3

Answer:

(-1;4)

Step-by-step explanation:

as the triangles are congruent

The coordinate of point F is (1-, 4). Therefore, option A is the correct answer.

A coordinate plane is a two-dimensional surface formed by two number lines. It is formed when a horizontal line (the X-axis) and a vertical line (the Y-axis) intersect at a point called the origin. The numbers on a coordinate grid are used to locate points.

From the given graph, the coordinate points are A(-5, 0), B(-5, -5) and C(2, -5).

Here, ΔABC and ΔDEF are congruent triangles.

So, the coordinate of point F are (1-, 4)

Therefore, option A is the correct answer.

Learn more about the coordinate plane here:

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Answer: 473 square meters

Step-by-step explanation:

Answer:

-102.1

Step-by-step explanation:

When adding negative numbers, act as if you are subtracting that same number, but in its positive form.

So in reality, you could rewrite the equation as: (-7.8) - 12 - 82.3 = -102.1

Answer:

X Intercepts: (3,0) , (-1,0)

Y Intercepts: None

Hope this helps.

Answer:

Question 6a: [tex]p \leq 16[/tex]

Question 6b: option d

Step-by-step explanation:

Question 6a: [tex]6p \leq 96\\6p/6 \leq 96/6\\p \leq 16[/tex]

Question 6b:

- closed dot since its equal to 16

- p is less than 16 (arrow pointing left)

Answer:

(x+5,y) = Yes

(5x,5y) = No

(.5x,.5y) = No

(x,-y) Yes

(-x,-y) Yes

Step-by-step explanation:

Answer:

Method of paragraph or essay development in which a writer analyzes the reason for - and / or the consequences of - an action , event, or decision

Answer:

C. Shows relationship between events, explains how one thing happens as a result of another

Step-by-step explanation:

Answer:

Step-by-step explanation:

I can't really explain, but Here comes the hoping:

Equation 1:

Equation 2:

Equation 3:

Equation 4:

Equation 5:

Answer:

J. 12 : 18

Step-by-step explanation:

Amy used 2 tea bags for every 3 cups of water to make iced tea

the ratio here is 2:3

x = 2:3

lets simplify our ratios

6 : 10 = 3 : 5 ≠ 2 : 3

5 : 6 = (doesn't simplify evenly) ≠ 2 : 3

9 : 15 = 3 : 5 ≠ 2 : 3

12 : 18 = 2 : 3 = 2 : 3

find their highest common factor and divide both the numbers by the same amount (HCF).

Ex.

12 : 18

12 ÷ 6 = 2

18 ÷ 6 = 3

2 : 3

Answer:

168 [tex]cm^{3}[/tex]

Step-by-step explanation:

Start by finding the whole prism's volume. 9 x 3 x 8 = 216 Then find the volume of the missing part. 8 x 6 x 1 = 48. Subtract the missing volume from the whole volume. 216 - 48 = 168

Answer:

Step-by-step explanation:

Remark

9.3 x and 60 degrees are all related to the Tangent of L or Tan(L) as you would find it on your calculator.

Givens

Formula

Tan(60) = opposite / Adjacent                Substitute Values

Solution

Tan(60) = 9.3 /  x                                      Multiply both sides by x

x*Tan(60) = x * 9.3 /x              

x* Tan(60) = 9.3                                         Divide both sides by Tan(60)

x * Tan(60) / Tan(60) = 9.3/Tan(60)

x = 9.3 / 1.7321

x = 5.369

Answer

x = 5.4                              

Answer:

x=63/8

Step-by-step explanation:

9/8=x/7

or, 9*7=x*8

or, 63=8x

x=63/8

Answer:

D

Step-by-step explanation:

cotangent = cos / sin        

                 = 4/3

using pythagorean theorem   4^2 + 3^3 = h^2      <=====  h = 5

      then cos = 4/5    sin = 3/5    

               then,  since    csc = 1/sin = 5/3

Answer:

Y less than or equal to zero

Step-by-step explanation:

The graph shows that its moving downwards, therefore the Y value is decreasing..

Answer:

1 hot dog = $1.50 each

1 hamburger = $1.75 each

Step-by-step explanation:

Answer:

The prices must be $1.50 and $1.75

Step-by-step explanation:

For instance, seven hot dogs and two hamburgers cost $14: 7D+2B=14

We also know that two hot dogs and seven hamburgers cost $15.25: 2D+7B=15.25

Now, if we combine these two equations, we have a system where EVERYTHING has to be true at the same time 

7D+2B=14

2D+7B=15.25

From here there are a couple trick you should know to solve a system of equation, especially substitution and elimination. I see a coefficient of 2, so I'd rather use substitution by dividing the entire first equation in half:

3.5D+B=7

Now I'll solve for B

B=7-3.5D

Now that I've solved for a variable, I can substitute the solution into the other equation

2D+7(    B   )=15.25

becomes

2D+7(7-3.5D)=15.25

Now I can distribute and solve for D:

2D+49-24.5D=15.25

22.5D=33.75

D=1.5

Now we can replace D from either (or both) of our original equations and see what B has to be

7(1.5)+2B=14

10.5+2B=14

2B=3.5

B=1.75

2(1.5)+7B=15.25

3+7B=15.25

7B=12.25

B=1.75

The prices must be $1.50 and $1.75. The most important part of all this is setting up the equations, the rest is just being careful with your calculations.

Answer:

9/12 or 75%.

Step-by-step explanation:

Let's first add the choices all up.

5+4+3= 12.

We have 12 movie choices in total.

Now, we know that we have 3 drama movie choices...so the chance we will choose drama is 3/12, but we are not finding that.  We want the chance she will NOT choose drama, so that would be 9/12.

*Since the chance she will choose drama is 3/12, the chance she will not choose is 9/12. 9+3 is 12, the total amout.*

Answer: 1980 calories

Step-by-step explanation:

290grams of carbs=1160g

60 grams of fat=540

70 grams of protein=280 calories

290 x 4=1160

60 x 9=540

70 x 4=280

1160+540+280=1980 calories

carbs provide 4 calories per gram

fat provides 9 calories per gram

protein provides 4 calories per gram

Step-by-step explanation:

the last 2 answer options are completely useless and outright nonsense, because all limits are going against +4.

so, an asymptote at x = -4 is not an option anywhere.

g(x) is always y, and the limit of the function is the limit of the y values.

we just evaluate for what x value is then y reaching that limit. but the sign of the y limit has no direct impact on the sign of the x value.

it is true that the case x = -4 needs to be checked too, but it turns out this just delivers g(-4) = 0.

now, about x = 4 :

when coming from the left side of +4 (increasing x), what is the sign of the function ?

we can simply use x = 3 to test this :

g(3) = 2(3+4)²/(3² - 16) = 2×49/-7

so, it is negative.

that means when getting closer and closer to +4 coming from that side we what get negative values, and the limit is -infinity.

when coming from the right side of +4 (decreasing x), what is the sign of the function ?

we can simply use x = 5 to test this :

g(3) = 2(5+4)²/(5² - 16) = 2×81/9

so, it is positive.

that means when getting closer and closer to +4 coming from that side we what get positive values, and the limit is +infinity.

so, the second answer option is correct.

because of these y limits, there is a vertical asymptote at x = 4 that kind of "connects" -infinity and +infinity in y direction at that location and symbolizes the limits of y.