Answer:
The volume of the tetrahedron is
[tex]\frac{-32}{3}[/tex]
Step-by-step explanation:
To find the volume of a tetrahedron with vertices (2, 0, 0), (0, 4, 0), (0, 0, 4), (2, 4, 4).
We know by definition that the volume of a tetrahedron with vertices [tex](x_{1}, y_{1}, z_{1}), (x_{2}, y_{2}, z_{2}), (x_{3}, y_{3}, z_{3})[/tex] is
[tex]\frac{1}{6}\begin{vmatrix}
2 & 0 & 0 & 1\\
0 & 4 & 0 & 1\\
0 & 0 & 4 & 1\\
2 & 4 & 4 & 1
\end{vmatrix}[/tex]
From here we have:
[tex]\frac{1}{6}\begin{vmatrix}
x_1 & y_1 & z_1 & 1\\
x_2 & y_2 & y_2 & 1\\
x_3 & y_3 & z_3 & 1\\
x_4 & y_4 & y_4 & 1
\end{vmatrix}[/tex]
Finding the determinant of that matrix we have:
[tex]\frac{1}{6} (-64)[/tex] = [tex]\frac{-32}{3}[/tex]
A deli sells sliced meat and cheese. One customer purchases 4 pounds of meat and 5 pounds of cheese for a total of $30.50. A sandwich shop owner comes in and purchases 11 pounds of meat and 14 pounds of cheese for $84.50. The system of equations below represents the situation.
4x + 5y = 30.50
11x + 14y = 84.50
Answer: I think it the second one
Step-by-step explanation:
Answer:
The variable x represents the - cost per pound of meat
The variable y represents the - cost per pound of cheese
The deli charges $4.50 for - a pound of meat
Step-by-step explanation:
got it correct for edgen 2020
Give 5 numbers that are divisible by 3. Show the process
Answer:
Ok, 9, 18, 24, 15, and 30
Step-by-step explanation:
3*3=9 - 9/3=3
6*3=18 - 3/18=6
3*8=24 - 24/3=8
3*5=15 - 15/3=5
3*10=30 - 30/3=10
it takes one half of a cup of flour to make a batch of Pancakes and has 6 cups of flour how many batches of Pancakes can he make
Answer:
12
Step-by-step explanation:
Since the recipe calls for 1/2 cup of flour, the equation would be 6x2
complete the given table following the pattern.
1
2
3
4
5
6
1
2
3
4
5
Number of
slices
Number of
Cherries
Number of Line
Segments
(All Lines)
Number of Outer
Line Segments
Number of
Inner Line
Segments
3
5
7
9
11
3
0
1
Answer:
7 is the answer to that jgf6bf6 reddish Ve
Make up a word problem or scenario that uses the equation 7p+10=24. Make sure to elaborate as much as possible.
Given:
The equation is [tex]7p+10=24[/tex].
To find:
The scenario that uses the given equation.
Solution:
If p is the price of a good. Initial supply of goods at price 0 is 10 and supply increasing by 7 units if the price increased by 1 unit, then at what price the supply will be 24 units.
According to this scenario,
Total supply = 10+7p
Equate total supply with 24, to find the price at which the supply will be 24 units.
[tex]7p+10=24[/tex]
Therefore, the required scenario is "If p is the price of a good. Initial supply of goods at price 0 is 10 and supply increasing by 7 units if the price increased by 1 unit, then at what price the supply will be 24 units."
HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!-2 times 5[/tex]
Answer:
3
Step-by-step explanation:
(43-20)-2*5
Step 1: 43- 20= 13
Step 2: 2*5 = 10
Step 3: 13 - 10 = 3
PEMDAS
Indicate if the two triangles or similar or not similar
Answer:
not similar,
77/66 does not equal 49/41
A class measured the radius and circumference of various circular objects. The results are plotted on the graph.Why might the measured radii and circumferences not be exactly proportional?
Answer:
Because it goes through the origin and the line is straight but there is still the empty space between the 4 and 6
Step-by-step explanation:
Answer:
Good
Step-by-step explanation:
Goodd
Calculate the number in the middle of 1.5 and 7.1
Answer:
0.5
Step-by-step explanation:
write the slope-intercept form of the equation of the line through (4,-5) perpendicular to 6x + 12y=13
Answer:
y=2x-13
Step-by-step explanation:
12y=-6x+13
y=-1/2x+13/2 is the line, so to find the line perpendicular to that, you find that the slope of the line perpendicular to it is 2 because it's the negative reciprocal of -1/2. Then multiply 2 and 4 to get 8 and subtract 13 to get -5. Now you know that -13 is the y-intercept.
I need help with this pls, 15 pts
I NEED HELP ASAP!!!!
Which of the 10 point problems are you solving?
D
E
F <
Show your thinking for your 10 point problem. (I chose F)
Help FOR #3!!!!!!!!!!! Please!!!!!!!!!!
Answer:
Standard Form
f(x)=10x2-7x-12
Vertex Form
y=10(x-720)^2-52940
Step-by-step explanation:
Tasha buys a shirt for $14.90. She pays with a $20 bill, and shares the change equally with her sister. How much change should Tasha's sister recieve? HELP ASAPP!!!
Answer:
$2.55 each
Step-by-step explanation:
Answer:
2.55
Step-by-step explanation:
Rocky is building a wall.
He estimates he needs 2000 bricks for the job he is doing.
The bricks are sold in packs of 100.
How many packs does he need?
Answer:
20 packs
Step-by-step explanation:
2000 / 100 = 20 packs
If 30% of cars sold are blue, how many blue cars could you expect in a group of 600 cars
Answer:
180 blue cars
Step-by-step explanation:
30/100=x/600
18000=100x
x=180
In a rectangle diagonal is 5cm ,breadth is 3cm .find the area and perimeter of the rectangle? (STEP BY STEP EXPLANATION)
Answer:
The area of rectangle is 12cm² and the perimeter is 14cm.
Step-by-step explanation:
First, you have to find the length of the rectangle using Pythagoras Theorem :
a² + b² = c²
a² + 3² = 5²
a² = 5² - 3²
a² = 16
a = √16
a = 4 cm
Next, you have to find the perimeter and area of rectangle :
Perimeter = 2(length + breadth)
P = 2(4 + 3)
P = 2(7)
P = 14 cm
Area = length×breadth
A = 4×3
A = 12 cm²
Set 35 between Pat and Sam in the ratio 4:3 how much money will each person get
Answer:
Pat gets 20 and Sam gets 15
Step-by-step explanation:
35 ÷ 7 = 5
5 x 4 = 20 (for Pat)
5 x 3 = 15 (for Sam)
Hurry Plz!!
Geneva was given a division equation and asked to place the decimal point in the
quotient to make the number sentence true. Geneva's answer is shown below.
358.584 : 8.92
4.02
Do you agree with Geneva's placement of the decimal point? Use mental math
and the division algorithm to support your answer.
Answer:
I disagree because the decimal point in the wrong place. 40.2
Step-by-step explanation:
• Here are some clues to a mystery number.
• The GCF of 18. 36, and me is 2.
I am a multiple of 5.
I am greater than 18 and less than 30.
What is the mystery number?
• The mystery number is
PLEASE HELP ME!!!
The mystery number is 20 for the given information.
What is Number system?A number system is defined as a system of writing to express numbers.
To find the mystery number, we need to find a number that satisfies all the given conditions:
The GCF of 18, 36, and the mystery number is 2.
The prime factorization of 18 is 2 x 3 x 3.
The prime factorization of 36 is 2 x 2 x 3 x 3.
The only common factor is 2 x 3 x 3, which is equal to 18.
This means that the mystery number must also be divisible by 2.
The mystery number is a multiple of 5.
Since the mystery number is a multiple of 5 and also divisible by 2, it must end in 0 or 5.
The mystery number is greater than 18 and less than 30.
The only number that satisfies all three conditions is 20.
Hence, the mystery number is 20 for the given information.
To learn more on Number system click:
https://brainly.com/question/22046046
#SPJ2
The reciprocal of 2 2/7
Answer:
7/16
Step-by-step explanation:
After a 40% discount the price of a pair of shoes was $50. What was the price before
the discount
Answer:
125
Step-by-step explanation:
x*0.40=50
50/0.40=125
40% of 125=50
x=125
what property is this 3(x-3) = 3x-9 what property is this.
Anyone know the answers to this?
Answer: 4
Step-by-step explanation:
Angle 8 is = to 4, they are corresponding.
Monica obtained the following results from her mathematics exams: 80,
82, 83, and 91. What score must she get on the next exam so that her
average score is 85
Answer:
89
Step-by-step explanation:
Answer:
A score of 89
Step-by-step explanation:
To find the average, we'll need to add all the results and divide them by the number of her exams. To do this, we'll need to add all her scores and one more (her next score to make the average 85): we'll call that x for now.
(80 + 82 + 83 + 91 + x) ÷ 5 = 85
(336 + x)/5 = 85
Multiply 5 on both sides
336 + x = 425
x = 89
Therefore, Monica will need an 89 on her next test for her average to be 85.
I hope this helped. Good luck and keep studying!
_ + _ = 16
= =
_ - _ =12
= =
26 16
8 + 8 = 16
16 - 14 = 12
I don't know how to solve it
9514 1404 393
Answer:
a = 102°
b = 78°
c = f = 58°
d = 122°
e = 26°
Step-by-step explanation:
The usual rules apply:
the sum of angles in a triangle is 180°the sum of angles making a right angle is 90°vertical angles are congruentcorresponding angles at a transversal crossing parallel lines are congruentangles of a linear pair are supplementary.__
There are a couple of angles we can find right away:
b corresponds to 78°, so has that measure
a is supplementary to b, so is 180° -78° = 102°
e is complementary to 64°, so is 26°
The unmarked angle between 78° and f is vertical to 44°, so we have ...
78° +44° +f = 180°
f = 58°
Angle c corresponds to angle f, so is 58°
Angle d is supplementary to angle c, so is 180° -58° = 122°
In summary, ...
a = 102°
b = 78°
c = f = 58°
d = 122°
e = 26°
In how many distinguishable ways can you arrange the letters in the word CONNECTICUT? *
Answer:
The number of distinguishable arrangements are 1,663,200.
Step-by-step explanation:
The word is: CONNECTICUT
The number of ways to arrange a word when no conditions are applied is:
[tex]\frac{n!}{k_{1}!\cdot k_{2}!\cdot k_{3}!...\cdot k_{n}!}[/tex]
Here k is the number of times a word is repeated.
In the word CONNECTICUT there are:
3 Cs
2 Ns
2 Ts
And there are a total of n = 11 letters
So, the number of distinguishable arrangements are:
[tex]\frac{n!}{k_{1}!\cdot k_{2}!\cdot k_{3}!...\cdot k_{n}!}=\frac{11!}{3!\times 2!\times 2!}[/tex]
[tex]=\frac{39916800}{6\times 2\times 2}\\\\=1663200[/tex]
Thus, the number of distinguishable arrangements are 1,663,200.
The count in a bacteria culture was 800 after 15 minutes and 1200 after 40 minutes. Assuming the count grows exponentially,
What was the initial size of the culture?
Answer:1) bacteria size = b(initial) * e^(r * t)
initial size = 300
final size = 1600.
Substituting the values into the main equation:
1600 = 300 * e^(r * 35 - 20)
solving for 'r'.
1600 = 300 * e^(r * 15)
1600/300 = e^(r * 15)
taking natural log on both sides to eliminate the power
ln(16/3) = ln[e^(r * 15)]
ln(16/3) = r * 15
r = ln(16/3) / 15
= 0.11159843
= 11.16%
To find the initial bacteria size,
Given: t = 20
300 = b * e^(0.1116 * 20)
Solving for b:
300 = b * e^2.232
b = 300/e^2.232
b = 32
Step-by-step explanation:
For any number n>1, is |(2 - 41)" A. greater than 1? B. less than 1? C. equal to 1?
Answer:
2. 2. =1=13.
Step-by-step explanation:
Answer:
The answer may be A. Greater then
Step-by-step explanation:
sorry if it's wrong
