Answer:
[tex]\mathbf{V = \dfrac{16}{3}}[/tex]
Step-by-step explanation:
From the information given:
A = (4,0,0) B = (0,4,0) C = (0,0,1) D = (4,4,1)
[tex]\overline{ AB}[/tex] = (0,4,0) - (4,0,0) = (-4, 4, 0)
[tex]\overline{ BC} =[/tex] (0,0,1) - (0,4,0) = (0, -4, 1)
[tex]\overline{ CD}[/tex] = (4,4,1) - (0,0,1) = (4, 4, 0)
The Volume of the tetrahedron [tex]V = \dfrac{1}{6} \bigg| AB \times BC \times CD \bigg|[/tex]
The Volume of the tetrahedron [tex]V = \dfrac{1}{6} \left\begin{vmatrix}-4,&4&0\\0,&-4&1\\4&4&0\end{vmatrix}\right[/tex]
[tex]V = \dfrac{1}{6}\bigg [ -4(-4 *0 - 1*4) -4(0*0-1*4) +0(0*4--4*4) \bigg ][/tex]
[tex]V = \dfrac{1}{6}\bigg [ -4(0 - 4) -4(0-4) +0(0+16) \bigg ][/tex]
[tex]V = \dfrac{1}{6}\bigg [ 16 + 16 +0 \bigg ][/tex]
[tex]V = \dfrac{1}{6}\bigg [ 32 \bigg ][/tex]
[tex]\mathbf{V = \dfrac{16}{3}}[/tex]
Find the smallest number which is exactly divisible
by 15 20 and 30
Answer:
60
Step-by-step explanation:
The smallest number that is divisible by 15, 20 , and 30, must have the needed factors of each of these numbers:
15 = 3 * 5
20 = 2 * 2 * 5
30 = 2 * 3 * 5
Then the minimum common factor must have the following factors to satisfy the divisibility of all of the numbers above:
2 * 2 * 3 * 5 = 60
Write an equation in standard form for the line, where the points (-2, -1) and (0, 4) are on the line
Answer:
An equation in standard form for the line is:
[tex]\frac{5}{2}x-y=-4[/tex]
Step-by-step explanation:
Given the points
(-2, -1) and (0, 4)The slope between two points
[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-2,\:-1\right),\:\left(x_2,\:y_2\right)=\left(0,\:4\right)[/tex]
[tex]m=\frac{4-\left(-1\right)}{0-\left(-2\right)}[/tex]
[tex]m=\frac{5}{2}[/tex]
Writing the equation in point-slope form
As the point-slope form of the line equation is defined by
[tex]y-y_1=m\left(x-x_1\right)[/tex]
Putting the point (-2, -1) and the slope m=1 in the line equation
[tex]y-\left(-1\right)=\frac{5}{2}\left(x-\left(-2\right)\right)[/tex]
[tex]y+1=\frac{5}{2}\left(x+2\right)[/tex]
[tex]y=\frac{5}{2}x+4[/tex]
Writing the equation in the standard form form
As we know that the equation in the standard form is
[tex]Ax+By=C[/tex]
where x and y are variables and A, B and C are constants
so
[tex]y=\frac{5}{2}x+4[/tex]
[tex]\frac{5}{2}x-y=-4[/tex]
Therefore, an equation in standard form for the line is:
[tex]\frac{5}{2}x-y=-4[/tex]
The school Library was building a new one-room addition. the architects drawing shown below uses the scale 1/8 in = 1ft
Dimensions: 2 1/4 and 3 3/16
Using the dimensions indicated on the drawing, what is the total area of the new room?
Answer:
the total are is 459
Step-by-step explanation:
3 3/16 divided by 1/8 = 25 1/2 or 25.5
2 1/4 divided by 1/8 = 18
so 18 x 25.5 = 459
hope this helps
The total area of the new room is 459.
What is the scale factor?The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.
WE are given that school Library was building a new one-room addition. the architects drawing shown below uses the scale 1/8 in = 1ft
Dimensions: 2 1/4 and 3 3/16
Therefore,
3 3/16 divided by 1/8 = 51/2 or 25.5
2 1/4 divided by 1/8 = 18
Thus we have the area
= 18 x 25.5
Area = 459
The total area of the new room is 459.
Learn more about scale factor here:
https://brainly.com/question/11178083
#SPJ2
What is the coefficient of the third term in this expression? a^2+3c^3+6b^3
Answer: The coefficient is 3c
Step-by-step explanation:
what is 200000x 2000000
Answer:
400，000，000，000
Step-by-step explanation:
2*2=4
and 5 zeros plus 6 zeros equals 11 zeros.
Answer: the answer is 400000000000
Step-by-step explanation:
20 times 20 is 40 and we add all zeros
hope this helps!
Michael owns dogs, hamsters and fish in the ratio 2:3:6
If he has 6 hamsters, how many pets does he have?
Answer:
11
Step-by-step explanation:
I think you just add the ratios together.
Solve for b.
Ab + c = d
B= (d-c)/a
B= a + c/d
B= a/c-d
Answer:
B
Step-by-step explanation:
just took this test
When a rate is simplifed so that it has a denominator of 1 unit, it is called a(n) ___________ rate.
Answer:
called unit rate .
Step-by-step explanation:
help please ASAP!!!!!
you can zoom in to see better
Answer:
true, false, and false
Step-by-step explanation:
pls if u answer ill give brainliest :))) PLSS
When evaluting an expression, is it easier to combine terms first or substitute values first?
Answer:
Substitute values first
An accountant who is currently earning $42,380 annually expects a 6.5% raise. What is the amount of the
expected raise?
Answer:
$2754.70
Step-by-step explanation:
which number is IRRATIONAL
because when you look for the root of ninety, it gives you a result that is not a natural or Rational number, but a completely Irrational number.
the result is 9.4868329
Step-by-step explanation:Irrational numbersare numbers that cannot be expressed as the ratio of two whole numbers. This is opposed to rational numbers, like 2, 7, one-fifth and -13/9, which can be, and are, expressed as the ratio of two whole numbers.
hope this help!!
Answer:
c)
Step-by-step explanation:
Since sqrt(90) is an irrational number, by definition it cannot be represented as a ratio of two integers.
PLSSSSSSSSSSSSSSSSSSSSSSSSSSS HELPPPPPPPPPPPPPPPPPPPPPPPPP
Last week, Molly decided to get her favorite photograph enlarged to make a poster. When she got the poster enlarged, there was a mark on it. The mark, which had length of 1/6 ft. and width 1/9 ft., came from a mark on the photograph that had length 1/4 in. and width 1/6 in. Find the ratio of the length of the mark on the photograph in inches to the length of the mark on the poster in inches. Use pencil and paper. Find the ratio using feet instead. Is the result the same? Explain.
Answer:
example...
2/3 = 4/6 has the same meaning as 2:3 = 4:6
Hope this helped!
Andre rode his bike at a constant speed. He rode 1 mile in 5 minutes. Which of these equations represents the amount of time t (in minutes) that it takes him to ride a distance of d miles?
Answer:
5minutes and the the distance is 1miles
Answer:
t=5d
Step-by-step explanation:
Given that Andre rode his bike at a constant speed.
Number of miles driven = 1 mile
Time taken to drive 1 mile = 5 minutes.
Then speed can be calculated using formula:
Speed = Distance / Time
Now we have to find the amount of time t (in minutes) taken by him to right distance d so we can again use same formula.
Speed = Distance / Time
or
Time = Distance / Speed
Plug the given values
t = 5d
Hence find answer will be equation t=5d.
2/3 as a decimal and also percent
Answer:
0.6 as a decimal and 60 percent
Point A is located on the coordinate planet (3,-6) Point B is directly across the x-axis from point A and is the same distance from the x-axis as point A
What are the coordinates of point B?
Answer:
(3,6)
Step-by-step explanation: it is a reflection across the x-axis which is positive (3,6)
Help please this is so hard!!
Answer:
use it to help you
See the explanation for a 'tip'
Explanation:
Quotient means 'the answer after dividing'.
If you get really stuck this is one (bit long) way of dealing with it.
Firstly lets for the moment forget about the negative and just deal with
-96÷12
Write as 96 12
Notice that both numbers are even so we can divide by 2
96÷2=48
12÷2=6
Again they are both even
48÷2=24
6÷2=3
The two digits of 24 are such that
2+4=6
and 6 is exactly divisible by 3 so 24 is also exactly divisible by 3. So now we can do this:
24÷3=8
3÷3=1
Now we put the negative back in giving −8
Which weighs more: a watermelon that weighs 7.5 kilograms or a baby that weighs 12 pounds? Explain your reasoning. (Note: 1 pound is about 0.45 kilograms and 1 kilogram is about 2.2 pounds.)
Answer:
The watermelon.. I think
Step-by-step explanation:
Multiply 7.5 times 2.2 and you get 16.5, which is greater than 12. Please correct me if wrong on this because everybody makes mistakes.
is the expression 32/-8 undefined? If not find the quotient.
Answer:
the quotient is 4
Step-by-step explanation:
Determine the solution set of (3x - 5)2 = 36.
{-1/3, 11/3}
{11/3}
{-6, 6}
Answer:
[tex]the \: solution \: set \:is \to \{{-6, 6} \}[/tex]
sal recorded the outdoor temperature as -4°F at 7:30 am . at noon , it was 22°F . sal said the temperature changed by 18°F because 22-4=18. Is sal right or wrong .
Answer:
Sal is wrong, correct answer is 26°FStep-by-step explanation:
Initial temperature = -4°FTemperature at noon = 22°FTemperature change:
22 - (-4) = 22 + 4 = 26°FSal is wrong as the difference should be calculated as subtraction of the two values and absolute value of the result should be taken as the answer
Answer:
Sal was wrong as the change of temperature is 26°F
Step-by-step explanation:
recorded temperature at 7:30 A.M. = -4°F
at noon = 22°F
change of temperature = 22 - (-4) = 26°F
therefore, Sal was wrong as the change of temperature is 26°F
Look at the factors of 24 and 32.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 32: 1, 2, 4, 8, 16, 32
The GCE of 24 and 32 is
Answer: 8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
Given the following formula, solve for t v= u + at
A t= a(v+a)
b t= a(v-u)
c t=v-u/a
d t=v+a/a
Answer:
rc
Step-by-step explanation:
rc
What is a mutual fund’s
A pool of money where investors buy shares and a fund manager invests them and gives the investor the return; the way that most Americans invest their money because of the ease. hope that helps!
Solve for x (2x-8) (9x-10)
Answer
x+3=17
Step-by-step explanation:
Answer: 18x2 -92x+ 80
Step-by-step explanation:
What division problem can be represented using the number line?
A number line going from 0 to StartFraction 10 Over 3 EndFraction in increments of one-third. An arrow goes from 0 to five-thirds and from five-thirds to StartFraction 10 Over 3 EndFraction.
StartFraction 10 Over 3 EndFraction divided by five-thirds
Five-thirds divided by StartFraction 10 Over 3 EndFraction
2 divided by five-thirds
2 divided by StartFraction 10 Over 3 EndFraction
Answer:
It's the first answer.
Step-by-step explanation:
Answer:
The Answer is A
Step-by-step explanation:
Ok
Put -9,-4, and -10 in order from least to greatest. You can use the number line to help.
-2
-10
0
4
6
-8
2
8
-6
10
-10
Answer:
X=5.086
Step-by-step explanation:
432.34 on the number line, converted to negotiable /85 decimal places, divided by the sum of 432.34/85:
X=5.086
Edit: Gime branlies
A new truck costing $60,000 with a residual value of $6,000
whats 2+2? geng geng geng geng geng
Answer:
4
Step-by-step explanation:
Answer:
the answer is 4 geng geng geng geng
psdt: thanks for the points
Step-by-step explanation:
have a good night ^-^
Combine like terms 3y2 + 3(4y2 - 2)
Step-by-step explanation:
[tex]3y {}^{2} + 3(4y {}^{2} - 2) \\ \\ {3y}^{2} + 12 {y}^{2} - 6 \\ 15 {y}^{2} - 6[/tex]
Answer:
15y² - 6
Step-by-step explanation:
3y2 + 3(4y2 - 2)
Distribute: 3y² + 12y² - 6
Add like terms: 15y² - 6
I hope this helped, please mark Brainliest, thank you!
