find the volume of the parallelepiped with adjacent edges pq, pr, and ps. p(−2, 1, 0), q(4, 4, 4), r(1, 4, −1), s(3, 6, 1)
The volume of the parallelepiped with adjacent edges PQ, PR, and PS is 24 cubic units.
What is parallelepiped?Six parallelograms come together to form a three-dimensional shape called a parallelepiped (the term rhomboid is also sometimes used with this meaning). It is comparable to a parallelogram in the same way that a cube is comparable to a square. In Euclidean geometry, the four concepts—parallelepiped and cube in three dimensions, parallelogram, and square in two dimensions—are specified; however, only parallelograms and parallelepipeds exist in the setting of a more generic affine geometry, where angles are not discriminated.
There are three similar descriptions of a parallelepiped:
A polyhedron called a hexahedron, which has six parallelogram-shaped facesThree pairs of parallel faces on a hexahedron, andA prism with a parallelogram as its base.We have been that p(−2, 1, 0), q(4, 4, 4), r(1, 4, −1), and s(3, 6, 1) are the adjacent edges of parallelepiped
PQ = Q-P = <6,3,4>
PR = R-P = <3,3.-1>
PS= S-P = <5,5,1>
[ PQ PR PS] = [tex]\begin{vmatrix}6& 3 & 4 \\ 3& 3 &-1 \\ 5 & 5 & 1 \\ \end{vmatrix}\\ \notag&& \\[/tex]
= 6(3+5)-3(3+5)+4(15-15)
= 6×8-3×8+0
=48-24
=24
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What is the value of the exponential expression below?
16²
OA. 6
OB. 2
OC. 4
D. 8
The value of the exponential expression is 4 which is option (C).
Exponential equations, as the name suggests, involve exponents. The exponent (radix) of a number indicates how many times the number (radix) is multiplied.A number's exponent indicates how many times the number has been multiplied by itself. For example, 2×2×2×2 can be written as 24 because 2 is multiplied by 4. Here 4 is called the "exponent" or "power". In general, xn means multiply x by n times. Power law is given by[tex](a^m)^n=a^{m\times n}[/tex]We can write 16 as [tex]4^2[/tex] .
Using exponent property ,we get
[tex]16^\frac{1}{2}=((4)^2)^\frac{1}{2} \\\\16^\frac{1}{2}=4[/tex]
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The complete question below :
What is the value of the exponential expression below?
[tex]16^\frac{1}{2}[/tex]
A. 6
B. 2
C. 4
D. 8
-11(10x-10) = -110x+23
please help i do not understand
Answer: a. 17
b. an=-2.5n+24.5
Step-by-step explanation:
Term number: 3, 4, 5
Terms: 17, 14.5, 12
Term 3 is 17, term 4 is 14.5, and term 5 is 12.
a. The corresponding value to term 3 is 17.
b. Slope formula: m=(y2-y1)/(x2-x1) where x=term number and y=term.
m=(17-14.5)/(3-4)
m=2.5/(-1)
m=-2.5
y=mx+b ==> Linear equation with slope
12=-2.5(5)+b ==> substitute a term number and it's corresponding term
12=-12.5+b
b=12+12.5
b=24.5
y=-2.5x+24.5
an=-2.5n+24.5 ==> convert linear equation back to an form.
john thinks of a number,he adds 3 to a number and multiplies the number by 4 and then gets an answer of 10.find the number john was thinking of?
The number john was thinking of is -0.5
As in the given problem let john thinks of a number x.
He adds 3 to a number i.e x+3
Then he multiplies the number by 4 i.e. 4*(x+3)
The answer he gets is 10.
Thus we an write
4*(x+3)=10
or x+3=5/2
or x=(5/2)-3
=-0.5
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Ellason wants to solve the following system using the elimination method:
5x + 2y = 30
x + y = 8
What number should the equation x + y = 8 be multiplied by to eliminate y? (4 points)
Eight rational numbers are plotted on a number line.
A number line with Point A labeled at negative three halves. Point B is labeled at negative four thirds. Point C is labeled at negative three fourths. Point D is labeled at negative two thirds. Point E is labeled at two thirds. Point F is labeled at three fourths. Point G is labeled at four thirds. Point H is labeled at three halves.
Which of the following is true about opposite numbers?
Point D and Point A are opposite rational numbers because they are the reciprocal of each other.
Point D and Point E are opposite rational numbers because they are the same distance away from zero.
Point D and Point H are opposite rational numbers because they are the opposite reciprocals of each other.
Point D and Point F are opposite rational numbers because Point F is farther away from zero than Point D.
The correct option regarding opposite rational numbers is given as follows:
Point D and Point E are opposite rational numbers because they are the same distance away from zero.
What are opposite rational numbers?Rational numbers are all the numbers that can be represented by fractions. The opposite of a rational number is the number with the exchanged signal, for example, -2 is the opposite of 2 and vice-versa.
For this problem, we have that:
D = -2/3.E = 2/3.Same absolute value(distance from 0), different signals, hence the correct option is given by:
Point D and Point E are opposite rational numbers because they are the same distance away from zero.
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A given rectangle has an area of 20 square feet. What is the length for various widths??
Answer:
The area of a rectangle is the length multiplied by the width, so the width can be any factor of 20.
1, 2, 4, 5, 10 or 20
et u, v, w be three linearly independent vectors, and a, b, c be any three nonzero real numbers. prove that the vectors au, bv, cw are also linearly independent.
If your three vectors only have one or two components, they are guaranteed to not have linear independence.
What are components?A part is a practically free piece of any framework. It carries out some role and may require some information or produce some result. A part in programming is frequently addressed by classes. A part addresses at least one consistent errand.
Since, in the previous section we have derived the expression: cos θ = vx/V. sin θ = vy/V. Therefore, the formula to find the components of any given vector becomes: vx=V cos θ. vy=Vsin θ.
For instance, think about a vehicle. A constituent part or part of something more perplexing part of a vehicle. Likewise called: component any electrical gadget, for example, a resistor, that has unmistakable electrical qualities and that might be associated with other electrical gadgets to shape a circuit. Instances of part in a Sentence. the parts of an electric circuit He sells spare PC parts. The meeting is a vital part in the employing system. Difficult work has been a significant part of his prosperity.
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Find the point-slope equation for
the line that passes through the
points (-2, -20) and (9, 79). Use
the first point in your equation.
y - [?] = [](x-[])
The point slope equation for the line that passes through the points (-2, -20) and (9, 79) is 9 x - y - 2 = 0.
We are given the points as:
(- 2 , - 20) and ( 9 , 79)
We will first find the slope:
Slope = m = y₂ - y₁ / x₂ - x₁
m = 79 + 20 / 9 + 2
m = 99 / 11
m = 9
Now, we have to find the point-slope equation for the line that passes through the points (- 2, - 20) and (9, 79).
The point slope equation is:
y - [y₁] = [m](x-[x₁])
Substituting the values, we get that:
y + 20 = 9 ( x + 2 )
y + 20 = 9 x + 18
9 x - y + 18 - 20 = 0
9 x - y - 2 = 0
Therefore, the point slope equation for the line that passes through the points (-2, -20) and (9, 79) is 9 x - y - 2 = 0.
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Dwayne wants to redecorate his bedroom and decides to purchase new furniture. The following graph could be used to represent the value of the new bedroom furniture, f(x), after x years.
a graph of an exponential function which decreases through the points 0 comma 1100 and 2 comma 704
Which of the following statements is/are true based on the graph and the context of the problem?
The function is positive on its entire domain.
The domain is x ≥ 0 to represent the number of years after the bedroom furniture was purchased.
The x-intercept (0, 1100) represents the initial cost of the bedroom furniture.
I only
I and II only
I and III only
I, II, and III
The correct statements regarding the function are:
I and II only.
What are the correct statements regarding the function?The functions models the value of the furniture after x years, showing exponential decrease. We have that:
Time is never negative, hence the domain is x ≥ 0, representing the number of years since the furniture was purchases.The value of a product will never be negative, and a exponential function that is not shifted never touches 0, hence the function is positive on the entire domain.(0,1100) is the y-intercept, not the x-intercept, and represents the initial cost of the bedroom furniture.Hence statements I and II are correct.
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Answer:
l and lll only
Step-by-step explanation:
just did it
Write a variable expression that represents the following word phrase:
Four less than half the difference of 3 and x
Answer:
Answer: -4
Step-by-step explanation:
(3-x)/2 -4=-4
Step-by-step explanation:
Difference of 3 and x : 3-x
Half of it : (3-x)/2
And then four less : (3-x)/2 - 4
What is the equation of the line that passes through the point (8,6)
and has a slope of frac{1}{4}
[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ \cfrac{1}{4}}(x-\stackrel{x_1}{8}) \\\\\\ y-6=\cfrac{1}{4}x-2\implies y=\cfrac{1}{4}x+4[/tex]
ASAP. Please help me.
PLEASE HELP!
DONT UNDERSTAND NEED ANSWERS
Answer:
Answer is 3
Step-by-step explanation:
they want to know or ask what time the three plus the five will give u 14.
5x [(11-3) - (13-9)]
Answer: 20
Calculator helps lol
Passing through (3,3) and parallel to the line whose equation is 2x+y-2=0; slope intercept form.
Answer:
Step-by-step explanation:
y = -2x +2
y - 3 = -2(x -3)
y - 3 = -2x + 6
y = -2x + 9
123+ 1223e = 1200 e -5
Answer: I worked the equation out and it came as false
Step-by-step explanation:
Please help! I don’t exactly understand how to do this
Answer:
-6 -3
Step-by-step explanation:
please help
A triangle with vertices at (-6, 5), (-5, 1), and (-8, 2) is reflected over the y-axis What are the coordinates of the vertices of the reflected image? Enter the correct answers in the boxes. Show Hints Preimage coordinates Image coordinates (-6,5) (-5,1) (-8,2) 03
Answers:
(6, 5)
(5, 1)
(8, 2)
==================================================
Explanation:
The rule we use is [tex](\text{x}, \text{y}) \to (-\text{x}, \text{y})[/tex] when reflecting over the vertical y axis.
The x coordinate flips from positive to negative, or vice versa. The y coordinate stays the same. So a point like (-6, 5) reflects over to (6, 5). The x coordinate -6 flipped to +6 or simply 6. The y coordinate stayed at 5.
Use this idea to reflect the other points.
the radius of a circle is 15.9 in. Find the circumference to the nearest 10
Answer:
see method below
Step-by-step explanation:
circum = 2πr
= 2 x π x 15.9
work that out and will give you the answer in inches
you can use a calculator for π or use 3.142
Answer: 99.9
Step-by-step explanation:
2⋅15.9⋅π
C= 31.8π
99.9
help with this math questions
Answer: the answer is A because A for apple!
Step-by-step explanation:
How much principal must be deposited to earn $1,000 simple interest in 250 days at a rate of 5.05%?
The principal must be deposited to earn $1,000 simple interest in 250 days at a rate of 5.05% is $28,514.85
How is simple interest determined?
The simple interest on deposit is determined as the principal multiplied by the simple interest rate and the time of the deposit as shown below:
I=PRT
I=simple interest earned=$1,000
P=principal deposited=unknown
R=simple interest rate =5.05%
T=number of days that deposit lasted as a fraction of number of days in a year=250/360
$1000=P*5.05%*250/360
$1000=P*0.0350694444444444
P=$1000/0.0350694444444444
P=$28,514.85
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Determine the solutions of the equation:
x = −11 and x = 5
x = −81 and x = 45
x = −99 and x = 45
x = −99 and x = 99
The solutions of the absolute value equation are x = −99 and x = 45.
How to determine the solutions of the absolute value equation?Here we have the absolute value equation:
| (1/3)*x + 9| - 3 = 21
First, we can add 3 in both sides so we get:
| (1/3)*x + 9| = 21 + 3 = 24
This can be decomposed into two equations, we will get:
(1/3)*x + 9 = 24
(1/3)*x + 9 = -24
Solving these two we can get the two solutions.
The first one gives.
(1/3)*x = 24 - 9 = 15
x = 3*15 = 45
The second one gives:
(1/3)*x = -24 - 9 = -33
x = 3*-33 = -99
The solutions are x = −99 and x = 45.
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The table shows the proportional relationship between a hedgehog's
weight loss and the number of days of hibernation. How much weight does
the hedgehog lose during 120 days of hibernation?
Explain how you know that the relationship between the hedgehog's weight
loss and the number of days of hibernation is proportional.
The hedgehog’s total change in weight over 120 days is ____ ounces.
Answer:
-3.6
Step-by-step explanation:
proportional means the amount on the right is amount on the left multiplied by some coefficient - proportion. The proportion is calculated by dividing one side by another. Since you need to calculate weight based on days, you need the proportion of weight/days, so divide -0.27/9 or -0.78/26, in all cases you'll receive -0.03. This means for each day in hibernation hedgehog loses 0.03 pounds. 120 days will be 120*-0.03 which gives you -3.6
14.7 kilograms is how many pounds?
The given kilograms in pounds is 32.407952541177 pounds.
Given that there are 14.7 kilograms.
The SI unit of mass is the kilogram (kg). It is equal to the mass of the international prototype of the kilogram and One kg is approximately equal to 2.20462262184878 pounds.
One pound, the international peso, is legally defined as exactly 0. 5359237 kilograms.
To calculate the kilogram value with its corresponding value in pounds, simply multiply the quantity in kilograms by 2.20462262184878.
Pounds = kilograms × 2.20462262184878
Now, substitute kilograms=14 kilograms, we get
Pounds = 14.7× 2.20462262184878
Pounds=32.407952541177
Hence, in 14.7 kilograms there are 32.407952541177 pounds.
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4+9-(-2)
Pls help asp
Step-by-step explanation:
[tex]4 + 9 - ( - 2) \\ 4 + 9 + 2 = 15[/tex]
Answer:
15
Step-by-step explanation:
➲ Solve
[tex]4+9=13\\13-\left(-2\right)\\-\left(-2\right)=+2\\13+2\\13+2=15[/tex]
If James' total marks for the four terms was 256,and he represented his marks by a pie chart, what would be the size of the angle representing term 2
A possible name for this type of chart is Scatter Chart. James scored the most at first glance.
James tried to make his results look impressive in his first graph by drawing the graph from right to left instead of left to right.
This is a schematic of a data set showing the relationships between variable quantities. So if you look closely at the chart from left to right, you can see that Jane is the clear winner. Because James' results are not good and continue to decline.
Pie charts can be used to display percentages of the whole, representing percentages at a particular point in time.
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Simplify 6+√-80-
O 6+4/√5
O 6+16/51
O 6+4√5/
O 6+16/ √5
Answer:
what are u simplifying for?
Step-by-step explanation:
Does the figure above appear to have rotational symmetry? Is yes select the angles of rotation less than 360
Answer:
the answer should be 180