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The volume of the parallelopiped is 14 cubic units

The volume of a parallelopiped with vector sides a, b and c is given by

V = (a × b).c

Given that the parallelopiped has sides

So, we have that

(a × b) = (2, 1, 0) × (3, -1, 2) = (2 × 3)i × i + (2 × -1)i × j + (2 × 2)i × k + (1 × 3)j × i + (1 × -1)j × j + (1 × 2)j × k + (0 × 3)k × i + (0 × -1)k × j + (0 × 2)k × k

Since

So,

(a × b) = (2, 1, 0) × (3, -1, 2) = (6) × 0 + (-2)k + -(4)j + 3i + (-1) × 0 + (2)i + -(3)j + -(0)i + (0) × 0

= 0 -2k - 4j + 3i + 2i - 3j - 0 + 0

= 5i  -7j - 2k

= (5, -7, -2).

Since (a × b) = (5, -7, -2)

So, the volume of the parallelopiped is

V = (a × b).c

= (5, -7, -2).(4, 0, 3)

= 5 × 4 + (-7 × 0) + (-2 × 3)

= 20 - 0 - 6

= 14.

So, the volume is 14 cubic units.

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Answer:

y = 10

Step-by-step explanation:

given DEFG = SPQR

QR = FG

=> 2x - 4 = 12

=> 2x = 16

=> x = 8

angle PQR = EFG

=> 6y + x = 68

=> 6y + 8 = 68

=> 6y = 60

=> y = 10

Answer:

C)

Step-by-step explanation:

The line starts at (0,0) unlike the others

The best approximates the line of best fit is shown in Option A.

Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.

Given that;

Graph of the function is shown in figure.

Now, We know that;

A best line which is fit of the graph have same distance approximately.

Hence, The best approximates the line of best fit is shown in Option A.

Because it contain all the point approximately.

Thus, The best approximates the line of best fit is shown in Option A.

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A number between 47 and 53 such that the prime factors are not repeated is:

3*17 = 51

Remember that any number can be written as a product of prime factors.

If we want to find a number between 47 and 53, such that there are no repeated factors, we just need to take different primes and multiply them.

For example:

2*3*5*7 = 210

There are no repeated factors, but the number is not in the desired range.

2*5*7 = 70

Still not in the range.

You can try some times until you get for example:

3*17 = 51

This a number in the desired range, such that their prime factors are not repeated.

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Answer:

C= 2.18x + 2.39

Step-by-step explanation:

Answer:

B (2.6)

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

10x10x10 or 10*3......

The gestation period of humans ​(266 days) is ​146.3% percent longer than the gestation period of lions (108 days).

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100.

Given that, gestation period of humans = 266 days and gestation period of lions = 108 days

Number of days taken more by humans in gestation period =

266-108 = 158

Percentage = 158/108 × 100 = 146.3%

Hence, the gestation period of humans ​(266 days) is ​146.3% percent longer than the gestation period of lions (108 days).

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Answer:

ok, but what does z in the equation equal? Since its a letter it has to equal to a number

Answer:

E = 30.37 J

Step-by-step explanation:

Given that,

The spring constant of the spring, k = 300 N/m

The spring is stretched by 0.45 m, x = 0.45 m

We need to find the elastic energy stored in the spring. The formula for the elastic energy is given by :

[tex]E=\dfrac{1}{2}kx^2\\\\=\dfrac{1}{2}\times 300\times (0.45)^2\\\\=30.37\ J[/tex]

So, the required elastic energy is equal to 30.37 J.

Answer:

5e

5(e)

Step-by-step explanation:

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Answer:

x = the number of cars she needs to wash

Step-by-step explanation:

Answer:

Radical Approximation

of A=5√2

of B=2√13

of C is 3√7

Answer:

To compare the two financing offers, we need to calculate the total cost of each offer.

Part A: What is the total cost of offer 1?

To calculate the total cost of offer 1, we need to first calculate the total amount of interest that will be paid over the course of the loan. We can do this using the following formula:

Total interest = (interest rate/12) * loan amount * number of payments

In this case, the loan amount is $2,975, the interest rate is 24.90%, and the number of payments is 36 (3 years * 12 months/year). Plugging these values into the formula, we have:

Total interest = (0.2490/12) * $2,975 * 36

Calculating, we find that the total interest is approximately $1,534.89.

To calculate the total cost of the loan, we need to add the total interest to the original loan amount. In this case, the total cost is $2,975 + $1,534.89 = $4,509.89.

Therefore, the total cost of offer 1 is $4,509.89.

Part B: What is the total cost of offer 2?

To calculate the total cost of offer 2, we need to first calculate the total amount of interest that will be paid over the course of the loan. We can do this using the following formula:

Total interest = (interest rate/12) * loan amount * number of payments

In this case, the loan amount is $2,975, the interest rate is 22.90%, and the number of payments is 36 (3 years * 12 months/year). Plugging these values into the formula, we have:

Total interest = (0.2290/12) * $2,

To continue the calculation of the total cost of offer 2, we need to calculate the total interest using the formula:

Total interest = (interest rate/12) * loan amount * number of payments

In this case, the loan amount is $2,975, the interest rate is 22.90%, and the number of payments is 36 (3 years * 12 months/year). Plugging these values into the formula, we have:

Total interest = (0.2290/12) * $2,975 * 36

Calculating, we find that the total interest is approximately $1,405.70.

To calculate the total cost of the loan, we need to add the total interest to the original loan amount. In this case, the total cost is $2,975 + $1,405.70 = $4,381.70.

Therefore, the total cost of offer 2 is $4,381.70.

Part C: Which financing offer should the new homeowner choose?

Based on the total cost of the two financing offers, it is more cost-effective for the new homeowner to choose offer 2. Offer 2 has a lower total cost ($4,381.70) compared to offer 1 ($4,509.89), so it would be the better choice for the new homeowner.

Step-by-step explanation:

Answer:

[tex]x=\frac{1}{5}[/tex]

[tex]y = -\frac{1}{15}[/tex]

Step-by-step explanation:

4x - 3y = 1

x + 3y = 0

Req To Solve With Elimination:

Make Them Equal:

-> 4x - 3y = 1

-> 4x + 4 . 3y = 0

Simplify:

->  4x - 3y = 1

-> 4x + 12y = 0

-> 4x - 4x - 3y - 12y = 1

-> -3y - 12y = 1

-> -15y = 1

-> [tex]y = -\frac{1}{15}[/tex]

-> [tex]x+3(-\frac{1}{15} )=0[/tex]

-> [tex]x -\frac{1}{5}=0\\[/tex]

-> [tex]x=\frac{1}{5}[/tex]

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Answer:

4x – 3y = 1

x + 3y =​

Adding the equations gives us:

5x =1

x = .2

since 4x - 3y = 1

then -3y -1 = -4x then we multiply by -1

3y +1 = 4x

3y = 4*.2 -1

3y = .8 -1

3y = -.2

y = -.2 / 3  = -0.066666666...

For a double check you can use Cramer's Rule

http://www.1728.org/cramer.htm

Step-by-step explanation:

Answer:

1/8+1/8+1/8

Step-by-step explanation:

The denominator in the first fraction should match the others because you always need a common denominator to add or subtract. And 1+1+1 is 3.

Answer:

Looking at this, slope seems to be 2 for the graph

So, looking at your options, -4 is less than 2, therefore, the answer is

D, with slope -4

Answer:

D

Step-by-step explanation:

The graphed function rises 2 in y for each run of 1 in x

Therefor the slope is 2/1 = 2

-------------------------

A) goes up 6 for each run of 3

slope = 6/3 = 2

B) goes up 15 for each run of 3

slope = 15/3 = 5

C) this is in slope intercept for of y = mx + b

m is the slope = 6

D) this is in slope intercept for of y = mx + b

m is the slope = -4

-------------------------------------

only D has a slope less than 2

Answer:

y = .111x

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

The diagonals in a parallelogram bisect each other, creating two equal halves. So HV = 1/2 of XV

HV = XV/2

HV = 34/2

HV =17

The required value of HV = 17.

From the graph
For the parallelogram XWVY
XV = diagonal of parallelogram

parallelogram is quadrilateral whose opposite side is parallel.

XV = diagonal
XV = 34

Since the diagonal of a parallelogram bisect each other.
So,
HV = XV/2
HV = 34/2
HV = 17

Thus, The required value of HV = 17.

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Answer:

it is 75% i think

Answer:

[tex]24j -7[/tex]

Step-by-step explanation:

Given

[tex]Savings \to[/tex] j

Required

Express 7 less than 24 * j

First, we have:

[tex]24 * j = 24j[/tex]

7 less is then expressed as:

[tex]24j -7[/tex]

Answer:

Total intake in ML = 414 ml (Approx.)

Step-by-step explanation:

Given:

Apple juice intake = 2 oz

Chicken broth intake = 4 oz

Gelatin dessert intake = 3 oz

Hot tea intake = 5 oz

Find:

Total intake in ML

Computation:

1 oz = 29.5735 ml

Apple juice intake in ml = 2 x 29.5735

Apple juice intake in ml = 59.147 ml

Chicken broth intake = 4 x 29.5735

Chicken broth intake = 118.294 ml

Gelatin dessert intake = 3 x 29.5735

Gelatin dessert intake = 88.7205ml

Hot tea intake = 5 x 29.5735

Hot tea intake = 147.8675 ml

Total intake in ML = 59.147 ml + 118.294 ml + 88.7205ml + 147.8675 ml

Total intake in ML = 414.029 ml

Total intake in ML = 414 ml (Approx.)

Answer:

this is the graph and just find the slope each equation

You can sand 14.4 yd² of wood in 3.2 hours.

A ratio is used to compare two or more like quantities or numbers with the same units. It is often written with a colon, and when used in words, we say the ratio of one quantity "to" the second quantity. A rate is a ratio that compares two different quantities which have different units.

9:2

x:3.2

therefore;

x = (3.2 x 9)/2

x = 28.8/2

x = 14.4 yd² of wood

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Answer:

96

Step-by-step explanation:

24 divided by 1/4 is 96

you turn 24 into a fraction by putting a one under is and then you keep it change it flip it

24/1 Divided by 1/4

24/1 times 4/1

24 times 4= 96

1 times 1= 1

96/1=96

Answer:

  ∠HAF ≈ 64.90°

Step-by-step explanation:

You want the angle HAF, a base angle in the isosceles triangle formed by the face diagonals of the cuboid with dimensions 6 cm, 6 cm, and 8 cm.

The lengths of the diagonals can be found using the Pythagorean theorem:

  HA² = HD² + DA²

  HA² = 6² +6² = 2·6²

  HA = 6√2 . . . cm

  FA² = FB² +BA²

  FA² = 6² +8² = 36 +64 = 100

  FA = 10 . . . cm

Diagonal FH is the diagonal of a rectangle with the same dimensions as the rectangle whose diagonal is FA:

  FH = FA = 10 . . . cm

The angle A can be found using the law of cosines:

  FH² = FA² +HA² -2·FA·HA·cos(A)

  A = arccos((FA² +HA² -FH²)/(2FA·HA))

  A = arccos((100 +72 -100)/(2·10·6√2)) = arccos(72/(120√2))

  A = arccos(0.3√2) ≈ 64.90°

Angle HAF is about 64.90°.

Answer:

18.5 in=decimal feet,

Step-by-step explanation:

1)18.5/12=18.512

2)18.512=1.542 feet