algebra hcf
10xyz and 15y²z²​

A third alternative to the formulas I suggested in a comment is to use the vector cross product. Recast the three given points as points in 3D space with 0 z-coordinate:

A(20, 21, 0), B(8, 29, 0), and C(13, 1, 0)

Now consider two vectors,

u = B - A = 〈8, 29, 0〉 - 〈20, 21, 0〉 = 〈-12, 8, 0〉

v = C - A = 〈13, 1, 0〉 - 〈20, 21, 0〉 = 〈-7, -20, 0〉

Then recall the cross product identity,

||u × v|| = ||u|| ||v|| |sin(θ)|

where θ is the angle between the two vectors. The magnitude of u × v is equal to the area of the parallelogram spanned by u and v, and hence twice the area of the triangle of interest.

So we have

area = ||1/2 〈-12, 8, 0〉 × 〈-7, -20, 0〉||

area = 1/2 ||〈-12, 8, 0〉 × 〈-7, -20, 0〉||

area = 1/2 ||〈0, 0, 296〉||

area = 296/2

area = 148

[tex]f(x) = \sqrt{3x} + 7 \\ \\ f ^{ - 1} (x) = ( \sqrt{3x} + 7) ^{ - 1} \\ \\ f ^{ - 1} (x) = \frac{1}{ \sqrt{3x} + 7} \\ \\ \\ f ^{ - 1} (2) = \frac{1}{ \sqrt{3(2)} + 7} \\ \\f ^{ - 1} (2) = \frac{1}{ \sqrt{6} + 7} \\ \\ f ^{ - 1} (2) = \frac{1}{ \sqrt{6} + 7} \times \frac{ \sqrt{6} - 7 }{ \sqrt{6} - 7 } \\ \\ f ^{ - 1} (2) = \frac{ \sqrt{6} - 7 }{(6 - 49)} = \frac{ \sqrt{6} - 7 }{ - 43} \\ \\ f ^{ - 1} (2) = \frac{ \sqrt{6} - 7 }{ - 43} = \frac{2.449 - 7}{ - 43} \\ \\ f ^{ - 1} (2) = \frac{ - 4.551}{ - 43} \\ \\ f ^{ - 1} (2) = \frac{ 4.551}{ 43} =0.10584[/tex]

I hope I helped you^_^

Answer:

I HOPE IT WILL HELP YOU A LOT.

Answer:

the middle one is correct

Step-by-step explanation:

the first one is incorrect because the way negative numbers are ordered is incorrect it should be "-3, -2, -1"

the middle one is correct because the pattern is consistent and the order of the numbers are correct

the third one is incorrect because the pattern doesn't match "-15" isn't counting by twos 15 isn't an even number

hope I helped ❤

Explanation:

The first number line is incorrect because the -1, -2, -3 should be reversed to get -3, -2, -1. It's reversed because the negatives are a mirror image of the positive counterpart.

The second number line is correct. Each number shown is separated with a gap size of 20. This gap size stays the same throughout the number line.

The third number line is incorrect. The gap from -15 to -12 is 3 units, while the gap from -12 to -10 is 2 units. We see that the gap size isn't the same through the entire number line.

So to summarize: the gap size must be the same and the numbers must be written in the correct order.

Answer:

4

Step-by-step explanation:

The multiplication of both indices gives 4

Answer:

I believe quadrant 1

Step-by-step explanation:

There r quadrants on a graph, once (0,-3) is graphed it lands in the first quadrant sense it’s on that side

ask me questions if you need clarification

Given coordinate is (3,0)(3,0). This point lies on the x-axis because its y-axis is on origin. Therefore, it lies on the x-axis between the Quadrant I and Quadrant IV.

Answer: Distance = 4√5

Concept:

Here, we need to know the concept of the distance formula.    

The distance formula is the formula, which is used to find the distance between any two points.

If you are still confused, please refer to the attachment below for a clear version of the formula.

Solve:

Given information

(x₁, y₁) = (-8, -4)

(x₂, y₂) = (0, -8)

Given equation

[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substitute values into the equation

[tex]Distance=\sqrt{(0+8)^2+(-8+4)^2}[/tex]

Simplify values in the parentheses through addition

[tex]Distance=\sqrt{(8)^2+(-4)^2}[/tex]

Simplify exponents

[tex]Distance=\sqrt{64+16}[/tex]

Simplify by addition

[tex]Distance=\sqrt{80}[/tex]

Simplify the radical value into the simplest form

[tex]Distance=4\sqrt{5}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

It’s A.

Step-by-step explanation:

Took the test and got it right

Answer:

8

Step-by-step explanation:

[tex]6 + 12 - 5 \times 2 + 2(8 \div 4 - 2)[/tex]

[tex]6 + 12 - 10 + 2(2 - 2)[/tex]

[tex]6 + 12 - 10 + 2 \times 0[/tex]

[tex]6 + 12 - 10 + 0[/tex]

[tex] = 8[/tex]

4200

Step-by-step explanation:

10 × 150 = 1500

18 × 150 = 2700

So

1500 + 2700 = 4200

Answer:

The answer is 12 + 3 - x

Step-by-step explanation:

The keywords are "and" and "difference". "And" means adding and "difference" means subtracting. And if the phrase says/or writes a number before any keywords that represent an operation then, it means that number comes first before the sign or operation.

Hope I'm correct as this is the first time I am answering a question and I don't have a pen and paper with me right now XD.

Answer:

[tex] - ( - 6.8k + 8) \\ = + 6.8k - 8 \\ thank \: you[/tex]

Answer:

the answer is 10000+5000+9

Answer:

10,000+5,000+9

Step-by-step explanation:

that is the answer

Answer:

Step-by-step explanation:

Sin (A +  B) = Sin A *Cos B + Cos A *Sin B

Sin 75 = Sin (30 + 45)

           = Sin 30 * Cos 45 + Cos 30 * Sin 45

           [tex]= \dfrac{1}{2}*\dfrac{1}{\sqrt{2}}+\dfrac{\sqrt{3}}{2}*\dfrac{1}{\sqrt{2}}\\\\\\= \dfrac{1}{2\sqrt{2}}+\dfrac{\sqrt{3}}{2\sqrt{2}}\\\\= \dfrac{1+\sqrt{3}}{2\sqrt{2}}[/tex]

Answer:

for additive inverse you change the sign of the given number so i think its 7

Step-by-step explanation:

Answer:

(6, -3)

Step-by-step explanation:

Find the middle of the 2 coordinates.

8 --- 4

7 --- 5

6 --- 6

__________

-7 --- 1

-6 --- 0

-5 --- -1

-4 --- -2

-3 --- -3

Answer:

-21

Step-by-step explanation:

h(x) = -x-18

h(3) = -(3)-18 = -21

Answer:

[tex]h(3)=-21[/tex]

Step-by-step explanation:

One is given the following:

[tex]h(x) = -x - 18[/tex]

One is asked to find the value of ([tex]h(3)[/tex]). Substitute ([tex]3[/tex]) in place of ([tex]x[/tex]) and simplify to evaluate,

[tex]h(x)=-x-18\\\\h(3)=-(3)-18\\\\h(3)=-3-18\\\\h(3)=-21[/tex]

Answer:

a = ± [tex]\sqrt{\frac{x^2}{1-w} }[/tex]

Step-by-step explanation:

Given

x² = a² - a²w ← factor out a² from each term on the right side

x² = a²(1 - w) ← divide both sides by (1 - w)

[tex]\frac{x^2}{1-w}[/tex] = a² ( take the square root of both sides )

± [tex]\sqrt{\frac{x^2}{1-w} }[/tex] = a

Answer:

(G)77

Step-by-step explanation:

44+11=55.

55+22=77.

77+33=110.

110+44=154.

154+55=209.

Answer:

LP = 15

Step-by-step explanation:

LM = LP ( isosceles triangle sides will be equal )

10x - 5 = 7x + 1

Transpose to find the value of x

10x -7x = 1 + 5

3x = 6

x = 6/3

x = 2

now put 2 instead of x

10x - 5

10 (2) - 5

20 - 5

15

LP = 15

Answer:

x^2+8x

Step-by-step explanation:

(6x^2+ 10x – 1) + (-5x^2– 2x + 1)

=6x^2-5x^2+10x-2x-1+1

=x^2+8x

Answer:

x^2 +8x

Step-by-step explanation:

6x^2 +10x -1 -5x^ -2x +1

x^2 +8x

Answer:

Step-by-step explanation:

2000 * .125/12 = $20.83

at $100 remaining balance = $1920.81

at $75 remaining balance   = $1945.81

Answer:

first option

Step-by-step explanation:

Using the rule of exponents

[tex](\frac{a^{m} }{a^{n} }) ^{p}[/tex] = [tex]\frac{a^{mp} }{a^{np} }[/tex] , then

[tex](\frac{2^{5} }{^{2} } )^{4}[/tex]

= [tex]\frac{2^{5(4)} }{3^{2(4)} }[/tex]

= [tex]\frac{2^{20} }{3^{8} }[/tex]

Step-by-step explanation:

[tex] \frac{4}{p} - 8[/tex]

I hope it helped U

Answer:

The GCF of 39 and 3 is 3

Step-by-step explanation:

3/3= 1

39/3= 13

Answer:

13 = 13  

20 = 2^2 • 5  

9 = 32

Prime Factor   Number 13   Number 20   Number 9    L.C.M  

   2                         0                        2                     0               2

   3                          0                        0                     2               2                                                  

   5                          0                         1                     0                  1  

   13                         1                         0                    0                   1