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4 years ago

2. The fraction 84 by 98 in simplest form is

Mathematics

2 answers:

Ymorist [56]4 years ago

8 0

Answer: 6/7

Step-by-step explanation: Since the Greatest common factor of 84 and 98 is 14, you divide both sides of 84/98 by 14 to get 6/7

Alona [7]4 years ago

3 0

Answer:6/7

Step-by-step explanation:The greatest common factor of both numerator and denominator is 14.So if you divide 84 by 14 you will get 6 and if you divide 98 by 14 you get 7.

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If y=-x+1 and y=3x+1, what is the numerical value of (3x+y)

sukhopar [10]

Add the 2 equations together

y = -x+1

y =3x+1

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2y = 2x+2

divide by 2

y = x+1

y = -x+1

======= add these two equations together

2y = 2 divide by 2

y = 1

y = x+1

1 = x+1

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3x+y=3(0) +1=1

Answer =1

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3 years ago

The mass of 5m^3 of copper is 44800kg. Work out the density of copper.

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4 years ago

Find the area of the triangle with the given vertices. Use the fact that the area of the triangle having u and v as adjacent sid

Gnom [1K]

Answer:

The area of the triangle is $A=\sqrt{\frac{4027}{2}}$

Step-by-step explanation:

Using the fact that the area of the triangle having u and v as adjacent sides is given by

$A=\frac{1}{2}||{\bf u} \times {\bf v} ||$

We know that we want to take a cross product to compute the area of the triangle, but we need to be careful because it doesn't make sense if we take the cross product of points.

The first step is to build some vectors that describe this triangle.

According with the graph we can build the vectors:

${\bf AB}$ and ${\bf AC}$

The vector ${\bf AB}$ is the difference of point B minus point A

${\bf AB}=(5-3,5-5,0-9)=(2,0,-9)$

and the vector ${\bf AC}$ is the difference of point C minus point A

${\bf AC}=(-4-3,0-5,2-9)=(-7,-5,-7)$

Next we need to find the cross product of this vectors.

${\bf AB} \times {\bf AC}=\begin{pmatrix}2&0&-9\end{pmatrix}\times \begin{pmatrix}-7&-5&-7\end{pmatrix}$

This is the definition of cross product of two vectors in space:

Let ${\bf u} = u_1{\bf i}+u_2{\bf j}+u_3{\bf k}$ and ${\bf v} = v_1{\bf i}+v_2{\bf j}+v_3{\bf k}$ be vectors in space. The cross product of ${\bf u}$ and ${\bf v}$ is the vector

${\bf u} \times {\bf v}=(u_2v_3-u_3v_2){\bf i}-(u_1v_3-u_3v_1){\bf j}+(u_1v_2-u_2v_1){\bf k}$

Applying this definition we get

${\bf AB} \times {\bf AC}=\begin{pmatrix}2&0&-9\end{pmatrix}\times \begin{pmatrix}-7&-5&-7\end{pmatrix}$

$\begin{pmatrix}0\cdot \left(-7\right)-\left(-9\left(-5\right)\right)&-9\left(-7\right)-2\left(-7\right)&2\left(-5\right)-0\cdot \left(-7\right)\end{pmatrix}\\\\\begin{pmatrix}-45&77&-10\end{pmatrix}$

$||{\bf AB} \times {\bf AC}||=\sqrt{(-45)^2+(77)^2+(-10)^2} \\\\||{\bf AB} \times {\bf AC}||=\sqrt{2025+5929+100}\\\\||{\bf AB} \times {\bf AC}||=\sqrt{8054}$

The area of the triangle is

$A=\frac{1}{2}||{\bf AB} \times {\bf AC} ||=\frac{1}{2}\sqrt{8054}=\sqrt{\frac{4027}{2}}$

7 0

4 years ago

2. The fraction 84 by 98 in simplest form is​

2. The fraction 84 by 98 in simplest form is