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Pachacha [2.7K]
2 years ago
13

Colby left out reasons from his proof. Which reason best supports the statement?

Mathematics
2 answers:
Ivahew [28]2 years ago
8 0

Answer:

b

Step-by-step explanation:

Gwar [14]2 years ago
6 0
B is the correct answer
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If 20% discount on an item amounts to Rs 160, find the marked price of the item
valina [46]

Answer:

200

Step-by-step explanation:

Let market price = y

According to question

160+20% of y=y

160+20/100y=y

160=y-20/100y

160=100/100y-20/100y

160=80/100y

160×100/80=y

y=200

5 0
3 years ago
What was done to the previous equation?
zubka84 [21]
The “2” outside the brackets was multiplied onto everything that is inside the brackets.
4 0
2 years ago
Let L be the line with parametric equations x=5+t,y=6,z=−2−3t. Find the vector equation for a line that passes through the point
scZoUnD [109]

Answer:

The required equations are

(-5 \hat i + 7 \hat j + 8 \hat k )+\lambda \left((10+\frac {3}{\sqrt {10}})\hat i -\hat j +(6- \frac {9}{\sqrt {10}})\hat k\right)=0 and

(-5 \hat i + 7 \hat j + 8 \hat k )+\lambda \left((10-\frac {3}{\sqrt {10}})\hat i -\hat j +(6+ \frac {9}{\sqrt {10}})\hat k\right)=0.

Step-by-step explanation:

The given parametric equation of the line, L, is x=5+t, y=6, z=-2-3t, so, an arbitrary point on the line is R(x,y,z)=R(5+t, 6, -2-3t)

The vector equation of the line passing through the points P(-5,7,-8) and R(5+t, 6, -2-3t) is

\vec P + \lambda \vec{(PR)}=0

\Rightarrow (-5 \hat i + 7 \hat j - 8 \hat k )+\lambda \left((5+t-(-5))\hat i + (6-7)\hat j +(-2-3t-8)\hat k\right)=0

\Rightarrow (-5 \hat i + 7 \hat j - 8 \hat k )+\lambda \left((10+t)\hat i -\hat j +(6-3t)\hat k\right)=0\;\cdots (i)

The given equation can also be written as

\frac {x-5}{1}=\frac {v-6}{0}=\frac{z+2}{-3}=t \; \cdots (ii)

The standard  equation of the line passes through the point P_0(x_0,y_0,z_0) and having direction\vec v= a_1 \hat i +a_2 \hat j +a_3 \hat k is

\frac {x-x_0}{a_1}=\frac {y-y_0}{a_2}=\frac{z-z_0}{a_3}=t \;\cdots (iii)

Here, The value of the parameter,t, of any point R at a distance d from the point, P_0, can be determined by

|t \vec v|=d\;\cdots (iv)

Comparing equations (ii) and (iii)

The line is passing through the point P_0 (5,6,-2) having direction \vec v=\hat i -3 \hat k.

Note that the point Q(5,6,-2) is the same as P_0 obtained above.

Now, the value of the parameter, t, for point R at distance d=3 from the point Q(5,6,-2) can be determined by equation (iv), we have

|t(\hat i -3 \hat k)|=3

\Rightarrow t^2|(\hat i -3 \hat k)|^2=9

\Rightarrow 10t^2=9

\Rightarrow t^2=\frac {9}{10}

\Rightarrow t=\pm \frac {3}{\sqrt {10}}

Put the value of t in equation (i), the required equations are as follows:

For t= \frac {3}{\sqrt {10}}

(-5 \hat i + 7 \hat j - 8 \hat k )+\lambda \left((10+\frac {3}{\sqrt {10}})\hat i -\hat j +\left(6-3\times \frac {3}{\sqrt {10}})\hat k\right)=0

\Rightarrow (-5 \hat i + 7 \hat j - 8 \hat k )+\lambda \left((10+\frac {3}{\sqrt {10}})\hat i -\hat j +(6- \frac {9}{\sqrt {10}})\hat k\right)=0

and for t= -\frac {3}{\sqrt {10}},

(-5 \hat i + 7 \hat j - 8 \hat k )+\lambda \left((10+\left (-\frac {3}{\sqrt {10}}\right))\hat i -\hat j +(6-3\times \left(-\frac {3}{\sqrt {10}}\right)\hat k\right)=0

\Rightarrow  (-5 \hat i + 7 \hat j - 8 \hat k )+\lambda \left((10-\frac {3}{\sqrt {10}})\hat i -\hat j +(6+ \frac {9}{\sqrt {10}})\hat k\right)=0

8 0
3 years ago
Find the area of the carpet tile. Then find the area covered by 120 carpet tiles.
weqwewe [10]

The area of the carpet is the amount of space it occupies

  • The area of the carpet tile is 256 square inches
  • The area covered by 120 tiles is 30720 squares inches

<h3>How to determine the carpet area</h3>

The dimension of the carpet tile is 16 inches by 16 inches

So, the area is:

Area = 16 * 16

Evaluate the product

Area = 256

Hence, the area of the carpet tile is 256 square inches

For 120 carpet tiles, the area is:

Area = 120 * 256

Area = 30720

Hence, the area covered by 120 tiles is 30720 squares inches

Read more about areas at:

brainly.com/question/24487155

7 0
2 years ago
What angles are they ​
Doss [256]

Answer:

option d. vertical opposite angle

3 0
2 years ago
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