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Ganezh [65]
3 years ago
7

A rectangle with an area of 103 square feet is dilated by a scale factor of 3. What is the new area?

Mathematics
1 answer:
nekit [7.7K]3 years ago
8 0
Okay so a dilation means that you would multiply the area by your scale factor. 103 times 3 is 309. Your answer is 309
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Let​ T: set of real numbers R Superscript nℝnright arrow→set of real numbers R Superscript mℝm be a linear​ transformation, and
Klio2033 [76]

Answer:

\{T(v_1), T(v_2), T(v_3)\} is linearly dependent set.

Step-by-step explanation:

Given:  \{v_1,v_2,v_3\} is a linearly dependent set in set of real numbers R

To show: the set \{T(v_1), T(v_2), T(v_3)\} is linearly dependent.

Solution:

If \{v_1,v_2,v_3,...,v_n\} is a set of linearly dependent vectors then there exists atleast one k_i:i=1,2,3,...,n such that k_1v_1+k_2v_2+k_3v_3+...+k_nv_n=0

Consider k_1T(v_1)+k_2T(v_2)+k_3T(v_3)=0

A linear transformation T: U→V satisfies the following properties:

1. T(u_1+u_2)=T(u_1)+T(u_2)

2. T(au)=aT(u)

Here, u,u_1,u_2∈ U

As T is a linear transformation,

k_1T(v_1)+k_2T(v_2)+k_3T(v_3)=0\\T(k_1v_1)+T(k_2v_2)+T(k_3v_3)=0\\T(k_1v_1+k_2v_2+k_3v_3)=0\\

As \{v_1,v_2,v_3\} is a linearly dependent set,

k_1v_1+k_2v_2+k_3v_3=0 for some k_i\neq 0:i=1,2,3

So, for some k_i\neq 0:i=1,2,3

k_1T(v_1)+k_2T(v_2)+k_3T(v_3)=0

Therefore, set \{T(v_1), T(v_2), T(v_3)\} is linearly dependent.

6 0
3 years ago
Matt has a box that is 15 inches long and 5 inches wide. The volume of the box is 225 cubic inches. What is the height of the bo
Crazy boy [7]
The answer is 3 inches
8 0
3 years ago
Read 2 more answers
Determine the intercepts of the line.
andre [41]

Answer:

x-intercepts = (-3/4, 0)

y-intercepts = (0, 3/7)

Step-by-step explanation:

3 0
3 years ago
Can someone please help me with #3?
kap26 [50]

Answer:


Step-by-step explanation:

First, make sure you know which section of the number line you want as 1 and 2. Next, put 0.25 not right at 0 but very close, then put 0.75 farther but not too much from 0.25. Then for the decimal 1.99 put that very close to where you marked the 2 but, not on the 2. Finally, put 2.03  very close to 2 but not exactly on the 2. Also, make sure that the number line is marked evenly.

7 0
3 years ago
(PLEASE HELP ME)
Schach [20]
This right answer is D.
because -65 divided by -13 is 5
8 0
3 years ago
Read 2 more answers
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