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Setler79 [48]
3 years ago
10

1) 14 units2 2) 16 units2 3) 17 units2 4) 19 units2

Mathematics
1 answer:
horrorfan [7]3 years ago
7 0

Answer:

<h2><em><u>4th</u></em><em><u> </u></em><em><u>option</u></em><em><u>:</u></em><em><u> </u></em><em><u>19</u></em><em><u> </u></em><em><u>units2</u></em><em><u> </u></em></h2>

Step-by-step explanation:

<h3>The given figure can be divided as (i) upper rectangle, (ii) lower rectangle </h3>

<em><u>Then</u></em><em><u>,</u></em>

(i) Breadth of upper rectangle = 2 units

Length of upper rectangle = 8 - 1 = 7 units

<em><u>Therefore</u></em><em><u>, </u></em>

Area of the upper rectangle = 7 × 2 = 14 units2

(ii) Breadth of lower rectangle = 1 unit

Length of lower rectangle = 5 units

<em><u>Therefore</u></em><em><u>, </u></em>

Area of the lower rectangle = 5 × 1 = 5 units2

<em><u>Since</u></em><em><u>,</u></em>

Area of the figure is = <em>Area</em><em> </em><em>of</em><em> </em><em>upper</em><em> </em><em>rectangle</em><em> </em><em>+</em><em> </em><em>Area</em><em> </em><em>of</em><em> </em><em>lower</em><em> </em><em>rectangle</em><em> </em>

= 14 units2 + 5 units2

= <em><u>19 units2 (Ans) (4th option)</u></em>

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What fraction is larger 7/8 or 14/16
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Determine whether the set of vectors is a basis for ℛ3. Given the set of vectors , decide which of the following statements is t
schepotkina [342]

Answer:

(A) Set A is linearly independent and spans R^3. Set is a basis for R^3.

Step-by-Step Explanation

<u>Definition (Linear Independence)</u>

A set of vectors is said to be linearly independent if at least one of the vectors can be written as a linear combination of the others. The identity matrix is linearly independent.

<u>Definition (Span of a Set of Vectors)</u>

The Span of a set of vectors is the set of all linear combinations of the vectors.

<u>Definition (A Basis of a Subspace).</u>

A subset B of a vector space V is called a basis if: (1)B is linearly independent, and; (2) B is a spanning set of V.

Given the set of vectors  A= \left(\begin{array}{[c][c][c][c]}1 & 0 & 0 & 0\\ 0 & 1 & 0 & 1\\ 0 & 0 & 1 & 1\end{array} \right) , we are to decide which of the given statements is true:

In Matrix A= \left(\begin{array}{[c][c][c][c]}(1) & 0 & 0 & 0\\ 0 & (1) & 0 & 1\\ 0 & 0 & (1) & 1\end{array} \right) , the circled numbers are the pivots. There are 3 pivots in this case. By the theorem that The Row Rank=Column Rank of a Matrix, the column rank of A is 3. Thus there are 3 linearly independent columns of A and one linearly dependent column. R^3 has a dimension of 3, thus any 3 linearly independent vectors will span it. We conclude thus that the columns of A spans R^3.

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8 0
3 years ago
Which equation represents a line that is perpendicular to line PQ?
valentinak56 [21]

Answer:

B. y=1/3x+4

Step-by-step explanation:

Hi there!

We are given the line PQ and we want to find the line that is perpendicular to it

Perpendicular lines have slopes that are negative and reciprocal. When they are multiplied together, the result is -1

So first, let's find the slope of the line PQ

The point P is given as (-8, 7) and the point Q is given as (-4, -5)

The formula for the slope calculated from two points is \frac{y_2-y_1}{x_2-x_1} where (x_{1} y_1) and (x_2, y_2) are points

We have the needed information for the slope, but let's label the values of the points to avoid any confusion

x1=-8

y1=7

x2=-4

y2=-5

Now substitute into the formula (m is the slope, and remember: the formula contains SUBTRACTION):

m=\frac{(-5-7)}{(-4--8)}

simplify

m=\frac{-5-7}{-4+8}

add

m=-12/4

divide

m=-3

So the slope of the line PQ is -3

As said above, perpendicular lines have slopes that have a product of -1

So to find the slope of the line perpendicular to PQ, use this formula:

-3m=-1

divide both sides by -3

m=1/3

The only line that has a slope of 1/3 is B (y=1/3x+4), so B is the answer.

Hope this helps!

3 0
3 years ago
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