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OLEGan [10]
1 year ago
12

(1 point) The matrix 6 4 -7 k is invertible if and only if k is not equal to

Mathematics
1 answer:
alisha [4.7K]1 year ago
7 0

Answer:

  k ≠ -14/3

Step-by-step explanation:

A square matrix is invertible if and only if its determinant is not zero.

<h3>Determinant</h3>

The determinant of a 2×2 matrix is the difference of the products of the diagonal terms and the off-diagonal terms:

  det = (6)(k) -(-7)(4) = 6k +28

<h3>Restriction on k</h3>

The requirement that the determinant is not zero places a restriction on k.

  6k +28 ≠ 0

  k +14/3 ≠ 0 . . . . . . divide by 6

  k ≠ -14/3 . . . . . . . . subtract 14/3

For the matrix to be invertible, the value of k must not be -14/3.

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If a translation maps ∠I onto ∠K, which of the following statements is true?
jonny [76]

The statement which is true is  ΔGHI ~ ΔGJK.

<h3>What is Translation?</h3>

This is commonly used in geometry to describe a function which moves object at distances.

This therefore means that translation of ∠I onto ∠K means shifting of point I to point K.

The triangles given are HGI and JGK.

Translation in this scenario therefore means that the triangles are similar only if other angles are mapped to their corresponding angles.

It confirms that ΔGHI ~ ΔGJK thereby making it the most appropriate choice.

Read more about Translation here brainly.com/question/16253702

#SPJ1

3 0
2 years ago
Two adjacent sides of a parallelogram are 6mm and 10mm respectively, and they form an angle measuring 60. Find the area of the p
Snowcat [4.5K]

Answer:

51.96 mm² approximately

Step-by-step explanation:

the first thing you should know is that the area of a rectangle is base*height sin of (

the included angle i.e

Arectangle= bh sin90° since all angles of a rectangle are equal then the included angle is 90°

<em>Arectangle= bh sin90° since sin90 is 1 we simply use the equation bh because multiplying bh by one is bh. bearing this in mind , the area of the parallelogram can be calculated as:</em>

Aparallelogram= bh sin of sin of the included angle

Aparallelogram= bh sin of sin of the included angle Aparallelogram=6mm*10mm sin 60°

Aparallelogram= bh sin of sin of the included angle Aparallelogram=6mm*10mm sin 60°Aparallelogram=60mm² * 0.866

Aparallelogram= bh sin of sin of the included angle Aparallelogram=6mm*10mm sin 60°Aparallelogram=60mm² * 0.866Aparallelogram=51.96 mm² approximately

4 0
2 years ago
What is the distance between (−5,−4) and (-6,4)?
Helga [31]

The distance formula is:  d  =  sqrt( (x2 - x1)2 + (y2 - y1)2 )

 

For this problem, let (-5, -4) be the "first" point, so  x1 = -5  and  y2 = -4

                      and let (-6, 4) be the "second" point, so  x2 = -6  and  y2 = 4.

 

Then:  d  =  sqrt( (-6 - -5)2 + (4 - -4)2 )  =  sqrt( (-1)2 + (8)2 )  =  sqrt( 1 + 64 )  =  sqrt( 65)

 

The distance formula is just the Pythagorean Theorem applied to an x-y graph.

 

You would get the same final answer if you let (-5, -4) be the second point and (-6, 4) be the first point.

6 0
2 years ago
X2+5x=3x+11 and solve by completing the square
Butoxors [25]
x^2+5x=3x+11\\&#10;x^2+2x-11=0\\&#10;x^2+2x+1-12=0\\&#10;(x+1)^2=12\\&#10;x+1=\sqrt{12} \vee x+1=-\sqrt{12}\\&#10;x=-1+2\sqrt3 \vee x=-1-2\sqrt3
7 0
3 years ago
I need help with this please
alexdok [17]

Answer:

polygons

Step-by-step explanation:

this is a hexagon so the sum of interior angles is 720. so add all of those angles and expressions and set it equal to 720. collect like terms and solve for x

once you have x, evaluate and get the exact angle measurements.

8 0
2 years ago
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