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3 years ago

Find all real values of a such that the given matrix is not invertible.

Mathematics

1 answer:

motikmotik3 years ago

4 0

Answer:

The answer is "0,3,-3".

Step-by-step explanation:

Let the matrix is not invertible.

then |A|=0

$\left|\begin{array}{ccc}0&9&a\\a&1&7\\0&a&1\end{array}\right|=0$

$-a[9-a^2]=0\\\\a=0\\\\a=\pm 3\\\\a=0, 3,-3\\$

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The price of a gallon of gasoline increased from 2.50 a gallon to 2.75 a gallon what was the percent increase

Vera_Pavlovna [14]

The increase in price was 10%
2.5*.1=.25
2.5+.25=2.75
hope this helps

8 0

3 years ago

Carl knows that the area of a given circle is 400 cm2. He wants to defend an informal argument that the area of a circle can be

Marizza181 [45]

ANSWER:

A. Carl could divide the circle into a larger even number of congruent sectors. Then each sector would be smaller, and the approximation of the circle’s area will be closer to the actual area of the circle.

STEP BY STEP EXPLANATION :

Area of a Circle by Cutting into Sectors:

1. Cut a circle into equal sectors and the more we divided the circle up, the closer we get to being exactly right.

2.Rearrange the sectors, which resembles a parallelogram.

What are the (approximate) height and width of the parallelogram?

The height is the circle's radius.

The width (actually one "bumpy" edge) is half of the curved parts around the circle. In other words it is about half the circumference of the circle.

We know that:

Circumference = 2 × π × radius

And so the width is about:

Half the Circumference = π × radius

ow we just multply the width by the height to find the area of the rectangle:

Area = (π × radius) × (radius)

= π × radius2

Conclusion

Area of Circle = π r2

5 0

3 years ago

a jogger goes 1.2 miles east then turns south. If the jogger finishes 1.3 miles from the starting point, how far south did the j

mr_godi [17]

Answer:

.5 miles

Step-by-step explanation:

b = √c2 - a2

= √1.32 - 1.22

= √0.25

= 0.5

7 0

4 years ago

I don’t understand how to do this without plugging in numbers or using calculus. Please help. I’m studying for the SAT and I onl

Svetllana [295]

Step-by-step explanation:

Recall that for a quadratic equation y = ax² + bx + c in the X-Y plane, the x-location of the vertex (i.e maximum or minimum point) is given by

x @vertex = -b/2a

in this case your quadratic equation is

h = 4 + 20t - 5t² (rearranging in the form y = ax² + bx + c )

h = - 5t² + 20t + 4

hence a= -5, b = 20 and c = 4

applying the formula for vertex

t @ vertex = -b /2a = -(20) / (2)(-5) = -20/-10 = 2

therefore t = 2

8 0

3 years ago

A woman bought some large frames for $10 each and some small frames for $5 each add a closeout sale if she bought 20 frames for

vampirchik [111]

Answer:

The quantity of large frames is 7

The quantity of small frames is 13

Step-by-step explanation:

Given as :

The price of each large frames = $ 10

The price of each small frames = $ 5

The total number of both frames bought = 20

The price for both the frames = $ 135

Now,

Let the quantity of large frames = L

And The quantity of small frames = S

So , According to question

The total number of both frames bought = 20

Or, The quantity of large frames + the quantity of small frame = 135

Or, L + S = 20 ......A

And $ 10 L + $ 5 S = $ 135 ................B

Or, $ 10× ( L + S ) = $ 10× 20

Or, $ 10 L + $ 10 S = $ 200

( $ 10 L + $ 10 S ) - ( $ 10 L + $ 5 S ) = $ 200 - $ 135

Or , ( $ 10 L - $ 10 L ) + ( $ 10 S - $ 5 S ) = $ 65

Or, 0 + 5 S = 65

∴ S = $\frac{65}{5}$

I.e S = 13

So, The quantity of small frames = S = 13

Put the Value of S in eq A

So , L + S = 20

Or, L = 20 - S

Or, L = 20 - 13

∴ L = 7

So, The quantity of large frames = L = 7

Hence The quantity of large frames is 7

And The quantity of small frames is 13 Answer

7 0

3 years ago