EASY POINTS Which of the following statements is true?

(i) Use the formula for the determinant of a 2×2 matrix.

[tex]\begin{vmatrix}a&b\\c&d\end{vmatrix} = ad-bc[/tex]

[tex]\implies \det(A) = \begin{vmatrix}4 & -3 \\ 2 & 5\end{vmatrix} = 4\times5 - (-3)\times2 = \boxed{26}[/tex]

(ii) The adjugate matrix is the transpose of the cofactor matrix of A. (These days, the "adjoint" of a matrix X is more commonly used to refer to the conjugate transpose of X, which is not the same.)

The cofactor of the (i, j)-th entry of A is the determinant of the matrix you get after deleting the i-th row and j-th column of A, multiplied by [tex](-1)^{i+j}[/tex]. If C is the cofactor matrix of A, then

[tex]C = \begin{pmatrix}5&-2\\3&4\end{pmatrix}[/tex]

Then the adjugate of A is the transpose of C,

[tex]\mathrm{adj}(A) = C^\top = \boxed{\begin{pmatrix}5&3\\-2&4\end{pmatrix}}[/tex]

(iii) The inverse of A is equal to 1/det(A) times the adjugate:

[tex]A^{-1} = \dfrac1{\det(A)} \mathrm{adj}(A) = \boxed{\begin{pmatrix}\frac5{26}&\frac3{26}\\\\-\frac1{13}&\frac2{13}\end{pmatrix}}[/tex]

(iv) The system of equations translates to the matrix equation

[tex]A\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}6\\16\end{pmatrix}[/tex]

Multiplying both sides on the left by the inverse of A gives

[tex]A^{-1}\left(A\begin{pmatrix}x\\y\end{pmatrix}\right)=A^{-1} \begin{pmatrix}6\\16\end{pmatrix}[/tex]

[tex]\left(A^{-1}A\right)\begin{pmatrix}x\\y\end{pmatrix}=A^{-1} \begin{pmatrix}6\\16\end{pmatrix}[/tex]

[tex]\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}\frac5{26}&\frac3{26}\\\\-\frac1{13}&\frac2{13}\end{pmatrix} \begin{pmatrix}6\\16\end{pmatrix}[/tex]

[tex]\begin{pmatrix}x\\y\end{pmatrix}=\boxed{\begin{pmatrix}3\\2\end{pmatrix}}[/tex]

Check the picture below.

Answer:

D) 5

Step-by-step explanation:

Because 5x5=25 so the square root would be 5

The initial point of vector v if it has a magnitude of 10 and the terminal point (-3,3) is option B (-9,-5).

If we have given a vector v of initial point A and terminal point B

v = ai + bj

then the components form as;

AB = xi + yj

Here, xi and yj are the components of the vector.

Given;

The magnitude of 10 and the terminal point (-3,3).

v = ai + bj

v = [tex]\sqrt{a^2 + b^2}[/tex]

10 =  [tex]\sqrt{a^2 + b^2}[/tex]

AB = (-3 - a)i + (3 - b)j

If we put (-9,-5)then

AB = (-3 - a)i + (3 - b)j

AB = (-3 + 9)i + (3 + 5)j

AB = 6i + 8j

Put the value in the vector magnitude

10 =  [tex]\sqrt{a^2 + b^2}[/tex]

   = [tex]\sqrt{6^2 + 8^2}\\\\\sqrt{36+ 64}\\\\\sqrt{100}[/tex]

10 = 10

Thus, The correct option is B (-9,-5).

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Answer:

I think it's 5

Step-by-step explanation:

The distance from point A to 0 is 2, then to point B makes it 3, then to point C is a total of 5. Or you could just add the absolute value of A, which is 2, with the absolute value of C, which is 3 to get 5

Answer:

6.15 kilograms of pears

Step-by-step explanation:

The total is 8.2 kilograms. Since 1/4 of the weight is apples, we know that 3/4 of the weight is pears. So we multiply 8.2*0.75.

8.2*0.75=6.15

Therefore, the farmer sold 6.15 kilograms of pears at the farmer's market.

Answer:

Answer = 10 miles

Step-by-step explanation:

First lets make an equation we know that the pick up fee was $4.80 and that Fabian had to pay an extra $4 for every mile. The total amount Fabian paid was $44.80. So the equation would look like this, 4x+4.80=44.80. When we solve for x we find that the taxi ride was 10 miles.

Hope that helps! :)

The taxi ride was 10 miles long. Fabian traveled 10 miles from his house to the airport.

To calculate the distance of Fabian's taxi ride, let's denote the distance in miles as "d." The cost consists of a pick-up fee of $4.80 and a mileage charge of $4 per mile. So, the total cost can be represented as 4.80 + 4d. Given that the total fare was $44.80, we can set up the equation:

4.80 + 4d = 44.80

Now, solving for "d," subtract 4.80 from both sides:

4d = 40

Divide both sides by 4:

d = 10

Therefore, the taxi ride was 10 miles long. Fabian traveled 10 miles from his house to the airport.

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Answer:

52 x 7= 50 x 7 + 2 x 7

Step-by-step explanation:

Step-by-step explanation:

(5,2) & (10,-3)

the slope of the points are

y2 - y1 / x2- x1

-3-2/10-5

-5/5

-1

the mid point of the given points are

x= x1 + x2/2 , y= y1 +y2 /2

.

.

.

.

( , )

the equation of the line that passes through the given points are as

y+ y1 = m (x+ x1)

:. now put the value of the mid point in y1 and x1 and the value of slope in m

also find the mid point, it's hard to do it in a mobile without calculator and paper and pen

sorry

Answer:

65.3ft

Step-by-step explanation:

I think it might be this I'm not sure

The true statement is on a coordinate plane, a graph titled Chad's Cards has Damage on the x-axis and Defense on the y-axis. Points (1, 2), (2, 4), (3, 6), and (4, 8) are plotted.

Chad created a table that shows the ratio of his sports game cards.

Chad’s Cards

Card Type

Outfield

Infield

Catcher

Pitchers

Quantity

3

4

1

2

Next, Chad created the graph below showing possible ratios for Pitcher cards to Infield cards in his deck.

A coordinate plane is a graphing and description system for points and lines. A vertical (y) axis and a horizontal (x) axis make up the coordinate plane. There are four quadrants in the coordinate plane. The point where these lines connect is called the origin (0, 0).

Therefore the first statement is true,

On a coordinate plane, a graph titled Chad's Cards has Damage on the x-axis and Defense on the y-axis. Points (1, 2), (2, 4), (3, 6), and (4, 8) are plotted.

Therefore option A is correct.

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Answer:

this is right

Step-by-step explanation:

i know it is

Based on the figures given, and the line graph, we can tell that the months with the greatest change in average low temperature were May and July.

In the month of May, the temperature changed by:

= 60 - 51

= 9°F

In the month of July, the temperature changed by:

= 66 - 62

= 4°F

These two months therefore saw the largest changes in temperature and this is confirmed by the line graph.

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Answer:

i thank 4 for this players

Answer:

30%

Step-by-step explanation:

150-105 = 45

(45 / 150 ) * 100 = 30%

The percentage of 150 is left after giving out 105 is 30%

The given numbers are 150 and 105.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Now, the difference of numbers = 150-105=45

45/150 × 100

= 30%

Therefore, the percentage of 150 is left after giving out 105 is 30%

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"Your question is incomplete, probably the complete question/missing part is:"

What percentage of 150 is left after giving out 105.

Answer:

7 frnds will play soccer!

Step-by-step explanation:

8+5 = 13

20 - 13 = 7

I hope it helps u dear! (^^)

The angle BAC and DCA are alternate interior angles , Option D is the right answer.

What are Parallel Lines ?

The lines in a plane which never intersect and are at a same distance always are called Parallel Lines.

In the given question it is given that there are two lines FG and DE

The lines are parallel to each other , and transversal are AC and BC .

The angle BAC and DCA are alternate interior angles as AC is the transversal of the parallel lines.

Option D is the right answer.

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Answer: The correct answer is (-1, 2).

Step-by-step explanation: Find how many units the original F point is away from the center. It is 2 units away in terms of x, and 4 units away in terms of y. The x value has to be negative since the initial x point was already negative. -2/2 = -1. Hence, the x value is -1.  4/2 = 2. Hence, the y value is 2.

Step-by-step explanation:

Reflection in the x axis (x,y)—>(x,-y)

(-4,-3)—>(-4,3)

Step-by-step explanation:

Heres the answer And if it doesn't work tell me

Answer:

3x+3 ≥ 12

3x ≥ 9

x ≥ 3

So A is correct

Let me know if this helps or if you have any other questions!

Answer:

See below ~

Step-by-step explanation:

Finding the x-intercept :

Finding the y-intercept :

Take the two points and graph the inequality.

5 ounces per week x 12 weeks = 60 ounces

1 pound = 16 ounces

60 / 16 = 3 pounds 12 ounces

3 pounds 12 ounces + 8 pounds 3 ounces = 11 pounds 15 ounces

answer: 11 pounds 15 ounces

Answer:

$113.75

Step-by-step explanation:

First add 70.25 to 43.50 to get 113.75

Answer:

$113.75

Step-by-step explanation:

b-70.25=43.50

add 70.25 to each side ..

b-70.25=43.50

+70.25+70.25

simpilfy...b=113.75

Answer:

34 [units].

Step-by-step explanation:

1) according to the property of parallelogram (AC=BD and AB=CD) the required perimeter can be calculated as P=2AB+2AC;

2) the length of AB=7 (the coordinates 'y' are equal);

3) the length of AC:

[tex]|AC|=\sqrt{(1+5)^2+(-2-6)^2}=10.[/tex]

4) finally, the required perimeter is:

P=2(7+10)=34 [units].

[tex]x^3 y^4 \cdot x^5 y^{-5}\\\\=x^{5+3} \cdot y^{4-5}~~~~~~~~~~~~~~~~~~~~~~~;[a^m \cdot a^n = a^{m+n}]\\\\=x^8 y^{-1}\\\\=\dfrac{x^8}{y}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[a^{-n} = \dfrac 1{a^n},~~~ a \neq 0\right][/tex]

The area of the figure is 51.4 unit²

Figure ABCDEF is shown. A is located at 5, negative 8. B is located at 11, negative 8. C is located at 11, 0. D is located at 6

See attachment for the figure

The figure can be divided into the following shapes:

The area of the trapezoid is:

Area = 0.5 * (Sum of opposite sides) * height

So, we have:

Trapezoid 1 = 0.5 * (8 + 5) * 5 = 32.5

Trapezoid 2 = 0.5 * (5 + 4.8) * 2 = 9.8

The area of the triangle is:

Area = 0.5 * Base * Height

This gives

Triangle = 0.5 * 4.8 * 4 = 9.6

Add the individual areas

Area = 32 + 9.8 + 9.6

Evaluate the sum

Area = 51.4

Hence, the area of the figure is 51.4 unit²

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