A factory produces 72 pairs of
legging 6 minutes. At the same rate,how many pairs of leggings will the factory produce in 8 minutes?

The inverse of the matrix [tex]\vec A = \left[\begin{array}{cc}1&2\\3&4\end{array}\right][/tex] is represented by the matrix [tex]\vec A^{-1} = \left[\begin{array}{cc}-2&1\\\frac{3}{2} &-\frac{1}{2} \end{array}\right][/tex].

A matrix A has an inverse matrix if and only if its determinant is different than 0. Given that we have a matrix formed by 2 rows and 2 columns, we can obtain the following inverse matrix by using the following formula:

[tex]\vec A ^{-1} = \frac{1}{\det (\vec A)} \cdot adj (\vec A)[/tex]   (1)

Where [tex]adj (\vec A)[/tex] is the adjoint of the matrix, which is the transposed of the cofactor matrix.

If we know that [tex]\vec A = \left[\begin{array}{cc}1&2\\3&4\end{array}\right][/tex], then the inverse of the matrix is determined below:

[tex]\det (\vec A) = -2[/tex]

[tex]adj (\vec A) = \left[\begin{array}{cc}4&-2\\-3&1\end{array}\right][/tex]

[tex]\vec A^{-1} = -\frac{1}{2}\cdot \left[\begin{array}{cc}4&-2\\-3&1\end{array}\right][/tex]

[tex]\vec A^{-1} = \left[\begin{array}{cc}-2&1\\\frac{3}{2} &-\frac{1}{2} \end{array}\right][/tex]

The inverse of the matrix [tex]\vec A = \left[\begin{array}{cc}1&2\\3&4\end{array}\right][/tex] is represented by the matrix [tex]\vec A^{-1} = \left[\begin{array}{cc}-2&1\\\frac{3}{2} &-\frac{1}{2} \end{array}\right][/tex]. [tex]\blacksquare[/tex]

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Answer:

X ∣ Y

-5 ∣ 26

-4 ∣ 21

-3 ∣ 16

-2 ∣ 11

-1 ∣ 6

0 ∣ 1

1  ∣ -4

2 ∣ -9

3 ∣ -14

4 ∣ -19

5 ∣ -24

Answer: 12 gallons.

Step-by-step explanation: It takes 4 cups to make 1 quart.  It takes 4 quarts to make a gallon.  If you do the calculations, it takes 16 cups in total to make 1 gallon.  By dividing 192 / 16, you 12, which is how many gallons you get when you have 192 cups.

Let me know if this is right! :)

Answer:

C) 36 inches

Step-by-step explanation:

Let the diagonal be the hypotenuse and use Pythagoras' Theorem:

[tex]a^2+27^2=45^2\\a^2+729=2025\\a^2=1296\\a=36[/tex]

So, the length of the TV was 36 inches.

Answer:

The given quadratic expression can be factored as (2x - 3)(x + 1).

So  x + 1 = x - m ⇒ m = -1.

Step-by-step explanation:

Answer:

I hope this helps, you can ask any questions for clarification

Answer:

372

Step-by-step explanation:

This is because the formula is a+b/2 x h and 7 is a 24 is b and the other 24 is h so 7 + 24 = 31/2 x 24 is 312

Answer:

193.4 meters squared

Step-by-step explanation:

Area of rectangle = 7 X 15 = 105

Area of semi circle = 1/2 X π X R^2

R = 7.5

R squared = 56.25

π = 3.1415932654........

1/2 X 3.1415.... X 7.5^ 2 = 88.35729338

Rounded to one decimal place = 88.4

105 + 88.4 = 193.4m^2

Answer:

total marbles=3+10+8+4=25 marbles total

10 blue marbles/25 total marbles

10/25=2/5 probability

Step-by-step explanation:

Hello-

Here is the way that I learned to multiply decimals. First, remove the decimal points.

2.37 X 1.6

237 X 16

Then you multiply the numbers.

237 X 16 = 3792

Now, we move the decimal point three places to the left on our answer.

3.792

3.792 is our answer.

For the relation to not to be a function we need the same value of x in (x,y) that gives off different values (y).

Now plugging in the value of k,

hence , the relation won't be function if k would be equal to 3

The value of k for which the relation R = {(2k+1, 3), (3k−2, −6)} is not a function is k = 3.

In general terms, a function is a mathematical rule or relationship that maps one set of values (the input or domain) to another set of values (the output or range). In other words, it's a specific process that takes some input and produces a corresponding output.

For the given relation R to be a function, each input in the domain should have exactly one corresponding output in the range.

We can determine whether the relation R is a function by checking if both ordered pairs have the same first coordinate. If they do, then the relation is not a function.

Let's equate the first coordinate of the ordered pairs:

2k+1 = 3k-2

Solving for k, we get:

k = 3

If we substitute k = 3 into the relation, we get:

R = {(2(3)+1, 3), (3(3)−2, −6)}

R = {(7, 3), (7, -6)}

Since both ordered pairs have the same first coordinate of 7, the relation R is not a function.

Therefore, the value of k for which the relation R = {(2k+1, 3), (3k−2, −6)} is not a function is k = 3.

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Answer:

155.52mm

Step-by-step explanation:

the area of the rectangle. 16×16=256. the area of the semicircle. 3.14×8×8=100.48. subtract the semicircle from the rectangle 256_100.48= 155.52mm

Answer:

27.47 square mm

Step-by-step explanation:

Area square = 16x16= 256

           Half square=     255/2=128

Area circle    pi x 64 = 201.06...

semicircle        201.06.../2 = 100.53

                128-100.53 =27.47    

Answer:

congruent

Step-by-step explanation:

if r_1=r_2 then, they should be the same... -congruent

Answer:

14

Step-by-step explanation:

Hope it helps

Answer:

The median is 9

The Range is 13-5=8

The mean is 5+5+9+11+13/5=43/5=8 3/5=8.6

Answer:

Step-by-step explanation:

4.  m < 1 + m < 4 + m < 5 = 180

Answer:

x=10, CB=24

Step-by-step explanation:

To find x, we know that CD=AB. So first we set up an equation.

5x-18=2x+12

then we solve.

5x-18=2x+12

5x=2x+30

3x=30

x=10

To find CB, plugin x.

3(10)-6

30-6

24

CB=24

The volume of the composite fiqure as shown in the diagram above is 300 cm³.

A composite fiqure is a fiqure that can be divided into mor than one of the basic shapes.

Note: The composite fiqure is made up of two different cubiods

To calculate the volume of the composite fiqure, we use the formula below.

Formula:

Where:

Given:

Subsitute these values into equation 1

Hence, The volume of the composite fiqure as shown in the diagram above is 300 cm³.

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Answer:

value of missing angle is..57°

Step-by-step explanation:

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54° and 69°

the missing angle of the triangle.

let's consider the missing angle as n.

sum of interior angle of triangle= 180°

n+54°+69°= 180° (adding up to sum of interior angle of triangle)

n+123°= 180°

n= 180°-123°

n= 57°

Answer: 1/4

Step-by-step explanation: 1/8 plus 1/8 is 2/8. it can be simplified to 1/4

Answer:

you have to find the common ratio between the y and the x, like what you have to multiply x by to get y

Step-by-step explanation:

like if your table is

x / y

-2. 6

-1. 3

0. 0

1. -3

2. -6

the ratio would be -3

Evaluando la función dada, veremos que la dosis para el niño debe ser 640 mg.

La funcion que debemos utilizar es:

d = 0.08*A*D

Donde, A es la edad del niño, en este caso: A = 8

D es la dosis correspondiente para un adulto, D = 1,000 mg

Reemplazando eso obtenemos:

d = 0.08*8*1,000mg = 640mg

Así, podemos concluir que al niño se le debe recetar una dosis de 640 mg.

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24+24

.

                            .........................................                                

Answer:

c = 12

Step-by-step explanation:

This is a special triangle, also known as the 30-60-90 triangle. See the help image attached for another special triangle known as the 45-45-90 triangle. 30-60-90 triangle has specific rules that we can apply to this problem:

With that being said....

c = 2x

6 = x

a = x√3

We know that x = 6, so now solve for a & c:

c = 2(6) = 12

a = 6√3

Hope this helps!

Answer:

3x+12y=0

Step-by-step explanation:

x+2x=3x

5y+7y=12y

-3+3=0

Answer: 55 mph

Step-by-step explanation: rate=distance/time=275/5=55 miles per hour

Answer:

y goes from the top to the bottom postive to negative. Then x is from left to right. The left is negative the right is postive.

Step-by-step explanation:

x+y=35

1.89x+2.59y=79.95

y=35-x (and now we put this instead of 'y' in the second equation)

1.89x+2.59(35-x)=79.95 (now we solve this equation)

1.89x+90.65-2.59x=79.95

0.7x=10.7

x=15

y=35-15=20

ANSWER:

15 apples

20 oranges

Answer:

it's.. parallelogram..

Step-by-step explanation:

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Answer:

That is a parallelogram.

Step-by-step explanation:

Not a square, not a rectangle, not a trapezoid.

Answer:

Circle 1 = diameter of 10 cm

Circle 2 = radius of 10 cm

Step-by-step explanation:

           The radius is half the diameter.

           If both the radius and the diameter are the same length, then the circle with the radius of 10 is larger because 10 times 2 is a 20 cm diameter.

           The larger circle is circle #2. If we use the logic from above, the larger circle, #2, has a radius of 10 cm. This leaves us with circle #1 having a diameter of 10 cm.

Circle 1 has a diameter of 10

Circle 2 has a radius of 10

Diameter and Radius

The diameter is the distance from one point on a circle to the opposite side. Radius is the distance from the center of a circle to a point on the circle. This means that the diameter is twice the size of the radius.

Finding Diameter

One way to find out which circle is which is to find the diameter of both. We know that one of the circles had a diameter of 10. The circle that has a radius of 10 must have a diameter of 20 because 10*2=20. Since the circle with a radius of 10 has a diameter of 20, it must be the larger circle, Circle 2.

Reading the Graph

Additionally, you can read the figure given to you. The radius is from the center of a circle to the outside. The line drawn is 10 meters and goes from the center of circle 2 to the outside of circle 2. Thus, this circle must have a radius of 10.