what is the minimal number such that any 3-by-3 matrix with of its entries equal to zero is non-invertible

Answer:

For exercise 11: x = 64

For exercise 12: x = 66

For exercise 13: x = 89

For exercise 14: x = 99

Step-by-step explanation:

The sum of interior angles of an n-sided polygon = [tex](n- 2 )[/tex] x [tex]180^{o}[/tex]

where n = number of sides

For all the four figures in this exercise, n = 4

Therefore, Sum of interior angles = [tex](4 - 2)[/tex] x [tex]180^{o}[/tex]

                                                          = 2 x [tex]180^{o}[/tex]

                                                          = [tex]360^{o}[/tex]

For Exercise 11:

[tex]x^{o} + 100^{o} + 130^{o} + 66^{o} = 360^{o}[/tex]

[tex]x^{o} + 296^{o} = 360^{o}[/tex]

[tex]x = 360 - 296[/tex]

x = [tex]64^{o}[/tex]

Apply the above stated concept in the other three exercises

The solution of the system of equations is:

x = 3

y = 2

Here we want to solve the system of equations below:

2x + y = 8

x - 3y = -3

First, let's isolate one variable in one of the equations, I will isolate y on the first one.

y = 8 - 2x

Now we can replace that in the other one to get:

x - 3*(8 - 2x) = - 3

x - 24 + 6x = -3

7x = -3 + 24

7x = 21

x = 21/7 = 3

And the value of y is:

y = 8 - 2x = 8 - 2*3 = 2

The solution is x = 3 and y = 2.

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Answer: $3,000

(There are 7 days in a week) I don't know if i'm correct or not but it should be the answer.

The new co-ordinates of the point after transformation is (-3,9)

A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates,

Given here: The point g'(4,6)

The point transforms to  (x-7,y+3)

Thus the new points are 4⇒4-7=-3

6⇒6+3=9

Thus, The new co-ordinates of the point after transformation is (-3,9)

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Using equations, we know that the age of Geraldine and Steven is t - 4 and 2t - 8 respectively.

It basically consists of a variable, perhaps with an additional numerical constant.

To easily understand this concept, consider the example below. 3x – 4 = 5. It is a straightforward class 7 equation.

The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.

So, we have the following algebraic expression after converting the word problem:

To Geraldine:

g = t - 4

To Steven:
s = 2g

Inputting Tom's age into equation 1 results in:

g = t - 4

To determine Steven's age:

s = 2(t-4)

s = 2t - 8

Therefore, using equations, we know that the age of Geraldine and Steven is t - 4 and 2t - 8 respectively.

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Step-by-step explanation:

Find 1/4 of 56

56 / 4 = 14

Now

56-14=42

Now

42/7=6

6x4=24

42-24=18

18 copies left

Answer: Their car got an average of 23.6 miles per gallon.

BTW I just searched it up so I'm sorry if it is wrong.

The height of the cone is 24 centimetres.

A cone has a volume of 392π cubic centimetres and a radius of 7 centimetres. Therefore, the height of the cone can be found as follows;

Hence,

volume of a cone = 1 / 3 πr²h

where

Therefore,

volume = 392π

r = 7 cm

392π = 1 / 3 × π × 7² × h

392π = 49 / 3 πh

cross multiply

1176π = 49πh

divide both sides by 49π

h = 1176π / 49π

h = 24 cm

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Answer: It is 34$ per one ticket

Step-by-step explanation:

$374 divided by 11 is 34

Answer:

$34 per ticket

Step-by-step explanation:

We were told $374/11tickets.

We are looking for how much per 1 ticket.

Divide to find the per-ticket cost.

Use either 374÷11

374/11 .

374÷11 = 34

This means $34 per ticket.

Step-by-step explanation:

x=97+40 degree (being sum of two interior angle is equal to one exterior angle)

Answer:

(7^2)^2

Step-by-step explanation:

(7^-2)*(7^6)=7^-2+6

......since the base 7 is the same, when u multiply them, you should add the exponents and keep 7 as it is. That will be 7^4, which in equivalent to ans D(7^2)^2

Answer:

850 miles on 25 gallons

Step-by-step explanation:

Answer: 850 miles on 25 gallons is more efficient, meaning it covers a greater distance per gallon of fuel.

Step-by-step explanation:

Answer:

y = -x +8

Step-by-step explanation:

The line crosses the x axis at 8. So we know when y = 0 then x = 8

The line cross the y axis at 8. so we know when x = 0 then y = 8

the equation of a line we know to take the form y = mx + c

When x = 0 and y = 8, and y = mx+ c then then c =8

when y = 0 x = 8. y = mx + c, 0 = m(8) +8. for this to be true m must be equal to -1

so the equation of the line, the inequality is y = -x +8

Answer:

y = - [tex]\frac{5}{2}[/tex] x - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (0, - 2) ← 2 points on the line

m = [tex]\frac{-2-3}{0-(-2)}[/tex] = [tex]\frac{-5}{0+2}[/tex] = - [tex]\frac{5}{2}[/tex]

the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = - [tex]\frac{5}{2}[/tex] x - 2 ← equation of line

Answer:

160 tourists like only one place. This can be determined by using a Venn diagram. Of the 500 tourists surveyed, 350 like Pokhara, 200 like Chitwan, and 50 like both places. That leaves 20 who like neither of the two places. To get the number of tourists that like only one place, subtract the number of tourists who like both (50) and the number of tourists who like neither (20) from the total number of tourists surveyed (500), resulting in a total of 160 tourists who like only one place.

Answer:

  (x, y) = (4, 0)

Step-by-step explanation:

You want the solution to the system of equations ...

It often works well to start the solution process by putting both equations into standard form. We do that by removing any common factors from the coefficients. Here, we see that the second equation's coefficients each have a factor of 3, so we can remove that and rewrite the system as ...

Changing the coefficient of the y-term has no effect, telling us that y=0, and the equation reduces to ...

  5x = 20

  x = 4

More formally, if we subtract the first equation from the second, we get ...

  (5x +2y) -(5x -3y) = (20) -(20)

  5y = 0 . . . . . . simplify

  y = 0 . . . . . . . divide by 5

The solution is (x, y) = (4, 0).

The area of the given parallelogram is 6.6 square units.

The region or space occupied by a parallelogram in a two-dimensional plane is referred to as the area of a parallelogram. A unique category of a quadrilateral is a parallelogram.

A quadrilateral is referred to as a parallelogram if it has two sets of parallel opposite sides. A parallelogram can be anything from a rectangle to a square to a rhombus.

The area of the partogram is calculated as:-

Area =  Base x Height

Area = 2.2 x 3

Area = 6.6 square units

Therefore, the parallelogram will have an area of 6.6 square units.

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To verify if the representation is a function for this problem, we should verify if each input is mapped to a single output. If there is an input that is mapped to more than one output, then the relation is not a function.

A relation represents a function when each input value is mapped to a single output value.

On a graph, a function is represented if the graph contains no vertical aligned points, that is, if there are no values of x at which we could trace a vertical line that would cross the graph of the function more than once.

With arrows, only one arrow can depart from each value of x, or more than one arrow departing from the same value of x but necessarily arriving at the same value of y.

The problem is incomplete, hence the general procedure to verify if a relation represents a function was presented.

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The possible dimensions of rectangular room A are 9 and 3x - 2.

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle.

Given:

A fitness center has several rectangular rooms where exercise classes are held.

The area of Room A is 27x − 18 square units.

The area of the rectangle = length x width

27x − 18 = length x width

9 (3x - 2) = length x width.

Therefore, 9 and 3x - 2 are the dimensions.

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Answer: Let's call the measure of the angle x.

The complement of the angle is (90 - x) degrees, and the supplement is (180 - x) degrees.

So, using the information given in the problem, we can set up an equation:

5 * (90 - x) = 2 * (180 - x) - 24

Expanding both sides and simplifying, we get:

450 - 5x = 360 - 2x - 24

Solving for x, we get:

6x = 294

x = 49

Therefore, the measure of the angle is 49 degrees.

Step-by-step explanation:

Answer:

x = -16 and x = 1

Step-by-step explanation:

"Finding the roots" means solving the equation. We'll set the equation equal to 0 (replace f(x) with zero) and factor.

0 = x^2 + 15x - 16

0 = (x + 16)(x - 1)

This is factored.

Using the Zero Product Property, we separate this into two small equations.

x+16 = 0 and x-1 = 0

Solve these one-step equations.

x = -16 and x = 1

These are the roots (and roots are solutions, are zeros, are x-intercepts) If the question ask for zeros, roots, solutions or x-intercepts, set it equal to 0, factor and solve.

Answer:

4.5 inches

Step-by-step explanation:

Answer:

In the case presented, the range is the difference between the maximum value and the minimum value of the data. The range describes the breadth of the data and how much they vary from the minimum value to the maximum value. Therefore, the range indicates the dispersion of the data.

The statement indicates that the range is 5, which means that the most flights made by students is 5. Since the data has a narrow dispersion, we can conclude that most students have taken a similar number of flights, implying that most students have flown an amount close to the maximum number observed.

Therefore, the option that best describes the dispersion of the data is: "The data has a range of 5, which is a narrow dispersion. This means that most students have taken a similar number of flights."

Step-by-step explanation:

Answer:

0 < a < 6

or

(0, 6) in interval notation

Step-by-step explanation:

The area of the triangle is
[tex]Area \;A = \dfrac{1}{2}(base \cdot height)\\[/tex]

We are given base = 6 in, height = a and area A < 18 in²

Using the formula for area we get

[tex]A = (1/2)(6 \cdot a) = 3a[/tex]

We know this area is < 18

So 3a < 18

Dividing both sides by 3 gives us
3a/3 < 18/3

a < 6

So height a must be less than 6 inches.
Height cannot be 0 so the lower bound on height is

a > 0

Putting these together we get the rang of a as
0 < a < 6

In Interval notation this is written as (0, 6)

Hope that helps you. Have confidence in yourself and seek help for your doubts here or elsewhere on the net. You will succeed

The sketch of cylinder is shown in the figure.

Suppose that the radius of considered right circular cylinder be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

[tex]V = \pi r^2 h \: \rm unit^3[/tex]

Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.

Given;

Volume=36pi

Diameter=6cm

Now,

Radius=6/2=3cm

Volume= 36pi

pi*R^2*h=36pi

3^2*h=36

h=36/6

h=6cm

Therefore, by the given volume the radius and height will be 3cm and 6cm.

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Using the Pythagorean theorem, if AL is perpendicular to BD and CM is perpendicular to BD, then quadrilateral ABCD is a parallelogram.

In a parallelogram, the opposite sides are equal in length, i.e. AL = CD and BM = AD.

By the Pythagorean theorem, we know that the length of the diagonal BD can be found as the square root of the sum of the squares of AL and CM:

BD = √(AL^2 + CM^2)

Since AL = CD, the area of quadrilateral ABCD can be found as:

ar (quad.ABCD) = AL × BD

Substituting BD = √(AL^2 + CM^2) and combining the two equal length sides, we get:

ar (quad.ABCD) = (AL + CM) × √(AL^2 + CM^2) / 2

Finally, dividing both sides by √(AL^2 + CM^2) and using the fact that BD = √(AL^2 + CM^2), we get:

ar (quad.ABCD) = 1/2 × BD × (AL + CM)

Thus, we have proved that the area of quadrilateral ABCD is equal to 1/2 × BD × (AL + CM).

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One of the numbers is 21, and the other number is 2.5

What is an algebraic expression?

An algebraic expression is when we combine numbers and words to solve a mathematical problem.

Let's call one of the numbers "x". We know that x is 8 times greater than the other number, which we'll call "y". So we have:

y = x / 8

The product of x and y is 57, so:

x * y = 57

Substituting y = x / 8 into the equation above:

x * (x / 8) = 57

Expanding the right side of the equation:

[tex]x^2 / 8 = 57[/tex]

Multiplying both sides by 8:

[tex]x^2 = 8 * 57[/tex]

Solving for [tex]x^2[/tex]:

[tex]x^2 = 456[/tex]

Taking the square root of both sides:

[tex]x =\sqrt{456}[/tex]

x = 21

So, One of the numbers is 21, and the other number is 21 / 8 = 2.5.

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Work Shown:

A = the 1st marble is blue

B = the 2nd marble is green

Replacement is applied. This makes A and B independent.

P(A) = (4 blue)/(10 total) = 4/10 = 2/5

P(B) = (2 green)/(10 total) = 2/10 = 1/5

P(A and B) = P(A)*P(B) ... see note below

P(A and B) = (2/5)*(1/5)

P(A and B) = 2/25

Note: The equation is valid because events A and B are independent.