Which image would MOST LIKELY be used in an informational book about how automobiles have developed through history?

A. a chart showing the cost of cars
B. a blueprint of the very first car ever built
C. a picture showing cars on the highway
D.a time line showing when certain cars were built

a)The initial height of the flare when it is fired is 2m.

b)The height of the flare after 1 s is 38.75m

c)The flare reaches its maximum height after 2 seconds.

d) The maximum height of the flare is 65m.

e) The flare hits the water after 8 seconds.

The given equation which is h = -5.25t² + 42t + 2, can be used to solve the following questions:

a) To get the initial height of the flare when it is fired, the value of t = 0 must be used in the given equation:

h = -5.25(0)² + 42(0) + 2h

= 0 + 0 + 2h

= 2

Therefore, the initial height of the flare when it is fired is 2m.

b) To get the height of the flare after 1 s, the value of t = 1 must be used in the given equation:

h = -5.25(1)² + 42(1) + 2h

= -5.25 + 42 + 2h

= 38.75

Therefore, the height of the flare after 1 s is 38.75m

c)The maximum height of the flare is reached when the flare is at its peak.

Therefore, the time when the flare reaches its maximum height is found by dividing -b by 2a, where the equation is in the form of y = ax² + bx + c.

The equation h = -5.25t² + 42t + 2 is in the form of y = ax² + bx + c,

where a = -5.25, b = 42, and c = 2.t = -b/2a = -42/2(-5.25)

= -2

Therefore, the flare reaches its maximum height after 2 seconds.

d) To get the maximum height of the flare, the value of t = 2 must be used in the given equation:

h = -5.25(2)² + 42(2) + 2h

= -21 + 84 + 2h

= 65

Therefore, the maximum height of the flare is 65m.

e)When the flare hits the water, the height, h, is 0.

Therefore, the time when the flare hits the water is found by setting h = 0 in the given equation and solving for t:

0 = -5.25t² + 42t + 2

Using the quadratic formula:\($$t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$\)

where a = -5.25, b = 42, and c = 2.

= \(\frac{-42 \pm \sqrt{42^2 - 4(-5.25)(2)}}{2(-5.25)} $$t\)

= 8.003 or t = 1.331

Since time cannot be negative, the time when the flare hits the water is after 8 seconds. Therefore, the flare hits the water after 8 seconds.

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Solving the equation we get, x= -2.

What is equation?

In  algebra, the definition of an equation is a mathematical statement which shows that two mathematical expressions are equal. For example, 3x - 7= 14 is an equation, in which 3x - 7 and 14 are two expressions separated by an 'equal( '=')' sign. Solving the equation we will get the value of the unknown x=7.

Given equation is

                  3/2+2x/5=7/10

    Taking the constants to the right hand side of the equation we get,

                    2x/5= 7/10 - 3/2

         The lowest common denominator of 7/10 and 3/2 is 10

Multiplying by 10 to the both sides of equation we get,

                     (2x/5)×10 = (7/10-3/2)×10

                   ⇒ 4x = (7/10)×10 - (3/2)×10

                   ⇒ 4x = 7- 15

                  ⇒ 4x = -8

         Dividing both sides by 4 we get,

                      x = -2

Hence, solving the equation we get, x= -2.

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\(f(x) = 4tan(8\pi) + 4sec^2(8\pi)(x - 8\pi) + 8sec^2(8\pi)tan(8\pi)(x - 8\pi)^2/2!\)

This expression represents the first three nonzero terms of the Taylor series expansion for f(x) = 4tan(x) centered at c = 8π.

What is the trigonometric ratio?

the trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.

To find the first three nonzero terms of the Taylor series for the function f(x) = 4tan(x) centered at c = 8π, we can use the definition of the Taylor series expansion.

The general formula for the Taylor series expansion of a function f(x) centered at c is:

\(f(x) = f(c) + f'(c)(x - c)/1! + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...\)

Let's begin by calculating the first three nonzero terms for the given function.

Step 1: Evaluate f(c):

f(8π) = 4tan(8π)

Step 2: Calculate f'(x):

f'(x) = d/dx(4tan(x))

= 4sec²(x)

Step 3: Evaluate f'(c):

f'(8π) = 4sec²(8π)

Step 4: Calculate f''(x):

f''(x) = d/dx(4sec²(x))

= 8sec²(x)tan(x)

Step 5: Evaluate f''(c):

f''(8π) = 8sec²(8π)tan(8π)

Step 6: Calculate f'''(x):

f'''(x) = d/dx(8sec²(x)tan(x))

= 8sec⁴(x) + 16sec²(x)tan²(x)

Step 7: Evaluate f'''(c):

f'''(8π) = 8sec⁴(8π) + 16sec²(8π)tan²(8π)

Now we can write the first three nonzero terms of the Taylor series expansion for f(x) centered at c = 8π:

f(x) ≈ f(8π) + f'(8π)(x - 8π)/1! + f''(8π)(x - 8π)²/2!

Simplifying further,

Hence, \(f(x) = 4tan(8\pi) + 4sec^2(8\pi)(x - 8\pi) + 8sec^2(8\pi)tan(8\pi)(x - 8\pi)^2/2!\)

This expression represents the first three nonzero terms of the Taylor series expansion for f(x) = 4tan(x) centered at c = 8π.

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Hey There!!

Your best answer will be A.

Step-by-step explanation:

Because, The SAS stands for Side Angle Side if you need two sides and then the angle needs to be between them.

The first one works because the angle is in-between the 2 sides. The second one really doesn't work very well. Because, It actually have 2 angles and it only need one. Well, The third one it doesn't work because the angle isn't between from both sides. The fourth one doesn't work at all they are only sides and no angles. Hope This helps <3!!

Answer:

It is 50

Step-by-step explanation:

Answer:

50.

Step-by-step explanation:

150 = 2*3*5*5

250 = 2*5*5*5

From the common factors ( one pair of 2's and 2 pairs of 5's):

HCF = 2*5*5

= 50.

\(m\angle E=\sin \dfrac{\sqrt{10}}{2\sqrt5}=\sin \dfrac{\sqrt2}{2}=45^{\circ}\)

The correct substitution to rewrite the equation 16(x^3 + 1)^2 - 22(x^3 + 1) - 3 = 0 as a quadratic equation is:

c. u = (x^3 + 1)^2

By substituting u = (x^3 + 1)^2, the equation can be rewritten as 16u - 22u - 3 = 0, which is a quadratic equation in terms of u.

To solve the quadratic equation for u, you can use factoring, completing the square, or the quadratic formula. Once you find the solutions for u, you can substitute back (x^3 + 1)^2 for u to obtain the solutions for the original equation.

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Answer: option A is correct

Step-by-step explanation:

The given side lengths are

A) 5, 12, 13

B) 4, 4, 8

C) 2, 3, 4

To be able to form a right ange triangle, the given side lengths must be a Pythagorean triple. Pythagorean triple obeys the Pythagorean theorem such that

Hypotenuse² = opposite side² + adjacent side²

Hypotenuse = the longest side

Applying it to the given options,

A) 13² = 5² + 12² = 25 + 144

169 = 169

It forms a right angle triangle

B) 8² = 4² + 4² = 16 + 16

64 ≠ 32

It does not forms a right angle triangle

C) 4² = 3² + 2²

16 ≠ 13

It does not forms a right angle triangle

Answer:

Option A) 5, 12, 13 is a right angle triangle.

Option C) 2, 3, 4 is approximately a right angle triangle.

Step-by-step explanation:

A right angle triangle always follow pythagora's theorem which basically states that the addition of the squares of the two smaller sides must give the square of the largest side.

For option A)

5^2 + 12^2 = 25 + 144 = 169

Square root of 169 is 13, so it's correct.

For option B)

4^2 + 4^2 = 16 + 16 = 32

Square root of 32 is 5.65, which is not equal to 8. This is not a right angle triangle.

For option C)

2^2 + 3^2 = 4 + 9 = 13

Square root of 13 is 3.606, approximately 4. So this is approximately a right angle triangle.

If the answer requires that it must be exact then choose only A, Otherwise, A and C are correct.

There are no values of h that make b lie in the plane spanned by a₁ and a₂. The problem involves determining the value(s) of h for which the vector b lies in the plane spanned by the vectors a₁ and a₂.

1. The given vectors are a₁ = [1] and a₂ = [-5], and the vector b = [4, -4, -1, 2, h]. By setting up an equation using the linear combination of a₁ and a₂, we can find the value(s) of h that satisfy this condition. The answer will be one or more numerical values of h.

2. To check if the vector b lies in the plane spanned by a₁ and a₂, we need to determine if b can be expressed as a linear combination of a₁ and a₂. We can set up the equation:

b = c₁ * a₁ + c₂ * a₂,

where c₁ and c₂ are constants. Substituting the values of a₁, a₂, and b, we have:

[4, -4, -1, 2, h] = c₁ * [1] + c₂ * [-5].

3. Expanding this equation, we get the following system of equations:

4 = c₁ - 5c₂,

-4 = -5c₁,

-1 = 0,

2 = 0,

h = c₁.

4. From the third and fourth equations, we can see that -1 = 0 and 2 = 0, which are contradictory statements. Therefore, there is no value of h that satisfies the condition for b to lie in the plane spanned by a₁ and a₂.

5. In summary, there are no values of h that make b lie in the plane spanned by a₁ and a₂.

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The classification of the compounds according to their functional class: A | Aldehyde

B | Alcohol

C | Ketone

D | Amine

Compound A contains a carbonyl group (C=O) bonded to two alkyl groups (R-). This is the general structure of an aldehyde. Aldehydes are characterized by their strong, sweet odor.

They are also very reactive, and can be used to make a variety of other compounds, such as esters and carboxylic acids.

Compound B contains an oxygen atom (O) bonded to two alkyl groups (R-). This is the general structure of an alcohol. Alcohols are characterized by their ability to dissolve other polar compounds, such as water. They are also used in a variety of products, such as solvents, cleaners, and fuels.

Compound C contains a carbonyl group (C=O) bonded to a propyl group (CH3CH2CH2-) and an amino group (NH2). This is the general structure of a ketone.

Ketones are characterized by their strong, sweet odor. They are also very reactive, and can be used to make a variety of other compounds, such as esters and carboxylic acids.

Compound D contains a nitrogen atom (N) bonded to three alkyl groups (R-). This is the general structure of an amine. Amines are characterized by their basic properties. They are also used in a variety of products, such as pharmaceuticals, plastics, and fertilizers.

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Answer:

33.33333333333333%

Step-by-step explanation:

the increase = 100 ₹

then percentage of increase is = 100/300 *100 = 33.33333333333333%

Answer:

33.3333333333%

Step-by-step explanation:

\(\frac{400-300}{300} x 100\)

33.333333333%

Answer:

16

Step-by-step explanation:

If 3 x 4 = 12 then you need to do the same to the number 4 so 4 x 4 =16

Answer:

3 : 4 :: 12 : x proportion 3x = 48 product means/extremes Can you solve for x and answer?

(If not look below.)

Step-by-step explanation:

ratio: 3:4

so divide 12 by 3=4

and multiply 4 by 4=16

your friend sells 16 tickets

ratio is now 12:16

4 : 3 = 12 : x

x = 12 * 4  / 3  = 16

x,y,z=(smaller z-value)=(-56/3, -32/3, 16/3)

x,y,z=(larger z-value)=(56/3, 32/3, -16/3)

These are the points on the cone that are closest to the point (14, 8, 0).

In a two-dimensional space, a point is defined by two coordinates, typically denoted by (x, y), where x represents the horizontal position, and y represents the vertical position. In a three-dimensional space, a point is defined by three coordinates, typically denoted by (x, y, z), where x, y, and z represent the horizontal, vertical, and depth positions, respectively.

We want to minimize the distance between the point (14, 8, 0) and the surface of the cone defined by the equation z² = x² + y², subject to the constraint that we stay on the surface of the cone.

Let f(x,y,z) = (x-14)² + (y-8)² + z² be the function we want to minimize subject to the constraint g(x,y,z) = z² - x² - y² = 0.

The Lagrange multiplier method involves finding the critical points of the function L(x,y,z,λ) = f(x,y,z) - λg(x,y,z), where λ is the Lagrange multiplier.

So we have:

L(x,y,z,λ) = (x-14)² + (y-8)² + z² - λ(z² - x² - y²)

Taking the partial derivatives with respect to x, y, z, and λ, and setting them equal to zero, we get the following system of equations:

2(x-14) + 2λx = 0

2(y-8) + 2λy = 0

2z - 2λz = 0

z² - x² - y² = 0

The third equation simplifies to z(1-λ) = 0, which gives us two possibilities:

Case 1: z = 0

In this case, the fourth equation becomes -x² - y² = 0, which implies that x = y = 0. But this point does not lie on the surface of the cone, so it is not a valid critical point.

Case 2: λ = 1

In this case, the first two equations become x-14 = -xλ and y-8 = -yλ, which imply that x = -7λ and y = -4λ. Substituting into the fourth equation gives:

z² = x² + y² = 65λ²

To minimize the distance between the point (14, 8, 0) and the surface of the cone, we want to find the value of λ that minimizes the function f(x,y,z) subject to the constraint g(x,y,z) = 0. Substituting x = -7λ, y = -4λ, and z = √(65λ²) into f(x,y,z), we get:

f(λ) = (7λ-14)² + (4λ-8)² + 65λ²

To minimize this function, we take its derivative with respect to λ and set it equal to zero:

f'(λ) = 30λ - 80 = 0

Solving for λ, we get λ = 8/3. Substituting this back into x = -7λ, y = -4λ, and z = √(65λ²), we get:

x,y,z=(smaller z-value)=(-56/3, -32/3, 16/3)

x,y,z=(larger z-value)=(56/3, 32/3, -16/3)

These are the points on the cone that are closest to the point (14, 8, 0).

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Answer:

x = 1, -2, -7

Step-by-step explanation:

Just factor, you got this!

Answer:

B

Step-by-step explanation:

The graphs of y = 2cos(x) - 1 and y = 2sin(x + π/2) - 1 are both sinusoidal curves, which means they oscillate up and down periodically.

A sinusoidal curve is a type of curve that represents the behavior of a sinusoidal function. The sine function is periodic and oscillates between a maximum value and a minimum value as the input variable (usually x) changes.

The graphs of y = 2cos(x) - 1 and y = 2sin(x + π/2) - 1 are both sinusoidal curves, which means they oscillate up and down periodically.

Similarities:

1) Both curves have the same amplitude of 2, which means they oscillate between y = 1 and y = -3.

2) Both curves have the same vertical shift of -1, which means the lowest point of each curve is at y = -3 and the highest point is at y = 1.

3) Both curves have the same period of 2π, which means they repeat themselves every 2π units along the x-axis.

4) Both curves have the same frequency of one cycle per 2π units along the x-axis.

Differences:

1) The curve y = 2cos(x) - 1 is a cosine curve, which means it starts at its highest point and moves downwards. The curve y = 2sin(x + π/2) - 1 is a sine curve, which means it starts at its middle point and moves upwards.

2) The curve y = 2cos(x) - 1 reaches its highest point at x = 0 and its lowest point at x = π, while the curve y = 2sin(x + π/2) - 1 reaches its middle point at x = 0 and its highest and lowest points at x = π/2 and x = 3π/2, respectively.

3) The curve y = 2cos(x) - 1 is an even function, which means it is symmetric about the y-axis, while the curve y = 2sin(x + π/2) - 1 is an odd function, which means it is symmetric about the origin.

In summary, both curves have the same amplitude, vertical shift, period, and frequency, but they have different shapes and symmetry properties due to the use of cosine and sine functions.

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Answer:  8.94 is the length of GI

Step-by-step explanation: The two triangles are similar, so the ratios of the sides to each other will be the same.

the unknown length of GI in triangle FIG corresponds to the known length 20 of IH in Triangle GIH, and the known length 4 of side FI in triangle FIG corresponds to GI in Triangle GIH. So the ratio looks like 4:x as x:20

4/x = x/20  multiply both sides by x and 20 to "cancel" the denominators.

20x(4/x) = 20x(x/20)

80 = x²    Calculate the square roots  

√x² = x . √80 = 8.94

Overtime Hours Worked A random sample of 15 registered nurses in a large hospital showed that they worked on average 44. 2 hours per week. we can estimate with 90% confidence that the population mean of overtime hours worked by registered nurses in the hospital is between 42.5 and 45.9 hours per week.

The t-distribution is a probability distribution that is used to estimate the population mean of a normally distributed variable when the sample size is small or the population standard deviation is unknown.

To estimate the population mean with a 90% confidence interval, we can use a t-distribution with n-1 degrees of freedom, where n is the sample size.

First, we need to calculate the standard error of the mean, which measures the variability of sample means around the population mean. The formula for the standard error of the mean is:

SE = s / sqrt(n)

where s is the sample standard deviation and n is the sample size.

In this case, s = 2.6 and n = 15, so:

SE = 2.6 / sqrt(15) = 0.671

Next, we need to find the critical value of the t-distribution with 14 degrees of freedom and a 90% confidence level.

We can look this up in a t-table or use a calculator to find that the critical value is approximately 1.761.

Finally, we can calculate the confidence interval using the formula:

CI = X ± tα/2 * SE

where X is the sample mean, tα/2 is the critical value of the t-distribution, and SE is the standard error of the mean.

In this case, X = 44.2 and tα/2 = 1.761, so:

CI = 44.2 ± 1.761 * 0.671

CI = (42.5, 45.9)

Therefore, we can estimate with 90% confidence that the population mean of overtime hours worked by registered nurses in the hospital is between 42.5 and 45.9 hours per week.

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Answer:

i think its b

Step-by-step explanation:

Answer:

-1875

Step-by-step explanation:

An arithmetic sequence has a common difference as a sequence. Here the common differnece is -11.

So our sequence so far looks like,

(57,46,35,24....). We know the last term of the sequence is -207 and we need to find the nth term of that series so we use arithmetic sequence

\(a _{1} + (n - 1)d \)

where a1 is the inital value,

d is the common differnece and n is the nth term.

We need to find the nth term so

\(57 + (n - 1)( - 11) = - 207\)

\((n - 1)( - 11) = - 264\)

\(n - 1 = 24\)

\(n = 25\)

So the 25th term of a arithmetic sequence is last term, now we can use the sum of arithmetic sequence

which is

\( \frac{a _{1} + a _{n} }{2} n\)

\( \frac{57 + ( - 207)}{2} (25) = \)

\( \frac{ - 150}{2} (25)\)

\( - 75(25) = - 1875\)

Answer:

-1875

Step-by-step explanation:

57 , 46 , ......... -207

\(First \ term = \ a_{1} = 57\\\)

common difference = d = second term - first term = 46 - 57 = -11

\(n^{th} \ term = -207\\\\a + (n-1)*d=t_{n}\)

57 + (n-1)* (-11) = -207

57 - 11n + 11 = -207

     -11n + 68  = -207

            -11n   = -207 - 68

             -11n  = -275

                 n = -275/-11

                n = 25

\(S_{n}=\dfrac{n}{2}(a_{1}+l)\\\\\\S_{25}=\dfrac{25}{2}*(57 + (-207) )\\\\\\ =\dfrac{25}{2}* (-150)\\\\\\= 25 *(-75)\\\\= -1875\)

Graph y=3x, axes labeled by 5s, shows refunds based on attendance.

Certainly! Here is a graph of y = 3x, with the x-axis labeled in increments of 5. The y-axis represents the amount of money the manager would have to refund to the customers based on the number of people in the theater.

           ^

           |

 $15    |

 $10    |

  $5     |           *    

            |         *

   0-----+-------*----------------->

            |     *  

       x-axis  

As you can see, the y-axis is labeled in increments of $5, and each unit on the x-axis represents 1 person. So if, for example, there were 10 people in the theater, the manager would have to refund $30 ($10 per person). If there were 20 people in the theater, the manager would have to refund $60 ($3 per person).

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Step-by-step explanation:

y = mx + b

\( \frac{2}{3} = ( - 1)( - 1) + b\)

\( \frac{2}{3} - 1 = b\)

\( \frac{2}{3} - \frac{3}{3} = b\)

\( - \frac{1}{3} = b\)

Answer:

The next step would be to multiply your slope by your x value.

Step-by-step explanation:

The overall answer would is b=-1/3

BTW...if y'all have any questions for school (it can be any grade level or subject) just comment here and I will get to it as soon as I can!! ❤

Step-by-step explanation:

Area of circle = 2πr²

diameter = 14 cm

so,

after inserting values in the formula we got,

2 × 22/7 × 14

→ 2 × 22 × 2 = 44 × 2 = 88 cm²

hence, area of the circle is 88cm²

hope this answer helps you dear

This means that the original graph of y = 1/x is horizontally compressed by a factor of 4 and shifted downward by 3 units.

The given function is y = 1/x. To shrink it horizontally by a factor of 4, we can replace x with 4x. To shift it down 3 units, we subtract 3 from the function. Therefore, the transformed function is:

y = 1/(4x) - 3

This means that the original graph of y = 1/x is horizontally compressed by a factor of 4 and shifted downward by 3 units.

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Answer:

My friend is wrong because a straight angle either consists with two right angles or one obtuse angle and one acute angle.

Step-by-step explanation:

Acute angles are angles less than \(90^o\).

Your friend is correct, because all three angles can be acute

A straight line measures 180 degrees.

i.e.

\(\theta = 180\)

Divide by 3

\(\frac{\theta}{3} = \frac{180}{3}\)

\(\frac{\theta}{3} = 60\)

If all three angles on the straight line have a measure of \(60^o\)

Then your friend's claim is correct

Because \(60^o\) is an acute angle

Some other possible scenarios are:

Hence, your friend is correct

See attachment for illustration of one of the possible scenarios

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The statements that are true regarding the angles formed by the transversal and parallel lines are:

A. m∠1 = 70°.

B. m∠2 = 110°

C. m∠6 = 70°.

E. m∠9 = 50°

H. m∠16 = 130°

Given the following angle measures formed when two parallel lines ( being cut by two transversals:

Using relevant theorems, let's determine which of the statements are true:

Angles 4 and 1 are vertical angles, therefore they are congruent based on the vertical angles theorem.

m∠4 = m∠1

m∠1 = 70°.

m∠2 = 180 - m∠4 [linear angles theorem]

m∠2 = 180 - 70

m∠2 = 110°

m∠6 = m∠4 [base on the alternate interior angles theorem]

m∠6 = 70°.

m∠9 = 180 - m∠12 [based on the linear angles theorem]

m∠9 = 180 - 130

m∠9 = 50°

m∠16 = m∠12 [based on the corresponding angles theorem]

m∠16 = 130°

The statements that are true are:

A. m∠1 = 70°.

B. m∠2 = 110°

C. m∠6 = 70°.

E. m∠9 = 50°

H. m∠16 = 130°

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A matrix A is said to have only the trivial solution if the only solution to the system of equations, A x = 0, is the zero vector, x = 0.

The number of pivot columns in a matrix is equal to the rank of the matrix. Therefore, if A has only the trivial solution, it has rank 0, and so it has 0 pivot columns. To calculate the rank of a matrix, we can use the following formula: rank(A) = min(m, n) - dim(null A), where m and n are the number of rows and columns of A, respectively, and dim(null A) is the dimension of the null space of A.

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complete question:

Given an m x n matrix A, what is the number of pivot columns for A if it has only the trivial solution?