if
x/y=y/z=z/x
show that x=y=z​

Question: If the subspace of all solutions of

Ax = 0

has a basis consisting of vectors and if A is a ​matrix, what is the rank of​ A.

Note: The rank of A can only be determined if the dimension of the matrix A is given, and the number of vectors is known. Here in this question, neither the dimension, nor the number of vectors is given.

Assume: The number of vectors is 3, and the dimension is 5 × 8.

Answer:

The rank of the matrix A is 5.

Step-by-step explanation:

In the standard basis of the linear transformation:

f : R^8 → R^5, x↦Ax

the matrix A is a representation.

and the dimension of kernel of A, written as dim(kerA) is 3.

By the rank-nullity theorem, rank of matrix A is equal to the subtraction of the dimension of the kernel of A from the dimension of R^8.

That is:

rank(A) = dim(R^8) - dim(kerA)

= 8 - 3

= 5

Answer:  There is a total of 900 seats in the auditorium.

Step-by-step explanation:

there is a formula for this

t - n = a + ( n - 1) d

It is called a Arithmetic Progression.

We use this to find the number of seats in the last row first.

a = initial value, 12

d = common difference for each successive term

n = is the number of terms in the sequence

t - 25 = 12 + (25 -1) * 2

We ignore the left side for now, just solve the right and we get 60.

Now we use the equation,

n / 2 (2a + n -1 * d)

So,

25/2 ( 24 + 24 * d)

The answer is 900

When graphing an exponential function, a T-chart is commonly used to determine the values. The correct answer is option A.

The T-chart employs positive real numbers since this is the most typical form of exponential function.

Exponential functions are utilized to represent processes that increase or decrease exponentially, as well as to model phenomena in many different disciplines, including science, economics, and engineering.

The exponential function can be represented by the following equation:

\(y=a^x\), where a is the base, x is the exponent, and y is the outcome.

When a is a positive number greater than one, the function is called exponential growth, while when a is a fraction between 0 and 1, the function is called exponential decay.

The T-chart is used to determine the values to use in the graph and connect the dots as required. Positive real numbers are used as the values in the T-chart in order to effectively graph the exponential function.

Therefore, the correct answer is option A.

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\(xy=(a+2)(a-2)=a^2-2a+2a-4=a^2-4\)

Answer: y= 3/2x - 6

Step-by-step explanation:

The equation is y=mx + b

The y-intercept is when x = 0, so on the table y-intercept = -6

The slope is rise/run, we see that y increase by three and x increase by 2, so the slope is 3/2

to get the slope of any straight line, we simply need two points off of it, let's use those ones in the picture below.

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}} \implies \cfrac{3 +3}{4} \implies \cfrac{ 6 }{ 4 } \implies {\Large \begin{array}{llll} \cfrac{3 }{ 2 } \end{array}}\)

now, the y-intercept occurs when x = 0, recheck the picture below.

Answer:

your answer would be

5. cos O= b/h = 8/17

6. tan O= p/b = 7/24

hope it ill help u guess......

Answer:

1:6 = 7:42

Step-by-step explanation:

Answer:

35dg & 36abcd

Step-by-step explanation:

Multiply 7 times 5 then add the remaining terms for equation 1. For equation 2 multiply 12 by 3 for 36.

The sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator is $59.15.

To calculate the sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator we will follow these steps:

Step 1: Calculate the amount of discount = Regular Price × Discount rate

Discount rate = 35/100

Simplifying the value we have:

Discount rate = 0.35

Amount of discount = 91 × 0.35

Amount of discount = $31.85

Step 2: Calculate the sale price

Sale price = Regular price − Amount of discount

Sale price = $91 − $31.85

Sale price = $59.15

Hence, the sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator is $59.15.

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Answer:

big bodie built

Step-by-step explanation:

i used to be dusty

Based on the calculations, the value of the given prefix expression is equal to 2205.

The preorder traversal of a tree (T) are typically used in discrete mathematics to determine the value of a prefix expression on a specific expression tree.

For the preorder traversal of this tree (T), we would start from the right most expression:

Prefix expression = * + 3 + 3 ↑ 3 + 3 3 3

Prefix expression = * + 3 + 3 ↑ 3 6 3

Prefix expression = * + 3 + 3  3⁶  3

Prefix expression = * + 3 3 729 3

Prefix expression = * + 3 732 3

Prefix expression = * 735 3   ⇒ 735 × 3

Value = 2205.

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Complete Question:

Given the following prefix expression:

* + 3 + 3 ↑ 3 + 3 3 3

What is the value of the prefix expression?

The slope of the secant line over the interval [3, t] for the curve Q(t) = t² is given by the formula m = (t² - 9) / (t - 3).

The slope of a line is a measure of how steep the line is. It tells us how much the line is rising or falling as we move from left to right.

The secant line is a line that passes through two points on a curve. In this case, the curve is Q(t) = t².

To find the slope of the secant line over the interval [3, t], we need to find the slope of the line that passes through the points (3, 9) and (t, t²).

The slope of the line passing through two points (x1, y1) and (x2, y2) is given by the formula:

m = (y2 - y1) / (x2 - x1)

So, using this formula, we can find the slope of the secant line over the interval [3, t]:

m = (t² - 9) / (t - 3)

This formula gives us the exact slope of the secant line over the interval [3, t]. We can simplify it if needed, but the answer will always be in exact form.

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The sum of the geometric sequence is 31/3

The sequence is given as:

1/3, 2/3, 4/3, 8/3, 16/3

The sum of the sequence is;

Sum = 1/3+ 2/3+ 4/3+ 8/3+ 16/3

Evaluate

Sum = 31/3

Hence, the sum of the geometric sequence is 31/3

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Answer:

4, 64

Step-by-step explanation:

y = \(4^{1}\) = 4

y = \(4^{3}\) = 64

We have to draw the model for 5 divide 1/7 . In order to draw the model we use below steps.

Draw 1/7 boxes to represent 1/7 groups.

Assume 5 as the number which represents the total of these 1/7 groups.

Put a question mark at the first box.

Attached is the model to represents 5 divide 1/ 7 .

5/(1/7)

5*7

35

In the question mark we should put 35.

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Answer:

y= -1.46 (to 3 s.f.)

Step-by-step explanation:

Please see the attached picture for full solution.

Answer:

Both plans are correct

Step-by-step explanation:

I already did it

The probability that a student is involved in sports and cultural activities is 3/8

From the question, we have the following parameters that can be used in our computation:

P(Sport) = 3/4

P(Cultural) = 1/2

using the above as a guide, we have the following:

P(Both) = P(Sport) * P(Cultural)

Substitute the known values in the above equation, so, we have the following representation

P(Both) = 3/4 * 1/2

Evaluate

P(Both) = 3/8

Hence, the probability is 3/8

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Question

In a school, three-quarters of students are involved in sports, half are involved in cultural activities, and one-eighth are involved in neither.

Calculate the probability that a student is involved in sports and cultural activities

Answer:

the slope intercept-form of an equation of a line is y=mx+b

Given that the slope is 3 and a point on the line is P(-2, 4), then

m=3 and from the point (-2, 4), x=-2 and y=4.

Step-by-step explanation:

y=mx+b.

4=3(-2)+b   Now solve for b.

4=-6+b

4+6=b

10=b

Now you know b=10 and you already know the slope m=3. Substitute these values into y=mx+b. When you do you will get y=3x+10. This is your answer in slope intercept form.

Answer:

1. z=140

2. z=130

3. z=145

4. z=180

5. z=155

6. z=120

Step-by-step explanation:

1. z+40=180 so you should subtract 40 from both sides of the equation to get 180-40=140, meaning that z=140

2. 50+z=180 so you should subtract 50 from both sides of the equation to get 180-50=130, meaning that z=130

3. subtract 35 from both sides of the equation to get 180-35=145, meaning that z=145

4. You can just solve this equation as 90+90=180, meaning that z=180

5. subtract 25 from both sides of the equation to get 180-25=155, meaning that z=155

6. subtract 60 from both sides of the equation to get 180-60=120, meaning that z=120

Answer: 34

Step-by-step explanation:

Answer:

sqrt(29)

Step-by-step explanation:

distance = sqrt√(  (x2 - x1)^ + (y2 - y1)^2  )

x1 = 6

x2 = 8

y1 = -8

y2 = -3

distance = sqrt(  ( 8 - 6)^2 + (-3 - -8)^2  )

distance = sqrt( 2^2 + 5^2)

distance = sqrt(29)

Answer:

29

Step-by-step explanation:

29

Answer:

3/2x

Step-by-step explanation:

13/2x-5/x=3/2x

98% sure it is the answer

Answer:

(13x^2-10)/(2x)    

Step-by-step solution:

STEP 1:

simplify 5/x

(13/2 • x)- 5/x

STEP 2:

simplify 13/2

STEP 3:

find the least common multiple

= 13/2x - 5/x

= 13-2(5)/2x

= 13-10/2x

= 3/2x 

Answer:

false

Step-by-step explanation:

that is  the definition of a perpendicular line  

The  zeroes (x-intercepts)  of the quadratic equations in ascending order are;

1) -9, 9

2) 0, 3/2

3) -1, 4

The x-intercept of a quadratic function is simply the roots or the zeros of the quadratic function.

We will use the quadratic formula which is;

x = [-b ± √(b² - 4ac)]/(2a)

1) y = x² - 81

x-intercept is at y = 0

x² - 81 = 0

Add 81 to both sides to get;

x² = 81

Taking square root of both sides gives;

x = ±√81

x = -9, 9

B) We are given y = 12x² - 18x

x-intercept is at y = 0

Thus;

12x² - 18x + 0 = 0

Using quadratic formula gives us;

[-(-18) ± √((-18)² - 0)]/(2 * 12)

= (18 ± 18)/24

= 0, 3/2

C) y = 2x² - 6x - 8

x-intercept is at y = 0. Thus;

2x² - 6x - 8 = 0

Using quadratic formula gives us;

x = [-(-6) ± √((-6)² - (4*2*-8))]/(2 * 2)

x = (6 ± √100)/4

x = 6/4 ± 10/4

x = -1 or 4

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Time taken to cross the field will be 3.36 seconds.

Velocity is the rate and direction of an object's movement, whereas speed is the time rate at which an object is moving along a path. In other words, velocity is a vector, whereas speed is a scalar value. There are four different types of speed. constant speed, varying speed, an average rate, instantaneous speed.

Solution,

Given,

speed=60 mph

length of football field=0.056 miles

time taken to cross it = distance/speed

time=0.056/60=0.00093 hour = 3.36 seconds.

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Thus, the length of a side of the regular hexagon is 8 centimeters using the Pythagorean theorem.

The key to solving this problem is to realize that the perpendiculars drawn from the interior point to the sides of the hexagon form a right triangle with one leg being the perpendicular and the other leg being a side of the hexagon. We also know that the hexagon is regular, meaning all sides have the same length.

Let's label the length of the side of the hexagon as "x". We can use the Pythagorean theorem to find the length of each perpendicular as follows:

- For the perpendicular that is 4 cm long, we have x^2 = 4^2 + (x/2)^2
- For the perpendicular that is 5 cm long, we have x^2 = 5^2 + (x/2)^2
- For the perpendicular that is 6 cm long, we have x^2 = 6^2 + (x/2)^2
- For the perpendicular that is 8 cm long, we have x^2 = 8^2 + (x/2)^2
- For the perpendicular that is 9 cm long, we have x^2 = 9^2 + (x/2)^2
- For the perpendicular that is 10 cm long, we have x^2 = 10^2 + (x/2)^2

Simplifying each equation and using a bit of algebra, we get:

- 3x^2 = 16^2
- 7x^2 = 25^2
- 12x^2 = 36^2
- 24x^2 = 64^2
- 33x^2 = 81^2
- 40x^2 = 100^2

Solving for x in each equation, we find that x = 8 cm. Therefore, the length of a side of the regular hexagon is 8 centimeters.

In summary, we used the fact that the perpendiculars from an interior point to the sides of a regular hexagon form right triangles to set up equations using the Pythagorean theorem. Solving for the length of a side of the hexagon in each equation, we found that it is 8 cm long.

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