Let A be a matrix of size n × n such that
A – 2A^2 -A^4 + 3In = 0
Show that A is invertible and find its inverse.

The graph of the quadratic function y = 1.5x² + 4x - 2 is given by the image shown at the end of the answer.

The function for this given problem is defined as follows:

y = 1.5x² + 4x - 2.

a 1.5, b 4, c -2.

By Solving the equation we get these values,

x = -3.09, hence function passes through the point (-3.09, 0).

x = 0.43, hence function passes through the point (0.43, 0).

The y-intercept of this function is given by coefficient c = -2, hence the function also passes through the point (0, -2).

The x-coordinate vertex is given as follows:

x = -b/2a = -4/3 = -1.33.

Hence the y-coordinate vertex is of:

y = 1.5(-1.33)² + 4(-1.33) - 2 = -4.67.

Missing Information

The problem asks for the graph of the following function is given below:

y = 1.5x² + 4x - 2.

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Answer:

2. (x^2 + 3y)(x^2 - 3y)

Step-by-step explanation:

According to algebraic formula:

x^2 - y^2 = (x + y)(x - y)

We have x^4 - 9y^2 => (x^2)^2 - (3y)^2

=> (x^2 + 3y)(x^2 - 3y) or  (x^2 - 3y)(x^2 + 3y)

Answer:

(2) (x²-3y)(x²+3y)

Step-by-step explanation:

x⁴-9y²

Factor/GCF:

x⁴ = (x²)(x²)

-9y² = (-3y)(3y)

Combine:

(x²-3y)(x²+3y)

Answer: See attached.

Step-by-step explanation:

     The first one is incorrect because this equation shows 5 / 2, not 2/5.

     The second one is correct. 7/4 = 7/4.

     The third one is also correct. 12/4 = 12/4.

     It can help to rewrite both sides of the equation in the same format to make it easier to compare.

a) The three measures of central tendency are the 18 (mean), 14.5 (median, and 10 and 21 (mode).

(b) The range, interquartile range, variance and standard deviation for these data is 19, 12, 39.636, and 6.296, respectively.

(a) The three measures of central tendency are the mean, median, and mode.

Mean: (15 + 10 + 7 + 24 + 22 + 12 + 17 + 10 + 21 + 23 + 26 + 21)/12 = 18

Median: (12 + 17)/2 = 14.5

Mode: 10 and 21 (both appear twice in the data set)

b) Range: 26 - 7 = 19

Interquartile Range: Q3 - Q1 = 22 - 10 = 12

Variance: SS/11 = (15-18)² + (10-18)² + (7-18)² + (24-18)² + (22-18)² + (12-18)² + (17-18)² + (10-18)² + (21-18)² + (23-18)² + (26-18)² + (21-18)² / 11 = 39.636

Standard Deviation: √39.636 = 6.296

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Step-by-step explanation:

the error happened in line 2 :

(2x - 3)(6x + 2)

= 2x6x + 2×2x - 3×6x - 3×2 (instead of +3×2)

the error was using the wrong sign for the term 3×2. it was created by -3 multiplied by +2 = -3×2.

There will be 663 pupils if there are 17 instructors.

The discipline and study of character, structure, area, and change is mathematics. Mathematicians use rigorous deduction from carefully selected axioms and definitions to look for patterns, make new hypotheses, and establish the veracity of their findings.

Teachers Students

5                   130

10                   390

15                   585

20                   780

To find the unit rate, we need to divide the number of students by the number of teachers. For example, for the first row, the unit rate would be:

Unit rate = students/teachers = 130/5 = 26 students per teacher

We can repeat this calculation for each row:

For the second row, the unit rate is 390/10 = 39 students per teacher.

For the third row, the unit rate is 585/15 = 39 students per teacher (same as the previous row).

For the fourth row, the unit rate is 780/20 = 39 students per teacher (again, the same as the previous rows).

So, the unit rate is 39 students per teacher.

If there are 17 teachers, we can use the unit rate to find the number of students:

Number of students = unit rate x number of teachers

Number of students = 39 x 17 = 663

Therefore, if there are 17 teachers, there are 663 students.

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Answer:

mAngle EFG = 139°

mAngle IFH = 49°

Step-by-step explanation:

First, just look at the top half of the diagram. Straight across D, F, G is a straight line. That's 180° We can write an equation with the two marked angles added up, equal to 180° to solve for x and to solve for those two angles. See image.

Then look for two crossing lines that makes a giant x (not a variable, on the image) That's EH and DG. The angles that are across from each other are called Vertical angles and they are equal to each other. See image.

Last, see the bottom part of the image where an angle is marked with a little tiny square. That means its a right angle and is 90°. We can subtract to find the second angle that we're being asked to find. See image.

Answer: C. 1/2

Step-by-step explanation:

The coefficient is the number being multiplied by q. The sum is the additive total. To add fractions, they need a common denominator.

2/3 = 4/6

Adding a negative is the same as subtracting.

4/6 + (-1/6) = 4/6 - 1/6 = 3/6 = 1/2

Hope this helps!

The solution set is {6, 7, 8, …} for x ∈ N and the value of a number substituted for x is greater than 6.

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

Here, we have

Given: Inequality:

12+11/6x ≤  5+3x

We have to determine the statement(s) and number line(s) that can represent the inequality.

12+11/6x ≤  5+3x

12(6x) + 11 ≤  6x(5+3x)

72x +132 ≤ 30x + 18x²

42x + 132 ≤ 18x²

7x + 22x ≤  3x²

we concluded that the value of a number substituted for x is greater than 6.; b. The solution set is {6, 7, 8, …} for x ∈ N." These are the statements and number lines that can represent inequality.

Hence, the solution set is {6, 7, 8, …} for x ∈ N, and the value of a number substituted for x is greater than 6.

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Minimum - 2

First Quartile - 4

Median - 8

Third Quartile - 13

Maximum - 15

Answer: Let's use the trigonometric ratio of sine to find the measure of the larger acute angle of the right triangle. We have:

sin(theta) = opposite / hypotenuse

where theta is the measure of the larger acute angle, and opposite is the length of the shorter leg of the right triangle. Substituting the given values, we get:

sin(theta) = 2sqrt(6) / 2sqrt(15)

          = sqrt(2/5)

Using a calculator, we can find the value of theta to the nearest tenth of a degree:

theta = arcsin(sqrt(2/5))

     ≈ 38.2°

Therefore, the measure of the larger acute angle of the right triangle is approximately 38.2 degrees.

Step-by-step explanation:

Answer:

48 cups

Step-by-step explanation:

‐-------------------

The quotient of -2 1/2 and -3 1/3 is = 9/16

In the end, the quotient is what we obtain when we divide a number. Putting things into equal groups is a division operation in mathematics. It is symbolised by the glyph (). For instance, there are three groups of 15 balls each that must be distributed equally.

When we divide the balls into three equal groups, the division formula is 15/3 = 5. The quotient is 5 in this case. This indicates that each set of balls will include five balls.

In this case let us first convert the improper fractions into proper fractions:

-2 1/2 = -4+1/2 = -3/2

-3 1/3 = -9+1/3 = -8/3

Now to find the quotient we have to multiply the fraction's reciprocals:

-3/2 × 3/-8

= -9/-16

=9/16

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Answer:

2 tangents

with common points p and O touching both the circles only 2 tangets can be drawn

a. The equation "(a) x2+3​=x+4" gives the solution as x = 1.

b. The equation "(b) 2x-1​-x-4=2" gives the solution as x = -1.

To solve these radical equations, we will need to isolate the radical on one side of the equation and then square both sides to get rid of the radical. After that, we can solve for x using standard algebraic methods.

(a) x2+3​=x+4

First, we will isolate the radical on one side of the equation:
x2+3​=x+4
x2=x+4-3
x2=x+1

Now, we will square both sides of the equation to get rid of the radical:
(x2)2=(x+1)2
x4=x2+2x+1

Next, we will rearrange the equation and set it equal to zero:
x4-x2-2x-1=0

Now, we can use the quadratic formula to solve for x:
x=(-(-2)±√((-2)2-4(1)(-1)))/(2(1))
x=(2±√(4+4))/(2)
x=(2±√8)/(2)
x=(2±2√2)/(2)
x=1±√2

So, the solutions for x are 1+√2 and 1-√2.

(b) 2x−1​−x−4​=2

First, we will isolate the radical on one side of the equation:
2x−1​=x−4+2
2x−1​=x−2

Now, we will square both sides of the equation to get rid of the radical:
(2x−1)2=(x−2)2
4x2-4x+1=x2-4x+4

Next, we will rearrange the equation and set it equal to zero:
3x2=3

Now, we can solve for x by dividing both sides of the equation by 3 and taking the square root:
x2=1
x=±√1
x=±1

So, the solutions for x are 1 and -1.

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The sum of the digits of the number which when added to 2000 makes the resulting number divisible by 12,16,18 and 21 is 7

The smallest number which when added to 2000 makes the resulting number divisible by 12, 16, 18, and 21 is 312. The sum of the digits of x is 3 + 1 + 2 = 6.

To find the smallest number x that can be added to 2000 to make the resulting number divisible by 12, 16, 18, and 21, we need to find the least common multiple (LCM) of these numbers.

The LCM of 12, 16, 18, and 21 is 1008. Then we need to find the smallest multiple of 1008 that is greater than 2000. This is 1008 * 3 = 3024. The difference between 3024 and 2000 is 1024, so x = 1024.The sum of the digits of x is 1 + 0 + 2 + 4 = 7. Therefore, the sum of the digits of x is 7.

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Answer:

Let q be the number of quarters in the jar and d be the number of dimes in the jar.

The total number of coins in the jar is given as 54, so we can write:

q + d = 54

The total value of the coins is $16.85. We can express this as the sum of the values of the quarters and the dimes in the jar:

0.25q + 0.10d = 16.85

Therefore, the system of equations that can be used to determine the number of quarters and dimes in the jar is:

q + d = 54

0.25q + 0.10d = 16.85

It will take the second skater 20 seconds to catch up to the first skater and pass him/her.

In physics, speed and motion are related concepts that describe the movement of objects in space.

Speed is a scalar quantity that measures how fast an object is moving. It is the rate at which an object covers distance, typically measured in meters per second (m/s), kilometers per hour (km/h), or some other unit of distance per unit of time.

Motion, on the other hand, is the change in position of an object over time, with respect to a reference point. In physics, motion can be described in terms of displacement, velocity, and acceleration. Displacement refers to the change in position of an object relative to a reference point, while velocity describes how fast an object is moving in a specific direction.

Acceleration refers to the rate at which an object's velocity changes over time, either by increasing or decreasing in speed or changing direction.

In summary, speed is a measure of how fast an object is moving, while motion is the change in position of an object over time.

We can start by setting up an equation to represent the distance each skater travels, with t representing the time it takes for the second skater to catch up to the first skater:

Distance traveled by the first skater = Distance traveled by the second skater + 40 meters

Using the formula distance = rate × time, we can plug in the given rates and the unknown time to get:

12t + 40 = 14t

Simplifying this equation, we get:

40 = 2t

t = 20 seconds

Therefore, it will take the second skater 20 seconds to catch up to the first skater and pass him/her.

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The trigonometric ratios of sine and cosines indicates that we get;

Trigonometric ratios specify the relationship between two sides of a right triangle and the acute angle in the right triangle.

The specified equations are presented as follows;

1. sin(55) = cos(θ)

The sine of an angle is the ratio of the opposite side to the angle in a right to the hypotenuse side of the right triangle

The trigonometric ratio of the cosine of an angle is the ratio of the adjacent side to the angle to the hypotenuse side in a right triangle

The acute angles in a right triangle are complementary

Let A and B represent the acute angles of a right triangle, we get;

The adjacent side to the angle A is the opposite side to the angle B

The hypotenuse side remains the same, therefore;

cos(A) = sin(B), and sin(A) = cos(A)

Which indicates; sin(55) = cos(90 - 55) = cos(35)

sin(55) = cos(θ) = cos(35)

2. cos (28) = sin(90 - 28) = sin(62)

cos(28) = sin(62)

sin(θ) = sin(62) = cos(28)

3. cos(y) = sin(θ)

cos(y) = sin(90 - y)

cos(y) = sin(90 - y) = sin(θ)

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Answer:

13

Step-by-step explanation:

First drop the line.

How many units is it from Point [tex]r[/tex] to the x axis?

12.

How many units is it from Point [tex]r[/tex] to the y axis?

5.

Now we can use the Pythagorean Theorem.

[tex]12^5+5^2=c^2[/tex]

[tex]144+25=c^2[/tex]

[tex]c^2=169[/tex]

[tex]c=13[/tex]

The second smallest number that has 1, 2, 3, 4, and 5 as factors is 360.

What is factorization?

A number or other mathematical object is factorization or factored when it is written as the product of numerous factors, often smaller or simpler things of the same sort.

To find the smallest number that has 1, 2, 3, 4, and 5 as factors, we can simply multiply these numbers together, since they are all factors of their product:

1 × 2 × 3 × 4 × 5 = 120

Now we need to find the second smallest number with these factors. One way to approach this is to list out the multiples of 120 until we find a number that also has the factors 1, 2, 3, 4, and 5, and is larger than 120.

Multiplying 120 by 2, 3, 4, 5, and 6 gives us the multiples:

240, 360, 480, 600, 720

Checking each of these multiples, we see that only 360 has all the factors 1, 2, 3, 4, and 5. Therefore, the second smallest number that has 1, 2, 3, 4, and 5 as factors is 360.

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The response to the given question would be that As a result, when equation comparing their depths, Quesnel Lake is substantially shallower than Lake Baikal yet deeper than Great Slave Lake.

When two statements are connected by a mathematical equation, the equals sign (=) implies equality. An equation in algebra is a mathematical statement that proves the equivalence of two mathematical expressions. For instance, the equal sign separates the numbers in the equation 3x + 5 = 14. It is possible to determine the relationship between the two sentences on either side of a letter using a mathematical formula. The logo for the particular piece of software is frequently the same. as 2x - 4 = 2, for instance.  

From Quesnel Lake to Lake Baikal, the distance is 506 metres.

Lake Baikal is 5369 ft (or 1637.74 m) deep (one foot is equal to 0.3048 m).

Ratio of depths is 506 / 1637.74 0.31 (Depth of Quesnel Lake/Deep of Lake Baikal).

Around 31% of Lake Baikal's depth is in Quesnel Lake.

Great Slave Lake to Quesnel Lake: Quesnel Lake is 506 metres deep.

Great Slave Lake's depth is 2015 feet, or 614.18 metres (1 foot = 0.3048 m).

Ratio of depths is 506 / 614.18 0.82 (Depth of Quesnel Lake / Depth of Great Slave Lake).

Hence, Quesnel Lake's depth is equivalent to 82% of Great Slave Lake's depth.

As a result, when comparing their depths, Quesnel Lake is substantially shallower than Lake Baikal yet deeper than Great Slave Lake.

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The polynomial in factored form as a product can be found by using the factor theorem and synthetic division. The factor theorem states that if f(a) = 0, then (x-a) is a factor of f(x). We can use synthetic division to find the factors of f(x)=12x^(5)+5x^(4)-39x^(3)+9x^(2)+19x-6.

First, we need to find a value of x that makes f(x) = 0. We can use the rational root theorem to find possible rational roots. The possible rational roots are ±1, ±2, ±3, ±6. We can use synthetic division to test these possible roots.

Using synthetic division with x = 1, we get a remainder of -1, so x = 1 is not a root. Using synthetic division with x = -1, we get a remainder of 0, so x = -1 is a root and (x+1) is a factor of f(x).

Now we can divide f(x) by (x+1) using synthetic division to get the quotient 12x^(4)-7x^(3)-32x^(2)+41x-6. We can repeat the process of finding possible rational roots and using synthetic division to find the factors of this quotient.

The possible rational roots of the quotient are ±1, ±2, ±3, ±6. Using synthetic division with x = 1, we get a remainder of 8, so x = 1 is not a root. Using synthetic division with x = -1, we get a remainder of 0, so x = -1 is a root and (x+1) is a factor of the quotient.

We can divide the quotient by (x+1) using synthetic division to get the new quotient 12x^(3)-19x^(2)-13x+6. We can repeat the process of finding possible rational roots and using synthetic division to find the factors of this new quotient.

The possible rational roots of the new quotient are ±1, ±2, ±3, ±6. Using synthetic division with x = 1, we get a remainder of -14, so x = 1 is not a root. Using synthetic division with x = -1, we get a remainder of 0, so x = -1 is a root and (x+1) is a factor of the new quotient.

We can divide the new quotient by (x+1) using synthetic division to get the new quotient 12x^(2)-31x+6. We can repeat the process of finding possible rational roots and using synthetic division to find the factors of this new quotient.

The possible rational roots of the new quotient are ±1, ±2, ±3, ±6. Using synthetic division with x = 1, we get a remainder of -13, so x = 1 is not a root. Using synthetic division with x = -1, we get a remainder of 49, so x = -1 is not a root. Using synthetic division with x = 2, we get a remainder of 0, so x = 2 is a root and (x-2) is a factor of the new quotient.

We can divide the new quotient by (x-2) using synthetic division to get the new quotient 12x-3. This quotient cannot be factored further, so the factors of f(x) are (x+1)(x+1)(x+1)(x-2)(12x-3).

Therefore, the polynomial in factored form as a product is f(x) = (x+1)(x+1)(x+1)(x-2)(12x-3).

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The values of k that make the system inconsistent are k = 0 and k = 2.

The system obtained from the given augmented matrix is:
```
1 2 -1 | 4
0 -1 1 | 3
0 0 k^2-2k | -3k-3
```
For the system to be inconsistent, the last equation must be a contradiction, meaning that the coefficients of the variables are all zero but the constant term is nonzero. In other words, we need `k^2-2k = 0` and `-3k-3 ≠ 0`.

Solving for k in the first equation, we get:
```
k^2-2k = 0
k(k-2) = 0
```
So k = 0 or k = 2.

However, we also need `-3k-3 ≠ 0`, which means that k ≠ -1. Therefore, the values of k that make the system inconsistent are k = 0 and k = 2.

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The round-off of the number 216,777777 to 2 decimal places​ is 216.78.

When a number is rounded off, its value is preserved while it is moved closer to the next number. simplifying the number. It is done for whole numbers as well as decimals at different places of hundreds, tens, tenths, and so on.

A number can be rounded off to its lower value if the number after the decimal is between 0 and 4. If the number after it is between 5 and 9, it will be rounded up to its higher value.

To round 216,777777 to 2 decimal places, we look at the third decimal place, which is 7. Since 7 is greater than or equal to 5, we round up the second decimal place, which is 7. Therefore, 216,777777 rounded to 2 decimal places is 216,78.

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Answer:  39

Step-by-step explanation:   9 = ? - 30, add 30 on both sides you get 39=?