how to solve for x (proportions)

A linear transformation t defined by a square matrix a is an isomorphism if and only if a is nonsingular.

To prove this statement, we first recall that an isomorphism is a linear transformation that is both injective (one-to-one) and surjective (onto). If t is an isomorphism, then it is invertible, which means that there exists another linear transformation t^-1 such that t(t^-1(x)) = x and t^-1(t(x)) = x for all vectors x in the domain of t. In matrix notation, this means that aa^-1 = a^-1a = I, where I is the identity matrix.

Now suppose that a is nonsingular, which means that its determinant det(a) is nonzero. This implies that a^-1 exists and is also a square matrix. If we can show that t is injective and surjective, then we can conclude that t is an isomorphism. To prove injectivity, suppose that t(x) = t(y) for some vectors x and y. Then ax = ay, which implies that a(x - y) = 0. Since det(a) is nonzero, it follows that x - y = 0, which means that x = y. Thus, t is injective. To prove surjectivity, let z be an arbitrary vector in the range of t. Then there exists a vector y such that t(y) = z.

This implies that ay = z, which means that y = a^-1z. Thus, every vector in the range of t can be written as t(a^-1z), which shows that t is surjective. Therefore, we can conclude that t is an isomorphism if a is nonsingular. Conversely, if t is an isomorphism, then it must be invertible, which implies that a must be nonsingular, as we showed earlier. Thus, t is an isomorphism if and only if a is nonsingular.

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Answer:

42.1 for me

Step-by-step explanation:

goodluck ..

Answer:

i think its 49.6

Answer:

26 cm

Step-by-step explanation:

Answer:

26 cm!

If A extends to O which is half of the rectangle, and we need BD... We times AO by two to get BD. :)

Are you trying to write this from word form and convert it into an equation? If you could provide more details, I would be more than happy to help. Thanks!

Answer:

84 inches

Step-by-step explanation:

12 inches are in 1 foot, so you take the number of feet (28) and multiply by the number of inches in a foot (12)

28×12=336 (inches)

then you take 336 and divide by 4 to get your 4 equal pieces.

336 divided by 4 = 84, 84 inches

Answer:

The total bill = $20.85

Annie = $7.95

Suz = $4.17

Cynthia = $8.80

Step-by-step explanation:

Let the total bill = $x

For Annie

Annie, you had 3 slices and a medium soda so you should pay one-third of the bill. I'll chip in a dollar more than that, replied Annie.

Annie = 1/3 of x + $1

= 0.33x + $1

For Suz

And since you had only 2 slices and also ordered a small soda, you should pay 20% of the bill.

20% of x = 1/5x

= 0.2x

Cynthia said I ate 3 slices and had a large soda so I'll pay the remaining $8.80.

0.33x + $1 + 0.2 x + $8.80 = $x

Collect like terms

$1 + $8.80 = x - 0.33x - 0.2x

$9.80 = x - 0.53x

$9.80 = 0.47x

x = $9.80/0.47

x = $20.85106383

≈ $20.85

Therefore,

For Annie,

The total amount she is paying is

0.33x + $1

= 0.33 × $20.85 + $1

= $6.95 + $1

= $7.96

For Suz

= 0.2x

= 0.2 × $20.85

= $4.17

For Cynthia

= $8.80

Answer:

17. 86 miles

Step-by-step explanation:

Answer: To find the percentage of people with an IQ score less than 117, we need to calculate the z-score first. The z-score measures how many standard deviations an individual score is from the mean in a normal distribution.

The z-score formula is given by:

z = (x - μ) / σ

Where:

Let's calculate the z-score:

Now, we need to find the percentage of people with a z-score less than 1.1333. We can look up this value in the standard normal distribution table (also known as the Z-table) or use statistical software/tools.

Using the Z-table, we find that the percentage of people with a z-score less than 1.1333 is approximately 0.8708, or 87.08% (rounded to the nearest hundredth).

Therefore, approximately 87.1% of people have an IQ score less than 117.

The probability that it will rain both days is \(\frac{1}{4}\).

According to the question

Mr. and mrs. smith plan to roof the cabin on 2 consecutive days.

Assuming that the chance of rain is independent of the day

Probability is the chance that some event will happen.

It is the ratio of the number of ways a certain event can occur to the number of possible outcomes.

Probability = Number of ways it can occur/Total number of outcomes

Probability of rain on first day = 1/2

Probability of rain on second day = 1/2

Then

Probability of rain on both days = \(\frac{1}{2}\) × \(\frac{1}{2}\) = 1/4

Hence,

The probability that it will rain both days is \(\frac{1}{4}\).

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Answer:

We need to see the graph in order to solve this.

Step-by-step explanation:

No graph

Answer:

PQ = 31

QR = 31

PR = 47

Step-by-step explanation:

From the question, we have the vertex as Q

This means that we have the legs as PQ and QR; with PR as the base

The base angles of an isosceles triangle are equal and that means that the leg length values are equal

So, QR = PQ

Thus;

3x-2 = 5x-24

5x-3x = 24-2

2x = 22

x = 22/2

x = 11

So we have PQ as;

5(11) - 24 = 55-24 = 31

QR = 3(11) -2 = 33-2 = 31

PR = 5x-8 = 5(11)-8 = 55-8 = 47

Answer:

The saturday median is equal to the sunday median.

Step-by-step explanation:

Arrange your numbers in numerical order.

Count how many numbers you have.

If you have an odd number, divide by 2 and round up to get the position of the median number.

If you have an even number, divide by 2. Go to the number in that position and average it with the number in the next higher position to get the median.

The equation can be solved using the quadratic formula when the following expression is used: \($x=\frac{-(-4)+-\sqrt{(-4)^2-4(1)(3)}}{2(1)}$\)

The quadratic formula in elementary algebra is a formula that gives the solution(s) to a quadratic equation. In addition to the quadratic formula, there are various methods for solving quadratic equations, including factoring (direct factoring, grouping, and the AC technique), completing the square, graphing, and others.

The following general quadratic equation is given:

ax² + bx + c = 0

As a result, a polynomial equation with exponent two is referred to as a quadratic ("square-like") equation. Quadratum is the Latin word for square, and since the area of a square with side length x is given by x2, this is the case.

A quadratic equation's solution(s) can be found using the quadratic formula in elementary algebra. Graphing, factoring (direct factoring, grouping, AC technique), completing the square, and other methods can be used to solve a quadratic equation in addition to the quadratic formula.

The given equation is x² - 4x + 3 = 0

When compared to the quadratic equation's general equation, we get a = 1, b = -4, c = 3.

When the coefficient values for the Sridhar Acharya formula are put in,\($x=\frac{-(-4)+-\sqrt{(-4)^2-4(1)(3)}}{2(1)}$\) which gives Option (A).

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Answer:6

Step-by-step explanation:

8-6 = 2

Answer:

10

Step-by-step explanation:

Let the number be equal to y

Answer:

Therefore, the value of x is 5.

Step-by-step explanation:

We can match each equation to find the solutions.

\(8x-40=x^{2}-2x-15\)

\(0=x^{2}-2x-8x-15+40\)

\(x^{2}-10x+25=0\)

Now, we need solve this quadratic equation.

\((x-5)^{2}=0\)

Therefore, the value of x is 5.

I hope it helps you!

Answer:

\(10^{19}\)

\(10^{-6} * 10^{25} = 10^{19}\)

Step-by-step explanation:

10^46/ 10^-4 = \(10^{50}\)

\(\sqrt{10^{50} } = 10^{25}\)

Solution;

y=5x

Explanation;

The numerator and the denominator of the fraction in the simplest form will be 7 / 10.

A fraction is a portion of a whole number and a method of dividing a number into equal pieces. It is stated as the number of equal parts counted (the numerator) divided by the total number of parts (the denominator). A line separates these numerals.

A fraction simply means a number that is part of a whole number. It is illustrated as a/b where a = numerator and b = denominator. A numerator is the part of a fraction that is above the line and represents the number to be divided by another number that is below the line.

In this case, 0.7 will be written as 7/10. Here, it should be noted that 7 is the numerator and 10 is the denominator.

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Answer: -46 15/100

Explanation: (see pic attached)

Answer:

46 3/20

Step-by-step explanation:

Rewrite the decimal number as a fraction with 1 in the denominator

46.15=46.15/1

Multiply to remove 2 decimal places. Here, you multiply top and bottom by 10^2 = 100

46.15/1 x 100/100= 4615/100

Find the Greatest Common Factor (GCF) of 4615 and 100, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 5

4615/100 divided by 5/5= 923/20

Simplify the improper fraction

46 3/20

In conclusion

46.15= 46 3/20

I hope that helped ;)

Z = xy

To solve for y, divide both sides by x.

Y = z/x

Answer:

\(\underline{z = xy} \\ \boxed{ y = \frac{z}{x} }\)

This is how you construct a parent graph - it is the simplest form of the function, and has a basic shape.

The most basic form of a function is a parent function. Its essential shape is not changed in any manner. In mathematics, some graphs are frequently seen. Because of this, the graphs of quadratic functions, square roots, absolute values, cubics, and cube roots are among the original, widespread functions that are referred to as parent graphs.

For instance, you should still be able to identify the parabola that has undergone various transformations when you view a u-shaped graph that has been inverted and stretched vertically.

We can take a few examples to understand this concept further.

Hence, this is how you construct a parent graph - it is the simplest form of the function, and has a basic shape.

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The given statement " When the film is placed into the XCP (extension cone paralleling) holder with the smooth side of the film towards the throat, after processing, it will appear darker" is false because it will  lighter, not darker.

The smooth side of the film is the side that interacts with the X-ray radiation and receives the image, while the emulsion side contains the light-sensitive crystals that react to the radiation.

Placing the smooth side towards the throat ensures that the image is sharp and clear, as the X-ray beam travels through the teeth and soft tissues before reaching the film.

After processing, the exposed areas of the film turn dark, representing the captured X-ray image, while the unexposed areas remain light or clear.

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Answer:

208

Step-by-step explanation:

There are 5 weekdays in a week and 2 weekend days. Since there are 4 weeks, multiply 5 times 4 to get 20 weekdays/month, and 2 times 4 to get 8 weekend days/month. 20 times 8 (the hours she sleeps) is 160 hours, and 8 times 6 is 48 hours. Put together, you get 208 total hours.