For two invertible n by n matrices A, B,

where rank(A)=rank(B)=n,

is the following always true?

"rank(AB) = n"


If so,

I wonder how we can prove it.


If not,

I'd appreciate you if you show me a counterexample.


Thank you in advance.

Answers

Answer 1

The statement "rank(AB) = n" is not always true for invertible n by n matrices A and B with rank(A) = rank(B) = n.

Counterexample:

Consider the following counterexample:

[tex]A = \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}\\B = \begin{bmatrix} 1 & 0 \ 0 & 0 \end{bmatrix}[/tex]

Both matrices A and B are invertible, as they are both identity matrices. However, when we multiply them together, we get:

[tex]AB = \begin{bmatrix} 1 & 0 \ 0 & 0 \end{bmatrix}[/tex]

The rank of AB is 1, not n. In this case, n = 2, but rank(AB) = 1. Therefore, the statement "rank(AB) = n" is not always true for all invertible n by n matrices A and B with rank(A) = rank(B) = n.

In general, the rank of the product AB is less than or equal to the minimum of the ranks of A and B. So, in order for rank(AB) to be equal to n, both A and B need to have rank n individually, but that does not guarantee the rank of their product to be n as well.

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Related Questions

Joint probability of independent events J and K is equal to


Select one:
a. P(J) * P(K) - P(J * K)
b. P(J)- P(K)
c. P(J) * P(K)
d. P(J) * P(K) + P(J-K)
e. P(J) + P(K)


Note: Answer A is NOT the correct answer. Please find the correct answer. Any answer without justification will be rejected automatically.

Answers

The joint probability is found by multiplying the probability of event J by the probability of event K P(J and K) = P(J) * P(K) Option C.

When two events J and K are independent, it means that the occurrence or non-occurrence of one event does not affect the probability of the other event. In other words, the probability of event J happening is completely unrelated to the probability of event K happening.

The joint probability of two independent events J and K is the probability that both events J and K occur simultaneously. Since the events are independent, the probability of their intersection is equal to the product of their individual probabilities.

The joint probability is found by multiplying the probability of event J by the probability of event K.

This formula holds true for independent events because there is no interaction or dependency between the events. Each event has its own probability, and when they occur together, the joint probability is simply the product of their individual probabilities. Option C is correct.

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1. A student determines that one solution to a system of quadratic-quadratic equations is (2.1).
Determine the value of n if the equations are:
4x² - my=10
mx² + ny=20

Answer: -4

Answers

The value of n is approximately -0.327.

To determine the value of n, we can substitute the given solution (x = 2.1) into the system of equations:

4x² - my = 10 ...(1)

mx² + ny = 20 ...(2)

Substituting x = 2.1 into equation (1), we get:

4(2.1)² - my = 10

8.4 - my = 10

-my = 10 - 8.4

-my = 1.6

Now, substituting x = 2.1 into equation (2), we get:

m(2.1)² + ny = 20

4.41m + ny = 20

Since we already have an expression for -my from equation (1), we can substitute it into equation (2):

4.41m + (-1.6) = 20

4.41m - 1.6 = 20

4.41m = 20 + 1.6

4.41m = 21.6

To solve for m, we divide both sides by 4.41:

m = 21.6 / 4.41

m ≈ 4.9

Now that we have the value of m, we can substitute it back into equation (1) to solve for n:

4(2.1)² - 4.9y = 10

8.4 - 4.9y = 10

-4.9y = 10 - 8.4

-4.9y = 1.6

Finally, to solve for y, we divide both sides by -4.9:

y = 1.6 / -4.9

y ≈ -0.327

Consequently, n has a value of roughly -0.327.

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10 points for this question

Answers

OThe presence of identical fossil plants in both Antarctica and Australia, within the same rock formations, supports the hypothesis of a supercontinent and the process of plate tectonics by providing evidence of past land connections and the subsequent separation of continents due to tectonic activity.

How to explain the information

The presence of identical fossil plant species in rock formations of both Antarctica and Australia suggests that these two regions were once connected geographically. The similarity in the fossil record indicates that the plants existed in a shared ecosystem or environment at some point in the past.

The geological formations in which the fossil plants are found can provide further evidence. If the rock layers containing the fossils can be matched across Antarctica and Australia, it suggests that these regions were once part of the same landmass. This correlation supports the idea of a supercontinent.

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According to the Committee for the Study of the American Electorate, the voter turnout in the 2004 presidential election was higher in all but four states than it was in the 2000 election. The four states with lower voter turnout are listed below.

Answers

According to the Committee for the Study of the American Electorate, the four states with lower voter turnout in the 2004 presidential election compared to the 2000 election were Arkansas, Hawaii, Maryland, and Tennessee.

In the 2004 presidential election, voter turnout increased in most states compared to the 2000 election. However, Arkansas, Hawaii, Maryland, and Tennessee experienced a decrease in voter participation. This means that fewer eligible voters in these states cast their ballots in the 2004 election compared to the previous one.

The reasons behind the lower voter turnout in these states could vary and might be influenced by factors such as changes in voter registration laws, campaign strategies, voter demographics, or the overall political climate in each state during that particular election cycle.

It is worth noting that while voter turnout increased in most states, overall voter participation in the United States has been historically lower compared to some other democracies.

Efforts to increase voter engagement and turnout, such as expanding access to voting and improving voter education, continue to be important in ensuring that more eligible citizens exercise their right to vote and have their voices heard in the democratic process.

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PLS HELP WILL GIVE BRAINLIEST IF CORRECT (NO LINKS)

Identity m∠PKJ.

Answers

Answer:

measure of arc JL = 55°

measure of angle PKJ = 27.5°

In square $ABCD,$ $P$ is on $\overline{BC}$ such that $BP = 4$ and $PC = 1,$ and $Q$ is on $\overline{CD}$ such that $DQ = 4$ and $QC = 1.$ Find $\sin \angle PAQ.$

Answers

To find $\sin \angle PAQ,$ we can first observe that triangle $APQ$ is a right triangle since $AD$ is a diagonal of square $ABCD.$ Therefore, $\angle PAQ$ is a right angle.

We can use the Pythagorean Theorem to find the lengths of $AQ$ and $AP.$ Since $DQ = 4$ and $QC = 1,$ we have $AQ = DQ + QC = 4 + 1 = 5.$ Similarly, since $BP = 4$ and $PC = 1,$ we have $AP = BP + PC = 4 + 1 = 5.$

In a right triangle, the sine of a right angle is always $1.$ Therefore, $\sin \angle PAQ = \boxed{1}.$

Hope you understood and good luck
Final answer:

In triangle PAD, using the Pythagorean theorem, we find AD = 5√2. Given that ∠PAQ's opposite side is PQ, which equals 3, we have sin∠PAQ = PQ/AQ = √2/10.

Explanation:

In square ABCD, we are given that points P and Q are on lines BC and CD respectively such that BP=4 and PC=1, DQ=4 and QC=1. Considering triangle PAD, it is a right triangle in the given square, and, using the Pythagorean theorem, we can find the hypotenuse AD as AD = √(5² + 5²) = 5√2. The same reasoning, AD = AQ.

Because ∠PAQ is the angle we are interested in finding the sine of, we know that sin∠PAQ = opposite/hypotenuse. In this case, the opposite side is PQ which we determine is 3 using the given distances (PC+QC). So, sin∠PAQ = PQ/AQ = 3/(5√2) = √2/10. Thus, the sine of angle PAQ is √2/10.

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Please answer ASAP I will brainlist

Answers

Answer:

(a) The graph is entirely above the x-axis and rises from left to right, more steeply than the graph of y = 5^x.

(b) The second coordinate of the point with first coordinate 0 is 2.

The second coordinate of the point with first coordinate 1 is 10.

In rectangle ABCD, AB = x, BC =x + 2, and AC = x +4. Find the value of x.

Answers

Answer:

x = 6

Step-by-step explanation:

the diagonal AC divides the rectangle into 2 right triangles.

Consider the right triangle ABC with legs AB , BC and hypotenuse AC

using Pythagoras' identity in right triangle ABC

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

AB² + BC² = AC² ( substitute values )

x² + (x + 2)² = (x + 4)² ← expand factors using FOIL

x² + x² + 4x + 4 = x² + 8x + 16

2x² + 4x + 4 = x² + 8x + 16 ( subtract x² + 8x + 16 from both sides )

x² - 4x - 12 = 0 ← in standard form

(x - 6)(x + 2) = 0 ← in factored form

equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 2 = 0 ⇒ x = - 2

however , x > 0 , then x = 6

Scores on the Wechsler Adult Intelligence Scale for the 20 to 34 age group are approximately Normally distributed with mean 110 and standard deviation 15. How high must a person score to be in the top 4% of all scores? (Round your answer to the nearest whole number, if necessary.)

Answers

Answer:

The person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.

Step-by-step explanation:

What is defined as the normal distribution?

A normal distribution is a data set arrangement in which the majority of values cluster inside the center of the range and the remainder taper off symmetrically toward any extreme.

A histogram inside a normal distribution curve is sometimes used to design the curve.

The formula for the normal distribution is;

z = (x - μ)/σ

where,

z = z- score, taken fro table

Mean μ = 110

Standard deviation σ = 15

Sample mean x.

If we want to be in the top 5%, we must outperform 95% of the remaining scores. So we must investigate.

In with us standard normal probability table, look up 0.95 and get the Z score that corresponds to that.

z = 1.7

Put the value in formula ad find x.

1. 7 = (x - 110)/15

x = 25.5 + 110

x = 135.5

x = 136 (whole number)

Thus, the person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.

Landon finds some dimes and quarters under the couch cushions. How many coins does he have if he has 5 dimes and 10 quarters? How many coins does he have if he has d dimes and q quarters?

Answers

Answer:

15 coins, d + q coins

Step-by-step explanation:

If asking for the amount (in $)

5(.10) + 10(.25) = 2.5+.5 = $3

He would have 0.1d + 0.25q for d dimes and q quarters.

The graph of line I is shown below. Which of the following represents the slope of a line parallel to line P

Answers

Answer:

C) -1/3

Step-by-step explanation:

Slope=rise/run

Slope=-1/3

what is critical number

Answers

Answer:

A critical number can have different meanings depending on the context. In mathematics, a critical number is a value of x where the derivative of a function is zero or undefined. It helps to find the maximum and minimum of a function. In business, a critical number is a metric that represents a weakness or vulnerability that needs to be addressed and corrected to improve the performance and security of the company

Step-by-step explanation:

The cost to produce a bag of golf tees is modeled by the function that is graphed below.

Production Costs for Bags of Golf Tees

A graph has number of tees on the x-axis, and cost in dollars on the y-axis. A line goes through (0, 4) and (2, 5).

Which table shows this same function?
A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries negative 8, negative 4, 0, 4.
A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries 0, 4, 0, 4.
A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries 4, 5, 6, 7.
A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries 4, 8, 12, 16.

Answers

The table that shows the same function as the given graph is: A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries 4, 5, 6, 7.

To determine which table shows the same function as the given graph, we need to find the values of y corresponding to the given values of x on the graph.

Point A: (0, 4)

Point B: (2, 5)

Let's check each table:

A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries negative 8, negative 4, 0, 4.

In this table, the corresponding y-values for x = 0 and x = 2 are incorrect. The correct values should be 4 and 5, respectively. Therefore, this table does not represent the same function as the given graph.

A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries 0, 4, 0, 4.

In this table, the corresponding y-values for x = 2 and x = 6 are incorrect. The correct values should be 5 and 7, respectively. Therefore, this table does not represent the same function as the given graph.

A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries 4, 5, 6, 7.

In this table, the corresponding y-values for x = 0 and x = 2 match the given points on the graph. Therefore, this table represents the same function as the given graph.

A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries 4, 8, 12, 16.

In this table, the corresponding y-values for x = 2 and x = 4 do not match the given points on the graph. Therefore, this table does not represent the same function as the given graph.

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which of the following is equivalent to x^2 -5x +6

Answers

Hello!

x² - 5x + 6

= (x² - 2x) + (-3x + 6)

= x(x - 2) - 3(x - 2)

= (x - 2)(x - 3)

when 24/5and another number are added together the answer is 9. what is the number​

Answers

The number we're looking for, which when added to 24/5 results in 9, is 21/5 or 4.2 in decimal form.

Let's solve the equation: 24/5 + x = 9, where x represents the unknown number we're trying to find.

To isolate x, we'll start by subtracting 24/5 from both sides of the equation:

x = 9 - 24/5

To add these two fractions, we need a common denominator. The denominator of 9 is 1, and the denominator of 24/5 is 5. To find a common denominator, we multiply 1 by 5:

x = (9 * 5)/5 - 24/5

This gives us:

x = 45/5 - 24/5

Now we can combine the fractions with the same denominator:

x = (45 - 24)/5

Simplifying the numerator:

x = 21/5

Therefore, the number we're looking for is 21/5. In decimal form, it can be written as 4.2.

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If the base of a square building and an equilateral triangle building have the same perimeter, how do the areas of their floors compare?

Answers

Answer:

let, perimeter of square = 4a

where a = side of square

let, perimeter of the equilateral triangle = 3b

where b= side of triangle

therfore, 4a=3b

a/b = 3/4

area of the square = [tex]a^{2}[/tex]

are of the triangle = [tex]\frac{\sqrt{3} }{4} b^{2}[/tex]

dividing both the areas we get,

[tex]\frac{a^{2} }{\frac{\sqrt{3} }{4}b^{2} }[/tex]

[tex]a^{2}*\frac{4}{\sqrt{3} b^{2}}[/tex]

[tex]\frac{a^{2} }{b^{2} } * \frac{4}{\sqrt{3} }[/tex]

[tex]\frac{3^{2} }{4^{2} } * \frac{4}{\sqrt{3} }[/tex]

[tex]\frac{3\sqrt{3} }{4}[/tex]

hope you understand

Step-by-step explanation:

what comes next in the sequence
7,10,19,34

Answers

Based on the pattern we identified, the next term in the sequence would be 55.

The sequence should be 7, 10, 19, 34, 55

To identify the pattern and determine what comes next in the given sequence (7, 10, 19, 34), we need to examine the relationship between the terms and look for a consistent pattern.

If we calculate the differences between consecutive terms, we get:

10 - 7 = 3

19 - 10 = 9

34 - 19 = 15

By examining the differences, we notice that they are increasing by 6 each time.

This suggests that the sequence might be formed by adding an increasing number to each term.

Let's calculate the next difference:

15 + 6 = 21

Now, let's add this difference to the last term of the sequence:

34 + 21 = 55

Therefore, based on the pattern we identified, the next term in the sequence would be 55.

To summarize:

7, 10, 19, 34, 55

It's important to note that without further context or information, this pattern is just one of the possibilities and may not be the only correct answer.

Additional terms or a different pattern may emerge if more information is provided.

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NO LINKS!! URGENT HELP PLEASE!!

Answers

Answer:

a. 5π cm

b. 144π in²

c. 6 ft

Step-by-step explanation:

a.

The circumference of a circle is given by:

Circumference pf circle= πd

where d is the diameter.

In this case, d = 5 cm,

Therefore, Circumference of circle = π*5=5π cm

b.

The area of a circle is given by:
Area of circle=πr²,

where r is the radius. In this case, the diameter is d = 24 in,

so, the radius is r = d/2 = 24/2=12in

Therefore, Area of circle=π*12²=144π in²

c.

The area of a circle is given by:

Area of circle=πr²,

where r is the radius. In this case, Area is 36π ft²

Now substituting value

36π=πr²

dividing both side by π, we get

36=r²

[tex]r=\sqrt{36}=6[/tex]

r=6 ft.

Therefore, Radius is 6 ft.

Find the surface area of the prism.

A. 78 in2

B. 158 in2

C. 120 in2

D. 119 in2

Answers

Answer:

119in^2

Step-by-step explanation:

formula= 2(width×length+hight×length+hight×5

2×(5×8+3×8+3×5) = 119in^2

Find x intercepts y=(x+3) (6x-2)

Answers

Answer:

x = - 3 , x = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

to find the x- intercepts let y = 0 , that is

(x + 3)(6x - 2) = 0

equate each factor to zero and solve for x

x + 3 = 0 ( subtract 3 from both sides )

x = - 3

6x - 2 = 0 ( add 2 to both sides )

6x = 2 ( divide both sides by 6 )

x = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

the x- intercepts are then x = - 2 and x = [tex]\frac{1}{3}[/tex]

Paxton invests $4850 at 7.6%/a simple interest. If she wants the money to increase to $8000, how long will she need to invest her money?

Answers

Therefore, Paxton will need to invest her money for approximately 21.62 years to increase her investment from $4850 to $8000 at a simple interest rate of 7.6% per year.

To determine how long Paxton needs to invest her money in order for it to increase to $8000, we can use the formula for simple interest:

I = P * r * t

Where:

I = Interest earned

P = Principal (initial investment)

r = Interest rate per year (expressed as a decimal)

t = Time (in years)

Given that Paxton invests $4850 at an interest rate of 7.6% per year, we have:

4850 * 0.076 * t = 8000

Simplifying the equation:

369.8t = 8000

To find t, we divide both sides of the equation by 369.8:

t ≈ 8000 / 369.8 ≈ 21.62 years

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determine the surface area and volume

Answers

The surface area and the volume of the rectangular prism are 280 and 300

How to determine the surface area and volume

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

The rectangular prism

The surface area is caculated as

Surface area = 2 * (10 * 5 + 10 * 6 + 5 * 6)

Evaluate

Surface area = 280

For the volume, we have

Volume = 10 * 5 * 6

Evaluate

Volume = 300

Hence, the surface area and the volume are 280 and 300

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F(x)=square root of 9-kx^2/k show your work

Answers

Sure! Here’s the solution:

F(x)=k9−kx2​​

First, let’s square both sides to get rid of the square root:

F(x)2=k9−kx2​

Now, let’s multiply both sides by k to isolate the term with x^2:

kF(x)2=9−kx2

Next, let’s move all terms to one side of the equation:

kF(x)2+kx2=9

Finally, let’s factor out x^2:

x2(k+kF(x)2)=9

And solve for x^2:

x2=k+kF(x)29​

Answer:

√((9 - kx^2) / k)

Step-by-step explanation:

To show the work for evaluating the function f(x) = √(9 - kx^2) / k, we can follow these steps:

Step 1: Simplify the expression under the square root:

9 - kx^2

Step 2: Divide the expression by k:

(9 - kx^2) / k

Step 3: Take the square root of the expression:

√((9 - kx^2) / k)

Note: It is important to consider any domain restrictions or assumptions about the values of k and x that would make the expression valid. For example, if k is negative, the expression would have an imaginary result.

Han make sparkling juice by mixing 1. 5 liter of juice and 500 milliliter of sparkling water

Answers

Han will have 2 liters (or 2000 milliliters) of sparkling juice after combining 1.5 liters of juice and 500 milliliters of sparkling water.

To make sparkling juice, Han mixes 1.5 liters of juice and 500 milliliters of sparkling water.

To add the quantities together, we need to convert the units to the same measurement. We can convert the liters to milliliters since 1 liter is equal to 1000 milliliters.

1.5 liters is equal to 1.5 x 1000 = 1500 milliliters.

Now we have 1500 milliliters of juice and 500 milliliters of sparkling water.

To find the total quantity of the sparkling juice, we add the volumes of juice and sparkling water together:

1500 milliliters + 500 milliliters = 2000 milliliters

Therefore, Han will have a total of 2000 milliliters (or 2 liters) of sparkling juice by mixing 1.5 liters of juice and 500 milliliters of sparkling water.

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El perímetro de un módulo de vigilancia en forma de pentagono regular es de 35 metro, si un trabajador se le encargo pintar uno de sus muros para lo cual cobrar por metro lineal ¿cuantos metros pintará?

Answers

Answer:El pintor debe pintar un muro de módulo de vigilancia, que es un pentágono regular, por tanto, procedemos a buscar cuántos metros debe pintar: P = 5·L 35 m = 5·L L = 35 m / 5 L = 7 m En consecuencia, al pintar un muro, el trabajador pintará 7 m.

Step-by-step explanation:

Final answer:

El trabajador pintará 7 metros de muro, ya que esa es la longitud de cada lado del pentágono regular cuyo perímetro es de 35 metros.

Explanation:

Un pentágono regular es una figura con cinco lados iguales. Si su perímetro total es de 35 metros, entonces cada lado del pentágono mide 35 metros dividido entre 5, que resulta igual a 7 metros. Entonces, si el trabajador debe pintar uno de los muros del pentágono regular, la cantidad de metros lineales a pintar será igual a la longitud de uno de sus lados. Por lo tanto, el trabajador pintará 7 metros de muro.

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what is e^0? and e^infinity?

Answers

e^0 equals 1. e^infinity is undefined.

In mathematics, e^0 is equal to 1. This is because any number raised to the power of 0 is always equal to 1. The number e, which is approximately equal to 2.71828, follows this rule as well. So, when e is raised to the power of 0, the result is 1.

On the other hand, e^infinity is undefined. As the exponent approaches infinity, the value of e^infinity increases without bound. It does not converge to a specific number or approach any finite value.

In calculus and mathematical analysis, this is expressed by saying that the limit of e^x as x approaches infinity is equal to infinity.

The exponential function e^x is a fundamental mathematical concept with many applications in various fields such as physics, engineering, and finance.

Understanding the behavior of this function at different values of x, including 0 and infinity, is important for solving equations, modeling growth and decay processes, and studying the properties of exponential functions.

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If f(x) = 16x2, what is the value of f(2.5)?

Answers

Answer:

f(2.5) = 100

Step-by-step explanation:

to evaluate f(2.5) substitute x = 2.5 into f(x)

f(2.5) = 16(2.5)² = 16 × 6.25 = 100

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.

x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

Answers

The correct representations of the inequality –3(2x – 5) < 5(2 – x) are options 1 (x < 5) and 3 (–6x + 15 < 10 – 5x).

To determine the correct representations of the inequality –3(2x – 5) < 5(2 – x), let's simplify the expression and analyze the options:

First, we simplify the inequality:

–3(2x – 5) < 5(2 – x)

–6x + 15 < 10 – 5x

Now let's analyze the options:

x < 5: This option represents the solution to the inequality. It indicates that x must be less than 5 for the inequality to hold true.

–6x – 5 < 10 – x: This is not a correct representation of the inequality. The sign of the x-term on the right side of the inequality is incorrect.

–6x + 15 < 10 – 5x: This option represents the solution to the inequality. It correctly represents the simplified inequality we obtained earlier.

A number line from negative 3 to 3 in increments of 1, with an open circle at 5 and a bold line starting at 5 and pointing to the right: This representation does not accurately represent the solution to the inequality. The inequality is not satisfied at x = 5, so the circle should be closed.

A number line from negative 3 to 3 in increments of 1, with an open circle at negative 5 and a bold line starting at negative 5 and pointing to the left: This representation is not correct as it does not represent the solution to the inequality.

Therefore, choices 1 (x 5) and 3 (-6x + 15 10 - 5x) are the proper expressions of the inequality -3(2x - 5) 5(2 - x).

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Gabby is going on holiday and needs to exchange some pounds (£) for euros (€)
. How many euros can she get for £21? Give your answer to 2 decimal places.
£1
Exchange rate
= €1.13

Answers

Gabby can get €23.73 for £21 when using the exchange rate of £1 = €1.13.

To calculate how many euros Gabby can get for £21, we need to use the exchange rate of £1 = €1.13.

To find the number of euros, we multiply the amount in pounds (£21) by the exchange rate (€1.13):

£21 * €1.13 = €23.73

Therefore, Gabby can get €23.73 for £21 when using the exchange rate of £1 = €1.13.

This means that for every pound exchanged, Gabby will receive €1.13. So, by multiplying the amount in pounds (£21) by the exchange rate (£1 = €1.13), we can determine the equivalent amount in euros.

It's important to note that exchange rates can fluctuate, and the rate provided here is just an example. When exchanging currency, it's always advisable to check the current exchange rates as they may vary. Additionally, some currency exchange services may charge fees or have different rates, so it's essential to consider those factors as well.

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A total of 27 students are in your class. There are nine more males than females.

How many females are in your class?

Answers

9 females. 18 males.
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