Find the measure of the indicated angle.
99⁰
96⁰
98⁰
92°
L
120°
K
N
M
64

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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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:

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.

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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Answer:

C) -1/3

Step-by-step explanation:

Slope=rise/run

Slope=-1/3

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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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 missing dimensions from the given expression should be completed with the following:

(81.) A) 2

(82.) AD) x

(83.) E) 12

The expression as a product should be written as: DE) 2(x + 12).

In Mathematics and Geometry, a factored form simply refers to a type of quadratic expression that is typically written as the product of two (2) linear factors and a constant.

In this scenario and exercise, we would complete the table above by showing the factored form and expanded form of each of the given expressions as follows;

       x           12

2      2x         24

Note: 2x/2 = x.

        24/2 = 12.

Next, we would write the expression 2x + 24 as a product as follows;

(2x + 24) = 2(x + 12).

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Solution

verified

Verified by Toppr

The circumference of circle is 2πr=176

2×

7

22

×r=176

r=176×

22

7

2

1

r=7×4=28cm

Area of circle is πr

2

=

7

22

×28×28=88×28=2464cm

2

The statement is:

O True

Work/explanation:

The following statement is true, because 1x is indeed the same thing as x. So when combining like terms, 2x + x is the same thing as 2x + 1x, which evaluates to 3x.

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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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

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.

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.

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Answer:

Using the sine function, we have:

sin(angle) = opposite / hypotenuse

sin(22 degrees) = opposite / 18 feet

We can rearrange this equation to solve for the opposite side (height of the building):

opposite = sin(22 degrees) * 18 feet

Calculating this:

opposite ≈ 6.24 feet

Therefore, the base of the ladder from the base of the building is approximately 6.24 feet.

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.

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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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.

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

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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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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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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Hello!

x² - 5x + 6

= (x² - 2x) + (-3x + 6)

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

= (x - 2)(x - 3)

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:

Step-by-step explanation:

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

9 - kx^2

(9 - kx^2) / k

√((9 - kx^2) / k)

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]

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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The x-intercepts, y-intercept, vertex, and axis of symmetry for the given function g(x) = x² + 4x + 3 have been plotted on the graph below.

In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the given quadratic function, we can logically deduce that the graph would be a upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).

Since the leading coefficient (value of a) in the given quadratic function g(x) = x² + 4x + 3 is positive 1, we can logically deduce that the parabola would open upward and the x-intercept (roots) is given by the ordered pair (-3, 0) and (-1, 0).

In conclusion, the vertex is given by the ordered pair (-2, -1) and the minimum value is -1.

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Answer:

x-intercepts = (-3, 0) and (-1, 0)

y-intercept = (0, 3)

Vertex = (-2, -1)

Axis of symmetry:  x = -2

Step-by-step explanation:

Given quadratic function:

[tex]g(x) = x^2 + 4x + 3[/tex]

[tex]\hrulefill[/tex]

To find the x-intercepts of the given function g(x), set g(x) equal to zero and solve for x.

Set g(x) = 0:

[tex]x^2 + 4x + 3 = 0[/tex]

Factor the quadratic equation:

[tex]x^2+x+3x+3=0[/tex]

[tex]x(x+1)+3(x+1)=0[/tex]

[tex](x + 3)(x + 1) = 0[/tex]

Set each factor equal to zero and solve for x:

[tex]x + 3 = 0 \implies x = -3[/tex]

[tex]x + 1 = 0 \implies x = -1[/tex]

Therefore, the x-intercepts are at (-3, 0) and (-1, 0).

[tex]\hrulefill[/tex]

To find the y-intercept of g(x), substitute x = 0 and solve for y.

[tex]\begin{aligned}x=0 \implies y&= (0)^2 + 4(0) + 3\\y& = 0 + 0 + 3 \\y&= 3\end{aligned}[/tex]

Therefore, the y-intercept is at (0, 3).

[tex]\hrulefill[/tex]

The x-value of the vertex of a parabola in the form y = ax² + bx + c is x = -b/2a.

For the function g(x), a = 1, and b = 4.

Therefore, the x-coordinate of the vertex is:

[tex]\textsf{$x$-coordinate of vertex} = \dfrac{-b}{2a} = \dfrac{-4}{2(1)} = -2[/tex]

To find the y-coordinate of the vertex, substitute x = -2 into function g(x):

[tex]\begin{aligned}x=-2 \implies y &= (-2)^2 + 4(-2) + 3\\y& = 4-8 + 3 \\y&= -1\end{aligned}[/tex]

Therefore, the vertex is at (-2, -1).

[tex]\hrulefill[/tex]

The axis of symmetry of a vertical parabola is the x-coordinate of its vertex.

As the x-coordinate of the vertex is -2, the axis of symmetry is x = -2.

[tex]\hrulefill[/tex]

The best estimate for the amount of juice Barry made is 235 cups.

In this question, Jessica and Barry squeezed oranges for juice. Jessica squeezed 235 cups of juice. Barry made 14 cups less than Jessica. Barry estimated that Jessica squeezed about 212 cups of juice. We need to find the best estimate for the amount of juice Barry made.

Let's begin by finding the amount of juice Barry actually made. Barry made 14 cups less than Jessica, which means he made: 235 - 14 = 221 cups of juice.

Now, let's compare this to Barry's estimate. Barry estimated that Jessica squeezed about 212 cups of juice. Since Jessica actually squeezed 235 cups of juice, her estimate was too low by:235 - 212 = 23 cups.

So, we can apply this error to Barry's estimate to get a better estimate for the amount of juice he made. If Barry's estimate was 212 cups, and he underestimated by 23 cups, then he actually made:212 + 23 = 235 cups of juice. Therefore, the best estimate for the amount of juice Barry made is 235 cups.

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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.

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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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.

Answer:

measure of arc JL = 55°

measure of angle PKJ = 27.5°

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: