Alina flipped a nickel 10 times. It landed on heads 7 times and tails 3 times. If she flips the coin again, what is the probability of getting tails?

So the answer is: it took 35.56 minutes to get home on day one.

To find out how long it took to get home on day one, we need to work backwards from day five. Here's how:

On day five, it took 15 minutes to get home. This was 50% faster than on day four, which means that on day four it took 15 minutes / 0.5 = 30 minutes.

On day four, it took 30 minutes, and this was 2 minutes less than on day three. So on day three it took 30 minutes + 2 minutes = 32 minutes.

On day three, it took 32 minutes, and this was 20% longer than on day two. So on day two it took 32 minutes / 1.2 = 26.67 minutes.

On day two, it took 26.67 minutes, and this was 75% of the time it took on day one. So on day one it took 26.67 minutes / 0.75 = 35.56 minutes.

So the answer is: it took 35.56 minutes to get home on day one.

Here's the answer formatted with HTML:

To find out how long it took to get home on day one, we need to work backwards from day five. Here's how:

So the answer is: it took 35.56 minutes to get home on day one.

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Answer:

The expression log3 2x + 3 log3 4x can be condensed to log3 8x + 3. This is because log3 4x = 2 log3 2x, so when we add the two logarithms together, the result is log3 8x + 3

Step-by-step explanation:

The function g(x) is given as follows:

To shift the exponential function f(x) = -7x+1 two units to the right, we need to replace x with (x-2) in the equation.

This is because when x is replaced with (x-2), the function will have the same output value as before when x was 2 units less.

Thus, the shifted function g(x) can be written as:

g(x) = f(x-2)

g(x) = -7(x-2) + 1

g(x) = -7x + 15

So, the function g(x) is given by g(x) = -7x + 15, and it is the same as f(x) shifted 2 units to the right.

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The respοnse tο the given questiοn wοuld be that As a result, it will take equatiοn arοund 9.7 days frοm the day Sandy placed her sandwich in her lοcker fοr 500 bacteria tο cοmpletely cοver it.

When twο statements are cοnnected by a mathematical equatiοn, the equals sign (=) implies equality. An equatiοn in algebra is a mathematical statement that prοves the equivalence οf twο mathematical expressiοns. Fοr instance, the equal sign separates the numbers in the equatiοn 3x + 5 = 14. It is pοssible tο determine the relatiοnship between the twο sentences οn either side οf a letter using a mathematical fοrmula. The lοgο fοr the particular piece οf sοftware is frequently the same. as 2x - 4 = 2, fοr dinstance.

This issue's expοnential equatiοn is as fοllοws:

N(t) = N0  × [tex]e^{(kt)[/tex] ×  (kt)

We can utilise the abοve infοrmatiοn tο determine the values οf N0 and k:

N(4) = 71 × N(7) = 185

When we enter these numbers intο the equatiοn, we οbtain:

71 = N0  × [tex]e^{(4k)[/tex]  × (4k)

185 = N0  × [tex]e^{(7k)[/tex]   × (7k)

185/71 =  [tex]e^{(3k)[/tex]  × (3k)

As a result, the equatiοn fοr this issue is:

N(t) = 23.77  × [tex]e^{(0.3056t)}[/tex]  × (0.3056t)

We may set N(t) equal tο 500 and sοlve fοr t tο see hοw many days it will take fοr 500 germs tο grοw:

500 = 23.77  × [tex]e^{(0.3056t)}[/tex] × (0.3056t)

9.7 days based οn t = ln(500/23.77) / 0.3056.

As a result, it will take arοund 9.7 days frοm the day Sandy placed her sandwich in her lοcker fοr 500 bacteria tο cοmpletely cοver it.

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All the angle measures are as follows: m∠A = 160°, m∠B  = 142°, m∠C = 120°, m∠D  = 156°, m∠E = 31°, m∠F = 111°

We know that a hexagon is a six-sided polygon and also a convex hexagon which basically means that the hexagon's vertices are pointed outwards.

And with no interior angle has an angle measuring of more than 180°.

We know that the number of sides in the polygon = 6.

And the total sum of the irregular angle = (4 - 2) x 180° = 720°.

7x - 8 + 4x + 46 + 5x + 6x + 12 + x + 7 + 5x - 9 = 720°.

28x = 720 - 48

x = 24

Substituting all the values of x = 24 to all the interior angle measures,

Now, all the measures are:

m∠A = 7x - 8 = 160°

m∠B = 4x + 46 = 142°

m∠C = 5x = 120°

m∠D = 6x + 12 = 156°

m∠E = x + 7 = 31°

m∠F = 5x - 9 = 111°

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The best method to solve this system is elimination using subtraction and the solution is (12, 16).

First, we need to get one of the variables to have the same coefficient in both equations so we can eliminate it. In this case, the y variable already has the same coefficient of -2 in both equations.

Next, we subtract the second equation from the first equation to eliminate the y variable:

3x - 2y = 4
-(2x - 2y = -8)

This gives us:

x = 12

Now, we can plug this value of x back into one of the original equations to solve for y:

3(12) - 2y = 4
36 - 2y = 4
-2y = -32
y = 16

So the solution to this system is (12, 16).

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The value of x is 57 degrees. This was obtained by the use of the trigonometric ratios.

A right triangle, also known as a right-angled triangle, is one that we can say that an angle in this triangle would be 90 degrees.

The Pythagorean theorem can be used to obtain the lengths of the various sides that we have in the right angled triangle. This is one of the fundamental theories in the right angled triangle.

Let us now use the cosine to find the angle as shown below;

We know that;

Cos x = 11/20

x = Cos-1(11/20)

x = 57 degrees

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a. The greatest possible distance from  Austin to san Antonio is 335.77 mi, b. the Least possible distance to Austin to san Antonio is 120.03 mi.

Distance refers to the physical length or space between two points or objects. It is an important concept in mathematics, physics, and everyday life. Distance can be measured in various units such as meters, feet, kilometers, miles, or light-years, depending on the context and scale of the measurement.

In mathematics, distance is often measured using the Euclidean distance formula, which calculates the distance between two points in a plane or in three-dimensional space. The formula is given by:

d = √((x2 - x1)² + (y2 - y1)²)

where d is the distance between the two points, (x1, y1) and (x2, y2).

In physics, distance is often used to describe the separation between two objects or particles. The distance between two objects can affect the strength of gravitational or electromagnetic forces between them. Distance is also an important concept in special relativity, where it is affected by the relative motion of observers and the distortion of spacetime.

a. Greatest possible distance from  Austin to san Antonio= Distance from Austin →Houston → san Antonio.

Austin - Houston = 146.43 mi

Houston - San Antonio = 189.34 mi

Total  distance= 146.43+ 189.34= 335.77 mi

b. Least possible distance to Austin to San Antonio = the shortest distance = x

By Pythagoras theorem

(189.34)² = (146.43)²+ x²

x² = (189.34)²- (146.43)²

x² = 35849.63- 21441.744

x² = 14407.89

x =√14407.89

x = 120.03

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The complete question is:

An estimate for the mean age of the 50 people on the bus is 34 years.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Let us calculate the sum of the products of the midpoints and their respective frequencies, and divide by the total frequency to obtain the estimated mean age.

The midpoint and frequency data for each age group can be represented as follows:

Age group      Midpoint        Frequency

0 < h ≤ 20           10                    20

20 < h ≤ 40         30                    10

40 < h ≤ 60         50                     10

60 < h ≤ 80         70                     10

To calculate the estimated mean age, we can use the formula:

Estimated mean age = (Σ(midpoint × frequency)) / total frequency

Estimated mean age = ((10 × 20) + (30 × 10) + (50 × 10) + (70 × 10)) / (20 + 10 + 10 + 10)

Estimated mean age = (200 + 300 + 500 + 700) / 50

= 1700 / 50

= 34

Therefore, an estimate for the mean age of the 50 people on the bus is 34 years.

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Answer:

a)  The angle subtended by the chord at the centre of the circle is 120°.

b)  The length of the minor arc is 12.57 cm (2 d.p.).

The perimeter of the minor segment formed by a chord and minor​ arc is 22.96 cm (2 d.p.).

Step-by-step explanation:

The chord of a circle is the base of an isosceles triangle, where its congruent sides are the radii of the circle.

The height of the isosceles triangle is the perpendicular bisector of the chord from the central angle.

The angle subtended by the chord at the centre of the circle is twice the angle formed by the radius and the perpendicular bisector (marked θ on the attached diagram).

To find the measure of angle θ, use the cosine trigonometric ratio.

[tex]\begin{aligned}\implies \cos \theta&=\sf \dfrac{adjacent\;side}{hypotenuse}\\\\\cos \theta &=\sf \dfrac{3}{6}\\\\\cos \theta &=\sf \dfrac{1}{2}\\\\\theta &=\arccos\left(\sf \dfrac{1}{2}\right)\\\\\theta &=60^{\circ}\end{aligned}[/tex]

As the angle subtended by the chord at the centre of the circle is twice angle θ:

[tex]\implies 2\theta=2 \cdot 60^{\circ}=120^{\circ}[/tex]

Therefore, the angle subtended by the chord at the centre of the circle is 120°.

A minor arc is less than 180° and is equal to the central angle.

Therefore, as the angle subtended by the chord at the centre of the circle is 120°, the minor arc is the part of the circumference between the two endpoints of the chord (marked in red on the attached diagram).

To find the length of the minor arc, use the arc length formula.

[tex]\boxed{\begin{minipage}{6.4 cm}\underline{Arc length}\\\\Arc length $= \dfrac{\pi r\theta}{180^{\circ}}$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in degrees.\\\end{minipage}}[/tex]

Therefore:

[tex]\begin{aligned}\implies \textsf{Arc length}&= \dfrac{\pi \cdot 6 \cdot 120^{\circ}}{180^{\circ}}\\\\&= 4 \pi\\\\&= 12.57\; \sf cm\;(2\;d.p.)\end{aligned}[/tex]

Therefore, the length of the minor arc is 12.57 cm (2 d.p.).

To calculate the perimeter of the minor segment formed by the chord and minor​ arc, we need to calculate the length of the chord.

[tex]\boxed{\begin{minipage}{10.2 cm}\underline{Chord length}\\\\Chord length $=2r\sin\left(\dfrac{\theta}{2}\right)$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle (in degrees) subtended at the center by the chord.\\\end{minipage}}[/tex]

Therefore:

[tex]\begin{aligned}\implies \textsf{Chord length}&= 2 \cdot 6 \cdot \sin \left(\dfrac{120^{\circ}}{2}\right)\\\\&= 12 \cdot \sin \left(60^{\circ}\right)\\\\&= 12 \cdot \dfrac{\sqrt{3}}{2}\\\\&= 6\sqrt{3}\; \sf cm\end{aligned}[/tex]

Therefore, the perimeter of the minor segment formed by the chord and minor​ arc is:

[tex]\begin{aligned}\implies \textsf{Perimeter}&=\textsf{Minor arc length}+\textsf{Chord length}\\&=4 \pi + 6 \sqrt{3}\\&=22.96\; \sf cm\;(2\;d.p.)\end{aligned}[/tex]

Using long division the quotient of  (2x^3-5x^2+3x-6) divided by (x+4)  is 2x^2 - 13x + 55.

Quotients are often used in algebra and other branches of mathematics to solve equations and expressions involving division. They are also commonly used in everyday life, such as when calculating the cost per unit of a product, or the average speed of a journey.

For example, if we divide 10 by 2, the quotient would be 5, since 10 divided by 2 equals 5. Similarly, if we divide 12 by 3, the quotient would be 4, since 12 divided by 3 equals 4.

Now let find the quotient using long division:

2x^2 - 13x + 55

_______________________

x + 4 | 2x^3 - 5x^2 + 3x - 6

- (2x^3 + 8x^2)

---------------

- 13x^2 + 3x

- (-13x^2 - 52x)

---------------

55x - 6

- (55x + 220)

-----------

-226

Therefore, the quotient is 2x^2 - 13x + 55 and the remainder is -226.

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v1, v2, and v3 are linearly independent

Yes, the vectors v1, v2, and v3 are linearly independent.

To verify this, we can set up the equation:
a1v1 + a2v2 + a3v3 = 0

If the vectors are linearly independent, then the only way to solve this equation is if a1 = a2 = a3 = 0.

Substituting the values for v1, v2, and v3 into the equation yields:

-123 - 3a1 + 16 - 4a2 - 4a3 - 1640a3 = 0

Solving for a1, a2, and a3, we get:

a1 = 0, a2 = 0, a3 = 0

Therefore, the vectors v1, v2, and v3 are linearly independent.

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Answer: If the length of a rectangle is 2 inches more than its width, we can write:

length = width + 2

We can also rearrange this equation to solve for the width in terms of the length:

width = length - 2

Both of these equations relate the length l of the rectangle to its width w.

Step-by-step explanation:

Answer:

The discounted price of the shoes is:

$70 x 0.65 = $45.50

The amount of sales tax is:

$45.50 x 0.05 = $2.275

Therefore, the total amount you will pay for the shoes is:

$45.50 + $2.275 = $47.775

Rounded to two decimal places, the amount you will pay is $47.78.

Answer:

G = 5.333

Step-by-step explanation:

Given: G(3) = 4^2

3 times G is 3G:

3G = 4^2

4 squared is 16:

3G = 16

Divide both sides by 3:

G = 5.333

The solution to the given system of equations is:
x = -4/7
y = -9/14
z = 18/7

To write the given system of equations in row-reduced echelon form, we will first need to convert the equations to an augmented matrix, and then use row operations to reduce the matrix to its row-reduced echelon form.

The augmented matrix for the given system of equations is:

| -15 -10 -20 | -6 |
| 9 12 30 | 15 |
| 3 2 10 | 6 |

We will now use row operations to reduce the matrix to its row-reduced echelon form:

Divide the first row by -15 to get a leading 1 in the first row:

| 1 2/3 4/3 | 2/5 |
| 9 12 30 | 15 |
| 3 2 10 | 6 |

Subtract 9 times the first row from the second row, and 3 times the first row from the third row:

| 1 2/3 4/3 | 2/5 |
| 0 2 6 | 3 |
| 0 -4/3 -2/3 | 18/5 |

Divide the second row by 2 to get a leading 1 in the second row:

| 1 2/3 4/3 | 2/5 |
| 0 1 3 | 3/2 |
| 0 -4/3 -2/3 | 18/5 |

Add 4/3 times the second row to the third row:

| 1 2/3 4/3 | 2/5 |
| 0 1 3 | 3/2 |
| 0 0 14/3 | 54/5 |

Divide the third row by 14/3 to get a leading 1 in the third row:

| 1 2/3 4/3 | 2/5 |
| 0 1 3 | 3/2 |
| 0 0 1 | 18/7 |

Subtract 3 times the third row from the second row, and 4/3 times the third row from the first row:

| 1 2/3 0 | -16/21 |
| 0 1 0 | -9/14 |
| 0 0 1 | 18/7 |

Subtract 2/3 times the second row from the first row:

| 1 0 0 | -4/7 |
| 0 1 0 | -9/14 |
| 0 0 1 | 18/7 |

The row-reduced echelon form of the given system of equations is:

| 1 0 0 | -4/7 |
| 0 1 0 | -9/14 |
| 0 0 1 | 18/7 |

So, the solution to the given system of equations is:

x = -4/7
y = -9/14
z = 18/7

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Answer:

Let's assume that we have an odd integer represented by the variable "n". Then, according to the definition of an odd integer, we can write it as follows:

n = 2k + 1

Where "k" is any integer.

Now, we need to find the square of "n". We can write it as follows:

n^2 = (2k + 1)^2

n^2 = 4k^2 + 4k + 1

Now, we can simplify the expression:

n^2 = 4k(k + 1) + 1

We can observe that the expression 4k(k + 1) is always an even number. This is because when we multiply two consecutive integers (k and k + 1), we always get an even result. Therefore, we can write:

4k(k + 1) = 8m

Where "m" is any integer. Substituting this expression into the previous equation, we get:

n^2 = 8m + 1

This shows that the square of any odd number is always 1 more than a multiple of 8, which is what we wanted to prove.

Answer:

The answer is 8

Step-by-step explanation:

If n is "any integer", then 2n+1 is "any odd number."

The square of any odd number is then ...

 (2n+1)² = 4n² +4n +1 = 4n(n+1) +1

Since n is any integer, one of n and n+1 will be an even integer, so the product 4n(n+1) will be divisible by 8.

Then the sum 4n(n+1) +1 is one more than a number divisible by 8, hence ...

 the square of an odd number is 1 more than a multiple of 8.

Using Cramer's Rule, we cannot solve this system of linear equations because the determinant of the coefficient matrix is 0. However, we can conclude that the system has infinitely many solutions.

Using Cramer's Rule, we can solve the system of linear equations 13x - 6у = 17 and 26x -12y = 8 by following these steps:

Step 1: Find the determinant of the coefficient matrix, which is:

| 13 -6 |
| 26 -12 |

= (13)(-12) - (-6)(26)

= -156 - (-156)

= 0

Step 2: Since the determinant of the coefficient matrix is 0, we cannot use Cramer's Rule to solve this system of equations.

Step 3: We can check if the system has no solution or infinitely many solutions by comparing the ratios of the coefficients of x and y in the two equations.

The ratio of the coefficients of x in the two equations is 13/26 = 1/2, and the ratio of the coefficients of y in the two equations is -6/-12 = 1/2. Since these ratios are equal, the system has infinitely many solutions.

Using Cramer's Rule, we cannot solve this system of linear equations because the determinant of the coefficient matrix is 0. However, we can conclude that the system has infinitely many solutions.

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The point on the line segment that is 3/4 of the way from A to B is (8,5.5).

To find the point on the line segment that is 3/4 of the way from A to B, we can use the formula for finding a point on a line segment:

P = (1-t)A + tB

Where P is the point we are trying to find, A and B are the endpoints of the line segment, and t is the fraction of the distance from A to B that we want to find. In this case, t = 3/4.

Plugging in the values for A, B, and t, we get:

P = (1-3/4)(5,-5) + (3/4)(9,9)

Simplifying, we get:

P = (1/4)(5,-5) + (3/4)(9,9)

P = (1.25,-1.25) + (6.75,6.75)

P = (8,5.5)

So the point on the line segment that is 3/4 of the way from A to B is (8,5.5).

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Answer:

A) vertical asymptote: X = -3

Horizontal asymptote: y = -9

Step-by-step explanation:

sorry I don't know how to explain it

After watching "Nike an Example of a TNC (Transnational Corporation)" and reviewing the readings and notes, it is clear that Nike's production of shoes and clothing around the world has had a significant effect on the standard of living of workers in the countries where it produces ("the global South") and in the countries where it sells its products ("the global North").

In the global South, Nike's production has led to the creation of jobs and an increase in income for workers. However, these workers often face poor working conditions and low wages, which can negatively impact their standard of living. Additionally, the environmental impact of Nike's production can also have a negative effect on the standard of living for workers and their communities.

In the global North, Nike's production has led to the availability of affordable and fashionable clothing and shoes. However, the low prices of these products are often achieved through the exploitation of workers in the global South, which can lead to ethical concerns for consumers. Additionally, the environmental impact of Nike's production can also have a negative effect on the standard of living for consumers and their communities.

Overall, Nike's production of shoes and clothing around the world has had a significant effect on the standard of living of workers in the global South and consumers in the global North. While there are some benefits, such as job creation and affordable products, there are also significant negative impacts, including poor working conditions, low wages, and environmental degradation.

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To evaluate det(A) by a cofactor expansion along a row or column of our choice, we will use the following formula:

det(A) = a11C11 + a12C12 + a13C13 + ... + a1nC1n

where aij is the element in the ith row and jth column of matrix A, and Cij is the cofactor of that element.

For simplicity, we will choose to expand along the first row of matrix A.

det(A) = 5C11 + 0C12 + 0C13 + 1C14 + 0C15 + 3C16 + 3C17 + 3C18 + (-1)C19 + 0C110

Now, we will find the cofactors of each element in the first row.

C11 = (-1)1+1det(M11) = det(M11) = (5)(4)(3)(54) - (3)(2)(4)(3) = 3240 - 72 = 3168

C12 = (-1)1+2det(M12) = -det(M12) = -(0)

C13 = (-1)1+3det(M13) = det(M13) = (0)

C14 = (-1)1+4det(M14) = det(M14) = (3)(4)(3)(54) - (2)(2)(4)(3) = 1944 - 48 = 1896

C15 = (-1)1+5det(M15) = -det(M15) = -(0)

C16 = (-1)1+6det(M16) = det(M16) = (2)(4)(3)(54) - (2)(2)(4)(3) = 1296 - 48 = 1248

C17 = (-1)1+7det(M17) = -det(M17) = -(2)(3)(3)(54) - (2)(2)(4)(3) = -972 - 48 = -1020

C18 = (-1)1+8det(M18) = det(M18) = (1)(3)(3)(54) - (2)(2)(4)(3) = 486 - 48 = 438

C19 = (-1)1+9det(M19) = -det(M19) = -(1)(4)(3)(54) - (2)(2)(4)(3) = -648 - 48 = -696

C110 = (-1)1+10det(M110) = det(M110) = (0)

Now, we will substitute the cofactors back into the formula and simplify.

det(A) = 5(3168) + 0(0) + 0(0) + 1(1896) + 0(0) + 3(1248) + 3(-1020) + 3(438) + (-1)(-696) + 0(0)

det(A) = 15840 + 1896 + 3744 - 3060 + 1314 + 696

det(A) = 19430

Therefore, det(A) = 19430.

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Answer:

You must get a 89%

Step-by-step explanation:

81+89=170

170/2= 85%

Answer:

100

Step-by-step explanation:

hope this helps! :))

Answer: 100

Step-by-step explanation:

A perfect square can be found when you multiply the same integer twice. 100 is a perfect square because 10 * 10 = 100. You multiply 10 twice in the equation.

Answer: 4 quarts / 1 gallon

Step-by-step explanation: or C!! hope this helps!!

The Idempotent laws, Associative laws, Commutative laws, Distributive laws, Identity laws, Domination laws, Double Complement law, Complement laws, and De Morgan's laws are all types of identities that are used in set theory and Boolean algebra. These identities are used to simplify expressions and to prove the equivalence of two expressions.

The Idempotent laws state that the union or intersection of a set with itself is equal to the set itself:
A u A = A
AnA = A

The Associative laws state that the order in which sets are grouped does not matter when taking the union or intersection:
(AU B) U C = Au (B U C)
(AnB) nc =An(Bnc)

The Commutative laws state that the order in which sets are listed does not matter when taking the union or intersection:
Au B = B U A
AnB = BnA

The Distributive laws state that the union or intersection of a set with the intersection or union of two other sets is equal to the intersection or union of the set with each of the other sets:
Au (B n C) = (Au B) n (Au C)
An(B u C) (AnB) u (An C)

The Identity laws state that the union of a set with the empty set is equal to the set itself, and the intersection of a set with the universal set is equal to the set itself:
Au 0 = A
AnU = A

The Domination laws state that the intersection of a set with the empty set is equal to the empty set, and the union of a set with the universal set is equal to the universal set:
Ano =0
Au U = U

The Double Complement law states that the complement of the complement of a set is equal to the set itself:
A = A
AnA = U = 0
Au A = U 0 = U

The Complement laws state that the union of a set with its complement is equal to the universal set, and the intersection of a set with its complement is equal to the empty set:
AuB = AnB
AnB = Au B

De Morgan's laws state that the complement of the union of two sets is equal to the intersection of the complements of the sets, and the complement of the intersection of two sets is equal to the union of the complements of the sets:
AuB = AnB
AnB = Au B

The Absorption laws state that the union of a set with the intersection of the set with another set is equal to the set itself, and the intersection of a set with the union of the set with another set is equal to the set itself:
Au (AnB) = A
An(A U B) = A

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The area of the one rectangular panel is equal to 220 ft².

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

Generally speaking, the opposites sides of a rectangle are equal;

DN = WF

12x + 4 = 20x - 8

20x - 12x = 8 + 4

8x = 12

x = 3/2.

Side DN = 12x + 4 = 12(3/2) + 4 = 22 feet.

DW = NF

5y - 5 = 2y + 4

y = 3

Side DW = 5y - 5 = 5(3) - 5 = 10 feet.

Area of rectangular panel = DN × DW

Area of rectangular panel = 22 × 10

Area of rectangular panel = 220 ft².

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a. The product of (5x-2) and (6x²+7x -4 ) is 30x³+23x²-34x+8

b. The product of (5x - 2) and (6x2 +7x - 4) is not equal to The product of (2 – 5x) and (6x2

+7x - 4)

Product is results that comes from multiply two or more terms or expression together.

For example, 5x × 2 = 10. The product here is 10 and the two terms are 5x and 2.

therefore,

(5x-2)( 6x²+7x-4)

using distributive law

5x( 6x²+7x-4) + (-2)(6x²+7x-4)

= 30x³+ 35x²-20x -12x²-14x+8

collect like terms

30x³ + 35x²-12x²-20x-14x+8

= 30x³+23x²-34x+8

b. The product of (2 – 5x) and (6x2 +7x - 4)

= 2(6x2+7x - 4) -5x(6x2+7x - 4)

= 12x²+14x-8-30x³-35x²-20x

= -30x³+12x²-35x²+14x-20x-8

= -30x³ - 23x²-6x-8

therefore the product of (5x - 2) and (6x2 +7x - 4) is not equal to The product of (2 – 5x) and (6x2

+7x - 4)

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All congruent segments are QR ≅ LM, RS ≅ MN and QS ≅ LN

The triangles are said to be congruent if their corresponding sides and angles are congruent to each other.

Given are two congruent triangles QRS and LMN, we need to deduce the corresponding congruent parts,

So, according to the definition of congruent triangles :-

Sides :-

QR ≅ LM, RS ≅ MN and QS ≅ LN

Angles :-

∠ Q ≅ ∠ L, ∠ R ≅ ∠ M and ∠ S ≅ ∠ N

Hence, the congruent segments are QR ≅ LM, RS ≅ MN and QS ≅ LN

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The expression after applying distributive property is

[(-5/8) × (-3)] + [(-5/8 ) × (-7)] = 50/8

Distributive property shows us how to multiply an arithmetic number or an algebraic expression with two or more numbers or expressions within brackets.

This can be symbolically represented as :

X ( Y + Z ) = XY + XZ

here, we have,

The expression given here is -5/8 (-3 + (-7)).

Applying distributive property, we get,

-5/8 (-3 + (-7)) =  [(-5/8) × (-3)] + [(-5/8 ) × (-7)]

                 = (15/8) + (35/8)

                 = 50/8

The expression - 5/8(-3 + (-7)) after applying distributive property changes to the expression [(-5/8) × (-3)] + [(-5/8 ) × (-7)] = 50/8.

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