Solve the system of linear equations by elimination.
5x+6y=50
x-6y=-26

The order of the group generated by a and b under matrix multiplication is a^2b^3.

Start with the identity matrix:

I = [1 0 ; 0 1]

Multiply it by a:

a*I = [1 1; 0 1]

Multiply it by b:

b*a*I = [1 2; 0 1]

Multiply it by a:

a*b*a*I = [2 3; 0 1]

Multiply it by b:

b*a*b*a*I = [2 5; 0 1]

Multiply it by a:

a*b*a*b*a*I = [4 3; 0 1]

Therefore, the order of the group generated by a and b is a^2b^3.

The order of the group generated by a and b under matrix multiplication is a^2b^3.

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The solution for the equations (2x + 5y = 18) and (3x + 1.5y = 9) will be x = 1.5 and y = 3.

A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."

Given that the system of the equations is (2x + 5y = 18) and (3x + 1.5y = 9). The equations by substitution method can be solved as,

(2x + 5y = 18)

(3x + 1.5y = 9)

Rewrite the equation (2x + 5y = 18) as,

x = ( 18 - 5y) / 2

Substitute the value of x in the second equation,

3x + 1.5y = 9

3  ( 18 - 5y) / 2 + 1.5y = 9

( 54 - 15 y) /2 + 1.5y = 9

54 - 15y + 3y = 18

-12y = -54 + 18

-12y = -36

y = 3

The value of x will be calculated as:-

2x + 5y = 18

2x + ( 5x 3 ) = 18

2x + 15 = 18

2x = 3

x = 1.5

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If their assembly rates continue, based on an equation, Summer will catch up with Jin in 52 minutes.

An equation refers to a statement claiming the equality of two or more mathematical expressions.

Using the equation sign (=) mathematicians show that expressions are equal or equivalent.

Jin's assembling rate per minute = 12 parts

Summer's assembling rate per minute = 15 parts

The number of parts already assembled by Jin before Summer started = 156 parts

Let the minutes used by Jin or Summer = n

The total parts assembled by Jin in n minutes = 156 + 12n

The total parts assembled by Summer in n minutes = 15n

For Summer to catch up to Jin, 15n = 156 + 12n

Grouping like terms:

15n - 12n = 156

3n = 156

n = 52

Thus, in 52 minutes, the number of assembly parts by Summer will equal Jin's.

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Answer: 311/500 and 62.22%

Step-by-step explanation:

Fraction: 0.622 = 622/1000 = 311/500

Percent: 0.6222 = 62.22 % (Move decimal 2 places down)

The decimal 0.622 in the form of simplest fraction as 311/500 and in percent is 62.2%.

To convert 0.622 to a fraction in simplest form, write it as follows:

0.622 = 622/1000

Now, simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

622/1000 = (311 × 2)/(500 × 2)

                 = 311/500

So, 0.622, when expressed as a fraction in simplest form, is 311/500.

To convert 0.622 to a percent, multiply it by 100:

0.622 × 100 = 62.2%

Therefore, 0.622 is equivalent to 311/500 or 62.2%.

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Step-by-step explanation:

To get the total amount of sandwiches sold in the first week, we would need to add up all of the ham, tuna, and cheese sandwiches.

32 + 46 + 18 = 96

The shop sold 96 sandwiches in the first week.

To find out how many more sandwiches the store sold in the second week, we will need to add up all of the sandwiches again.

38 + 43 + 24 = 105

The shop sold 105 sandwiches in the second week.

Taking 105, we can subtract 96 from it to get how many more sandwiches the shop sold in week 2.

105 - 96 = 9

The shop sold 9 more sandwiches in the second week.

Answer:

9 books

Step-by-step explanation:

The value for x is 1 or -6. The solution has been obtained by using logarithm.

A logarithm is the power to which a number must be raised in mathematics in order to produce other numbers. It is the most useful way to express really large numbers.

We are given [tex]log_3 \frac{3(2-x)}{x(x+2)} = 0[/tex]

Solving the equation, we get

[tex]log_3 \frac{3(2-x)}{x(x+2)} = 3^0[/tex]  (Using the property of log)

On multiplying both sides by x(x+2), we get

[tex]log_3 \frac{3(2-x)}{x(x+2)} x(x+2) = 3^0 x(x+2)[/tex]

⇒3 (2−x) = x(x+2)

⇒ 6 - 3x=x² +2x

= x²+5x-6=0

⇒ x²+6x-x-6=0

⇒ (x+6)(x-1)=0

⇒ x = 1,-6

Hence, the value for x is 1 or -6.

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There is a possible translation of the form g(x) = f(x) + k for which the graph y=g(x) will have no x-intercepts.

A translation is a movement to a graph or figure in which only the position of the figure changes, either left, right, up or down, keeping the inclination, orientation and congruence.

The translations are represented as follows:

Hence, for the function to have no x-intercepts, the function must be shifted up as though the minimum value of the function is greater than zero.

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Answer:

  z = √30

Step-by-step explanation:

Given similar right triangles with hypotenuse segments marked 3 and 7, you want to know the length of short leg z adjacent to the segment marked 3.

The fact that all of these triangles are similar gives rise to some "geometric mean" relationships:

  hypotenuse/short side = 10/z = z/3

  30 = z² . . . . . . . multiply by 3z

  z = √30 . . . . . . take the square root

__

Additional comment

The other two geometric mean relations are ...

  x = √(7·10) . . . . . hypotenuse/long side: 10/x=x/7

  y = √(7·3) . . . . . . short side/long side: y/7=3/y

The triangles are similar by AA: each has a right angle, and an angle in common with the largest triangle. Triangles similar to the same triangle are similar to each other.

In the equation [tex](1/4)^{x-2} = 16[/tex], The value of the exponent x is 0.

A number's exponent tells you how long you will need to multiply it in order to get the result. For instance, because 8 is multiplied by itself 3 times, 8 8 8 can be written as 83.

Here, 3 is the "exponent" or "power," which indicates how many times the number 8 is multiplied by itself, and 8 is the "base," which stands for the number being multiplied.

The number of times a number must be multiplied by itself is what a power or exponent, in essence, indicates. The base in this situation can be any integer, fraction, or decimal. Any value, positive or negative, can be assigned to the exponent.

Given

[tex](1/4)^{x-2} = 16[/tex]

[tex](1/4^{x-2}) = 16[/tex]

1 = 16 × [tex]4^{x-2}[/tex]

1 = 16 × [tex](2^2)^{x-2}[/tex]

[tex]$1 = 16 \times \frac{ 2^{2x}}{2^4}[/tex]

[tex]$1 = \frac{ 16 \times2^{2x}}{2^4}[/tex]

[tex]$1 = \frac{ 16 \times2^{2x}}{16}[/tex]

[tex]$1 = 2^{2x}[/tex]

1 = 2²⁽⁰⁾ The only possible exponent that values in 1 is when exponent is 0

1 = 1

x = 0

Thus, In the equation [tex](1/4)^{x-2} = 16[/tex], The value of the exponent x is 0.

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The quotient of the expression,

9(7y - 15) /  (110 - 6y ÷ 4) is 18(7y - 15) / (55 - y).

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

We have an expression,

9(7y - 15) /  (110 - 6y ÷ 4)

Simplifying,

9(7y - 15) /  (110 - 6y ÷ 4),

= 9(7y - 15) x 4 / (110 - 6y)

= 36(7y - 15) / (110 - 6y)

= 18(7y - 15) / (55 - y)

Therefore, the quotient is 18(7y - 15) / (55 - y).

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The circumference of the circle in terms of π  is 7π yards. Option B

The formula for calculating the circumference of a circle is expressed as;

C = 2πr

Given that the parameters are;

The formula for calculating the radius of a circle is given as;

Radius = d/2

Where; d is the diameter of the circle

From the information given,

Diameter = 7 yards

Radius = 3.5 yards

Now, substitute the value

Circumference = 2× 3. 5 ×π

Multiply the values

Circumference = 7π yards

Thus, the value is 7π yards

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Answer: 7 yards

Step-by-step explanation:

a) The block-spring system has an elastic potential energy equal to 2.517 joule.

b) The block has speed of approximately 1.513 meters per second.

In this problem we must analyze the energy and kinematics of spring-block system with no irreversibilites (no friction). Part A - Elastic potential energy is determined when spring is entirely deformed:

U = (1 / 2) · k · x²

Where:

If we know that k = 895 N / m and x = 0.0750 m, then the elastic potential energy of the block-spring system is;

U = (1 / 2) · (895 N / m) · (0.0750 m)²

U = 2.517 J

The elastic potential energy of block-spring system is 2.517 joule.

Part B - And the speed can be determined by principle of energy conservation and work-energy theorem:

K = U

Where K is translational kinetic energy, in joules.

(1 / 2) · m · v² = U

v² = 2 · U / m

v = √(2 · U / m)

If we know that U = 2.517 J and m = 2.20 kg, then the speed of the block is:

v = √[2 · (2.517 J) / (2.20 kg)]

v ≈ 1.513 m / s

The speed of the block after leaving the spring is approximately 1.513 meters per second.

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The purchase cost of fixtures can become tax deductible is referred to as a true statement.

This is referred to as the imposition of compulsory levies on individuals or entities by governments in other to fund government spending and various public expenditures.

Office fixtures such as furniture would typically be considered a long-term asset because it isn't typically replaced on a yearly basis which is why they are not deductible from a business's taxable income. However in a scenario where the fixtures start going through the process of depreciation, amortization or depletion then it becomes tax deductible.

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The property if VW+WY=ZY, and VW + WY=XZ, then XZ=ZY is referred to as a transitive property.

This states that “if two quantities are equal to the third quantity, then we can say that all the quantities are equal to each other”.

A good example of its application can be seen here which is if x = y, and y = 7, then x must equal 7 which when observed in what was given above corresponds with this type of property and is therefore the reason why it was chosen as the correct choice.

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Legal precedent means that a decision on a definite principle or question of law has already been made by a court of higher authority, such as a call or supreme court. below such a decision, lower courts defer to, or adhere to, that prior decision in similar cases.

The commitment of lower courts may be used as precedent for courts of similar jurisdiction, but higher courts are not bound by the resolution of lower courts.

The use of legal precedent helps secure court rulings remain consistent among similar cases. To this end, courts are bound to cling to prior decisions made by a higher court on a same legal matter.

Because a judge is bound by these previously made decisions, this is mentioned to as binding precedent. anew, following the principle of glare decisis, binding precedent promotes the maintenance of answers to legal questions already established.

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For the given function C(x) = 0.37 + (x - 1)0.11 the cost of mailing a 1.6-ounce letter is $0.436

The term function in math is defined as a relation between a set of inputs having one output each.

Here we have given that certain mailing service's first class mail rates are $0.37 for the first ounce and $0.11 for each additional ounce or fraction thereof up to 3.5 ounces.

Let us consider that the term C refers that cost in dollars of a first class mailing and x refers the weight in ounces.

The the function for the given situation is written as,

=> C(x) = 0.37 + (x - 1)0.11

Here we have given that we need to find the cost of mailing a 1.6-ounce letter which defines that the value of x is 1.6, then the cost is calculated as,

=> C(x) = 0.37 + (1.6 - 1) 0.11

=> C(x) = 0.37 + 0.066

=> C(x) = 0.436.

Complete Question:

A certain mailing service's first class mail rates are $0.37 for the first ounce and $0.11 for each additional ounce or fraction thereof up to 3.5 ounces. Find the function of the situation and the cost of mailing a 1.6-ounce letter.

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Answer:

5.5cm

Step-by-step explanation:

The volume of a cuboid is given by

V = lbh

where l is the length

b is the breadth

h is the height.

We know that

V = lbh = 440 cm^3

Given l = 10 cm, h = 8 cm

So, we can find b by substituting these values in the above equation

440 = 10 * b * 8

Solving for b, we get:

b = 440 / (10*8)

b = 5.5cm

So, the breadth of the cuboid is 5.5 cm.

Both Candice and Joel used a proof by contradiction.

Candice began her proof by assuming the statement was false (by supposition) and then used the vertical angles theorem, definition of congruence, and additional property of equality to arrive at a contradiction.

By demonstating that assuming a proposition to be false results in a contradiction, proof by contradiction establishes the truth or validity of a proposition in logic.

Joel began his proof by assuming the statement was true and used the angle addition postulate, vertical angles theorem, definition of congruence, and subtraction property of equality to arrive at a conclusion that the statement was true.

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The independent variable in this study is sleep deprivation, as the study aims to investigate the effects of sleep deprivation on the ability to drive.

This study is an experimental study that measures the effects of sleep deprivation on the ability to drive. The sample size is 19 professional drivers, and the study uses a within-subjects design as each driver participated in two experimental sessions: one after normal sleep and one after 27 hours of total sleep deprivation. The treatments were assigned in random order, meaning that each driver has an equal chance of being assigned to either the sleep deprivation or normal sleep condition. The outcome variable in this study is performance on a variety of tasks, including a driving simulation. The independent variable in this study is sleep deprivation, as the study aims to investigate the effects of sleep deprivation on the ability to drive.

Thus, The independent variable in this study is sleep deprivation, as the study aims to investigate the effects of sleep deprivation on the ability to drive.

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Answer: The probability that all generators in a sample of 8 are defective can be calculated by finding the number of ways that 8 defective generators can be selected out of 48 total generators, divided by the total number of ways that any 8 generators can be selected out of 48 total generators.

The number of ways to select 8 defective generators out of 48 total generators is:

C(8,8)*C(40,0) = 1

The total number of ways to select 8 generators out of 48 total generators is:

C(48,8) = 1,907,725

The probability that all generators in a sample of 8 are defective is:

1/1,907,725

If a sample of 8 generators is selected, find the probability that none in the sample are defective.

The number of ways to select 8 non-defective generators out of 48 total generators is:

C(40,8) = 45,765

The total number of ways to select 8 generators out of 48 total generators is:

C(48,8) = 1,907,725

The probability that none in the sample are defective is:

45,765/1,907,725

Both of these are reduced fraction.

Answer:

It belongs in quadrant 3.

The parametric equations for the line are:

x(t) = 5 + t, y(t) = 5 - t and z(t) = t

Given that the line through (5, 5, 0) and perpendicular to both i + j and j + k

We know that the symmetric form of the equation of the line is given by,

[tex]\frac{x-x_1}{a} =\frac{y-y_1}{b} =\frac{z-z_1}{c} =t[/tex]

Let us assume that x₁ = 5, y₁ = 5 and z₁ = 0

Evaluating the product of ( i + j) and ( j + k ) we get,

( i + j) × ( j + k )

= i - j + k

The value of a = 1, b = -1 and c = 1.

Substitute all the values in the above equation we get,

[tex]\frac{x-x_1}{a} =\frac{y-y_1}{b} =\frac{z-z_1}{c} =t[/tex]

[tex]\frac{x-5}{1} =\frac{y-5}{-1} =\frac{z-0}{1} =t[/tex]

so, the parametric form of the equation would be,

x(t) = x₁  + at

x(t) = 5 + (1)t

x(t) = 5 + t

y(t) = y₁  + bt

y(t) = 5 + (-1)t

y(t) = 5 - t

And z(t) = z₁  + ct

z(t) = 0 + (1)t

z(t) = t

Thus, the parametric equations: x(t) = 5 + t, y(t) = 5 - t and z(t) = t

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The complete question is:

Find parametric equations and symmetric equations for the line. (Use the parameter t.) The line through (5, 5, 0) and perpendicular to both i + j and j + k

x(t), y(t), z(t) = ?

The rate at which the water is now flowing from the tap is 50 cubic centimeters per second.

Unit rate is the amount of one quantity for a unit amount of the other quantity.

In other words it compares 1 unit of some quantity with different amount of another quantity.

Given that,

Time taken to fill the watering can of 4 liter = 40 seconds.

4 liter = 4000 cm³

Time taken to fill the watering can of 4000 cm³ = 40 seconds

Unit rate of flow of water = 4000 / 40 = 100 cm³ / sec

Now the rate at which water flows is halved.

Rate = 100 / 2 = 50 cm³ / sec

Hence the rate of the flow of water now is 50 cubic centimeters per second.

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The complete question is as follow :

Water flows at a steady rate from a tap it takes 40 seconds to fill a 4 liter watering can from the tap. The rate at which water flows is halved.

4litre=4000cm³

Find the rate at which the water is now flowing from the tap. Give your answer in cubic centimeters per second (cm³/s).

Answer:

You do not need to add any skim milk.

Step-by-step explanation:

Step-by-step explanation:

percentages are represented by hundredths in calculations.

2 1/2% = 2.5% = 0.025

2% = 0.02

we are mixing the 3 L 2.5% milk with x L of 0% milk.

and we are ending up with (3 + x) L of 2% milk.

so, we have

3×0.025 + x×0 = (3 + x)×0.02 = 3×0.02 + 0.02x

3×0.005 = 0.02x

0.015 = 0.02x

x = 0.015/0.02 = 0.75

so, 0.75 L have to be added to dilute the milk to 2%.

The tension in each wire when a 180-lb cylinder is suspended from point d is 52.8

The term tension is defined as the tensile load in the wire as it is continuously fed between the wire guides that are used to keep the wire straight between said guides.

While we looking into the following diagram we have identified that the following values are known.

Here the width is 180 lb.

And the distance between the two wires on all the sides is 22 inches, 24 inches and 18 inches.

Then the tension is calculated as,

=> (22 x 24 x 18)/180

=> 9504/180

=> 52.8

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The solution of the system of equations is given by the ordered pair (10, 85).

The solution tells us that the height of both Drone A and Drone B would be the same after 10 minutes.

In this scenario, heights of drones are represented by the following system of equations:

y = 8x + 5     .......equation 1.

y = 6x + 25    .......equation 2.

where:

By equating equation 1 and equation 2, number of minutes since the drones were released can be calculated as follows;

8x + 5 = 6x + 25

8x - 6x = 25 - 5

2x = 20

x = 20/2

x = 10 minutes.

Next, we would determine the height when x = 10 minutes:

y = 8(10) + 5

y = 80 + 5

y = 85 meters.

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So. the left Riemann sum is 23.74 ft^2.

Given the information in the table:

(a) To use a left Riemann sum with three subintervals to approximate the integral of A(h) with respect to h, we need to divide the interval of integration [0,10] into three equal subintervals. The width of each subinterval is (10-0)/3 = 3.33 ft. The left Riemann sum can be calculated as:

(A(0) * 3.33) + (A(2) * 3.33) + (A(5) * 3.33) = (50.3 * 3.33) + (14.4 * 3.33) + (6.5 * 3.33) = 16.80 + 4.78 + 2.16 = 23.74 ft^2

(b) This approximation represents the total area of the horizontal cross section of the tank up to a specific height h.

(c) The Riemann sum is an underestimate of the actual integral. This is because the Riemann sum uses the left endpoint of each subinterval to approximate the area under the curve, but the actual area under the curve is always greater than or equal to the area of the rectangles.

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Answer:

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

Let the husband's age be h and wife's age be w.

The difference of their age is 3 and sum is 73:

The difference between the squares is:

Answer:

219

Step-by-step explanation:

H-W=3

H+W =73

2H=76

H=38

W=35

38² -35² = 219

a. The table for the weekly weight of Julie is illustrated below.

b. The recursive definition for this sequence is y = 180 - 2x.

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Given, Julie is trying to lose weight.

She now weighs 180 pounds and every week for eight weeks, she was able to lose 2 pounds.

The list of her weight every week for eight weeks is,

week 1 = 180 - 2 = 178 pounds.

week 2 = 178 - 2 = 176 pounds.

week 3 = 176 - 2 = 174 pounds.

week 4 = 174 - 2 = 172 pounds.

week 5 = 172 - 2 = 170 pounds.

week 6 = 170 - 2 = 168 pounds.

week 7 = 168 - 2 = 166 pounds.

week 8 = 166 - 2 = 164 pounds.

The equation that represents her weekly weight loss is,

y = 180 - 2x, Where 'x' represents the number of weeks and y represents the final weight.

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