This math sheet is making me scratch my head. Can I have help with all of the questions? I just need the answers (check pdf or attached png). Number 3 and 4 are the tricky ones. (keeps getting taken down)

As a result, the vector x whose coordinate vector relative to the basis B is [5 4] in R² is (45/11, -54/11).

A vector is a matrix that has only one row or one column. A row vector is a matrix with only one row. Example Because it only contains one row, the matrix is a row vector. A column vector is a matrix with only one column. A vector is a quantity linear array. A matrix is a two-dimensional array of values. Tensors are three-dimensional and higher-dimensional arrays that exist. A matrix can be thought of as a sequence of column vectors, but it can also be thought of as a sequence of row vectors; both interpretations are valid.

Here,

To find the vector x in R² whose coordinate vector relative to the basis B is [5 4], we need to express the vector x as a linear combination of the basis vectors [5 -6] and [-7 2].

Using the formula [x]_B = [5 4] = a[5 -6] + b[-7 2], where a and b are scalars, we can solve for a and b:

5 = 5a - 6b

4 = -7a + 2b

Solving for a and b using the system of equations:

a = 9/11

b = 14/11

So, x = 9/11 [5 -6] + 14/11 [-7 2] = (45/11, -54/11).

So, the vector x whose coordinate vector relative to the basis B is [5 4] is (45/11, -54/11) in R².

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Above that the statement indicates just simple interest equals $157.92.

With only the coordination mechanism and a fixed interest rate, simple yearly interest is interest connected to borrowing. Compounding, wherein borrowers are obligated to pay tax on the principal as well as interest that rises over a number of pay periods, is not included. Simple interest is calculated by multiplying the original by calendar, rate of return and time period.

Due to it,

P = $1305.17

R = 11/10%

T = 11 months

Now, Simple Interest = P*R*T/100

Simple Interest = 1305.17 * 1.1 * 11/100

Simple Interest = 157.92

Therefore, Simple Interest is $157.92

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The estimated value of the variable x is 8. 24

it is important that we know algebraic expressions are expressions with terms, coefficients, variables, constants and factors.

They are also expressions with mathematical expressions.

From the information given, we have that;

8.9(x – 4.2) = 35.99

Now, divide both sides by 8.9, we get;

x - 4. 2 = 4. 04

collect the like terms, we have;

x = 4. 04 + 4.2

Add the collected like terms, we have;

x = 8. 24

Hence, we can say that the student's solution was incorrect and the value is 8.24

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Answer:

Use -3 as a factor 4 times to find the value of (-3)^4. The answer is 81

Step-by-step explanation:

To solve (−3)^4, use -3 as a factor four times. This can be done by multiplying -3 by itself four times: (-3)(-3)(-3)(-3) = 81. Alternatively, you can use the square root property to find the value of (−3)^4. The square root property states that if a number is multiplied by itself two times, then the square root of that number is equal to one of the numbers used in the multiplication. In this case, the square root of 81 is -3, which is equal to one of the numbers used in the multiplication. Therefore, (−3)^4 = 81.

ax+b-(cx+d)=

ax+b-cx+d=

x(a-c)+b-d

Answer:

Step-by-step explanation:

To solve the problem, we start by labeling 1/3 of 3/8 like this:

N1/D1 of N2/D2

Then we use this fraction of a fraction formula to solve the problem:

(N1 x N2) / (D1 x D2)

When we enter 1/3 of 3/8 into the formula, we get:

(1 x 3) / (3 x 8) = 3/24

Therefore, the answer to 1/3 of 3/8 in its lowest form is:

1/3 of 3/8 = 1/8

Answer:

See below

Step-by-step explanation:

The linear relation of the given Rate of Change and Initial Value is y = 2/3x + 10

Suppose that we have to measure the rate of change of y as x changes, then we have:

[tex]Rate = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]\rm when \: x=x_1, y = y_1\\when\: x = x_2, y= y_2[/tex]

Note that, we divide by the change in independent variable so that we get some idea of how much the dependent quantity changes as we change the independent quantity by 1 unit.

We are given the parameters as;

Constant Rate of Change: 2/3

Initial Value:10

Since we know that linear relation between x and y is y = m x + b, where

m is the rate of change

b is the initial value

Therefore,

y = 2/3x + 10

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The best estimate for the blue shark population would be = 234.

The total number of blue sharks that was tagged and released = 36 blue sharks.

The total number of sharks that the government corral = 130.

The number of sharks among the corral sharks that are tagged = 20

Since 130 = 20

X. = 36

Make X the subject of formula;

X = 130× 36/20

= 468/20

= 234.

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0.156 is the  unit rate games per loss.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Plug in the values from the table to the above formula.

Slope is nothing but rate of change.

m=17-12/68-36

m=5/32

m=0.156

Hence, 0.156 is the unit rate games per loss.

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Using algebraic expression, the semiannual property tax bill is (x * a / 1000) / 2

The semiannual property tax bill can be expressed algebraically as:

Semiannual Property Tax Bill = (Assessed Value * Annual Property Tax Rate / 1000) / 2

Where x is the assessed value and a is the annual property tax rate in dollars per $1,000 of assessed value.

So, the equation can be written as:

Semiannual Property Tax Bill = (x * a / 1000) / 2

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The remainder spent on phone cards is $187.2

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

Amount = $360

He spends ½ on lunch, and a %4 on transportation

The remainder spent on phone cards is calculated as

Phone cards = (1 - 1/2 - 4%) * 360

Evaluate the product

Phone cards = 187.2

Hence, the amount is $187.2

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1. line parallel to given line is:  y = 5/3 x + 2

2.  

parallel line becomes: y = 1/2x - 6

perpendicular line becomes: y = - 2x + 14

Slope intercept form is a method of formulating an equation for a line in the form y = mx + b in mathematics. The b stands in for the line's y-intercept, while the m denotes the line's slope. In order to identify a point on a line or to solve for y given an input of x, the slope intercept form is utilised. A straight line's slope and the location of its y-axis intersection are utilized to get the general equation of the line using the slope intercept equation. y = mx + b is the formula for the slope intercept.

1.

3y - 5x = 15

or, 3y = 5x + 15

or, y = 5/3 x + 5

This is slope intercept form of line.

Thus, slope (m) = 5/3

Parallel lines have same slope. Thus, all lines having slope m = 5/3 will be parallel to each other.

Thus, example of line parallel to given line is:  y = 5/3 x + 2

2.

for parallel line:

Given that,

y = 1/2x - 4

The slope intercept form of line is: y = mx + b

goes through the point (8, -2)

now comparing these two equations we get:

y = 1/2x + b

or, -2 = 1/2 (8) + b

or, b = - 6

thus, parallel line becomes: y = 1/2x - 6

for perpendicular line:

y = 1/2x - 4

as we know, m₁ = - 1/m₂

so, slope becomes: - 2

Thus, y = mx + b

after putting the point (8, -2) we get the value of b:

-2 = -2 (8) + b

or, b = 14

Thus, perpendicular line becomes: y = - 2x + 14

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The value of x, y, and z for the train and number of passengers are 0, -32, and 32 respectively.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

The total number of trains are 20. This is represented as:

x + y + z = 0  

The accommodation of passengers is represented as:

2x + 3y + 5z = 64......(2)

During market day the train used is:

3x + 2y + 4z = 64.......(3)

Multiply the equation 2 with 3 and equation 3 with 2:

6x + 9y + 15z = 192

6x + 4y + 8z = 128

Subtract the two equations:

5y + 7z = 64..........(4)

Multiply the first equation by 2:

2x + 2y + 2z = 0

2x + 3y + 5z = 64.

Subtract the two equations:

-y - 3z = -64

y + 3z = 64..........(5)

Multiply the equation 5 by 5.

5y + 15z = 320

5y + 7z = 64

Subtract the two equations:

8z = 256

z = 32

Substitute the value of z in equation 5:

y + 3z = 64.

y + 3(32) = 64

y + 96 = 64

y = - 32

Using equation 1:

x + y + z = 0

x - 32 + 32 = 0

x = 0

Hence, the value of x, y, and z are 0, -32, and 32 respectively.

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the equation of the line tangent to the curve y at x = 3 is y = 36x - 102.  The slope of the tangent line to the curve y at x = 3 is 36.

The equation of the line tangent to the curve y at x = 3 can be written using the point-slope form of a line, which is:

y - y1 = m(x - x1)

where m is the slope of the line, (x1, y1) is a point on the line, and m and (x1, y1) are known. In this case, m = 36 and (x1, y1) = (3, y). Substituting these values into the equation above, we get:

y - y = 36(x - 3)

y = 36x - 102

So the equation of the line tangent to the curve y at x = 3 is

y = 36x - 102.

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first we have to make a common denominator

then we just add or subtract depends on the sign

last (optional) i just used a calculator to see approximately what will the asnwer be

The initial value problem (2x - y) + (2y - x)y' = 0, y(1) = 3 has the particular solution y = -x²/2 + 2x + 1/2, and is valid for all x except for x = 2y.

An initial value problem is a differential equation that is given with an initial condition, which is a specific value for the solution of the equation at a particular point.

Problem 9 and 10 involve solving the same initial value problem: (2x - y) + (2y - x)y' = 0, y(1) = 3. To solve this initial value problem, we must find the general solution to the differential equation and then use the initial condition to determine the particular solution.

First, we must find the general solution to the differential equation (2x - y) + (2y - x)y' = 0. We can rearrange the equation to get (2y - x)y' + (2x - y) = 0. This is a separable differential equation, so we can separate the variables and integrate both sides to get:

y' = -(2x - y)/(2y - x)

∫(y')dy = -∫(2x - y)/(2y - x)dx

y = -x²/2 + 2x + C

Where C is an arbitrary constant of integration. To find the particular solution, we can use the initial condition y(1) = 3. We can substitute this into the general solution to find the value of C:

3 = -1/2 + 2 + C

C = 3 + 1/2 - 2 = 1/2

So the particular solution is y = -x²/2 + 2x + 1/2. This solution is valid for all values of x such that 2y - x ≠ 0, which means that the solution cannot be evaluated for x = 2y. This is because the denominator in the differential equation would be zero, which would make the equation undefined.

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The x- and y-intercepts of the graph of the function f(x) = −4|x + 3| + 8 are as follows;

x-intercepts = -5 and -1.

y-intercept = -4.

In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

In Mathematics, the y-intercept is sometimes referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

In this exercise, we would use an online graphing calculator to plot the linear function in order to determine the x-intercepts and y-intercepts as shown in the image attached below.

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The slope of the line is -3/2

Th general formula for the equation of a line is expressed as;

y = mx + c

Given that the parameters are given as;

The slope of the line is given as;

Slope, m = y₂ - y/x₂ - x₁

Substitute the coordinates, we have;

Slope, m = 5 - 2/-3 --1

Subtract the values

Slope. m = 3/-2

Hence, the value is -3/2

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The government has decided to veto the most recent welfare reform legislation. Working mothers, who would be required to work only twenty hours per week will have to adapt rather than the current requirement of thirty.

A relative clause, also known as an adjective clause, is a type of dependent clause that serves to describe a noun in a sentence. Even though it is made up of several words rather than just one, it functions as an adjective. All of the words in an adjective clause work together to modify the noun or pronoun.

The adjective clauses in a sentence are dependent clauses, which are a group of words that consist of a subject and a verb, but it is not a complete sentence that can stand alone. They usually begin with a relative pronoun, but it can be omitted, and they come after the noun they describe.

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Answer:

the different materials affect the textures and the feel of the surface.

Part (a)

Reason:

The car loses 15% of its value in one year. It keeps the remaining 85% (since 100-15 = 85).

The 85% then converts to the decimal form 0.85

=================================================

Part (b)

Reason:

The exponential equation shown in bold above is of the form

y = a*b^x

where,

==================================================

Part (c)

Work Shown:

y = 25000*(0.85)^x

y = 25000*(0.85)^10

y = 25000*0.19687440434072

y = 4921.86010851808

y = 4921.86

Answer:

To calculate the percentage change when a price of £40 is increased to £70, we can use the following formula:

Percentage Change = (New Value - Old Value) / Old Value * 100

Plugging in the numbers:

Percentage Change = (£70 - £40) / £40 * 100 = £30 / £40 * 100 = 75%

So the price has increased by 75%.

The acceleration needs to for a 5kg hammer to create a force of 10N is 2 m / s².

Acceleration of any object is defined as the variation in the speed of the object with the variation of time. Acceleration is a vector term and to define it we require both the magnitude and the direction. The unit of acceleration can be m / sec², miles / sec², etc.

Given that the weight is 5 kg and the force applied is 10N. The acceleration will be calculated as below,

Force =  Mass x Acceleration

Acceleration = Force / Mass

Acceleration = 10 / 5

Acceleration = 2 m/ s²

Therefore, the acceleration will be 2 m/ s².

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The equilibrium point for the market is reached when the number of units is 955 and the price is $82.8.

What is meant by the equilibrium of supply and demand?

The only price at which consumer and producer desires coincide is equilibrium, or when the quantity of the good that consumers want to buy equals the quantity that producers want to sell.

The equilibrium quantity is the amount that both parties seek equally. Any other price causes the market to be out of equilibrium since the amount requested does not match the quantity supplied. On a graph, the equilibrium is represented by the intersection of the supply and demand curves (S and D).

Given,

 Demand equation for a cordless screwdriver: p = 91.4 -0.009x

Supply equation for the cordless screwdriver:  p=6.4+0.08x

where,

  p = price in dollars

 x = number of units

The equilibrium point for this market is

 demand = supply

91.4 -0.009x = 6.4+0.08x

 85 = 0.089x

x = 955 units

Price = 6.4 + 0.08 * 955 = $82.8

The equilibrium point for the market is reached when the number of units is 955 and the price is $82.8.

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Answer:

5×5=25-10=15&$%#%$%%^/<=^$^$

The reason that best supports Statement 7 in the given proof is given as follows:

D. Subtraction property of equality.

The statement 6 in the proof is given as follows:

132 + m < C = 180º.

Then the statement 7 is defined as follows:

m < C = 48º.

The angle measure of 48º was obtained subtracting 180 by 132, which was done to isolate the angle measure of C, which we did subtracting both sides of the equality by 132.

This is the subtraction property of equality, hence the correct option is given by option D.

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Answer is a = 1000.

[tex]a-0.15a=850[/tex]

[tex]a(\frac{a}{a} -\frac{0.15a}{a}) =850\\ \\a(1-0.15)=850[/tex]

[tex]\frac{a(1-0.15)}{(1-0.15)} =\frac{850}{(1-0.15)} \\ \\a=\frac{850}{(1-0.15)}\\ \\a=1000[/tex]

If this answer is correct, substituting "a" by the calculated value "1000" in the original equation should return a true statement. Let's test it.

[tex](1000)-0.15(1000)=850\\ \\[/tex]

That's correct. Our answer is a = 1000!

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The rate of interest that Gordon paid using the ordinary interest method is 9.63%.

The ordinary interest method is based on 360 days instead of 365 days.

The rate of interest based on the ordinary interest method uses the same formula as the rate of interest based on the 365 days calendar method.

Principal amount of loan = $600

Interest for 90 days = $14.25

Rate of interest = R

R = (Interest x 100)/(Principal x Time)

= $14.25 x 100 x 360/($600 x 90

= $513,000/$54,000

= 9.5%

Thus, the rate of interest paid by Gordon for borrowing $600 from the bank and paying $14.25 for 90 days is 9.5%.

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