find the slope of this line

Answer:

[tex]\textsf{1.} \quad a_n=174-6n[/tex]

[tex]\textsf{2.\;a)} \quad A=5000\left(1.019\right)^{4t}[/tex]

   b)  9.25 years (to the nearest quarter)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8 cm}\underline{General form of an arithmetic sequence}\\\\$a_n=a+(n-1)d$\\\\where:\\\phantom{ww}$\bullet$ $a_n$ is the nth term. \\ \phantom{ww}$\bullet$ $a$ is the first term.\\\phantom{ww}$\bullet$ $d$ is the common difference between terms.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

Given terms of an arithmetic sequence:

Substitute the given values into the arithmetic sequence formula to create two equations:

[tex]\implies a_{28}=a+27d=6[/tex]

[tex]\implies a_{22}=a+21d=42[/tex]

Subtract the second equation from the first equation to eliminate a and solve for d:

[tex]\implies 6d=-36[/tex]

[tex]\implies d=-6[/tex]

Substitute the found value of d into one of the equations and solve for a:

[tex]\implies a+27(-6)=6[/tex]

[tex]\implies a-162=6[/tex]

[tex]\implies a=168[/tex]

Substitute the found values of a and d into the formula to create an equation for the nth term of the sequence:

[tex]\implies a_n=168+(n-1)(-6)[/tex]

[tex]\implies a_n=168-6n+6[/tex]

[tex]\implies a_n=174-6n[/tex]

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given values:

Substitute the given values into the compound interest formula to create an equation with respect to time, t:

[tex]\implies A=5000\left(1+\dfrac{0.076}{4}\right)^{4t}[/tex]

[tex]\implies A=5000\left(1.019\right)^{4t}[/tex]

To find when the value of the investment will be worth more than $10,000, substitute A = 10000 into the equation:

[tex]\implies 10000 < 5000\left(1.019\right)^{4t}[/tex]

[tex]\implies 2 < \left(1.019\right)^{4t}[/tex]

[tex]\implies \ln 2 < \ln\left(1.019\right)^{4t}[/tex]

[tex]\implies \ln 2 < 4t\ln\left(1.019\right)[/tex]

[tex]\implies \dfrac{\ln 2}{4 \ln\left(1.019\right)} < t[/tex]

[tex]\implies t > 9.20672924...[/tex]

Therefore, the investment will be worth more than $10,000 from 9.25 years (to the nearest quarter).

Options options A, B, D and F prove the triangle ABC is similar to triangle QRS by the side-angle-side similarity theorem.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

Given that, triangle ABC is similar to triangle QRS by the side-angle-side similarity theorem.

A) AB/QR=BC/RS (Corresponding sides are in ratio)

B) ∠C≅∠S (Corresponding angles are equal)

D) AB/QR =AC/QS (Corresponding sides are in ratio)

F) ∠A≅∠Q (Corresponding angles are equal)

Therefore, options A, B, D and F are correct answers.

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Answer:

It would have changed by 25 dollars.

So on solving the provided question we can say that here, in triangle ABC and XYZ;  by SSS property they are similar.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here,

AB = XY

AC = XZ

BC = ZY

by SSS property, they are similar.

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Answer:

42, 50, 60

Step-by-step explanation:

42 is less than or equal to y.

That means y is greater than or equal to 42.

Answer: 42, 50, 60

Domain of  y=|x-4|-2 : (-∞, ∞) by -∞ < x < ∞

Range of y=|x-4|-2: [-2, ∞) by F(x) ≥ -2

When a function is applied to its entire set of outputs, the set of outputs it produces is known as its range. The set of things that really leave the function machine after you give it all the inputs is referred to as the range in the metaphor. The set of possible output values for a function is its range.

The range of values that can be plugged into a function is known as its domain. The x values for a function like f are contained in this collection (x). The collection of numbers that the function assumes is known as its range. Following the insertion of an x value, the function outputs this sequence of values.

Domain of  y=|x-4|-2 : (-∞, ∞) by -∞ < x < ∞

Range of y=|x-4|-2: [-2, ∞) by F(x) ≥ -2

Axis interception points of |x - 4| - 2:

X Intercepts: (2, 0), (6, 0), Y Intercepts: (0, 2)

Asymptotes of |x - 4| - 2 : None

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Result is x = - 2 and y = 1.6 so the ordered pair ( -2, 1.6) is the solution of the system equations.

It is a mathematical expression that shows the equalities between two or more terms. There are different types of equation such as linear equation, quadratic equation, exponential equation and so on.

Given, the two systems of equation.

y = - 0.5x + 0.6

and y = x + 3³₅

rewrite the second equation and get y = x +18/5

                                                       5y = 5x + 18 ....  equation 2

                   the first equation is multiplied by 5 and we get.

                                               5y = - 2.5 x + 3

                                               5y = 5x +18

                                            -          -     -

                        we will now solve the above equations by addition method.

                                       0 = - 7.5 x - 15

                                    7.5 x = - 15

                                     x = -2

        putting the value of x in any equation, we get the value of y = 1.6

    x = - 2 and y =1.6

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As a result, if [f(x) is (x)], then the equation [y is f(-x + 2)] defines the graphed function.

[y = f(-x + 2)] is the equation that describes the graphed function.

As stated in the question, a reference graph diagram and details on the function f(x), which equals the square root of "x," are given.

From the four possibilities provided, we are expected to select the equation that best explains the graphed function.

We will employ the trial-and-error approach to this problem, employing the possibilities to identify the best solution.

First off, the graph's x-axis and y-axis are both broken at (4, 0) and respectively (0, 2). As a result, [y = f(x)] requires that our equation be equal to 0 when (x = 4) is replaced and to 2 when (x = 0).

Taking into account option (A), we obtain, by substituting (x = 4) for (y = f[(- x) + 4] = sqrt[(- x) + 4]

y = sqrt[(- 4) + 4]

furthermore, y = sqrt (4 - 4)

furthermore, y = sqrt (0)

or, y = 0

The result of replacing (x = 0) is y= [(-0)+4]

or y = sqrt(4) or y = 2 or y = (4-0)

As a result, option (A) is satisfied at locations (4, 0) and (0, 2).

Similar results may be obtained for the other three possibilities by substituting and checking: for (x = 4), (y 0), and for (x = 0), (y 2).

As a result, if [f(x) = (x)], then the equation [y = f(-x + 2)] defines the graphed function.

A function in mathematics is an operator that, given an input, will carry out a predetermined series of operations.

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Answer:

<d=102°[Vertically opposite angles are equal]

<e=36°[Vertically opposite angles are equal]

<d+<f+<e=180°[Sum of angle on St.line supplementary]

or,102°+36°+<f=180°

or,<f=180°-102°-36°

:.<f=42°

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If a client of Kurtis's opens an account that earns 6% compounded annually and deposits $4,000 initially with additional deposits of $4,000 each year for 5 years, the account's balance (future value) will be $27,901.27.

The future value is the amount of the present investments compounded into the future at an interest rate.

The future value can be determined using an online finance calculator as follows:

N (# of periods) = 5 years

I/Y (Interest per year) = 6%

PV (Present Value) = $4,000

PMT (Periodic Payment) = $4,000

Results:

Future Value (FV) = $27,901.27

Sum of all periodic payments = $20,000 ($4,000 x 5)

Total Interest = $3,901.27

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Answer:

$22,548

Step-by-step explanation:

Option D is correct, [tex](\frac{1}{512}) ^{\frac{1}{3} }[/tex] is equivalent to [tex](\frac{1}{64}) ^{\frac{1}{2} }[/tex]

An expression is combination of variables, numbers and operators.

Let us simplify using [tex]a^{\frac{n}{m} } =\sqrt[m]{a^{n} } :\sqrt[3]{\frac{1}{512} }[/tex]

Rewrite the expression using [tex]\sqrt[n]{ab} =\sqrt[n]{a} .\sqrt[n]{b} :\frac{1}{\sqrt[3]{512} }[/tex]

Factor and rewrite the radicand in exponential form :1/8

simplify using [tex]a^{\frac{n}{m} } =\sqrt[m]{a^{n} } :\sqrt{\frac{1}{64} }[/tex]

Rewrite their expression using  [tex]\sqrt[n]{ab} =\sqrt[n]{a}.\sqrt[n]{b} :\frac{1}{\sqrt{64} }[/tex]

Factor and rewrite the radicand in exponential form : 1/8

Hence, option D is correct, [tex](\frac{1}{512}) ^{\frac{1}{3} }[/tex] is equivalent to [tex](\frac{1}{64}) ^{\frac{1}{2} }[/tex]

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Answer:

[tex]\frac{15}{16}[/tex]

Step-by-step explanation:

We will use the rule of KCF (Keep, Change, Flip) to solve a problem where a fraction divides by a fraction. We will start out with our original expression:

[tex]\frac{5}{8} / \frac{2}{3}[/tex]

Then, we will keep the first number, change the division sign to multiplication, and flip the last fraction, giving us:

[tex]\frac{5}{8} * \frac{3}{2}[/tex]

Then, you multiply the numerators and denominators, giving you:

[tex]\frac{15}{16}[/tex]

Then, you cannot simplify further. So, your answer is [tex]\frac{15}{16}[/tex].

Hope this helped!

Therefore , the solution of the given problem of order comes out to be

1/8 < 1/6 < 2/3 < 10 .

Thus putting things where they belong in accordance with some norm. The shapes in this image are arranged according to how many sides it have. Another illustration is to sort the integers 3, 12, 5, 2, and 9 from highest through lowest.

Here,

Given :

2/3 , 1/6 . 1/8 and 10

So ,

To form a proper order from least to greatest

Thus , ascending order:

So,

=> 1/8 < 1/6 < 2/3 < 10

Therefore , the solution of the given problem of order comes out to be

1/8 < 1/6 < 2/3 < 10 .

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The linear function f with the given values is y = -2x + 5

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

a slope of -2 and a y-intercept of 5

A linear equation can be represented as

f(x) = mx + c

Where

m = slope

c = y-intercept

This means that

m = -2

c = 5

Substitute the known values in the above equation, so, we have the following representation

y = -2x + 5

Hence, the function is y = -2x + 5

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The numerator for the following rational expression G/h + 8/h = ?/h will be g + 8.

Simply put, a rational expression is the product of two polynomials. Or to put it another way, it is a fraction with polynomials as the numerator and denominator. A function whose value is determined by a rational expression is said to be rational.

Rational expressions resemble fractions with variable denominators and frequently, numerators as well. As you can see, there is h is denominator on both right hand side and left hand side. So, you can eliminate it and can consider all numerators as a whole at a time. Then, it will be: G+8 = G+8

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Complete question

What's the numerator for the following rational expression? G/h + 8/h = ?/h

The other two sides of the triangle are 2.795 and 4.095 respectively.

Generally, The right triangle is a right-angled triangle where one angle is 90 degrees.

If the hypotenuse is 5 and one acute angle is 34°, we can use trigonometry to find the other two sides of the triangle.

Using sine function, the side opposite to 34° angle is

=(sin 34°) * hypotenuse

= 0.559 * 5

= 2.7959

Using cosine function, the side adjacent to 34° angle is (cos 34°) * hypotenuse = 0.819 * 5

= 4.095

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From the graph, a possible solution to the inequalities x + y ≥ 16 and 0.01x + 0.05y ≤ 0.4 is (15, 2)

An equation shows how two or more numbers and variables are related to each other.

Let x represent the number of pennies and y represent the number of nickels. One penny = $0.01 and one nickel = $0.05

She has a minimum of 16 coins, hence:

x + y ≥ 16     (1)

Also:

It is no more than $0.40 combined, hence:

0.01x + 0.05y ≤ 0.4    (2)

From the graph, a possible solution is (15, 2)

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Dividing 3x³ - 4x² - 9x + 15 by 3x + 5. will yield a quotient of x² - 3x + 2 and a remainder of 5 that is (x² - 3x + 2) + 5/(3x + 5).

Applying the long division method will require us to; divide, multiply, subtract, bring down the next number and repeat the process to end at zero or arrive at a remainder.

We shall divide the 3x³ - 4x² - 9x + 15 by 3x + 5 as follows;

3x³ divided by 3x equals x²

3x + 5 multiplied by x² equals 3x³ + 5x²

subtract 3x³ + 5x² from 3x³ - 4x² - 9x + 15 will result to -9x² - 9x + 15

-9x³ divided by 3x equals -3x

3x + 5 multiplied by -3x equals -9x² - 15x

subtract -9x² - 15x from -9x² - 9x + 15 will result to 6x + 15

6x divided by 3x equals 2

3x + 5 multiplied by 2 equals 6x + 10

subtract 6x + 10 from 6x + 15 will result to a remainder of 5

Therefore by the long division method, 3x³ - 4x² - 9x + 15 by 3x + 5 gives a quotient x² - 3x + 2 and a remainder of 5 and can be written as (x² - 3x + 2) + 5/(3x + 5).

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Because its a 1 in 6 chance to roll a five and a 1 in 4 chance to roll a yellow then you do 6 x 4 = 24.

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Answer:

B,D,E

Step-by-step explanation:

Those should be you're answers

Answer:

Maths

Step-by-step explanation:

Maths

Maths is a great way to get a job and then she can u me a little more about it and let me know if maths is a good fit for me and I can make it work for you

Answer is:

Step-by-step explanation:

6

The absolute value will be used over distance coordinate formula when the line is parallel to either the y-axis or x-axis.

The common formula to find the distance between two coordinates is expressed as;

D = √[(x₂ - x₁)² + (y₂ - y₁)²]

Now, this formula is very useful when the two coordinates don't have their x coordinates equal or y coordinates equal and when the line is parallel to either the y axis or x axis.

When we have a case where the line is parallel to wither the y or x axis, then it is pertinent to note that if one coordinate is negative and the other is positive, we know that opposites have the same distance from zero, hence have the same absolute value.

Thus, we can find the absolute value to get the length.

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Answer:

You graph them.

Go to desmos and put the equations in the calculator. It will graph them for you. Or you could graph them on paper, like the y-intercept is the amount you start with, like 11 or 2 in question 3. then you go two up and one to the side or 1 up and one to the side, depending on how many x there is. or how much the slope is. Like y=x+2 is where you start with (0,2) plot it and then you go one up, one to the side, and then repeat twice. Then plot the line. and in y=11-2x you plot (0,11) and then go down two, one to the side, and repeat twice. Then plot the line.

In question 4, y=3-2x, plot point (0,3) and then go two down, one to the side, and repeat twice. Plot the line. in y=1+2x, plot point (0,1) and then go two up, one to the side.

that's how you plot the slope equation.

Step-by-step explanation:

The product of each addend times the third number (7 x 9 = 63) is the sum of two numbers multiplied by a third number.

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The correct answer is true, When using the simple interest formula the time t, is expressed in the same period as the rate.

We can say that the answer is true due to the following reasons,

As we already know, the formula for simple interest is:

Simple Interest = Principal Amount * Rate of Interest * Time of interest

Here the Principal amount is the amount that is deposited and over which we will be receiving our interest.

We all know the rudimentary rule of solving any question is that the units and dimensions of the variables and values should be correct. It means that when we are solving any question where the unit being used is different from the required one, we need to perform unit conversion to get the necessary unit.

When it comes to Simple Interest, the variable unit is time, that is, it can be in hours, days, weeks, months, or years. The rate of interest is generally given in "per annum" which means 'per year.' Therefore we need the unit of time in the year or according to the unit in which rate is given to us.

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Answer:

y = (2/5)x - 3

Step-by-step explanation:

Brainliest pls

Answer: y = mx + b

y=-3  x=0 and m=2/5

-3 = (2/5)0 + b

Since 2/5(0) is 0, b must be -3

Step-by-step explanation: Since you know the slope and you know one point, all you have to do is plug the slope and the coordinates into the slope-intercept form and solve for b. You can check your answer by finding another point on the line and verifying that the equation works for that point, as well. Add the slope to the given point and you get ( 5 , -1 )

-1 = (2/5)5 - 3

-1 = 2 - 3 -1 = -1 So you know your answer is correct

Answer:

Step-by-step explanation:

9.5

Darren makes $210.83 monthly payments over a period of 5 years. Therefore, option D is the correct answer.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time.

Given that, principal =$11,000, rate of interest =3% and time period = 5 years.

Now, S.I. =(11,000×3×5)/100

= $1650

Now, 11,000+1650 =$12650

In 5 years there are 60 months

So, 12650/60

= $210.83

Therefore, option D is the correct answer.

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The expression which represents the total cost of renting is C = nx.

What is an expression?

An expression is a mathematical phrase that can contain numbers, variables, and operators. It represents a value or a calculation, but it does not necessarily have an equal sign (=) to indicate that it is an equation.

Let us consider that, renting a Canoe for one hour is  $ x.

The total cost of renting is represented by C.

Since renting a Canoe for one hour is  $ x.

So that, for n hours, renting cost  = n*x

The total cost of renting, C= nx

Hence, the expression which represents the total cost of renting is C = nx.

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