1 5/6= 1/2x+1 solve for x

Transformed equation for f(x)-5 is the function h(x)=2x-4.

A functional equation in mathematics is, broadly speaking, an equation that has one or more functions as variable. A functional equation, however, is frequently used in a more narrow sense, where it refers to an equation that connects many values of the same function.

An equation that transforms into another equation and has roots that are the opposite of those in the given equation is said to be a transformation. To grasp the transformation equation, this transformation process must be made easy.

f(x)=2x+1

Transforming the function f(x)-5, we get

h(x)=2x+1-5

h(x)=2x-4

h(x) is a function which is made by shifting f(x) 5 units downward.

Hence, transformed equation for f(x)-5 is h(x)=2x-4.

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The value of p(3) is p(3)=12.

Here, we have,

Synthetic division :

It is a shorthand method of dividing polynomials for the special case of dividing by a linear factor whose leading coefficient is 1.

The given function is,

p(z)=8z⁴-17z³-20z²-4z+15                  

We have to find  p(3)  

Substitute z= 3 in above function.

p(3)=8×3⁴-17×3³-20×3²-4×3+15                

     =12      

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Answer: a ticket to an amusement park is $100 per person. you have a coupon for $20 off of the admission price. the amusement park is also having a promotion where if you bring an empty pepsi can you can take an additional $4 off of the total admission cost. how much do you have to pay to be admitted to the amusement park after the coupons? (it would be $76)

Step-by-step explanation: my brain thought this up

Answer:

Step-by-step explanation:

Mikes mom gave him 100 dollars to spend and his favorite toy shop. Mike bought a Lego set which cost him 20 dollars. When he bought a lollipop which cost him 4 dollars.

The formula for the exponential function passing through the points (-2,768) and (2, 3) is:

[tex]y = 48 \times ((3/768)^{1/4})^x[/tex]

We have,

To find a formula for the exponential function passing through the points (-2, 768) and (2, 3), we can use the general form of an exponential function: y = a x [tex]b^x[/tex], where "a" is the initial value or y-intercept, and "b" is the base of the exponential function.

Let's start with the first point (-2, 768).

Plugging in the values, we have:

768 = a x [tex]b^{-2}[/tex]

Next, let's consider the second point (2, 3).

Plugging in the values, we have:

3 = a x b²

Now we have a system of equations:

768 = a x [tex]b^{-2}[/tex]

3 = a x b²

To solve this system, we can divide the second equation by the first equation:

3/768 = (a x b²) / (a x [tex]b^{-2}[/tex])

Simplifying further:

3/768 = [tex]b^4[/tex]

Taking the fourth root of both sides:

[tex](b^4)^{1/4} = (3/768)^{1/4}\\b = (3/768)^{1/4}[/tex]

Now we can substitute the value of b back into either of the original equations to solve for a.

Let's use the first equation:

[tex]768 = a \times b^{-2}[/tex]

Substituting [tex]b = (3/768)^{1/4}:[/tex]

[tex]768 = a \times ((3/768)^{1/4})^{-2}[/tex]

Simplifying:

[tex]768 = a \times (3/768)^{-1/2}[/tex]

Now, we can simplify the right-hand side:

[tex]768 = a \tmes (768/3)^{1/2}[/tex]

Simplifying further:

[tex]768 = a \times (256)^{1/2}[/tex]

Taking the square root of 256:

768 = a x 16

Solving for a:

a = 768 / 16 = 48

Therefore,

The formula for the exponential function passing through the points (-2,768) and (2, 3) is:

[tex]y = 48 \times ((3/768)^{1/4})^x[/tex]

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Step-by-step explanation:

If Kneaders in Lehi sold 4000 rolls last year and expects a 22% increase in sales this year, the number of rolls they will bake this Thanksgiving can be calculated as follows:

Calculate the 22% increase in sales:

22% of 4000 = 0.22 x 4000 = 880

Add the increase to last year's sales to get the total expected sales this year:

4000 + 880 = 4880

Therefore, Kneaders in Lehi will bake approximately 4880 rolls this Thanksgiving rounded to the nearest whole roll.

Answer:

4,880 rolls, see explanation below :)

Step-by-step explanation:

1.22(4000)= 4,880

and you instantly get your answer.

if you don't understand I basically did 1.22 times 4000 and got 4,880.

Formula: X + %increase/decrease x orginal amount/amount sold last year of rolls, (we can assume there is an invisible 1 in front of the x)

Basically Everything Behind This, Kind of (sorry I'm not the best explainer! :( ;

Here in this case 22% as a decimal is 0.22, how we get to a decimal from a percent: 22 divided by a 100= 0.22. and we got the decimal for 22%!

So X + 0.22= 1.22, and remember the X has an invisible 1 in front of it. so 1 + 0.22= 1.22 in other words.

Now the other value we have is 4000, so we multiply it by 1.22 and get 4,880. And this is how we got to our answer.

1. HP price for Susie is R 282600 and David is R 179300

2. The difference between the total price paid by Susie and David  is R 103300

3. The interest that Susie and David have to pay as a percentage of the cash price​ is 117.38% and 37.92%

The HP price, also known as the hire purchase price, is the total amount that a buyer pays for a product when purchasing it through a hire purchase agreement.

It includes the cash price of the product plus any interest and fees charged by the lender.

Here we have

3.1.1, For Susie:

The cash price of the car is R 130000.

She pays a 10% deposit, which is:

= [10/100] × 130000 = R 13000

=> HP price =  the cash price - the deposit

=>  130000 -  13000 = R 117000

She will pay monthly installments of R 4600 for 3 years,

which is 36 months.

Therefore, the total amount she will pay is:

36 x 4600 = R 165600

Therefore, the total amount she will pay is R 165600

The HP price for Susie is,  

117000 + 165600 = R 282600

For David:

The cash price of the car is R 130000. He pays a 35% deposit, which is:

=> [ 35/100] × 130000 = R 45500

The HP price = 130000 - 45500 = 84500

He will pay monthly installments of R 3950 for 2 years, which is 24 months. Therefore, the total amount he will pay is:

24 × 3950 = 94800

The HP price for David is, therefore:

=> 84500 + 94800 = R 179300

3.1.2, The difference between the total price paid by Susie and by David  

=  282600 - 179300 = R 103300

3.1.3

For Susie:

The total interest she has to pay is the difference between the HP price and the cash price, which is:

=> 282600 - 130000 = R 152600

The interest rate as a percentage of the cash price is:

=> (152600/130000) × 100% = 117.38%

For David:

The total interest he has to pay is the difference between the HP price and the cash price, which is:

=> 179 300 - 130 000 = R 49 300

The interest rate as a percentage of the cash price is:

=> (49 300/130000) × 100% = 37.92%

Therefore,

1. HP price for Susie is R 282600 and David is R 179300

2. The difference between the total price paid by Susie and David  is R 103300

3. The interest that Susie and David have to pay as a percentage of the cash price​ is 117.38% and 37.92%

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Answer:

acute

Step-by-step explanation:

9 is bigger than 6

12 is bigger than 9

therefore all the angles will be smaller than a right angle

this makes the triangle acute

The solution to the system of equations is [tex]x = -3/4 $ and $ y = -3^{1/2}.[/tex] The solution has been obtained by using substitution method.

What is substitution method?

The substitution approach is one approach of solving equation problems. To use the substitution method, obtain an expression for one variable in terms of the second variable using one equation. Replace that variable with that expression in the second equation after that.

We are given system of equations as:

y = -2x - 5

y = 2x - 2

Now, by using the substitution method, we get

⇒-2x - 5 = 2x - 2

⇒-4x = 3

⇒x = -3 / 4

On substituting the value of x in y = 2x - 2, we get

⇒y = 2(-3/4) - 2

⇒y = (-3/2) - 2

⇒y = -7/2

Hence, the solution to the system of equations is[tex]x = -3/4 $ and $ y = -3^{1/2}.[/tex]

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The simplified expression is [[3,0,6], [-4,-6,3], [-1,4,0]].

The given expression is [[-2,-2,4],[-6,-2,5],[-5,-1,5]] + [[5,2,2],[2,-4,-2],[4,5,-5]]. To simplify it, add the corresponding elements of each matrix:

[[-2,-2,4] + [5,2,2] = [3,0,6],
[-6,-2,5] + [2,-4,-2] = [-4,-6,3],
[-5,-1,5] + [4,5,-5] = [-1,4,0]]

Therefore, the simplified expression is [[3,0,6], [-4,-6,3], [-1,4,0]].

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Answer:

E(2,-4), F(8,0), and G(5,3).

Step-by-step explanation:

Reflection in the y-axis means the signs of the x-coordinates should be flipped.

Answer:

Answer A

Step-by-step explanation:

I know that you already have the answer, but I wanted to show you a picture.

The Cartesian equation of the curve is y = 0. This is a horizontal line at y = 0.

To find the Cartesian equation of the curve, we need to eliminate the parameter θ from the parametric equations.

First, let's rearrange the first equation to isolate θ:
2x = cotθ - cscθ
2x + cscθ = cotθ
cscθ - cotθ = -2x
1/(sinθ) - 1/(tanθ) = -2x
1/(sinθ) - (cosθ)/(sinθ) = -2x
(cosθ)/(sinθ) = 1/(sinθ) + 2x
cosθ = 1 + 2x*sinθ

Now, let's rearrange the second equation to isolate θ:
4y = 2cscθ - 2cotθ
2y = cscθ - cotθ
2y + cotθ = cscθ
cotθ - cscθ = -2y
1/(tanθ) - 1/(sinθ) = -2y
(cosθ)/(sinθ) - 1/(sinθ) = -2y
(cosθ)/(sinθ) = 1/(sinθ) - 2y
cosθ = 1 - 2y*sinθ

Now we can set the two equations equal to each other and solve for sinθ:
1 + 2x*sinθ = 1 - 2y*sinθ
4x*sinθ = -4y*sinθ
sinθ = -4y/4x
sinθ = -y/x

Finally, we can use the Pythagorean identity, sin^2θ + cos^2θ = 1, to find the Cartesian equation:
(-y/x)^2 + cos^2θ = 1
y^2/x^2 + cos^2θ = 1
cos^2θ = 1 - y^2/x^2
cosθ = √(1 - y^2/x^2)

Substituting this back into one of the original equations, we get:
1 + 2x*sinθ = 1 - 2y*sinθ
1 + 2x*(-y/x) = 1 - 2y*(-y/x)
1 - 2y^2/x = 1 + 2y^2/x
4y^2/x = 0
y^2 = 0
y = 0

So the Cartesian equation of the curve is y = 0. This is a horizontal line at y = 0.

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The mark down rate for the dress originally tagged at Php 5,220 but now being sold at Php 4,900 is 6.13%.

To calculate the mark down rate, use the formula:

Mark down rate = (Original Price - Discounted Price) / Original Price

Plugging in the numbers:

Mark down rate = (5,220 - 4,900) / 5,220 = 0.0613

To convert to a percentage, multiply 0.062 by 100 and you will get 6.13%.

Therefore, the mark down rate for the dress is 6.13%.

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The correct answer is (e) Between 890,000 and 900,000 people.

To find out how many people from this city will have a monthly income between £2,000 and £2,300, we need to use the z-score formula:

z = (x - μ) / σ

where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

First, we'll find the z-score for £2,000:

z = (2000 - 2075) / 162 = -0.46

Next, we'll find the z-score for £2,300:

z = (2300 - 2075) / 162 = 1.39

Using a z-table, we can find the corresponding probabilities for these z-scores. The probability for a z-score of -0.46 is 0.3228, and the probability for a z-score of 1.39 is 0.9177.

To find the probability of having a monthly income between £2,000 and £2,300, we need to subtract the smaller probability from the larger probability:

0.9177 - 0.3228 = 0.5949

This means that approximately 59.49% of the population will have a monthly income between £2,000 and £2,300. To find out how many people this represents, we'll multiply the probability by the total population:

0.5949 * 1,500,000 = 892,350

Therefore, the answer is (e) Between 890,000 and 900,000 people.

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Answer:

6969696969696969695969696966969696969696969699६9६9६9६959596869494982285959585868586868696959695968684828282828३8474747474848475757718१883757474839485747747474747474747474747484858384848485858587575757585848484848585857494857585958584858585858685969686(696066969686868696960

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{20})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{22}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{22}-\stackrel{y1}{20}}}{\underset{\textit{\large run}} {\underset{x_2}{-1}-\underset{x_1}{(-2)}}} \implies \cfrac{2}{-1 +2} \implies \cfrac{ 2 }{ 1 } \implies 2[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{20}=\stackrel{m}{ 2}(x-\stackrel{x_1}{(-2)}) \implies y -20 = 2 ( x +2) \\\\\\ y-2=2x+4\implies {\Large \begin{array}{llll} \end{array}} y=2x+6\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

The domain of a function is the set of all possible input values (x) for which the function is defined.

The range of a function is the set of all possible output values (f(x)) that the function can produce.

For the given function f(x) = 2^(x+1), the domain includes all real numbers because we can substitute any real number for x and obtain a valid output.

To find the range, we can examine the behavior of the function as x approaches positive and negative infinity. As x approaches negative infinity, the exponent (x+1) becomes very large negative number, and 2^(x+1) approaches zero. As x approaches positive infinity, the exponent (x+1) becomes very large positive number, and 2^(x+1) approaches infinity. Therefore, the range of the function is (0, infinity).

So, the domain is (-infinity, infinity) and the range is (0, infinity).

The measure of width of the computer is 75.89 inches.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

The ratio of a and b is denoted as a : b.

Given that,

Ratio of diagonal to length of a rectangular computer = 13 : 7

This means that,

If diagonal = 13k and length = 7k for some constant k.

Given Actual length = 18 inches.

3k = 18

k = 18/3 = 6

So Diagonal length = 13 × 6 = 78 inches

We know that, the length, width and diagonal of a rectangle form a right angled triangle.

Let width of the rectangular computer be x.

Using Pythagorean Theorem,

(Length)² + (Width)² = (Diagonal)²

18² + x² = 78²

x² = 78² - 18²

x² = 5760

x = 75.89 inches.

Hence the measure of width is 75.89 inches.

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Answer:

410=50x+10

Step-by-step explanation:

your total is 410 so to get there you have to know the number of nights which is x. the 10 is a one time fee so you only need that once and not per night.

Answer:

no it is not a trick question

Therefore, the probability that a randomly chosen product was prepared on preparation stations 6, 7, and 8 is 0.25, or 25%.

The probability that a randomly chosen product was prepared on preparation stations 6, 7, and 8 can be found using the formula:

P(event) = number of favorable outcomes / total number of possible outcomes

In this case, the number of favorable outcomes is 3, since there are 3 preparation stations that we are interested in (6, 7, and 8). The total number of possible outcomes is 12, since there are 12 preparation stations in total.

So, the probability that a randomly chosen product was prepared on preparation stations 6, 7, and 8 is:

P(event) = 3 / 12

P(event) = 0.25

Therefore, the probability that a randomly chosen product was prepared on preparation stations 6, 7, and 8 is 0.25, or 25%.

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The mode of the set {2, 5, 6, 8, 9, 11, 15} is the number that appears most frequently in the set. In this case, all of the numbers appear only once, so there is no mode.

The mode of a set of numbers is the value that appears most frequently in the set. To find the mode of the set {2, 5, 6, 8, 9, 11, 15}, we need to count how many times each number appears and then determine which number appears most frequently.

From the set, we can see that no number appears more than once. Therefore, there is no single number that appears most frequently and we cannot determine a mode for this set.

In some cases, a set of numbers may have multiple modes if two or more numbers appear with the same frequency. For example, the set {1, 2, 2, 3, 3, 3, 4, 5, 5} has two modes, 2 and 3, since both of these numbers appear three times in the set.

However, in the case of the set {2, 5, 6, 8, 9, 11, 15}, there are no repeating numbers, so there is no mode.

In conclusion, the mode of the set {2, 5, 6, 8, 9, 11, 15} is undefined as there are no repeating numbers in the set.

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By applying synthetic division concept, it can be concluded that if f(v) = 8v⁴ + 34v³ - 26v² + 21v + 11, then, f(-5) = 6.

Synthetic division is a shorthand way of dividing polynomials where we can divide the coefficients of the polynomial by omitting variables and exponents. As a result, we get the coefficient of the quotient and the remainder.

Polynomial remainder theorem states that the value of p in argument b is equal to the remainder of the polynomial division p(x) / (x - b). Specifically, p(x) is divided by x - b with a remainder of zero if, and only if, b is a root of p.

We have the following polynomial:

f(v) = 8v⁴ + 34v³ - 26v² + 21v + 11

To find f(-5) using synthetic division, we will divide the polynomial f(v) by (z + 5). The steps are as follows:

1. Put the coefficients in a row and multiply the outside coefficient by the divisor: 8(-5)= -40.

2. Add the inside coefficient to the product from the previous step: -40 + 34 = -6.

3. Multiply the result from the previous step by the divisor: -6(-5) = 30.

4. Add the next coefficient to the product from the previous step: 30 - 26 = 4.

5. Multiply the result from the previous step by the divisor: 4(-5) = -20.

6. Add the next coefficient to the product from the previous step: -20 + 21 = 1.

7. Multiply the result from the previous step by the divisor: 1(-5) = -5.

8. Add the last coefficient to the product from the previous step: -5 + 11 = 6.

The final result of the synthetic division is 6, so the answer to the question is f(-5) = 6.

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The value of function h(x)=5 at x tends to [tex]2^{+}[/tex] will be 5.

In mathematics, a functional equation is, in the broadest sense, an equation in which one or more functions appear as variable. A functional equation, however, is frequently used in a more narrow sense, where it refers to an equation that connects many values of the same function. For instance, the logarithmic functional equation effectively describes the logarithm functions.

log⁡(x×y)=log⁡(x)+log⁡(y).

lim h(x)=5 at x tends to [tex]2^{+}[/tex]

Given function is constant.

Value of function at x tends to [tex]2^{+}[/tex]will be 5

Hence, the value of h(x)=5 at x tends to [tex]2^{+}[/tex] will be 5

Graph of the given function is attached below;

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The correct statement regarding the domain and the range of the quadratic function are given as follows:

D. The domain is all real numbers, the range is y ≥ -4.

Hence, on a graph, the values are given as follows:

Meaning that option D is correct.

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Answer:

y = -43x - 175

Step-by-step explanation:

Slope-intercept form is y = mx + b

m = -43

x = -4

y = -3

-3 = -43(-4) + b

b + 172 = -3

b = -3 - 172 = -175

=> y = -43x - 175

The symbols, in accordance with the provided assertion, are 27 ÷ 3 + 5 × 2 = 19

A object must imply a meaning that is distinct from its true definition in order to be referred to as a symbol; a symbol is a thing that transcends class or type. A emblem might signify several different things.

The triple bar, also known as the tribar, or, is a sign that denotes the equality of two distinct objects and has a variety of context-dependent meanings. Logic and arithmetic are its two primary applications. It looks like a third line attached to an equals symbol (=).

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The probability of observing 2 heads is 1/4, the probability of observing 1 head is 2/4, and the probability of observing 0 heads is 1/4.

The question is asking what the probability of getting two heads (x=2) and one head (x=1) when tossing a coin.

The probability of getting two heads is P(x=2) = 1/4 and the probability of getting one head is P(x=1) = 2/4.

It is important to remember that the sum of all the probabilities in an experiment must equal 1.

In this case, P(x=2) + P(x=1) = 1/4 + 2/4 = 3/4. This means that the probability of observing 0 heads, represented as P(x=0), must be equal to 1/4 in order for the sum of all the probabilities to equal 1.

In conclusion, the variable x is used to represent the number of heads observed in a coin toss experiment, and the probabilities of observing different numbers of heads are given as fractions.

The probability of observing 2 heads is 1/4, the probability of observing 1 head is 2/4, and the probability of observing 0 heads is 1/4.

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7 / 15  is the probability that it will be orange. A marble drawing is a separate action. In other words, the results of drawing a marble will not be influenced by each other.

We must ascertain the sample space, the number of occurrences in the sample space, and the number of successful outcomes in order to calculate the necessary probability. The colour determines every consequence that can occur when drawing a marble. The total number of marbles is 15, including 7 orange and 8 blue. Hence, there are 7+5=15 elements in the sample space.

As we are interested in drawing an orange marble and returning the orange marble to the urn after each drawing, the number of favourable events, in this case, is 7. Due to their independence, past drawings won't have an impact on the most recent ones. The likelihood of an event P(A) = total outcomes / favourable outcomes can be used to define A as the ratio of the number of favourable outcomes to the number of total outcomes in the sample space.

Hence, the following is true for the event P(A₀)= total outcomes / favorable outcomes 7 / 15

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Three points that are equivalent to the polar point (7,40°) are (7,400°), (7,-320°), and (7,760°). These points are equivalent because they all have the same magnitude of 7, but their angles differ by multiples of 360°.

In polar form, these points are written as:
- (7,400°) = 7cis(400°)
- (7,-320°) = 7cis(-320°)
- (7,760°) = 7cis(760°)

These points are equivalent because the angle in polar coordinates is measured modulo 360°. This means that any angle that differs by a multiple of 360° will be equivalent. For example, 40° is equivalent to 400° because 400° - 40° = 360°. Similarly, -320° is equivalent to 40° because -320° + 360° = 40°, and 760° is equivalent to 40° because 760° - 720° = 40°.

In conclusion, the three points that are equivalent to the polar point (7,40°) are (7,400°), (7,-320°), and (7,760°), and they are written in polar form as 7cis(400°), 7cis(-320°), and 7cis(760°).

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