7 Describe the error in solving the equation
(1) 3 (X + 4) = 13
(2) 3x + 4 =13
(3) 3 x = 9
(14)X = 3

The non-real solutions of the polynomial expression are x = (1 + 2√-5)/3 and x = (1 - 2√-5)/3

The equation of the polynomial expression is given as:

3x5 + 25x4 + 26x3 – 82x2 + 76x = 48

Rewrite the equation as

3x^5 + 25x^4 + 26x^3 – 82x^2 + 76x - 48 = 0

The points on the graph are given as

(-6, 0), (-5, 500), (-2.5, -450), (0, - 50), (1, 0), (2, 400).

Write out the x-intercepts

(-6, 0) and (1, 0)

This means that

Real solution = -6

Real solution = 1

Rewrite the above as

x = -6 and x = 1

So, we have

x + 6 = 0 and x - 1 = 0

Multiply

(x + 6)(x - 1) = 0

The next step is to divide the polynomial equation 3x^5 + 25x^4 + 26x^3 – 82x^2 + 76x - 48 = 0 by (x + 6)(x - 1) = 0

This is represented as

3x^5 + 25x^4 + 26x^3 – 82x^2 + 76x - 48/(x + 6)(x - 1)

Using a graphing calculator, we have

3x^5 + 25x^4 + 26x^3 – 82x^2 + 76x - 48/(x + 6)(x - 1) = 3x^3 + 10x^2 - 6x + 8

So, we have

3x^3 + 10x^2 - 6x + 8

Factorize

(x + 4)(3x^2 - 2x + 2)

Next, we determine the solution of the quadratic expression 3x^2 - 2x + 2 using a quadratic formula

So, we have

x = (-b ± √(b² - 4ac))/2a

This gives

x = (2 ± √((-2)² - 4 * 3 * 2))/2 * 3

So, we have

x = (2 ± √-20)/6

This gives

x = (2 ± 4√-5)/6

Divide

x = (1 ± 2√-5)/3

Split

x = (1 + 2√-5)/3 and x = (1 - 2√-5)/3

So, the conclusion is that

Using the polynomial expression, the non-real solutions are x = (1 + 2√-5)/3 and x = (1 - 2√-5)/3

Read more about polynomial expression at

https://brainly.com/question/17517586

#SPJ1

Answer:

23

Step-by-step explanation:

12 * 2= 24

24-1= 23

Recall that a whole circle is equal to 360°.

Espresso accounts for 5 out of 100 people surveyed.

Therefore,

The proportion of the circle that is represented by the espresso segment is 18°.

Answer: K= -9

Step-by-step explanation:

5k−3(2k)−9=0

Multiply 3 and 2 to get 6.

5k−6k−9=0

Combine 5k and −6k to get −k.

−k−9=0

Add 9 to both sides. Anything plus zero gives itself.

−k=9

Multiply both sides by −1.

k=−9

(Hope this helps)

The weight of the elephant on planet B given the ratio of the weights on planet A an B is 72 pounds.

Ratio is used to compare two or more quantities together. It shows the number of times that one quantity is contained in another quantity. In this question, the weight of the elephant on Planet B is 100/3 times that of Planet A.

In order to determine the weight of the elephant on Planet B, multiply the ratio of the weight in planet B by the weight in Planet A and divide by the ratio of weight in planet A.

Weight in Planet B = (3 x 2400) / 100 = 72 pounds

To learn more about ratios, please check: https://brainly.com/question/25927869

#SPJ1

To find the answer you substitute in the expression the g by -4 and the m by 3, as follow:

To evaluate:

1. Make operations in parenthesis:

2. Multiplication

3. Addition:

The point lie in Quadrant IV (8 , -9).

Quadrant in coordinate geometry is divided into four parts which is called Quadrants.

And, To find the in which quadrant does point (8, -9) lie ?

Now According to the above explanation is that:

We have, Point is (8, -9)

Thus, we can clearly see that

This point is lie in Quadrant IV (8 , -9).

Hence, The point lie in Quadrant IV (8 , -9).

Learn more about Quadrants at:

https://brainly.com/question/350459

#SPJ1

In finding a number between 9/8 and 10/8, we can use the average of these two.

We can ensure that this number lies between this two.

where a and b are the two numbers

So we have :

Therefore, one number that lies between 9/8 and 10/8 is :

The correct options are,

A. Rectangle ABCD is similar to rectangle EFGH.

D. The dilation is an enlargement.

F. The scale factor of the dilation is 2.5.

The similarity criteria of rectangles are that their corresponding sides should be proportional to each other. The ratio of their corresponding length is equal to L = 25÷10, which gives L=2.5, and the ratio of their corresponding width is equal to W = 15÷6, which gives w = 2.5. Hence, both rectangles are similar.

The dilation is an enlargement because the size of the rectangle is increased by a scale factor of 2.5.

The scale factor of the dilation is the ratio of the sides, which is equal to 2.5.

Learn more about rectangles at

https://brainly.com/question/8061132?referrer=searchResults

#SPJ1

Answer:

x = 7

y = 5

(7, 5)

Step-by-step explanation:

From the way, this question looks I'm going to assume substitution.

x + y = 12

x - y = 2

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

2x = 14

÷2   ÷2

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

x = 7

x + y = 12

7 + y = 12

-7          -7

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

y = 5

I hope this helps!

First we need to find the slope by using two points

(15,190)=(t1,y1)

(25,170)=(t2,y2)

Then we calculate the y-intercept

we isolate the b

The equation is

Step-by-step explanation:

the range is the interval or set of all valid y (functional result) values.

we see that y goes continuously through every value between +5 (we see no y values bigger than that) and -5 (we see no y values lower than that).

the filled dots also tell us that the end points would be included (if this would be a necessary information - it is not, because the curve reaches +5 and -5 also in between).

so, the range is

-5 <= y <= +5

Answer:

consistent system with equation [tex]y=6x+5[/tex]

Step-by-step explanation:

[tex]18x-3y=-15[/tex],   [tex]-6x+y=5[/tex]

To solve by substitution, we have to isolate a variable in one of the equations. I will isolate y in the second equation.

[tex]-6x+y=5[/tex]

+6x           +6x

[tex]y=6x+5[/tex]

Next, substitute this y value for y in the first equation:

[tex]18x-3y=-15[/tex]

[tex]18x-3(6x+5)=-15[/tex]

and distribute.

[tex]18x-18x-15=-15[/tex]

[tex]-15=-15[/tex]

We are left with an equality of constants. This means that the system of equations is actually just one equation, meaning it has an infinite number of solvable points (this is sometimes called consistent). And, its equation is just what we solved for in the first step:

[tex]y=6x+5[/tex]

The value of (f+g)(x) is c(x) = 2x² + (-2)x + 1.

How can we add linear functions?
Addition of two individual functions, a(x) and b(x); linearly, results in the formation of the functional addition, c(x) of the two functions, such as
c(x) = a(x) + b(x) = (a+b)(x) – (i)
Domain of a quadratic equation:
The domain of a quadratic function f(x) is the set of x-values for which the function is defined, and the range is the set of all the output values, as is the case with any function (values of f). Any x is a valid input for quadratic functions because their domain is typically the entire real line. Generally, for a quadratic equation the domain goes from (-∞ ,∞ ).

Given, f(x)= 2x² - 3x + 5 and  g(x)= x - 4
Let, y = c(x) denote the value of the function (f+g)(x).
Here, following available literature,
c(x) = (f+g)(x) = f(x) + g(x)   [Using (i)]
c(x) = (2x² - 3x + 5)+(x - 4) = 2x² - 3x + 5 + x - 4  = 2x² + (-2)x + 1
Therefore, y = c(x) = 2x² + (-2)x + 1 is the value of (f+g)(x).

To learn more about addition of functions, tap on the link below:
https://brainly.com/question/14630324

#SPJ9

In the equation [tex](2x^{9} y^{n})(4x^{2}y^{10}) = (8x^{11}y^{20})[/tex] value of n = 10

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6 is multiplied by itself four times, yielding 6 6 6 6. You can write this as 64. In this case, the exponent is 4 and the base is 6.

[tex](2x^{9} y^{n})(4x^{2}y^{10}) = (8x^{11}y^{20})[/tex]

exponents multiplied with the same base: am * an = a{m + n}

On the powers of x, use the Rule of Multiplying Exponents.

⇒ x⁹ * x²  = x⁹⁺² = x¹¹

The powers of y operate similarly.

⇒ [tex]y^{n} * y^{10} = y^{n + 10} = y^{20}[/tex]

Since y¹⁰⁺¹⁰ = y²⁰

Therefore in the given equation, the value of n = 10

To know more about exponents, refer to this link:

https://brainly.com/question/3009444

#SPJ9

It is found that the displacement between t= 0  and t = 1 second is of 0.536 m.

The equation of motion is given by:

x(t) = 4 sin(πt + π/2)

The displacement between t= 0  and t = 1 second is given by:

d = x(1) - x(0)

Hence,

position of the object when t = 1

x(1) = 4sin(π(1) + 1 (π/2))

= 4 sin (π + π/2)

= 4 sin (3π/2)

= 4 x √3/2

= 2√3

= 3.464

position of the object when t = 0

x(0) = 4sin(π(0) + (π/2))

= 4 sin (0 + π/2)

= 4 x 1

= 4

Then,

d = x(1) - x(0)

= 4 - 3.464

= 0.536(approx)

Therefore, the displacement of the object between t = 0 and t = 1 is 0.536.

To learn more about displacement refer here

https://brainly.com/question/25901490

#SPJ1

yes

yes

yes

yes

yes

yes

no

Answer:

[tex]{ \tt{ \frac{dy}{dx} + 2x + 1 = 2 }} \\ \\ { \tt{ \frac{dy}{dx} = - 2x + 1 }} \\ \\ { \tt{dy = ( - 2x + 1) \: dx}} \\ \\ { \tt{ \int dy = \int( - 2x + 1) \: dx}} \\ \\ { \tt{y = - {x}^{2} + x + c}} \\ \\ { \tt{y = - x(x + 1) + c}}[/tex]

Answer:

[tex]y=-x^2+x+\text{C}[/tex]

Step-by-step explanation:

Given equation:

[tex]\dfrac{\text{d}y}{\text{d}x}+2x+1=2[/tex]

[tex]\text{Isolate $\dfrac{\text{d}y}{\text{d}x}$}:[/tex]

[tex]\implies \dfrac{\text{d}y}{\text{d}x}+2x+1-2x-1=2-2x-1[/tex]

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=-2x+1[/tex]

Multiply both sides by dx to get all the terms containing y on the left side, and all the terms containing x on the right side:

[tex]\implies \text{d}y=(-2x+1)\;\text{d}x[/tex]

Integrate both sides:

[tex]\implies \displaystyle \int 1\;\text{d}y=\int(-2x+1)\;\text{d}x[/tex]

Fundamental Theorem of Calculus

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Integrate each term separately:

[tex]\implies \displaystyle \int 1\;\text{d}y=\int -2x\;\text{d}x+\int 1\;\text{d}x[/tex]

Take the constant outside the integral:

[tex]\implies \displaystyle \int 1\;\text{d}y=-2\int x\;\text{d}x+\int 1\;\text{d}x[/tex]

Integrate, using the rules given below:

[tex]\implies y=-2 \cdot \dfrac{1}{1+1}x^{(1+1)}+x+\text{C}[/tex]

[tex]\implies y=-x^2+x+\text{C}[/tex]

Integration rules:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Integrating a constant}\\\\$\displaystyle \int n\:\text{d}x=nx+\text{C}$\\(where $n$ is any constant value)\end{minipage}}[/tex]

Learn more about integration here:

https://brainly.com/question/27805589

https://brainly.com/question/28278135

Step-by-step explanation:

You will want to divide the cost of $4.99 by 100, this will give you the cost per yard.

Answer:

$4.99 / 100 = $0.0499

About 5 cents per yard.

Please give thanks, 5 stars, and brainliest answer :)

A figure is dilated by a scale factor of 3 if the origin is the center of dilation, What is the new vertex, a', if the old vertex was located. at A(3,4)?​

_______________________________________

Please, give me some minutes to take over your question

__________________________________________

10

Step-by-step explanation:

f(2)=

3(2)+4

3x2+4

using PEMDAS multiplication comes first

6+4

=10

Answer:

f(2) = 10 and f(3) = 13

Step-by-step explanation:

In this context f(2) means "what is y when x equals 2?"  How about when x = 3?  So we plug the values into the equation and solve for f(x) - which is basically what we called "y" in algebra.

We will label the base angles of the triangle as "x".

Since the vertex angle is 3 times the measure of the base angle, the vertex angle will be equal to 3x:

The following image represent the angles in the isosceles triangle:

Now we use the following property of triangles:

The sum of all of the internal angles in a triangle must be equal to 180°.

Thus, we add the angles and equal them to 180°

We combine the terms on the left:

And divide both sides by 5:

And since x=36, the vertex angle will be:

answer: 108°

The statement is true. This is an example of Factorization being correct as it takes the factors of the quadratic equation set them equal to 0 and then calculates the value of x.

In the given question, an example of factorization is taken for the equation x²+4x-21 which is factorized using the Middle-Term split rule. We have to find out if the example is conducted correctly.

Factorization is the rule to factorize an equation such that its factors if multiplied together form the equation itself.

We will verify the factorization, for equation x²+4x-21

=> x² + 4x - 21

=> x² + 7x -3x -21

=> x(x + 7) -3(x + 7)

=> (x + 7)(x - 3) = 0

=> x = -7, x = 3

Hence, the statement is True.

To know more about Factorization, Click here:

brainly.com/question/26723450

#SPJ9

Answer:

Step-by-step explanation:

x = -A x 2/7 + 10

Answer:

-3.5 (or -3.50); each cup of coffee is $3.50

Step-by-step explanation:

the slope of the function is what is in front of the x

that is

-3.50 or just -3.5

this means that each cup of coffee is $3.50

The value of f(x+​h) is x² + 2xh + h² - 9, the value of f(x+​h)−​f(x) is 2xh + h², and the value of (f(x+h)−f(x))/h is 2x + h.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The function:

f(x) = x² - 9

(a) f(x + h)

f(x + h) = (x + h)² - 9

f(x + h) = x² + 2xh + h² - 9

​(​b)​ f(x+​h)−​f(x)

= x² + 2xh + h² - 9 - (x² - 9)

f(x+​h)−​f(x)  = 2xh + h²

​(​c) (f(x+h)−f(x))/h

= (2xh + h²)/h

= 2x + h

Thus, the value of f(x+​h) is x² + 2xh + h² - 9, the value of f(x+​h)−​f(x) is 2xh + h², and the value of (f(x+h)−f(x))/h is 2x + h.

Learn more about the function here:

brainly.com/question/5245372

#SPJ1

[tex]{\Large \begin{array}{llll} y = ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=-1\\ y=\frac{5}{4} \end{cases}\implies \cfrac{5}{4}=ab^{-1}\implies \cfrac{5}{4}=\cfrac{a}{b} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} x=3\\ y = 320 \end{cases}\implies 320=ab^3\implies 320=ab^{4-1}\implies 320=ab^4 b^{-1} \\\\\\ 320=ab^4\cdot \cfrac{1}{b}\implies \stackrel{\textit{substituting from the previous equation}}{320=\cfrac{a}{b}b^4\implies 320=\cfrac{5}{4}b^4}\implies 320\cdot \cfrac{4}{5}=b^4 \\\\\\ 256=b^4\implies \sqrt[4]{256}=b\implies \boxed{4=b} \\\\\\ \cfrac{5}{4}=\cfrac{a}{b}\implies \cfrac{5}{4}=\cfrac{a}{4}\implies \boxed{5=a}~\hfill {\Large \begin{array}{llll} y =5(4)^x \end{array}}[/tex]

Answer:

d ≈ 11.40

Step-by-step explanation:

K: (-4, -6); L: (5, 1)

    (x₁, y₁)     (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(5 - (-4))² + (1 - (-6))²

d = √(5 + 4)² + (1 + 6)²

d = √(9)² + (7)²

d = √81 + 49

d = √130 ≈ 11.40

I hope this helps!

For the given 14 digit credit card, the value of first letter A is found as 4.

For the given question;

The formula for finding the sun of nth terms of the AP are-

Sn = n/2(a + l)

From the given 14 digits credit card, consider initial 3 letters.

A,_, 8

The sum of three consecutive numbers is 18.

Thus, applying Sum formula of AP

Sn = n/2(a + l)

Put the values;

18 = 3/2(A + 8)

Simplifying;

3A + 24 = 36

A = 12/3

A = 4

Thus, the value of the first digit of the credit card is found as 4.

To know more about arithmetic progression, here

https://brainly.com/question/24191546

#SPJ13

Solution

From the given graph,

The maxima is

The minima isThe inetrev

aterval inwh which the function is increasing is

dec

For x = 2

Since:

The function is discontinuous at x = 2. Besides since the function has a vertical asymptote on one of the sides, we can conclude it is a infinite discontinuity.

For x = 6:

Since:

The function is discontinuous at x = 6, at this point the function has a jump discontinuity