The length of the rectangular shed is 2x^2 + 3x - 1 feet, and the width is x + 4 feet. Write polynomials that represent the perimeter and area. Calculate the perimeter and area if x = 10 feet. Include correct units of measure

The exact solutions of the quadratic equation are:

\(4- \sqrt{10}\)  and \(4+ \sqrt{10}\)

The given quadratic equation is:

\(x^2-8x+6=0\\\\x^2-8x=-6\)

Add \(2^2\) to both sides

\(x^2-8x+4^2=-6+4^2\\\\(x-4)^2=-6+16\\\\(x-4)^2=10\\\\x-4=\pm \sqrt{10} \\\\x=4 \pm \sqrt{10}\)

The exact solutions of the quadratic equation are:

\(4- \sqrt{10}\)  and \(4+ \sqrt{10}\)

Learn more on completing the square method here: https://brainly.com/question/10449635

Answer:

To find the cube root of a number is a bit more complicated and in our days is considered impractical, but here is a method explained. Look at the 2nd example scrolling down about 1/3 of the page

If you want to know the concept of square roots and cube roots ?

the square root of a number is that number which when multiplied by itself two times gives us that number

e.g.

√64 = x , so that (x)(x) = 64

and from our multiplication table we know that

(8)(8) = 64 , so that

√64 = 8

the cube root of a number is that number which when multiplied by itself three times gives us that number

e.g.

∛64 = x , so that (x)(x)(x) = 64 , and thus x = 4 because 4x4x4 = 64

so ∛64 = 4

for 9 I wrote Any decimal which terminates is rational

any decimal which has a repeat is rational

any decimal which does not show any repeating decimals and which is never-ending is irrational

Step-by-step explanation:

Error rate refers to the frequency or proportion of errors made in a particular context or process. It is commonly used in various fields such as statistics, computer science, and quality control.

To find the error rate for the training subset, we can use the fact that the average error rate is 0.06.

Let's denote the error rate for the training subset as E_train. We can express the average error rate as:

average error rate = (error rate for training subset + error rate for test subset) / 2

0.06 = (E_train + error rate for test subset) / 2

Multiplying both sides of the equation by 2, we get:

0.12 = E_train + error rate for test subset

Since K=1, the error rate for the test subset would be 0.12 - E_train.

Therefore, we can expect the error rate for the training subset to be 0.12 - E_train.

To know more about Error Rate visit:

https://brainly.com/question/30748171

#SPJ11

Answer:

A 4/3

Step-by-step explanation:

to long to explain but its right

The required equation function j which is the transformation of \(f(x)= x^{1/2}\) is  \(j(x)= (x+2)^{1/2}\) .

As we can see in the graph the functions j and f are similar but the graph of j is 2 units left of f. So, function f(x) has a domain of real number greater than equal to zero, while as the function j is 2 units left of f then its equation is given as  \(j(x)= (x+2)^{1/2}\)  where the domain of j is all real numbers greater then or equal to -2.

Thus, the equation of function j is the transformation of \(f(x)= x^{1/2}\) is  \(j(x)= (x+2)^{1/2}\) .

Learn more about the transformation of the function here:

https://brainly.com/question/26896273

#SPJ1

In the question the graph is missing, a graph has been added on behalf of the incomplete question.

Answer:

5

Step-by-step explanation:

206 = 0

26 = 1

3 = 2-higher

206+26=232+3=235

3/235

6/470

235 is about 200

5/400

1. y-intercept is (0, -a/b).

2. x-intercept is (-a, 0).

3. vertical asymptote at x = b.

4. horizontal asymptote at y = 1.

5. Draw the function with these features above in mind. The function will approach the vertical asymptote as x approaches b and the horizontal asymptote as x goes to positive or negative infinity. The function will cross the x-axis at x = -a and the y-axis at y = -a/b.

(i) Determine the y-intercept:
To calculate the y-intercept, set x = 0 and solve for f(x). The y-intercept is the point at which the function crosses the y-axis.

f(0) = (0 + a) / (0 - b) = a / (-b)

So, the y-intercept is (0, -a/b).

(ii) Determine any x-intercept(s):
To find the x-intercept, set f(x) = 0 and solve for x. The x-intercept is the point at which the function crosses the x-axis.

0 = (x + a) / (x - b)

0 = x + a
x = -a

So, the x-intercept is (-a, 0).

(iii) Identify any vertical asymptotes:
A vertical asymptote occurs when the denominator of a function is equal to zero, but the numerator is not.

x - b = 0
x = b

Vertical asymptote at x = b.

(iv) Determine whether f has a horizontal asymptote or slant asymptote:
To determine if a function has a horizontal or slant asymptote, compare the degrees of the numerator and denominator:

Numerator degree: 1 (x has degree 1)
Denominator degree: 1 (x has degree 1)

Since the degrees are the same, there is a horizontal asymptote. The horizontal asymptote is the ratio of the leading coefficients, which in this case is 1/1 = 1.

So, there is a horizontal asymptote at y = 1.

(v) Sketch the function:
To sketch the function, keep in mind the following features:
- y-intercept at (0, -a/b)
- x-intercept at (-a, 0)
- Vertical asymptote at x = b
- Horizontal asymptote at y = 1

Now, draw the function with these features in mind. The function will approach the vertical asymptote as x approaches b and the horizontal asymptote as x goes to positive or negative infinity. The function will cross the x-axis at x = -a and the y-axis at y = -a/b.

Learn more about slant asymptote.

brainly.com/question/30720381

#SPJ11

Answer:

r^1 = -3-square root21/4

r^2 = -3+square root21/4

Step-by-step explanation:

Answer:

I honestly don’t know I am gonna guess

Step-by-step explanation:

1/12?

. 。 • 　ﾟ 。 　. .

　. . 　。 。　. .

. 。 ඞ 。 . • 　• .

.

ﾟ Bread was Not An Impostor. 。　. .

' 1 Impostor remains 　。 .

ﾟ 　. 　. , . .. . .

Have a nice day UwU

Answer:

43°

Step-by-step explanation:

m∠ABD = m∠1 + m∠2

Substitute:

68° = m∠1 + (m∠1 + 18°)

68° = m∠1 + (m∠1 + 18°)

68° = 2(m∠1) + 18°

50° = 2(m∠1)

25 = m∠1

Know that we know that m∠1 is, we can add 18* to find m∠2

25° + 18° = 43°

-Chetan K

Answer:

Step-by-step explanation:

Triangle MNP is a right triangle with the following values:

Interior angles of a triangle sum to 180°. Therefore:

m∠M + m∠N + m∠P = 180°

m∠M + 58° + 90° = 180°

m∠M + 148° = 180°

m∠M = 32°

To find the measures of sides MN and NP, use the Law of Sines:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Substitute the values into the formula:

\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)

\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)

Therefore:

\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)

\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)

To find the perimeter of triangle MNP, sum the lengths of the sides.

\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)

Answer:

560÷c = p (p is price of one btw)

Step-by-step explanation:

Answer:

The fully factored form of the function f(x) is : (x+5)(x-1)(x-3)

Step-by-step explanation:

Answer:

i) The approximate solutions are: \(x_{1} \approx -0.207\), \(x_{2} \approx 1.207\).

ii) The approximate solutions are: \(x_{1}\approx -0.5\), \(x_{2} \approx 1.5\).

Step-by-step explanation:

i) The best approach to estimate graphically the solution of \(4\cdot x^{2} - 4\cdot x - 1 = 0\) is graphing the following system of equations:

\(y = 4\cdot x^{2}-4\cdot x - 1\) (1)

\(y = 0\) (2)

And labeling the points in which both intersects each other. We include the result in the image 'solution-i'. The approximate solutions are: \(x_{1} \approx -0.207\), \(x_{2} \approx 1.207\).

ii) The best approach to estimate graphically the solution of \(4\cdot x^{2} - 4\cdot x - 1 = 2\) is graphing the following system of equations:

\(y = 4\cdot x^{2}-4\cdot x - 1\) (1)

\(y = 2\) (2)

And labeling the points in which both intersects each other. We include the result in the image 'solution-ii'. The approximate solutions are: \(x_{1}\approx -0.5\), \(x_{2} \approx 1.5\).

\( \Large{\boxed{\sf d = \sqrt{40} }} \)

\( \\ \)

The distance between two points is given by the following formula:

\( \Large{\sf d = \sqrt{(x_B - x_A)^2 + (y_B - y_A)^2}} \)

Where:

\( \\ \)

First, let's identify our values:

\( \sf (\underbrace{\sf -3}_{\sf x_A} \: , \: \overbrace{\sf 2}^{\sf y_A}) \: \: and \: \: (\underbrace{\sf 3}_{\sf x_B} \: , \: \overbrace{\sf 0}^{\sf y_B}) \)

\( \\ \)

Now, substitute these values into our formula:

\( \sf d = \sqrt{\sf (3 - (-3))^2 + (0 - 2)^2} \\ \\ \sf d = \sqrt{\sf 6^2 + (-2)^2} \\ \\ \sf d = \sqrt{\sf 36 + 4 } \\ \\ \boxed{\boxed{\sf d = \sqrt{40} }} \)

\( \\ \)

\( \hrulefill \)

\( \\ \)

▪️Learn more about finding the distance between two points here:

↣https://brainly.com/question/21152362

To find the rank of A, we count the number of nonzero rows in either A or B. The rank represents the number of linearly independent rows or columns in the matrix. The dimension of the null space, also known as the nullity, is calculated by subtracting the rank from the number of columns in A. Additionally, we can find bases for the column space of A, the row space of A, and the null space of A.

To summarize:

- Rank(A) = Number of nonzero rows in A or B (same for row space)

- Dim(Nul(A)) = Number of columns in A minus Rank(A) (same for null space)

- Bases for the column space, row space, and null space of A need to be determined.

To find a basis for the column space of A, we take the pivot columns from the row-reduced form of A (or B). These pivot columns form a linearly independent set that spans the column space of A.

To find a basis for the row space of A, we take the nonzero rows from the row-reduced form of A (or B). These rows form a linearly independent set that spans the row space of A.

To find a basis for the null space of A, we solve the homogeneous system of equations A*x = 0. The basic solutions obtained represent a basis for the null space of A.

By following these steps, we can determine the bases for the column space, row space, and null space of the given matrix A, which is row equivalent to matrix B.

To learn more about row-reduced form click here : brainly.com/question/30401478

#SPJ11

The integer for vector 1 {2,6,-7}, integer for vector 2 is 10,8,-14}, integer for vector 3 is {4,12,-14}, integer for vector 4 is {14,-2,-7} and integer for vector 5 is {22,0,-14}. (all these vectors are in span {V1 and V2})

List five vectors in Span {v_1, v_2}?

1) V1+v2={8,2,-7 }+{-6,4,0 }

={2,6,-7}

2) 2v1+v2={16,4,-14}+{-6,4,0}

={10,8,-14}

3)2v1+2v2={16,4,-14}+{-12,8,0}

={4,12,-14}

4)V1-v2={8,2,-7}-{-6,4,0}

={14,-2,-7}

5)2v1-v2={16,4,-14}-{-6,4,0}

={22,0,-14}

All of these vectors are contained within the span.

{v1,v2}={av1+bv2:ab∈r}

A matrix is a rectangular variety of ordered numbers (real or complex) or functions .Assume we want to express the following information about   Ram and his two friends Rohan and Yash's possession of pens and pencils:
Ram       has      20     pens       and       7       pencils,

Rohan    has      15     pens       and       5       pencils,

Yash       has      12     pens       and       3       pencils

Now, this could be arranged in tabular form as follows,
⎢20  7⎢
⎢15   5⎢                            
⎢12   3⎢        

To learn more about vectors

https://brainly.com/question/13322477

#SPJ4

Answer:

Here are ten numbers:

3 7 2 4 7 5 7 1 8 8

a)

Write down the mode. 7

b)

Work out the median.

c)

Calculate the mean. add all and divide by 10

d)

What is the range? 7

Answer:

Mode: 7

Median: 6

Mean: 5.2

Range: 5

Step-by-step explanation:

For the mode you have to find which number is present the most times

For the median you have to find the middle number if the total sum of numbers is an odd number, and find the average of the two if it is an even number ,like i did here (7+5)/2=6

For the mean you have to add every number and then devide with the total number of the numbers given:

(3+7+2+4+7+5+7+1+8+8)/10=5.2

For the range you have to find the largest number and subtract the smallest number from it (8-3)=5

The probability that you earn 10 points, then 5 points, then 10 points is 0.000356 or 0.0356%.

We can approach this problem by using the multiplication rule of probability, which states that the probability of two or more independent events occurring together is the product of their individual probabilities.

First, we need to find the probability of drawing a card worth 10 points. There are 16 cards in the deck that are worth 10 points (4 tens, 4 jacks, 4 queens, and 4 kings) out of a total of 52 cards. Therefore, the probability of drawing a card worth 10 points on the first draw is 16/52 or 4/13.

Next, we need to find the probability of drawing a card worth 5 points. There are four cards in the deck worth 5 points, all of which are fives. Therefore, the probability of drawing a card worth 5 points on the second draw is 4/51, since there are only 51 cards left in the deck.

Finally, we need to find the probability of drawing another card worth 10 points on the third draw. Since we already drew a card worth 10 points, there are only 15 such cards left in the deck out of 50 remaining cards. Therefore, the probability of drawing another card worth 10 points on the third draw is 15/50 or 3/10.

Using the multiplication rule, we can find the probability of earning 10 points, then 5 points, then 10 points as follows:

P(10 points, 5 points, 10 points) = P(10 points on first draw) * P(5 points on second draw) * P(10 points on third draw)

P(10 points, 5 points, 10 points) = (4/13) * (4/51) * (3/10)

P(10 points, 5 points, 10 points) = 12/33,726

P(10 points, 5 points, 10 points) is approximately 0.000356 or 0.0356%.

To learn more about cards click on,

https://brainly.com/question/1638577

#SPJ4

The answer is 13. The Pythagorean theorem can be used to determine the hypotenuse.

A triangle's third side must always be between (but not exactly equal to) the other two sides' total and difference in length. The answer is 13. The Pythagorean theorem can be used to determine the hypotenuse.The theorem informs us that if we designate that side as side "c"

c² = 5² + 12²\s c² = 25 +144 = 169\s c = √169 = 13

The third side measures 13 units in length.

Further commentary

The three digits (5, 12, and 13) form a "Pythagorean triple."

They can be utilized to create a right triangle because they are integers.

The triples (3, 4, 5), (7, 24, 25), and (8, 15, 17) are other triples that are frequently encountered in algebraic problems.

It might be worthwhile for you to keep these in mind.

The third side is 13 when you observe side lengths of 5 and 12, therefore you don't need to do any math to determine this.

To learn more about Pythagorean theorem refer

https://brainly.com/question/231802

#SPJ1

Answer:

6 Cars

Step-by-step explanation:

let the number of blue car be x.

5:3=10:x

or,5/3=10/x

or,5x=30

or,x=30/5 •°•x=6

Answer:

Step-by-step explanation:

The problem is that you cannot be sure that either triangle (it actually requires both of them) contain a right angle

What you have so far is SSA which is not one of the fundamental congruency triangles. In order to be certain of congruency the angle must be made up of the 2 given sides. You are certain that SAS will produce congruency. You are not so sure of  r SSA. There are proofs of this on the internet. I urge you to look into it. Though not long, following it step by step takes a lot of patience. A cup of strong coffee is a good idea.

Answer:

the question has some problems

The formula will return 5, because none of the conditions in the nested IF statement are true for the value of A1 being "C".

The formula =IF(A1="A",1,IF(A1="B",2,IF(A1="D",4,5))) is a nested IF statement that checks the value of cell A1 and returns a corresponding value based on the conditions.

In this case, the value of A1 is "C". Therefore, the first condition, A1="A", is not true, so the formula moves on to the second condition, A1="B". This condition is also not true, so the formula moves on to the third condition, A1="D". However, this condition is also not true, because the third condition has a typo, where there is an extra space before the "D". Therefore, the formula evaluates the final "else" option, which is 5.

Thus, the formula will return 5, because none of the conditions in the nested IF statement are true for the value of A1 being "C".

Learn more about "Nested IF " : https://brainly.com/question/14915121

#SPJ11

The correct options are A)  X-1 <1 and D) X+4 < 6.

Given, we need to find all the inequalities for which the solution set is x < 2. We know that if x < a then the solution set will lie on the left side of a in the number line. Therefore, for x < 2 the solution set will be on the left side of 2 on the number line. So, let's check each option:

A. X-1 <1 - Adding 1 to both sides of the inequality we get: X < 2

Here, the solution set is x < 2. So, option A is correct.

B. X2 <0 - There is no real value of x for which x² < 0. So, the solution set is null. Therefore, option B is incorrect.

C. X 3 < 1 - Subtracting 3 from both sides we get: X < -2. The solution set is x < -2. So, option C is incorrect.

D. X+4 < 6 - Subtracting 4 from both sides we get: X < 2. Here, the solution set is x < 2. So, option D is correct.

Therefore, the correct options are A and D.

Learn more about inequalities visit:

brainly.com/question/20383699

#SPJ11

The area of the figure which consists of two congruent triangles and a rectangle is calculated as: 52 cm².

In the diagram given above, we see a composite figure consisting of two triangles that are congruent, and a rectangle, therefore:

Area of the figure = area of the two triangles + area of rectangle.

The Area of the two triangles:

base = 8 cm²

height = 4.5 cm²

Area of the two triangles = 2(1/2 * base * height) = base * height

Area = 8 * 4.5 = 36 cm²

Area of rectangle = length * width = 4 * 4

= 16 cm²

Total area = 36 + 16 = 52 cm²

Learn more about area of figure on:

https://brainly.com/question/30721292

#SPJ1

Answer:

Step-by-step explanation:

So, the point of this is to make x the only thing on one side, so we can see what x is!

Okay so first subtract 8 on both sides...

5x= 25

Now we need to divide on both sides!

That equals...

x=5

So now we know that x=5!

Hope this helped!! :D

If you have any questions whatsover, make sure to comment!

The equations that represent direct variation is y = 2x and y = 2

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

y = 2x

y = x + 4

y = x

y = 3/x

A direct variatiin equation is represented as

y = mx

Where

m is the constant of variation

Using the above as a guide, we have the following:

y = 2x and y = x take the form y = mx

Hence, the equation of direct variation are y = 2x and y = 2

Read more about direct variation

https://brainly.com/question/6499629

#SPJ1