the _____ (if any) are determined by the values of x that make f(x)=0. to find them, solve the quadratic equation:

The length of the rectangle is approximately 41.34 inches.

Let's assume the width of the rectangle is represented by the variable w. According to the given information, the length of the rectangle is four less than twice the width, which can be expressed as 2w - 4.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 128 inches. Since a rectangle has two pairs of equal sides, we can set up the equation:

2w + 2(2w - 4) = 128.

Simplifying the equation, we get:

2w + 4w - 8 = 128,

6w - 8 = 128,

6w = 136,

w = 22.67.

So, the width of the rectangle is approximately 22.67 inches. To find the length, we can substitute this value back into the expression 2w - 4:

2(22.67) - 4 = 41.34.

Therefore, the length of the rectangle is approximately 41.34 inches.

In summary, the length of the rectangle is approximately 41.34 inches. This is determined by setting up a system of equations based on the given information: the perimeter of the rectangle being 128 inches and the length being four less than twice the width.

By solving the system of equations, we find that the width is approximately 22.67 inches, and substituting this value back, we obtain the length of approximately 41.34 inches.

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Answer:

true

Step-by-step explanation:

because there's less humidity

The total amount that would be found in the account after 4 years, would be $ 641. 69

The total amount after 4 years in Arik's account can be found by the formula :

= A = Amount invested x ( 1 + r /n )ⁿ

The variables are:

Amount invested = $ 500

r = 6.25% = 0. 0625

n = 12

t = 4 years

The total amount is then :

A = 500 x ( 1 + 0. 0625 / 12 ) ^ ⁽¹² ˣ ⁴ ⁾

A = $ 641. 69

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The difference between original loan and unsubsidized loans at the time of graduation is =  8302.57 - 7855 = $447.57

What is meant by a loan?

A loan is a type of debt that a person or other entity incurs. The lender advances the borrower a certain amount of money, typically on behalf of a business, financial institution, or government. The borrower accepts a specific set of terms in return, which may include any economic costs, interest, a repayment schedule, and other requirements.

The lender may occasionally need collateral to protect the loan and guarantee repayment. Major purchases, investments, renovations, debt reduction, and company endeavours are just a few uses for loans. Loans aid in the expansion of already existing businesses. The growth of an economy's total money supply and fostering competition are made possible by loans to new enterprises.

Given,

 Time to graduate = 18 months

Amount of loan for 3 semesters = $7855

Unsubsidized loan

rate of interest = 3.7%

Subsidized Stafford Loan

rate of interest = 4.7%

Amount after 6 months for each loan

P = $7855

r1 =  3.7%

r2 = 4.7%

t (in years) = 18 months = 1.5 years

Number of times compounded in a year n = 12

Amount of  Unsubsidized loan at the time of graduation

= \(P(1 + \frac{r}{n})^{nt}\)

= \(7855(1 + \frac{0.037}{12})^{12*1.5}\)   = $8302.57

Amount of the Subsidized Stafford Loan at the time of graduation

= \(P(1 + \frac{r}{n})^{nt}\)

= \(7855(1 + \frac{0.047}{12})^{12*1.5}\)   = $8427.60

Therefore the difference between the balance amount of the original loan and the unsubsidized loan at the time of graduation is

=  8302.57 - 7855 = $447.57

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No, acute angle can not be equal to 90. if an angle equal to 90 then it is a right angle.

Acute angle

An angle smaller than the right angle is called an acute angle. In other words, the angle which is less than 90 degrees forms an acute angle.

An angle which is measuring less than 90 degrees is called an acute angle. This angle is smaller than the right angle (which is equal to 90 degrees). For example, ∠30o, ∠45o, ∠60o, ∠75o, ∠33o, ∠55o, ∠85o, etc. are all acute angles.

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Answer:

go foward 5 3/4 from 0 then go back 1/4 because its negative and youll get 5 1/4 as the last spot you land step-by-step explanation:

Answer:

38ft squared

Step-by-step explanation:

W w w www w w w w w. E w w w w w. Ww

Answer:

C. 42 ft^2

Step-by-step explanation:

2 * 6 = 12

3 * 10 = 30

30 + 12 = 42

Hence, the answer is C.

\(2y + 4(y + 1)\)

Expand the brackets.

\(2y + 4y + 4\)

Add the like terms.

\(6y + 4\)

Answer:

  6   y +    4  

Step-by-step explanation:

=> 2y+4(y+1)

=> 2y+4y+4

=> 6y+4

The function g(x) = 4(x + 3)² - 68 is the function which is mapped to 32 at x = 2 option (B) g(x) = 4(x + 3)² - 68 is correct.

To find the solution, add 2 to the function's x-values and compute the value.

What is a function?

It is described as a particular kind of relationship, and each value in the domain is associated to exactly one value in the range according to the function. They have a predetermined domain and range.

We have:

A function which is at x = 2 mapped to 32

The above statement means that at x = 2

The value of the function will be 32

The given functions:

f(x) = -3x² - 4

Plug x = 2

f(2) = -3(2)² - 4

f(2) = -16

g(x) = 4(x + 3)² - 68

Plug x =2

g(2) = 4(2 + 3)² - 68

g(2) = 100 - 68

g(2) = 32

Thus, the function g(x) = 4(x + 3)² - 68 is the function which is mapped to 32 at x = 2 option (B) g(x) = 4(x + 3)² - 68 is correct.

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The labor productivity of this manufacturing process in terms of dollars per labor hour is $73.47.

To find the labor productivity of this manufacturing process in terms of dollars per labor hour, we need to calculate the total revenue from the tuxedos and divide it by the total number of labor hours.

Total revenue from tuxedos = 96 tuxedos * $225 per tuxedo

                                               = $21,600

Total number of labor hours = 7 employees * 42 hours per employee

                                               = 294 labor hours

Labor productivity = Total revenue / Total number of labor hours

                               = $21,600 / 294 labor hours

                               = $73.47 per labor hour

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Answer:

The sequence converges to 1

Step-by-step explanation:

Find the limit of the sequence as n approaches infinity

\(\lim_{n \to \infty} \frac{n}{6}sin(\frac{6}{n})\)

\(\lim_{n \to \infty}\frac{sin(\frac{6}{n})}{\frac{6}{n}}\)

\(\lim_{n \to \infty}\frac{cos(\frac{6}{n})*-\frac{6}{n^2} }{-\frac{6}{n^2}}\)

\(\lim_{n \to \infty} cos(\frac{6}{n})\)

\(cos(0)\)

\(1\)

Therefore, since the sequence approaches a limit of 1, then it converges.

The new expression by using distributive property is: 209.25

What is distributive property?

In mathematics, the distributive property tell the solution method for the expression who are in the form of a(b + c). In this, first add the expression which are in the parenthesis and later multiply it.

According to the question, the given expression is as follows:

70[2.50+(−0.60)]+25[3.75+(−0.70)]

Using distributive property, whose list contains parenthesis, exponents, multiplication/division, addition/subtraction. This is the list in which the given expression need to simplify.

First parenthesis calculation,

2.5 + - 0.6 = 1.9 and 3.75 + - 0.7 = 3.05

Now, substitute the values:

70(1.9) + 25(3.05)

Multiply it: 133 + 76.25;

Add it: 209.25

Hence, the new expression by using distributive property is: 209.25

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Answer:

77

Step-by-step explanation:

just took the quiz

The probability of winning a certain lottery is p = 1/64,481. For a single play, the expected number of wins is E(X) = 1*p + 0*(1-p) = p.

The variance of the number of wins for a single play is\(Var(X) = p(1-p) = 1/64,481 * 64,480/64,481 = 64,480/64,481^2\).

For 669 plays, the expected number of wins is 669p and the variance of the number of wins is \(669Var(X) = 669(64,480/64,481^2) = 668.99/64,481\).

The standard deviation is the square root of the variance, so the answer is approximately sqrt(668.99/64,481) = 0.309.

Therefore, the closest answer choice is D) 0.3.

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Answer:

The constant difference is 8

Step-by-step explanation:

-6 + 8 = 2

10 + 8 = 18

Assume a stick of length 1 is randomly broken into two portions. The smaller piece's estimated length is 0.25.

The random variable L (the length for the shorter stick) has a uniform distribution.

Thus the probability density function for L is as follows:

This means 2 for all length in the range 0 - 0.5

Now, we calculate the expected value for random variable L as seen on the attachment. Based on the calculation, 0.25 is the smaller piece's estimated length for the randomly broken stick.

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The maximum area of a rectangle that is above the x-axis and below the graph of a parabola can be determined using calculus. The parabola is given by the equation y = ax^2 + bx + c, and the rectangle's dimensions are x (width) and y (height).

The area of the rectangle is given by A = xy. To find the maximum area, we need to find the maximum value of A. To do this, we can substitute the parabola equation for y in the area equation:
A = x(ax^2 + bx + c)
Next, we take the derivative of A with respect to x:
dA/dx = a(3x^2) + b(2x) + c
To find the critical points, we set dA/dx to zero:
0 = 3ax^2 + 2bx + c
Now, we solve for x to find the critical points. These points will help us determine where the maximum area occurs. After identifying the maximum point, we can substitute the x-value back into the parabola equation to find the corresponding y-value. Finally, the maximum area can be calculated by multiplying the obtained x and y values:
Max Area = x_max * y_max.

Hence, The maximum area of a rectangle that is above the x-axis and below the graph of a parabola can be determined using calculus. The parabola is given by the equation y = ax^2 + bx + c, and the rectangle's dimensions are x (width) and y (height).

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To find the lengths of the sides of a triangle with vertices a, b, and c, we can use the distance formula. By calculating the distance between each pair of vertices, we can determine the lengths of the sides ab, bc, and ca.

Let's assume that the coordinates of vertex a are (x1, y1), the coordinates of vertex b are (x2, y2), and the coordinates of vertex c are (x3, y3). The distance formula between two points (x1, y1) and (x2, y2) is given by:

d = √((x2 - x1)² + (y2 - y1)²)

To find the length of side ab, we calculate the distance between points a and b. Similarly, to find the lengths of sides bc and ca, we calculate the distances between points b and c, and c and a, respectively.

Once we have the coordinates of the vertices and apply the distance formula to each pair of vertices, we obtain the lengths of the sides ab, bc, and ca, which represent the distances between the respective vertices of the triangle.

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Answer:

A:59 B:48

Step-by-step explanation:

A triangle is equal to 180 degrees. So the equation would be

73+x+(x-11)=180. To find the value of x, add all of the same values

73-11+x+x which is equal to 62+2x=180. Then subtract 62 from both sides

62-62+2x=180-62  so the equation is now 2x=118 now you divide each side by 2 to get x=59. now to get angle b you subtract 11 from 59 to get 48

The concave mirror should be placed at a distance of 2r from the wall to form a real image of the object on the wall. The magnification of the image is expressed using three significant figures is -0.500.

if the object is placed at a distance r in front of a concave mirror whose radius of curvature is also r, then the image is formed at the same distance r behind the mirror. This is a special case called the "center of curvature" configuration.

To form a real image on the wall, the mirror must be placed such that the object is beyond the mirror's focal point. The focal length of the mirror is half of its radius of curvature, so the focal length is f = r/2.

If the object is placed at a distance x from the mirror, then using the mirror equation:

1/f = 1/do + 1/di

where do is the distance of the object from the mirror and di is the distance of the image from the mirror. In this case, do = x and di = r, so we get:

1/r = 1/x - 1/f

Substituting f = r/2, we get:

1/r = 1/x - 2/r

Solving for x, we get:

x = 2r

Therefore, the mirror should be placed at a distance of 2r from the object to form a real image on the wall.

To find the magnification of the image, we use the magnification equation:

m = -di/do

where m is the magnification, di is the distance of the image from the mirror, and do is the distance of the object from the mirror. In this case, do = x = 2r and di = r, so we get:

m = -r/(2r) = -1/2

Therefore, the magnification of the image is -0.500.

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The solutions of given function;

(a) k = -12

(b) f'(3) = 0

(c) f'(x) = 0

Given info,

A function f is defined for all real numbers and has the following three properties:

\(f(1)=5 \quad f(3)=21 \quad f(a+b)-f(a)=k a b+2 b^{2}f(1)\\\)

for all real numbers a and b where k is a fixed real number independent of a and b.

To find,

(a) Use a = 1 and b = 2 to find k.

\(f(a+b)-f(a)=k a b+2 b^{2}f(1)\)

f(1 + 2) - f(1) = k(1 * 2) + 2 * 2² * f(1)

f(3) - f(1) = 2k + f(1) * 8

21 - 5 = 2k + 8 * 5

16 = 2k + 40

-2k = 24

k = -12

(b) Find f'(3).

f(3) = 21

f'(3) = d/dx(21) = 0

(c) Find f'(x) for all real x.

f'(x) = 0

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Answer:

x ≠ -4, -1, 3

Step-by-step explanation:

\(\frac{x}{x+4}+ \frac{12}{x^2} +5x+4 = \frac{8x}{5x-15}\)

\(12/(x^2+5x+4) = 8x/(5x-15)\)

\(\frac{12}{((x+1)(x+4))} = \frac{8x}{(5(x-3))}\)

\(\\ \tt\hookrightarrow \dfrac{x}{x+4}+\dfrac{12}{x^2+5x+4}=\dfrac{8x}{5x-15}\)

\(\\ \tt\hookrightarrow \dfrac{x}{x+4}+\dfrac{12}{(x+1)(x+4)}=\dfrac{8x}{5(x-3)}\)

So Domain=(-4,-1,3)

Answer:

90.24 divided by 6.3

Step-by-step explanation:

For reaching to the answer, we have to test each of the options given

The first option says that the divisor and dividend is 90.24 and dividend is 6.3

Now if we rounded it

So it would be 90 and 6

So, the quotient is

= 90 ÷ 6

= 15

Hence, the first option is correct

i.e. 90.24 divided by 6.3

And, all the other options are wrong

Answer:

118.54

Please make me brainiest

Explain

22×3.14÷2= 34.54

8×13= 104-20= 84

84+34.54= 118.54

The given equation 3–√ 7–√>10−−√ is true and we can prove this by following the given steps:

For proving that 3–√ 7–√>10−−√, we can assume that 3–√ 7–√ ≤ 10−−√.

Then we can square both sides and simplify:

(3–√ 7–√)² ≤ 10

9 - 6√21 + 7 ≤ 10

16 - 6√21 ≤ 10

6√21 ≥ 6

√21 ≥ 1

This is true, so our assumption is correct.

But this contradicts the fact that 3–√ 7–√>0, since both 3 and 7 are greater than √2, so their difference must be positive.

Therefore, our assumption that 3–√ 7–√≤10−−√ must be false.

Thus, we conclude that 3–√ 7–√>10−−√.

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The true proportion of the side lengths of the quadrilaterals is A'B'/AB

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

Quadrilaterals ABCD and A'B'C'D

These quadrilaterals are similar

So, it means that the corresponding side lengths are proportional

So. we have

Side length = AB

Corresponding side length = A'B'

The true proportion is then represented as

k = Corresponding side length/Side length

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

k = A'B'/AB

Hence, the proportion is A'B'/AB

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Open questions:

Closed questions:

Open questions allow individuals to express their thoughts, feelings, and opinions freely. These questions promote exploration and encourage the respondent to provide unique and personal insights.

Closed questions provide limited options for responses and are useful when seeking specific information or clarifying details. They are used in surveys, assessments etc.

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Answer:

Step-by-step explanation:

angle 4 is congruent to angle 4 because they are alternate interior angles.

angle 5 is congruent to angle 3 because they are alternate interior angles.

angle 1+angle 2+angle 3 is equal to (=) angle 1+angle 2+angle 3

angle 1+angle 2+angle 3=180 degree(being sum of interior angles of a trianngle)

Answer:

1.370025503 ×10^27

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

formula is 1/2(a+b)xh

a is long base b is short base

h is for height

since

a= 3

b=2

h=8

1/2(3+2)x8

so it be 5/2x8

so it be 5x 4 because 2 divide 8 which make it 4 then time it with 5

so answer is 20