One of the roots of equation x^(2)-(3p-4)x+11p-5=0 is 8. Find the other root. Find the value of p.

The answer of this question is equation [-6x+4y=16].

An equation is a mathematical statement that shows the equality between two expressions, typically separated by an equal sign. It can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The goal of solving an equation is to find the value of the variable that makes the equation true.

In mathematics, a system refers to a collection of mathematical objects or entities that are related or interconnected in some way.

System A

5x-y=-11

3x-2y=-8

System B

5x-y=-11

-2(3x-2y)=-8×(-2)

5x-y=-11

-6x+4y=16

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The number of men living in the village is 260.

A collection of many linear equations that include the same variables is referred to as a system of linear equations. A linear equation system is often composed of two or more linear equations with two or more variables.A linear equation with two variables, x and y, has the following general form:

                                           \(ax + by = c\)

Given:

Total inhabitants in the village: 817

Number of children: 241

There are 56 more women than men in the village

Total adults = Total inhabitants - Number of children

Total adults = 817 - 241

Total adults = 576

Let number of men in the village be 'x' and number of women in the village be 'y',

∴ y=x+56 (given) ..................(1)

Also, x+y=576 .................(2)

From equation (1) and (2),

x + (x + 56) = 576

2x + 56 = 576

2x = 576 - 56

2x = 520

x = 520 / 2

x = 260

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Answer:

The like terms would be 3x and -3x.

Step-by-step explanation:

If you add the like terms together you would get 0x and be left with -2y.

Answer:

For number 5, it is D

For number 6, it is A

Step-by-step explanation:

For number 5, we have the dimensions options here.

We first need to check to see if all the choices give the perimeter of 34, as sometimes there are trick answers.

We know the 34 is the perimeter because we are looking for area, so we add the two given numbers and double it to find the perimeter since we have the length and width.

*(Formula for perimeter is 2(L + W)  )

(I already checked them all, and they all give to be 34 so they are all safe.)

Then we find the areas of each.

*(Formula for area is L * W   {the " * " symbol represents multiplication.)

We multiply 12 by 5 to get 60.

We multiply 13 by 4 to get 52.

We multiply 10 by 7 to get 70.

We multiply 9 by 8 to get 72.

Since we are looking for the greatest area, we look for the greatest number, which is the 72.

Therefore the 9 by 8 option, or D is correct.

For number 6, we are looking for the minimum perimeter and we have the area, so we set the same thing up except modified slightly.

We first check if all the areas are 64 to look for a trick answer.

We multiply 8 by 8 to get 64.

We multiply 1 by 64 to get 64.

We multiply 6 by 6 to get 36. (WHAT?!!?!! omg me big brain lolza. {nah jk})

We multiply 32 by 2 to get 64.

So we know the 6 by 6 option or C is wrong.

Then we look for the perimeters of the dimension solutions.

(This will skip C so it will go A, B, and then D, since we know C is incorrect and is unrelated now.)

2 ( 8 + 8 ) =  32

2 ( 1 + 64 ) =  130

2 ( 32 + 2 ) =  68.

Since we are looking for the smallest perimeter, it is the smallest answer this time.

So it must be A, since 32 is the smallest.

Hope this helps!

Answer:

To change Tim's running rate from kilometers per hour to minutes per mile, we need to use unit conversion factors.

First, we need to convert the distance from kilometers to miles. One kilometer is equal to 0.621371 miles. Therefore, 50 kilometers is equal to:

50 km * 0.621371 mi/km = 31.06855 miles

Next, we need to convert the time from hours to minutes. One hour is equal to 60 minutes. Therefore, 4.5 hours is equal to:

4.5 hours * 60 min/hour = 270 minutes

Now, we can calculate Tim's running rate in minutes per mile by dividing the time by the distance:

270 min / 31.06855 miles = 8.69805 minutes per mile

So the expression that will allow Tim to change his running rate to minutes per mile is:

(4.5 hours * 60 min/hour) / (50 km * 0.621371 mi/km)

Step-by-step explanation:

duh

The area of the larger figure that is similar to the smaller one is: 28.2 m².

Where A and B represent the areas of two similar figures, and a and b are their corresponding side lengths, respectively, the formula that relates their areas and side lengths is:

Area of figure A / Area of figure B = a²/b².

Given that the two figures are similar as shown in the image above, find each of their respective side lengths if we are given the following:

Perimeter of smaller figure = 20 m

Area of smaller figure = 19.6 m²

Perimeter of larger figure = 34m

Area of larger figure = x

Therefore:

20/34 = a/b

Simplify:

10/17 = a/b.

Find the area (x) of the larger figure using the formula given above:

10²/12² = 19.6/x

100/144 = 19.6/x

100x = 2,822.4

x = 2,822.4/100

x ≈ 28.2 m²

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Possible rational zeros:
1. \(\frac{1}{1}\)
2. \(\frac{-1}{1}\)
3. \(\frac{3}{1}\)
4. \(\frac{-3}{1}\)
5. \(\frac{9}{1}\)
6. \(\frac{-9}{1}\)
7. \(\frac{1}{2}\)
8. \(\frac{-1}{2}\)
9. \(\frac{3}{2}\)
10. \(\frac{-3}{2}\)
11. \(\frac{9}{2}\)
12. \(\frac{-9}{2}\)

The rational zeros theorem, also known as the rational root theorem, helps us determine all the possible rational zeros of a polynomial equation. In this case, we have the polynomial equation \(f(x) = 4x^3 + 8x^2 - 2x + 9\).

To find the possible rational zeros, we need to consider the factors of the constant term (in this case, 9) and the factors of the leading coefficient (in this case, 4). The factors of 9 are ±1, ±3, and ±9. The factors of 4 are ±1 and ±2.

Now, let's list all the possible rational zeros by taking the ratio of these factors. We can write them in the form of \(\frac{p}{q}\), where \(p\) is a factor of 9 and \(q\) is a factor of 4.

Possible rational zeros:
1. \(\frac{1}{1}\)
2. \(\frac{-1}{1}\)
3. \(\frac{3}{1}\)
4. \(\frac{-3}{1}\)
5. \(\frac{9}{1}\)
6. \(\frac{-9}{1}\)
7. \(\frac{1}{2}\)
8. \(\frac{-1}{2}\)
9. \(\frac{3}{2}\)
10. \(\frac{-3}{2}\)
11. \(\frac{9}{2}\)
12. \(\frac{-9}{2}\)

These are all the possible rational zeros of the given polynomial equation. However, it's important to note that not all of these values will necessarily be zeros of the equation. To determine which of these values are actually zeros, we can use synthetic division or substitution to evaluate the polynomial at each possible zero.

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Answer:

hehe

Step-by-step explanation:

please

why

Answer: .416666667

Step-by-step explanation: Take 80 and divide it by 192.0= .416666667

Answer:

4. 1/5

Step-by-step explanation:

Answer:

2n-7=3n-3

Step-by-step explanation:

2n-7=3n-3

There are 2 n variable tiles and 7 -1 tiles for the first and 3 n variable tiles and  3 -1 tiles for the seconds.

Answer:

40, 32

Step-by-step explanation:

Ratio = 5 : 4

Shares are = 5x , 4x

5x + 4x = 72

        9x = 72

          x = 72/9

          x = 8

5x = 5 * 8 = 40

4x = 4 *8 = 32

He has $14 9/10 to spend on gift C

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

Total = $30

Gift A = $9 7/10

Gift B = $5 2/5

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

Gift C = Total - Gift A - Gift B

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

Gift C = 30 - 9 7/10 - 5 2/5

Evaluate

Gift C = 14 9/10

Hence, the amount is $14 9/10

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The statement "secondary data should be gathered first because this type of information is less expensive to obtain" is actually false because it has already been collected, there are some important factors to consider.

Primary data is data that is collected specifically for the purpose of the research project at hand. This type of data can include surveys, interviews, experiments, and observations. On the other hand, secondary data is data that has already been collected by someone else for a different purpose.

Firstly, it's important to consider the quality of the data. Secondary data may not always be reliable or up-to-date, which could impact the accuracy of your research findings. In some cases, you may need to spend time and resources verifying the accuracy of the secondary data, which could end up being more expensive in the long run.

Additionally, it's important to consider the specific needs of your research project. Depending on your research question, primary data may be necessary to obtain the specific information you need. In other cases, secondary data may be sufficient.

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The radius of the circle is approximately 1.13 kilometers.

The formula for the area (A) of a circle is:

4 = π\(r^2\)

where r is the radius of the circle and π (pi) is a constant approximately equal to 3.14.

We are given that the area of the circle is 4 square kilometers. So we can set up an equation:

4 = π\(r^2\)

To solve for r, we can divide both sides of the equation by π and then take the square root of both sides:

r = √(4/π)

r ≈ 1.13 km

Therefore, the radius of the circle is approximately 1.13 kilometers.

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Answer:

2.95 x 24 + 4

2.95 x 10 = 29.50

29.50 x 2 = 59.00

59.00 + 4 = 63.00

2.95x4 =11.80

74.80 total

hope I helped

Answer:

2.95 x 24 + 4

53.95

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The Cost of one case of soda is ~

\( \fbox \colorbox{black}{ \colorbox{white}{cost} \: \: \: \: \: \: \: \: \colorbox{white}{ = } \: \: \: \: \: + \colorbox{white}{476.92}}\)

The solution is in attachment ~

Answer:

1) 4.5 x 10^3 =4,500

2)5.78 x 10^-2

3) 5.7 x 10^1 = 57

4) 6.256 x 10^-3 = 0.006256

5) 7.3 x 10^2 = 730

6) 4.2 x 10^-5 = 0.000042

7) 7x10^-3 = 0.007

8) 2.563 x 10^1

9) 3.0025 x 10^2 = 300.25

10) 1.456 x 10^-1

Answer:

Step-by-step explanation:

You first have to find the area of the square grid

To find this you multiply the sides

14 * 14 = 196

Next you have to find the area of the triangle

To find the area of a triangle you use the equation

h is height

b is base

Put in the values you know

Multiply

The area of the triangle is 49 inches squared

You divide the area of the triangle by the area of the square

196 / 49 = 4

The answer is 4 triangles

Yes, the given coordinates X(1,-3), Y(6,1), Z(2,2) are the vertices of a triangle.

1. Calculate the distance between the points X and Y using the distance formula:

d = √[(x2 - x1)2 + (y2 - y1)2]

d = √[(6 - 1)2 + (1 - (-3))2]

d = √[52 + 42]

d = √25 + 16

d = √41

d = 6.4

2. Calculate the distance between the points Y and Z using the distance formula:

d = √[(x2 - x1)2 + (y2 - y1)2]

d = √[(2 - 6)2 + (2 - 1)2]

d = √[(-4)2 + 12]

d = √16 + 12

d = √28

d = 5.3

3. Calculate the distance between the points Z and X using the distance formula:

d = √[(x2 - x1)2 + (y2 - y1)2]

d = √[(1 - 2)2 + (-3 - 2)2]

d = √[(-1)2 + (-5)2]

d = √1 + 25

d = √26

d = 5.1

Since each side of a triangle must have a length greater than 0, and the distances calculated above are all greater than 0, then the given coordinates X(1,-3), Y(6,1), Z(2,2) are the vertices of a triangle.

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The odd cubic function f(x) = x³ - 4x² + 5 is approaching (x → ∞, y → ∞).

A polynomial function's final behavior is how its graph behaves as x gets closer to positive or negative infinity.

The graph's final behavior is determined by a polynomial function's degree and leading coefficient.

The function f(x) = x³ - 4x² + 5 is an odd cubic function that is symmetric about the origin.

As x approaches negative infinity the function f(x) also approaches negative infinity but at a faster rate and as approaches positive infinity the function f(x) also approaches positive infinity at a faster rate.

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Answer:

2

Step-by-step explanation:

An arithmetic progression with first term a and common difference d has the following first 6 terms:

a, a + d, a + 2d, a + 3d, a + 4d, a + 5d

We are given a = 1 and a + 5d = 11.

1 + 5d = 11

5d = 10

d = 2

Answer: The common difference is 2.

Answer:

c=3

Step-by-step explanation:

Angle sum of a triangle is 180°

(19c+16)°+13c°+(17c+17)°=180°

collect the like terms i.e

19c+13c+17c+16+17=180°

49c°+33°=180°

49c°=180°-33°

49c°=147

dividing by 49 both sides

49c/49=147/49

c=3

Answer:

Step-by-step explanation:

To model all of the possible amounts of money (m) Ronaldo spends on gas each week, an inequality of $29.15 is used.

Therefore,

For instance lowest amount $2.40.

$2.40 × 8.5 = $20.40

Highest Amount $2.65.

$2.65 × 8.5 = $29.15

$2.40 ≤ m ≤ $29.15.

Hence, To model all of the possible amounts of money (m) Ronaldo spends on gas each week, an inequality of $29.15 is used.

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Answer:

Step-by-step explanation:

The equation of a hyperbola with directrices at x = ±2 and foci at (6, 0) and (−6, 0) is y squared over 48 minus x squared over 12 equals 1.

The equation of the hyperbola is the equation which is used to represent the hyperbola in the algebraic equation form, with the value of center point in the coordinate plane and foci.

The standard form of the equation of the hyperbola can be given as,

\(\dfrac{(y-k)^2}{b^2}-\dfrac{(x-h)^2}{a^2}=r^2\)

Here (h,k) is the center of the hyperbola, (b) is the transverse axis, and (a) is the conjugate axis.

The foci of the hyperbola is,

\((h,k\pm c)\)

The directrix is,

\(y=k\pm \dfrac{a^2}{c}\)

A hyperbola is given with directrices at x = ±2 and foci at (6, 0) and (−6, 0). Thus, the directrix is,

\(y=k\pm \dfrac{a^2}{c}\\\pm 2=k\pm \dfrac{a^2}{c}\\\dfrac{a^2}{6}=2\\a^2=12\\\)

It is known that,

\(a^2+b^2=c^2\\\)

Put the value of a and c,

\((12)+b^2=6^2\\b^2=36-12\\b^2=24\)

The value of center is (0,0). Thus, the equation of hyperbola is,

\(\dfrac{(y-0)^2}{24^2}-\dfrac{(x-0)^2}{12^2}=1\\\dfrac{y^2}{24^2}-\dfrac{x^2}{12^2}=1\)

Thus, the equation of a hyperbola with directrices at x = ±2 and foci at (6, 0) and (−6, 0) is y squared over 48 minus x squared over 12 equals 1.

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Answer:

x = y = 104°

Step-by-step explanation:

The sum of the interior angles = 360°

The opposite angles x and y are congruent , that is y = x , then

92 + 60 + x + x = 360

152 + 2x = 360 ( subtract 152 from both sides )

2x = 208 ( divide both sides by 2 )

x = 104

Then

x = y = 104°

Answer:

  42, 38, 34, 30

Step-by-step explanation:

You want the first 4 terms of the sequence described by ...

  an = 42 -4(n -1), n ∈ ℕ

You can write the first 4 terms of the sequence by evaluating the 'an' expression for n = 1, 2, 3, 4.

Or, you can recognize the expression describes a sequence with a first term of 42 and a common difference of -4. That is, each term is 4 less than the one before.

The terms you want are ...

  42, 38, 34, 30

__

Additional comment

The equation for the n-th term of an arithmetic sequence is ...

  an = a1 +d(n -1)

where a1 is the first term, and d is the common difference. Comparing this to the given equation, we see a1 = 42, d = -4.

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The solution is, x_1 = -2 + 2√3 and, x_2 = -2 - 2√3, are solutions to the equation below.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

here, we have,

1) Since we've been given the equation x²+4x +4=12 then let's solve it to find the roots

2) Applying the resolutive formula

x²+4x +4=12

x²+4x +4-12 =0

x²+4x -8=0

now, we know, here,

D = b² - 4ac

so, solving we get,

D = 48

Now, the roots are,

x = -b ± √D / 2a

so, here, we get,

x_1 = -2 + 2√3

x_2 = -2 - 2√3

Hence, The solution is, x_1 = -2 + 2√3 and, x_2 = -2 - 2√3, are solutions to the equation below.

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