if 6x-1=29, what is the value of x2+x

Answer:

x < 5

Step-by-step explanation:

[tex]2x - 4 < 6[/tex]

[tex]2x < 10[/tex]

[tex]x < 5[/tex]

.........................................................

After solving the given equation using quadratic formula we gat solutions as 0.83 and 0.169

What is quadratic formula?

Any quadratic problem can be solved using the quadratic formula. The equation is first changed to have the form ax2+bx+c=0, where a, b, and c are coefficients. After that, we enter these coefficients into the following formula: (-b±√(b²-4ac))/(2a).

On simplifying the given equation we get,

(2x-3)²=4x

4x²+9-12x = 4x

4x²-16x+9 = 0

Comparing with ax²+bx+c = 0

a = 4, b = -16, c = 9

Quadratic formula is:

[tex]\frac{-b +- \sqrt{b^2-4ac} }{2a}[/tex]

putting the values from question we get,

[tex]\frac{16 +- \sqrt{16^2-4(4)(9)} }{216}[/tex]

[tex]\frac{16 +- \sqrt{256-144} }{32}[/tex]

[tex]\frac{16 +- \sqrt{112} }{32}[/tex]

[tex]Solution 1 = \frac{ 16+ 10.58 }{32} = 0.83[/tex]

[tex]Solution 2 = \frac{16 - 10.58}{32} = 0.169[/tex]

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Complete question

(2x-3)²=4x solve using quadratic formula

The linear regression equation that represents this data is given as follows: y = 22x - 518.

Using this equation, when 38 passes are thrown, the expected yardage is of 318 yards.

To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.

In the context of this problem, the input and output are given as follows:

The points to be inserted in the calculator are given as follows:

(39, 360), (35, 235), (35, 262), (37, 249), (40, 338).

Hence the equation is given by:

y = 22x - 518.

With 38 passes, the expected yardage is calculated as follows:

y = 22(38) - 518 = 318 yards.

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[tex]0.744\div6[/tex]

Simplify:

[tex]\frac{0.744}{6}[/tex]

[tex]=0.124[/tex]

Answer: 2 years

Step-by-step explanation: If Joe was meant to serve 5 years but then his sentence got shortened by 3 years, that means we need to use subtraction. 5 minus 3 equals 2. Therefore, the answer is 2 years.

The measure that would most correctly answer this question is standard deviation.

What is standard deviation?

The standard deviation is measure of how spread out data from mean.

Step-by-step explanation:

Average age of respondents in a survey is [tex]49[/tex] years. Researcher interested in finding out if most respondents are close to [tex]49[/tex] years or not.

Hence here measures of dispersion fact will be used.

Measures of dispersion are range and standard deviation.

Range is nothing but the difference between maximum and minimum values of the data.

Standard deviation gives proper idea about how far the data values are scattered from the mean point [tex]49[/tex] years.

Therefore the correct option is standard deviation.

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1. The pairs for each tent, based on common factors of 40, are given as follows (1, 40), (2, 20), (4, 10), (5, 8), (8, 5), (10, 4), (20, 2), and (40, 1).

2. Matching the number of tents with the number of boys is as follows:

     1                                          40

    2                                          20

    3                                          No match

    4                                          10

    5                                          8

    6                                          No match

    7                                          No match

The factors of a number are the numbers that can divide it exactly or without a remainder.

For instance, the factors of the number, 40, are 1, 2, 4, 5, 8, 10, 20, and 40.

Thus, there are 8 ways that the tents can be arranged to accommodate the campers (boys) based on the factors of 40.

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Answer:

x = 11

Step-by-step explanation:

the area (A) of a trapezium is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the perpendicular height between the bases b₁ and b₂

here h = 4 , b₁ = x , b₂ = 6 and A = 34 , then

[tex]\frac{1}{2}[/tex] × 4 × (x + 6) = 34

2(x + 6) = 34 ( divide both sides by 2 )

x + 6 = 17 ( subtract 6 from both sides )

x = 11

The age of the radioactive artifact is approximately 19029.6 years old

Radioactivity is the phenomenon of the spontaneous disintegration of unstable atomic nuclei to atomic nuclei to form more energetically stable atomic nuclei. Radioactive decay is a highly exoergic, statistically random, first-order process that occurs with a small amount of mass being converted to energy.

To solve this problem, we have to find the disintegration constant and we can use the formula of half-life of the sample to do that.

The half-life of a sample is given as;

[tex]T_\frac{1}{2}=\frac{ln}{\lambda}\\T_\frac{1}{2} =\frac{ln}{5715} \\ T_\frac{1}{2} = 0.000121\\[/tex]

The formula of radioactivity is given as

[tex]N = N_oe^(^-^\lambda ^t)[/tex]

Substituting the values into the equation

[tex]N = N_oe^(^-^\lambda ^t)\\\frac{N}{N_o} = e^-^(^\lambda ^t)\\0.1 = e^-^(^0^.^0^0^0^1^2^1^*^t^)\\t = 19029.6 years[/tex]

The artifact is approximately 19029.6 years.

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Answer: b=13

Step-by-step explanation:

b=39/3

b=13

Answer:  its 13  

Step-by-step explanation

Answer:

769 and 858

Step-by-step explanation:

Every hour, the distance between the two planes increases by 2x + 89

2 hours = 4x + 178

3254 = 4x + 178

4x = 3076

x = 769

Answer:

SSS

Step-by-step explanation:

We know the length of DE and JK are the same because as shown in the diagram, they are both equal to 15 cm. While we know that EF and KL are congruent because it is shown that both sides are 8 cm long. Even though we are not sure of the exact lengths of FD or LJ, we are aware that they are the same length sue to the ticks found on both sides on the triangles, indicating that they are both the same length.

Solution

- The rule for this transformation is given below:

- Based on this rule, f(x + 8) will shift the graph 8 units to the left

Final Answer

Shifted left (OPTION B)

The following investments were done:

In this problem we must determine how much money from a $ 8,000 investment has been deposited in each account based on overall yield after a period of one year. In accordance with the statement, the person deposited the following quantities in each account:

Metal: x

Glass: 2 · x

Paper: 8,000 - 3 · x

And the yield function is equal to:

280 = x · (4 / 100) + 2 · x · (5 / 100) + (8,000 - 3 · x) · (2 / 100)

280 = 0.04 · x + 0.1 · x + 160 - 0.06 · x

120 =  0.08 · x

x = 1500

The person made an investment of $ 1,500 in the metal account, $ 3,000 in the glass account and $ 3,500 in the paper account.

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lets remember what it means compound continuously,

the interest never stopped, the balance is earning interest at all time

Joseph is 22 and he wants to know how much money he will have at 55

55-22=33

his balance will gain interest for 33 years, this is our time

there is a 7% rate

the formula is

P(t)= P(0) e ^rt

our t is 33

rate=7%

Joseph will have a balance at age 55, 45,334.99 dollars

An equation for the line of best fit for a men's height, y, based on her shoe size, x is; y = 0.25x + 66.6

A line of best fit can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.

In this scenario, the men's shoe size would be plotted on the x-axis of the scatter plot while her height would be plotted on the y-axis.

By critically observing the scatter plot (see attachment) which models the data, we can reasonably deduce that an equation for the line of best fit is given by:

y = 0.25x + 66.6

Interpret the meaning of the residual from part B is given below.

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The mistake that Dolly have in her conclusion is A. Her experiment lasted for 10 weeks since she did not record what she ate for 2 weeks. That her experiment lasted for 10 weeks since she did not record what she ate for 2 weeks.

An experiment is carried out in order to get more information about a particular thing.

In this case, at the end of the 10 weeks, she graphed her weight over time and noticed that for the two weeks she didn't write down anything she lost weight.

Therefore, this caused the mistake that was noticed.

In conclusion, the correct option is A.

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Answer:

1 x 10^16

Step-by-step explanation:

Given (x+ c) is a common factor of (x^2- ax- b )and (2x^2+b)

x= -c is a root of x^2- ax- b= 0 and x^2+ b= 0

Concept used

Quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

-b±√b²-4ac/2a

i) 1- 2a+b= 0

ii) 4+ b^b- 2a= 0

4- 2a+b=0,4+ b- 2a= 0

2a+b= 2c+d

2(c−a)= b−d

(c−a)/ (b−d)​= 2

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Answer:

A. 1/6 would be the answer I think

The graphed function in the slope-intercept form can be written as:

y = -4*x - 2

A general linear function in the slope-intercept form is written as:

y = m*x + b

Where m is the slope and b is the y-intercept.

On the graph, we can see that our line intercepts the y-axis at y = -2, so the y-intercept is b = -2, replacing that we get:

y = m*x - 2

We also can see that the line passes through (-1, 2), replacing these values on the linear equation we get:

2 = m*(-1) - 2

m = -2 - 2

m = -4

Thus, the linear function in the graph is:

y = -4*x - 2

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Answer:

Step-by-step explanation:

solve for x

2x+14=-21-5

2x+14=-26

subtract 14 from both sides

2x+(14-14)=-14-26

2x=-14-26

2x=-40

divide both sides of 2x = -40 by 2

[tex]\frac{2x}{2} =\frac{-40}{2}[/tex]

2/2=1

x=[tex]\frac{-40}{2}[/tex]

x= -20

We need to know how to interpret a graph to solve the problem. (a) h is a function of t. (b) Approximate  height of the projectile affter 0.5 second is 20 feet and after 1.25 seconds is 30 feet (c).The approximate domain is [0,2.5] and range is [0,30] (d) t is not a function of h.

(a) h is a function of t since the height of the projectile varies with time. The input values of the function is the time interval and the output values is the height of the projectile.

(b) The approximate height of the projectile after 0.5 second according to the graph is 20 feet and the height of the projectile after 1.25 second according to the graph is 30 feet.

(c)The domain of the function is [0,2.5] and the range of the function is [0,30].

(d) t is not a function of h.

Therefore a) h is a function of t. (b) Approximate  height of the projectile affter 0.5 second is 20 feet and after 1.25 seconds is 30 feet (c).The approximate domain is [0,2.5] and range is [0,30] (d) t is not a function of h.

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The problem says you have 10 books arranged on a shelf and then you are choosing 4 books in alphabetical order.

Given that you are choosing books with an order (alphabetical) it means the order does matter, then it is a permutation (which is an ordered combination).

In this case, no repetitions are allowed because you can't repeat a book in the selection, they'll be 4 different books from the shelf, the formula you have to use is:

Then n=10 and r=4, replace these values:

Then, can be chosen 5040 different groups of books.

The answer is option D.

The equation written when r is the subject is:

[tex]\displaystyle{r=\dfrac{5p}{m}-n}[/tex]

To make the term r as the subject of equation means to isolate r-term. In order to do that, we will apply properties of equality.

Properties of equality are properties regarding equations/equality where states that when either sides are done by something (addition, subtraction, multiplication, division, etc.) then the other sides will also act the same as the acted side.

Example

Suppose we are given an equation of x = y. In this case, x and y are equal to each other. If x = 1 then y = 1. If we decide to add +2 to x we’d have to add it to y too so the result will be x + 2 = y + 2.

Same also applies to other equations!

Isolating r-term, first, we will apply division property where we divide both sides by m-term:

[tex]\displaystyle{\dfrac{m(n+r)}{m}=\dfrac{5p}{m}}\\\\\displaystyle{n+r=\dfrac{5p}{m}}[/tex]

Next, we use subtraction property to subtract both sides by n:

[tex]\displaystyle{n+r-n=\dfrac{5p}{m}-n}\\\\\displaystyle{r=\dfrac{5p}{m}-n}[/tex]

Please let me know if you have any questions!

The number of pounds when company A and B have same amount is 16 pounds.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe a scenario.

In this case, shipping company A charges a flat fee of $7 plus $0.50 for each pound shipping company B charges a flat fee of $11 plus $0.25 for each pound.

Let each pound be represented by p.

Company A will be 7 + 0.50p

Company B will be 11 + 0.25p

We will equate both equations.

7 + 0.50p = 11 + 0.25p

Collect like terms

0.50p - 0.25p = 11 - 7

0.25p = 4

Divide

p = 4 / 0.25

p = 16

The number of pounds is 16 pounds.

The complete information is given below.

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shipping company A charges a flat fee of $7 plus $0.50 for each pound shipping company B charges a flat fee of $11 plus $0.25 for each pound. How many pounds will give an equal amount?

The dimensions are Width = 7 feets ; length = 20 feets

As given,

Meadow area is 140 square feet.

Height = W (smaller dimension and 2 sides)

Height = L (longer dimension and 1 side)

Fence yards equal 34 feet;

Hence,

L + W = 34

L + 2W = 34

L = 34 - 2W - - - (1)

Recall:

Area = L * W = 140

Substitute value of L

140 = (34 - 2W) * W

140 = 34W - 2W²

2W² - 34W + 140 = 0

W² - 17W + 70 = 0

W² - 10W - 7W + 70 = 0

W(W - 10) - 7(W - 10) = 0

(W - 10) = 0 or (W - 7) =0

W = 10 or W = 7

We choose the shorter width because length should be as long as possible:

W = 7

L + 2W = 34

L = 30 - 14

L = 20 feets

Therefore, The measurements are 7 feet wide and 20 feet long.

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Answer: y = 15

Step-by-step explanation:

Combine multiplied terms into a single fraction

-6 = -2y/5

Then, multiply both sides by 5 to get:

-30 = -2y

Last, you divide both sides by -2 to get:

15 = y or y = 15

Hope this helps!

Draw of a modelled object

Answer:

x = 11,2 inchs

Step-by-step explanation:

I infer that the units are in inches.

8-3 = 5

Then:

By the Pythagorean Teorem:

x² = 10² + 5²

x² = 100 + 25

x² = 125

√x² = √125

x = 11.18

to the nearest tenth:

x = 11.2 inches