What are the solutions of the equation (x + 2)2 + 12(x + 2) - 14 = 0? Use u substitution and the quadratic formula to solve.

Answer:

[tex]\large\boxed{x=-1\ or\ x=1}[/tex]

Step-by-step explanation:

[tex]x^4+3x^2-4=0\\\\x^{(2)(2)}+3x^2-4=0\qquad\text{use}\ (a^n)^m=a^{nm}\\\\(x^2)^2+3x^2-4=0\qquad\text{substitute}\ x^2=t\geq0x=\\\\t^2+3t-4=0\\\\t^2+4t-t-4=0\\\\t(t+4)-1(t+4)=0\\\\(t+4)(t-1)=0\iff t+4=0\ \vee\ t-1=0\\\\t+4=0\qquad\text{subtract 4 from both sides}\\t=-4<0\\\\t-1=0\qquad\text{add 1 to both sides}\\t=1>0\to x^2=1\\\\x^2=1\to x=\pm\sqrt1\to x=-1\ \vee\ x=1[/tex]

so we know the terminal point is at (9, -3), now, let's notice that's the IV Quadrant

[tex]\bf (\stackrel{x}{9}~~,~~\stackrel{y}{-3})\impliedby \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{9^2+(-3)^2}\implies c=\sqrt{81+9}\implies c=\sqrt{90} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf cos(\theta )=\cfrac{\stackrel{adjacent}{9}}{\stackrel{hypotenuse}{\sqrt{90}}}\implies \stackrel{\textit{rationalizing the denominator}}{\cfrac{9}{\sqrt{90}}\cdot \cfrac{\sqrt{90}}{\sqrt{90}}\implies \cfrac{9\sqrt{90}}{90}}\implies \cfrac{\sqrt{90}}{10}\implies \cfrac{3\sqrt{10}}{10}[/tex]

[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\displaystyle\sum \limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf S_{20}=\displaystyle\sum \limits_{n=1}^{\stackrel{\stackrel{n}{\downarrow }}{20}}~\stackrel{\stackrel{a_1}{\downarrow }}{3}(\stackrel{\stackrel{r}{\downarrow }}{1.5})^{n-1}\implies S_{20}=3\left(\cfrac{1-1.5^{20}}{1-1.5} \right)\implies S_{20}=3\left(\cfrac{1-\stackrel{\approx}{3325.3}}{-0.5} \right) \\\\\\ S_{20}=3\left(\cfrac{-3324.3}{-0.5} \right)\implies S_{20}=3(6648.6)\implies S_{20}=19945.8[/tex]

19945.8 to simplify, the answer is

Answer:

x=1+2√2 or x=1−2√2

Step-by-step explanation:

Let's solve your equation step-by-step.

3x2−6x=21

Step 1: Since the coefficient of 3x^2 is 3, divide both sides by 3.

3x2−6x

3

=

21

3

x2−2x=7

Step 2: The coefficient of -2x is -2. Let b=-2.  

Then we need to add (b/2)^2=1 to both sides to complete the square.

Add 1 to both sides.

x2−2x+1=7+1

x2−2x+1=8

Step 3: Factor left side.

(x−1)2=8

Step 4: Take square root.

x−1=±√8

Step 5: Add 1 to both sides.

x−1+1=1±√8

x=1±√8

x=1+2√2 or x=1−2√2

Answer:

17.C

18.A

Step-by-step explanation:

17. Slope=(y2-y1)/(x2-x1)

=(-1-(-2))/(4-(-3))

=1/7

18.Slope=(y2-y1)/(x2-x1)

=(9-6)/(2-0)

=3/2

Do you want 19 and 20 too?

Question 1:

For this case we have that by definition, the slope of a line is given by:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]

Where:

[tex](x_ {1}, y_{1}) and (x_ {2}, y_{2})[/tex]are two points through which the line passes.

[tex](x_ {1}, y_{1}) = (- 3, -2)\\(x_ {2}, y_{2}) = (4, -1)[/tex]

Substituting in the equation:

[tex]m = \frac {-1 - (- 2)} {4 - (- 3)} = \frac {-1 + 2} {4 + 3} = \frac {1} {7}[/tex]

ANswer:

Option C

Question 2:

For this case we have that by definition, the slope of a line is given by:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]

Where:

[tex](x_ {1}, y_{1}) and (x_ {2}, y_{2})[/tex] are two points through which the line passes.

[tex](x_ {1}, y_{1}) = (0,6)\\(x_ {2}, y_{2}) = (2,9)[/tex]

Substituting in the equation:[tex]m = \frac {9-6} {2-0} = \frac {3} {2}[/tex]

ANswer:

Option A

Question 3:

For this case we have that by definition, the slope of a line is given by the following formula:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]

Where:

[tex](x_ {1}, y_{1}) and (x_ {2}, y_{2})[/tex]are two points through which the line passes.

We have as data:

[tex]m = \frac {7} {8}\\(x_ {1}, y_{1}) = (- 2,1)[/tex]

Substituting in the formula:

[tex]\frac {7} {8} = \frac {y_ {2} -1} {x_ {2} - (- 2)}\\\frac {7} {8} = \frac {y_ {2} -1} {x_ {2} +2}[/tex]

We substitute each of the points and see if the equality is met:

Point A: (6,8)

[tex]\frac {7} {8} = \frac {8-1} {6 + 2}\\\frac {7} {8} = \frac {7} {8}[/tex]

Equality is met.

Answer:

Option A

Question 4:

For this case we have that by definition, the slope of a line is given by the following formula:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]

Where:

[tex](x_ {1}, y_{1}) and (x_ {2}, y_{2})[/tex]are two points through which the line passes.

We have as data:

[tex]m = \frac {1} {6}\\(x_ {1}, y_{1}) = (0, -3)[/tex]

Substituting in the formula:

[tex]\frac {1} {6} = \frac {y_ {2} - (- 3)} {x_ {2} -0}\\\frac {1} {6} = \frac {y_ {2} +3} {x_ {2} -0}[/tex]

We substitute each of the points and see if the equality is met:

Point A: (-3,0)

[tex]\frac {1} {6} = \frac {0 + 3} {- 3-0}\\\frac {1} {6} = \frac {3} {- 3}[/tex]

It is not fulfilled!

Point B: (6, -2)

[tex]\frac {1} {6} = \frac {-2 + 3} {6-0}\\\frac {1} {6} = \frac {1} {6}[/tex]

Equality is met!

ANswer:

Option B

Answer:

[tex]\displaystyle \frac{54}{5405}[/tex].

Step-by-step explanation:

How many unique combinations are possible in total?

This question takes 5 objects randomly out of a bag of 50 objects. The order in which these objects come out doesn't matter. Therefore, the number of unique choices possible will the sames as the combination

[tex]\displaystyle \left(50\atop 5\right) = 2,118,760[/tex].

How many out of that 2,118,760 combinations will satisfy the request?

Number of ways to choose 2 red candies out a batch of 28:

[tex]\displaystyle \left( 28\atop 2\right) = 378[/tex].

Number of ways to choose 3 green candies out of a batch of 8:

[tex]\displaystyle \left(8\atop 3\right)=56[/tex].

However, choosing two red candies out of a batch of 28 red candies does not influence the number of ways of choosing three green candies out of a batch of 8 green candies. The number of ways of choosing 2 red candies and 3 green candies will be the product of the two numbers of ways of choosing

[tex]\displaystyle \left( 28\atop 2\right) \cdot \left(8\atop 3\right) = 378\times 56 = 21,168[/tex].

The probability that the 5 candies chosen out of the 50 contain 2 red and 3 green will be:

[tex]\displaystyle \frac{21,168}{2,118,760} = \frac{54}{5405}[/tex].

The median is 8. You have to arrange it and then since it’s an even number add the two middle numbers and divide by 2.

ANSWER

The median is 8

EXPLANATION

The given date set is 3,10,1, 6, 10,3,11,14

We rearrange the data set in ascending order of magnitude to get:

1,3,3,6,10,10,11,14

There are two numbers {6,10} in the middle of the data set after arranging in ascending order.

The median is the mean of thesecond two numbers.

The median is

[tex] \frac{6 + 10}{2} = \frac{16}{2} = 8[/tex]

Therefore the median is 8

Answer:

Step-by-step explanation:

A direct variation suggest that the value of x in the equation would greatly affect the value of y such that when x is increasing, y also increases and the other way around. The equation for a direct variation is that,

                              y  = kx

Substituting the given values in the ordered pair,

                          5 = k(4)   ; k = 5/4

answer: y = kx hope this helps

Answer:

The median is 72.

Answer:

72

Step-by-step explanation:

68  69  71  71  72  72  74  74  76

68  76  69  74  71  74  71  72  72

72 is the median

ANSWER

See attachment.

EXPLANATION

The given function is

[tex]y = \sqrt[3]{x + 1} - 2[/tex]

The parent function is

[tex]y = \sqrt[3]{x} [/tex]

When we shift the parent graph to the left one unit, and down 2 units, we obtain the graph of the given function.

The graph of this function is shown in the attachment.

Answer: Last option

Step-by-step explanation:

Note that when the point is not included in the function is marked with an empty circle, and when the point is included in the function is marked with a filled circle.

From the interval [tex]0\leq x <3[/tex] f(x) is represented by the slanted line [tex]-x +4[/tex] that cuts the y-axis at [tex]y = 4[/tex]

The starting point of the line must be filled and the end point must be empty.

Then, from the interval [tex]x \geq 3[/tex] f(x) is defined by the horizontal line [tex]y = 6[/tex]. The starting point of this line is marked with a filled circle because it includes the point [tex]x = 3[/tex]

Therefore the correct option is option D or the last graph (from left to right)

Answer:

last one

Step-by-step explanation:

The probability of obtaining at random without replacement two gum balls is 3/11.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Given, A gumball machine contains six yellow gumballs and five orange gumballs.

So, N(Y) = 6 and N(O) = 5 and the number of sample space N(S) = 11.

Therefore, The probability of obtaining at random without replacement two gum balls is,

P(YY) = (6/11)×(6 - 1)/(11 - 1).

P(YY) = (6/11)×(5/10).

P(YY) = 30/110.

P(YY) = 3/11.

learn more about probability here :

https://brainly.com/question/743546

#SPJ2

Answer:

Step-by-step explanation:

Function g(x) = x - 2 is in the denominator.  We cannot divide by zero, so the domain of (f/g)(x) is x ≠ 2.

To find the domain of f(x)/g(x), consider where g(x) is not zero as division by zero is undefined. The domain is all real numbers except x = 2.

The domain of f(x)/g(x) is determined by the values of x that make the expression defined while avoiding division by zero. To find the domain, we need to consider where g(x) is not equal to zero, as division by zero is undefined.

Given: f(x) = (x+1)⁻¹ and g(x) = x-2. As g(x) is not zero at x = 2, the domain of f(x)/g(x) is all real numbers except x = 2.

The study where a scientist selects 400 people who snore to observe how many hours they snore, and calculates the average time as 4.2 hours, is an observational study.

When a scientist selects 400 people who snore at night to test how many hours they actually snore, and they gather data on the average length of time, which is 4.2 hours, this type of study is known as an observational study.

In an observational study, researchers simply observe the subjects in a study without manipulating any variables. This is different from an experimental study, where scientists would manipulate certain factors to observe the effects.

Therefore, the correct answer to your question is that the study is an observational study.

Nicole has 25 ten-dollar bills.

To find out how many ten-dollar bills Nicole has, we can divide the total amount of money she has by the value of each bill.

$250 / $10 = 25

Therefore, Nicole has 25 ten-dollar bills.

Answer in detail:

Nicole has $250 in ten-dollar bills. This means that she has 25 groups of $10.

We can divide $250 by $10 to find out how many groups of $10 she has.

$250 / $10 = 25

Therefore, Nicole has 25 ten-dollar bills.

Another way to look at it is this way:

If Nicole has 1 ten-dollar bill, then she has $10.

If Nicole has 2 ten-dollar bills, then she has $20.

If Nicole has 3 ten-dollar bills, then she has $30.

And so on.

So, to find out how many ten-dollar bills Nicole has, we can simply divide the total amount of money she has by the value of each bill.

Hello There!

So we know Some number added to 27 gets a sum of -12

We can figure this out by subtracting 27 from -12 so we would go back.

Once we subtract, -39 will be x and that is our answer.

The correct answer is -39

(5 x 10) + (8 x 1) + (8 x 0.1)

OR

50 + 8 + .8

Fifty-eight and eight tenths

Hope this helped!

Hello!

-EXPANDED FORM- To make the number 58.8 in expanded form, we start out with the number 50 and then add 8 ones to it and finally add .08

-WORD FORM- To make the number 58.8 in word form, the answer would be Fifty-Eight and Eight Tenths

Answer:

The diagram is shown in the attached image

Explanation:

We are given that Yin labelled her diagram a rectangle

This means that the shape she drew:

1- Is a four sided closed polygon

2- Has equal opposite sides (each two opposite sides are equal)

3- Has parallel opposite sides (each two opposite sides are parallel)

4- Has 4 right angles (all its interior angles are 90°)

This is shown in the attached image

Hope this helps :)

[tex]\bf (\stackrel{x_1}{10}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{-10}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-(-5)}{-10-10}\implies \cfrac{-1+5}{-20}\implies \cfrac{4}{-20}\implies -\cfrac{1}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-5)=-\cfrac{1}{5}(x-10) \\\\\\ y+5=-\cfrac{1}{5}x+2\implies y=-\cfrac{1}{5}x-3[/tex]

all together there are 23

there are 23 states

Answer:

The value of the expression is [tex]0.1544[/tex]

Step-by-step explanation:

we have

[tex][(38*\frac{1}{4})+(33\%*18)]/100[/tex]

we know that

[tex](38*\frac{1}{4})=\frac{38}{4}=9.5[/tex]

[tex](33\%*18)=(33/100)*18=0.33*18=5.94[/tex]

substitute

[tex][9.5+5.94]/100[/tex]

[tex][15.44]/100[/tex]

[tex]0.1544[/tex]

Answer:

B)5/3

Step-by-step explanation:

"3x + 5y = 15."

Rewrite in slope-intercept form.

The slope-intercept form is  

y=mx+b

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

y=mx+b

Subtract  3x  from both sides of the equation.

5y=15−3x

Divide each term by  "5"  and simplify.

5y/5=15/5−3x/5

"5" and "5" cancel each other out

Divide  15  by  5

y=3-3x/5

Reorder  3  and  −3x/5

y=-3x/5+3

Rewrite in slope-intercept form.

y=−3/5x+3

Slope:-3/5

The equation of a perpendicular line to  y=−3x/5+3  must have a slope that is the negative reciprocal of the original slope.

mperpendicular=−1/(−3/5)

Simplify the result.

mperpendicular=5/3

hope this helps!

To find the slope of a line perpendicular to the line 3x + 5y = 15, you first find the slope of the given line, which is -3/5 after rearranging to slope-intercept form. The slope of the perpendicular line is then the negative reciprocal of -3/5, which is 5/3.

To find the slope of a line perpendicular to the given line 3x + 5y = 15, we first need to find the slope of this given line. For this we rearrange the equation into y=mx+b (slope-intercept) form. The given equation can be rewritten as y = -3/5x + 3. Therefore, the slope of this line (m) is -3/5.

The slope of a line perpendicular to the original line is the negative reciprocal of the slope of the original line. Therefore the slope of a line perpendicular to 3x + 5y = 15 is the negative reciprocal of -3/5, which is 5/3. So, the correct answer is B. 5/3.

https://brainly.com/question/34849567

#SPJ2

Answer:

The simplest form of (a + b - c )(a + b + c ) is a² + 2ab + b² - c²

Step-by-step explanation:

* Lets revise how to multiply two brackets with three terms

∵ (a + b - c)(a + b + c)

- Multiply the first term of the first bracket by the three terms of the

 second bracket

∵ a × a = a²

∵ a × b = ab

∵ a × c = ac

- Then multiply the second term in the first bracket by the three terms

 of the second bracket

∵ b × a = ba

∵ b × b = b²

∴ b × c = bc

- Then multiply the third term term in the first bracket by the three terms

 of the second bracket

∵ -c × a = -ca

∵ -c × b = -cb

∵ -c × c = -c²

- Now add all these terms together

∴ a² + ab + ac + ba + b² + bc + -ca + -cb + -c²

- We have like terms lets add them

∵ ab = ba  , ac = ca , bc = cb

∴ a² + (ab + ba) + (ac + -ca) + (bc + -cb) + b² + -c²

∴ a² + 2ab + 0 + 0 + b² - c²

∴ a² + 2ab + b² - c²

∴ The simplest form of (a + b - c )(a + b + c ) is a² + 2ab + b² - c²

The answer is:

[tex]a^{2} +b^{2} -c^{2} +2ab[/tex]

To solve the problem, we need to remember the distributive property.

The distributive property is defined by the following way:

[tex](a+b)(c+d)=ab+ad+bc+bd[/tex]

Also, we need to remember how to add like terms. The like terms are the terms that share the same variable and the same exponent, for example:

[tex]x+x^{2}+x=x^{2} +2x[/tex]

We were able to add the first and the third term because they share the same variable and the same exponent.

Now, we are given the following expression to simplify:

[tex](a+b-c)(a+b+c)[/tex]

So, applying the distributive property and adding like terms, we have:

[tex](a+b-c)(a+b+c)=(a*a)+(a*b)+(a*c)+(b*a)+(b*b)+(b*c)-(c*a)-(c*b)-(c*c)\\\\(a+b-c)(a+b+c)=a^{2}+ab+ac+ba+b^{2} +bc-ac-bc-c^{2}\\\\(a+b-c)(a+b+c)=a^{2} +b^{2} -c^{2} +2ab[/tex]

Hence, we have that the given expression is equal to:

[tex]a^{2} +b^{2} -c^{2} +2ab[/tex]

Have a nice day!

Answer:

D. 5/6

Step-by-step explanation:

If there is 6 numbers (6 possible outcomes) and your roll is not a four, there is 5 other numbers you could get so its 5/6.

Hope this helps!

Answer:

Given,

f(x)=x^2+6

g(x)=2x-1

Now,

g[f(x)]=g(x^2+6) since f(x)=x^2+6

=2(x^2+6)-1 since x > x^2+6

=2x^2+12-1

=2x^2+11

In order to find g[f(x)], we substitute the equation for f(x) into the equation for g(x). We replace every 'x' in g(x) with f(x) to get g(f(x)) = 2*(x^2 + 6) - 1. After simplification, we get g[f(x)] = 2x^2 + 11.

In the world of mathematics, g[f(x)] represents the composition of two functions, f(x) and g(x). In this case, f(x) = x^2 + 6, and g(x) = 2x - 1. The composition of these two functions, expressed as g[f(x)], involves plugging the equation for f(x) into the equation for g(x).

Here's how we do it:

First, we take the f(x) = x^2 + 6. Then we put this into g(x), replacing every 'x' in g(x) with our function f(x). So, g(f(x)) = 2*(x^2 + 6) - 1. Simplifying, we find:

g(f(x)) = 2x^2 + 12 - 1 = 2x^2 + 11.

Therefore, the content loaded f(x) = x^2 + 6, g(x) = 2x - 1, g[f(x)] = 2x^2 + 11.

https://brainly.com/question/17348508

#SPJ2

Answer:

-6.47+4.70i.  

Brainliest

Step-by-step explanation:

100% sure

Answer:-6.47+4.70i

Step-by-step explanation:

Took test ,, good luck !!!

Answer: rotation

Step-by-step explanation:

a rotation about 90degrees

The transformation of Figure 1 results in Figure 2 is Rotation.

A transformation is a broad phrase covering four distinct methods of changing the shape and/or position of a point, line, or geometric figure. The Pre-Image is the original shape of the object, and the Image during the transformation is the final shape and location of the object.

Transformations in geometry are categorized into three;

As we translate, we move a figure in any direction.

When we flip a figure over a line, we call this reflection.

When we rotate a figure a given amount around a point, we call this rotation.

As we dilate, we enlarge or contract a figure.

Learn more about Transformation here:

https://brainly.com/question/10209321

#SPJ3

Answer:

its A

Step-by-step explanation:

F is the midpoint of AA' because E.G. bisects AA'.

E ) a three-dimensional box-shaped figure, with six identical square faces

Answer:

Option A.

Step-by-step explanation:

Box for a deck of cards will be in the shape of rectangular prism.

A rectangular prism has two parallel rectangular bases, 2 sides parallel to each other along width and 2 similar parallel rectangular sides along the height.

Therefore, option A. "a three dimensional shape with two similar, parallel rectangular bases and sides that are parallelogram" will be the correct option.

The greatest common factor is 2x

2 can go into both 10 and 12

and so can x