Rewrite this inequality so that one side is 0.

x2 − 2x + 1 < x − 1

Answers

Answer 1

To rewrite the inequality so that one side is 0, simply subtract x and add 1 to both sides, resulting in the inequality x² - 3x + 2 < 0.

To rewrite the inequality x² - 2x + 1 < x - 1 so that one side is 0, we follow these steps:

Bring all terms to one side of the inequality by subtracting x and adding 1 to both sides, resulting in x² - 3x + 2 < 0.

Now, the inequality is set up with one side equal to 0, and we can analyze or solve the inequality from here.


Related Questions

Find the range of ƒ(x) = –2x – 5 for the domain {–2, –1, 1, 2}.

Answers

-2(-2)-5= -1      -2(-1)-5=-3   -2(1)-5=-7     -2(2)-5=-9

By substituting each value of the domain of x in the function and solving it we will get the range of the function for respective domain

The given function is :

f(x) = -2x - 5

For x = -2 , f(x) is:

f(-2) = (-2*-2) - 5 = 4 - 5 = -1

For x = -1, f(x) is :

f(-1) = (-2*-1) - 5 = 2 - 5 = -3

For x = 1 , f(x) is

f(1) = (-2*1) - 5 = -2 -5 = -7

For x = 2, f(x) is

f(2) = (-2*2) - 5 = -4 -5 = -9

The range is -1 , -3 , -7 , -9

Hope this helps ..!!

Thank you :)


Graph this function f(x)=x^2-4x-5

Answers

In order to graph this function you need to get axis of simmetry (by dividing the number with the squared x between the other number with the x), the vertex where the function changes its direction and the x and y axes cutting points.

Answer:

Step 1: a = 1, b = -4

Step 2: x = 2, f(2) = -9

Step 4: (5,0) and (-1,0)

Step 6: f(0) = -5

On the graph the points plotted are (-1,0) , (0,-5) , (2,-9) , and (5,0)

Graph the following inequality and then select the correct graph below.

y ≤ x - 2

Answers

It would be the third graph for y<=x-2

Hope it helps.

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]y\leq x-2[/tex]

The solution of the inequality is the shaded area below the solid line

The equation of the line is [tex]y= x-2[/tex]

The slope of the line is positive [tex]m=1[/tex]

The y-intercept of the line is the point [tex](0,-2)[/tex]

The x-intercept of the line is the point [tex](2,0)[/tex]

therefore

the graph in the attached figure

.help please and thank you

Answers

it is the SAS Postulate
Use Side Angle Side (SAS)

What is the simplest form of (8x2)3?

Answers

[tex] (8x^2)^3 = [/tex]

[tex] = 8^3 \times (x^2)^3 [/tex]

[tex] = 512x^{2 \times 3} [/tex]

[tex] = 512x^6 [/tex]

What are the roots of the polynomial equation?

x2−14x−32=0

Answers

x2−14x−32=0
We can easily factor that into:
(x +2) * (x -16) = 0
x1 = -2
x2 = 16




We are given the quadratic equation :

[tex] x^{2} -14x-32=0 [/tex]

Now let us use AC method to factorise it.

Step 1:

Find product of A and C

A=1 and C =-32

A*C =-32

Step 2:

Find factors of -32 such that they add up to give -14.

Factors of -32 that add up to give -14 are -16 and 2.

Step 3:

Rewrite the equation using factors found in step 2.

[tex] x^{2} -16x +2x -32 =0 [/tex]

Step 4:

Factoring by grouping.

[tex] x(x-16) +2(x -16) =0 [/tex]

[tex] (x-16) (x+2) =0 [/tex]

Step 5:

Find roots.

x-16=0 gives x=16

x+2=0 gives x=-2

Answer : Roots of the given Polynomial equation are 16 and -2.


We are given the quadratic equation :

[tex] x^{2} -14x-32=0 [/tex]

Now let us use AC method to factorise it.

Step 1:

Find product of A and C

A=1 and C =-32

A*C =-32

Step 2:

Find factors of -32 such that they add up to give -14.

Factors of -32 that add up to give -14 are -16 and 2.

Step 3:

Rewrite the equation using factors found in step 2.

[tex] x^{2} -16x +2x -32 =0 [/tex]

Step 4:

Factoring by grouping.

[tex] x(x-16) +2(x -16) =0 [/tex]

[tex] (x-16) (x+2) =0 [/tex]

Step 5:

Find roots.

x-16=0 gives x=16

x+2=0 gives x=-2

Answer : Roots of the given Polynomial equation are 16 and -2.


The data set represents a bimonthly progression of gasoline prices over the course of several months in an unspecified city. Use a graphing calculator to determine the quadratic regression equation for this data set. x 0 2 4 6 8 y 2.86 2.89 2.93 3.04 3.11 a. c. b. d.

Answers

The answer to this question id D

Answer:

y = 0.0027*x^2 + 0.0111*x + 2.8574

Step-by-step explanation:

Using Excel the procedure is:

First, insert x and y values in a table format, as can be seen in the figure

Then, select data

Next, go to insert tab and inside charts options select scatter plot without any lines

Finally, select a point in the plot, right-click, add trend line, polynomial order 2 and check display equation option

Choose the option that correctly completes the statement.

A triangle must have _____ one acute angle.
at most
at least

Answers

at least one acute angle
at least is the answer 

What is the area of this polygon?

Answers

The above polygon is a pentagon 
The polygon has a rectangle and a triangle 
Area of triangle FSCW
 = Length × width
 =  9 × 2
 = 18 square units
area of triangle FNS
 = 1/2 × base× height
 = 1/2 × 9 × 6
  = 27 square units
Therefore the area of the polygon is
   = 27 + 18
   = 45 square units

Construction is under way at an airport. This map shows where the construction is taking place. If Road A and Road B are parallel, what is the distance from P to Q on Road C?

Answers

Assuming that Road C is perpendicular to Roads A and B.


650(2000) = 800x + 800(650)

                                   x = 975 ft
the answer is 975 feet

can someone help me with this?

Answers

Add up the values in row 1 and row 2, which correspond to the groups "under age 12" and "13 to 30 years old" respectively

6+7 = 13 individuals under age 12
7+4 = 11 individuals 13 to 30 years old
13+11 = 24 people total from the two groups

There are 6+7+7+4+4+1 = 29 people total from the entire survey

So the final answer is 24/29. It cannot be reduced further.

helppppppppppppppppppppppp

Answers

Answer:
10.3 units

Explanation:
Triangle ABC is a right-angled triangle. This means that we can apply special trig functions.
We are given that:
angle B = 25 degrees and AB = 4 units
Therefore:
cos(B) = adjacent / hypotenuse
cos(25) = 4 / BC
BC = 4.414 units
tan(B) = opposite / adjacent
tan(25) = AC / 4
AC = 1.865

Finally, we can get the perimeter as follows:
perimeter = AB + BC + AC
perimeter = 4 + 4.414 + 1.865
perimeter = 10.279 which is approximately 10.3 units

Hope this helps :)
Known Values Angle A = 90°
Side c = 4 
Angle B = 25° 
Step #1: Find angle C by subtracting the other 2 angles from 180°. 
C = 180° - A° - B° 
C = 180° - 90° - 25° 
C = 65°
Step #2: Use the Law of Sines to find side a. 
a / sin(A) = c / sin(C) 
a / sin(90°) = 4 / sin(65°) 
a = (sin(90°) x 4) / sin(65°) 
a = 4.414
Step #3
: Use the Law of Sines to find side b. 
b / sin(B) = c / sin(C) 
b / sin(25°) = 4 / sin(65°) 
b = (sin(25°) x 4) / sin(65°) 
b = 1.865
So you have the sides
c = 4
b = 1.865
a = 4.414

The perimeter is all the sides added up
P = 4 + 1.865 + 4.414
P = 10.279
That can be rounded to 10.3 units

Hope this helps!

The measure of Angle E, the angle of elevation from point A to point B, is ( 3 x plus 1 ). The measure of Angle D, the angle of depression from point B to point A, is 2 ( x plus 8 ) Find the measure of each angle.

Answers

Let
E----------------> angle of elevation
D----------------> angle of depression
we know that
E=(3x+1)
D=2(x+8)
remember that
angle of elevation is equals to angle of depression------> by alternate angles
then 
E=D
(3x+1)=2(x+8)-----------> 3x+1=2x+16----------> 3x-2x=16-1-----> x=15
E=3*15+1-------> 46°
D=2*15+16-----> 46°

the answer is
the measure of angle of elevation and angle of depression is 46°

Calculate the principal amount which earns $500 simple interest over 3 Years at a rate of 8% p.a round to the nearest cent

Answers

$500 was earned over 3 years
so, to find one year
500 ÷ 3 = $166.67

Interest for one year is $166.67
Interest rate for one year is 8%

8% = 166.67
1% = $20.83
100% = $2083.33

Principal amount is $2083.33

Final answer:

To find the principal amount that would earn $500 in simple interest over 3 years at an 8% annual rate, divide the interest by the product of the rate and period. The principal amount is $2083.33.

Explanation:

Calculating the Principal Amount from Simple Interest

To calculate the principal amount that earns $500 in simple interest over 3 years at a rate of 8% per annum, we can utilize the simple interest formula:
Interest = Principal × rate × time. Plugging in the known values, we get $500 = Principal × 0.08 × 3. This yields the equation $500 = Principal  × 0.24.

To find the Principal, we divide $500 by 0.24, which gives us approximately $2083.33. Therefore, the initial principal amount is $2083.33.

Using the completing-the-square method, rewrite f(x) = x2 + 10x + 7 in vertex form.

Answers

Let's begin with moving the constant to the side with f(x):
f(x) - 7 = x² + 10x

Next let's add (half of 10)² to both sides of the equation: btw that is 25 but on the right side we will leave it as 5² because it will make the factoring easier

f(x) - 7 + 25 = x² + 10x + 5²

Lets simplify the left side a bit and factor the perfect square trinomial on the right.

f(x) + 18 = (x + 5)²

Finally move the constant back to the side with the binomial

f(x) = (x + 5)² - 18

The vertex is (-5, -18)

Using the completing-the-square method the vertex form of the function

f(x)  =  x²  +  10x  +  7 is f(x)  =  (x  +  5)²  -  18

The given function is:

f(x)  =  x²  +  10x  +  7

Comparing f(x)  =  x²  +  10x  +  7 with f(x) = ax² + bx + c

a  = 1,  b = 10,  c  = 7

(b/2)²  =  (10/2)²  =  5²

Add and subtract 5² to the right hand side of the equation

f(x)  =  x²  +  10x + 5² +  7 - 5²

f(x)   =  x²  +  10x  +  5²  +  7 - 25

f(x)   =  x²   +  10x  +  5²  - 18

f(x)  =  (x  +  5)²  -  18

f(x)  =  (x  +  5)²  -  18 is of the form f(x) = a(x - h)² + k which is the vertex form of a quadratic equation

Therefore, the vertex form of the function f(x)  =  x²  +  10x +  7 is

f(x)  =  (x  +  5)²  -  18

Learn more here: https://brainly.com/question/19105786

Sylvia is going to pick out a souvenir hat while she is on vacation. She knows the price of the hat will increase by 5% when she pays sales tax. She writes the expression h + 0.05h to find the total amount she will pay for the hat if it costs h dollars. Jin correctly writes another expression, 1.05h, that will also find the the total amount Sylvia will pay for the hat if it costs h dollars. Use the drop-down menus to explain what each part of Sylvia's and Jin's expressions mean.

Answers

We will evaluate both expressions step by step.

 Sylvia's espression:
 h + 0.05h
 h: Original hat price.
 0.05h: Increase of 5% due to sales tax.

 Jin's expressions:
 1.05h 
 h: Original hat price.
 1.05: Factor for which you must multiply the original price to add 5% due to sales tax.

Answer:

Step-by-step explanation:

Sylvia's expression

H: Price of hat

0.05: percent sales tax

0.05 h: amount of sales tax Sylvia will pay

h+0.5 h: total amount Sylvia will pay

Jin's Expression

1.05: One whole plus percent sales tax

H: price of hat

1.05 h: total amount Sylvia will pay

helpppppppppppppppppppppppppppppp

Answers

x³-x²-17x-15║(x-5)
-------------------------------
-x³+5x²             (x²+4x+3)----------- > the quotient q(x)
4x²-17x-15
-4x²+20x
3x-15
-3x+15

the quotient q(x) is  x²+4x+3
the answer is the option x²+4x+3

Picture included!
What is the slope of the line shown in the graph?

A.) -1
B.) -2
C.) 1/2
D.) 2

Answers

By looking at the point 1,1 and 0,3 you rise two and over one creating the ratio 2/1 which reduces down to 2 
:D
so, notice in the picture, let's use those points of 0,3 and 1,1

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 0 &,& 3~) % (c,d) &&(~ 1 &,& 1~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-3}{1-0}\implies \cfrac{-2}{1}\implies -2[/tex]

Mrs. Rodriguez has 18 packages of pens in stock at her store on monday. On tuesday, she has 5/6 the number of pens she had on monday. On Wednesday, she has 2/5 of the number of pens she had on tuesday. How many packages of pens does she hve on Wednesday?

Answers

she should have 6 pens left over

Mrs. Rodriguez has 18 packages of pens in stock at her store on Monday.

[tex] Number \; of\; packages\; of \; Pens\; on\; Monday=18\\ \\ [/tex]

On Tuesday, she has 5/6 the number of pens she had on Monday, which means...

[tex] Number \; of\; packages\; of \; Pens\; on\; Tuesday=\frac{5}{6} \; of \ 18 = \frac{5}{6} \times 18=\frac{90}{6}=15\\ [/tex]

On Wednesday, she has 2/5 of the number of pens she had on Tuesday, which means...

\\ Number \; of\; packages\; of \; Pens\; on\; Wednesday = \frac{2}{5} \; of \ 15=\frac{2}{5} \times 15=\frac{30}{5}=6

Conclusion:

Number of packages of pens does she have on Wednesday is 6 Packages

PLEASE HELP
8.04b

1. Eliminate the parameter.
x = 5t, y = t + 8

A) y = 5x + 8
B) y = x divided by five + 8
C) y = 5x - 8
D) y = x divided by five - 8

2. Eliminate the parameter.
x = square root of x , y = 3t + 7

A) y = 3x2 + 7
B) y = 3 square root of x + 7, x ≥0
C) y = 3 square root of x - 7, x ≥0
D) y = 3x2 - 7

3. Eliminate the parameter.
x = t2 + 2, y = t2 - 4

A) y = x - 6, x ≥ 1
B) y = x + 6, x ≥ 1
C) y = x2 - 6, x ≥1
D) y = x2 + 6, x ≥1

4. Eliminate the parameter.
x = 4 cos t, y = 4 sin t

Answers

These are four questions and four answers:

Question 1. Eliminate the parameter. x = 5t, y = t + 8
 
Answer: option B: y = (x / 5) + 8 ↔ x divided by 5 + 8

Explanation:

1) From x = 5t => t = x / 5

2) Substitute t in y = t + 8 => y = (x / 5) + 8

Which is the option B) y = the division of x by 5, added to 8.

Question 2. Eliminate the parameter.

There is an error in the question, because it says x = √x

If the righ question is x = √t , y = 3t + 7 , then the a
nswer is the option A) y = 3x^2 + 7

Explanation:

1) Given: x = √t , y = 3t + 7

2) from x = √t => t = x^2

3) Substitute t = x^2 in y = 3t + 7

=> y = 3 x^2 + 7 ↔ option A) y = x^2 + 7

Question 3. Eliminate the parameter.

x = t^2 + 2, y = t^2 - 4

Answer: option A) y = x - 6

Explanation:

1) From x = t^2 + 2 => t^2 = x - 2

2) Substitute t^2 in y = t^2 - 4

=> y = x - 2 - 4

=> y = x - 6, since t^2  is ≥ 0, then x ≥ 0

=> option A) y = x - 6, x ≥ 1

Question 4. Eliminate the parameter.
x = 4 cos t, y = 4 sin t

Answer: x^2 + y^2 = 16

Explanation:

1) Square both sides of x = 4 cost

=> x^2 = (4 cos t)^2

x^2 = 16 (cos t)^2

2) Square both sides of y = 4 sin t

y^2 = 16 (sin t)^2

3) Add x^2 and  y^2

x^2 + y^2 = 16(cos t)^2 + 16 (sin t)^2

=> x^2 + y^2 = 16 [ (cos t)^2 + (sin t)^2 ]

4) since (cos t)^2 + (sin t)^2 = 1

x^2 + y^2 = 16

Eugene knows the circumference of a circle is 125.6 meters. Does he have enough information to find the area?

Answers

[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r\quad \begin{cases} r=radius\\ -----\\ C=125.6 \end{cases}\implies 125.6=2\pi r\implies \cfrac{125.6}{2\pi }=\boxed{r} \\\\\\ \textit{area of a circle}\\\\ A=\pi r^2\qquad \qquad \implies A=\pi \left( \boxed{\cfrac{125.6}{2\pi} } \right)^2[/tex]

Answer:

the answer is a

Step-by-step explanation:

i did the test

Which of these sequence is an arithmetic sequence??

Answers

Answer:

a and c

Step-by-step explanation:

Which statement about this product is true?

0.44 ×(−5 3/4)


It is equal to 0 because 0.44 rounded to the nearest whole number is 0, and 0 times any number is 0.


It is equal to −5 3/4 because 4/4 is equal to 1, and 1 times any number equals that number.


It is greater than −3 because 0.44 × 5 3/4 is less than 1/2 × 6


It is less than −5 3/4 because multiplying by a number less than 1 gives a smaller number.

Answers

Answer:

It is greater than −3 because 0.44 × 5 3/4 is less than 1/2 × 6

Step-by-step explanation:

i guessed it and it was right so ye.

find the arithmetic mean an of an-1 = 3.9 and an+1 = 7.1

a. 11
b. 5.5
c. 3.7
d. 1.6

Answers

Answer:

Step-by-step explanation:

Alright, lets get started.

We are asked to find arithmetic mean of two terms given.

For finding arithmetic mean, we add up the values and divide the sum by the number of values.

Here we have given two numbers , below

[tex]a_{n-1}=3.9[/tex]

[tex]a_{n+1}=7.1[/tex]

So, mean of these two numbers will be = [tex]\frac{3.9+7.1}{2}[/tex]

So, mean of these two numbers will be = [tex]\frac{11}{2}=5.5[/tex]

So, arithmetic mean for given two numbers are 5.5  :  Answer (b)

Hope it will help :)

Answer:

b.  5.5

Step-by-step explanation:

FOR LEARNING ONLY.. not necessary to read, but I hope it helps!

you start with:

[tex]a_{n-1}=3.9\\a_{n-1}=7.1[/tex]

arithmetic questions like this are like finding an average.

so you add the values while dividing by the total of values there are.

in this case:

[tex]\frac{7.1+3.9}{2}[/tex]

which is simplified to:

[tex]\frac{11}{2}[/tex]

then decimal:

[tex]5.5[/tex]

50 POINTS!
A high school coach wants to buy new shirts for the 25 members of the track team. The coach must spend less than $300 on the shirts and needs to figure out how much he can spend per shirt, s. Which of the following must be true about the inequality and the resulting graph? Check all that apply

A)The inequality should be written as 25s<300.

B)The inequality should be written as 25s>300.

C)The circle is open.

D)The circle is closed.

E)The arrow points left.

F)The arrow points right

Answers

The inequality should be written as 25s <300, The circle is open, and The arrow points left.

Answer:

Step-by-step explanation:

A,C,E

please help attachment on please don't skip any parts

will get brainliest

Answers

I’m sorry but there isn’t an attachment.

A jar contains 17 orange,7 pink, and 4 black marbles. A marble is drawn at random.What is the probability that the marble is pink or orange

Answers

Sample space = 17 + 7 + 4 = 28
P(pink) = 7/28
P(orange) = 17/28
P(pink or orange) = P(pink) + P(orange)
P(pink or orange) = 7/28 + 17/28
P(pink or orange) = 24/28
P(pink or orange) = 6/7 or 0.857143 or 85.7%

A sine function has the following key features:

Period = 12

Amplitude = 4

Midline: y = 1

y-intercept: (0, 1)

The function is not a reflection of its parent function over the x-axis.

How would this graph look??

Answers

Final answer:

A sine function with an amplitude of 4, period of 12, midline of y = 1, and y-intercept of (0, 1) would oscillate between 5 and -3, with a wave repeating every 12 units along the x-axis and starting upward from the y-intercept.

Explanation:

The graph of the sine function with the given properties will have the following characteristics:

The amplitude is 4, which means the function will oscillate 4 units above and below the midline.

The period is 12, indicating that it takes 12 units along the x-axis for the function to repeat its pattern.

The midline is y = 1, so the center of oscillation is not at the x-axis but is shifted upwards by 1 unit.

The y-intercept is (0, 1), which means the function starts at the midline.

Since the function is not a reflection over the x-axis, it means that it starts off going upwards from the midline.

Mapping these points, we can sketch the sine graph starting from the point (0, 1), curving up to a maximum of 5 (midline + amplitude), then down through the midline, reaching a minimum of -3 (midline - amplitude), and back to the midline at (12, 1), completing one full cycle.

Find the constant of variation k for the inverse variation. Then write an equation for the inverse variation. Y=4.5 when x = 3

Answers

[tex]\bf \qquad \qquad \textit{inverse proportional variation}\\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \textit{we also know that } \begin{cases} y=4.5\\ x=3 \end{cases}\implies 4.5=\cfrac{k}{3}\implies 4.5(3)=k \\\\\\ 13.5=k\qquad therefore\qquad \boxed{y=\cfrac{13.5}{x}}[/tex]

Find the simplified form of the expression. Give your answer in scientific notation.

(9 x 10 5)(6 x 10 -7)

A. 5.4 x 10 -34

B. 1.5 x 10 -1

C. 5.4 x 10 -1

D. 1.5 x 10 -34

Answers

We have that exponents satisfy [tex]a^x*a^y=a^{x+y}[/tex]
Now we get: [tex](9*10^5)(6*10^{-7})=9*6*10^5*10^{-7}[/tex] by associativity of multiplication.
This is equal to: [tex]54*10^{5+(-7)}=54*10^{-2}[/tex] by the property we stated above, for a=10. Scientific notation requires that the coeeficient in fron tof the power of 10 is between 1-10 and thus since 54=10*5.4, we have that the expression is equal to: 5.4*10*[tex]10^{-2}[/tex]=[tex]5.4*10^{-1}[/tex]. Hence the correct answer is C
Other Questions
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