The best answer from the choices provide is x = -1 or x = -1
Given the expression
[tex]x^2 + 2x + 1 = 0[/tex]
Factorizing the given expression
[tex](x^2 +x)+(x + 1) = 0\\[/tex]
Factor out the common variable from both brackets
[tex]x(x+1)+1(x+1)=0\\(x+1)(x+1)=0\\x+1 \ and \ x+1=0\\x =0-1 \ and \ x=0-1\\x=-1 \ and \ x =-1[/tex]
Hence the best option is x = -1 or x = -1
Learn more about factorization here: https://brainly.com/question/16099992
The solutions for [tex]f(x) = x^{2}+2\cdot x + 1 = 0[/tex] are [tex]x_{1} = x_{2} = -1[/tex].
We can estimate the roots by a numerical approach, which consists in evaluating the quadratic function ([tex]f(x) = x^{2}+2\cdot x + 1 = 0[/tex]) for a set of values of [tex]x[/tex]. We consider the set of values between [tex]-4\le x \le 4[/tex]:
[tex]\,\,\,\,\,\,x \,\,\,\,\,\,\,\,f(x)\\-4\,\,\,\,\,\,\,\,\,\,\,\,9\\-3\,\,\,\,\,\,\,\,\,\,\,\,4\\-2\,\,\,\,\,\,\,\,\,\,\,\,1\\-1\,\,\,\,\,\,\,\,\,\,\,\,0\\.\,\,\,0\,\,\,\,\,\,\,\,\,\,\,\,\,1\\.\,\,\,1\,\,\,\,\,\,\,\,\,\,\,\,\,4\\.\,\,\,2\,\,\,\,\,\,\,\,\,\,\,\,\,9\\.\,\,\,3\,\,\,\,\,\,\,\,\,\,\,\,\,16\\.\,\,\,4\,\,\,\,\,\,\,\,\,\,\,\,\,25\\[/tex]
According to the previous input, we conclude that roots of the quadratic formula are [tex]x_{1} = x_{2} = -1[/tex].
The solutions for [tex]f(x) = x^{2}+2\cdot x + 1 = 0[/tex] are [tex]x_{1} = x_{2} = -1[/tex].
At a gas station during a road trip, Gerard has $32.00 to spend on fuel and windshield washer fluid for his car. Fuel costs $2.75 per gallon, and each bottle of windshield washer fluid costs $3.00. The car's average fuel efficiency is 38 miles per gallon. If Gerard must fill his car with enough fuel to drive 250 miles, what is the maximum number of bottles of windshield washer fluid Gerard can buy? (Note: all prices include taxes.)
Answer:
Step-by-step explanation:
Total amount with Gerald = $32
Cost of fuel per gallon = $2.75
Cost of each bottle of windshield = $3
38 miles per gallon. If Gerard must fill his car with enough fuel to drive 250 miles,
Total gallons of fuel = 250 miles / 38 miles
= 6.5789473684210 gallons
Total cost of fuel = Total gallons of fuel × cost per gallon
= 6.5789473684210 × $2.75
= $18.1
Amount left for windshield = Total amount with Gerald - Total cost of fuel
= $32 - $18.1
= $13.9
what is the maximum number of bottles of windshield washer fluid Gerard can buy?
= Amount left for windshield / Cost of each bottle of windshield
= $13.9 / $3
= 4.6333333333333 bottles
Maximum number of bottles =
4 bottles
A student survey was conducted at a major university. Data were collected from a random sample of 206 undergraduate students, and the information that was collected included physical characteristics (such as height and handedness), study habits, academic performance and attitudes, and social behaviors. In this exercise we will focus on exploring relationships between some of those variables. The variables are:
Answer:
Students Major
Cheat reporting response
Number of Alcohols taken
Student's Height
Step-by-step explanation:
The Variables are the following:
Categorical variables
1. Major – The student's majors -
Arts & Social Science or STEM
2. Cheat - Response about reporting cheating - Yes or No
Quantitative Variables
3. Alcohol - Number of alcoholic beverages consumed in a typical week
4. Height - Self-reported height (in inches)
The diagram shows the graph of a quadratic dinction y=f(x).
State
(a) the roots of the equation when f(x) = 0,
(b) he equation of the akis of symmetry of the curve
Pls help me
Answer:
hodrvyeieiwb was the only one to win a lot
Answer:
the roots are x= -4 and x=6
the equation of the axis of symmetry is x^2-2x-24
Step-by-step explanation:
to find the roots you go to the area where the graph is touching the x axis because y is 0 on the x axis
to find the equation use the values of the x intercepts which are -4 and 6
(x+4)(x-6)
solve this into an equation by multiplying everything in the first brackets by every thing in the second the answer you are likely to come up with is x^2-2x-24
I hope this helps
What’s the answer? I don’t understand the question and I came to see if you all can help
Answer:
15/2 that is the answer man
Use trigonometric identities to solve each equation within the given domain.
–sin2(x) = cos(2x) from [–π, π]. PLEASE SHOW WORK!!!
It looks like the equation is
-sin²(x) = cos(2x)
Recall the half-angle identity for sine:
sin²(x) = (1 - cos(2x))/2
Then the equation can be written as
-(1 - cos(2x))/2 = cos(2x)
Solve for cos(2x):
-1/2 + 1/2 cos(2x) = cos(2x)
-1/2 = 1/2 cos(2x)
cos(2x) = -1
On the unit circle, cos(y) = -1 when y = arccos(-1) = π. Since cosine has a period of 2π, more generally we have cos(y) = -1 for y = π + 2nπ where n is any integer. Then
2x = π + 2nπ
x = π/2 + nπ
In the interval [-π, π], you get two solutions x = -π/2 and x = π/2.
What must be true if [tex]\frac{x}{y}[/tex] / [tex]\frac{3a}{b} =\frac{3a}{b}[/tex]? Assume a[tex]\neq[/tex]0, b[tex]\neq[/tex]0, and y[tex]\neq[/tex]0.
Answer:
4th option is correct
Step-by-step explanation:
Hi, I need help with this!!! I don’t understand this :-(
Answer: See image and explanation below
Step-by-step explanation:
The problem gives us 6 points to draw into the sketch.
The first and second point gives the domain and range of the sketch. The last 4 points tell us the coordinates.
Let's do the first two points. This tells us that the sketch should not go further (-3,0) and (3,0) of the x-axis, and should not go further (0,0) and (0,4) of the y-axis.
For the last 4 points, we can convert them to coordinates and graph them. The points would be (-2,3), (1,2), (-3,0), (3,0), and (0,4).
After we draw the 5 points listed above onto the graph, we can connect the points.
In the image I attached, the lines are straight, but when you draw it out, you should make your lines more curved.
can someone help me make these into square root graphs? i thought i knew how, but trying it is confusing me
Answer:
Step-by-step explanation:
The table below gives the distribution of milk
chocolate M&M's
Color
Brown
Red
Yellow
Green
Orange
Blue
Probability
0.13
0.13
0.14
0.16
0.20
0.24
If a candy is drawn at random, what is the probability
that it is not orange or red?
PLZ HELP!!!!!
Explanation:
The probability of picking red is 0.13
The probability of picking orange is 0.20
The probability of picking either of these is 0.13+0.20 = 0.33
So the probability of picking neither of them is 1 - 0.33 = 0.67
There's a 67% of this happening.
Answer:
0.34
Step-by-step explanation:
because the probability of red is 20 and the probability of orange is 14 20 + 14 is 34.
The height, h, in metres, of a rocket t seconds after it is launched is approximately modelled by the quadratic relation h = 80t - 16t2. To the nearest second, how long is the rocket in the air?
Answer: 5 s
Step-by-step explanation:
Given
Height of the rocket can be modelled as [tex]h=80-16t^2[/tex]
Rocket will land on earth when it's height becomes 0
[tex]\Rightarrow 80t-16t^2=0\\\Rightarrow t(80-16t)=0\\\\\Rightarrow t=0\ \text{or}\ t=\dfrac{80}{16}=5\ s[/tex]
Neglecting 0 value
Thus, rocket remains in air for 5 s.
Does anyone know the answer to this? I’m getting confused
Answer:
0
Step-by-step explanation:
Substitute b into -3.
Hence,
(b+3)(b²-5b+7)=(-3+3)(-3²-15+7)
=(0)(1)
=0
The area of a rectangle is 33 ft^2, and the length of the rectangle is 5 ft less than double the width. Find the dimensions of the rectangle.
Answer:
Length = 6
Width = 5.5
Step-by-step explanation:
Let's use the variable x to represent the width:
x = width
The question says that the length of the rectangle is "5 ft less than double the width". This length can be represented like this:
2x - 5 = length
To find the area of a rectangle, you multiply the width and length, so we are going to write an equation where we multiply the width and length and set it equal to 33 ft^2, which is the area:
(x)(2x - 5) = 33
Now use basic algebra to solve for x:
2x^2 - 5x = 33
2x^2 - 5x - 33 = 0
2x^2 + 6x - 11x - 33 = 0
(2x^2 + 6x) + (-11x - 33) = 0
2x(x + 3) - 11(x + 3) = 0
(2x - 11) (x + 3) = 0
x = 11/2, -3
x either equals 11/2 or -3. However, remember that x represents the width, and you can't have a negative number for a width, so x = 11/2 or 5.5.
Now plug in 5.5 to the length expression and simplify:
2(5.5) - 5
11 - 5 = 6
The length is 6 and the width is 5.5.
Hope this helps (●'◡'●)
A rectangle is 12 feet long and 5 feet wide. If the length of the rectangle is increased by 25% and the width is decreased by 20%, what is the change in the area of the rectangle? The change in the area of the rectangle is
Answer:
no change in area
Step-by-step explanation:
The original area is
A = 12*5 = 60 ft^2
The new length and width
l = 12 + .25 (12) = 12+3 =15
w = 5 - .2 (5) =5-1 = 4
The new area is
A = l*w =15*4 = 60 ft^2
The area is the same
The sum of twice a number and 9 is-25
Tulio will invest $1,000,000 at 5% annual interest. Determine how much money will Tulio have after 10 years if the interest is calculated using the following methods.
Answer:
$1,500,000
Step-by-step explanation:
Given
Principal = $1,000,000
Rate = 5%
Time = 10years
Interest = PRT/100
Interest = 1000000*5*10/100
Interest = 100000*5
Interest = $500,000
Amount after 10years = $1,000,000+ $500,000
Amount after 10years = $1,500,000
Help anyone can help me do this question,I will mark brainlest.
Answer:
Answer is in attached image
I hope it help...
Write An expression of the fourth degree with a leading coefficient of 5, a quadratic term with a coefficient of 3, a linear term with a coefficient of -8 and a constant of six.
Answer:
[tex] {5x}^{4} + 3 {x}^{2} - 8x + 6[/tex]
Step-by-step explanation:
Math
explain why the following equation is nonlinear. y=3x^5
plz help
Answer:
A linear equation is an equation of a straight line, which means that the degree of a linear equation must be 0 or 1 for each of its variables. In this case, the degree of variable y is 1 and the degree of variable x is 5 .
Therefore, it is not linear.
How to find a parallel sides of trapezium length 7.3mm and 5.3mm ,and it's height is 5mm calculate the area of a trapezium
Answer:
31.50 mm²
Step-by-step explanation:
A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs
Characteristics of a trapezoid
It has 4 vertices and edges
If both pairs of its opposite sides of a trapezoid are parallel, it becomes a parallelogram
Area of a trapezoid = 1/2 x (sum of the lengths of the parallel sides) x height
1/2 x ( 7.3 + 5.3) x 5 = 31.50 mm²
What should be done so that the expression will have a value of 28?
6 + 2 + 32 × 2
Answer:
6+2+(32×2)
6+2+(64)
8+64
72
difference between 72 and 28
72-28
=44
add 44 to make the value 28
Please i need help lllll
Answer:
C
Step-by-step explanation:
A function x values must correspond to one y values.
One y values can correspond to two different x values.
C shows this isn't a function
which linear function shows a direct variation
Answer:
a pod t.v. Ka ssh Mic yummy
a company's stock was selling at 28 a share. a month later, it was selling at 21 a share. what is the percent loss?
Answer:
25% loss
Step-by-step explanation:
Take the original amount and subtract the new amount
28 -21 = 7
Divide by the original amount
7/28 = .25
Change to percent form
25%
25% loss
Find out the values of x and y from the following ordered pairs.
(x + y, 2) = (13, 2x – y)
Answer:
(x, y) = (5,8)
Step-by-step explanation:
Comparing the ordered pairs we get, x+y=13 and 2=2x-y. Solving it we will get, x=5 and y=8
Question 4 of 5
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used
Match each explicit formula to its corresponding recursive formula.
(8) = 5(5)(1-1)
(n) = 3 +5(n-1)
(3) = 5+3(1-1)
7(n) = 3(5)(n-1)
$(n) = 5 +5(n-1)
f(1) = 5
(*) = 3;(n - 1), for 3
(1) = 5
(n) = f(n-1) +5, for n?
f(1) = 5
f(n) = f(n-1) + 3, for n?
Given:
The recursive formulae.
To find:
The correct explicit formulae for the given recursive formulae.
Solution:
If the recursive formula of a GP is [tex]f(n)=rf(n-1), f(1)=a, n\geq 2[/tex], then the explicit formula of that GP is:
[tex]f(n)=ar^{n-1}[/tex]
Where, a is the first term and r is the common ratio.
The first recursive formula is:
[tex]f(1)=5[/tex]
[tex]f(n)=3f(n-1)[/tex] for [tex]n\geq 2[/tex].
It is the recursive formula of a GP with a=5 and r=3. So, the required explicit formula is:
[tex]f(n)=5(3)^{n-1}[/tex]
Therefore, the required explicit formula for the first recursive formula is [tex]f(n)=5(3)^{n-1}[/tex].
If the recursive formula of an AP is [tex]f(n)=f(n-1)+d, f(1)=a, n\geq 2[/tex], then the explicit formula of that AP is:
[tex]f(n)=a+(n-1)d[/tex]
Where, a is the first term and d is the common difference.
The second recursive formula is:
[tex]f(1)=5[/tex]
[tex]f(n)=f(n-1)+5[/tex] for [tex]n\geq 2[/tex].
It is the recursive formula of an AP with a=5 and d=5. So, the required explicit formula is:
[tex]f(n)=5+(n-1)5[/tex]
[tex]f(n)=5+5(n-1)[/tex]
Therefore, the required explicit formula for the second recursive formula is [tex]f(n)=5+5(n-1)[/tex].
The third recursive formula is:
[tex]f(1)=5[/tex]
[tex]f(n)=f(n-1)+3[/tex] for [tex]n\geq 2[/tex].
It is the recursive formula of an AP with a=5 and d=3. So, the required explicit formula is:
[tex]f(n)=5+(n-1)3[/tex]
[tex]f(n)=5+3(n-1)[/tex]
Therefore, the required explicit formula for the third recursive formula is [tex]f(n)=5+3(n-1)[/tex].
Can someone please help me with this I’m struggling
Answer:
Equation: [tex]70=(x+3)x[/tex]
x = -10 or x = 7
x = 7 (width can't be negative)
x + 3 = 10
Step-by-step explanation:
Represent the width of the rectangle by x. "The length of a rectangle EXCEEDS the width by 3" means the length is 3 LONGER than the width, so the length is represented by the expression x + 3.
Area = (length)(width)
70 = (x + 3)x
Multiply out the right side.
[tex]70=x^2+3x\\x^2+3x-70=0[/tex]
Factor the left side.
[tex](x+10)(x-7)=0[/tex]
Each binomial could equal 0, so
[tex]x+10=0 \text{ or }x-7=0\\x=-10\text{ or }x=7[/tex]
The negative solution does not make sense as the width of a rectangle.
x = 7, making the length, x + 3 = 10
Answer:
Pls mark this as brainiest
Step-by-step explanation:
Area of the rectangle = length x breadth
consider 'x' to be width
therefore length = x+3
area = (x+3)*x
Area = 70 square
x = 7
x+3 = 7+3
= 10
verification
7 x 10
= 70
Question 4(Multiple Choice Worth 4 points)
.
(08.03)Solve the system of equations and choose the correct answer from the list of options.
X + y = -3
y = 2x + 2
a- five over 3, four over 3
b-negative five over 3, negative four over 3
c- negative 3 over 5 negative 3 over 4
D- 3 over 4, 3 over 5
Answer:
Hello,
Answer B (-5/3,-4/3)
Step-by-step explanation:
I am going to use the substitution 's method.
[tex]\left\{\begin{array}{ccc}x+y&=&-3\\y&=&2x+2\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}y&=&2x+2\\x+2x+2&=&-3\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}y&=&2x+2\\3x&=&-5\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}x&=&-\dfrac{5}{3} \\\\y&=&2*(-\dfrac{5}{3})+2\\\end {array} \right.\\\\\\\boxed{\left\{\begin{array}{ccc}x&=&-\dfrac{5}{3} \\\\y&=&-\dfrac{4}{3}\\\end {array} \right.\\}[/tex]
HELP QUICK PLEASE!
Which postulate, if any, could be used to prove the triangles are congruent?
Hypotenuse-Leg (HL)
Side-Angle-Side (SAS)
O Side-Side-Side (SSS)
The triangles cannot be proved congruent.
Answer:
Side-Side-Side (SSS)
Step-by-step explanation:
Side-Side-Side is a rule used to prove whether a given set of triangles are congruent. The SSS rule states that: If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.
Can someone help me with this math homework please!
Answer:
Graph number 3 is correct :)
Answer:
It's the 3rd pic
Step-by-step explanation:
It's written in y=mx+b form
the m is slope so 2/3 is the slope. You go up 2 and right 3
b is the y-intercept
hope this helps
A telephone plan charges a regular monthly amount plus charges for the number of minutes of use (x) as shown in the equation y = 0.28x + 65. What are the slope and y-intercept? HELP
Answer:
Slope: 0.28
y-intercept: (0,65)
Answer:
slope: .28 y-int: 65
because y=mx+b m is slope and b is the y intercept
