The minimum value of the function occurs at [tex]\( x = -\frac{5}{2}[/tex], and the function reaches its minimum value of [tex]\( -\frac{1}{4} \)[/tex] at this point.
To find the minimum value of the quadratic function [tex]\( f(x) = x^2 + 5x + 6[/tex], we can use the vertex formula. The vertex of a quadratic function [tex]\( ax^2 + bx + c \) is given by the point \( \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right) \).[/tex]
[tex]For \( f(x) = x^2 + 5x + 6 \), \( a = 1 \), \( b = 5 \), and \( c = 6 \).[/tex]
The x-coordinate of the vertex is [tex]\( -\frac{b}{2a} = -\frac{5}{2(1)} = -\frac{5}{2} \).[/tex]
To find the minimum value, we substitute [tex]\( x = -\frac{5}{2} \)[/tex] into the function:
[tex]\[ f\left(-\frac{5}{2}\right) = \left(-\frac{5}{2}\right)^2 + 5\left(-\frac{5}{2}\right) + 6 \]\[ = \frac{25}{4} - \frac{25}{2} + 6 \]\[ = \frac{25}{4} - \frac{50}{4} + \frac{24}{4} \]\[ = \frac{-1}{4} \][/tex]
So, the minimum value of the function occurs at [tex]\( x = -\frac{5}{2}[/tex], and the function reaches its minimum value of [tex]\( -\frac{1}{4} \)[/tex] at this point.
What is the rational number equivalent to 1 point 28 with a bar over 28? 1 and 6 over 97 1 and 28 over 99 1 and 8 over 33 1 and 5 over 16
Answer: The answer is [tex]1\dfrac{28}{99}.[/tex] .
Step-by-step explanation: The given rational number is
[tex]R=1.\bar{28}.[/tex]
We are to select the correct expression from the options that is equivalent to the given rational number.
Let us consider that
[tex]x=1.\bar{28}\\\\\Rightarrow x=1.28\bar{28}\\\\\Rightarrow 100\times x=100\times 1.28\bar{28}\\\\\Rightarrow 100x=128.\bar{28}\\\\\Rightarrow 100x=128+.\bar{28}\\\\\Rightarrow 100x=127+x\\\\\Rightarrow 100x-x=127\\\\\Rightarrow 99x=127\\\\\Rightarrow x=\dfrac{127}{99}\\\\\Rightarrow x=1\dfrac{28}{99}.[/tex]
Thus, the correct option is [tex]1\dfrac{28}{99}.[/tex]
What do the vertical lines mean?
Final answer:
In art, vertical lines suggest stability and structure, contrasting with calming horizontal lines and dynamic diagonal lines. These lines help define shapes, indicate motion, and guide the viewer through the composition.
Explanation:
The term vertical lines in the context of art and design, refers to lines that run up and down the canvas or design space, perpendicular to the horizon. These lines can convey a variety of meanings and emotions in visual compositions. According to a description by Oliver Harrison, vertical lines are seen as visually stable and can be associated with structures like tree trunks or classical columns, suggesting strength and stability.
The domain of the following relation R {(6, −2), (1, 2), (−3, −4), (−3, 2)} is
{−3, −3, 1, 6}
{−4, −2, 2, 2}
{−4, −2, 2}
{−3, 1, 6}
Answer:
Option 4th is correct
the domain of the following relation R is:
[tex]\{-3, 1, 6\}[/tex]
Step-by-step explanation:
Domain is the set of all values of x-coordinates where function is defined.
Given the Relation:
[tex]R = \{(6, -2), (1, 2), (-3, -4), (-3, 2)\}[/tex]
The ordered pairs are in the form of (x, y)
Domain = Set of all values of x.
In the given relation:
x-values = { 6, 1, -3}
⇒[tex]\text{Domain} = \{-3, 1, 6\}[/tex]
therefore, the domain of the following relation R is:
[tex]\{-3, 1, 6\}[/tex]
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Which of the binomials below is a factor of this trinomial?
x² + 2x - 48
A. x + 8
B. x - 3
C. x - 8
D. x + 3
Let’s assume the following statements are true: Historically, 75% of the five-star football recruits in the nation go to universities in the three most competitive athletic conferences. Historically, five-star recruits get full football scholarships 93% of the time, regardless of which conference they go to. If this pattern holds true for this year’s recruiting class, answer the following:
a. Based on these numbers, what is the probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship?
b. What are the odds a randomly selected five-star recruit will not select a university from one of the three best conferences? Explain.
c. Explain whether these are independent or dependent events. Are they Inclusive or exclusive? Explain.
Find the probability that 3 randomly selected people all have the same birthday. ignore leap years. round to eight decimal places.\
The probability that 3 randomly selected people all have the same birthday is 1 in 48,627,125.
Explanation:In order to find the probability that 3 randomly selected people all have the same birthday, we need to consider the total number of possible outcomes and the number of favorable outcomes. There are 365 days in a year (excluding leap years) and each person's birthday is independent of the others. Therefore, the probability of each person having the same birthday as the previous person is 1/365. To calculate the probability that all 3 people have the same birthday, we multiply the probabilities together:
P(3 people have the same birthday) = (1/365) * (1/365) * (1/365) = 1/48,627,125
Thus, the probability that 3 randomly selected people all have the same birthday is approximately 0.0000000206, rounded to eight decimal places.
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Determine the exact value of
sin(−135)°.
Identify the reference angle, Theta
Theta=?
We will see that the exact value is √2/2 = 0.707, and the reference angle is 45°.
How to determine the reference angle?
We know that for any angle θ we have that:
sin(θ) = sin(θ + n*360°)
Where n is an integer value.
To find the reference angle of a given angle θ, we just need to find a value of n such that:
0 ≤ θ + n*360° ≤ 360°
So we can write our angle in the normal range.
in this case, our angle is -135°
Then we can write:
0 ≤ -135° + n*360° ≤ 360°
Is immediate to notice that we must take n = 1
0 ≤ -135° + 1*360° ≤ 360°
0 ≤ -135° + 1*360° ≤ 360°
0 ≤ 225° ≤ 360°
Now we know that θ = 225°.
Ok, this lies on the third quadrant, when an angle lies on the third quadrant, to get the reference angle you just need to subtract 180°.
We will get:
225° - 180° = 45°
So the reference angle is 45°.
Finally, to get the exact value we use:
sin (-135°) = sin(225°) = cos(45°) = √2/2 = 0.707
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What is most likely the line of best fit for this scatter plot?
Line A
Line B
Line C
Line D
Let f(x) = x + 8 and g(x) = x2 − 6x − 7. find f(g(2)). −7 −3 10 33 open study
What is the cardinality of the set {ø, {ø}, {ø, {ø}}}?
Factor this expression completely and then place the factors in the proper location on the grid. Note: Place factors alphabetically in the grid! ab + 4 + a + 4b
Answer:
The required form of the given expression is : (a + 4)(b + 1)
Step-by-step explanation:
The given expression is : ab + 4 + a + 4b
We need to factor he given expression and arrange the factors in the alphabetic order.
To find the factors of the given expression, we need to use the concept of algebra :
ab + 4 + a+ 4b
First rearranging the terms in order to form the factors :
= ab + 4b + 4 + a
= b(a + 4) + 1(4 + a)
= b(a + 4) + 1(a + 4)
= (b + 1)(a + 4)
Now, the factors in the alphabetic order :
= (a + 4)(b + 1)
Hence, the required form of the given expression is : (a + 4)(b + 1)
What is the solution of \sqrt(2x+4)=16?
x = 6
x = 72
x = 126
no solution
The solution of the expression will be;
⇒ x = 126
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ √(2x + 4) = 16
Now,
Solve the expression as;
The expression is,
⇒ √(2x + 4) = 16
Square both side, we get;
⇒ 2x + 4 = 16²
⇒ 2x + 4 = 256
⇒ 2x = 256 - 4
⇒ 2x = 252
⇒ x = 126
Thus, The solution of the expression will be;
⇒ x = 126
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Which of the following quadrilaterals have diagonals that are perpendicular to each other? Check all that apply.
A. Rectangle
B. Square
C. Parallelogram
D. Rhombus
Answer:
B. Square
D. Rhombus
Step-by-step explanation:
If you take a rhombus ABCD, its all sides are congruent. Lets take E as the point where the diagonals of a rhombus meet. Now it is known fact that the point where diagonals meet, they bisect each other.
Since, for sides, AB , CD,AD and CB are congruent
For diagonals, AC = BD
As E is the bisecting point for diagonals,
AE = EC and ED = EB
Now by SSS postulate, we can prove that all four triangles formed by rhombus are congruent
ΔAED , ΔBEC , ΔEDC and ΔAEB are congruent
Now the angles
∠AED, ∠AEB, ∠CED and ∠CEB are congruent as well,
So, we know that sum of interior angles of any quadrilateral is 360°
So each angle is 360/4 = 90°
This calculation is valid for square as well.
Answer:
B and D
Step-by-step explanation:
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What's the mean of 0,1,3,2
The value of 4 in 943,268
The value of the digit 4 in the number 943,268 is 40,000 because it is in the ten thousand place.
The value of the digit 4 in the number 943,268 depends on its place value in the number.
In 943,268:
- The digit 4 is in the ten-thousands place.
So, the value of the digit 4 in 943,268 is:
4 × 10,000 = 40,000
Therefore, the value of the digit 4 in 943,268 is 40,000.
Factor completely then place the answer in the proper location on the grid. Write the answer in descending powers if x
6x^4+15x^3y^2+3x^2y^3
Since the population size is always larger than the sample size, then the sample statistic:
Short fill in-
If two angles are adjacent and supplementary, then they are examples of the _____ Postulate.
Linear pair Postulate. Two angles are a linear pair if the angles are adjacent and the two unshared rays form a line. Below is an example of a linear pair: The linear pair postulate states that two angles that form a linear pair are supplementary.
Mr. Thompson borrowed $3,000. He repaid the loan with an interest charge of $500 in 36 equal monthly payments. What approximate annual percentage rate did he pay? Find the answer to the nearest tenth of a percent.
Given: WA = NO, WS = NT, W = N.
A)SSS
B) SAS
C) ASA
D)AAS
Answer with explanation:
It is given that ,
In two triangles, ΔWAS and ΔNOT
1. WA = NO
2. W S = NT
3. ∠W=∠N
≡ΔWAS ≅ ΔNOT
The Angle is included between two sides .
So,these two triangles are congruent by ,SAS.
Option B:→ S AS
Which of the following is the definition of term? A. an ordered set of numbers B. an element in a sequence C. a sequence in which terms are given by multiplying the previous term by a common ratio D. a sequence in which terms are not given by multiplying the previous term by a common ratio
In basketball, when monica takes her first free throw, she has a 50% chance of scoring. if she takes an additional throw, she has a 75% chance of scoring on this throw if she scored on the immediately previous throw, but only a 25% chance of scoring on this throw if she didn't score on the immediately previous throw. suppose she has to take a set of three free throws in a row, and she doesn't score on the first one. what is the probability that she scores at least once on one of the subsequent two throws?
Mia is standing 210 yd from a radio tower. The angle of elevation from where she is standing on the ground to the top of the tower is 11°. How tall is the radio tower?
Sally found that a solution of x = 2 was extraneous for her function. What would be a possible denominator in Sally's function?
4x + 8
2x + 12
x^2 − 4
x^2 − 16
Answer:
[tex]x^2-4[/tex]
Step-by-step explanation:
Sally found that a solution of x = 2 was extraneous for her function.
Extraneous solution is a solution that makes the denominator 0
Possible denominator are given . LEts plug in 2 for x and check which option gives us 0
[tex]4x+8=4(2)+8= 16[/tex]
[tex]2x+12=2(2)+12=4+12= 16[/tex]
[tex]x^2-4= (2)^2-4= 4-4=0[/tex]
[tex]x^2-16= (2)^2-16= 4-16= 12[/tex]
[tex]x^2-4[/tex] gives us 0 when we plug in 2 for x.
So x=2 was extraneous solution for [tex]x^2-4[/tex]
PLEASEEE help shape equation puzzle
Which three lengths could be the lengths of the sides of a triangle? 9 cm, 22 cm, 11 cm10 cm, 15 cm, 24 cm12 cm, 5 cm, 17 cm21 cm, 7 cm, 6 cm
Answer: 10, 15, 24 is your answer
Step-by-step explanation:
What's the answer help me out please ?
George plans to cover his circular pool for the upcoming winter season. The pool has a diameter of 20 feet and extends 12 inches beyond the edge of the pool. A rope runs along the edge of the cover to secure it in place.
a.
What is the area of the pool cover?
b.
What is the length of the rope?
so use a basic formula here:
area of a circle = πr²
and the circumference of a circle = πd
a)
therefore the area of the pool cover is π multiplied by the radius² (which is the diameter of the pool cover plus the extra 12 inches divided by two, so the radius is 21/2 or 10.5) is 346.36(to two decimal places.)
b)
Using the same diameter, we can work out the length of the rope by multiplying the diameter (10.5) by π, which is 32.99 (to two decimal places).