The quadratic function, f(x) = 3·x² + 6·x, has the following values;
1. The function has a minimum value
2. The y-intercept of the function is (0, 0)
The axis of symmetry is; x = -1
The x-coordinate of the vertex is; x = -1
3. The table of values can be presented as follows;
x [tex]{}[/tex]-2 -1 0
f(x) [tex]{}[/tex]0 -3 0
The vertex is (-1, -3)
4. Please find attached the graph of the function
What is a quadratic function?A quadratic function is a function that has 2 as the highest power of the variables.
The specified function is; f(x) = 3·x² + 6·x
1. The coefficient of x² in the specified quadratic function, which indicates the existence of a minimum or maximum value is positive, therefore, the function has a minimum value
2. The y-intercept is the value of the function when x = 0, therefore;
f(0) = 3 × 0² + 6 × 0 = 0
Therefore, at the y-intercept, x = 0, and f(x) = 0
The y-intercept is (0, 0)
The axis of symmetry is a line that passes through the vertex
A the vertex, we get, f'(x) = 6·x + 6 = 0
Therefore; 6·x + 6 = 0
6·x = -6
x = -6/6 = -1
f(-1) = 3·(-1)² + 6 × (-1) = -3
The vertex is (-1, -3)
Therefore, the axis of symmetry is the line x = -1
The x-coordinate of the vertex of the function is; x = -1
3. A table of values for the function can be presented as follows;
x [tex]{}[/tex] f(x)
-6 [tex]{}[/tex] 72
-5 [tex]{}[/tex] 45
-4 [tex]{}[/tex] 24
-3 [tex]{}[/tex] 9
-2 [tex]{}[/tex] 0
-1 [tex]{}[/tex] -3
0 [tex]{}[/tex] 0
1 [tex]{}[/tex] 9
2 [tex]{}[/tex] 24
3 [tex]{}[/tex] 45
4 [tex]{}[/tex] 72
5 [tex]{}[/tex] 105
4. . Please find attached the graph of the function created with MS Excel
Learn more about quadratic functions in algebra here:
https://brainly.com/question/29374664
#SPJ1
Four more than twice the sum of a number and three is negative 5
Answer: It is A
Step-by-step explanation:
Composition of functions worksheet
using f(x) = 8x squared and g(x) (2x+8), find:
The composition of the function are as follows:
(g ∘ g) (x) = 4x + 16
(f ∘ g) (x) = 16x + 64
f [g(7)] = 6x - 28
g [f(3)] = -30x - 10
What is a Composite Function?
If we are given two functions, we can compose one function into the other to produce a third function. The steps needed to complete this operation are the same as those needed to solve any function for any given value. These are referred to as composite functions.
We have,
i] f(x) = 8x and
g(x) = (2x+8)
(g ∘ g) (x) = g[g(x)]
Substitute x with (2x+8) in the function g(x) = (2x+8).
= 2((2x+8))+8
= 4x + 16
(f ∘ g) (x) = f [g (x)]
Substitute x with (2x+8) in the function f(x) = 8x.
(f ∘ g) (x) = 8(2x+8)
= 16x + 64
ii] f(x) = 6x + 2 and g(x) = x -5
f [g(7)] = 6(x-5) + 2
= 6x - 28
g [f(3)] = (6x + 2 ) - 5
= -30x - 10
Hence, the composition of the function is:
(g ∘ g) (x) = 4x + 16
(f ∘ g) (x) = 16x + 64
f [g(7)] = 6x - 28
g [f(3)] = -30x - 10
To learn more about the composition of the function visit,
https://brainly.com/question/10687170
#SPJ1
Segment BD bisects angle ABC measure angle ABC equals 7x. The measure angle ABD equals 3x+25. Find the measurement of angle DBC
The measurement of angle DBC is 100°. It can be obtained by the properties of bisector of an angle and algebriac multiplication.
What is angle bisector?
An angle bisector is the ray or line segment that divides the angle into two equal parts.
Since the segment BD bisects angle ABC hence,
∠ABC = ∠ABD+∠DBC ..... (1)
Also, since segment BD bisects angle ABC hence,
∠ABD = ∠DBC
Use this fact in equation (1)
∠ABC = ∠ABD+∠ABD
∠ABC =2 ∠ABD
Now, substitute values and use algebriac multiplication.
7x = 2(3x+25)
7x = 6x+50
7x - 6x= 50
x=50
Now, substitute the value of x in the expression of ∠ABD.
∠ABD = 3x+25
∠ABD = 3(50)+25
∠ABD = 100
Now, since ∠ABD = ∠DBC hence, ∠DBC = 100.
Hence, the measurement of angle DBC is 100°.
Learn more about angle bisector from the following link:
https://brainly.com/question/24334771
#SPJ4
In the figure below, points D, B, E, F, and lie in plane X.
Points A and C do not lie in plane X.
For each part below, fill in the blanks to write a true statement.
The blanks are filled as below
(b) G and E are distinct points that are collinear.(c) F, D, B, and G are distinct points that are coplanar.(d) Suppose line AD is drawn on the figure. Then AD and AC are distinct lines that intersect.What are collinear points?Collinear points are those that are situated along a single straight line.
Collinear points are those that are on a line either close to or far from another point, it can be more than two points.
While coplanar points imply lying on the same plane
In the diagram,
E, F, and G are collinear points
D, B, E, F, and G are coplanar points
A, B, and C are another collinear points
Learn more about collinear points at:
https://brainly.com/question/2234342
#SPJ1
Simplify. Rewrite the expression in the form y^n. y^5/y^3=
Answer:
y^2
Step-by-step explanation:
a^m/a^n = a^(m - n)
y^5/y^3 = y^2
5 divided by 19 vvchgdvbdvvvdbbxbvxvvdhhsjjshhhdbhshhhdhhshshhshdggdhshgdgfduhf
2(x-4 1/2)=-6.1 hellllllppppp meeeee
Answer:
[tex]x=1.45[/tex]
Step-by-step explanation:
[tex]2\left(x-4 \frac{1}{2} \right)=-6.1 \\ \\ 2\left(x-\frac{9}{2} \right)=-6.1 \\ \\ 2x-9=-6.1 \\ \\ 2x=2.9 \\ \\ x=1.45[/tex]
Gianna can wash 6 cars in 2 hours. At this rate, how many cars can Gianna wash in 5 hours?
Gianna washes 15 cars in 5 hours as her rate of washing cars is 3 cars per hour.
What is unitary method?
The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
According to the given question:
Gianna can wash 6 cars in 2 hours
Therefore, in 1 hour she can wash 6/2 cars which is 3 cars.
Gianna's rate of washing cars is 3 cars per hour
Hence by unitary method, Gianna at this rate can washes 5 x 3 cars that is 15 cars.
Gianna washes 15 cars in 5 hours as her rate of washing cars is 3 cars per hour.
To know more about unitary method visit
https://brainly.com/question/23423168
#SPJ1
PLEASE HELP 50 POINTS
The trigonometric expression cos 3x / (sin x · cos x) is equivalent by trigonometric formulas to the trigonometric expression csc x · cos 2x - sec x · sin 2x. (Correct choice: A)
How to find an expression equivalent to another trigonometric expressionIn this problem we find the definition of a trigonometric expression, whose equivalent expression must be found by using algebra properties and trigonometric formulas. First, write the trigonometric function:
cos 3x / (sin x · cos x)
Second, use trigonometric formulas:
cos (x + 2x) / (sin x · cos x)
(cos x · cos 2x - sin x · sin 2x) / (sin x · cos x)
cos 2x / sin x - sin 2x / cos x
csc x · cos 2x - sec x · sin 2x
The equivalent trigonometric expression is csc x · cos 2x - sec x · sin 2x.
To learn more on trigonometric equations: https://brainly.com/question/22624805
#SPJ1
2 websites sell the same type of headphone cost of headphone in website A is 49.95 and the postage is 4.39. The headphones in website B is 47.68 and the postage is 6.95. Including the postage which website is cheaper and by how much
Answer:
Website A is cheaper by 29 cents
Step-by-step explanation:
A
49.95 + 4.39 = 54.34
B
47.68 + 6.95 = 54.63
54.63 - 54.34 = 0.29
Answer:
the difference is 0.29 cents
website A is cheaper
Step-by-step explanation:
(47.68 + 6.95) - (49.95 + 4.39)
54.63 - 54.34 = 0.29
The soccer field is 105 meters long. The football field is 120 yards long. Which is longer?
The football field is longer than soccer field.
What is a expression? What is a mathematical equation? What is unit conversion?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.
We have a soccer field that is 105 meters long and a football field is 120 yards long.
In one yard, we have -
1 yard = 0.9144 meters
Then, in 120 yards, we will have -
120 x 0.9144 = 109.728 meters
Now, 109.728 meters > 105 meters.
Therefore, the football field is longer than soccer field.
To solve more questions on dimensions and unit conversion, visit the link below -
brainly.com/question/4613077
#SPJ1
Which expression is equivalent to (6x^-9x) - (2x - 3)?
The equivalent expression of (6x² - 9x) - (2x -3) is 6x² - 11x + 3
What is an equivalent expression?Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.
In other words, equivalent expressions are expressions that have similar value or worth but do not look the same.
To find equivalent expression we can simplify the expression.
Therefore,
(6x² - 9x) - (2x -3)
open the brackets
6x² - 9x - 2x + 3
combine like terms
Therefore,
(6x² - 9x) - (2x -3) = 6x² - 11x + 3
learn more on equivalent expression here: https://brainly.com/question/6997280
#SPJ1
A shopping mall has 226 stores on 4 levels. Each level of the mall has about the same number of stores. Which of the following are reasonable estimates for the number of stores on each level
The number of stores in each level of the shopping mall are 56 stores.
How to solve an equation?An equation is an expression that can be used to show the relationship between variables and numbers. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
Let x represent the number of stores on each level.
A shopping mall has 226 stores on 4 levels. If there are same number of stores in each level:
(4 × x) = 226
4x = 226
Divide
x = 226 / 4
x = 56.5
There are about 56 stores per level.
Find out more on equation at:
brainly.com/question/2972832
#SPJ1
1. Write two equivalent expressions to represent the area of this rectangle.
2. Write two equivalent expressions to represent the perimeter of this rectangle.
(pls add an explanation)
The perimeter of a rectangle is 2x+6 units and the area of a rectangle is 5x-10 square units.
Given that, the breadth of a rectangle =5 units and the length of a rectangle =(x-2) units.
What is the perimeter of a rectangle?The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).
Here, perimeter =2(x-2+5)
= 2(x+3)
= 2x+6 units
Area of a rectangle =length × width
= (x-2) × 5
= 5x-10 square units
Therefore, the perimeter of a rectangle is 2x+6 units and the area of a rectangle is 5x-10 square units.
To learn more about the perimeter of a rectangle visit:
https://brainly.com/question/15287805.
#SPJ1
18 Which expression uses the greatest common factor and distributive property to write 18 + 24 as a product? Circle the letter of the correct answer.
The expression that uses the greatest common factor and distributive property to write the given expression, 18 + 24, is 6(3 + 4)
Writing an expression using the Greatest common factor and distributive propertyFrom the question, we are to determine the expression that uses the greatest common factor and the distributive property to write the given expression.
The given expression is
18 + 24
First, we will determine the greatest common factor of 18 and 24
18 = 2 × 3 × 3
24 = 2 × 2 × 2 × 3
Thus,
The greatest common factor is 2 × 3 = 6
Now, we will write the expression using the greatest common factor and the distributive property
18 + 24
6(3 + 4)
Hence, the expression is 6(3 + 4)
Learn more on Writing an expression here: https://brainly.com/question/28401321
#SPJ1
the sum of two number 12 when three times the first number is added to 5 times the second number the results is 44
Answer:
one number is 8 and other is 4
Step-by-step explanation:
So we can say x+y=12.
And 3x+5y=44
For x+y=12, we can subtract x to get: y=12-x
Plug that in to get 3x+5(12-x)=44
3x+60-5x=44
Subtract 44: -2x+16=0
2x=16
x=8
12-8=4.
If you roll a standard six-sided die a thousand times and add up the total number of pips, which approximate sum could you reasonably expect to end with?
1) 16.7% probability of rolling 10+.
2) 50% probability an odd number is rolled.
3) 7 is the most likely total result.
These are all the possible outcomes:
(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)
(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)
(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)
(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)
(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)
(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)
There are 36 possible outcomes
1) what is the probability of rolling 10+?
There are 6 possible outcomes in which 10+ is rolled:
(4,6), (5,5),(5,6), (6,4), (6,5),(6,6).
So there is a 6/36 = 0.167 = 16.7% probability of rolling 10+.
2) what is the probability of rolling an odd number?
There are 18 possible outcomes in which an odd number is rolled.
So there is a 18/36 = 0.5 = 50% probability an odd number is rolled.
3) what is the total that is most likely to result?
There are 6 outcomes in which 7 is rolled.
So 7 is the most likely total result.
learn more about of probability here
https://brainly.com/question/11234923
#SPJ4
visit your local library: on a recent saturday, a total of 1343 people visited a local library. of these people, 253 were under age 10, 466 were aged 10-18, 174 were aged 19-30, and the rest were more than 30 years old. one person is sampled at random. (a) what is the probability that the person is less than 19 years old? (b) what is the probability that the person is more than 10 years old? part 1 of 2 (a) what is the probability that the person is less than 19 years old? round your answer to four decimal places.
Probability of people less than 19 year old = 0.5343
Probability of people greater than 10 year old = 0.8116
What is probability?
Mathematical descriptions of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the probability of an event, with 0 roughly denoting impossibility and 1 denoting certainty.
People under age 10 = 253
People between the age of 10-18 = 466
People between the age of 19-30 = 174
People above the age of 30 = 450
Total no. of people = 1343
a) people less than 19 years old = 253+466 = 719
probability of people<19 year old = P(age<19) = 719/1343 = 0.5354
b) people of age greater than 10 = 466+174+450 = 1090
probability of people >10 year old = P(age>10) = 1090/1343 = 0.8116
To learn more about probability:
https://brainly.com/question/13604758
#SPJ4
If X is the midpoint of TV, TV bisects RS, and TR is parallel to VS, state five pairs of objects (segments or angles) that must be congruent and give a reason why for each pair.
According to the Alternate Interior Angles Theorem, when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.
Alternate Interior Angle Theorem?According to the Alternate Interior Angles Theorem, when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.Is it true or false that different interior angles are always congruent? Although untrue, this assertion is a typical misunderstanding. Keep in mind that when the lines are parallel, alternate inner angles are congruent.Alternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposing sides of the transversal when two lines are crossed by another line (referred to as the Transversal). These two pairs of alternate interior angles in this illustration are c and f.To learn more about Congruent refer to:
https://brainly.com/question/2938476
#SPJ1
Answer to this question
In the picture
[tex]tan(\alpha - \beta) = \cfrac{tan(\alpha)- tan(\beta)}{1+ tan(\alpha)tan(\beta)} \\\\[-0.35em] ~\dotfill\\\\ cos(\alpha )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\qquad \textit{let's find the opposite} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]
[tex]\pm\sqrt{5^2 - 3^2}=b\implies \pm 4=b\implies \stackrel{IV~Quadrant}{-4=b}~\hfill tan(\alpha)=\cfrac{\stackrel{opposite}{-4}}{\underset{adjacent}{3}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]tan(\alpha - \beta) \implies \cfrac{\stackrel{tan(\alpha)}{-\frac{4}{3}}- \stackrel{tan(\beta)}{\frac{4}{3}}}{1+ \stackrel{tan(\alpha)}{\left( -\frac{4}{3} \right)}\stackrel{tan(\beta)}{\left( \frac{4}{3}\right)}}\implies \cfrac{~~ \frac{-8 }{3 } ~~}{1-\frac{16}{9}}\implies \cfrac{~~ \frac{-8 }{3 } ~~}{\frac{-7}{9}} \\\\\\ \cfrac{-8}{3}\cdot \cfrac{9}{-7}\implies \cfrac{24}{7}\implies {\Large \begin{array}{llll} 3\frac{3}{7} \end{array}}[/tex]
Give a number in the form of a/b o that when it i divided by 100, the reult would be 0. 014 (write in fraction in reduce form)
The reduced form of the fraction would be 2.8/2.
What is a fraction?
A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters.
Given that a/b is a fraction and when it is divided by 100 it will result in 0.014.
So we can write,
[tex]\frac{\frac{a}{b} }{100}=0.014\\\\ \frac{a}{b}=0.014*100\\\\\frac{a}{b}=1.4\\[/tex]
Now 1.4 can be written as
a/b = 2.8/2
Hence, the reduced form of the fraction would be 2.8/2.
To learn more about reduced fractions, visit:
https://brainly.com/question/78672
#SPJ4
A cylindrical rod of steel (e = 207 gpa) having a yield strength of 310 mpa is to be subjected to a load of 11,100 n. If the length of the rod is 500 mm, what must be the diameter to allow an elongation of 0. 38 mm?.
the diameter to allow an elongation of 0. 38 mm therefore required diameter is 7.65 mm
Given the data in the question;
F = 11100 N
l₀ = 310 mm = 0.31 m
E = 207 GPa = 207 × 10⁹ N/m²
Δl = 0.38 mm = 0.0005 m
So, lets assume the deformation is elastic;
d₀ = √( [4l₀F] / [πEΔl] )
we substitute
d₀ = √( [4 × 0.38 × 11100] / [π × (207 × 10⁹) × 0.0005]] )
d₀ = √( 10123.2 / 172787595.947 )
d₀ = √( 5.85875 × 10⁻⁵ )
d₀ = 0.007654 m
d₀ = ( 0.007654 × 1000 )mm
d₀ = 7.65 mm
Therefore, required diameter is 7.65 mm
learn more about of diameter here
https://brainly.com/question/23848936
#SPJ4
a punch recipe calls for 1 1/2 quarts of sparkling water and 3/4 of a quart of grape juice. how much of each ingredient would you need to make 75 quarts of punch?
50 quarts of sparking water and 25 quarts of grape juice are needed for 75 quarts of punch.
What are ratios and proportions?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.
Given that a punch recipe calls for 1(¹/₂) quart of sparkling water and 3/4 of a quart of grape juice.
The ratio of sparkling water to grape juice is,
1(¹/₂) : (3/4 quarts) = (3/2) : (3/4) = 2 : 1
The amount sparkling water in the total volume is 2 : (2+1) = 2/3 of the total volume. For a volume of 100 quarts, the sparkling water content is
2/3 · 75quarts = 50 quarts
Then the grape juice content is,
1/3 · 75 quarts = 25 quarts
Therefore, 50 quarts of sparking water and 25 quarts of grape juice are needed for 75 quarts of punch.
To know more about ratios and proportions follow
https://brainly.com/question/2914376
#SPJ1
Bob bad $50. he spent $28.67 for a new backpack. How much money does he have left?
Answer: $21.33
Step-by-step explanation: 50 - 28.67 = 21.33
Write an inequality that could be used to represent all solutions for x: the quotient of a number and three minus twelve is less than 12
We can write the given statement as inequality as -
-(x/9) < 12
What is linear inequality? What is the law of Reversal and law of Trichotomy? What is the general equation of a Straight line?Linear inequalities are defined as expressions in which two linear expressions are compared using the inequality symbols.
y > mx + cy < mx + cy ≥ mx + cy ≤ mx + cReversal property : If (a > b) then (b < a) and if (a < b) then (b > a).
Law of Trichotomy : The "Law of Trichotomy" says that - only one of the following is true : (a < b) or (a = b) or (a > b).
The general equation of a straight line is y = mx + c
Other possible equations of lines are -
(y - y₁) = m(x - x₁) {Point - slope form}(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁) {Two point - slope form}x/a + y/b = 1 {intercept form}x cos(β) + y sin(β) = L {Normal form}We have the following statement -
"the quotient of a number and three minus twelve is less than 12".
We can write the inequality as -
-(x/9) < 12
Therefore, we can write the given statement as inequality as -
-(x/9) < 12
To solve more questions on straight line inequalities, visit the link below-
brainly.com/question/20400984
#SPJ1
Givenf(x)=4x^2 - 1, and g(x) = 2x - 1, find g(f(2)).
Given f(x) = x^2 and g(x)=x - 1, write each composite function.State the domain of each:2.f(g(x)) 3.g(f(x))
The value of the function g(f(2)) is 29 and 2.f(g(x)) is (x - 1)(2x - 2).
What is a composite function?When the output of one function is given to the input of another function they are called composite functions.In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).
Given, f(x) = 4x² - 1. and g(x) = 2x - 1.
Now, g(f(2)) is the output of f(2) is the input of g(x).
∴ f(2) = 4(2)² - 1.
f(2) = 15.
Now, g(f(2)) = 2(15) - 1.
g(f(2)) = 29.
Also given,
f(x) = x² and g(x) = x - 1.
Now, 2.f(g(x)).
2.f(g(x)) = 2.f(x- 1).
2.f(g(x)) = 2(x - 1)².
2.f(g(x)) = 2(x² - 2x + 1).
2.f(g(x)) = 2x² - 4x + 2.
2.f(g(x)) = 2x² - 2x - 2x + 2.
2.f(g(x)) = 2x(x - 1) - 2(x - 1).
2.f(g(x)) = (x - 1)(2x - 2).
There is no restriction to the domain of this quadratic function.
learn more about domain and range here :
https://brainly.com/question/28135761
#SPJ1
A game consists of drawing three cards at random from a deck of playing cards. You win $3 for each red card that is drawn. It costs $2 to play. For one play of this game, the sample space S for the net amount you win (after deducting the cost of play) is
Select one:
a. S = {$0, $1, $2, $3}
b. S = {$0, $3, $6, $9}
c. S = {-$2, $1, $4, $7}
The sample space S for the net amount you win (after deducting the cost of pay) is S = {-$2, $1, $4, $7}.
What is cost?
A cost is the worth of money that has been expended in the production or delivery of a good or service and is therefore no longer accessible for use in accounting, retail, research, or accounting. In business, the cost may be one of acquisition, in which case the cost is the sum of the money used to obtain it.
Let, a game consists of drawing three cards at random from a deck of playing cards.
You win $3 for each red card that is drawn.
It costs $2 to play.
After deducting the cost of pay the amount will start from -$2.
For first red card drawn you win $3.
So, the amount becomes, -$2 + $3 = $1.
For second red card drawn you again win $3.
So, the next amount becomes $1 + $3 = $4.
For third red card drawn the amount becomes,
$4 + $3 = $7.
Hence, the sample space S for the net amount you win is
S = {-$2, $1, $4, $7}.
To know more about the cost, click on the link
https://brainly.com/question/25109150
#SPJ4
Help please help help please help help me
Answer:
103
Step-by-step explanation:
angle 1 and angle 5 are the same as each other.
After the consumption of an alcoholic beverage, the concentration of alcohol in the bloodstream (blood alcohol concentration, or BAC) surges as the alcohol is absorbed, followed by a gradual decline as the alcohol is metabolized. The function C(t) = 1. 35te−2. 802t † models the average BAC, measured in mg/mL, of a group of eight male subjects t hours after rapid consumption of 15 mL of ethanol (corresponding to one alcoholic drink). A. What is the maximum average BAC during the first 3 hours? (Round your answer to three decimal places. ) mg/mL b. When does it occur? (Round your answer to two decimal places. ) h
The maximum average BAC during the first 6 hours is about 0.177 mg/ml.
What is average ?
The middle number in a group of numbers is the average value, which is determined by dividing the sum of all the values by the variety of values.
When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.
The maximum is found where the derivative of C(t) is zero.
dC/dt = 1.35e^(-2.802t) -(1.35t)2.802e^(-2.802t) = 0
Solving for t gives ...
t = 1/2.802
So, the maximum C(t) is ...
C(1/2.802) = 1.35/2.802e^(-1) ≈ 0.177 . . . . . mg/mL
The maximum average BAC during the first 6 hours is about 0.177 mg/mL.
Learn more about average
brainly.com/question/24057012
#SPJ4
Find the perimeter of a quadrilateral with the following vertices.
(−6, −2), (0, −10), (5, 2), (−1, 10)
a.40
b.52
c.23
d.46
The perimeter of the quadrilateral is 46 units, so the correct option is d.
How to find the perimeter of the quadrilateral?The perimeter is equal to the sum of the lengths of all the sides of the quadrilateral.
Remember that the length of a segment whose endpoints are (x₁, y₁) and (x₂, y₂) is:
L = √( (x₁ - x₂)^2 + (y₁ - y₂)^2)
The length between the first two vertices: (−6, −2), (0, −10)
L₁ = √( (-6 - 0)^2 + (-2 + 10)^2) = 10
The length between the second two vertices: (0, −10), (5, 2)
L₂ = √( (0 - 5)^2 + (-10 - 2)^2) = 13
The length between the third two vertices: (5, 2), (−1, 10)
L₃ = √( (5 + 1)^2 + (2 - 10)^2) = 10
The length between the fourth two vertices: (−1, 10), (−6, −2)
L₄ = √( (-1 + 6)^2 + (10 + 2)^2) = 13
Then the perimeter is:
P = 10 + 13 + 10 + 13 = 46
The correct option is D.
Learn more about perimeter.
https://brainly.com/question/24571594
#SPJ1