The roots of the quadratic equation x² - 8x + 16 = 0 are real and equal which is 4.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The quadratic equation is given below.
x² - 8x + 16 = 0
The value of the discriminant is given as,
D = b² - 4ac
D = (-8)² - 4(1)(16)
D = 64 - 64
D = 0
The roots of the equation are calculated as,
x² - 8x + 16 = 0
x² - 4x - 4x + 16 = 0
x(x - 4) - 4(x - 4) = 0
(x - 4)(x - 4) = 0
x = 4, 4
The roots of the quadratic equation x² - 8x + 16 = 0 are real and equal which is 4.
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what is the equation of the horizontal asymptote associated with this function . describe waht this means in termsof the mouths ph overtimer
The horizontal asymptote of function f(x) is y=6.5, which is a straight line, which means that even if time is infinite, the pH of the mouth will not rise above 6.5, which is the normal pH of the mouth.
A function's horizontal asymptote is a horizontal line with which the function's graph appears to coincide but does not actually coincide. The horizontal asymptote is used to determine the behavior of the function.
When either lim x f(x) = k or lim x - f(x) = k, the horizontal asymptote of a function y = f(x) is a line y = k. . It is commonly abbreviated as HA. In this case, k is a real number that the function approaches when x is extremely large or extremely small.However, the maximum number of asymptotes that a function can have is 2.
Given,
[tex]f(x)=\frac{6.5x^2-89.4x+3734}{x^2+576}[/tex]
The horizontal asymptote of the function f(x) can be determined by
[tex]y=\lim_{x \to \infty} f(x)\\\\=\lim_{x \to \infty}\frac{6.5x^2-89.4x+3734}{x^2+576}\\\\=\lim_{x \to \infty}\frac{x^2(6.5-\frac{89.4}{x}+\frac{3734}{x^2})}{x^2(1+\frac{576}{x^2})}\\\\=\lim_{x \to \infty}\frac{(6.5-\frac{89.4}{x}+\frac{3734}{x^2})}{(1+\frac{576}{x^2})}\\\\=\frac{(6.5-\frac{89.4}{ \infty}+\frac{3734}{ \infty})}{(1+\frac{576}{ \infty})}\\\\=\frac{6.5-0+0}{1+0}\\\\=\frac{6.5}{1}=6.5[/tex]
Thus, the horizontal asymptote of function f(x) is y=6.5 which is straight line which means even the time reaches infinity the pH of mouth will not increase more than 6.5, which is the normal pH of mouth.
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Your question is incomplete, here is the complete question.
The function [tex]f(x)=\frac{6.5x^2-89.4x+3734}{x^2+576}[/tex] models the pH level f(x) of a mouth x minutes after eating food containing sugar. The graph of this function is shown.
What is the equation is the horizontal asymptote associated with is function? Describe what this means in terms of mouth's pH level over time.
Javier wants to prove that the base angles of an isosceles triangle are congruent. To do this, he draws triangle ABC,
with AB = BC. He will then prove that ZA and C are congruent by dividing triangle ABC into two triangles and
using triangle congruence.
Which of the following must be part of Javier's proof?
drawing a line parallel to AC through the midpoints of AB and BC
drawing a line parallel to BC through the midpoints of AB and AC
drawing a line perpendicular to AC through point B
drawing a line perpendicular to BC through point A
Answer:
C. Drawing a line perpendicular to [tex]\overline{AC}[/tex] through point [tex]B[/tex]
Step-by-step explanation:
The triangles formed by the perpendicular can be proved congruent by HL, and thus [tex]\angle A \cong \angle C[/tex] by CPCTC.
When using a 6 sided cube, what is the probability of rolling a 3, then not rolling a 3, and then rolling an even number?
Answer:
5/72
Step-by-step explanation:
You want the probability of rolling a 6-sided die 3 times with the sequential outcomes 3, not 3, even number.
Sequential outcomesThe probability of any given sequence of outcomes is the product of the probabilities of the outcomes individually. (We assume independence.)
P(3) = 1/6
P(not 3) = 1 -P(3) = 5/6
P(even) = 1/2
Then the probability of the given sequence is ...
P(3, 3', even) = (1/6)(5/6)(1/2) = 5/72
The probability of the given sequence is 5/72.
__
Additional comment
The outcomes are independent if the probability of occurrence does not depend on any previous outcome.
Can Someone Please Solve This By Using The Formula a^2+b^2=c^2
Answer: a= 16
Step-by-step explanation:
a^2 + 30^2 = 34^2
a^2 + 900 = 1,156
a^2 = 256
a = 16
What is 2’s absolute value
Answer:
2
Step-by-step explanation:
The way to find the absolute value of a number is to remove the negative symbol (-) if it has one.
The number 2 does not have one, so just leave it as it is.
Another way to think about it is, how far is 2 from 0 on a number line? Well, 2 is obviously 2 units away from 0.
Which is a nonlinear function?
A function y = x² which is nonlinear function. the correct option is A.
What is linear function?In mathematics, linear refer to a proportional behaviour that can be modelled with a line, the functions that model this behaviour are called linear functions, and their graphs are lines.
Now, linear expression refers to an expression which has variables with an exponent equal to 1,
Linear functions are in the form of y = mx + c and have a constant slope.
But Nonlinear functions have a slope that varies between points.
Also, the linear functions are polynomials with highest exponent equal to 1 and all others are non linear.
Here, the correct option is A. y = x²
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Which scatter plot best illustrates a strong positive correlation?
Answer:
A
Step-by-step explanation:
You want to select the scatter plot with strong positive correlation.
CorrelationCorrelation is a measure of how well one variable's values track the values of another variable. Perfectly correlated variables will have a scatter plot that is a straight line. The sign of the correlation (positive, negative) matches the sign of the slope of the line.
The less correlated values are, the more their scatter plot looks like a random placement of points. When there is no correlation at all, knowing the value of one of the variables gives no clue about the value of the other one.
Computed values of correlation range from -1 to +1.
Strong positive correlationWhen the plot begins to resemble a line with positive slope, the variables plotted in the scatter plot have strong positive correlation. That is shown in the attached scatter plot.
ticket prices at an outdoor theatre performance are $2.50 for children and $5.00 for adults. one evening, $6350 is collected from a total of 1900 people attending. how many adults and how many children attend?:
As the ticket prices at an outdoor theatre performance are $2.50 for children and $5.00 for adults. one evening, $6350 is collected from a total of 1900 people attending. There are 640 adult and 1260 childrens.
Given in the questions:
Ticket price in outdoor Theater = $2.50
For Children = $5.00
Total tickets collected in evening = $6350(collected from 1900 people)
Let p be the adult and
1900 - p be the children's who attained the show.
Now,
2.5 × (1900- p) +5p = 6350
⇒ 4750 - 2.5p +5p =6350
⇒ 2.5p = 1600
⇒ p = 1600/2.5
⇒ p = 640
Since,
p = 640
Therefore,
1900 - p = children
⇒ Children = 1900 - 640
⇒ Children = 1260
Therefore, there are total 640 adults and 1260 children's in the theater.
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Amelia i buliding 3 quare garden bed that are all the ame ize. He arrange them ide by ide to eparate certain plant. Amelia want to know the total area of the garden
The total area of 3 square garden beds = [tex]3s^{2}[/tex] square units
What exactly is a square shape?A square is a closed two-dimensional shape with four equal sides and four vertices. Its opposing sides are perpendicular to each other. A square can also be thought of as a rectangle with equal length and width. Many things resemble the square shape when you look around.
What is the formula for the area of a square?A square's area is equal to its side. As a result, the area of a square equals Side2 square units. and the perimeter of a square is equal to four side units.
Given:
She want to bulid = 3 square garden beds
All are for same size,
Therefore total area of three square garden beds = 3 × area of one square garden bed
[tex]area of 3 garden beds = 3 ( s^{2} )\\area of 3 garden beds = 3 s^{2}[/tex]
Therefore, total area of 3 square garden beds = [tex]3s^{2}[/tex] square units
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Tickets to a basketball game can be ordered online for a set price per ticket plus a $5. 50 service fee. The total cost in dollars for ordering 5 tickets is $108. 0. Which linear function represents c, the total cost, when x tickets are ordered? (a service fee is a single fee applied to the total, no matter the number of tickets purchased). C(x) = 5. 50 + 20. 50x c(x) = 5. 50x + 20. 50 c(x) = 5. 50 + 21. 60x c(x) = 5. 50x + 21. 60.
The linear function that represents c, the total cost, when x tickets are ordered is
c=5.50+20.50x
What is the equation in math?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
What are the 3 types of equations?There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.
Let
The overall price is c.
the quantity of tickets, x
the price of one ticket, excluding service charges, is z.
Knowing this
108=5.50+5z
finding z
z=20.50
therefore
The linear equation equals
c=5.50+20.50x
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Which expression does not factor? m3 1 m3 – 1 m2 1 m2 – 1
The expression that does not factor on the mentioned is m² + 1.
Why it cannot be factor?Because other expression can be factored, while m² + 1 has no factor form. For make it clear we can calculate to find the form expression and find the calculate power or result.
m³ + 1 =
The formula to calculate it is, a³ + b³ = m³ + 1³ And then it could be, (m + 1) (m² - m + 1).m³ - 1 =
The formula to calculate it is, a³ + b³ = m³ - 1³ a³ + b³ = (a + b) (a² - ab + b²)And then the power could be, (m - 1)(m² + m + 1²) = (m-1)(m² + m + 1).m² - 1 =
The formula to calculate it is, a² - b² = (a + b)(a - b).and then it could be, m² - 1 = (m + 1)(m - 1).
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a mail-order business prides itself in its ability to fill customers' orders in less than six calendar days, on average. periodically, the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders. on one occasion when a sample of 39 orders was selected, the average number of days was 6.65 with a population standard deviation of 1.5 days. calculate the appropriate test statistic to test the hypothesis.
Therefore ,Since 2.7406 > 2.023, reject H0 and conclude that the mail-order business is not achieving its goal.
What is test statistics ?A test statistic is a statistic used for testing statistical hypotheses. A test statistic, which is a tally of a data set that can be used to conduct the test and boils the data down to a single figure, is a common way to characterize a hypothesis test.
Here,
a) H0 : u > 6 days
Ha : u < 6 days
Thus,
n=39
x'=6.65
α=1.5
b) test statistics = Z
Z=[tex]\frac{x'-u}{\alpha /\sqrt{n } }[/tex]
Z=[tex]\frac{6.65-6}{1.5 /\sqrt{39 } }[/tex]
Z=2.71
c) p value =P(Z<2.71)
p value = 1 - P(Z<2.71)
p value = 0.9966
Since 2.71 > 2.023, reject H0 and conclude that the mail-order business is not achieving its goal.
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The following equation is an example of a literal equation.
2(z+a)=4b
A. Solve the given equation for the variable a. In your final answer, include all of your work.
B. In two or more complete sentences, explain the specific process that you followed in solving for a.
Answer:
a = 2b - z
Step-by-step explanation:
2(z+a) = 4b
z + a = 4b/2
z + a = 2b
a = 2b - z
Determine which set of side measurements could be used to form a right triangle. 4, 11, 20 16, 21, 25 5, 13, 25 3, 4, 5
The triangle with sides measuring 3, 4, 5 will form a Right Nagle Triangle
What is Pyhtagorean Theorem?
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship in Euclidean geometry between the three sides of a right triangle. It indicates that the area of the hypotenuse square is equal to the sum of the areas of the squares on the other two sides.
Solution:
(i) 4, 11, 20
20² = 4² + 11²
400 = 16 + 121
400 ≠ 137 #Not a right angle triangle
(ii) 16, 21, 25
25² = 16² + 21²
625 = 256 + 441
625 ≠ 697 #Not a right angle triangle
(iii) 5, 13, 25
25² = 5² + 13²
625 = 25 + 169
625 ≠ 194 #Not a right angle triangle
(iv) 3, 4, 5
5² = 3² + 4²
25 = 9 + 16
25 = 25 #Right angle triangle
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Write at least 6 equivalent expressions to the expression below.
12x - 6
Answer:
Here are six equivalent expressions to 12x - 6:
6(2x - 1)
3(4x - 2)
2(6x - 3)
1(12x - 6)
4(3x - 1)
(12x - 6) + 0
These expressions are all equivalent to 12x - 6 because they all have the same value, regardless of the value of x. This is because the terms on the right side of the equation cancel out, leaving only the constant value on the left side. For example, in the first expression, 6(2x - 1), the 2x and -1 terms cancel out, leaving only 6. This is the same for the other expressions listed above.
Step-by-step explanation:
Answer:
12x - 612x + (-6)12(x) + (-1)(6)12(x - 0.5)12x + (-1)(-6)12(x - 1/2)Step-by-step explanation:
Here are six equivalent expressions to the given expression:
12x - 612x + (-6)12(x) + (-1)(6)12(x - 0.5)12x + (-1)(-6)12(x - 1/2)Note that in each of the above expressions, the value of 12x - 6 is preserved, but the terms and the order of operations may be different. For example, in the second expression, the subtraction has been expressed as addition with a negative number, and in the fourth and sixth expressions, the subtraction has been expressed as multiplication with a fraction.
Gabriel models the volume of a popcorn box as a right rectangular prism and the box can hold 74 cubic inches of popcorn when it is full. Its width is 3\frac{1}{2}3
in and its height is 77 in. Find the length of the popcorn box in inches. Round your answer to the nearest tenth if necessary.
The popcorn box in a shape of a rectangular prism will thus have a length of 0.3 inches in inches.
What is a rectangular prism?A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism.
A rectangular prism also refers to a cuboid.
A cuboid and a rectangular prism have the same cross-section.
Quadrilaterals make up its faces.
So, a popcorn box's volume is modeled by Gabriel as a right rectangular prism, and a full box can store 74 cubic inches of popcorn.
Its height is 77 in, and its breadth is 3 1/2 in.
Then, the prism's width will be:
W = 3 + 1/2
W = 7/2
Consequently, the popcorn box's length in inches will be:
V = LWH
74 = L * 7/2 * 77
L = 0.2745 = 0.3
Therefore, the popcorn box in a shape of a rectangular prism will thus have a length of 0.3 inches in inches.
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18 plums cost $12. how many pluma can u buy for $2
Answer: 18 plums cost 12 dollar means
1 plum costs 18 divide by 12
That means 1 dollar and 50 cents for 1 plum
that is 1 plum for 2 dollar
Answer:
Step-by-step explanation:
the answer its 3
There are 750 registered voters in one precinct in a primary selection 64 out of 100 voters actually vote how many persons in the precinct voted
Out of the 750 registered voters in the precinct, 480 people actually voted in the primary selection.
What is an expression? What is a expression? What is a mathematical equation? A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.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, of the given problem.We have 750 registered voters in one precinct and in a primary selection 64 out of 100 voters actually voted.
Out of 100 people, only 64 voted. So, the percentage of people voted can be calculated as follows -
64 = x% of 100
64 = x/100 x 100
x = 64%
So -
64% 0f 750
(64/100) x 750
480
Therefore, 480 people out of 750 registered voters in one precinct actually voted.
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I need help fast! :)
Using the formula of slope of a line, the slope in the graph is -2/3
Slope of a LineThe slope of a line is defined as the change in y-coordinate with respect to the change in x-coordinate.
The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx.
Hence, the change in y-coordinate with respect to the change in x-coordinate is given by the formula
m = y₂ - y₁ / x₂ - x₁
Taking two coordinate from the line;
A = (0, 4)B = (6, 0)Substituting the values into the formula below
m = y₂ - y₁ / x₂ - x₁
m = 0 - 4 / 6 - 0
m = -4 / 6
m = -2/3
The slope is -2/3
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Which point is a solution to the system of inequalities graphed here?
y ≤ 2x + 2
y2-5x + 4
Both equations are satisfying by substituting (5, 0) in the system of inequalities.
What is a system of inequalities?
"A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system."
Given
System of inequalities graphed equation
y ≤ 2x + 2.................(1)
y ≥ -5x + 4................(2)
Substituting the point (5, 0) in equations 1 and 2
y ≤ 2x + 2
⇒ 0 ≤ 2(5) + 2
⇒ 0 ≤ 27
It is true
y ≥ -5x + 4
⇒ 0 ≥ -5(5) + 4
⇒ 0 ≥ -25 + 4
⇒ 0 ≥ -21
It is also true
In this option, Both equations are satisfying by substituting (5, 0)
Both equations are not satisfying by substituting (0, 5)
Hence, Both equations are satisfying by substituting (5, 0) in the system of inequalities given.
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A traveler is walking on a moving walkway airport. The traveler must walk back on the walkway to get a bag he forgot. The travelers ground speed is 2ft/s against the walkway and 8ft/s with the walkway. What is the travelers speed off the walkway? What is the speed of the moving walkway?
The travelers speed off the walkway is
The speed of the moving walkway is
If a traveler is walking on a moving walkway airport. The traveler's speed off the walkway is 5 ft/sec and the speed of the moving walkway is 3 ft/sec.
What is speed?Speed can simply be defined as how fast an object move.
Let t represent the traveler's speed in ft/sec
Let w represent the walkway's speed in ft/sec
So,
t-w =2
t+w=8
Add the equation
2t =10
Divide both side by 2t
t= 10/2
t=5fr/sec ( traveler's speed )
Speed of moving walkway
t+w =8
5+w=8
w=8-5
w=3ft/sec
Therefore the traveler's speed off the walkway is 5 ft/sec and the speed of the moving walkway is 3 ft/sec.
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Triangle bcd was dilated using the rule d subscript q, one-half. what are the values of the unknown measures? m∠c'b'd' = ° cq = b'd' =
The values of unknown measures are m∠C'B'D' = 95°, CQ = 6 and B'D' = 11
We are given that triangle BCD was dilated using the rule d subscript q, one-half.
Since the sum of the measure of all the angles in a triangle is 180°.
m∠C'B'D = 180° - m∠B'C'D' - m∠B'D'C'
m∠B'C'D = m∠BCD, m∠B'D'C' = m∠BDC (by dilation)
m∠C'B'D = 180° - 34° - 51° = 95°
[tex]\frac{B C}{B^{\prime} C^{\prime}}=\frac{B D}{B^{\prime} D^{\prime}}=\frac{36}{18}=2[/tex]
[tex]B^{\prime} D^{\prime}=\frac{1}{2} B D[/tex]
= 1/2(22)
=11
The dilated triangles are similar to each other.
Hence, we can say that ΔC'P'Q ∼ ΔCPQ,
[tex]\frac{C^{\prime} Q}{C Q}=\frac{C^{\prime} D^{\prime}}{C D}=\frac{D^{\prime} Q}{P Q}[/tex]
C Q= C'Q x [tex]\frac{C D}{C^{\prime} D^{\prime}}[/tex]
=C'Q x [tex]\frac{B C}{B^{\prime} C^{\prime}}[/tex]
=2 C'Q
=2(3)
=6
Thus, m∠C'B'D' = 95°, CQ = 6 and B'D' = 11.
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Answer: 95, 6, 11
Step-by-step explanation:
Where’s the center of dilation located?
Answer: Dilations centered at the origin
Step-by-step explanation:
You can dilate figures on the coordinate plane. The origin is often used as the center of dilation. If you are dilating a figure centered at the origin, you can multiply the coordinates of the points in the preimage by the scale factor to determine the points in the image.
What are the three rules for using the infinitive?
Answer: Rule 1: Gerunds can be used as a subject of a sentence. Rule 2: Both gerunds and infinitives can be used as objects of a sentence. Rule 3: Infinitives should be used after many adjectives.
Step-by-step explanation:
A line passes through the points (4,19) and (8,23) Write a linear function rule in terms of x and y for this line.
the linear function rule = y __
The equation of line passing through points [tex](x_{1} ,y_{1} )[/tex] = (4,19) and [tex](x_{2},y_{2})[/tex] =
( 8,23 ) is represented in the slope intercepted form as y = x + 15
What is the Slope Intercept Form ?When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilise the slope intercept formula,
y = mx + b. (0, b) The symbol b in the formula stands for the y value of the y intercept point.
According to the given information
We are given with two points
[tex](x_{1} ,y_{1} )[/tex] = (4,19)
[tex](x_{2},y_{2})[/tex] = ( 8,23 )
So
Now we need to find the slope of the given line having the above coordinate points
m = [tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
Putting the values
We get
m = [tex]\frac{23-19}{8-4}[/tex]
m = [tex]\frac{4}{4}[/tex]
m = 1
Equation of line passing through points [tex](x_{1} ,y_{1} )[/tex] = (4,19) and having
slope = 1
[tex]y-y_{1} = m(x-x_{1})[/tex]
y - 19 = x - 4
y = x + 15
So
The equation of line passing through points [tex](x_{1} ,y_{1} )[/tex] = (4,19) and [tex](x_{2},y_{2})[/tex] =
( 8,23 ) is represented in the slope intercepted form as y = x + 15
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Solve the equation.
5x + -3 = 5x + 20
Answer:
Step-by-step explanation:
x=23
I think
5x+-3=5x+20
add 3 on both sides canceling the -3 so then you get
5x=5x+23
subtract the 5x from both sides so then you get
x=23
Find the coordinates
(Simplify your answer.)
A (-6x, 4y)
D
B (-2x, -4y)
of midpoint D.
W
Midpoint Formula
X1+X2
Y1+y2
yı+y2)
2
M = (x¹+x²,
D = ([?],
C (8x, -2y)
Enter
The coordinates of midpoint D from the given triangle ABC is (-4x, 0).
What is the midpoint of a line segment?A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments.
The formula to find the midpoint of line segment is (x, y) = [(x1+x2)/2, (y1+y2)/2]
From the given figure, the coordinates are A(-6x, 4y) and B(-2x, -4y) and C(8x, -2y)
D(x, y)=[(-6x-2x)/2, (4y-4y)/2]
= (-4x, 0)
Therefore, the coordinates of midpoint D is (-4x, 0).
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12. If g(x) = -4²-3r + 2, determine g(−2).
C
Answer:
Step-by-step explanation:
simplify the expression √24 + 3.85
Answer: Simplify each radical, then combine.
Exact Form:
2√6+ 3.85
Decimal Form:
8.74897948
State the domain and range for the following relations.