x² - x - 6 = 0 is the standard form quadratic equation with solutions of -2 and 3.
A quadratic equation with two solutions is what?There are two roots—or solutions—to a quadratic equation with real or complex coefficients. These two possibilities may or may not be distinct, and they may or may not be true. The standard quadratic equation, Y=x2x6, can be solved using the set of solutions 2, 3, which are given.
The elements of a quadratic equation whose solutions are -2 and 3 are (x + 2) and (3, respectively) (x - 3).
The total value of the quadratic equation is 0.
We can add the two elements together to obtain the quadratic equation in standard form:
(x + 2) (x - 3) = x²-3x+2x-6
Simplifying this expression, we get:
x²- x - 6 = 0
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Can someone write this 0.698, 0.2, 0.099, 0.18 in order please?
Answer:
0.099, 0.18, 0.2, 0.698.
Step-by-step explanation:
determine whether or not the distribution is a probability distribution and select the reason(s) why or why not. x 2 4 6 p(x) 15 15 15 select all that apply: the given distribution is not a probability distribution, since the sum of probabilities is not equal to 1. the given distribution is a probability distribution, since the sum of probabilities is equal to 1. the given distribution is not a probability distribution, since at least one of the probabilities is greater than 1 or less than 0. the given distribution is a probability distribution, since the probabilities lie inclusively between 0 and 1.
The given distribution is not a probability distribution.
The given distribution is not a probability distribution, since the sum of probabilities is not equal to 1. A probability distribution must satisfy two conditions: 1) the probabilities must lie inclusively between 0 and 1, and 2) the sum of probabilities must be equal to 1.
In this case, the sum of probabilities is 15+15+15 = 45, which is not equal to 1. Therefore, the given distribution is not a probability distribution. The other options are incorrect because they do not accurately describe the given distribution.
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(3x) raised by 2x is equal to (9x raised by 2)raised by 2
we have shown that [tex](3x)^2x = (9x^2)^2,[/tex] which is the equation you provided. This is true for any value of x, so the equation is valid. The statement you have provided is a mathematical equation that involves exponentiation. To understand this equation, we need to know the rules of exponents.
The rule for exponentiation with the same base states that when we have a base raised to multiple exponents, we can simply multiply the exponents. In other words, [tex](a^b)^c = a^(b*c).[/tex] Using this rule, we can simplify the right-hand side of the equation to [tex](9x^2)^2 = 81x^4.[/tex]
Now, let's look at the left-hand side of the equation:[tex](3x)^2x[/tex]. To simplify this expression, we can use the distributive property of exponents. That is, [tex](a^b)^c = a^(b*c).[/tex] Using this rule, we can write[tex](3x)^2x as (3x^2)^x.[/tex]Then, using the rule for exponentiation with the same base, we can write this as [tex]3^(2x) * x^(2x).[/tex]
So now we have the equation [tex]3^(2x) * x^(2x) = 81x^4.[/tex]We can simplify this equation further by dividing both sides by[tex]x^(2x) to get 3^(2x) = 81x^(4-2x).[/tex] Simplifying the right-hand side, we get [tex]3^(2x) = 81x^(2(2-x)) = 81x^(4-2x).[/tex]
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The midpoint M of bar (RS) has coordinates (10.5,9). Point R has coordinates (1,10). Find the coordinates of point S.
Step-by-step explanation:
the midpoint between 2 points A (xa, ya) and B (xb, yb) is
M ((xa + xb)/2, (ya + yb)/2)
(xa + xb)/2 = 10.5
(ya + yb)/2 = 9
let's say R = A
(1 + xb)/2 = 10.5
(10 + yb)/2 = 9
1 + xb = 21
xb = 20
10 + yb = 18
yb = 8
S = (20, 8)
a function is said to be differentiable at if exists. for some -values the derivative may not exist and we say that the function is not differentiable there. at which of the following locations is a function not differentiable? discontinuity cusp horizontal tangent line vertical tangent line
The location at which a function is not differentiable is a Vertical tangent line
A function may not be differentiable at some points. Such points are known as non-differentiable points. Let's take a look at each of the given terms to figure out the non-differentiable points. Discontinuity: A discontinuity is when a function's graph is interrupted by a break or hole.
It occurs when a function is undefined at a certain point. It may be classified into three categories: removable, jump, and infinite. Functions may not be differentiable at removable discontinuities but are differentiable at jump and infinite discontinuities. A discontinuous point is not the same as a non-differentiable point because it may be differentiable at other points of the function.
Cusp: A cusp is a sharp corner formed by a curve. It happens when the slope of the function approaches infinity. The curve is not differentiable at the cusp. Horizontal Tangent Line: When the slope of a function approaches zero, it creates a horizontal tangent line. The function may or may not be differentiable at this point depending on the shape of the graph.
It may be differentiable or not differentiable. Therefore, it is not a non-differentiable point. Vertical Tangent Line: When a function's slope approaches infinity, it creates a vertical tangent line. The function is non-differentiable at this point. A vertical tangent line is always a non-differentiable point.
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If point A is the starting position, how high Is a rider after 3 seconds?
After 3 seconds, the rider is still at their starting height of 0 metres.
The height of a rider after 3 seconds can be calculated using the equation h(t) = v₀t - (1/2)gt², where h(t) is the height of the rider in metres at time t, v₀ is the initial velocity in metres per second, and g is the acceleration due to gravity in metres per second squared.
Assuming v₀ is 0, since the rider is just starting, and g is 9.81, then the height of the rider after 3 seconds is h(3) = 0 - (1/2)(9.81)(3²) = -44.355. Since this is a negative number, the rider is still at their starting height of 0 metres after 3 seconds.
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help me with this please im stuck
Answer:
refer to the attachment
15 The table shows values of s and t.
S
t
0.2
7.5
0.5
1.4
0.9
Is s inversely proportional to f? Explain why.
(2 marks)
Answer:
s is inversely proportional to t
Step-by-step explanation:
As s increases, t decreases. They are inversely proportioanl when that happens.
the physician orders digoxin 0.25 mg po daily. the pharmacy supplies the following medication. the dosage strength of the digoxin can be expressed as: ? m g 1 t a b l e t
To calculate the dosage strength of digoxin, which is supplied by the pharmacy in mg per tablet, the physician orders digoxin 0.25 mg po daily.
In other words, The physician ordered 0.25 mg of digoxin to be administered orally every day. The medication provided by the pharmacy is to be taken in tablet form. To calculate the amount of digoxin in each tablet, you need to divide the ordered dose by the amount of tablets.
The equation is:Dose Ordered / Tablets = Dose per tablet
Substitute the known values:Dose Ordered = 0.25 mgTablets = 1 tablet0.25 mg / 1 tablet = 0.25 mg per tablet.
Therefore, the dosage strength of the digoxin supplied by the pharmacy is 0.25 mg per tablet.
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pls help meee 100 points
Explain why this comparison is either reasonable
3.4< 3.36
WHAT DO I PUT IN
100 points if you help mee
Answer: The comparison "3.4 < 3.36" is reasonable because 3.36 is greater than 3.4.
The decimal point separates the whole number part of a number from the fractional part. In this case, 3.36 has a greater whole number part (3) than 3.4, and both have the same decimal part (0.36). So, 3.36 is greater than 3.4.
Therefore, the statement "3.4 < 3.36" is a true and reasonable comparison.
Step-by-step explanation:
Select the equation that is true.
A.
2
2
3
×
4
=
8
2
3
B.
2
2
3
×
5
8
=
1
2
3
C.
2
2
3
×
2
3
=
2
4
9
D.
2
2
3
×
4
3
5
=
8
6
15
Answer:
D is the only possible answer
A persons lung capacity can be modeled by the function C(t) = 250sin(2x/5 * t) + 2450 where C(t) represents the volume in mL present in the lungs after t seconds. State the maximum value of this function over one full cycle and explain what this value represents
The maximum value of a full cycle can be 2700 mL, this gives the maximum volume of air inhaled by a person during one breath. The function C(t) = 250sin(2I/5(t))+2450.
It shows the capacity of the lung of a person at any point of time t in milliliters (mL).
We not only need to find the one full cycle but also determine the period of function and it is given by:
T = 2I/(2I/5)
T = 5 seconds.
This means that the function completes one full cycle every 5 seconds.
To find the maximum value of the function over one full cycle, we need to find the maximum value of sin(2π/5(t)). The maximum value of sin(2π/5t) is 1, this happens at 2π/5(t) = π/2 + nπ, and n is considered as an integer.
So, the maximum value of the function occurs when sin(2I/5(t)) = 1, Substituting this into the original function, we get maximum value, Cm:
Cm = 250(1) + 2450
= 2700 mL.
The maximum value of a full cycle can be 2700 mL, this gives the maximum volume of air inhaled by a person during one breath.
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A circle has a radius of 5.4 cm. What is the exact length of an arc formed by a central angle measuring 45°?
The length of the arc with a central angle of 45° is 4.24 cm
What is an equation?An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.
The length of an arc formed on a circle with a central angle Ф and radius r is:
Length of arc = (Ф/360) * 2πr
Given the circle radius is 5.4 cm and the central angle is 45°, hence:
Length of arc = (Ф/360) * 2πr = (45/360) * 2π(5.4) = 4.24 cm
The length of the arc is 4.24 cm
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Which point lies on the circle represented by the equation (x − 3)2 + (y + 4)2 = 62?
Therefore, any of these two points lies on the circle represented by the equation. [tex](x - 3)^2 + (y+4)^2=6^2.[/tex]
What is circle?A circle is a geometric shape that consists of all the points that are a fixed distance, called the radius, from a given point, called the center. The distance from the center to any point on the circle is always the same. A circle can also be defined as the set of points in a plane that are equidistant from a given point, which is the center of the circle. Circles are often studied in geometry and have a number of important properties, such as their circumference, area, and diameter. They are also widely used in mathematics, physics, and engineering, and have many practical applications in fields such as architecture, art, and design.
by the question.
The equation of the circle in standard form is:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
where (h, k) is the center of the circle and r is the radius.
Comparing this with the given equation:
[tex](x - 3)^2 + (y + 4)^2 = 6^2[/tex]
we can see that the center of the circle is at point (3, -4) and the radius is 6.
To find a point on the circle, we can substitute any value for x or y and solve for the other variable. For example, let's choose x = 0:
[tex](0 - 3)^2 + (y + 4)^2 = 6^2[/tex]
[tex]9 + (y + 4)^2 = 36[/tex]
[tex](y + 4)^2 = 27[/tex]
[tex]y + 4=±\sqrt{27}[/tex]
[tex]y = -4±\sqrt{27}[/tex]
So, the two points on the circle are:
(0, -4 + √27) and (0, -4 - √27)
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14x +5y = 31 slve for x
Answer: x = 31 over 14 − 5y over 14
Step-by-step explanation: Move all terms that don't contain x to the right side and solve.
how many solutions the linear system have
Answer:
It all depends on the linear system
Step-by-step explanation:
A system of linear equations usually has a single solution but sometimes it can have no solution (parrel lines) or infinite solutions (same line).
I hope this helped
The answer is Three.
One solution.
Infinitely many solutions.
No Solutions at all.
1. Suppose that there is a forest with 10,000 rabbits. We randomly select 100 of them, place a nonremovable mark on them, and set them free in the forest. After a couple of days, the marked rabbits mixed well with other living ones in the forest, and we randomly catch 50 rabbits from the forest. Find the probability that the sample of 50 rabbits contains exactly 2 marked rabbits.
The probability that the sample of 50 rabbits contains exactly 2 marked rabbits is 1/2.
Explain about the hypergeometric distribution?When sampling from either a small population without replacement, the hypergeometric distribution consists of a discrete probability distribution which determines the likelihood that an event occurs k times in n trials.
The absence of replacements in the hypergeometric distribution sets it apart from the binomial distribution.As a result, it is frequently used in random sampling to ensure statistical quality. A straightforward, indication would be choosing team members at random from a population of males and girls.The given data:
Total market sample of rabbits = 100.
Randomly selected rabbits = 50.
Let the probability that the sample of 50 rabbits contains exactly 2 marked rabbits be P(E).
Then, using hypergeometric distribution;
P(E) = ⁵⁰C₂ / ¹⁰⁰C₂
Solve the probability using the combination.
P(E) = 25*49 / 50*49
P(E) = 25/50
P(E) = 1/2
Thus, the probability that the sample of 50 rabbits contains exactly 2 marked rabbits is 1/2.
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Of the 90 families in our barangay,60 are engaged in farming and the rest are in fishing. What percent of the families are engaged in farming?
Answer:
66.67%
Step-by-step explanation:
There are two ways to solve this problem depending on which way you like. Percentages are based on a 0-100 system and thus you can start by dividing 100/90. This will give you an amount of 1 family. We are looking for 60 families, so multiply that value by 60 to get how much of a percentage 60 families is.
The other way is to divide 90 by 60, and then multiply that result by 100 to give you a percent.
Regardless of your preferred method, both answers are the same.
What would a suitable class width be if your highest observed value (i.e., H) is equal to 400, your lowest observed value (i.e., L) is equal to 50, and your number of observations (i.e., n) is equal to 100?
100
The suitable class width would be 3.5 if your highest observed value is equal to 400, your lowest observed value is equal to 50, and your number of observations is equal to 100.What is a class width?The class width is the width of each interval in a frequency distribution. It is found by subtracting the smallest value from the largest value and then dividing by the number of classes.Class width = (highest value - lowest value) / number of classesWhere,H = highest observed value = 400L = lowest observed value = 50n = number of observations = 100Using the formula:Class width = (H - L) / nClass width = (400 - 50) / 100Class width = 350 / 100Class width = 3.5Thus, the suitable class width would be 3.5 if your highest observed value is equal to 400, your lowest observed value is equal to 50, and your number of observations is equal to.
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Dos ingenieros deciden medir la altura de una montaña cercana a un pueblo que está a 1200 msnm. Miden la cima de la montaña desde el punto "A" señalado en el gráfico con un ángulo de elevación de 37°, luego avanzan hacia al punto "B" que dista 480 m del punto "A" y vuelven a medir la cima con un ángulo de elevación de 45°. ¿Cuál es la altura de la montaña respecto al nivel del mar?
The height of the mountain above sea level is 777.94 m.
The two engineers can calculate the height of the mountain by using the principle of trigonometry. Firstly, they must calculate the altitude of the mountain from the point A, which can be done by using the formula h = tan (angle of elevation) * d, where h is the altitude, angle of elevation is the angle of elevation measured from point A and d is the distance between point A and the mountain. In this case, the altitude from point A is h = tan(37°) * 1200 = 1645.58 m. Secondly, they can calculate the altitude from point B, which can be done by using the same formula h = tan (angle of elevation) * d, where h is the altitude, angle of elevation is the angle of elevation measured from point B and d is the distance between point B and the mountain. In this case, the altitude from point B is h = tan(45°) * 480 = 867.64 m. Finally, the height of the mountain above sea level can be calculated by subtracting the altitude from point B from the altitude from point A, i.e. h = 1645.58 m - 867.64 m = 777.94 m.
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A straight trail leads from the Alpine Hotel,
elevation 8000 feet, to a scenic overlook,
elevation 11,100 feet. The length of the trail is
14,100 feet. What is the inclination (grade) of
the trail?
The inclination or grade of the trail from the Alpine Hotel to the scenic overlook is 21.9%.
The inclination or grade of a trail is the ratio of the change in elevation to the length of the trail, expressed as a percentage. To find the inclination of the trail from the Alpine Hotel to the scenic overlook, we need to first calculate the change in elevation.
Change in elevation = 11,100 feet - 8,000 feet = 3,100 feet
Now we can calculate the inclination or grade of the trail as follows:
Grade = (change in elevation / length of trail) x 100%
Grade = (3,100 / 14,100) x 100%
Grade = 0.219 x 100%
Grade = 21.9%
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Mabel has $30,000 in a savings account that earns 11% annually. The interest is not compounded. How much interest will she earn in 2 years?
please help :(
Step-by-step explanation:
If the interest is not compounded, it means that Mabel will earn a simple interest of 11% per year on her principal amount of $30,000.
The formula for calculating simple interest is:
Interest = (Principal x Rate x Time)
Where:
Principal = $30,000
Rate = 11% = 0.11 (as a decimal)
Time = 2 years
So, substituting the values in the formula, we get:
Interest = (30,000 x 0.11 x 2) = $6,600
Therefore, Mabel will earn $6,600 in interest over a period of 2 years.
5, 6, 8, ___ , 15, ___
18, 20, 24, ___ , 38, ___
25, 28, 34, ___ , ___ , 70
55, 54, 51, 46, ___ , ___ , 19
82, 81, 78, ___ , 66
0 + 6 = ___+ 0
___ + 9 = 9 + 14
20 x ( 4 + ___) = ( 20 x 4 ) + (20 x 3)
9 + ( 6 + 5 ) = (9 + 6) + ___
10 x (___ + 6) = (10 x 8) + (10 x ___)
Answer:
5, 6, 8, 11, 15, 20
5+1=6+2=8+3=11+4=15+5=20
18, 20, 24, 30, 38, 48
18+2=20+4=24+6=30+8=38+10=48
55, 54, 51, 46, 39, 30, 19
55-1=54-3=51-5=46-7=39-9=30-11=19
82, 81, 78, 73, 66
82-1=81-3=78-5=73-7=66
0+6=6+0
6=6
14+9=9+14
23=23
20x(4+3)=(20x4)+(20x3)
20x7=80+60
140=140
9+(6+5)=(9+6)+5
9+11=15+5
20=20
10x(4+6)=(10x8)+(10x2)
100=100
Step-by-step explanation:
Solve for X.
3x + 3 - x + (-7) > 6
A. x > (-5)
B. x > 5
C. x > 2.5
D. x < 5
Answer:
B
Step-by-step explanation:
3x + 3 - x + (-7) > 6
2x + 3 - 7 > 6
2x - 4 > 6
2x > 10
x > 5
Answer:
B. x > 5
Step-by-step explanation:
3x + 3 - x + (-7) > 6
3x - x + 3 - 7 > 6
2x + (-4) > 6
2x - 4 > 6
2x > 6 + 4
2x > 10
x > 10 / 2
x > 5
:D
Yolanda makes 6 goals and 2 penalties ending the game with 16 points and neel earns 4 goals and 2 penalties and ends the game with 6 points use x and y to represent the number
the number of goals Yolanda scores without penalties is x = 8, and the number of goals Neel scores without penalties is y = 0.
Let x be the number of goals Yolanda scores without penalties, and let y be the number of goals Neel scores without penalties.
According to the problem, Yolanda makes 6 goals and 2 penalties, so her total number of goals is:
x + 6
And her total number of points is:
(x + 6) + 2(1) = x + 8
Similarly, Neel scores 4 goals and 2 penalties, so his total number of goals is:
y + 4
And his total number of points is:
(y + 4) + 2(1) = y + 6
We know that Yolanda ends the game with 16 points, so we can write:
x + 8 = 16
Subtracting 8 from both sides, we get:
x = 8
We also know that Neel ends the game with 6 points, so we can write:
Y + 6 = 6
Subtracting 6 from both sides, we get:
y = 0
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What is the value of sinD?
The value of sin(D) is 7/25 after the application of the Pythagoras theorem.
What is a Pythagoras theorem?The Pythagorean theorem is a fundamental theorem in geometry that describes the relationship between the sides of a right triangle. It claims that the hypotenuse's square length, which is the side that faces the right angle, is equivalent to the total of the squares of the lengths of the other two sides in a right triangle. The theorem can be formulated mathematically as:
c² = a² + b²
where, even the lengths for the remaining two sides (the legs) of the right triangle are a and b, and c is the length of the hypotenuse.
The Pythagorean theorem may be employed to determine the triangle's third side's length:
DE²= FD² + EF²
25² = 24² + EF²
625 = 576 + EF²
EF² = 49
EF = 7
Now, we can use the definition of sine to find sin(D):
sin(D) = opposite/hypotenuse = EF/DE = 7/25
Therefore, the value of sin(D) is 7/25.
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Where have i gone wrong?
I need an answer!
Answer:
a)6
b)15 and -15
Step-by-step explanation:
a)5*5*5*5*5*5 there is 6 5's so, we can show it as, [tex]5^{6}[/tex]
[tex]5^{6}[/tex]=[tex]5^{x}[/tex]
x=6
b) in this one you found one of the answers of y which is 15.
but [tex]15^{2}=-15^{2}\\so y=15\\and y=-15[/tex]
Answer:
The answer is down below
Step-by-step explanation:
a) 5×5×5×5×5×5=5^x
5×5×5×5×5×5=5⁶
b)y²=225
square both sides
√y²=√225
y=15
PLEASE SHOW WORK!!!!!!!!!
Help plsss
Determine if it’s linear
The functions are classified as follows:
a) Linear.
b) Linear.
c) Linear.
d) Non-linear.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses tbe y-axis.Hence, from the definition, a function is classified as linear if the highest exponent of both x and y is of one.
A term x on the denominator has an exponent of -1, hence item d is not a linear function.
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The linear equations in the options are:
a) 5x - 9 + 7y = x - 4
b) 0.01x - 0.7y = 2.2
c) -3x = 4
How to deterimine if it is linear?We say that an equation is linear if the dependence with the veriables is only of first degree.
For example, equations of the form:
a*x + b*y = c
Are linear, because the variables x and y have an exponent of 1.
Then, the options that show linear equations are:
a) 5x - 9 + 7y = x - 4
b) 0.01x - 0.7y = 2.2
c) -3x = 4
The last option is non linear, because x is on the denominator.
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Wyatt made a scale drawing of a picnic area near the river. The picnic area, which is 84 yards long in real life, is 231 inches long in the drawing. What scale did Wyatt use?
The scale that Wyatt used is 1 inch represents 0.36 yards
What is the scale?The scale is used to keep the proportion of the dimensions between the scale drawing and the original diagram similar. The scale provides information on the proportional relationship between the scale of the drawing and the original image.
Scale of the drawing = original length / length of the drawing
84 / 231 = 0.36 yards
This means that 1 inch is represented by 0.36 yards
Alternatively, it can be written as 1 : 0.36 yards
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