A quadratic function has no real roots and does not intersect the x-axis if the discriminant of the function is less than zero.
How do you tell if a quadratic equation doesn't have any true roots?How many roots f(x) has is shown by the discriminant's value: - The quadratic function has two unique real roots if b2 - 4ac > 0 A repeated real root exists in the quadratic function if b2 - 4ac = 0. The quadratic function doesn't have any real roots if b2 - 4ac is less than 0.
Formula for the quadratic 4x2-8x9=0
4x2−8x−9=0
The answers can be found using the quadratic formula.
−b±√b2−4(ac)/2a
Replace the values
a=4
, b=−8
, and
c=−9
Then enter it into the quadratic formula to find
x.8±√(−8)2−4⋅(4⋅−9)/2⋅4
Simplify.
To continue, tap...
x=2±√13/2
There are various ways to display the outcome.
precise form:
x=2±√13/2
Number Form:
x=2.80277563…,−0.80277563…
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Full Question = What is the nature the roots of quadratic equation 4x²-8x+9=0?
the base of a triangular pyramid is a right-angled triangle with a hypotenuse of 6 cm and an acute angle of 30°. all side faces form 60° with the base. calculate the exact volume of the pyramid
Answer:
To calculate the volume of a triangular pyramid, we can use the formula:
V = (1/3) * B * h
where V is the volume, B is the area of the base, and h is the height of the pyramid.
Since the base of the pyramid is a right-angled triangle, we can use the Pythagorean theorem to find the length of the other two sides, which are the legs of the triangle. The hypotenuse is 6 cm and the angle opposite to the hypotenuse is 30°, so we can use the sine function to find the length of the other leg:
sin(30) = opposite / hypotenuse
opposite = (sin(30) * hypotenuse) = (1/2 * 6) = 3
Now we can use the area formula for a right-angled triangle:
B = (1/2) * base * height = (1/2) * 3 * 6 = 9
To find the height of the pyramid, we can use the fact that all side faces form an angle of 60° with the base. We can use the sine function to find the height of the pyramid:
sin(60) = opposite / hypotenuse
opposite = (sin(60) * hypotenuse) = (√3/2 * 6) = 3√3 cm
Now we can substitute the values of B and h into the volume formula:
V = (1/3) * B * h = (1/3) * 9 * 3√3 = 3√3 cm³
So the exact volume of the triangular pyramid is 3√3 cm³.
Step-by-step explanation:
Name (show your step) -15 24 21,2) 1. Simon has twin younger brothers. The sum of the ages of the three brothers is 48 and the difference between his age and the age of one of his younger brothers is 3. How old is Simon? B+b=48
Answer:
Simon's age is 18.
Step-by-step explanation:
Let Simons age be s and the age of each twin be t.
s + 2t = 48
s - t = 3
Subtract the second equation from the first:
s - s + 2t - (-t) = 45
2t + t = 45
3t = 45
t = 45/3 = 15.
Now we find Simon's age by plugging t = 15 in the second equation:
s - t = 3
s - 15 = 3
s = 3 + 15 = 18.
11. Graph the system of equations, then estimate
the solution.
Y= 1.5 41
ya-1.51 + 55
Answer:
The equation y=-1.5x+5.5 forms a straight line with a slope of -1.5 and a y-intercept of 5.5. Graphically, the solution can be estimated to be around (3.3, -1.05).
I need help.
Can someone answer this question for me?
there are 3 parts to this question.
By drawing every diagonal from one vertex in a convex, n-sided polygon, the polygon can be decomposed into n - 2 triangles.
How to obtain the sum of the internal angle measures?The sum of a the internal angle measures of a polygon of n sides is given by the equation presented as follows:
S(n) = 180(n - 2).
Hence the sum of the internal angle measures of a triangle, composed of three sides, is given as follows:
180.
Thus the number of triangles on a polygon of n sides is given as follows:
180(n - 2)/180 = n - 2.
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Does the commutative property apply to all real numbers?.
The commutative property applies only to addition and multiplication of real numbers.
What is commutative property in math?
This law simply states that with addition and multiplication of numbers, you can change the order of the numbers in the problem and it will not affect the answer. Subtraction and division are NOT commutative.
so as ask in question that, does the commutative property apply to all real numbers?
The commutative property applies to addition and multiplication of real numbers, meaning that a + b = b + a and a * b = b * a for any real numbers a and b.
However, it does not apply to subtraction or division, meaning that a - b ≠ b - a and a / b ≠ b / a for all real numbers a and b.
Therefore, the commutative property applies only to addition and multiplication of real numbers.
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Dakota earned $10.50 in interest in Account A and $35.00 in interest in Account B after 21 months. If the simple interest rate is 3% for Account A and 5% for Account B, which account has the greater principal? Explain. Which account has the greater principal? Select the correct answer below and fill in the answer boxes to complete your choice.
Account B has more money than account A. Then account that has the greater principal will be account B.
What is simple interest?Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.
The formula for interest is written as,
I = (PRT)/100
Where P is the principal, R is the rate of interest, and T is the time.
Dakota procured $10.50 in revenue in Record An and $35.00 in revenue in Record B following 21 months. In the event that the straightforward financing cost is 3% for Record An and 5% for Record B.
Then the account has the greater principal will be given as,
10.50 = [P₁ x 3 x (21/12)] / 100
1050 = 5.25P₁
P₁ = $200
35 = [P₂ x 5 x (21/12)] / 100
3500 = 8.75P₂
P₂ = $400
Account B has more money than account A. Then account that has the greater principal will be account B.
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The half-life of a particular
radioactive substance is 6 seconds.
If you started with 50 grams of this
substance, how much of it would
remain after 30 seconds?
First, complete the equation:
Remaining Amount = [?](1 -[])
The substance having half-life of 6 seconds and quantity of 50 gm initially will remain 1.5625gm after 30seconds.
What is half-life of a substance?
When we talk about half life, we are talking about the time taken for exactly half of the mass of the radioactive mass in question to have disintegrated.
More like, the amount of time it takes for the radioactive mass to have lost exactly half of its mass.
Now,
Since it is just 5 half lives, we can proceed manually
In the first, we shall have 25g left
in the second, we shall have 12.5g left
In the third, we shall have 6.25g left
In fourth, we shall have have 3.125g left
and finally, in the fifth, we shall have 1.5625g.
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What is the property of a circumcircle?.
The property of circumcircle is that the circumcircle always passes through all three vertices of a triangle.
A circumcircle is a circle that traverses a triangle's three vertices. It is also known as a "circumscribed circle." Every triangle's three vertices fall within the circumcircle.
The object's Center is defined as the point at where all of the triangle's perpendicular bisectors intersect. The circumcenter is the name of this Centre. The triangle's triangle might have its Centre within or outside the circle. The radius of the circumcircle is also known as the triangle's circumradius. In a right triangle, the Centre is located precisely at the midpoint of the hypotenuse, and the hypotenuse is a diameter of the circumcircle.
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What is the best graph for two variables?.
The scatter plot is the type of graph that is most frequently used to show the relationship between two numerical variables.
The graphs that show the association between two variables in a data set are called scatter plots. It shows data points on a two-dimensional plane or a Cartesian system.
The independent variable or attribute is represented by the X-axis, and the dependent variable is plotted using the Y-axis. To describe these charts, diagrams or graphs are usually employed. An XY graph, scatter chart, or scattergram are other names for a scatter plot. The scatter diagram plots numerical data pairings with one variable on each axis to show the relationship between them.
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Which graph represents the linear equation y = −5x − 2? a graph of a line that passes through the points negative 1 comma 3 and 0 comma negative 2 a graph of a line that passes through the points negative 2 comma negative 2 and 0 comma negative 3 a graph of a line that passes through the points negative 4 comma negative 1 and 0 comma negative 2 a graph of a line that passes through the points negative 3 comma 1 and 0 comma negative 5
Answer:
I am positive it is B guys!
Step-by-step explanation:
took da quiz
How to find the end behavior of a graph?
Graph behavior as x approaches is referred to be the end behavior of a polynomial function.
How do you identify the desired outcome? Graph behavior as x approaches is referred to be the end behavior of a polynomial function.The leading term of the function—that is, the term with the highest n-value for axn an x n, where n is a positive integer and an is any nonzero number—allows us to predict the final behavior.Look at the leading term of the polynomial function to understand its end behavior.Graph behavior as x approaches is referred to be the end behavior of a polynomial function.Given that the leading term has the largest power, its behavior will dominate the graph since it will increase much more quickly than the other terms as x gets extremely large or very tiny.To learn more about polynomial function refer
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A teacher has $140 to spend on 12 pizzas for a class party. If the teacher has a $20 coupon, which inequality could she use to find p, the amount she can spend on each pizza?
The inequality of p is p < 10
How to determine the inequality of pFrom the question, we have the following parameters that can be used in our computation:
Total amount = $140
Coupon = $20
Number of people = 12
The inequality of p is then represented as
p < (Total amount - Coupon)/Number of people
Substitute the known values in the above equation, so, we have the following representation
p < (140 -20)/12
Evaluate
p < 10
Hence, the inequality is p < 10
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Y = 1/4(4)^x ; x = 3/2
Evaluating the exponential equation:
y = (1/3)*4^x
on x = 3/2 gives y = 8/3.
How to evauate the exponential equation?Here we have the following exponential equation:
y = (1/3)*4^x
And we want to evaluate it on x = 3/2, to do so, we just need to replace the variable on the equation by the given number.
We will get:
y = (1/3)*4^(3/2)
The power part can be rewrite as:
y = (1/3)*√4^3
y = (1/3)*2^3
y = (1/3)*8 = 8/3
That is the value of the equation when evaluated on x = 3/2.
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What is the y coordinate of the solution of the following system 3x 2y 7y − 3x 11?.
So, the y-coordinate of the solution of the system of equations 3x + 2y = 7 and y - 3x = 11 is 6.
To find the y-coordinate of the solution of a system of equations, we can use one of the methods for solving systems of equations, such as substitution, elimination, or graphing. In this case, we will use substitution method.
The system of equations is:
3x + 2y = 7
y - 3x = 11
We can solve for y in the second equation and get:
y = 3x + 11
Now we can substitute this expression of y into the first equation:
3x + 2(3x + 11) = 7
3x + 6x + 22 = 7
9x + 22 = 7
9x = -15
x = -5/3
Now we can substitute this value of x into the second equation:
y = 3(-5/3) + 11
y = -5 + 11
y = 6
So, the y-coordinate of the solution of the system of equations 3x + 2y = 7 and y - 3x = 11 is 6.
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What is the mirror image of 4 20?.
The mirror image of the coordinates is (4, - 20)
The term coordinates is defined are ordered pairs of points that help us locate any point in a 2D plane or 3D space.
Here we have given the coordinates (4, 20).
And we need to find the mirror image of given coordinates.
As per the definition of coordinates the rule of Mirror image of (x , y ) in the x - axis is written ( x , -y).
Here we have the value of x as 4 and the value of y as 20.
When we apply the rule on the given coordinates then we get the resulting points,
=> (4, 20) = (4, - 20)
Complete Question:
What is the mirror image of the coordinate (4,20)?
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Find the slope of a line perpendicular to the line whose equation is 6x-9y=2166x−9y=216. Fully simplify your answer.
Answer: -3/2
Step-by-step explanation:
To find the slope of the line perpendicular to the given one, we first need to change the equation to y=mx+b to find the original slope.
[tex]6x-9y=216[/tex] [subtract both sides by -6x]
[tex]-9y=-6x+216[/tex] [divide both sides by -9]
[tex]y=\frac{2}{3} x-24[/tex]
Now we know slope is 2/3. The slope of the perpendicular line is the opposite sign and reciprocal of the slope.
Opposite would make it -2/3.
Reciprocal would be -3/2.
So the slope is -3/2.
What is ten more than 99?.
The answer of 10 more than 99 is 109.
The answer of 10 more than 99 is 109 which can be derived using simple mathematical calculations.
To find 10 more than 99, you can add 1 to the original number 99.
10 + 99 = 109
It's a simple arithmetic operation where you add a specific number, in this case, 10, to the original number.
An arithmetic operation is a mathematical process that combines two or more numbers to produce a new number. The most basic arithmetic operations are addition, subtraction, multiplication, and division.
Addition: It is the process of combining two or more numbers to find their sum. For example, 2 + 3 = 5 is an addition operation.
Subtraction: It is the process of finding the difference between two numbers. For example, 5 - 3 = 2 is a subtraction operation.
Multiplication: It is the process of finding the product of two or more numbers. For example, 3 x 4 = 12 is a multiplication operation.
Division: It is the process of finding the quotient of two numbers. For example, 12 ÷ 3 = 4 is a division operation.
Therefore, The answer of 10 more than 99 is 109.
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Write the equation of the absolute value function y = –|x| translated left 4 units.
Answer:
8kg:800g:4000g
1kg=1000g
8kg=8000g
8000:800:4000
80:8:40
10:1:5
Please help asap me will give brainliest
Correct options are B, E. The point (0, -5) lies on the graph. The function is undefined for x = 1.
Mathematical functions
The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x.
In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The range is made up of all values that the function's output can take.
Given,
the function is y = 2x + 5 / x - 1
⇒ The value of x ≠ -1, as function can become undefined.
⇒ Horizontal Asymptote is 2
the value of y for x = 0,
y = 2x + 5 / x - 1
y = 2(0) + 5 / 0 - 1
y = -5
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Fernando loves to make music playlists. He likes to keep the same ratio of country songs to rock songs. On his summer playlist, he has 100 country songs and 24 rock songs. On his road trip playlist, Fernando has 25 country songs.
How many rock songs are on Fernando's road trip playlist?
Answer:0 on his road trip playlist
Step-by-step explanation:
What is the value of 3 by 5 2 by 7 is equal to?.
After addition, 3/5 + 2/7 can be expressed as a fraction as 31/35.
Math is not complete without fractions. The same fundamental procedures that may be applied to integers also apply to fractions. To solve the given problem, we need to add the given fractions using the common denominator property of fractions.
The Least Common Multiple (LCM) of 5 and 7 is 35. Hence, the common denominator is 35.
So, 3/5 + 2/7 = (3 × 7) / (5 × 7) + (2 × 5) / (7 × 5)
= 21/35 + 10/35
= 31/35.
Hence, 3/5 + 2/7 can be represented as 31/35 as a fraction after addition.
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Miss Massey is getting married soon. She would like to hire a professional who will come to her house and do hair and makeup for the bridal party on her wedding day. She has narrowed it down to two possible choices. A woman from Livingston Salon charges an initial fee of $30 and then an additional $18 per hour. Alternatively, a team from Beauty by Tom offers a free consultation and then charges a higher hourly rate of $28. If it takes a certain amount of time to finish everyone's hair and makeup, Miss Massey will end up paying the same amount either way. How long would that take? How much would Miss Massey end up paying?
Answer:
h
Step-by-step explanation:
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Seven less than double a number is the same as fourteen more than the number, what is that in an algebraic equation
Answer:
2x - 7 = x + 14
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The three (3) statements which are true include the following:
A. The radius of the circle is 3 units.
B. The center of the circle lies on the x-axis.
D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
What is the equation of a circle?In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r² ....equation 1.
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.From the information provided above, we have the following equation of a circle:
x² + y² – 2x – 8 = 0 ......equation 2.
In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:
x² – 2x + y² = 8 = 0
x² – 2x + (2/2)² + y² = 8 + (2/2)²
x² – 2x + 1 + y² = 8 + 1
(x – 1)² + (y - 0)² = 9 .......equation 3.
Comparing equation 1 and equation 3, we have the following:
Center (h, k) = (1, 0)
Radius (r) = 3
Additionally, this line and the center of the given circle lies on the x-axis (x-coordinate) because the y-value is equal to zero (0).
(x – 0)² + (y - 0)² = 3²
x² + y² = 9.
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Five le than a number i le than or equal to 6 time the number. What inequality can be written to repreent thi tatement?
The inequality statement will be x-5 ≤ 6.
Inequalities are mathematical expressions that contain variables and numerical terms that are separated by the inequality symbol.
An inequality can be derived from a statement of words, which must be correctly interpreted in order to yield the appropriate inequality.
When there are more than and fewer than values in the inequality, we know that the variable must be in the middle.
The inequality symbols are greater than, less than, greater than or equal, and less than, or equal.
There are two conditions given in the question as mentioned below:
1. Five less than a number
2. the number is less than or equal to 6
Let x be the number,
x-5 ≤ 6
So, the inequality statement will be x-5 ≤ 6
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HELP HELP
If the lengths of two sides of a triangle are 10 and 14, the length of the third side may be:
(a) 22
(b) 2
(c) 24
(d) 4
Answer:
(A) 22
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
the answer is 24 according to therom 3
S=9 Please help quick8th grade geometry
Considering triangle HRC, the equations that can be used to solve for the value of w are
B. 9² + w² = (√125)²cos y = w / √125sin 36.4 = w / √125cos 53..6 = w / √125tan (90 - x) = 9 / wHow to solve for the value of wThe triangle HRC is a right triangle and can be solved by various methods such as: Pythagoras theorem given by the the formula
hypotenuse² = opposite² + adjacent²
plugging the values as in the problem
m² = s² + w²
(√125)² = 9² + w²
Applying SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
solving for w using cos, CAH
cos y = w / m
cos y = w / √125
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What is the solution of |( 2x 3 )|= 7 *?.
The value of x for the equation 2x-3=7 is x=5
Given the equation:
2x-3=7
Here, we have to determine the value of
For that, transposition method should be used.
Now, transpose 3 to the right hand side of the above equation.
2x=7+3
Now, add the terms on the right side of the above equation, we get
2x=10
Now, we have to divide both sides by 2 we get
[tex]\[\frac{{2x}}{2} = \frac{{10}}{2}\][/tex]
Simplify further, we get
x=5
Thus, the required solution is x=5
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Find the distance between the points p(8, 2) and q(3, 8). Round to the nearest tenth.
The distance between the given set of points is 7.8 units.
To find the distance between two points in a coordinate plane, we can use the distance formula.
The distance formula states that the distance between two points (x1, y1) and (x2, y2) is given by the square root of ((x2 - x1)^2 + (y2 - y1)^2).
In this case, we are given the points p(8, 2) and q(3, 8). Therefore, we can plug in the coordinates of these points into the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Distance = √((3 - 8)^2 + (8 - 2)^2)
Distance = √((-5)^2 + 6^2)
Distance = √(25 + 36)
Distance = √61
The square root of 61 is approximately 7.8 which rounded to the nearest tenth is 7.8.
Therefore, The distance between the given set of points is 7.8 units.
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Write in ordinary form 1.01×10-4
The normal written form of the number given as in the task content is; 0.000101.
What is the normal representation of the given number in the task content?It follows from the task content that the normal representation of the given number as in the task content is to be determined.
On this note, since the given number is; 1.01 × 10-⁴, it follows that the given normal representation of the number requires shifting the decimal point 4 spaces to the left so that we have;
= 0.000101.
Ultimately, the required normal representation of the number is; 0.000101.
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