The value of b can be -32 or +32 to ensure that the equation has only one true solution.
What is discriminant of the equation?The discriminant is the quadratic formula section behind the square root symbol: b2-4ac. The discriminant indicates whether there are two solutions, one solution, or none at all. The "discriminant" is the argument (that is, the contents) of the square root, which is the equation b2 4ac, because by utilizing its value, you may "discriminate" between (that is, determine the difference between) the various solution types.
Here,
The discriminant of the equation is ...
d = b² -4ac
d = b² -4(2)(128)
d = b² -1024
In order for there to be one real solution, we must have d=0. So ...
0 = b² -1024
1024 = b²
±√1024 = ±32 = b
The value of b can be -32 or +32 to cause the equation to have one real solution.
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What are 2 types of coordinate reference systems?
The two main types of coordinate systems used in mathematics and physics are Cartesian and Polar Coordinates.
What is coordinates system?A coordinate system is a system used to identify and locate a point in space. It is the basis for maps, navigation and surveying. Coordinate systems can be two-dimensional or three-dimensional, and can use a variety of units such as latitude, longitude, and feet. Coordinate systems are used in a variety of fields such as engineering, architecture, geology, and navigation. Coordinate systems help to identify and locate points in space and are essential for charting and mapping the physical world.
Cartesian Coordinates, named after the French mathematician and philosopher René Descartes, use a two-dimensional plane to represent points with an x-axis and a y-axis. These coordinates are expressed as ordered pairs (x,y) and represent points in relation to the origin (0,0). This can be used to plot graphs and equations, and is the most commonly used coordinate system.
Polar Coordinates are based on a two-dimensional plane centered on a pole. Points are expressed as ordered pairs (r,θ) where r is the distance from the pole and θ is the angle from the polar axis. This coordinate system is useful for finding distances and angles in a circle. It is used frequently in physics and astronomy.
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vi. The value of a machine depreciates 20% annually. If its present value is Rs. 20,000, its value
after 2 years will be
step-by-step
Answer:
12,800
Step-by-step explanation:
20% of 20000 is 4000
20000-4000=16000
20% of 16000 is 3200
16000-3200=12,800
1/216 as a power of 6
1/216 as a power of 6 is 6^-3. The solution has been obtained by using the concept of exponents.
What is an exponent?
A number's exponent demonstrates how many times we are multiplying a given number by itself. For instance, 2^4, indicates that we are multiplying 2 itself by four times. 2*2*2*2 is its expanded form. The power of a number is another name for an exponent. A whole number, fraction, negative number, or decimal are all acceptable.
We are given 1/216 which is to be written as a power of 6.
We know that 216 is the cube of 6.
This means that 216 can be written as 6^3.
Also, 1/n is written as n^-1
So, 1/216 can be written as 6^-3.
Hence, 1/216 as a power of 6 is 6^-3.
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A group of friend went to lunch. The bill before ale tax and tip wa $37. 50. A ale tax of 8% wa added. The group then tipped 18% on the amount after the ale tax wa added. What wa the amount, in dollar, of the ale tax?
What wa the total amount the group paid, including tax and tip?
As per the given tax percentage, the sales tax is $3 and the total amount paid by the group including the tip is $47.25
Here we have given that the bill before sale tax and tip is $37.50.
Here we have know that there was a tax of 8%.
And the there was a tip of 18%.
As we all know that the tip is after the tax, then it's not going to affect it, and we can essentially ignore it.
Therefore here the real question here is just what is 8% of $37.50.
Now, here we have to find the percent of something, then first you need to put the percent as a decimal.
Then we get the 8% in decimal form is 0.08 where as 18% as 0.18
Now, we have to multiply the percent in decimal form by the number.
Then we get,
=> 37.50 dollars × 0.08 = 3 dollars.
=> 37.50 dollars × 0.18 = 6.75 dollars.
And the total amount pair is calculated as,
=> 37.50 + 3 + 6.75
=> 47.25
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How do I write eight more than three times the sum of a number and one in simplified form 
Therefore , the solution to the given problem of equation comes out to be4x-3y = 6 as a standard equation in all the above options.
An equation's definitionAn equation is a representation of two identical variables in mathematics, one on either side of an equals sign. Common difficulties can be solved using equations. We frequently seek pre algebra help when faced with obstacles in real life. Lessons in pre-algebra cover the basics of mathematics.
Here,
Given : 4x-3y = 6
-4x + 2y =8
=> y = 4/5x + 4
=> 4/5x + 2y = 6
Thus ,
From the above following equations we get ,
4x-3y = 6
as a standard equation in all the above options.
Therefore , the solution to the given problem of equation comes out to be 4x-3y = 6 as a standard equation in all the above options.
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On solving the provided question, we can say that the equation that cab be formed the data is as 8 > 3x => x>2.6666666667
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
the equation that cab be formed the data is as
eight more than three times the sum of a number
let the number be x.
8 > 3x
x> 8/3
x>2.6666666667
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There are 2 boats for
every 5 cars. If altogether
there are 56 boats and
cars, how many cars are
there?
Answer:
Below
Step-by-step explanation:
5 out of ( 5 + 2) vehicles are cars 5 / 7 are cars
5/7 * 56 = 40 cars
Please help i need to pass the geometry
, Which recursive sequence would produce the sequence
2,-6, 34
Recursive sequence would produce the sequence 2,-6, 34 is a1 = 2 and an = 2an-1 - 4
How can the recursive sequence be found?To identify a recursive sequence in which terms are defined using one or more preceding terms that are presented.Step 1, Find the nth term (an) of an arithmetic progression and the common discrepancy, d.Step 2, Use the formula an+1 = a + d to plug in the values and find the (n+1)th term, which will then reveal the following terms.A recursive formula is written in two parts: the first term is stated, and the formula connecting the succeeding terms is also stated. 10 through 35 in the following numerical order. Come up with a recursive formula. An arithmetic sequence is shown in this example (the same number, 5, is added to each term to get to the next term).Recursive sequence would produce the sequence 2,-6, 34 is a1 = 2 and an = 2an-1 - 4.To learn more about Recursive sequence refer to:
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Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (x,y) be the unknown endpoint. Apply the midpoint formula, and solve the two equations for x and y.)
midpoint: (-21,8) endpoint: (-13,6)
the other endpoint is------------------------.
Using formula of midpoint of a line, the endpoint have coordinates of (-29, 10)
What is Midpoint of a LineThe midpoint of a line is a point that divides the line into two equal parts. The coordinates of the midpoint can be found by taking the average of the x-coordinates of the endpoints and the average of the y-coordinates of the endpoints.
The formula of midpoint of a line is given as
M(x, y) = (x₂ + x₁) / 2, (y₂ + y₁) / 2
-21, 8 = (x₂ + x₁) / 2, (y₂ + y₁) / 2
For x - coordinate;
-21 = (x₂ + x₁) / 2
-21 = -13 + x₁ / 2
-21 * 2 = -13 + x₁
-42 = -13 + x₁
x₁ = -42 + 13
x₁ = -29
For y - coordinate
8 = (y₂ + y₁) / 2
8 = (6 + y₁) / 2
16 = 6 + y₁
y₁ = 16 - 6
y₁ = 10
The endpoint is (-29, 10)
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This week, the price of apples at the farmers market increased 20%. If the price this week is $1.68, what was the price before the increase?
Answer: $1.4
Step-by-step explanation:
let the price before the increase be x
1.2*x = 1.68
x=1.68/1.2 = 1.4
Price before increase = $1.4
Which of the following is not a Pythagorean triplet 3 4 5 6 8 10 8 15 16 10 24 26?
Answer:
8, 15, 16
Step-by-step explanation:
8, 15, 16 is not a Pythagorean triple because it doesn't satisfy the Pythagorean Theorem:
[tex]a^2 + b^2 = c^2[/tex]
When we plug this set of numbers into the theorem:
[tex]8^2 + 15^2 \stackrel{?}{=} 16^2[/tex]
[tex]289 \neq 256[/tex]
we get an inequality, not an equality which would make this set of numbers a Pythagorean triple.
Note that all of the other given triples satisfy the Pythagorean Theorem.
a quadrilateral with one right angle must be rectangle ?
Answer:
[tex]\Huge \boxed{\boxed{\textbf{False}}}[/tex]
Step-by-step explanation:
A quadrilateral must have four right angles in order to be a rectangle, not simply one. A quadrilateral with a single right angle, however, can take on a wide range of shapes, like a right angled triangle or an irregular quadrilateral. A shape having multiple sides and one right angle, for example, could be an irregular quadrilateral.
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________________________________________________________
Select the correct answer. Which expression is equivalent to 8x^2^3 sqrt 375x + 2^3 sqrt 3x^7, if x=0?
Note that the expression that is equivalent to 8x² ∛375x + 2∛3x⁷, if x ≠ 0 is: 42x²∛3x (Option B). Even if x = 0, then none of the answers would apply because the expression would automatically = 0.
What is the rationale for the above answer?To prove the above lets us factor and rewrite the radicand in exponential form as follows:
8x² ∛(5³ * 3x) + 2∛(3x⁶ * x)
Rework the expression using
ⁿ√ab = ⁿ√a * ⁿ√b:8x² * ∛5³ * ∛3x + 2∛x⁶ * ∛3x
Simplify the expression 8x² * 5∛3x + 2x² ∛3x
Multiply the monomials to get:
40x² ∛3x+2x²∛3x; Taking the coefficients for the like terms we have:
(40 + 2)x² ∛3x
Calculate the sum to get 42x²∛3x
Thus the simplified version of 8x² ∛375x + 2∛3x⁷, if x ≠ 0 is: 42x²∛3x
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Full Question:
Select the correct answer. Which expression is equivalent to 8x² ∛375x + 2∛3x⁷, if x ≠ 0
A) 42x³
B) 42x²∛3x
C) 10x⁴∛125x
D) 10x²∛125x³
What is the oldest prime number?
The concept of the oldest prime numbers is an ancient one and has been known since ancient times. The ancient Greeks were the first to systematically study prime numbers
The largest and oldest data collection in mathematics is prime numbers. What is it about them that has intrigued mathematicians for millennia?
They were very much aware of the existence of prime numbers and the fundamental theorem of arithmetic, the statement that every positive integer greater than 1 can be represented uniquely as the product of primes. So, it is hard to determine the oldest prime number known, but it's been studied throughout human history.
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Which graph could be the graph of f(x)
The graph which could be the graph of the polynomial f( x) with roots-8,-5, 1, and 2 is Graph 4.
What is Polynomial function?
A polynomial function is a function that involves onlynon-negative integer powers or only positive integer expounders of a variable in an equation like the quadratic equation, boxy equation, etc. For illustration, 2x 5 is a polynomial that has exponent equal to 1.
Given that;
Root of polynomial = 4.
This means that the polynomial f( x) has 4 roots.
Now, when f( x) = 0, we're told that the 4 roots are;
x = -8
x = -5
x = 1
x = 2
Now, the roots of a polynomial on a graph are the points where the graph wind crosses the x- axis which are called the x-intercepts. Looking at all the given graphs, the only bone that crosses the x-axis at the points x = -8, x = -5, x = 1 and x = 2 is the last graph which is Graph 4. In conclusion, the graph of the polynomial f( x) with roots-8,-5, 1, and 2 is Graph 4.
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1
Write the place value of the underlined digit in each number. The place values are
spelled correctly for you here:
hundreds
tens
ones
tenths
hundredths
Therefore , the solution of probability problem In the absence of digit usage restrictions, 1000000 postcodes are possible, as are 900000 when the first integer cannot be 9.
Why do you use the word probability?The ratio of all possible outcomes to all outcomes in a large group of equally as likely alternatives that result in a specific event determines how likely it is for that event to occur. A branch of mathematics that studies probability a situation or occurrence that is likely to occur the characteristic or state of just being likely of range 0 to 1.
Here ,
1) If there aren't any digit restrictions, there are 1000000 zip codes, or 10*10*10*10*10.
2) 9*10*10*10*10=900000 is the maximum number of postal codes that could exist if the initial number is not 7.
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Help ASAP Please right now 1&2
1. The statement that is false is: If two figures have the same shape, then they are congruent.
2. The dashed line appears to be a line of symmetry.
Properties of congruent shapes.When two or more shapes have their length of sides and measure of internal angles to be equal, then it can be inferred that they are congruent. But shapes can be similar, but not congruent.
A line of symmetry is a straight line drawn in such a way that it divides a given shape into two equal parts. So that a shape may have more than one line of symmetry.
From the given questions, we can deduce that;
1. If two figures are similar, they may not be congruent. So that the statement that is false among the given option is A. If two figures have the same shape, then they are congruent.
2. Considering the dashed line drawn through the shape, it appears that it is a line of symmetry.
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because x is an unbiased estimator for μ
A unbiased estimator is a statistic that accurately reflects the population mean, μ. A statistic is unbiased when the mean of its sampling distribution is equal to μ.
Mathematically, this can be expressed as:
E(x) = μ
Where E(x) is the expected value of x and μ is the population mean.
This means that if we take a sample from a population and calculate the mean from that sample, the expected value of that mean should be equal to the population mean. This can be seen in the following example:
Let's say we have a population with a mean of 30. We take a sample of size 5 from this population and calculate the sample mean, x. The expected value of x should be equal to 30. We can calculate this using the formula:
E(x) = ∑xi/n
Where xi are the values in the sample and n is the sample size.
For our example, E(x) = (30 + 30 + 30 + 30 + 30) / 5 = 30
This shows that x is an unbiased estimator of μ.
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the equation?
Does the point (51, 2) satisfy the equation y = 3x + 45?
yes
no
The difference of x and one third is greater than or equal to one third of x
value of x is greater than or equal to half.
What is inequality?A mathematical expression shows the unequal comparison between two or more terms.
Inequalities can be greater than, less than, greater than or equal and less than or equal.
What is the expression of the above inequality?The difference of x and one third is greater than or equal to one third of x.
The statement can be written as x -1/3 ≥ x1/3
x -1/3 ≥ x/3
x - x/3 - 1/3 ≥ x/3- x/3 [ subtract x/3 from both parts]
2x/3 - 1/3 ≥ 0
now add 1/3 on both parts
we get, 2x/3 -1/3 + 1/3 ≥1/3
2x/3 ≥ 1/3
2x ≥ 1
x ≥1/2
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Find the slope of a line perpendicular to the line whose equation is x - 2y = 14.
Fully simplify your answer.
The slope of a line perpendicular to the line whose equation is x - 2y = 14 is -2
What is the equation of straight line ?
The equation of straight line is
y = mx + b
where m is slope of the straight line .
Given ,
The equation is x - 2y = 14 .
So, the equation in slope-intercept form would be 2y = x -14,
which then becomes y = 0.5x - 7
giving a slope of -0.5.
The slope of the perpendicular line is a negative reciprocal,
so 0.5 is the same as (1/2), so the positive reciprocal of that is -2,
meaning the slope of the perpendicular line will be -2.
Hence, The slope of a line perpendicular to the line whose equation is x - 2y = 14 is -2
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2. Match the picture of the triangle to the correct name for its center. 1. Orthocenter 2. Incenter 3. Circumcenter 4. Centroid
Centroid, Incenter, Circumcenter,Orthocenter are the name of its center
Explain centers are defined for a triangle?OrthocenterThe orthocenter is the intersection of the altitudes of the triangle. Each altitude intersects a vertex and is orthogonal to the opposite side. The orthocenter will not be inside the triangle if the triangle is obtuse. The orthocenter of a right triangle is the right-angle vertex.IncenterThe incenter is the center of an inscribed circle of a triangle. The incenter must be the same distance from each side, so will be at the point of intersection of the angle bisectors. It always lies inside the triangle.CentroidThe centroid is the "center of gravity" of the triangle, the point at which the triangle could be balanced. Each median divides the triangle into two equal areas, so the intersection of medians marks a spot with equal area (weight) in every pair of opposite directions.CircumcenterThe circumcenter is the center of a circle that circumscribes the triangle. It is equidistant from the three vertices, so lies on the intersection of the perpendicular bisectors of the sides. It will lie outside the triangle for obtuse triangles. It is the midpoint of the hypotenuse of a right triangle.
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What is the number of solutions for the system x 2y 0 and 3x 4y 20 0?
The number of solutions for the system of equations x - 2y = 0 and 3x + 4y = 20 is one.
For the given pair of equations x − 2y = 0 and 3x + 4y = 20;
a₁/a₂ = 1/3
b₁/b₂ = -2/4 = -1/2
c₁/c₂ = 0/-20 = 0
As the given pair of linear equation satisfies a₁/a₂ ≠ b₁/b₂,
The graph of these equations will be a pair of lines intersecting at a unique point, which is the solution of the given pair of equations.
Let's verify this by calculating the solution of the given system
x = 2y eqn(1)
3x + 4y = 20 eqn(2)
Now, put the value of x in eqn(2), we get
3 × 2y + 4y = 20
10y = 20
y = 2
Now, put the value of y in eqn(1), and we get
x = 2 × 2 = 4
Thus, the solution is x = 4, y = 2.
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How do you draw a perpendicular line in Class 7?
A perpendicular line is one that is perpendicular or 90 degrees to another line. In order to draw a perpendicular line in Class 7, it is important to understand the formula and calculation associated with it.
The formula associated with perpendicular lines is that the product of the slope of the two lines must be equal to -1. This means that if one line has a slope of m1, then the slope of the perpendicular line must be -1/m1.
In order to calculate the slope of a line, we must use the formula m = (y2-y1)/(x2-x1), where m is the slope, (x1,y1) is the first point, and (x2,y2) is the second point. With this information, we can use the formula to calculate the slope of the line we want to draw a perpendicular line to, and then use the formula m = -1/m1 to calculate the slope of the perpendicular line.
Finally, with the slope of the perpendicular line, we can use the point-slope form of the equation of a line, y-y1=m(x-x1), to plot the equation of the line and draw it on the graph. This formula can be used to draw a perpendicular line in Class 7.
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If f(x) = 3x² + 2 and g(x)=x2-9, find (f- g)(x).
OA. 2x² - 7
OB. 2x² +11
OC. 4x²-7
OD. 4x² +11.
Answer:
B. 2x² + 11
Step-by-step explanation:
(f - g)(x) means:
f(x) - g(x)
We've been given what each of these is equal to, so substitute that in:
3x² + 2 - (x² - 9)
Simplify. Don't forget to distribute that minus in the middle to both terms in x² - 9
3x² + 2 - x² + 9
Next, combine like terms.
2x² + 11
An inflatable ball can be modeled as a hollow sphere. Miguel
measures the outer diameter of the ball to be 50 cm. If the
material that makes up the ball has a thickness of 1.25 cm, find
the total volume of material that makes up the ball. Round your
answer to the nearest hundredth if necessary. (Note: diagram is
not drawn to scale.)
we can find the total volume of material that makes up the ball by subtracting the volume of the hollow space from the volume of the sphere:
V = 20,834 cm^3 - 19,848.44 cm^3
= 985.56 cm^3
what is volume?Volume is a measure of the amount of space occupied by an object or a substance. It is typically measured in units such as cubic meters (m^3), cubic centimeters (cm^3), or cubic feet (ft^3).
What is diameter?Diameter is a measure of the distance across the widest part of a circular object, such as a circle or a sphere. It is equal to twice the radius of the object and is typically measured in units such as millimeters (mm), centimeters (cm), or inches (in). It is a linear measurement.
To find the total volume of material that makes up the ball, we need to find the volume of the sphere and then subtract the volume of the hollow space in the center.
We can begin by calculating the volume of the sphere using the formula for the volume of a sphere:
V = (4/3) * pi * r^3
Where V is the volume, pi is approximately 3.14, and r is the radius of the sphere.
The outer diameter of the ball is 50 cm, so the radius of the sphere is (50/2) = 25 cm.
Substituting these values into the formula, we get:
V = (4/3) * 3.14 * (25 cm)^3
= (4/3) * 3.14 * 15,625 cm^3
= 20,834 cm^3
Next, we need to find the volume of the hollow space in the center of the ball, which is the same as the volume of a smaller sphere with a radius of (25 cm - 1.25 cm) = 23.75 cm.
So the volume of the hollow space is :
V = (4/3) * pi * (23.75 cm)^3
= (4/3) * 3.14 * (23.75 cm)^3
= 19,848.44 cm^3
Finally, we can find the total volume of material that makes up the ball by subtracting the volume of the hollow space from the volume of the sphere:
V = 20,834 cm^3 - 19,848.44 cm^3
= 985.56 cm^3
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Two parallel train tracks, S and T, are cut by another train track, U. The train track U creates an interior angle of 101 with track S.
How can you use this information to solve for the measure of the same side interior angle made by track T and track U?
The measure of the same side interior angle made by track T and track U is; 79 degrees
How to find same side interior angles?Same side interior angles are defined as two angles that are on the interior of or between the two lines and particularly on the same side of the transversal. The same-side interior angles usually sum up to 180 degrees. Finally, when two parallel lines are intersected by a transversal line they will form 4 interior angles.
Now, we are told that the train track U creates an interior angle of 101 with track S.
Thus, using same side interior angles definition, the measure of the same side interior angle made by track T and track U is;
same side interior angle = 180 - 101
= 79 degrees
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What are the 6 types of math?
Therefore , the problem of mathematics comes out to be Algebra , geometry , trigonometry and etc.
What exactly is mathematics?In the study of mathematics, a variety of subjects are studied, including numbers, figures, logic, quantity, equations, and arrangements. Through the use of numerical variable computations, math enables students to find answers to issues.
Here,
Thus the 6 main branches of pure mathematics are
1) Algebra
2) Geometry.
3) Trigonometry.
4) Calculus.
5) Probability and
6)statistics.
the solution of the given problem is Algebra , geometry , trigonometry , calculus , probability and statistics.
Therefore , the problem of mathematics comes out to be Algebra , geometry , trigonometry and etc.
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What are the types of graphs for Class 7?
Frequency distribution graphs, exponential graphs, logarithmic graphs, trigonometric graphs, and statistical graphs are among the six types of graphs (such as bar, pie, and line graphs).
A straightforward two-dimensional graph is created when a vertical and horizontal line join at the origin. The y axis is vertical whereas the x axis is horizontal. In simple line graphs, the x and y axes are split into regularly spaced sections and assigned integer values.
There are eight main categories of graphs: linear, power, quadratic, polynomial, and they are all used to organise how information is presented.
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Do the lengths 5 12 and 13 form a right triangle?
The lengths 5, 13 and 12 can form a right angled triangle as they follow Pythagoras theorem.
The lengths can form a right triangle if they follow Pythagoras theorem. The longest side will be hypotenuse which is 13. Remaining will be base and height.
Pythagoras theorem -
Perpendicular² = Base² + Height²
Keep the values in formula
13² = 12² + 5²
Taking square on each side of the equation
169 = 144 + 25
Performing addition on Right Hand Side of the equation
169 = 169
Thus, the righ triangle can be formed based on the mentioned dimensions.
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