If we use the method of completing the square to solve the quadratic equation x² + 5x - 1 = 0, we have to add (-25/4) to convert it to (x + 5/2)² - 29/4 = 0
The standard form of a quadratic equation is:
ax² + bc + c = 0
Three methods for solving a quadratic equations:factoringcompleting the squareabc formulaIn this case, the quadratic function is:
x² + 5x - 1 = 0
To solve it using the "complete the square" method, write the equation as:
(x + 5/2)² - 1 + .... = 0
The blank part in the above equation means we need to add a number to make the equality still holds.
Note that:
(x + 5/2)² = x² + 5x + 25/4
Hence,
(x + 5/2)² - 1 = x² + 5x + 25/4 - 1
Hence, we need to add (-25/4) to make the original equality holds:
(x + 5/2)² - 1 + (-25/4) = 0
(x + 5/2)² - 29/4 = 0
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Anybody know how to solve this??? Plsss
Answer:
12,34
Step-by-step explanation:
For 'a'
8x=(2x+72) [vertically opposite angle]
8x-2x=72
6x=72
x=72/6
x=12
For 'b'
4x+20+x-10=180° [ being straight angle ]
4x+x+20-10=180°
5x+10=180°
5x=180-10
x=170/5
x=34
What are the 4 types of division?.
There are four types of division are:
DividendDivisorQuotient RemainderNow, According to the question:
Division is one of the four basic math operations with addition, subtraction, and multiplication. Division is an important operation because it is common in everyday life and helps people understand multiplication better. Division is splitting a group into equal parts. Division is used to split up a class into equal groups for a game or activity or even split a pizza into equal portions between a group of friends.
The dividend is the number that is being divided in the division process.The number by which the dividend is being divided by is called the divisor. The quotient is a result obtained in the division process.Sometimes, we cannot divide things exactly.Learn more about Division at:
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how many solutions does 3(2x+1)=2(3x+2) have
The given expression 3(2x+1) = 2(3x+2) does not have a solution.
What is Linear equation ?
A linear equation is an equation that can be written in the form ax + b = 0, where x is a variable and a and b are constants. This type of equation is used to describe relationships between two variables, and it can be used to find the solution to a variety of problems.
Given expression ,
3(2x+1) = 2(3x+2)
3*2x+3 = 2*3x + 4
shifting 6x to the LHS , we get
6x+3 = 6x+ 4
6x-6x = 4-3
As 6x-6x is 0 , so there is no solution
0 = -1
Here we do not have a solution as there is no x exponent.
Hence, The given expression 3(2x+1) = 2(3x+2) does not have a solution.
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When using substitution to solve a linear system how do you know if the system is inconsistent?.
The first step in determining whether a linear system is inconsistent is to identify whether the lines are parallel. Check to see if the lines have a y-intercept in common, if so.
This result establishes an inconsistent system due to the fact that two parallel lines with distinct y-intercepts will never intersect.
If there is at least one solution to a linear equations system, it is said to be a consistent system. The system is regarded as inconsistent if there is no solution.
When the lines are parallel to one another, a system of linear equations cannot become inconsistent in any other way. The slope of parallel lines is the same. Therefore, comparing the slopes is a good way to ascertain whether the system is inconsistent. The comparison is simple if the linear equations are written in the point-slope or slope-intercept form. In order to determine the coefficient of x and compare slopes, it is a good idea to solve for y on all equations that are in a different form and express them in the slope-intercept form. The equation system is inconsistent if the slopes are equal to one another.
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What is a 45 degree triangle called?.
A 45-degree triangle is called a right-angle triangle.
A 45-degree angle is exactly half of a 90-degree angle formed between two rays.
It is equal to half of a straight angle or a 90-degree angle. An angle bisector of a 90-degree angle creates two equal 45-degree angles. The 45-degree angle can be found in many everyday objects, such as scissors, doors, and windows. It is also known as the angle created by a square's diagonal and its sides.
It is an acute angle and two angles measuring 45 degrees form a right angle or a 90-degree angle. We know that an angle is formed when two rays meet at a vertex.
Thus, A 45-degree triangle is called a right-angle triangle.
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How do you find the properties of a 30 60 90 triangle?.
A 30-60-90 triangle has one right angle, with the other two angles measuring 30 and 60 degrees. The shortest side is half as long as the hypotenuse, while the middle side is equal to the shortest side multiplied by the square root of 3. The area can be found using (1/2) x base x height, with the perimeter equal to the sum of all three sides.
A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.
In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.
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I seriously need help on this question, can someone help?
Answer:
a. A + C < B + C
Step-by-step explanation:
when we know that A < B, then adding the same amount to both sides did not change the relationship between both sides.
this is like having a balance with 2 cups. one side is heavier than the other, so the heavier cup is down.
if we add the same weight to both cups, the situation will not change.
that is why a. is the right answer.
b. would only be right, if C is negative.
for positive C the same argument as for A applies. a smaller amount (or weight) stays smaller also after multiplying both sides by the same number.
but because this option would only be right for a subset of the possible values, this is not true in general.
c.
this is not true at all.
if we multiply the expression by -1, then the inequality sign has to flip. < becomes >, > becomes <.
which did not happen here.
Write the equation of the hyperbola with centre at (4, 2), vertex at (4, 5), one asymptote with equation 4y - 3x = -4.
x2a2y2b2=1 x 2 a 2 y 2 b 2 = 1 is the conventional form of a hyperbola equation with the origin as the center and the vertices (a,0) (a, 0) and co-vertices (0b), (0b).
How do you find the equation of a hyperbola given center and vertex?A right circular cone and a plane are intersected at an angle that intersects both of the cone's halves to create a hyperbola in analytic geometry. There are two distinct unbounded curves that result from this intersection, and they are mirror reflections of one another.The set of all points (x, y) in a plane that are part of a hyperbola has a positive constant as the difference between their distances from the foci.Every hyperbola, like the ellipse, has two axes of symmetry. A line segment called the transverse axis, which has vertices for endpoints and runs through the hyperbola's centre. On the transverse axis-containing line, the foci are located. The co-vertices serve as the endpoints of the conjugate axis, which has a perpendicular relationship to the transverse axis. When the transverse and conjugate axes connect, they form the centre of a hyperbola. Two asymptotes also cross the centre of every hyperbola. The asymptotes of a hyperbola's branches are as it moves out from its center.When graphing the hyperbola and its asymptotes, the central rectangle of the hyperbola, whose sides run across all of its vertices and covertices and are centred at its origin, is a valuable tool. Simply draw and extend the diagonals of the central rectangle to represent the hyperbola's asymptotes.The axes in this section will either be on or be parallel to the x- and y-axes, and we will focus on hyperbolas that are positioned vertically or horizontally in the coordinate plane. The two situations that we'll look at are those that have the origin as their centre of gravity and those that have it somewhere else.The Complete Question is hyperbola equation.
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The following triangles are similar. Which of the properties could be used to solve x:
if the triangles are similar , then ,
The small trapezoid is a scaled-down version of the large trapezoid, but is also a mirror image.
So the side x corresponds to the length 45 in the larger trapezoid.
[tex]45 = 2x + 4 \\ 2x = 45 - 4 \\ x = \frac{41}{2} \\ x = 20.5[/tex]
Alex ran 4 1/2 kilometers in 3/4 of an hour. How many kilometers he ran per hour?
First convert the distance she ran from a mixed number to a improper fraction:
• 4-1/2 equals 9/2.
Since this a unit rate problem divide the km by the time traveled.
• 9/2 (km) ÷ 3/4 (hour). When you divide a number by a fraction use (Keep-Change-Flip).
• 9/2 × 4/3 = 36/6 miles/hour.
That's means 36/6 = 18/3 = 6 km/ hour.
A5=768 and a2=12; given two term in a geometric equence find the 8th term and the recurive formula
The recursive formula for this geometric sequence is , an = a(n-1) * 64, where a(n-1) is the previous term of the sequence.
What is geometric ?
A geometric sequence is a sequence of numbers such that the quotient between any two consecutive terms is always the same, this common ratio is denoted by "r" and the first term of the sequence is denoted by "a1". A geometric sequence can be represented by the following formula
a_n = a_1 * r^(n-1)
Given a5=768 and a2=12, we can find the value of the common ratio (r) by dividing the two terms:
r = a5 / a2 = 768 / 12 = 64
To find the 8th term of the geometric sequence, we can use the formula:
an = a1 * r^(n-1)
where a1 is the first term, r is the common ratio, and n is the position of the term.
Given the 8th term, we can substitute the values
a8 = a1 * r^(8-1) = a1 * 64^7 = a1 * 64^7
To find the recursive formula, we can use the formula:
an = a(n-1) * r, where a(n-1) is the previous term of the sequence
So the recursive formula for this geometric sequence is , an = a(n-1) * 64, where a(n-1) is the previous term of the sequence.
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A geometric sequence is a set of numbers where any two consecutive terms' quotients are always the same. The first term in the series is indicated by the letter "a1," and the common ratio is indicated by the letter "r". The following formula can be used to describe a geometric sequence.
Given a5=768 and a2=12, we can find the value of the common ratio (r) by dividing the two terms:
r = a5 / a2 = 768 / 12 = 64
To find the 8th term of the geometric sequence, we can use the formula:
an = a1 * r^(n-1)
where a1 is the first term, r is the common ratio, and n is the position of the term.
Given the 8th term, we can substitute the values
a8 = a1 * r^(8-1) = a1 * 64^7 = a1 * 64^7
tangent lines help (15 pts)
The required perimeter of the polygon is 92 cm.
What is a polygon?Polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,
Examples of polygons, equilateral triangles, squares, pentagons etc
here,
∠B ≅ ∠C
tangent drawn from D = tangent drawn from B
tangent drawn from D = 11.5 cm
The perimeter of the polygon is given = as the sum of a tangent from all points
= 11.5 + 11.5 + 11.5 + 11.5 + 10.5 + 10.5 + 12.5 + 12.5
= 92 cm
Thus, the required perimeter of the polygon is 92 cm.
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What is modulus of 4i?.
The modulus of the complex number 4i is 4.
Now, According to the question:
Consider the given number 4i .
The number is a complex number which is of the form z = x + iy .
We can write the above question as z = 4i where x = 0 and y = 4 . The modulus of the complex number is given by:
[tex]|z| =\sqrt{Re(z)^2+Im(z)^2}[/tex]
where real part is x and imaginary part is y. Hence the modulus of a complex number is :
[tex]|z| =\sqrt{0^2+4^2}[/tex]
[tex]|z| = \sqrt{16} \\[/tex]
|z| = 4
Hence the modulus of the complex number 4i is 4.
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y is directly porportional to x
when y=30 and x=6
a)work out an equation connecting y and x
b)work out the value of y when x =12
a. The equation connecting y and x is: y = 5x.
b. The value of y = 60.
What is the Equation of a Direct Proportional Relationship?Given that y is directly proportional to x, the equation that is connecting y and x can be expressed as y = kx, where k is the constant of proportionality.
a. We are given that when y = 30, x = 6, therefore, find the value of k by substituting the values of x and y into y = kx:
30 = k(6)
30/6 = k
5 = k
k = 5
Substitute the value of k into y = kx to write the equation:
y = 5x
b Substitute x = 12 into y = 5x:
y = 5(12)
y = 60
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Which relation is a function?
Responses
{(1, 2), (2, 3), (3, 4), (4, 5)}
{(1, 2), (3, 4), (5, 6), (1, 8)}
{(1, 2), (2, 1), (1, 3), (3, 1)}
{(0, 2), (0, 4), (0, 6), (0, 8)}
The relation that is a function is
{(1, 2), (2, 3), (3, 4), (4, 5)}
Option A is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
A function can have different inputs but the same output.
i.e many to one.
But a function can not same input and different output.
i.e one to many.
Now,
{(1, 2), (2, 3), (3, 4), (4, 5)}
This is a function because each input has a different output.
This is a one-to-one function.
{(1, 2), (3, 4), (5, 6), (1, 8)}
This is not a function because 1 has different outputs 2 and 8.
{(1, 2), (2, 1), (1, 3), (3, 1)}
This is not a function because 1 has different outputs 2 and 3.
{(0, 2), (0, 4), (0, 6), (0, 8)
This is not a function because 0 has different outputs 2, 4, 6, and 8.
Thus,
{(1, 2), (2, 3), (3, 4), (4, 5)} is a function.
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6) Se tienen 60 lápices, 90 esferos y 120 borradores y se quieren distribuir paquetes en los que haya
estos tres tipos de artículos. ¿cuál es el máximo número de paquetes que se puede armar usando
todos los artículos? ¿Cuántos lápices, esferos y borradores deben ir en cada paquete?
5 pencils, 2 pens, and 3 erasers should go in each package.
The goal is to determine the maximum number of packages that can be built using 60 pencils, 90 pens, and 120 erasers, each package containing 5 pencils, 2 pens, and 3 erasers. To achieve this, we need to calculate the number of packages each item can be used in and take the minimum result.
Starting with pencils, we can make 60/5 = 12 packages. For pens, we can make 90/2 = 45 packages. Finally, for erasers, we can make 120/3 = 40 packages. The minimum result is 40 packages, meaning that the maximum number of packages we can build is 40.
Therefore, each package should contain 5 pencils, 2 pens, and 3 erasers. Any extra items will not be used in the packages. By taking the minimum result, we ensure that all items are used in an equal manner and no items are left unused. In conclusion, the maximum number of packages that can be built using 60 pencils, 90 pens, and 120 erasers is 40, each containing 5 pencils, 2 pens, and 3 erasers.
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What is the scale factor in the dilation if the coordinates of A are (-7, 6) and the coordinates of Care (-4, 3)?
D
B
d
21
OLE
18-
45-
42-
9-
B'6
Dº 6'3-
-24-21-18-15-12-9-6-33- 3 6 9 12 15 18 x
-6-
60325
-9
42
►
The scale factor in the dilation can be found by comparing the coordinates of the original image (A) and the new image (B). The coordinates of A and B must be provided in order to determine the scale factor.
What is the scale factor in the dilation if the coordinates?The scale factor in the dilation can be found by comparing the coordinates of A and B. The x-coordinate of A is -7 and the x-coordinate of B is -4, which means that the x-coordinate of B is 3 units closer to the origin than the x-coordinate of A. Similarly, the y-coordinate of B is 3 units closer to the origin than the y-coordinate of A. Therefore, the scale factor in the dilation is 3. This means that the image of A is 3 times larger than the preimage, and the image of B is 3 times closer to the origin than the preimage of A. The scale factor can be found by dividing the distance between the coordinates of A by the distance between the coordinates of B. For example, if the coordinates of A are (4,5) and the coordinates of B are (8,10), the scale factor would be 2, as the distance between the coordinates of B is twice the distance between the coordinates of A. It is important to note that the scale factor applies to both the x and y coordinates and is the same value for both.To learn more about coordinates of Care refer to:
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x is an obtuse angle and sin x = 0.43.
Find the value of x.
Answer: 154.53
Step-by-step explanation:
sin x° = 0.43
t = arcsin (0.43) = 25.47
x= 18 - t= 18 - 25.47 = 154.53
Answer the following question in the picture
How do you write greater than or equal to 6?.
The correct way to write greater than or equal to 6 is A ≥6 where it tells that A having greater than or equal to value than 6.
In mathematics,
→The greater than symbol (>) is used to indicate that one value is larger than another. For example, if we say "A > B," this means that the value of A is greater than the value of B.
→The less than symbol (<) is the opposite, it indicates that one value is smaller than another. For example, if we say "A < B," this means that the value of A is less than the value of B.
→The greater than or equal to symbol (≥) indicate that one value is larger than or equal to another. For example, if we say "A ≥ B," this means that the value of A is greater than or equal to the value of B.
→The less than or equal to symbol (≤) indicate that one value is smaller than or equal to another. For example, if we say "A ≤ B," this means that the value of A is less than or equal to the value of B.
These symbols are commonly used in mathematical expressions, equations, and inequalities.
To write "greater than or equal to 6" in mathematical notation, you would use the greater than or equal to symbol (≥) followed by the letter 6. For example:
A ≥6
This means that A having greater than or equal to 6.
Therefore, the correct way to write greater than or equal to 6 is A ≥6 where it tells that A having greater than or equal to value than 6.
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please help me
[tex] \sqrt[4]{ - 81} [/tex]
Answer:
3 ⁴√-1
Step-by-step explanation:
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
In a baket of muffin 15% of the muffin are blueberry. How many are not blueberry?
The percentage that is not blueberry in a bake of muffin is 85%
What is a percentage?Percentage is defined as the number that represents a ratio of a total that is divided by 100 equal parts. It is represented by the symbol %.
To solve this problem we must perform the following algebraic operations with the given information:
Information about the problem:
%Total = 100%Blueberry = 15%Not blueberry = ?Calculating the percentage that is not blueberry in a bake of muffin:
% Not blueberry = %Total - %blueberry
% Not blueberry = 100 - 15
% Not blueberry = 85
85% of the bake is not blueberry
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Help someone tell me what’s x??
The length of the rectangle side x is equal to 35.33 cm approximately to 2 decimal place using the trigonometric ratio of tangent.
What are trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
We shall represent the intercept of the diagonal lines in the rectangle with O so that we consider the right triangle ∆AOx, then we solve for the length of Ax and multiply the result by 2 to derive the value of x as follows:
angle 54 and m∠AOD are supplementary so;
m∠AOx = (180 - 54)/2 {m∠AOD/2}
m∠AOx = 63°
tan 63° = (x/2) ÷ 9
tan 63° = x/2 × 1/9 {change division to multiplication}
tan 63° = x/18
x = 18 × tan 63° {cross multiplication}
x = 35.3270
Therefore, 35.33 cm approximately to 2 decimal place is the length of the rectangle side x using the trigonometric ratio of tangent.
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Noah earn 37 for 4 hr of babyitting. At thi rate how much more would he earn for 9 hr
The rate he would he earn for 9 h will be 83.25
Your pay for each hour of labor is expressed as an hourly rate. You might need to estimate your income for other applications or change your own budget after comparing the hourly and salaried pay rates.
The sum of money charged, received, or earned for each hour of work: Instead of paying for the things the advisers try to sell you, you pay a set or hourly charge for their time.
Noah earns 37 for 4 hr of babysitting.
so if you divide 37 by 4 you get the rate per hour
which is 9.25 so if you multiply 9 times 9.25
The rate he would earn for 9 h will be
you would get 83.25.
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Suppose you through a ball horizontally. How is the way the ball moves similar to the motion of the planets around the sun?
The forces acting on a horizontally moving ball in the air are gravity or the force of its own weight, and the force that displaces the ball in the horizontal direction.
What is force?Force is an external agent that acts on a body to cause it to move or stop. There are various types of forces, such as magnetic forces, nuclear forces, frictional forces, and so on.
The product of a moving body's mass and acceleration yields force, which is derived from Newton's second law of motion. As a result, as the mass of the object increases, the force required to change its state increases.
The forces acting on a moving ball horizontally are the normal force that displaces it in that direction and the downward force of gravitation equal to its weight. Air resistance acting on the ball can also be considered.
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Bowling Green middle school has 600 students. in Aiko’s class, 6 10 students prefer summer to spring. based on these results, how many students prefer summer
The number of students who prefer summer is equal to 60 students.
How to determine the number of students who prefer summer?In order to determine the number of students who prefer summer, we would multiply the total number of students in Bowling Green middle school by the number of students in Aiko’s class who prefer summer to spring.
Mathematically, an expression which models the number of students who prefer summer is given by;
Number of students who prefer summer = 6/10 × 600
Number of students who prefer summer = 0.6 × 600
Number of students who prefer summer = 60 students.
Based on these results, we can logically conclude that 60 students in Aiko’s class who prefer summer to spring.
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Complete Question:
Bowling Green middle school has 600 students. in Aiko’s class, 6 out of 10 students prefer summer to spring. Based on these results, how many students prefer summer?
hi can you help it will help me
The exact value of the letter D is three and three-tenths.
What is a number line?A number line is a one-dimensional horizontal line where we can represent any real number. The origin of the number line is represented by zero left to it are all negative real numbers and right to it are all positive real numbers.
By observing the number line there are 10 subsections between two integers.
The letter D is in between two integers 3 and 4 so it can be from 3.1 to 3.9.
In between those ten subsections, the letter D is in the third subsection.
Therefore it is Three and three-tenths.
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An architect is designing a water fountain for a park. She uses the given function to model the water jets flowing from the fountain's nozzles,
where h(x) gives the height of the water jet, in feet, x feet from its starting point.
The two adjacent columns that show an interval with an average rate of change of -0.3 are column 7ᵗʰ and 8ᵗʰ.
We have a function used by an architect is designing a water fountain for a park. The function is defined as h(x) = - x²/20 + x + 15
where h(x) --> height of the water jet, in feet,
x --> distance from its starting point in feet.Also , the average rate of change = - 0.3
Average rate of change is used to measure the change in value of function per unit, on average over an interval. It is derived from the slope line which is formed bu joining the end points of graph. Formula is represented as
A(x) = {F(b) - F(a)}/(b - a)
where b and a are end points of interval.
In this case, this formula is used as
A(x) = {H(x₂) - H(x₁)}/(x₂ - x₁ )
=> -0.3 = {H(x₂) - H(x₁)}/(x₂ - x₁ )
As we see in above figure the difference between the any two values of x is equals to 2 i.e., the final value - initial value = 2 in an interval.
So, x₂ - x₁ = 2
=> -0.3 = {H(x₂) - H(x₁)}/2
=> -0.3× 2 = H(x₂) - H(x₁)
=> -0.6 = H(x₂) - H(x₁)
=> H(x₂) = H(x₁) - 0.6
so, the columns which follows this relationship are the following
distance , x 12 14
Height of jet , h(x) 19.8 19.2
Hence, the required relationship is H(x₂) = H(x₁) - 0.6.
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Complete question:
An architect is designing a water fountain for a park. She uses the given function to model the water jets flowing from the fountain's nozzles,
where h(x) gives the height of the water jet, in feet, x feet from its starting point. select two adjacent columns that show an interval with an average rate of change of -0.3
Can a 9 12 15 form a triangle?.
Yes, it is possible to draw a triangle.
This will be done by the property: the sum of two sides of a triangle should be more than the third side.
(9cm + 12cm) =15cm
21cm = 15cm
LHS>RHS
A triangle is possible.
A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.
In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.
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Can someone help me with this please?
Pleas show steps.
Solving the system of equations:
x + y = 45
y = 2x
We can see that he made a total of 30 hot dogs and 15 hamburgers.
How to write and solve the system of equations?We can define the variables:
x = number of hamburgersy = number of hot dogs.We know that he cooked a total of 45 dishes, then we can write the equation
x + y = 45
And he cooked twice as many hot dogs as hamburgers, then we can write:
y = 2x
Then we can write a system of equations at:
x + y = 45
y = 2x
We can replace the second equation into the first one, then we have:
x + (2x) = 45
3x = 45
x = 45/3
x = 15
And the solution of y is:
y = 2x
y = 2*15 = 30
The solution of the system is:
x = 15
y = 30
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