The quadratic equation in standard form given the sum and product of roots is
x² - (α + β)x + αβ = 0.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
A polynomial with degree 2 is called a quadratic equation.
Now,
The standard form of a quadratic equation is ax² + bx + c.
Now,
Let the roots of the quadratic equation be α and β.
α + β = -b/a
αβ = c/a
Thus,
The quadratic equation is x² - (α + β)x + αβ = 0.
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How do you find the inverse of 2?
Additive inverse of 2 is -2.
Multiplicative Inverse of 2 is 1/2.
What is Inverse ?To produce a result equal to 0, add the original number and the additive inverse by simply reversing the sign of the integer. On the basis of negation of the original number, the characteristics of additive inverse are listed below. For instance, if x is the starting number, then -x is x's additive inverse.
A multiplicative inverse or reciprocal for a number x is a number that, when multiplied by x, produces the multiplicative identity, or 1. It is represented by 1/x or x/1. A fraction a/b has a multiplicative inverse of b/a. Divide 1 by the real number to obtain the multiplicative inverse of the number.
A function that "undoes" another function is called an inverse. In other words, if f(x) generates y, then y entered into the inverse of f creates x. An invertible function is one that has an inverse, and the inverse is indicated by the symbol [tex]f^{-1}[/tex].
Additive inverse of 2 is -2.
Multiplicative Inverse of 2 is 1/2.
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Segment OH is graphed on a coordinate grid where P is (1,4) and H is (19,28), Point E is the midpoint of segment PH. If point A is graphed 2/3 of the way along the segment from P to E, then what are the coordinates of point A?
The coordinates of point A are (23/5, 44/5).
What is a line segment?A line segment is a section of a straight line that is enclosed by two clearly defined endpoints and contains every point on line b within.
Given:
The ratio = 2:3
P is (1,4) and H is (19,28)
Calculate the mid-point coordinates as shown below,
E = (1 + 19 / 2), (28 + 4 / 2)
E = (10, 16)
Calculate the coordinates of point A,
A = (2 × 10 + 3 × 1 / 2+3) , (16 × 2+ 4 × 3 / 2+3)
A = (23/5, 44/5)
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Write and expression for: Twice the sum of 5 and a number z.
Answer:
10 + 2z
Step-by-step explanation:
2( 5+z)
10 + 2z
How do you solve a quadrilateral problem?
Answer:
It depends on what the question is.
Step-by-step explanation:
these are two separate questions, please answer both. Thank youuu !!
Answer:
answers are T,F,T
Step-by-step explanation:
Just had this worksheet
How many perfect squares are two-digit and divisible by $3?$
There are 2 perfect squares that are two-digit and divisible by 3.
To find the two-digit perfect squares that are divisible by 3, we can start by finding all the two-digit perfect squares and then check which ones are divisible by 3. The two-digit perfect squares are:
4: 16
5: 25
6: 36
7: 49
8: 64
9: 81
Now we can check which of these numbers are divisible by 3:
16: not divisible
25: not divisible
36: divisible
49: not divisible
64: not divisible
81: divisible
Thus, there are two two-digit perfect squares that are divisible by 3: 36 and 81.
So, the answer is 2.
7.
Shino typed
-4²
into a calculator and got -16. Then Shino
typed
(-4)²
into a calculator and got 16. Can you
explain to Shino why she got two
different answers?
Type a response
Answer:
order of operations
Step-by-step explanation:
You want to know why -4² = -16 and (-4)² =16.
Order of operationsThe calculator properly applied the order of operations to -4². In evaluating, this expression, the exponentiation operation is performed first. That means this is evaluated as ...
-4² = -(4×4) = -16
When the parentheses include the minus sign, as in the second expression, the squaring operation is applied to -4, not to 4:
(-4)² = (-4)×(-4) = 16
PLEASE HELP ME ANSWER THIS QUESTION
WHY is the number of roots less than or equal to the degree
The number of roots of a polynomial is always less than or equal to the degree of the polynomial because the degree of f(x) is the sum of the degrees of the factors
Why is the number of roots less than or equal to the degree?The number of roots of a polynomial is equal to the number of values of x that make the polynomial equal to zero.
The degree of a polynomial is the highest exponent of the variable in the polynomial. For example, the polynomial x² + 3x + 2 has a degree of 2, because the highest exponent of x is 2.
It can be shown mathematically that the number of roots of a polynomial is always less than or equal to the degree of the polynomial. This is known as the Fundamental Theorem of Algebra.
Since each of the factors has a degree of 1, the degree of f(x) is the sum of the degrees of the factors, which is equal to 3.
Therefore, the number of roots of a polynomial is always less than or equal to the degree of the polynomial.
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How do you know if two figures are similar by transformations?
Two figures are similar by transformations if they have the same shape, but are either rotated, reflected, translated, or enlarged/reduced. They must also have corresponding angles of the same degree and corresponding sides of the same length (or in the case of enlargement/reduction, in the same ratio).
Transformations – what are they?Four distinct approaches to modify the position and/or shape of a point, line, or geometric figure are collectively referred to as transformations. The Pre-Image of the object is its initial shape, while the Image, after transformation, is the final shape and location of the thing.
Describe a transformation example.A drastic change in shape or appearance is called a transformation. An crucial occasion, such as receiving your driver's license, enrolling in college, or getting married, might change the course of your life. Extreme, dramatic change is what we refer to as transformation.
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How old is 12 grade in Korea?
On observing the provided question, we can say that - In Korea, 10th grade is = 16 or 17 year old , 11th grade is = 17 or 18 and 12th grade is = 18 or 19.
What is grade?
Grading may be done using letters, numbers, percentages, points, or descriptions. The most prevalent grades are in the form of letters, and they usually correspond to a variety of percentages or points. Many people consider "A" and "B" grades to be "good." D and F grades are referred to as "poor grades." Commonly regarded as average is a "C."
We can say that
In Korea,
10th gradis = 16 or 17 year old ,
11th grade is = 17 or 18 and 12th grade is = 18 or 19.
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A new fountain in the shape of a hexagon will have 6 sides of equal length. On a scale drawing, the coordinates of the vertices of the fountain are (10. 5, 8), (14. 5, 5), (10. 5, 2), (5. 5, 2), (1. 5, 5), and (5. 5, 8). How long is each side of the fountain?.
Each side of the fountain is 5 units .
Given :
All the sides of the hexagon are equal.
Vertices of the fountain are :
( 10.5 , 8 ), ( 14.5 , 5 ), ( 10.5, 2 ), ( 5.5, 2 ), ( 1.5, 5 ), and ( 5.5, 8 ).
we know that ,
Distance = √( x2 - x1 )^2 + ( y2 - y1 )^2
= √( 14.5 - 10.5 )^2 + ( 5 - 8 ) ^2
= √4^2 + 3^2
= √ 16 + 9
= √25
= 5 units
we know that all the sides of the hexagon are equal so the length of each side of hexagon or fountain is 5 units .
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What is the equation of the line that passes through the point (8, -3) and has a slope of 1/4?
Answer:
y=1/4x-5
Step-by-step explanation:
y=mx+b is slope intercept form
m is slope
b is y intercept
we know m is 1/4 so we fill it in
y=1/4x+b
fill is the coordinates to find b
-3=1/4(8)+b
-3=2+b
-2. -2
-5=b
place b in
y=1/4x-5
hopes this helps
Answer:y=1/4x-5
Step-by-step explanation:
Your point was (8,-3) and your rise is 1 and your run is 4 so if you want to get from 0 to 8 and count by 4 you need to move twice, and if you established that you will move twice then you need a number that you add 2 to that will give you -3. And that number is -5 so your y-intercept is
Write an equation of a line that doesn’t have a x-intercept
X= (any number that isn't 0)
so X=1 X=2 x=3 those would all work
the x intercept is when any point on the x axis is intercepted, and any line with a slope that isn't 0 will always intersect that point. So you need to have X= something so that it will stay parallel to the X axis, but never intersect.
These are two separate questions, thank you :))
I don't see the picture. Can you send it in the message.
Graph g(x)=2x2−4x−16 Use the parabola
The parabola Refer the attached figure, x- intercepts are (4,0) and (-2,0)
Quadratic function = f(x) = 2x²-4x-16.
To find: The graph of the quadratic function using parabola tool?
First we find the vertex form of the equation.
f(x) = 2x²-4x-16
Where, a=2 ,b=-4 , c=-16
Vertex is V,
[tex]v=\frac{-b}{2a} , f(\frac{-b}{2a})\\\\\frac{-b}{2a} = \frac{4}{4} =1\\\\f(\frac{-b}{2a})=f(1)\\\\=-10[/tex]
So, The vertex of the equation is (1,-10).
Now, we find y- intercept by putting x=0 in the equation
[tex]y=2(0)^{2} -4(0)-16\\\\y=-16[/tex]
y- intercept (0,-16)
Now, we find x- intercept by putting y=0 in the equation.
[tex]2x^{2} -4x-16=0\\\\x^{2} -2x-8=0\\\\x^{2} -4x+2x-8=0\\\\x=4 \ and \ x=-2[/tex]
x- intercepts are (4,0) and (-2,0)
Placing all the points and plot a graph.
Refer the attached figure below.
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The temperature in Mexico City is 43 degrees Celsius. What is the corresponding temperature in Fahrenheit
Answer:109.4 Fahrenheit
Step-by-step explanation:
What are the missing parts that correctly complete the proof?
∠ABP = ∠CBP (By angle bisector).∠PXB = ∠PYB (All right angles are congruent).BP = BP (Common side).ΔBXP = ΔBYP (By ASA rule).PX = PY (corresponding sides of congruent triangles are the same).
What is congruence?If two figures are exactly the same in sense of their length side all things then they will be congruent.
In other meaning, if you can copy a figure then that copy and the original figure will be congruent.
As per the given two bisectors' angle.
∠ABP = ∠CBP (By angle bisector)
∠PXB = ∠PYB (All right angles are congruent).
BP = BP (Common side)
ΔBXP = ΔBYP (By ASA rule)
PX = PY (corresponding sides of congruent triangles are the same)
Hence "∠ABP Equals ∠CBP (By angle bisector). ∠PXB = ∠PYB (All right angles are congruent). BP = BP (Common side) (Common side). ΔBXP = ΔBYP (By ASA rule). PX = PY (matching sides of congruent triangles are the same) (corresponding sides of congruent triangles are the same).".
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How do I notify SSS for EC sickness benefit?
The claim for the EC sickness benefit are filed at any SSS branch or representative office nearest the member's residence or place of work.
Here we need to find the way to notify SSS for EC sickness benefit.
In order to find the solution, we must know that what is meant by SSS for EC sickness benefit.
The term SSS for EC sickness benefit is defined as the benefits under the EC program may be enjoyed simultaneously with benefits under the social security program effective June 1984.
Based on the definition, we have identified that the notification process is done through the E-Services tab and click on "Submit SS Sickness Benefit Reimbursement Application (SBRA)."
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What is the slope of the line that passes through the points (-1, 1) and
(-1,4)? Write your answer in simplest form.
Answer:
undefined
Step-by-step explanation:
You want the slope of the line through points (-1, 1) and (-1, 4).
SlopeThe two points lie on the vertical line x = -1. A vertical line has undefined slope.
The slope of the line is undefined.
__
Additional comment
The slope is the ratio of rise to run. For a vertical line, the "run" is zero for any chosen "rise." Division by zero gives an undefined result.
Which of the following equations has the sum of its roots as 3 a 2x² 3x 6 0 B X² 3x 3 0 C √ 2x² 3 √ 2x 1 0 D 3x² 3x 3 0?
The equation x² + 3x - 3 = 0 has the sum of its roots as 3. This can be found by using the quadratic formula, which gives us two roots x1 and x2. Their sum is x1 + x2 = 3, which is the sum of the roots of the equation.
The correct answer is B: x² + 3x - 3 = 0
The equation has the form of ax² + bx + c = 0.
a = 1, b = 3, c = -3
The sum of the roots can be found using the quadratic formula:
x = (-b ± √(b² - 4ac))/2a
x = (-3 ± √(9 - 4*1*(-3))/(2*1)
x = (-3 ± √15)/2
x = (-3 ± 3√5)/2
x1 = (3 - 3√5)/2
x2 = (3 + 3√5)/2
The sum of the roots is x1 + x2 = 3.
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What is the vertical asymptote of X 4?
The vertical asymptote of X 4 is x = 4, which means that as x approaches 4, the function approaches infinity.
The vertical asymptote of a function is an x-value at which the function tends to approach infinity. In the case of X 4, the vertical asymptote is x = 4. This means that as x approaches 4, the function X 4 approaches infinity. This can be seen by examining the function. As x approaches 4 from the left, the denominator of X 4 becomes increasingly small while the numerator remains constant. This means that the function's value becomes increasingly large as x approaches 4, eventually resulting in an infinite value. In the same way, as x approaches 4 from the right, the denominator of X 4 becomes increasingly large while the numerator remains constant. This means that the function's value becomes increasingly small, eventually resulting in an infinite value. Thus, the vertical asymptote of X 4 is x = 4.
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What is the coefficient of x² in 3x²?
The coefficient of the variable x² in the expression 3x² is 3
Given that,
The expression is 3x²
To find : The coefficient of the variable x² in the expression
Coefficient is the number that is beside the variable in the equation.
The coefficient of x in 3x² is 3
A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6
As we can see that the term that is in multiplication with x² is 3.
Hence, the coefficient of x² in the equation 3x² is 3.
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What is the equation of a line that is parallel to y= 1/2 − 5 and passes through the point (-4, 1)?
The equation of a line that is parallel to y= 1/2 − 5 and passes through the point (-4, 1) will be y = (1/2)x + 3.
What is the equation of a parallel line?Let the condition of the line be hatchet + by + c = 0. Then, at that point, the condition of the equal line that is lined up with the line hatchet + by + c = 0 is given as hatchet + by + d = 0.
The equation of the line is given below.
y = (1/2)x - 5
The equation of the parallel line to the given line is written as,
y = (1/2)x + d
The equation of the line passing through (-4, 1), then we have
1 = (1/2) × (-4) + d
1 = - 2 + d
d = 3
The condition of a line that is lined up with y= 1/2 − 5 and goes through the point (- 4, 1) will be y = (1/2)x + 3.
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5/8 subtracted by 3/4
Answer:
Step-by-step explanation:
[tex]x_{123} \sqrt{x} x^{2} \alpha \int\limits^a_b {x} \, dx \lim_{n \to \infty} a_n \lim_{n \to \infty} a_n x_{123} \frac{x}{y} \sqrt[n]{x} \sqrt[n]{x} \alpha \sqrt{x} 5#\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \alpha[/tex]√β⇄ΜΒΑςΘWhich quadrilateral has all 4 sides of equal length?
Answer:
Rhombus
Step-by-step explanation:
A rhombus is a type of quadrilateral in which all four sides are of equal length. Also, the diagonals are perpendicular to one another and bisect each other too.
A baseball is hit upwards with a velocity of 60 feet per second. The height of the ball above the ground, in feet, at time t seconds is given by h(t)=-18t^2+60t+4. How long after the ball is hit does it strike the ground?
The ball is hits the ground after 3.4 seconds it strike s
How to determine how long after the ball is hit does it strike the ground?From the question, we have the following parameters that can be used in our computation:
h(t)=-18t^2+60t+4.
Rewrite as
h(t) = -18t² + 60t + 4
When the ball hits the ground, we have
h(t) = 0
So, the equation becomes
-18t² + 60t + 4 = 0
Divide through by 2
-9t² + 30t + 2 = 0
So, we have
9t² - 30t - 2 = 0
Using a graphing tool, we have
t = 3.4
Hence, the time is 3.4 seconds
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Your school plans to give the freshman class a pizza party if they spend a total of at least $7,000 on
yearbooks and class rings. Each yearbook costs $35 and each class ring costs $60.
Part A: Write an inequality in slope intercept form that best represents this scenario. Make sure to create your
KEY!
Considering the definition of an inequality, the inequality that best represents this scenario is 35x + 60y≥ 7000
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
Inequality in this caseIn this case, you know that:
They spend a total of at least $7,000 on yearbooks and class rings. Each yearbook costs $35 and each class ring costs $60.Being:
"x" the number of yearbook."y" the number of class ring.the inequality that expresses the scenario is
35x + 60y≥ 7000
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What is the equation of a line having a slope of 5 and whose y-intercept is 8?
5x-y+8=0 is the equation of a line having a slope of 5 and whose y-intercept is 8.
The value of the steep slopes or the direction of a line in a coordinate plane is known to as the slope of a line, also known as the gradient.
A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. Mostly on y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.
given information like Slope=m=5 and Y intercept equals c=8,
A line's equation is y=mx+c.
As a result of the information provided, the equation for a line is y=5x+8.
A line must have the equation 5x-y+8=0.
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Deandre wants to measure the height of a tree. He sights the top of the tree, using a mirror that is lying flat on the ground. The mirror Is 31 ft from the tree, and Deandre is standing 7.4 ft from the mirror, as shown in the figure. His eyes are 6 ft above the ground. How tall is the
tree? Round vour answer to the nearest foot
Answer: If Debra, the mirror, and the bottom of the tree are points on the ground all on one line, then the two right triangles are these: LEFT: y and 33 as the legs and unknown hypotenuse. RIGHT: 6 and 9.7 as legs and unknown hypotenuse. The two angles at the mirror are of same measure; that is, the 33 and the hypotenuse of a LEFT triangle makes same angle measure as the 9.7 and the hypotenuse of the RIGHT triangle.
Note, these are two SIMILAR triangles.
y/33 = 6/9.7
In addition, Y = 20.4
highlight%28y=20.4%29
Step-by-step explanation:
plsssssssssssssssss help
Answer:
1/2
Step-by-step explanation:
do trust me on this one if you dare go head
Answer: 1/2
Step-by-step explanation:
Do the rise over run strategy, go up 1 and then right 2