Final answer:
To find the quadratic equation with roots 5 and -2, we can use the quadratic formula. Substituting the values of the roots into the formula, we get the equation (x - 5)(x + 2) = 0.
Explanation:
A quadratic equation in standard form is written as ax² + bx + c = 0, where a, b, and c are constants. To find the equation with roots 5 and -2, we can use the fact that the solutions of a quadratic equation are given by the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).
Substituting the values of the roots into the quadratic formula, we have:
x = (-b ± √(b² - 4ac)) / (2a)
For the first root, x = 5:
5 = (-b ± √(b² - 4ac)) / (2a)
Substituting a = 1, b = -7, and c = 10, we get:
5 = (-(-7) ± √((-7)² - 4(1)(10))) / (2(1))
Simplifying further:
5 = (7 ± √(49 - 40)) / 2
5 = (7 ± √9) / 2
5 = (7 ± 3) / 2
So, the first root gives us the equation:
x = 5, which translates to x - 5 = 0.
For the second root, x = -2:
-2 = (-b ± √(b² - 4ac)) / (2a)
Substituting a = 1, b = -7, and c = 10, we get:
-2 = (-(-7) ± √((-7)² - 4(1)(10))) / (2(1))
Simplifying further:
-2 = (7 ± √(49 - 40)) / 2
-2 = (7 ± √9) / 2
-2 = (7 ± 3) / 2
So, the second root gives us the equation:
x = -2, which translates to x + 2 = 0.
Therefore, the quadratic equation in standard form with roots 5 and -2 is:
(x - 5)(x + 2) = 0
The number of days between Aug. 9 and Jan. 3 is
How do I find dy/dx of the equation 4x^3-3xy^2+y^3=28 at the point (3,4)?
To find dy/dx of the equation 4x^3 - 3xy^2 + y^3 = 28 at the point (3,4), you can use implicit differentiation and solve for dy/dx.
Explanation:To find dy/dx of the equation 4x^3 - 3xy^2 + y^3 = 28 at the point (3,4), we need to use implicit differentiation. We differentiate both sides of the equation with respect to x, treating y as a function of x. Thus, we get:
12x^2 - 3y^2 - 3x(2y(dy/dx)) + 3y^2(dy/dx) = 0
Now we substitute x = 3 and y = 4 into the equation and solve for dy/dx:
12(3)^2 - 3(4)^2 - 3(3)(2(4)(dy/dx)) + 3(4)^2(dy/dx) = 0
Paco buys a carton of eggs. the carton has 2 rows of eggs. there are 6 eggs in each carton. how many eggs are in the carton
The total number of eggs in the carton is 12, as there are 2 rows with 6 eggs each, and you calculate the total by multiplying these two numbers.
Paco buys a carton with 2 rows of eggs and there are 6 eggs in each row.
To find the total number of eggs in the carton, you multiply the number of rows by the number of eggs in each row: 2 rows× 6 eggs per row equals a total of 12 eggs in the carton.
So, in this case, the number is 12, and the unit is eggs.
1. A bag of chips costs $3.79 including tax Mr.Connor wants to purchase chips for his class and has a $15 budget. Write and inequality to solve for the number of bags of chips Mr.Connor can purchase with his budget
A. $15x > $3.79
B.$15x < $3.79
C $3.79 > $15
D. $3.79 < $15
(There is a flat line under all the greater than and less than signs)
2. A cab charges $1.75 for the first mile $0.25 for each additional mile. Write and solve an inequality to determine how many miles eddie can travel if he has $15
A. $1.75 + $0.25x < $15; x < 53 miles
B. $1.75 + $0.25x > $15; x >53 miles
C. $0.25 + $1.75x < $15; x< 8 miles
D.$0.25 + $1.75x > $15; x > 8 miles
what is the solution set of the equation?
8/x+2=(x+4)/(x-6)
a. {-12,4}
b. {12}
c. {4,6}
d. {-4,12}
What is the solution to the system of linear equations
A. (-3,0)
B. (-3,3)
C. (0,2)
D. (3,1)
What number represents the same amount as 2 hundreds 14 tens 3 ones
The representation of the given number will be given below such that it sum should be 343.
What is summation?A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities. Here are always an integer number of terms in a summation.
There might simply be two terms, but there might also be 100,000 or a million. Summations exist with an infinite number of parameters.
The summation is to add or subtract any two or more terms by doing the operation.
The representation of 200, 14, and 3 will be
200 hundred
14 tens
+ 3 ones
--------------------
343
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PRE-ALGEBRA HELPPPP!!
Answer:
yeet
Step-by-step explanation:
how do i work out sinx+2sinxcosx=0 in radians?
jika f(x)= 1/2 x - 1 dan g(x)= 2x 4. Maka nilai (gof)^-1 (10) adalah ...
a. -9
b. -8
c. 8
d. 9
e. 10
the area of a rectangle is 15x^2y^5. if the length is 5xy^3, what is the width?
Find equation of the axis of symmetry of Y= -3x^2+12x-7
oli has a volume of 9000cm3 and a density of 0.8g/cm3
what is the mass of the oil
for tomoz plz help
Translate the phrase into a math expression.
Twenty divided by the sum of 4 and 1.
(1+4) ÷ 20
20 ÷ (1+4)
1 + (4÷20)
(20÷4) + 1
Answer:
[tex]\displaystyle 20 \div (1 + 4)[/tex]
Explanation:
It is EXACTLY how it sounds, and of course, you must include grouping symbols to separate both parts of the expression.
I am joyous to assist you anytime.
SOLVE. integration of (1-v) /(1+v^2)
Answer:
[tex]tan^-1( v) - \frac{1}{2} ln(1+{v}^2) +c[/tex] is the answer.
Step-by-step explanation:
∫[tex]\frac{1-v}{1+{v}^2} \\\frac{1}{1+{v}^2}- \frac{v}{1+{v}^2}}[/tex]
∫[tex]\frac{dv}{1+{v}^2}[/tex]-∫[tex]\frac{2v}{1+{v}^2}[/tex]dv
[tex]{tan}^{-1} (v)-\frac{1}{2} ln(1+{v}^2) +c[/tex]
Latonya bought flowers for her mother. She spent $45. Each tulip was $1 and each rose was $2. She bought 3 more tulips than roses.
Let t be the number of tulips. Which algebraic sentence would help you figure out how many tulips Latonya bought?
A. t + 2(t + 3) = 45
B. t + 2(t – 3) = 45
C. 2t (t + 3) = 45
D. -3t + 2t = 45
In ∆ABC shown below, ∡BAC is congruent to ∡BCA. Given: Base ∡BAC and ∡ACB are congruent.
Prove: ∆ABC is an isosceles triangle.
Construct a perpendicular bisector from point B to line segment AC.
Label the point of intersection between this perpendicular bisector and line segment AC as point D.
m∡BDA and m∡BDC is 90° by the definition of a perpendicular bisector.
∡BDA is congruent to ∡BDC by the definition of congruent angles. Line segment AD is congruent to line segment DC by _______1________.
∆BAD is congruent to ∆BCD by the _______2________. Line segment AB is congruent to line segment BC because corresponding parts of congruent triangles are congruent (CPCTC).
Consequently, ∆ABC is isosceles by definition of an isosceles triangle.
options are:
a)1. Angle-Side-Angle (ASA) Postulate
2. corresponding parts of congruent triangles are congruent (CPCTC)
b) 1. corresponding parts of congruent triangles are congruent (CPCTC)
2. Angle-Side-Angle (ASA) Postulate
c) 1. the definition of a perpendicular bisector
2. Angle-Side-Angle (ASA) Postulate
d) 1. corresponding parts of congruent triangles are congruent (CPCTC)
2. the definition of a perpendicular bisector
Refer to the image attached.
Given: [tex]\angle BAC[/tex] and [tex]\angle BCA[/tex] are congruent.
To Prove: [tex]\Delta ABC[/tex] is an isosceles triangle.
Construction: Construct a perpendicular bisector from point B to line segment AC. Label the point of intersection between this perpendicular bisector and line segment AC as point D.
Proof:
Consider [tex]\Delta BDA, \Delta BDC[/tex]
[tex]\angle BDA = \angle BDC= 90^\circ[/tex]
(By the definition of perpendicular bisector)
[tex]AD=DC[/tex] (By the definition of perpendicular bisector)
So, Line segment AD is congruent to DC by the definition of perpendicular bisector.
[tex]\angle BAC[/tex] = [tex]\angle BCA[/tex] (given)
So, [tex]\Delta BDA \cong \Delta BDC[/tex] by ASA congruence postulate.
∆BAD is congruent to ∆BCD by the ASA congruence Postulate.
Line segment AB is congruent to line segment BC because corresponding parts of congruent triangles are congruent (CPCTC).
So, Option C is the correct answer.
If x2 − 8xy + 12y2 = 8 and x − 6y = 3, then x − 2y =
Tom gets $12 off a box of chocolates that had an original price of $48. What percentage is the discount ?
A highway map of Ohio has a coordinate grid superimposed on top of the state. Springfield is at point (1, –4) and Columbus is at point (7, 1). The Springfield youth soccer team is going to Columbus to see a professional soccer match. The map shows a highway rest area halfway between the cities. What are the coordinates of the rest area? What is the distance between Springfield and Columbus? (One unit = 5.38 miles)
"The graph below shows the population of mice in an ecosystem where the mice are not allowed to enter or leave.
Which best describes the population at point A?
A.The death rate is higher than the birthrate.
B.The population is decreasing.
C.The birthrate is higher than the death rate.
D.It has reached carrying capacity"
The point marked A is the point where the birth rate is higher than the death rate.
What is birth rate/ death rate?The term birth rate refers to the rate at which new organims are introduced into the population and the death rate refers to the rate at which individuals exit in the population.
In this case, when we observe the graph, we can see that the point marked A is the point where the birth rate is higher than the death rate.
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what is the domain of the composite function G ( F ( x ) )
Which of the following best describe perpendicular lines? A.lines that are not in the same plane B. Lines that meet at a 90* angle C. Lines that meet at a 45' angle D. Lines that are coplanar and do not intersect
A line is said to be perpendicular to another line if the two lines intersect at a right angle. An angle is said to be a right angle if its measure is 90 degrees.
The question is asking us to select the option which best describes a perpendicular lines.Among all the options given option B states :Lines that meet at a 90* angle.
Option B is the right answer.
The perpendicular lines are those lines that meet at a 90* angle. That is option B.
Perpendicular linesPerpendicular lines are those lines that meet at an angle of 90°. To further explain the perpendicular lines, a diagram above is used.
Line AB is perpendicular to XY because AB and XY intersect each other at 90°.
Some of the characteristics of perpendicular lines include:
These lines always intersect at right angles.Adjacent sides of a square and a rectangle are always perpendicular to each otherTherefore, perpendicular lines are those lines that meet at a 90* angle.
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Can someone help me...again?
The cost of a service call to fix a washing machine can be expressed by the linear function y=45x+35 where y represents the total cost and x represents the number of hours it takes to fix the machine. What does the slope represent?
a-the cost for each hour it takes to repair the machine
b=the cost for coming to look at the machine
c-the total cost for fixing the washing machine
d-the amount of time that it takes to arrive at the home to make the repairs
Answer:
The slope represents the cost for each hour it takes to repair the machine.
Step-by-step explanation:
We are given that the cost of a service call to fix a washing machine can be expressed by the linear function
[tex]y=45x+35[/tex]
Where
y=Total cost of a service to fix the machine.
x=Number of hours takes to fix the machine
We have to find that slope in this function what represents.
General equation of line is given by
[tex]y=mx+c[/tex]
Where m=Slope of line
c=y- intercept
Comparing the general equation with the given function
We get m=45,c=35
m=45 represents the cost for each hour it takes to repair the machine because when number of hours multiplied by 45 then we get total cost of x hours.
Hence, the slope represents the cost for each hour it takes to repair the machine.
Does this set of ordered pairs represent a function? Why or why not?
{(–2, 2), (–1, 2), (3, –1), (3, 1), (4, 11)}
A. Yes, because there are two x-values that are the same.
B. No, because two of the y-values are the same.
C. Yes, because every x-value corresponds to exactly one y-value.
D. No, because one x-value corresponds to two different y-values.
Find the measure of an angle whose measure is 18 degrees less than one-half of the measure of its complement.
If x represents the measure of the angle, then which of the following expressions would equal x?
90 - (0.5x - 18)
0.5(90 - x - 18)
0.5(90 - x) - 18
Answer:
The answer is C, 0.5(90 - x) -18
Step-by-step explanation:
tan^4x-sec^4x=1-2 sec^2(x)
verify
A radio commercial for a loan company states: “You only pay $0.29 a day for
each $500 borrowed.” If you borrow $1,500 for 120 days, what amount will you
repay, and what annual interest rate is the company actually charging?
Write an equation that models the sequence 400, 200, 100, 50, ...