The values of k are 3, – 3 for which roots of the quadratic equation are real and equal.
What is a quadratic equation?
An equation containing one term in which the unknown is squared and no term in which it is raised to a power higher than 2.
Given: 3x² + 2kx + 3 = 0
Comparing with standard quadratic equation ax² + bx + c = 0
a = 3 b = 2k c = 3
Given that the roots of the equation are real and equal
Thus, D = 0
Discriminant D = b² – 4ac = 0
(2k)² – 4.3.3 = 0
4k² – 36 = 0
4k² = 36
k² = 9 taking square root on both sides
k = 3 or k = – 3
Hence, The values of k are 3, – 3 for which roots of the quadratic equation are real and equal.
For more references on quadratic equation, click;
brainly.com/question/17177510
#SPJ4
Latifa writes down a number
She says
If i find the cube root of that number and then quadruple the answer,I get 16
What number did Latifa write down?
Answer:
64?
Step-by-step explanation:
Basically the idea is we suppose the number she thinks of is "x"
She says that if she cube roots the number and then quadruples it (means multiply by 4 I think) she gets 16. We set this up as equation below:
[tex]4\sqrt[3]{x} = 16\\\sqrt[3]{x} = 4\\x = 4^{3}\\ x= 64[/tex]
This is my best guess, not totally sure sorry
Directions: The Johnson family is redesigning their backyard this spring. They want to include a sandbox area,
a swing set area, a patio area, a pool area and a grill area. Their plans for the yard layout in feet is shown in the
figure below. Use the figure and your knowledge of polynomials, perimeter, and area to solve the following:
1) The formula for area is,
⇒ Area of rectangle = Length × Width
And, The formula for perimeter is,
⇒ Perimeter = 2 (Length + width)
2) An expression for the length of the south side of the yard is,
⇒ Length = (5x + 2) + (x² - 9) + (x² - 7x + 12)
3) The simply expression for the length of the south side of the yard is,
⇒ Length = 2x² - 2x + 5
4) An expression for the perimeter of the pool area is,
⇒ Perimeter = 2 ( (x² + 10) + (8x + 8) )
5) 5) The simply expression for the perimeter of the pool area is,
⇒ Perimeter = 2x² + 16x + 36
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The Johnson family is redesigning their backyard this spring. They want to include a sandbox area, a swing set area, a patio area, a pool area and a grill area.
Now,
1) The formula for area is,
⇒ Area of rectangle = Length × Width
And, The formula for perimeter is,
⇒ Perimeter = 2 (Length + width)
2) An expression for the length of the south side of the yard is,
⇒ Length = (5x + 2) + (x² - 9) + (x² - 7x + 12)
3) The simply expression for the length of the south side of the yard is,
⇒ Length = (5x + 2) + (x² - 9) + (x² - 7x + 12)
= 5x + 2 + x² - 9 + x² - 7x + 12
= 2x² - 2x + 5
4) An expression for the perimeter of the pool area is,
⇒ Perimeter = 2 ( (x² + 10) + (8x + 8) )
5) The simply expression for the perimeter of the pool area is,
⇒ Perimeter = 2 ( (x² + 10) + (8x + 8) )
= 2 (x² + 10 + 8x + 8)
= 2 (x² + 8x + 18)
= 2x² + 16x + 36
Learn more about the rectangle visit:
https://brainly.com/question/2607596
#SPJ1
what is x if 2/9+x=11/18?
Answer:
x = 7/18
Step-by-step explanation:
what is x if 2/9+x=11/18?
2/9 + x = 11/18
x = 11/18 - 2/9
x = 63/162
x = 7/18
check
2/9 + 7/18 = 11/18
11/18 = 11/18
the answer is goodThe value of x is -1/4 Order these expressions from least to greatest:
X
1-x
x-1
-1÷x
Answer:
Step-by-step explanation:
-1 divided by x
1 - x
X - 1
6) Set up and solve an equation to
find x PLEASE SHOW WORK AND ALSO TELL ANSWER I NEED HELP also it is NOT 37.5
Answer:
is not 37.5
it's 25
Step-by-step explanation:
25+25+15+115=180
50+130=180
180=180
Answer:
25°
Step-by-step explanation:
25 + x + 15 = 3x – 10 ( Sum of two opposite interior angles is equal to the exterior angle)
40 + x = 3x - 10
40 + 10 = 3x - x
50 = 2x
[tex]x = \frac{50}{2} [/tex]
x = 25°
A small radio transmitter broadcasts in a 31 mile radius. If you drive along a straight line from a city 41 miles north of the transmitter to a second city 42 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter
On solving the provided question, we can say that the slope's the intersection points are: (20.698, 42.197) and (43.998,16.527), the transmitter is within range between those to points along the line.
what is slope?A line's slope determines how steep it is. A mathematical equation for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two spots. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is employed to express it. The y-intercept is located at a location where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).
city - north at (0,65)
city-east at (59,0)
Slope is m=(-65/59)
[tex]B= y - mx = 65 - (-65/59)(0) = 65[/tex]
The equation of the line between the cities is y = (-65/59)x + 65
[tex]x^2 + ( (-65/50)x + 65) )^2 = 47^2[/tex]
the intersection points are:
(20.698, 42.197) and (43.998,16.527)
The transmitter is within range between those to points along the line.
To know more about slope visit:
https://brainly.com/question/3605446
#SPJ4
what's the equation of a line in slope-intercept form of a line that has a slope of -6 and contains (3,-4)
HELP ME PLEASE!!!!!!
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- 6}(x-\stackrel{x_1}{3}) \implies y +4= -6 (x -3) \\\\\\ y+4=-6x+18\implies {\Large \begin{array}{llll} y=-6x+14 \end{array}}[/tex]
How do you tell what type of triangle it is based on side lengths?
By adding the squares of the triangle's two smaller sides and comparing the result to the square of a largest side, you may determine whether triangle is acute, obtuse, or right.
Define the type of triangle?Equilateral triangle:The equilateral triangle comes first. All three sides of this triangle are the same length, and each angle measures exactly 60 degrees. An equilateral triangle is Triangle A.
A right triangle:This triangle has two acute angles, which are angles smaller than 90 degrees in length, but one right angle (as well as angle which measures 90 degrees). A right triangle is triangle B.
Isosceles triangle:The isosceles triangle is another. This triangle has two sides that are the same length.
Scalene triangle:The scalene triangle comes next. This triangle has three different lengths for its three sides.
Acute triangle:The acute triangle is the next type of triangle and has three acute angles.
Obtuse triangle:The obtuse triangle is the last triangle. Two of the angles of this triangle are sharp, and one of the angles is obtuse, which is defined as being more than 90 degrees.
Thus, by adding the squares of the triangle's two smaller sides and comparing the result to the square of a largest side, you may determine whether triangle is acute, obtuse, or right.
To know more about the type of triangle, here
https://brainly.com/question/1058720
#SPJ4
john is 7 years younger than jane. the sum of their age is 10 years ago was 55 years. how old are they now
Answer: John is 29 years old and Jane is 36 years old.
Step-by-step explanation:
There are many parts to this problem, so let's start by defining John as x and Jane as y.
We know that the sum of their age 10 years ago was 55, which gives us x+y-10=55. The reason we put -10 is because of 10 years ago. If you think about it in terms of now, 10 years back is 55, so now they would be 65 years old. So we can have either x+y-10=55 or x+y=65. For simplicity, I will use x+y=65.
We also know that John is 7 years younger than Jane, which gives x=y-7.
Luckily, we have x defined for us, so we can directly substitute that into our equation.
[tex](y-7)+y=65[/tex] [combine like terms]
[tex]2y-7=65[/tex] [add both sides by 7]
[tex]2y=72[/tex] [divide both sides by 2]
[tex]y=36[/tex]
Now we know that y=36, we can plug that into either equations to find x.
[tex]x+36=65[/tex] [subtract both sides by 36]
[tex]x=29[/tex]
This concludes that John is 29 years old and Jane is 36 years old.
Each square inch of your body has about 6. 5 × 10^2 pores. Suppose the top of your foot has an area of about 2. 0 × 10^1 in. ^2. About how many pores are on the top of your foot?
The number of pores that are on the top of your foot is approximately 13,000 pores on the top of your foot.
To find the number of pores on the top of your foot, we can multiply the area of the top of your foot in square inches by the number of pores per square inch.
The area of the top of your foot is 2.0 x 10^1 in^2 and each square inch of your body has about 6.5 x 10^2 pores. So, the number of pores on the top of your foot can be calculated as:
2.0 x 10^1 in^2 * 6.5 x 10^2 pores/in^2 = 130 x 10^2 pores = 13000 pores
So, there are approximately 13,000 pores on the top of your foot.
Learn more about unit conversions and dimensional analysis here: https://brainly.com/question/18559676
#SPJ4
Are undecidable problems unsolvable?
Therefore , the solution to the given problem of algorithm comes out to be it fall under the category of undecidable questions, which is a subtype of unsolvable problems.
Define algorithm.An algorithm is a process for carrying out a computation or resolving a challenge. Algorithms work as a detailed set of guidelines that lead hardware- or software-based routines through a series of predetermined actions step by step. Algorithms are frequently used in all areas of IT.
Here,
A problem is considered undecidable if there is no algorithm that can be created that will consistently return a true or false answer for each input value.
Only issues that should have a yes-or-no response (such as: does my code contain a bug?) fall under the category of undecidable questions, which is a subtype of unsolvable problems.
Therefore , the solution to the given problem of algorithm comes out to be it fall under the category of undecidable questions, which is a subtype of unsolvable problems.
To know more about algorithm , visit:
https://brainly.com/question/29289479
#SPJ4
How do you tell if a log function is increasing or decreasing?
If the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
What is a logarithmic function?
A logarithmic function is a type of mathematical function that expresses the power to which a given number (the base) must be raised in order to produce a certain value. It is typically written in the form: [tex]f(x) = log_b(x),[/tex] where b is the base of the logarithm.
To determine whether a logarithmic function is increasing or decreasing, you can look at the sign of the derivative of the function. If the derivative is positive, the function is increasing; if the derivative is negative, the function is decreasing.
In the case of logarithmic functions, the derivative of [tex]f(x) = log_b(x)[/tex] is f'(x) = 1/x*ln(b), which is always positive for x > 0, so the logarithmic function is increasing for any base b.
Hence, if the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
To learn more about the logarithmic functions, visit:
https://brainly.com/question/13473114
#SPJ4
If the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
What is a logarithmic function?
A logarithmic function is a type of mathematical function that expresses the power to which a given number (the base) must be raised in order to produce a certain value. It is typically written in the form: [tex]f(x)=log_b(x)[/tex]. where b is the base of the logarithm.
To determine whether a logarithmic function is increasing or decreasing, you can look at the sign of the derivative of the function. If the derivative is positive, the function is increasing; if the derivative is negative, the function is decreasing.
In the case of logarithmic functions, the derivative of [tex]f(x)=log_b(x)[/tex]. is f'(x) = 1/x*ln(b), which is always positive for x > 0, so the logarithmic function is increasing for any base b.
Hence, if the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
To learn more about the logarithmic functions, visit:
brainly.com/question/13473114
#SPJ4
Deshaun deposits $4,000 into an account that pays simple interest at an annual rate of 6% . He does not make any more deposits. He makes no withdrawals until the end of 2 years when he withdraws all the money.
After 2 years, Deshaun will have earned $4,000 * 6% = $240 in interest.
The total amount of money in the account at the end of 2 years will be $4,000 + $240 = $4,240. This is the amount Deshaun will withdraw.
expert that helps you learn core concepts.
See Answer
Raul works at a movie theatre. The function f(x) represents the amount of money Raul earns per ticket, where x is the number of tickets he sells. The function g(x) represents the number of tickets Raul sells per hour, where x is the number of hours he works. Show all work to find f(g(x)), and explain what f(g(x)) represents.
f(x) = 2x2 + 16
g(x) = √5x^3
The required function that gives [tex]f(g(x))[/tex] that represents the total amount of money Raul earned is
[tex]f(g(x)) = 10x^{3}+16[/tex]
What is a function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
Mostly functions are written as f(x) where x is the input of the function.
Given,
[tex]f(x) = 2x^{2}+16[/tex]
[tex]g(x)[/tex] = [tex]\sqrt{5x^{3} }[/tex]
If [tex]f(x)[/tex] represents amount of money Raul earns per ticket and [tex]g(x)[/tex] represents number of tickets Raul sells per hour, where x is the number of hours he works, then,
[tex]f(g(x))[/tex] represents the total amount of money Raul earned in a day.
To find [tex]f(g(x))[/tex], substitute value of [tex]g(x)[/tex] in the place of x in function [tex]f(x)[/tex] .
[tex]f(g(x))[/tex] = [tex]f[/tex]([tex]\sqrt{5x^{3} }[/tex])
= 2( [tex]\sqrt{5x^{3} }[/tex])² +16
= 10x³ + 16
Therefore the required function is [tex]f(g(x)) = 10x^{3}+16[/tex].
To learn more about functions, follow the link.
https://brainly.com/question/25638609
#SPJ4
please help me !!
literally struggling right now !!
For each object, choose an appropriate scale for a drawing that fits on a regular sheet of paper.
Objects (A-E)
Scales (1 - 7)
А
Scales
AA person
1. 1:17
B A footballfeld (220 yards by 53 yards)
2. 1 cm: 1m
c The state of Washington (about 240 miles by 380 miles) 3 1:1000
The floor plan of a house
4. Itimile
E A rectangular farm (5 miles by 2 mile)
5 1:100,000
& 1 mm 1 km
7. 1:10,000,000
B
С
E
The appropriate scale for a drawing are-
2) 1 cm: 1 m 3) 1:10005) 1:100,0001) 1 in: i ft4) 1 ft : 1 mileExplain the term scale of drawing?When ever a drawing is said to be "to scale," it signifies that each piece is proportionate to the genuine or hypothetical entity; it may be smaller or larger by a specific amount.The scale describes the actual length that each length just on scale graphic corresponds to.The appropriate scale for a drawing that fits on a regular sheet of paper
A. A person : 2) 1 cm: 1m B. A football field (120 yards by 5 1/3 yards) : 3) 1:1000C. The state of Washington (about 240 miles by 360 miles) : 5) 1:100,000D. The floor plan of a house : 1 in: i ftE. A rectangular farm (6 miles by 2 mile) : 4) 1 ft : 1 mileTo know more about the scale of drawing, here
https://brainly.com/question/810373
#SPJ4
The correct question is attached-
Identify similarities and differences in finding the volume of cylinders, cones, and spheres.
The volume of the cone is one third the volume of the cylinder.
The volume of a sphere is 2/3 of the volume of a cylinder with same radius, and height equal to the diameter
How to illustrate the information?Similar to a prism, a cylinder has two bases, but they are circles rather than polygons. A cylinder's sides are also curved rather than flat. A cone has a vertex that is not on the base and a single circular base. The sphere is a figure in space with equal distances between each of its points and the center.
The cone's volume is one-third that of the cylinder. A sphere's volume is 2/3 that of a cylinder with the same radius, and its height is equal to its diameter.
Learn more about cone on:
https://brainly.com/question/28109167
#SPJ1
What are the two types of angles?
The two types of Angles of the triangle are Acute Angle ( angle that are less than 90 degree) and Obtuse Angle ( angle between 90 and 180 degree ).
What are Angles ?
The Angle is defined as the geometrical shape that is constructed by joining two rays to each other at their end points.
The two types of angles of the triangle are Acute Angle and Obtuse Angle :
(i) Acute Angle :
An angle can be called as Acute if the measure of the angle is less than 90 degree .
(ii) Obtuse Angle :
an angle can be called as Obtuse if the measurement of the angle is greater than 90 degree and less than 180 degree .
Learn more about Angles here
https://brainly.com/question/12167245
#SPJ4
a group of classmates surveyed how other students travel to school the results of the survey are shown in the table at right make a circle graph showing the results of the survey using percents, bus- 90, ride bike- 30, ride in car- 75, walk- 45.
So, on solving the provided question, we can say that equation of diagonal WY is 13.03 units
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
by d=√((x2 – x1)² + (y2 – y1)²).
Coordinates of W = (-4,5) and Y = (3,-6)
= √((3 – (-4))² + (-6 – 5)²)
= √170
= 13.03 units
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
The start of an arithmetic sequence is shown below.
Work out the nth term
Work out the 30th term in this sequence.
4 - 13 - 22 - 31
Therefore , the solution of the given problem of arithmetic mean comes out to be a(30) = 265.
Define arithmetic mean.When all of the values in a set of data have the same unit of measurement, such as when all of the numbers are heights, miles, hours, etc., this technique is utilized. Take the numbers 4, 7, 9, and 10 as an illustration. The count of numerals is 4, and the sum of the numbers is 30. 30 divided by 4 equals 7.5, which is the numbers' arithmetic mean.
Here,
Given that there is a common difference between each word, this is an arithmetic sequence. In this instance, the following term is obtained by adding 9 to the phrase before it in the sequence.
Alternatively put,
=> an=a1+d(n−1)
.Arithmetic Sequence:
d=9
This is the formula of an arithmetic sequence.
=>an=a1+d(n−1)
Substitute in the values of
=> a1 =4 and
d=9
.=>an=4+9(n−1)
Simplify each term.
Tap for more steps...
an=4+9n−9
Subtract 9 from 4
an=9n−5
Thus 30th term :
=> a(30)=9(30)−5
=> a(30) = 265
Therefore , the solution of the given problem of arithmetic mean comes out to be a(30) = 265.
To know more about arithmetic mean , visit
https://brainly.com/question/13000783
#SPJ1
Adam and Kim are paid an hourly rate at their jobs. Adam earns $186 for 8 hours of work, before taxes. The table below shows the amount
Kim earns, before taxes.
Who earns the most money per hour and by how much?
A.Adam earns $5.25 more per hour than Kim.
B.Kim earns $5.25 more per hour than Adam.
C.Adam earns $42.00 more per hour than Kim.
D.Kim earns $42.00 more per hour than Adam.
H 3,7,12
$ 54,125,216
Therefore the correct answer is A. Adam earns $5.25 more per hour than Kim.
Define percentage.A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Define Fraction.Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
Adam earns $186 for 8 hours of work, so his hourly rate is $186/8 = $23.25 per hour
Kim earns $54 for 3 hours of work, so her hourly rate is $54/3 = $18.00 per hour
Kim earns $125 for 7 hours of work, so her hourly rate is $125/7 = $17.86 per hour
Kim earns $216 for 12 hours of work, so her hourly rate is $216/12 = $18.00 per hour
Adam earns $23.25 per hour and Kim earns $18.00 per hour on average.
Adam earns $23.25 - $18.00 = $5.25 more per hour than Kim.
Therefore the correct answer is A. Adam earns $5.25 more per hour than Kim.
To know more about Ratio visit:
brainly.com/question/13419413
#SPJ1
The average price for houses in the area is $280,000, and the standard deviation is $12,000. What is
the price of a house whose z score is 2.5?
When working with a normal distribution, you can use the z-score to determine how many standard deviations away from the mean a certain data point is.
Given that the average price for houses in the area is $280,000 and the standard deviation is $12,000, we can use the z-score formula to find the price of a house whose z-score is 2.5:
z = (x - mu) / sigma
where x is the price of the house, mu is the mean price of houses in the area, and sigma is the standard deviation of the price of houses in the area.
In this case, we are looking for the value of x, which is the price of a house whose z-score is 2.5, so we can rearrange the formula to solve for x:
x = (z * sigma) + mu
x = (2.5 * $12,000) + $280,000
x = $350,000
So the price of a house whose z-score is 2.5 is $350,000
It's worth noting that the value of Z-Score 2.5 is considered an outlier, it is usually very rare to find houses that far from the average and standard deviation.
convert 20% profit into profit amount
Answer: To convert 20% profit into a profit amount, you would multiply 20% by the revenue or cost of the item or service.
Let's say,
You have revenue of $1000
So,
20/100 * 1000 = $200
So the 20% profit on the revenue of $1000 is $200.
It's important to note that profit is the amount of money you make after you subtract your costs from your revenue. It's the amount you have left after all the expenses, taxes and other deductions are made.
Step-by-step explanation:
if AG=5x-24 and GB=3x-12, find GB
The value of line GB is 6
How to determine the value of the lineFrom the diagram shown, we can see that AG, GB and AB form a triangle with two of its sides being equal.
Also, line AG = line GB
Where;
Line AG = 5x - 24Line GB = 3x - 12Then, we have;
Line AG = LIne GB
Substitute the expressions, we have;
5x - 24 = 3x - 12
Collect like terms
5x - 3x = - 12 + 24
Add or subtract like terms
2x = 12
Divide both sides by the coefficient of x
x = 12/ 2
x = 6
The, GB = 3(6) - 12 = 6
Hence, the value is 6
Learn more about line segment here:
https://brainly.com/question/17374569
#SPJ1
∆ABC is divided into three smaller triangles and one quadrilateral. Area of ∆AFE is 4, Area of ∆AFC is 9, area of ∆DFC is 7. Find the area of quadrilateral BEFD.
The area of quadrilateral BEFD is 15.32units²
How to find the area of quadrilateral BEFD?Let the area of ∆ABC be A
Let the area of ∆AFE be X
Let the area of ∆AFC be Y
Let the area of ∆DFC be Z
Using Ladder theorem:
1/A + 1/Y = 1/(X+Y) + 1/(Y+Z)
Since X = 4, Y = 9 and Z = 7, we have:
1/A + 1/9 = 1/(4+9) + 1/(9+7)
1/A + 1/9 = 1/13 + 1/16
1/A = 1/13 + 1/16 - 1/9
1/A = 53/1872
A = 1872/53
A = 35.32
area of ∆ABC = area of ∆AFE + area of ∆AFC + area of ∆DFC + area of quadrilateral BEFD
35.32 = 4 + 9 + 7 + area of quadrilateral BEFD
35.32 = 20 + area of quadrilateral BEFD
area of quadrilateral BEFD = 35.32 - 20
area of quadrilateral BEFD = 15.32unit²
Learn more about area of quadrilateral on:
brainly.com/question/22297305
#SPJ1
two electric irons were sold at Rs.1050 each. If one was sold at a loss of Rs.300 and the other at a profit of Rs.450, what was the total cost price? Find the profit or loss
Answer:
Step-by-step explanation:
Selling price of two irons is Rs.1050 each.
Loss on one iron = Rs.300
Profit on second iron = Rs.450
We know that ,
Cost price = Selling price + loss ,when loss is given
and cost price = Selling price - profit ,when profit is given.
therefore, cost price of first iron = 1050 + 300 =1350 rupees
cost price of second iron = 1050 - 450 = 600 rupees
total cost price = 1350 + 600 = 1950 rupees
total selling price = 1050 + 1050 = 2100 rupees
since total cost price < selling price
so, there is a profit of 2100 - 1950 = 150 rupees.
At which points are the equations y = x2 3x 2 and y = 2x 3 approximately equal?
The quadratic equations are approximately equals at the points (0.618,4.236) and (-1.618 , -0.236)
What in mathematics is a quadratic equation?
A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0.
The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem.
we have
y = x² + 3x + 2 .............(a)
y = 2x + 3 ...................(b)
To solve the system of equations equate equation A to equation B
x² + 3x + 2 = 2x + 3
Group terms that contain the same variable
x² + 3x + 2 - 2x - 3 = 0
x² + x - 1 = 0
The formula to solve a quadratic equation of the form ax² + bx+ c is equal to
in this problem we have
x² + x - 1 =0
so, a= 1
b = 1
c = -1
substitute in the formula
x = -1 ± √1² - 4(1)(-1)/2(1)
x = -1 ±√5/2
x = -1+√5/2 = 0.618
x = -1 - √5/2 = - 1.618
Find the values of y
for x = 0.618
y = 2(0.618) + 3 = 4.236
for x = - 1.618
y = 2(-1.618) + 3 = -0.236
Learn more about quadratic equation
brainly.com/question/30098550
#SPJ4
The complete question is -
At which points are the equations y = x2 + 3x + 2 and y = 2x + 3 approximately equal?
Analyzing
K
Which statements correctly describe the properties of heat? Select all that apply.
A. Heat is an essential component of life on Earth.
B. Heat is energy that flows from one object to another.
%
4
&
Prt Scna
Thus , Heat moves from a hotter object to a colder one, which accurately sums up the properties of the heat equation. Energy moves from one item to another in the form of heat.
What is equation?An equation is a mathematical formula that expresses equality by joining two expressions together with the equal symbol =. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. An equal sign is a part of all mathematical formulas, including equations. Often, algebra is used in equations. In mathematics, algebra is employed when we don't know the precise quantity to calculate
Here,
Heat's characteristics
The direction of this transmission is always determined by the temperature differential between the bodies.
To achieve an equilibrium temperature, heat is transferred from the hotter to the cooler body.
As a result of the fact that a body and its surrounds are at different temperatures, we can infer that heat is the energy that is transferred between them.
To know more about equation visit:
brainly.com/question/649785
#SPJ1
Find the equation for the line running
to y = -5x + 5 and passes through the
perpendicular
point (10,7).
let's reword this a bit differently, since it looks jumbled
let's find the equation of a line that is perpendicular to y = -5x + 5, and it also passes through (10 , 7), well, keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-5}x+5\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ -5 \implies \cfrac{-5}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-5} \implies \cfrac{1}{ 5 }}}[/tex]
so we're really looking for the equation of a line with a slope of 1/5 and that it passes through (10 , 7)
[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ \cfrac{1}{5}}(x-\stackrel{x_1}{10}) \\\\\\ y-7=\cfrac{1}{5}x-2\implies {\Large \begin{array}{llll} y=\cfrac{1}{5}x+5 \end{array}}[/tex]
Examine this set of ordered pairs. (7,9), (4,18), (−3,11), (16,18), (4,−11) Is the set of ordered pairs a function? Choose the answer that is entirely correct.
The set of ordered pairs represents the function.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.
Given:
The set of ordered pairs:
(7,9), (4,18), (−3,11), (16,18), (4,−11)
Pairs written as input and output of the relation.
In the attached table,
To prove function:
A relation has an input value which corresponds to an output value. When each input value has one and only one output value, that relation is a function.
And here each input is connected to precisely one output.
Therefore, this is a function.
To learn more about the function;
brainly.com/question/28303908
#SPJ1