To find the discriminant and nature of the roots of a quadratic equation, you can use the quadratic formula.
Write the quadratic equation in the form of ax² + bx + c = 0, where a, b, and c are constants, and x is the variable.
Calculate the discriminant using the formula
b² - 4ac.
Use the discriminant to determine the nature of the roots:
If the discriminant is greater than 0, the roots are real and distinct.
If the discriminant is equal to 0, the roots are real and identical (i.e., the equation has only one root).
If the discriminant is less than 0, the roots are complex and not real numbers.
To find the roots of the quadratic equation, you can use the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a. The plus-minus sign indicates that there are two possible solutions, and the square root of the discriminant is used to find them.
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The chords PQand RS of a circle are produced to meet at T outside the circle. If O is the centre of the circle, show that PTR=½(POR-QOS)
Answer:
hard one goof luck
Step-by-step explanation:
10x-7y=-8 in slope-intercept form
Answer: 10/7x + 8/7
Step-by-step explanation:
Slope intercept form : y = mx + b
10x - 7y = -8
-7y = -10x - 8
7y = 10x + 8
y = 10/7x + 8/7
x-5y=-6
7x-3y=42
Solve each system using substitution
Answer:
Step-by-step explanation:
To solve the system of equations using substitution, we first need to isolate one of the variables in one of the equations. We can start by solving the first equation for y:
x - 5y = -6
y = (x + 6) / 5
Now we can substitute this expression for y into the second equation:
7x - 3y = 42
7x - 3((x + 6) / 5) = 42
Simplifying and solving for x:
(35/5)x - (3/5)x - 18/5 = 42
32x = 210+18
x=57/8
Now we can substitute this value of x back into the first equation to find the value of y:
y = ((57/8) + 6) / 5
y = 21/8
So the solution of the system is (x, y) = (57/8, 21/8).
The dimensions of a beanbag toss target are given in the diagram below.
12 in
24 in
48 in
What is the measure of the angle of incline, 9, of the target? Enter your answer to the nearest degree in the box below.
0=
The angle of incline, of the target θ = 14.036.
What is the formula for the angle of elevation?The angle of elevation or depression can be calculated using the following formula: t a n = O A, where A is the horizontal distance between the observer and the point and O is the length of the side opposite the angle of elevation or depression, or the object's perpendicular distance from the horizontal line.
To calculate the slope percentage, multiply the result by 100 after dividing the height difference between two points by their separation. The rise is the height difference between two locations. The distance between the locations is known as the run. The result is that (rise / run) x 100 is equal to the percent slope.
Given,
the height of triangle = 12in
base of triangle = 48 in
tan θ = perpendicular / base
tanθ = 12/48
θ = tan ⁻¹( 12/48)
θ = 14.036
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Complete question -
the owner of sports complex wants to carpet a hallway connecting two building the carpet costs $1.50 per square foot. how much does it cost to carpet the hallway?
The cost of the carpet is $526.75
What is the area of any shape?
The area of a shape is a measure of the size of the region occupied by the shape. The formula for finding the area of a shape depends on the specific shape being considered
Based on the information given:
The carpet costs $1.75 per square foot
Get the area of the carpet
Area = 24(7) + 7(15) + 0.5(28) + 0.5(28)
Area of the composite figure = 273 + 28
Area of the composite figure = 301 ft²
Cost of the carpet = 301 * 1.75
Cost of the carpet = $526.75
Hence, the cost of the carpet is $526.75
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Answer: the Coat is $526.75
PLEASE HELP!!!
given m=-1 and b=2, which is the equation of the line?
equation of a line : y=mx+b
Answer : y= -1x+2
What is the inverse of a parabola graph?.
Parabola is called as a curve that is formed by the locus of a point whose distance from a fixed point and from a fixed line is the similar.
This set point is called focus, while the fixed line is known as the directrix of parabola.
Parabola does not have any inverse. Let a parabola having equation y = x^2,
it is graph looks like a U-Shaped curve opening up.
Here does not have an inverse as it fails the horizontal line test.
The inverse equation y=√x, only has the positive input values from the domain of parabola.
If we are constrain the domain to be greater than zero, then only it is possible for the function to pass the horizontal line test.
Therefore, Parabola does not have an inverse.
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Van has 45 new baseball cards. He puts them in a binder that holds 9 cards on each page. How many pages dose he fill?
To find out how many pages Van fills with his new baseball cards, we need to divide the total number of cards by the number of cards that fit on each page.
He has 45 baseball cards and each page holds 9 cards.
So, we can divide 45 by 9.
45 / 9 = 5
Therefore, Van fills 5 pages with his new baseball cards.
It's worth noting that this method gives the number of full pages that are filled and if there are any remaining cards, we have to add one more page for the remaining cards.
4. Mariela purchases a used microwave for $50. She marks the price up 60%. If a 5.8% sales tax is also added, what is the final price of the microwave?
Mariela spends $50 on a used microwave. By 60%, she raises the price. When a 5.8% sales tax is additionally included, the ultimate cost is 20 in 60% and 47.1 in 5.8%.
How do you mark up 60%?Cost plus markup % multiplied by cost is the formula used to increase a product's markup percentage. Let's say you're utilising a markup of 60% and the item costs $75. multiplying by 60 percent $75. Now you have $45. For instance, the markup percentage would be 50% if the cost to produce your product was $50 and the selling price was $75: ($75 - $50) / $50 =.50 × 100=50%.
0.6 is 60 hundredths of a unit, thus write it as 0.60. 60% is equal to 60 hundredths. The decimal point can alternatively be shifted two places to the right to find the % equivalent. As a result, the markup equation is now: markup = 100 × (revenue - cost) / cost. Last but not least, use revenue = cost + cost × markup / 100 to determine the selling price.
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A line of 20cm ha 4 point ( A,B,C,D ). Line AB=8. 6cm, Line AD=20cm BC=CD
Work out the length of BC
The length of BC is 5.7 cm
A dot is used to symbolise a point, which is a place in any space (.). It does not have any size, shape, length, or height. A line segment has a beginning and an end, but a line is stretched in both directions towards infinity.
It is given that the length of AB is 8.6 cm and length of AD is 20 cm.
Also, BC=CD
As there are 4 points (A, B, C, D) on the line and the length of the lone is 20 cm, we can say
AB+BC+CD= 20 --------------- (1)
Let us consider that BC=CD= x (say)
Substituting the values in equation (1),
8.6+ x+ x=20
Or, 2x =11.4
Or, x=11.4/2
Or, x=5.7 cm
Therefore, we can say that the length of BC is 5.7 cm.
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What is a 45 degree angle called?.
A 45 degree angle is called an acute angle
There are 5 types of angles according to their measure:
1) Acute angle: it is the one that measures more than 0° and less than 90°.
2) Right angle: an angle that measures 90°.
3) Obtuse angle: an angle measuring more than 90° and less than 180°.
4) Extended angle: an angle measuring 180°.
5) Complete angle: an angle that measures 360°.
What is an angle?An angle is the opening formed by two half-straights (sides) with the same origin called vertex. For example, within a triangle there are three angles, which in total add up to 180°.
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If 4/3 of water are Enough to water 2/5 of the plants in the house, How much water is necessary to water all the Plants in the house? write an equation to represent the situation, and then find find the answer
Amount of water necessary to water all the plants in the house is 10/3.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given that,
Amount of water needed to water 2/5 of plants = 4/3
Equation representing the amount of water needed to water 5/5 of plants = (4/3) / (2/5)
= (4/3) × (5/2)
= 10/3
Hence 10/3 of water is needed to water all the plants in the house.
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There are 67 bikes in the bike
remaining bikes are red.
rack outside a school. Out of all the bikes, 33 are silver. Half of the
Estimate how many bikes are red.
Answer:
17
Step-by-step explanation:
67 minus 33 leaves 34 red bikes but divided that by half gives you 17
help plsssssssssssss
Answer:
-28
Step-by-step explanation:
f(-4) = 5(-4) - 2³ = -20 - 8 = -28
Do the equations 4x 3y 1 5 and 12x 9y 15 represent a pair of coincident lines?.
The given equations do not represent a par of coincident lines. As the equations do not satisfy the conditions.
It is given that the pair of equations are,
4x + 3y - 1 = 5 and 12x + 9y = 15
To determine if the equations represent a pair of coincident lines.
Here we get, a₁ = 4, b₁ = 3, c₁ = -1
a₂ = 12, b₂ = 9, c₂ = -15
So, a₁/a₂ = 4/12 = 3
b₁/b₂ = 3/9 = 3
c₁/c₂ = -1/-15 = 1/15
Therefore,
[tex] \frac{a1}{a2} = \frac{b1}{b2}≠ \frac{c1}{c2} [/tex]
Thus, the given equations do not represent a pair of coincident lines
Now, if you put these equations in any graphing software or here I have used Desmos then you will get the graph (attached image), which further shows that the lines do not coincide.
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WILL MARK BRAINLIEST!! 20 POINTS PLEASE HELP ASAP GEOMETRY!
A person is looking from a car to the top of a building. The angle of elevation to the top of the building from the car is 32°. The building is 200 feet away. How tall is the building? Round to the nearest foot
Answer:
124.29ft (approximately 125ft)
Step-by-step explanation:
Refer to the Image
HELP ME PLEASE!!!!!!!!!!!!!!
Answer:
35
Step-by-step explanation:
35
Answer: 25
Step-by-step explanation:
How many solutions does the nonlinear system of equations graphed below
have?
It depends on the specific nonlinear system of equations. Generally speaking, there could be one or multiple solutions, or there could be no solutions.
What is nonlinear system?A nonlinear system is a system of equations or functions which does not yield a linear relationship or linear solution when solved. A nonlinear system is often difficult to solve due to its inherently complex nature. Nonlinear systems can be found in multiple areas, such as engineering, economics, and mathematics.
If the equations are linear, then there will be exactly one solution. If the equations are nonlinear, then there could be no solutions, one solution, or multiple solutions (including infinitely many solutions). To find the exact number of solutions, you would need to solve the system of equations.
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On March 14 at 1:59, people celebrate Pi Day by eating pie. Why do you
think people celebrate on this day at this time?
Answer:
They celebrated it on March 14 at 1:59 because...
The first few digits of pi are --- 3.14159
The date of March 14 is 3/14. Then you add the 1:59 it makes the first few digits of pi.
Step-by-step explanation:
The tradition to celebrate Pi Day on 14th March started in the late 80's, when the physicist Larry Shaw organized the first Pi Day celebration at the San Francisco Exploratorium. Since then, Pi Day has become a popular way for mathematicians, educators, and students to celebrate and share their interests in mathematics. Many schools, universities, and math clubs around the world host events, such as pi recitation contests, pi-themed games, and pie-eating contests, to celebrate this day.
Eating pie is also a way to join the celebration, as the word "pi" sounds like "pie". People often eat different types of pie on Pi Day, such as pizza pie, sweet pies, and savory pies to celebrate the mathematical constant pi and its connection to the word “pie”.
What system is Y =- 2x 3?.
The equation Y = -2x + 3 is a linear equation in slope-intercept form.
This equation represents a straight line with a slope of -2 and a y-intercept of 3.
The slope -2 tells us that for every unit increase in x, the value of y will decrease by 2. The y-intercept 3 tells us that the line passes through the point (0,3) on the coordinate plane.
It's a line that goes down as the slope is negative and the line can be represented by a graph, that can be easily plotted using the slope and the y-intercept. This equation can be used to model real-world situations like linear regression and many other fields.
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A job hotline service charges $25 plus a 4% commission, c, on the first month of earnings if it finds work for a client. Write an equation that represents the total cost, T, to find a job through the hotline. What is the cost if a client earns $1500 the first month? Please someone help!!!!
im stuck on this question pls, thank you!
Answer: Area = 28.3cm²
Circumference = 18.9cm
Step-by-step explanation:
Area = πr²
= π × 3²
= 28.27
= 28.3cm² (estimate to 3s.f always)
Circumference = 2πr
= 2 x π x 3
= 18.85
= 18.9cm (estimate to 3s.f always)
The area and the circumferences of the circle are 28.27 square meters and 18.85 meters.
Given is a circle with radius 3m we need to determine the area and the circumferences of the circle,
To determine the area and circumference of a circle with a radius of 3m, we can use the following formulas:
Area of a circle: A = πr²
Circumference of a circle: C = 2πr
Here, "r" represents the radius of the circle, and "π" (pi) is a mathematical constant approximately equal to 3.14159.
Let's calculate the values:
Area:
A = πr²
A = 3.14159 x (3m)²
A = 3.14159 x 9m²
A ≈ 28.27 square meters
Therefore, the area of the circle is approximately 28.27 square meters.
Circumference:
C = 2πr
C = 2 x 3.14159 x 3m
C ≈ 18.85 meters
Therefore, the circumference of the circle is approximately 18.85 meters.
Hence the area and the circumferences of the circle are 28.27 square meters and 18.85 meters.
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Is a triangle 180 or 190?.
Answer:
Step-by-step explanation:
180 degrees in total
Ue the entence to anwer the quetion. Mot doctor ay many people who don't get enough leep every night truggle with illne and tre. Which kind of evidence i thi an example of? (1 point)
This kind of evidence is an example of a claim. Hence, the correct answer is option 1.
A claim is a statement or assertion that is made about a particular topic or issue. In this case, the statement is being made by "doctors" and is being presented as evidence of a causal relationship between lack of sleep and negative health outcomes. The statement is not an argument, which would include reasoning or logic to support the claim, nor is it a testimony or excerpt, which would be a statement or quote from a specific person or source.
Option 2, "an argument," is incorrect because it suggests that reasoning or logic is being provided to support the claim. However, in the sentence provided, there is no indication that any reasoning or logic is being presented to support the claim that many people who do not get enough sleep each night suffer from illness and stress. Usually, an argument has a claim and evidence or reasoning to back up that claim.
Option 3, "a testimony or an excerpt," is incorrect because it suggests that a statement or quote is being provided from a specific person or source. However, in the sentence provided, there is no indication of a specific person or source providing the statement. Instead, the statement is being attributed to "doctors" in general rather than any specific individual. A testimony would typically include a statement or quote from a specific person or source, given under oath or affirmation in a formal legal setting.
This question should be provided as:
Use the sentence to answer the question. Most doctors say many people who don't get enough sleep every night struggle with illness and stress. Which kind of evidence is this an example of? Responses:
A claim An argument A testimony or an excerptThe correct answer is option 1.
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You and your friend enter a drawing with 3 different prizes. A total of 15 people entered the drawing, and prizes are awarded randomly.
There are 2730 ways to award the prizes.
What is the probability that you win first prize and your friend wins second
prize?
A. 1/2730
B. 15/2730
C. 1/15
D. 13/2730
The probability that you win first prize and your friend wins second
prize is option D: 13/2730.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
Total number of prizes awarded = 3
Number of people entering the drawing competition = 15
Number of ways to award the prize = 2730
Out of the 3 prizes the first and the second is needed.
So, the prize for the first and the second positions are fixed and there is no need to consider the remaining 13 people to win the prize.
Hence the remaining number of people who can win the 3rd prize = 13
The number of ways one of them wins the 3rd prize = 13
The total number of ways = 2730
Therefore, the probability of the first 2 prizes fixed and the remaining 3rd awarded to the rest of the 13 people is 13/2730.
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The price of a TV i £260
In a ale the price i decreaed by 20%
Work out the price of the TV in the ale
The price of the TV is £208.
given the initial price of the TV as £260
now the Percentage rebate on TV is 20%
so the rebate is given by
=> 20 /100 * 260
=> 2 *26
=> 52
so total off on the TV is £52
Actual price of the TV is £260 - £52 = £208
Describe percentage rebate:An initial product or service price reduction that is expressed as a percentage of the original price is known as a percentage rebate. It is a technique for providing a discount or incentive to clients, and it is typically provided for a brief period of time or on particular goods or services. For instance, a 10% rebate on a product would entitle the buyer to a 10% discount off the list price.
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associative property commutative property distributive property
Different properties, significance of those properties and their applications in mathematics.
Associative property : Associative law states that the order of grouping the numbers does not matter. This law holds for addition and multiplication but it doesn’t hold for subtraction and division. This can be observed from the following examples.
Addition:
a+ (b+c) = (a+b) + c
Subtraction:
a-(b-c) ≠ (a-b) – c.
Multiplication:
a x (b x c) = (axb) x c
Division:
a ÷ (b ÷ c) ≠ (a ÷ b) ÷ c
Distributive property : This property is used to eliminate the brackets in an expression. The distributive property states that each term inside the bracket should be multiplied with the term outside. This property is very useful while simplifying the expressions and solving the complicated equations.
Addition:
a(b+c) = ab + ac
Subtraction :
a(b-c) = ab – ac
Commutative property : This property states that there is no change in result though the numbers in an expression are interchanged. Commutative property holds for addition and multiplication but not for subtraction and division.
Addition:
a+b = b+a.
Subtraction:
a-b ≠ b-a.
Multiplication:
a x b = b x a
Division:
a ÷ b ≠ b ÷ a.
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4/9of the spectators in a football match are males. If 200 of them are females, how many spectators are there in the competition?
4/9 of the spectators in a football match are males. If 200 of them are females, then the total number of spectators is 360.
What is the proportion?
A proportion is two ratios that have been set equal to each other; a proportion is an equation that can be solved. When I say that a proportion is two ratios that are equal to each other, I mean this in the sense of two fractions being equal to each other. For instance, 5/10 equals 1/2.
Given that 4/9 of the fans in a football match are men and 200 are women. We must determine the total number of spectators at the football game.
If 4/9 of the total spectators are men, the remaining 5/9 are women.
Let x be the total number of spectators.
Mathematically,
5/9 of x = 200
5/9 × x = 200
5x = 1800
X = 360
As a result, the total number of spectators is 360.
The number of male spectators may also be calculated.
Males + Females = Total number of spectators
360 = Males + 200
Males = 160
Therefore, 4/9 of the spectators in a football match are males. If 200 of them are females, then the total number of spectators is 360.
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Why is addition commutative and subtraction is not?.
Addition is commutative because the order in which two numbers are added does not affect the result.
Commutative property is applicable only for addition and multiplication processes. Thus, it means we can change the position or swap the numbers when adding or multiplying any two numbers.
Addition is commutative because the order in which two numbers are added does not affect the result. For example, 1 + 2 = 2 + 1 = 3. In contrast, subtraction is not commutative because the order in which two numbers are subtracted does affect the result. For example, 1 - 2 = -1, but 2 - 1 = 1. The operation is different when the order of the numbers are changed.
so, addition is commutative because the order in which two numbers are added does not affect the result.
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Samuel bought a 0.9-liter box of juice and two cans of juice, 350 ml each. What is the total volume of the juice he bought?
Answer:
1.6 L or 1600 mL
Step-by-step explanation:
You want to know the total volume of one 0.9 L box and two 350 mL boxes.
UnitsThe units are related by ...
1 L = 1000 mL
VolumeThen the volumes of the given boxes are ...
0.9 L = 900 mL
350 mL = 0.35 L
You can add the volumes in either of the like units:
900 mL + 2 × (350 mL) = 1600 mL
0.9 L + 2 × (0.35 L) = 1.6 L
The total volume of the juice boxes is 1.6 L or 1600 mL.
__
Additional comment
You can convert the units a couple of ways.
Multiply the unit equivalence equation by an appropriate factor:Because the fraction has equal measures in the numerator and denominator, it does not change the size of the volume. It only changes the units of the volume.
