Landscaping : You are planting a tree at the incenter of your triangular front yard. Use the diagram to determine how far the tree is from the house.
Answers
The hypotenuse of the triangle is equal to 14.14 feet, and thus the distance of the tree from the house is 14.14 feet.
What is triangle?Triangle is a three-sided, two-dimensional shape with three angles. It is one of the basic shapes in geometry and is formed by connecting three straight lines. Triangles can be classified based on their angles and sides. An equilateral triangle has all three sides equal in length and all three angles are equal. An isosceles triangle has two sides equal in length and two angles equal. An scalene triangle has all three sides and angles different in length and measure.
In order to determine the distance of the tree from the house, the Pythagorean theorem can be used. The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side (hypotenuse).
Looking at the diagram, the sides of the triangle are 10 feet, 10 feet, and 12 feet. If we label the sides as a, b, and c, then we can use the Pythagorean theorem to solve for c:
a2 + b2 = c2
102 + 102 = c2
100 + 100 = c2
200 = c2
√200 = c
Therefore, the hypotenuse of the triangle is equal to 14.14 feet, and thus the distance of the tree from the house is 14.14 feet.
To know more about triangle click-
https://brainly.com/question/1058720
#SPJ1
Related Questions
Question Joe is climbing the ladder and stops when his feet are vertically 3.2 feet above the ground and horizontally 2.4 feet from the base of the ladder. Which equation represents this new situation and can be used to find how far Joe climbed up the ladder? Select the correct answer. 3.2 + 2.4 = c 3.22 + 2.42 = c2 3.22 + b2 = 2.42 a2 + 2.42 = 3.22
Answers
The distance Joe climbed up the ladder is c.
3.22 + b2 = 2.42 is the correct equation.
What is the Pythagoras theorem?
The Pythagorean theorem is a fundamental concept in geometry and mathematics, named after the ancient Greek mathematician Pythagoras. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).
3.22 + b2 = 2.42 is the correct equation that represents the situation of Joe's position on the ladder. It uses the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the ladder) is equal to the sum of the squares of the lengths of the other two sides (the horizontal and vertical distances from the base of the ladder to Joe's feet). In this case, c is the distance that Joe climbed up the ladder, and b and a are the horizontal and vertical distances, respectively.
So, by solving the equation:
3.22 + b2 = 2.42
b = √ (2.42 - 3.22)
Then use the Pythagorean theorem again to find the length of the ladder (c)
c = √(3.22 + b^2)
Hence, the distance Joe climbed up the ladder is c.
To learn more about the Pythagoras theorem, visit:
https://brainly.com/question/343682
#SPJ1
Find the mean of the data in the dot plot below.
\text{ cm} cmstart text, space, c, m, end text
Answers
The mean of the data in the dot plot is equal to 1.6.
What is a dot plot?In Mathematics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.
Based on the dot plot, the number of jokers include the following:
Number of jokers frequency
0 1
1 1
2 2
3 1
Next, we would determine the total number of jokers as follows;
Total number of jokers = 0 + 1 + 2 + 2 + 3
Total number of jokers = 8
Now, we can calculate the mean of the data as follows;
Mean = F(x)/n
Mean = 8/5
Mean = 1.6.
Read more on dot plots here: brainly.com/question/18466974
#SPJ1
Which of the following can be the sides of a right triangle?
2.5 cm, 6.5 cm, 6cm
In the case of right angled triangles, identify the right angles.
Answers
So, none of these sides can be the sides of a right triangle.
In a right triangle, one of the sides is the hypotenuse and the other two sides are called legs. The hypotenuse is always the longest side and the side opposite the right angle. The two legs are the shorter sides and the sides that form the right angle.
In the given triangle 2.5 cm, 6.5 cm, 6cm none of these sides can be the sides of a right triangle because according to the Pythagorean theorem, In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
So, for a right angled triangle with legs of 6cm and 6.5cm the hypotenuse must be greater than 6.5cm and smaller than sqrt(6^2 + 6.5^2) = 8.66cm but the hypotenuse is 2.5cm which is less than 6.5 cm. So it is not a right triangle.
It is important to note that in a right triangle, one of the angles is always 90 degrees and is called the right angle. The side opposite to the right angle is the hypotenuse and the other two sides are the legs.
To learn more about Right Angled Triangle
Visit; brainly.com/question/3770177
#SPJ4
Drag each length to the correct location on the triangle. Each length can be used more than once, but not all lengths will be used.
What are the missing side lengths of the triangle?
5√2
2.5
10
5
5√3
45°
Reset
5
Next
45°
Answers
The measure of the missing side lengths of the triangle is adjacent side = 5 and hypotenuse = 5√2.
What are trigonometric ratios?
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle.
To find the side of a right triangle:
A right-angle triangle has one of its angles as 90 degrees.
Therefore,
using trigonometric ratios,
tan 45 = opposite/adjacent
tan 45 = opposite / 5
opposite side = (tan 45) * 5
opposite side = 1 * 5 = 5
Therefore,
adjacent side = 5
sin 45 = opposite / hypotenuse
1/√2 = 5 / hypotenuse
hypotenuse = 5√2 /1
hypotenuse = 5√2
Hence, the missing side lengths of the triangle are adjacent side = 5 and hypotenuse = 5√2.
To learn more about the right triangle visit,
https://brainly.com/question/13276558
#SPJ1
what must you include in every confidence argument you write in order to receive full points and have a complete argument? (check all that apply.)
Answers
Things that must you include in every confidence argument you write in order to receive full points and have a complete argument are:
Discussion of the R^2 value and its meaning. Description of how well you think the line fits the points visually.Discussion of how far into the future/past you are predicting away from the data.Real world support. (This is support that explains why you believe the trend will - or won't! - continue in the future.)Confidence argument is An explanation for why there should be confidence is emphasized in a confidence argument (a case mostly supported by evidence that a process is safe).
The system's overall assurance case must have certain elements in a confidence argument. This contains:
discussion of the significance of the R2 value.Describe how well you believe the line visually fits the points.Talk about how far you can extrapolate the data's results into the past or future.real-world assistance.There must be enough belief in the reliability of the proposed solution.There must be sufficient assurance in the proper application of the alleged solution.Authentic backing for proposed solutionsLack of assurance for claimed remedies. In other words, reliability has been establishedYour question is incomplete but most probably your full question attached below
Learn more about argument athttps://brainly.com/question/9895066
#SPJ4
How are exponential and logarithmic functions related?
Answers
The relation between logarithmic function and exponential function is they both are inverse of each other.
As given in the question,
Relation between logarithmic function and exponential function is given by:
Logarithmic function is inverse of the exponential function.Logarithmic function is represented by x = logₐ⁰ y.Exponential function is represented by y = aˣ .We can replace 'a' by 'e'.In exponential function a⁵ × a⁷ = a⁵ ⁺ ⁷.In logarithmic function log ( 5 × 7 ) = log 5 + log 7.Therefore, relation between the logarithmic function and the exponential function is that both are inverse of each other.
Learn more about logarithmic here
brainly.com/question/30085872
#SPJ4
The letters from the word FOOTBALL are written on 8 cards with one letter on each card. One card will be drawn randomly and then placed back into the stack. If this experiment is repeated 840 times, about how many times should you expect to draw a consonant?
Answers
Answer:
You should expect to draw a consonant about 560 times.
Step-by-step explanation:
The word FOOTBALL has 5 consonants - F, T, B, L and L. Therefore, you should expect to draw a consonant 5 times out of every 8 draws. 5/8 = 0.625, so for 840 draws you should expect to draw a consonant approximately 840 x 0.625 = 560 times.
The number of times you should expect to draw a consonant is 525.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Given that,
The letters from the word FOOTBALL are written on 8 cards with one letter on each card.
One card will be drawn randomly and then placed back into the stack.
Number of consonants in the word = 5 [F, T, B, L and L]
Total number of letters = 8
Probability of finding consonant each time = 5/8
If this experiment is repeated 840 times,
Number of times you should draw a consonant = 840 × (5/8) = 525
Hence the required number of times is 525.
Learn more about Probability here :
https://brainly.com/question/11034287
#SPJ2
how many ways are there to pick two successive cards (without replacement) from a normal 52 card deck so that: (a) the first is an ace and the second is not a queen? (b) the first is a spade and the second is not a queen (beware the queen of spades!)
Answers
(a) There are four aces in a standard deck of playing cards: the ace of clubs, the ace of diamonds, the ace of hearts, and the ace of spades.
There are 48 cards that are not queens, so there are 4 × 48 = 192 ways to pick two successive cards from a deck of playing cards so that the first is an ace and the second is not a queen.
(b) There are 13 spades in a standard deck of playing cards, but one of them is the queen of spades.
Therefore, there are 12 spades that are not queens, so there are 12 × 48 = 576 ways to pick two successive cards from a deck of playing cards so that the first is a spade and the second is not a queen.
For more questions like Cards click the link below:
https://brainly.com/question/15731732
#SPJ4
What is the distance of the point (- 12/5 from the origin?
Answers
13 units is the distance from the given point (-12, 5) to the origin.
What do we mean by distance?Both statistical and qualitative methods can be used to determine how far apart two things or points are.
The word "distance" in physics can refer to an actual length or, more frequently, to an estimate based on a range of other factors.
The length of the line segment that connects any two points on a plane provides the distance between those spots.
To calculate the distance between two points, one commonly uses the equation d=((((x2 - x1)2 + (y2 - y1)2).
So, the given point is:
(-12, 5)
Assume that O (0, 0) is the origin and that M (-12, 5) is the provided location.
The distance between M and O is:
= √(−12−0)2+(5−0)2
= √(−12)2+(5)2
= √144+25
= √169
= √13×13
= 13 units
Therefore, 13 units is the distance from the given point (-12, 5) to the origin.
Know more about distance here:
brainly.com/question/26550516
#SPJ4
Question 2 of 3
Draw a triangle with vertices (1, 3), (2, 5), and (4, 3). Then perform the following transformation: a reflection
across the y-axis.
Answers
Answer:
To reflect a triangle across the y-axis, you need to negate the x-coordinate of each vertex.
The original triangle with vertices (1, 3), (2, 5), and (4, 3) will be reflected across the y-axis to become a new triangle with the following vertices: (-1, 3), (-2, 5), and (-4, 3).
Keep in mind that a reflection across the y-axis means that the object is flipped along the y-axis. Therefore, the x-coordinate of each vertex is multiplied by -1, which flips the object horizontally.
Which ordered pair is in the solution set of the system of inequalities y ≤ 3x + 1 and x - y > 1?
Answers
The solution set for the system of inequalities is (-1, -2).
Option A is the correct answer.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
y ≤ 3x + 1 ____(1)
x - y > 1 _____(2)
From (1 ) and (2) we get,
y = 3x + 1
Substituting in x - y = 1
x = 1 + y
x = 1 + 3x + 1
x - 3x = 2
-2x = 2
x = -1
Substituting in x = 1 + y
-1 = 1 + y
y = -1 - 1
y = -2
This means,
The solution set is (-1, -2).
Thus,
The solution set is (-1, -2).
Learn more about inequalities here:
https://brainly.com/question/20383699
#SPJ1
A new dirt bike valued at $9000 loses 18 percent of its value each year write an exponential function that models the value of the bike. And how much does the bike cost after 4 yrs
Answers
This exponential function can be used to model the value of a dirt bike valued at $9000 over time. The function expresses the amount of value the bike loses each year, which is 18%. This means that the value of the bike decreases by 18% each year.
f(x) = 9000(0.82)^x
After 4 years, the bike costs $6955.12.
f(x) = 9000(0.82)^x
After 100 years, the bike costs $8.87.
This exponential function can be used to model the value of a dirt bike valued at $9000 over time. The function expresses the amount of value the bike loses each year, which is 18%. This means that the value of the bike decreases by 18% each year. After 4 years, the bike would cost $6955.12. After 100 years, the bike would cost $8.87. This exponential function can be used to determine the value of the bike at any given time, depending on the number of years that have passed since the bike was purchased.
Learn more about function here
https://brainly.com/question/29633660
#SPJ4
evaluate "-3(2)+2^2+3(-2)"
Answers
Answer: The order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction) should be followed to get the correct result.
-3(2) = -6
2^2 = 4
3(-2) = -6
-6 + 4 + (-6) = -8
Therefore, "-3(2)+2^2+3(-2) = -8"
Step-by-step explanation:
Quick Answer:
The order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction), should be followed to obtain the correct result.
The answer is -8
Explanation:
PEDMAS stands for :
P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
So,
-3(2) = -6
2^2 = 4
3(-2) = -6
-6 + 4 + (-6) = -8
As a result, the correct response is, -8
Learn more about the order of operations here:
brainly.com/question/26499272
In ABC, AD is the angle bisect of What is BD?
Answers
Since AD is the angle bisector of <BAC, then BD is 1.9 inches.
Properties of an angle bisector.An angle bisector is a line that divides a given angle into two equal measure after its construction.
Given that AD is the angle bisector of <BAC, then we have;
From triangle ADC, applying the Pythagorean theorem;
/Hyp/^2 = /Adj/^2 + /Opp/^2
4^2 = 3^2 + AD^2
16 = 9 + AD^2
AD^2 = 16 - 9
= 7
AD = 7^1/2
= 2.64
AD = 2.6
So that, from triangle ABD we have;
/Hyp/^2 = /Adj/^2 + /Opp/^2
3.2^2 = 2.6^2 + BD^2
10.24 = 6.76 + BD^2
BD^2 = 10.24 - 6.76
= 3.48
BD = 3.48^1/2
= 1.8655
BD = 1.9 inches
Learn more about the properties of angle bisector at https://brainly.com/question/13878372
#SPJ1
d=16, 22, 26, 36 please help
Answers
Answer:
it is + 10 then + 4 and that is how you get your answer
Is the ordered pair (- 2 2 A solution of the linear inequality?
Answers
No, the ordered pair (-2, 2) is not a solution of the linear inequality because it does not satisfy the inequality.
An ordered pair is a pair of numbers that are related to each other in a specific order. An ordered pair can be used to represent a point on a graph. In order for an ordered pair to be a solution of a linear inequality, it must satisfy the inequality. This means that the ordered pair must make the inequality true when it is substituted into the equation. For example, if the linear inequality is "x + 2 > 3," then for (-2, 2) to be a solution, it must make the inequality true. This would mean that -2 + 2 > 3, which is not true, so (-2, 2) is not a solution of the linear inequality.
Learn more about inequality here
https://brainly.com/question/28823603
#SPJ4
What makes a problem extraneous?
Answers
Extraneous Solutions arise due to the squaring of both sides of a square root equation which will result in 2 solutions (the positive and negative number).
When you are solving equations with square roots, you have to always check whether your answer is correct by substituting with the variable. If the solution does not support the equation it is known as an extraneous solution.
One of the numbers in the solution of an extraneous problem will be an extraneous solution or an extra solution which does not fulfil the original equation.
For example,
x = 4 (original equation)
Squaring both sides of the equation
x² = 16
x = -4, 4
Substituting x = -4 into the original equation
-4 is not equal to 4
To know more about Extraneous Solutions, here
https://brainly.com/question/14054707
#SPJ4
Select the correct answer.
What is the additive inverse of ?
A. -16 5/7
B. 16 7/5
C. -16
D. -16 7/5
Answers
-16 5/7 is the additive inverse of 16 5/7.
What is additive inverse?
An additive inverse of a number is the value, which on adding with the original number results in zero value.
given a number 16 5/7
The additive inverse of a number is the number that completes the number to '0' when added.
thus,
the additive inverse of 16 5/7 is - 16 5/7.
Therefore, the additive inverse of 16 5/7 is -16 5/7.
Learn more about additive inverse here:
https://brainly.com/question/13715269
#SPJ1
Complete question:
What is the additive inverse of 16 5/7?
please help solve for missing side!
Answers
7. A rock that originally had a mass of 1.00 gram of uranium-238 now has only 0.50 grams.
How old is the rock if the half-live of uranium-238 is 4.5 billions of years.
Answers
The age of the rock is 4.5 billion years. Since the ratio of the remaining amount of uranium-238 is half of the original amount.
What is decay?
The half-life of a quantity is the time it takes to reduce to half of its initial value. In nuclear physics, the term is commonly used to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used to describe any type of exponential decay in general.
Given that a rock that originally had a mass of 1.00 gram.
The formula of decay is
A(t) = A₀ (0.5)^(t/ti)
Putting A₀ = 1.00 gram, A(t) = 0.50 gram, ti = half life = 4.5 billions = 4500000000.
0.50 = 1 (0.5)^(t/4500000000)
0.5 = (0.5)^(t/4500000000)
Taking logarithm function on both sides:
log (0.5) = log[(0.5)^(t/4500000000)]
Applying the power rule of logarithm:
log (0.5) = (t/4500000000)]log[(0.5)
Cancel out log (0.5) from both sides:
1 = t/4500000000
t = 4500000000
t = 4.5 billions
To learn more about half-life, click on the below link:
https://brainly.com/question/13656440
#SPJ1
I tried the problem 3 times and I keep getting the same wrong answer. I can't find out my mistake.
Answers
The distance that is closes to the distance that Steven walked around the pool is B. 62. 83 ft
How to find the perimeter of a circle ?The perimeter of a circle refers to the distance around that circle and it is also called the circumference of the circle.
This circumference can be found by the formula:
= π x diameter
This means that the closest distance that Steven walked around the circular swimming pool is:
= π x 20
= 62. 86 ft
In conclusion, the distance that Steven was able to walk around the pool is closest to 62. 83 ft.
Find out more on perimeter at https://brainly.com/question/1229669
#SPJ1
Select all the correct answers
assume these hexagons are similar. Which changes will result in a pair of non similar hexagons?
a- doubling each side length in ABCDEF
b- subtracting 1 from each side length in GHIJKL
c- adding 15 degrees to angles G, H, and I and subtracting 15 degrees from angles J, K and L
d- reducing each side length in GHIJKL by one third of the original length
e- adding 3 to each side length in GHIJKL
Answers
On assuming the given Hexagons are similar then the changes that will result in pair of Non Similar Hexagons is :
(c) adding 15° to angles G, H, and I and subtracting 15° from angles J, K and L .
The Hexagons are said to be similar if they have matching sides in the same proportion .
If the same operation is performed on every side of the hexagon , then the hexagon will remain similar ,
So , from the given operation , the operation that is not performed on each side or on each hexagon , it will result in Non similar hexagon .
The operation performed in option (c) performs addition on G, H, I and subtraction on angles J, K, L .
Therefore , it will result in Non Similar Hexagons .
Learn more about Similarity here
https://brainly.com/question/24426815
#SPJ4
A shop sells potatoes and carrots.
The shop orders 50. 4 kg more potatoes than carrots
32% of the total weight is carrots.
How many kilograms of potatoes does the shop order?
Answers
The 95.2 kilograms of potatoes by the shop order. With the unit sign kg, the kilogram serves as the International System of Units' unit of mass.
What is meant by kilograms?The term "kilo" is frequently used in common speech and is a unit of measurement that is widely used in research, engineering, and commerce worldwide. It denotes "a thousand grams.the metric system's fundamental unit of mass is the kilogram (kg). The mass of 1,000 cubic centimeters of water is very nearly equal to one kilogram, although it was initially intended to be exactly equal. The precise definition of a pound is 0.45359237 kg.A shop sells potatoes and carrots
let c = carrots
let p = potatoes
let TW = Total weight
The shop orders 50.4 kg more potatoes than carrots
p = 50.4 kg + c
Total weight = Mass of p + Mass of c
TW = 50.4 kg + c + c = 50.4 kg + 2c …. (i)
32% of the total weight is carrots
c = (32 /100 ) * Total weight = 0.32 TW
TW = c / 0.32 …. (ii)
50.4 kg + 2c = c / 0.32
Multiply all through by 0.32
16.128 + 0.64c = c
c - 0.64c = 16.128
0.36 c = 16.128
c = 16.128 / 0.36 = 44.8 kg
Potatoes = 50.4 kg + c = 50.4 kg + 44.8 kg = 95.2 kg
Hence, the answer is 95.2 kg ordered by the shop.
To learn more about kilograms refer to:
https://brainly.com/question/9301317
#SPJ1
What are the 3 types of graphs called?
Answers
The three types of graphs are bar graphs, line graphs and pie chart
The three types of graphs can be noted as -
Bar graph - It is a form of a chart in which distinct values or data sets are represented by rectangular bars. The bars, which can be horizontal or vertical, can be used to compare various values or data sets. A bar graph might be used, for instance, to compare the population of several cities or the sales of various items.
Line graph - It changes or trends over time are represented by a series of points connected by lines. To track changes in data, such as stock prices, temperature, or population increase, line graphs are frequently utilised. The progression of the data through time can be demonstrated by the line.
Pie chart - This chart employs a circular shape divided into wedges to depict percentages or proportions of a whole. The size of wedges indicates the percentage or proportion of each wedge's respective category, with each wedge standing for a separate category. A pie chart could be used to display the allocation of revenue among various departments within a corporation or the breakdown of spending in a budget.
Read more about graphs on:
https://brainly.com/question/25184007
#SPJ4
The sum of two numbers is 2490. Find the numbers if 8.5% of the first is equal to 6.5% of the second.
Answers
Thus the numbers are 1411 and 1079 respectively.
ABC is reflected to A'B'C' in such a way that A (1, 4) →A'(1, 6), B (3, 1)→B'(3, 9) and C (7,5) →C (7,5). Find the axis of reflection using graph.
Answers
Triangle ABC is first mirrored over the x-axis, then across the y-axis, to form triangle A'B'C.
How to find the calculation?A′B′C is created by reflecting ABC.A′B′C′'s vertices are A′(3, 1), B′(4, 2), and C′(6, 5), while ABC's vertices are A(-1, 3), B(2, 4), and C(-5, 6).Drawing ABC and ABC'B'C's two images on a two-dimensional coordinate plane.Triangle ABC is first mirrored over the x-axis, then across the y-axis, to form triangle A'B'C.A point's x- and y-coordinates switch positions when it is reflected across the line y = x. The x-coordinate and y-coordinate swap positions and become negated if you reflect over the line y = -x (the signs are changed). The line y = x is the point where the reflection of the point (x,y) across appears (y, x).When reflection occurs, the two images, the image and the pre-image, are congruent, which means neither the shape nor the size changes; only the shape's translation on the coordinate plane does.Reflection across y = x .The Complete Question.
To Learn more About Triangle ABC Refer To:
https://brainly.com/question/26155897
#SPJ1
Write your answer as a fraction in simplest form 7/4 x 6/5
Answers
Answer:
21/10
Step-by-step explanation:
42/20
divide both numerator and denominator by 2
=21/10
Plssss help me I need passing grades for Friday
Answers
The number that represent the product of ac is 18 and the sum of b is -9 .
The factored form of the trinomials is (x-3)(x-6)
What are Trinomials ?An algebraic statement with three on-zero terms separated by + or - is called a trinomial. A trinomial exists when three monomials are separated by addition or subtraction. The formula for a quadratic trinomial is ax² + bx + c, where a, b, and c are real, non-zero values.
An algebraic statement with variables and constants is a quadratic trinomial. It is written as ax² + bx + c, where a, b, and c are real non-zero values and x is the variable. Leading coefficient "a," linear coefficient "b," and additive constant "c" all refer to the same constant. A quadratic trinomial is also used to explain the discriminant D, which is expressed as D = b² - 4ac and determines the quantity of an expression. The discriminant aids in categorizing the many quadratic trinomial instances. A quadratic equation, such as ax² + bx + c = 0, is one in which the value of a quadratic trinomial with a single variable is zero.
The trinomial is x² - 9x + 18
In the expression ax² + bx + c
here a = 1, b = -9 and c = 18
The term that represent the product of ac = 1* 18 = 18
The term represent the sum of b = -9
Factoring The trinomial we get,
x² -9x + 18
= x² - 3x - 6x + 18
= x(x-3) -6(x-3)
=(x-3)(x-6)
To learn more about Trinomials refer to :
https://brainly.com/question/16347049
#SPJ1
The total area of the parallelogram and the triangle is 120 square meters. Find the value for x. (Length is 129, width is x, and height is 8
Answers
The value for x is 53 given the total area of the parallelogram and the triangle is 120 square meters.
To find the area of the parallelogram and the triangle, we can use the formulas for the area of a parallelogram and the area of a triangle. The area of a parallelogram is base times height, so in this case it would be 1298 = 1032 square meters.
The area of a triangle is (1/2) base heights, so for this case, it would be (1/2)1298 = 520 square meters. To find the value of x, we can use the given information that the total area of the parallelogram and the triangle is 120 square meters.
We can set up an equation: 1032 + 520 = 120. Solving for x, we get x = 53.
For more questions like Parallelogram click the link below:
https://brainly.com/question/29147156
#SPJ4
SLOPE TOPIC!! . Determine a possible second point with a y-coordinate of 8.
Please help!!! I will give brainliest
Answers
A possible second point with a y-coordinate of 8 is equal to 5.
How to calculate the slope of a line?In Mathematics, the slope of a straight line can be calculated by using this this mathematical expression;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
From the information provided above, we have the following slope and data points on the line:
Points on x-axis = (1, 2).
Points on y-axis = (_, 8).
Slope, m = 3/2
Substituting the given points into the slope formula, we have the following;
Slope, m = (y₂ - y₁)/(x₂ - x₁)
3/2 = (8 - 2)/(x₂ - 1)
3/2 = 6/(x₂ - 1)
Cross-multiplying, we have:
3(x₂ - 1) = 12
x₂ - 1 = 12/3
x₂ - 1 = 4
x₂ = 4 + 1
x₂ = 5
In conclusion, we can logically deduce that the second point (x₂) is 5.
Read more on slope here: brainly.com/question/3493733
#SPJ1