The line of elements from the lower left corner to the upper right corner of a second order determinant is called the main diagonal or simply the diagonal. In general, the diagonal of an n x n determinant consists of the elements a11, a22, ..., ann, where ai,i denotes the element in the i-th row and i-th column of the determinant.
teri's car holds 17.4 gallons og gas. if she can drive 478.5 miles ona full tank of gas, how many miles can she per gallons
Teri can drive approximately 27.47 miles per gallon of gas.
To find how many miles per gallon Teri can drive, we need to divide the total distance she can travel on a full tank of gas by the amount of gas she needs to fill the tank. This gives us the average number of miles she can travel on one gallon of gas.
Teri's car can hold 17.4 gallons of gas.
Teri can drive 478.5 miles on a full tank of gas.
Mathematically, we can represent this as:
Miles per gallon = Total distance traveled ÷ Amount of gas used
Plugging in the values we have:
Miles per gallon = [tex]\frac{478.4 miles}{17.4 gallons}[/tex]
Performing the division:
Miles per gallon = 27.47126437
Rounding to two decimal places, we get:
Miles per gallon ≈ 27.47
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What is 4 and 5/6 - 1 and 1/3 =
Answer:
Step-by-step explanation:
3
The volume of air in a persons lungs can be molded with a periodic function the graph below represents the volume of air ,in mL, in a persons long overtime measured in seconds, t.what is the amplitude and what does it represent in this context?
Amplitude of attached graph is 800 and here amplitude explains the maximum change in volume as compare to average volume.
Let us consider two point on the attached graph.
Lowest point as ( 0.5, 1000 )
Highest point as ( 2.5 , 2600 )
In a periodic function the volume of air in a person's lungs over time,
The amplitude is the distance between the maximum value of the function and its average value.
It is represented by y-coordinate.
Amplitude = ( 2600 - 1000 ) / 2
= 1600 / 2
= 800
In the context of the volume of air in a person's lungs,
The amplitude represents the maximum change in the volume of air from the average volume.
This is an important measure of lung function.
As it indicates how much air a person can take in and expel from their lungs with each breath.
The higher the amplitude, the greater the lung capacity and respiratory function of the person.
Therefore, the amplitude in the graph is equal to 800 and it represents the maximum variation in the volume of air from the average volume.
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The above question is incomplete, the complete question is:
The volume of air in a persons lungs can be molded with a periodic function the graph below represents the volume of air ,in mL, in a persons long overtime measured in seconds, t. What is the amplitude and what does it represent in this context?
Graph is attached.
HELPPPP!!!!!!!!
Median for Jamal:
hELP PLEASEE
(Q005) How does the Missouri Compromise reflect the strong sense of nationalism Americans felt for their country in the early 1800s?
What details can we learn from John Quincy Adams's diary entry? Use quotes directly from the primary source.
Answer: The Missouri Compromise of 1820 was a landmark agreement in American history that temporarily resolved the issue of slavery in the western territories. The compromise was driven by a sense of nationalism among Americans in the early 1800s, who were concerned about preserving the unity of the country and avoiding the outbreak of civil war.
The Missouri Compromise reflected this sense of nationalism by seeking to maintain a balance of power between the slave states and the free states. The compromise allowed Missouri to enter the Union as a slave state, but it also admitted Maine as a free state, and prohibited slavery in any new states formed north of the 36°30′ parallel. By preserving this balance of power, the Missouri Compromise helped to ease tensions between the North and the South, and prevent the outbreak of civil war for several decades.
John Quincy Adams's diary entry provides some insights into the political climate of the time, and the debates surrounding the Missouri Compromise. In his diary entry of February 24, 1820, Adams writes:
"The Missouri question still hangs over us like a black cloud. The ground of the controversy is evidently an apprehension of the preponderance of power in the Union, which by some is feared to be passing from the South to the North."
This quote suggests that there was a growing concern among some Southerners about the balance of power in the Union, and that this concern was driving the debates over the Missouri Compromise. Adams goes on to describe the debates in Congress, noting that "the debates upon the Missouri question are exceedingly able, ingenious, and eloquent." He also provides some insights into the strategies being used by different sides of the debate, noting that "the argument for restriction upon Missouri, is that it will preserve the balance of power in the Union; that the balance of power is a fundamental principle of the Constitution; and that this principle is essential to the preservation of the Union."
These quotes suggest that the Missouri Compromise was a highly contentious issue, and that the debates surrounding it were marked by a strong sense of nationalism among both supporters and opponents of the compromise. The compromise ultimately reflected a desire among Americans to maintain the unity and stability of the country, even as it grappled with the divisive issue of slavery.
Step-by-step explanation:
A circle is inscribed in a regular hexagon with side length 2 units.
What is the exact area of the circle?
The exact area of the inscribed circle is 12π square units.
What is circle?A circle is a geometric shape consisting of all the points in a plane that are equidistant from a given point called the center of the circle. The distance between the center and any point on the circle is called the radius of the circle.
According to question:The radius of the inscribed circle is also the distance from the center of the hexagon to each of its sides. To find this distance, we can divide the hexagon into six equilateral triangles, each with side length 2 units. The height of each triangle is √3 times the side length, or 2√3 units. The distance from the center of the hexagon to each side is equal to this height, or 2√3 units.
Therefore, the radius of the inscribed circle is 2√3 units. The area of the circle is given by the formula A = πr², where r is the radius. Substituting in the value of the radius, we get:
A = π(2√3)² = 12π
So the exact area of the inscribed circle is 12π square units.
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A farmer finds there is a linear relationship between the number of bean stalks, n , she plants and the yield, y, each plant produces. When she plants 30 stalks, each plant yields 25 oz of beans. When she plants 32 stalks, each plant produces 24 oz of beans. Find a linear relationship in the form y=mn+b that gives the yield when n stalks are planted.
The linear relationship between the number of bean stalks, n, and the yield, y, is y = -0.5n + 40. This equation can be used to predict the yield of beans for any number of bean stalks planted by the farmer.
To find the linear relationship between the number of bean stalks, n, and the yield, y, we can use the two data points provided by the farmer. We know that when 30 stalks are planted, each plant yields 25 oz of beans, and when 32 stalks are planted, each plant yields 24 oz of beans.
First, we need to find the slope, m, of the line. We can use the formula:
m = (y2 - y1) / (x2 - x1)
where x1 = 30, y1 = 25, x2 = 32, and y2 = 24.
m = (24 - 25) / (32 - 30) = -0.5
Next, we need to find the y-intercept, b, of the line. We can use the point-slope form of the equation:
y - y1 = m(x - x1)
where x1 = 30 and y1 = 25.
y - 25 = -0.5(x - 30)
y - 25 = -0.5x + 15
y = -0.5x + 40
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Geomatic sequance for this question
Answer:
a = 2
Step-by-step explanation:
Geometric series:
r = 3
n = 6
[tex]S_n=728[/tex]
[tex]\boxed{\bf S_n = \dfrac{a(r^n - 1)}{r- 1}}[/tex]
[tex]\dfrac{a*(3^6 - 1)}{3-1}=728\\\\ \dfrac{a * (729 -1)}{2}= 728\\\\ \dfrac{a * 728}{2} = 728[/tex]
[tex]a = 728 * \dfrac{2}{728}\\\\a = 2[/tex]
A pole that is 3 m tall casts a shadow that is 1.55 m long. At the same time, a nearby tower casts a shadow that is 49.25 m long. How
tall is the tower? Round your answer to the nearest meter.
m
The tower is approximately 95 meters(m) tall.
What is a meter?
A meter is the basic unit of length in the International System of Units (SI). It is defined as the distance light travels in a vacuum in 1/299,792,458 of a second.
What kind of unit is meter?
The meter is a unit of measurement for length or distance. It is commonly used in science, engineering, and daily life to measure the size or distance between objects.
According to the given information
Let's call the height of the tower h. We can use similar triangles to set up a proportion:
3 / 1.55 = h / 49.25
Simplifying this expression gives:
h = (3 * 49.25) / 1.55
h = 95.48
Rounding this answer to the nearest meter gives:
h ≈ *95 meters*.
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AOC and BOD are diameters of a circle prove that ABD and triangle DCA are congruent by RHS
Statement-Reason Proof:
If the circle has center O, then:
1.) BD = CA [Definition of Diameters of a Circle]
2.) Angle BAD = Angle CDA [Angle of Semicircle are Right Angles (90°)]
3.) AD = AD [Reflexive Property]
4.) Triangle DCA ≅ Triangle ABD [RHS Congruency Rule]
Find the value of � x, � y, and � z, in the rhombus below. 71 -8x+7 y+7 2z+5
I believe you meant to write the expression as follows: 71 = -8x + 7y + 7z + 5. This equation represents a relation between the values of x, y, and z in a rhombus where 71 is the sum of the diagonals of the rhombus.
How to calculate value of x,y and z for the given rhombus?
To solve for x, y, and z, we need to use additional information about the rhombus. Without any further information, we cannot determine unique values for x, y, and z.
However, we can make some observations based on the given equation:
The coefficient of x is negative (-8), which means that increasing x would decrease the value of the left-hand side of the equation. Therefore, we can conclude that x must be positive to satisfy the equation.
The coefficients of y and z are positive (7 and 7, respectively), which means that increasing y and/or z would increase the value of the left-hand side of the equation. Therefore, we can conclude that y and z must be non-negative to satisfy the equation.
With these observations in mind, we can come up with multiple solutions for x, y, and z that satisfy the given equation. Here are a few examples:
If we let x = 0, y = 11, and z = 9, then the equation is satisfied:
71 = -8(0) + 7(11) + 7(9) + 5
71 = 77
If we let x = 2, y = 10, and z = 8, then the equation is also satisfied:
71 = -8(2) + 7(10) + 7(8) + 5
71 = 71
Therefore, we cannot determine a unique solution for x, y, and z based on the given equation alone.
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An element with a mass of 540 grams decays by 12.8% per minute. To the nearest tenth of a minute, how long will it be until there are 110 grams of the element remaining?
Therefore, to the nearest tenth of a minute, it will be about 9.4 minutes until there are 110 grams of the element remaining.
What is initial amount?"Initial amount" usually refers to the starting quantity or value of something, such as money, an investment, or a substance. It is the amount or quantity that exists at the beginning of a particular time period or situation. For example, if you invest $1,000 in a savings account, the initial amount is $1,000. Similarly, if you are given 10 liters of water, the initial amount of water is 10 liters.
We can use the exponential decay formula to solve this problem:
[tex]N(t) = N₀ * e^{(-kt)}[/tex]
where N(t) is the amount of the element remaining at time t, N₀ is the initial amount of the element, k is the decay constant (which is equal to ln (1 - 0.128) = -0.142), and e is the base of the natural logarithm.
We can plug in the given values and solve for the time t when the remaining amount N(t) is equal to 110 grams:
[tex]110 = 540 * e^{(-0.142t)}[/tex]
Dividing both sides by 540, we get:
[tex]0.2037 = e^{(-0.142t)}[/tex]
Taking the natural logarithm of both sides, we get:
[tex]ln(0.2037) = -0.142t[/tex]
Solving for t, we get:
t = ln (0.2037) / (-0.142) ≈ 9.4 minutes
Therefore, to the nearest tenth of a minute, it will be about 9.4 minutes until there are 110 grams of the element remaining.
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The slope of the curve ƒ(x) = x2 + 2 at x = 3 is _______.
6
9
3
0
Answer:
The slope of the curve ƒ(x) = x^2 + 2 at x = 3 can be found by taking the derivative of the function with respect to x and evaluating it at x = 3.
ƒ(x) = x^2 + 2
Taking the derivative:
ƒ'(x) = 2x
Substituting x = 3:
ƒ'(3) = 2(3) = 6
Therefore, the slope of the curve ƒ(x) = x^2 + 2 at x = 3 is 6.
A plane ascends at a 28°
angle. When it reaches an altitude of 250 feet, how much ground distance has it covered? Round your answer to the nearest tenth.
(HINT: DRAW THE PICTURE)
Ground distance covered is ft.
(50 points)
According to trigonometry, the ground distance covered by the plane is approximately 478.7 feet, rounded to the nearest tenth.
What is trigonometry?
The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations.
The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations.
There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc).
The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.
To draw a diagram of the situation:
[tex]tan(28°) = opposite / adjacent\\tan(28^{0}) = 250 / x\\x = 250 / tan(28^{0})\\ x= 478.7 ft[/tex]
Therefore, the ground distance covered by the plane is approximately 478.7 feet, rounded to the nearest tenth.
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You want to take out a $210,000 mortgage (home loan).The yearly interest rate on the loan is 6%, and the loan is for 30 years. How much will your monthly payment be?
Using the formula for calculating monthly mortgage payments, with a loan amount of $210,000, yearly rate of 6% and time period of 30 years, the monthly mortgage payment comes out to be approximately $1,259.81.
Explanation:The calculation that needs to be done here involves a formula related to annuities, which is what monthly mortgage payments are classified as. The formula used to calculate a monthly mortgage payment is:
[tex]M = P [r(1 + r)^n]/[(1 + r)^n - 1][/tex]
Where:
M = monthly mortgage payment
P = loan amount (present value)
r = monthly interest rate
n = total number of payments (or total number of periods)
Plugging our given values into the equation:
P = $210,000 (this is the loan amount)
r = 6/100/12 = 0.005 (this is the monthly interest rate)
n = 30 x 12 = 360 (this is the number of periods, ie the total number of monthly payments over 30 years)
By substituting these values, one can calculate that:
M = [tex]210,000[0.005(1 + 0.005)^3^6^0] / [(1 + 0.005)^3^6^0 - 1][/tex]
Calculating this, we get M ≈ $1,259.81
So, the monthly mortgage payment would be approximately $1,259.81.
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The tables represent hat sizes measured in inches for two softball teams.
Pelicans
20 20 22
21 22 23
22.5 24 21.5
22 23.5 22
23.5 22 24.5
Seahawks
21 21 21
23.5 23.5 23.5
23.5 23.5 23.5
22.5 22.5 22.5
23 23 23
Which team has the largest overall size hat for their players? Determine the best measure of center to compare and explain your answer.
Pelicans; they have a larger mean value of about 22 inches
Seahawks; they have a larger mean value of about 23 inches
Pelicans; they have a larger median value of 22 inches
Seahawks; they have a larger median value of 23 inches
The team that has the largest overall size hat for their players is the Seahawks; they have a larger mean value of about 23 inches. The correct option is b.
What is the mean and median?The two most frequently used measures of center are mean and median. When we compare the mean numbers for the Pelicans and Seahawks, we can see that the Pelicans have a mean of roughly 22 inches and the Seahawks have a mean of roughly 23 inches.
Nevertheless, when the data is skewed or contains outliers, the mean may not be the best approximation of the center because the mean can be altered by extreme values or outliers. Thus, we also need to compare the median values. The median is the midway value in the ordered set of data.
Thus, the correct option is b, Seahawks; they have a larger mean value of about 23 inches.
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Answer:
Step-by-step explanation:
the right answer is b 23 inches seahawkS BRAINLIST and verified answer wanted
Emery bought 3 cans of beans that had a total weight of 2.4 pounds. If each can of beans weighed the same amount, which model correctly illustrates the relationship? Check all that apply.
The equation will be y = 2.4x. Thus, 2nd option is correct.
What is an Equations?Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
We can use a proportion to model the relationship between the number of cans and the total weight. Since we have three cans, we can represent the weight of each can as x, and the total weight as 2.4 pounds:
3x = 2.4
Solving for x, we get:
x = 0.8
Therefore, each can weighs 0.8 pounds.
Hence the equation will be y = 2.4x. Thus, 2nd option is correct.
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Emery bought 3 cans of beans that had a total weight of 2.4 pounds. If each can of beans weighed the same amount, which model correctly illustrates the relationship? Check all that apply.
y = 0.8x
y = 2.4x
y = 3x
y = x/2.4
The following inequalities represent a system.
y ≥ 5x + 2
y > −3x − 2
Which of the following graphs represents the system?
See the image linked below.
To graph system of inequalities y ≥ 5x + 2 and y > -3x - 2, draw lines for y = 5x + 2 and y = -3x - 2, then shade areas above each line. The intersection of shaded areas shows solutions to the system of inequalities.
Explanation:In order to graph the system of inequalities y ≥ 5x + 2 and y > -3x - 2 you would start by graphing each inequality as if it was an equality. For the first inequality, you would graph the line y = 5x + 2 and shade the area above the line because it's y 'greater than or equal to'. For the second inequality, you draw the line y = -3x - 2 and also shade the area above because it's y 'greater than'. The intersection of the shaded areas represents the solution to the system of inequalities. Therefore, the graph would have two shaded lines, with the common shaded area above both lines representing the solutions to the system of inequalities.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
Step-by-step explanation:
blank 1. no
blank 2. not constant because it is a nonlinear function.
Let the random variable Z follow a standard normal distribution. What is the P(Z> 1.2)?
Assume Z is a regular, standard random variable. The answer is P(Z 1.2), which is written as P(Z 1.2) = (1.2) =. 8849.
What does variable mean in plain English?An variables is just a sum that can change according to the fundamental math concept. The generic letters x, y, and z are often employed in mathematical expressions and equations. Thus a variable is a sign for a numeric value that is unknown.
What does the word "variable" mean?Every feature, number, or amount that can be gauged or quantified is referred to as a variable. A statistic may also be referred to as a data item. Examples of variables include age, sex, company revenue and costs, birth country, capital expenditures, class grades, eye colour, and vehicle kind.
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The probability of Z being greater than 1.2 is 0.11507, or approximately 11.51% (rounded to two decimal places).
What do you mean by probability?Probability is a mathematical concept that expresses the possibility or chance of an event happening.
A number between 0 and 1, with 0 signifying impossibility and 1 signifying certainty, is used to symbolize it.
The likelihood of an event occurring increases as the probability approaches 1.
To find the probability P(Z > 1.2) where Z follows a standard normal distribution, we need to use the standard normal distribution table or a calculator with a normal distribution function.
Using a standard normal distribution table, we look for the probability value that corresponds to a standard normal deviate of 1.2.
The table gives us the area under the standard normal curve to the left of 1.2, which is 0.88493. Therefore, the probability of Z being greater than 1.2 is:
P(Z > 1.2) = 1 - P(Z ≤ 1.2)
= 1 - 0.88493
= 0.11507
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6. Anna solved three problems on her math test. One of them was incorrect. Circle the problem that was solved incorrectly and find the correct answer.
32° 122°
B
4 . 10
83.2° X° A
83.2+74.1+×=180 157.3 +×= 180
x = 22.70
X
W 1420
M
X°
329 1089
142.7°
42+36.08+×= 180 78.08 +×= 180 ×= 101.92°
32 +×= 108 ×= 76°
It seems that the problem solved incorrectly is the one represented by letter A, which is trying to find the missing angle in a triangle. The correct answer is 74.1°, which can be obtained by subtracting the sum of the other two given angles (83.2° and 22.7°) from 180°.
The problem that Anna solved incorrectly is the last one: 32 + x = 108. The correct answer should be x = 76, not x = 108.
Explanation:In this math problem, Anna seems to be solving for unknown angles in several triangle problems. An important principle here is that the sum of the angles in a triangle always adds up to 180 degrees. Looking at the problems she solved:
83.2 + 74.1 + x = 180: The correct answer for x here is 22.7 degrees, and Anna solved it correctly.42 + 36.08 + x = 180: The correct answer for x here is 101.92 degrees, and Anna also solved this correctly.32 + x = 108: Misstep appears here. If we subtract 32 from both sides of the equation, the correct answer for x should be 76 degrees. However, Anna seems to have calculated x = 108, which is incorrect.So, the problem that was solved incorrectly is the last one: 32 + x = 108.
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Could someone please explain how to answer this question. I think its 66 but im not sure.
1. What is the volume of a cube with volume 27/64 cubic units
The volume of a cube with volume 27/64 cubic units is 3/4.
What is an edge line?All edge lengths of the cube are equal. Then the volume of the cube is 3/4 units.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
The volume of the cube is 27/64 cubic units.
We know the formula of the volume is given as
Volume = a³
[tex]a^3 = \sqrt[3]{\dfrac{27}{64} }[/tex]
a = 3/4
where a is the edge length of the cube.
The edge length of the cube is 3/4 units.
Therefore, the volume of a cube with a volume of 27/64 cubic units is 3/4.
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The complete question is: What is the side of a cube with volume 27/64 cubic units?
y=100(0.96)^x is an equation that can be used to represent the purchasing power of $100 after x years of inflation. what is the rate of inflation used to make this calculation?
What are the zeros of the equation 2x^2+16x-96=0
Using quadratic equations, we can find the zeros of the equation are -4 and 12.
What is a quadratic equation?Quadratic equations are second-degree algebraic expressions because they have the form ax² + bx + c = 0. The word "quadratic" is derived from the Latin word "quadratus," which meaning "square," and alludes to the fact that the equation's variable x is squared. To put it another way, a "equation of degree 2" is a quadratic equation.
Given equation:
2x²-16x-96=0
Factor out of the terms on the left side:
2 × x² - 2 × 8x - 2 × 48 = 0
⇒ 2 (x² - 8x - 48) = 0
⇒ x² - 8x - 48 = 0
⇒ x² + 4x - 12x - 48 = 0
⇒ x (x+4) -12(x+4) = 0
⇒ (x+4) (x-12) = 0
⇒ x = -4 or x = 12.
Therefore, zeros of the equation are -4 and 12.
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Mario Brothers, a game manufacturer, has a new idea for an adventure game. It can either market the game as a traditional board game or as a PC game, but not both. Consider the following cash flows of the two mutually exclusive projects. Assume the discount rate for both projects is 9 percent.
Year Board Game PC
0 −$ 1,550 −$ 3,400
1 760 2,100
2 1,300 1,640
3 280 1,150
a. What is the payback period for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
b. What is the NPV for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
c. What is the IRR for each project? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
d. What is the incremental IRR? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Please note this is for a Finance class for MBA program.
In a school computer lab, students must use a six-digit passcode to log on to the computers.
The digits 0-9 can be used in the passcodes.
a. How many different passcodes are possible if the digits can be repeated?
b. How many different passcodes are possible if the digits cannot be repeated?
a. the total number of different passcodes possible if the digits can be repeated is 10⁶
b. the total number of different passcodes possible is 151,200.
What is probability?The possibility or chance of an event occurring is measured by probability. It is stated as a number between 0 and 1, where 0 denotes an impossibility (i.e., an event that won't happen) and 1 denotes a certainty (i.e., an event that will happen) (i.e., an event that will always occur).
a. Since there are 10 digits (0-9) that can be used for each digit in the passcode, there are 10 options for each of the six digits.
Therefore, the total number of different passcodes possible if the digits can be repeated is 10⁶, which is equal to 1,000,000.
b. If the digits cannot be repeated, there are 10 options for the first digit, 9 options for the second digit, 8 options for the third digit, and so on.
Therefore, the total number of different passcodes possible is 10x9x8x7x6x5, which is equal to 151,200.
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Which of these quadratic functions is
represented by the graph below? (Graph is provided in the attachment file)
The function for the graph of the parabola given in the picture attached will be Option (H). f(x) = x² - 6x -1
What is the equation of the parabola?
The equation of a parabola depends on its vertex and focus. There are two possible orientations for a parabola, depending on whether it opens upward or downward (in the case of a vertical axis of symmetry) or leftward or rightward (in the case of a horizontal axis of symmetry).
Equation of a parabola in vertex form:
Equation of a parabola in vertex form is given by,
y = a(x - h)² + k
Here, (h, k) is the vertex of the parabola
Given in the graph,
Vertex of the parabola → (0, 2)
Parabola passes through the origin (4, 8).
The equation of the graph with vertex (0, 2) will be,
y = a(x - 0)² + 2
Since, the parabola passes through (4, 8),
8 = a(4 - 0)² + 2
8 = 16a + 2
a = 6/16
Substitute the value of 'a' in the equation of the parabola,
y = a(x - 0)² + 2
y = 6/16(x - 0)² + 2
y = 2/8(x - 0)² + 2
y = x² - 6x + 9 - 9
y = x² - 6x -1
Hence, the function representing the graph will be f(x) = x² - 6x -1
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One integer is 6 times another. I f the product of the two integers is 54. Find the integers.
Answer:
integers 3 and 18
Step-by-step explanation:
Can someone please help me with this problem involving Proofs of proportions or angle congruences using similarity.
By SAS congruence, triangles ΔVTW and ΔUTX are congruent.
Define SAS congruenceSAS congruence (Side-Angle-Side) is a criterion for the congruence of two triangles in Euclidean geometry. Two triangles are said to be congruent by SAS if they have two pairs of corresponding sides that are congruent, and the included angle between those sides is also congruent.
Formally, the SAS congruence theorem states that if two sides and the included angle of one triangle are congruent to the corresponding two sides and included angle of another triangle, then the triangles are congruent. In symbols, if triangle ABC is congruent to triangle DEF by SAS, we write:
AB = DE
AC = DF
∠A = ∠D
In the triangle ΔVTW and ΔUTX
TX/TW=TU/TV (given)
∠VTW=∠UTX(Vertically opposite angle)
By SAS congruence, ΔVTW≈ΔUTX
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