Answer: We can find the inequalities. One inequality has a line with y-intercept 2 and slope -1. The inequality is y >= -x + 2.
Step-by-step explanation:
Which of the following is equivalent to 4x²+ 6x-2+6 - 4x² - 6x?
a. -4
b. 4
c. 6
d. -2​
Therefore , the solution of the quadratic equation comes out to be x value is 4.
How to solve a quadratic equation?The quadratic solution x = ax2 + foo + c=0 is a regression model for one variable equations. According to the First Theorem of Algebra, this polynomial only has one solution because of its second order. Both straightforward and complex solutions are viable options. The term "quadratic formula" refers to a formula with four variables. According to this, there can only be a single squared word present. Mathematical variables or variables a, b, and c are often used to represent the unknown variable "X" in the formula "ax2 + bx + c = 0," which is frequently used to solve arithmetic problems.
Here,
Given :
=> 4x²+ 6x-2+6 - 4x² - 6x
=> 4x² - 4x² + 6x -6x -2 +6
=> 0 + 0 +4
=> 4
Therefore , the solution of the quadratic equation comes out to be x value is 4.
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Given that f(x) = x/3 - 1 and that g(x)=2x-5 a) Work out f(6) + g(3) b) Work out g^-1(7) c) Work out g^-1(7) – f^-1(1)
Answer:
A) 2 B) 6 C)0
Step-by-step explanation:
A)
f(6) = 6/3 - 1 = 1
g(3) = 2(3) - 5 = 1
f(6) + g(3) = 1 + 1 = 2
B)
Find the inverse of the function g(x)
x = 2y-5
-2y = -x-5
2y = x+5
y = (x+5)/2
g^-1(7) = 12/2 = 6
C)
g^-1(7) = 6
Find the inverse of the function f(x)
x = y/3 - 1
x+1 = y/3
y = 3x+3
f^-1(1) = 3+3 = 6
g^-1(7) – f^-1(1) = 6-6 = 0
The wind broke a 24 metres high tree. The top of this tree touches the ground. At what height did the tree break if the broken part makes an angle of 30° with the ground?
Answer: The height above ground at which the tree broke is 8 meters.
Step-by-step explanation:
Let the standing part of tree be of 'l' meters.
Therefore the broken part is of 24 - l meters.
By using trignometric functions
sin(30°) =[tex]\frac{Perpendicular}{Hypotenuse}[/tex]
[tex]\frac{1}{2}[/tex]=[tex]\frac{l}{24-l}[/tex]
⇒ 2 × l = 24 - l
⇒3 × l = 24
⇒ l = 8
∴ The height above ground at which the tree broke is 8 meters.
What is the vertex of the parabola? If the value of a changed to -6, -5, or 5, how would the vertex change?
The equation for the vertex's x-coordinate and the axis of symmetry is:
[tex]$x=\frac{-b}{2 a}[/tex]
What is vertex?It is common for two or more lines or edges to cross at a vertex, which is a specific point of a mathematical object. Angles, polygons, polyhedra, and graphs are the objects that contain vertices the most frequently. Nodes are another name for vertices in a graph. A vertex is a location where two rays or straight lines converge. Angles, which are expressed in degrees, contain vertices. Where the sides or edges of two-dimensional and three-dimensional things intersect is where they can also be found. As an illustration, a rectangle has four vertices due to its four sides. A vertex is a term used to refer to a node in a graph, which is a point on which the graph is defined and which may be connected by graph edges.The standard form of a parabola is y = a x² + + bx + c, where [tex]$a \neq 0$[/tex]
A parabola's vertex is its minimum or maximum point. The vertex is the smallest point and the parabola widens upward if a>0. Vertex is maximal point and parabola widens downward if a=0.
You must ascertain the x and y coordinates in order to determine the vertex.
The equation for the vertex's x-coordinate and the axis of symmetry is:
[tex]$x=\frac{-b}{2 a}[/tex]
To find the y-coordinate of the vertex, substitute the value for x into the equation and solve for y.
[tex]$y=a\left(\frac{-b}{2 a}\right)^2+b\left(\frac{-b}{2 a}\right)+c[/tex]
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A ladder,500cm long lean againt a building if the angle between the ground and the ladder?
So, theta = arctan(sqrt(500^2-d^2) / d) would give us the angle between the ground and the ladder where d is distance from the base of the ladder to the building.
The angle between the ground and the ladder can be found using the inverse tangent function (also known as arctan) and the Pythagorean theorem.
First, we need to find the ratio of the height of the ladder to the distance from the base of the ladder to the building. This ratio is known as the tangent of the angle between the ground and the ladder.
Let h be the height of the ladder and d be the distance from the base of the ladder to the building.
tan(theta) = h/d
Next, we can use the Pythagorean theorem to find the value of h:
d^2 + h^2 = 500^2
Now we can substitute the value of h in the first equation.
tan(theta) = sqrt(500^2-d^2) / d
To find the angle between the ladder and the ground, you can use the inverse tangent function on the above equation.
theta = arctan(sqrt(500^2-d^2) / d)
To find the exact value of the angle, you would need to know the value of d (distance from the base of the ladder to the building).
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if it's 3 in the morning eastern time zone, in what time zone is it 4 in the afternoon
it would be 1oclock the next day
-. Genry worked for 6 consecutive days and earned an average wage of $144 per day as a freelance
handyman. During the first 3 days, Genry averaged $132 per day. His average earned per day for
the next 2 days was $163. How much did he earn on the last day?
If Genry worked for 6 consecutive days and earned an average wage of $144 per day as a freelance handyman. Genry earned $142 on the last day.
How to find the amount earned?Total amount earned for the first 3 days =$132 × 3
Total amount earned for the first 3 days = $396
Total amount he earned for the next 2 days =$163 ×2
Total amount he earned for the next 2 days = $326
Total amount he earned for all 6 days = $144 x 6
Total amount he earned for all 6 days = $864
Now let find the amount Genry earned on the last day
Amount earned = $864 - $396 - $326
Amount earned = $142
Therefore Genry earned $142 on the last day.
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a random sample of students at a large university revealed that, of those who responded, 73% have part-time jobs, 65% participate in at least one school-sponsored activity, and 42% work part-time and participate in at least one school-sponsored activity. suppose we select a student at random. given that the student works part-time, what is the probability that the person participates in at least one school-sponsored activity? p(a|b)
The probability that the person participates in at least one school-sponsored activity given that the student works part-time is 0.58.
What is Conditional Probability?The possibility of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability.
Assume that events A and B are two independent occurrences with probabilities P(A) and P(B), respectively, such that the probability that event B will occur given that event A is given by: P(B|A) = P(A∩B)/P (A)
Given:
Percentage of the students who have part-time jobs, P(A) = 73%
Percentage of the students who participate in at least one school-sponsored activity, P(B)= 65%
Percentage of the students who work part-time and participate in at least one school-sponsored activity, P(A∩B) = 42%
The probability that the person participates in at least one school-sponsored activity given that the student works part-time is:
P(B|A) = P(A∩B)/P(A)
= 42/73
= 0.58
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Answer:
0.575
Step-by-step explanation:
nice job
Let the C.P. be Rs x. If a shopkeeper makes 12% loss by selling a watch for Rs 484, find C.P.
Answer:
To find the cost price (C.P.) of the watch, we need to use the following formula:
C.P. = Selling Price / (1 - Loss Percentage)
In this case, we know that the Selling Price is Rs 484 and the Loss Percentage is 12%. To use this formula, we first need to convert the Loss Percentage to a decimal:
12% = 0.12
Now we can plug in the values into the formula:
C.P. = 484 / (1 - 0.12)
Solving for C.P., we get:
C.P. = 484 / 0.88
C.P. = Rs 550
Therefore, the cost price (C.P.) of the watch is Rs 550.
Solve (x – 3)2 = 49. Select the values of x.
Answer:
x=27.5 hope it helps you..... and hi
Answer:
Step-by-step explanation:
1....Re-order terms so constants are on the left;
2(x - 3) =49
2.. Distribute;
2x-6 =49
3... Add 6 to both sides;
2x-6+6=49+6
4... Simplify;
2x=55
5..Divide both sides by the same factor;
2x=55
[tex]\frac{2x}{2}[/tex] = [tex]\frac{55}{2}[/tex]
6...Simplify;
x=[tex]\frac{55}{2}[/tex]
duri will stay warm in their sleeping bag when the temp is at least 30f. write this as an inequality
duri will stay warm in their sleeping bag when the temp is at least 30f. the situation will be written in inequality as 30F ≤ T. An inequality is used to express a comparison between two values.
In this case, the inequality states that the temperature, represented by the variable T, must be less than or equal to 30F in order for the person in the sleeping bag to stay warm. This means that if the temperature is 30F or higher, the person in the sleeping bag will stay warm. Inequalities use a few different symbols to represent the comparison relationship between two values.
In this case, the symbol used is ≤, meaning "less than or equal to". This symbol is used to indicate that the temperature must be 30F or lower in order for the person in the sleeping bag to stay warm. In more general terms, an inequality represents a comparison between two values that can be expressed on a number line.
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a water tank is shaped like a vertical circular cylinder. initially, the tank is 12.0 ft deep in water when a hole is opened (at time, ) in the bottom of the tank. after 1 hour the depth of water in the tank has dropped to 9.0 ft. how long will it take for all the water to drain from the tank?
it take for all the water to drain from the tank is 1 hour 11 min 26 sec for a water tank is shaped like a vertical circular cylinder
Using the Bernoulli's laws to use the conserved energy
Solve the speed and the radio of this speed of the tank is open to the air
p₀ + ρgh₀ + ½ρv₀² = p₁ + ρgh₁ + ½ρv₁²
5000Pa + 1000kg/m³ * 9.8m/s² * 0.800m + 0 = 0 + 0 + ½ * 1000kg/m³ *
v²
v² = 25.68 m²/s²
v1 = 5.06 m/s
Because it is open the cylinder tank so P=0 pa so:
0 Pa + 1000kg/m³ * 9.8m/s² * 0.800m + 0 = 0 + 0 + ½ * 1000kg/m³ * v²
v² = 15.68 m²/s²
v2 = 3.96 m/s
The ratio on the air is solve using both velocities so:
R = v1/v2 = 5.06 m/s / 3.96 m/s
R = 1.27
Now to find the time it takes for the tank to drain if the tank is open to the air
dh/dt = -u
dh/dt = -v * A/A'
dh/dt = v*(.02m)²/(2.0m)² = -v / 10000
and we can further substitute for v:
dh/dt = -(1/1e4)*√[(p+9800h)/500]
Solve replacing
-(1000/49)*√(49000h) = t + C
-(1000/49)*√(49000*0.8) = 0 + C
C = - 4040.6
Then when h = 0,
t = 4286 s
t = 1 hr, 11 min, 26 sec
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The US GDP (Gross Domestic Product) for 2014 was a reported 17. 555 trillion dollars. The current US population is about 320 million people. Round all answers to the nearest hundredth
The US GDP (Gross Domestic Product) for 2014 was reported to be the nearest hundredth is 17. 56 trillion dollars. The current US population is about 320 million people to the nearest hundredth.
The gross domestic product (GDP) is a commonly used indicator of the value added produced by the production of goods and services in a country over a certain time period (GDP). As a result, it also takes into account the money made from that manufacturing or the sum of money spent on finished goods and services (fewer imports). Although the gross domestic product (GDP) is the most important indicator for gauging economic activity, other metrics may be better suitable for gauging people's material well-being.
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from any point p outside a given circle, there are two lines through p that are tangent to the circle. explain why the distance from p to one of the points of tangency is the same as the distance from p to the other point of tangency. what special quadrilateral is formed by the center of the circle, the points of tangency, and p?
Two congruent right triangles are formed by the tangents and the line connecting P to the circle's centre. They are congruent because one of the pairs of matching sides in each of those two triangles is represented by the tangent segments from P to the sites of tangency with the circle.
The kite-shaped quadrilateral that is created by the two radii and the two tangents has two pairs of adjacent sides.
The radii, the tangents, and the line from P to the centre of the circle combine to form two congruent right triangles. The tangent segments from P to the sites of tangency with the circle are congruent because they represent one of the pairs of corresponding sides in each of those two triangles.The two radii and the two tangents combine to form a quadrilateral with two pairs of adjacent sides, which is why it is a kite.
Lines that cross a circle at a single point are known as tangents. Where the tangent crosses the radius of the circle, it is perpendicular to the tangent. Any curved shape can take into account tangent. Since the tangent is a straight line, its equation will take the form y = m x+ c .
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Reba bought a package with t cat treats.She gave 2 of the treats to her cat.Write an expression that shows the number of treats remaining.
Answer:
t - 2 = the number of treats remaining.
Step-by-step explanation:
Answer:
Step-by-step explanation:
t-2
ow many different id cards can be made if there are five digits on a card and no digit can be used more than once? what if digits can be repeated?
There are 30240 different id cards can be made if there are five digits on a card and no digit can be used more than once.
a) If repetition is allowed, then there are 10 ways to choose each of 5 digits. Hence, by the multiplication rule, we obtain that the total number of possible different ID cards is:
10⋅10⋅10⋅10⋅10 = 10⁵= 100000.
b) If repeats are not allowed, there are 10 ways to choose the first number, 9 ways to choose the second number (because we chose 1 digit as the first number), and 9 ways to choose the third number. There are 8 ways, 7 ways, and 7 ways to choose the 4th number. 6 ways to select the digit to select and the 5th digit.
So according to the multiplication rule the answer is:
10 × 9× 8×7×6 = 30240.
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four students wrote expressions using the variable t below. If t represents a positive integer, whose expression had the greatest value?a. Angelob. Brianc. Chrissyd. Devon
Devon's expression had the greatest value which is 20.
What is an expression?
In mathematics, an expression is a combination of numbers, variables, and operators (such as +, -, ×, ÷, etc.) that represents a mathematical value or relationship. Expressions can be simple or complex, and they can take on many different forms depending on the context.
They are also used to represent real-world problems, and also used to evaluate mathematical expressions to get numerical results.
Step-by-step explanation:
Let's use t=1 to compare all the expressions:
1. -5(12t+9)
if t = 1, -5(12+9) = -5(21) = negative number
2. 2(-6t-8)
if t = 1, 2(-6-8) = 2(-14) = negative number
3. -6(-2t+18)
if t = 1, -6(-2+18) = -6(16) = negative number
4. (-4(-3t-2)
if t = 1, -4(-3-2) = -4(-5) = 20 positive number
Therefore, Devon's expression had the greatest value which is 20.
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identify the inequality that represents the given graph
The inequality, [tex]y < -3x+6[/tex] represents the following graph.
What three instances of inequality?Income gap, gender inequality, access to health care, and social class are some of the most prominent examples of social inequality. Some people receive better and more skilled care in the medical field than others.
What are the two inequalities' rules?Rule 1: An inequality symbol remains unchanged when the same amount is added to or subtracted from both sides. Rule 2: The inequality symbol remains unchanged when both sides are multiplied or divided by a positive number.
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A palindromic number is a number that reads the same when the order of its digits is reversed.
What is the difference between the largest and smallest five-digit palindromic numbers that
are both multiples of 45?
Answer:
Step-by-step explanation:
A five-digit palindromic number is a number that has 5 digits and is the same when read forwards and backwards. A multiple of 45 is a number that is divisible by 45.
To find the largest five-digit palindromic number that is a multiple of 45, we need to find the largest five-digit palindrome and then find the largest multiple of 45 that is less than or equal to that palindrome.
The largest five-digit palindrome is 99999. The largest multiple of 45 less than or equal to 99999 is 99945.
To find the smallest five-digit palindromic number that is a multiple of 45, we need to find the smallest five-digit palindrome and then find the smallest multiple of 45 that is greater than or equal to that palindrome.
The smallest five-digit palindrome is 10001. The smallest multiple of 45 greater than or equal to 10001 is 10035.
To find the difference between the largest and smallest five-digit palindromic numbers that are both multiples of 45, we can subtract the smallest from the largest:
99945 - 10035 = 8910
So the difference between the largest and smallest five-digit palindromic numbers that are both multiples of 45 is 8910.
Solve for X, Leave in simplest radical form
Answer:
x=6
Step-by-step explanation:
[tex] \cos(60) = \frac{x}{12} \\ x = 12 \cos(60) = 6[/tex]
determine the minimum number of terms needed to find the sum of the infinite series 1/n^2 with an error less than 0.001.
The minimum number of terms needed to find the sum of the infinite series 1/n2 with an error less than 0.001 is 11.
1. Calculate the sum of the first 10 terms of the series.
S10 = 1 + 1/4 + 1/9 + 1/16 + 1/25 + 1/36 + 1/49 + 1/64 + 1/81 + 1/100
= 2.405
2. Calculate the 11th term of the series.
T11 = 1/121 = 0.00826
3. Calculate the sum of the first 11 terms of the series.
S11 = S10 + T11 = 2.405 + 0.00826 = 2.41326
4. Calculate the 12th term of the series.
T12 = 1/144 = 0.00694
5. Calculate the difference between the sum of the first 11 terms and the sum of the first 12 terms.
Difference = S11 - S12 = 2.41326 - (2.41326 + 0.00694) = -0.00694
6. Check if the difference is less than 0.001.
Yes, the difference is less than 0.001. Therefore, the minimum number of terms needed to find the sum of the infinite series 1/n2 with an error less than 0.001 is 11.
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answer follow up questions
reference:
2.3 birthdays
Rule B
John March 23
Kelly June 15
Julia April 8
Rule P
August 10 Josh
October 19 Peter
January 27 Angela
Find the length of the third side. If necessary, write in simplest radical form.
According to the Pythagorean theorem length of the third side is [tex]\sqrt{5}[/tex].
What is Pythagorean theorem?
The hypotenuse square in a right-angled triangle is equal to the sum of the squares of the other two sides, according to the Pythagoras theorem. A and B are the triangle's two legs, and C is the hypotenuse, hence this theorem can be written as c2 = a2 + b2. These triangles are also referred to as Pythagorean triangles.
Here in given right triangle side = 2 and hypotenuse = 3.
Now using Pythagorean theorem then,
=> [tex]side^2+side^2=hypotenuse^2[/tex]
=> [tex]side^2+2^2=3^2[/tex]
=> [tex]side^2[/tex]+4=9
=> [tex]side^2[/tex] = 9-4 = 5
=> side = [tex]\sqrt{5}[/tex]
Hence third side length of the right triangle is [tex]\sqrt{5}[/tex].
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What is the equation of the horizontal line through (−4,6)?
Check the picture below.
What is the difference between the values of I-10| and 19| ?
The difference between the given values of |-10| and 19 is - 9
What is an algebraic expression ?
Algebraic expression can be defined as the combination of variables , constants and exponents .
Algebraic expressions are the idea of expressing numbers the use of letters or alphabets with out specifying their actual values. The fundamentals of algebra taught us the way to explicit an unknown value the use of letters such as x, y, z, and so on. these letters are called here as variables. An algebraic expression may be a aggregate of both variables and constants. Any cost this is placed before and extended by way of a variable is a coefficient.
Given values ,
|-10| and 19
the difference ,
|-10| - 19 = 10-19
= -9
Hence, The difference between the given values of |-10| and 19 is - 9
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the national government plans to carry out a census to obtain information about various characteristics of the population. this census will involve all citizens completing a set of forms and returning them to the national bureau of statistics for analysis. the numerical summary measures obtained from the analysis of this population data are referred to as:
Data about a population is collected, recorded, and counted in a census. The numerical summary measures obtained from the analysis of this population data are referred to as parameters.
Censuses of agriculture, traditional culture, businesses, supplies, and even transportation are also prevalent, while the phrase is most often associated with national population and housing counts.
The UN defines the essential characteristics of population and housing censuses as "individual enumeration, universality within a defined territory, simultaneity, and defined periodicity," and suggests that population censuses be conducted at least once every ten years.
The United Nations has made recommendations for what information should be collected in a census, including official definitions, classifications, and other data that might help international organizations coordinate their efforts.
The complete question is attached as an image.
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What are the properties of solution Grade 7?
Solution Grade 7 is a saturated, neutral pH liquid solution made up of a mixture of water and salt, or other electrolyte, with a specific gravity of 1.0, a boiling point of 100°C, and a high electrical conductivity.
Solution Grade 7 is a type of liquid solution used in science experiments. It is typically made up of a mixture of water and salt, or some other electrolyte. It has the following properties:
1. It is a saturated solution, meaning that it contains the maximum amount of dissolved solute that the solvent can hold at a given temperature.
2. It has a neutral pH, meaning that it is neither acidic nor basic.
3. It has a specific gravity of 1.0, meaning that it has a density equal to that of pure water.
4. It has a boiling point of 100°C (212°F), meaning that it boils at the same temperature as pure water.
5. It has a high electrical conductivity, meaning that it can easily conduct electricity.
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Explain why if a symmetric matrix is diagonalizable then we can find an eigenbasis consisting entirely of orthonormal vectors.
If a symmetric matrix can be inverted into a diagonal matrix using another matrix, then it is diagonalizable. Accordingly, it may be said that there is a matrix P that can be inverted such that P-1 * A * P = D, where D is a diagonal matrix and A is the symmetric matrix. The diagonal entries of D are the appropriate eigenvalues, while the columns of P are the eigenvectors of A.
The matrix P is the foundation of the vector space because its columns are linearly independent and it is invertible. The inner product of any two different eigenvectors is 0, as A's eigenvectors are orthogonal to one another due to its symmetry.
We can divide each eigenvector by its norm to get an orthonormal basis from this collection of eigenvectors. As a result, a group of eigenvectors that are orthonormal to one another and serve as the vector space's orthonormal basis are produced.
Therefore, A symmetric matrix is diagonalizable and has an orthonormal eigen basis consisting of orthonormal eigenvectors, which can be obtained by dividing each eigenvector by its norm.
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determine the total time that will have elapsed when 12.5 grams of the original co-60 sample at the hospital remains unchanged. (write the number and unit only)
The total time that will have elapsed when 12.5 grams of the original co-60 sample at the hospital remains unchanged is 16 years
A radioactive isotope of cobalt with a half-life of 5.2713 years is cobalt-60.Nuclear reactors are used to artificially create it. Neutron activation of bulk samples of the monoisotopic and mononuclidic Co-59 is necessary for deliberate industrial manufacture.
Let, the initial amount of the Co 60 = 100 = A
Final amount = 12.5 = A'
We will use the following relation for calculating time elapsed in the decay
[tex]A' = A\frac{1}{2} ^{\frac{t}{t1/2} }[/tex]
Thus,
[tex]A' = A\frac{1}{2} ^{\frac{t}{t1/2} }[/tex]
[tex]12.5 = 100(\frac{1}{2}) ^{\frac{t}{5.2713} }[/tex]
(1/2)³ = [tex](\frac{1}{2}) ^{\frac{t}{5.2713} }[/tex]
3 = t/ 5.2713
t= 3 x 5.2713
t = 15.8139 ≅ 16 years
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the nicotine content in a single cigarette of a particu- lar brand has a distribution with mean 0.8 mg and standard deviation 0.1 mg. if 100 of these cigarettes are analyzed, what is the probability that the resulting sample mean nico- tine content will be less than 0.79? less than 0.77?
The probability that the sample mean nicotine content is less than 0.77 is approximately 0.0003.
The probability that the sample mean nicotine content will be less than 0.79 can be found by using the Central Limit Theorem. The Central Limit Theorem states that the distribution of the sample means approaches a normal distribution as the sample size increases. Since the sample size is 100, we can assume that the sample means nicotine content is approximately normally distributed.
The mean of the sample means nicotine content is equal to the population means, which is 0.8 mg. The standard deviation of the sample means nicotine content is equal to the population standard deviation divided by the square root of the sample size. So, the standard deviation of the sample means nicotine content is 0.1 mg/sqrt (100) = 0.01 mg.
Using these values, we can find the probability that the sample mean nicotine content is less than 0.79 by using the standard normal distribution table or calculator.
z = (0.79 - 0.8) / 0.01 = -1
Using a standard normal table or calculator, P(z < -1) = 0.1587.
So, the probability that the sample mean nicotine content is less than 0.79 is approximately 0.1587.
Similarly, for the sample mean nicotine content less than 0.77
z = (0.77 - 0.8) / 0.01 = -3
P(z < -3) = 0.0003
So, the probability that the sample mean nicotine content is less than 0.77 is approximately 0.0003
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