The linear inequality examples are as follows,
What is linear inequality?
Any two real numbers or two algebraic expressions associated with the symbol ‘<’, ‘>’, ‘≤’ or ‘≥’ form a linear inequality. For example, 9<11, 18>17 are examples of numerical inequalities and x+7>y, y<10-x, x ≥ y > 11 are examples of algebraic inequalities.
The examples of linear inequalities in two variables are:
3x < 2y + 5
8y – 9x > 10
9x ≥ 10/y
x + y ≤ 0
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What is the point of a triangle called?
The points of a triangle are known as vertices, and various triangle points are centroid, circumcenter, incenter and orthocenter.
A triangle is a three-sided polygon.
The triangle's three points are known as vertices.
Several triangle-related points:
A triangle's centroid is the point where three medians cut each other. A median is the line that connects a vertex to the opposite side's midpoint.At the circumcenter, the three perpendicular bisectors of a triangle's sides meet. The circumcenter is also the center of the circle formed by passing through the three vertices of the triangle. The orthocenter is the point at which the triangle's altitudes, or the perpendicular lines between each vertex and the opposite side, intersect.The incenter of a triangle is the point at which the three bisectors of the triangle's interior angles intersect. This is also the center of the inscribed circle, also known as the triangle's incircle.A triangle's Euler line is the line that connects the orthocenter, circumcenter, and centroid. It also contains the Nine Point Circle's center.Thus, the points of a triangle are known as vertices, and various triangle points are centroid, circumcenter, incenter and orthocenter.
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The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a line. a(t) = t + 6, v(0) = 7, 0 ≤ t ≤ 10 (a) Find the velocity at time t. v(t) = Correct: Your answer is correct. m/s (b) Find the distance traveled during the given time interval.
a) The function velocity of the particle is v(t) = 0.5 · t² + 6 · t + 7, b) The distance traveled by the particle is 467 feet.
How to determine the velocity and the distance traveled by a particleIn this problem we have the equation that represents the acceleration of a particle. The function velocity (v) is obtained by integrating the function acceleration (a) and the function position is obtained by integrating the function velocity. Now we present the definitions of each function:
Velocity
v(t) = ∫ a(t) + C
Position
s(t) = ∫ v(t) + C
Where C is the integration constant.
The distance traveled during the time interval is found means of definite integrals:
Δs = [tex]\int\limits^b_a {v(x)} \, dx[/tex]= s(b) - s(a)
a) First, determine the function velocity of the particle:
v(t) = ∫ (t + 6) dt + C
v(t) = 0.5 · t² + 6 · t + C
7 = C
v(t) = 0.5 · t² + 6 · t + 7
b) Second, determine the distance traveled in the given time interval:
Δs = s(10) - s(0)
Δs = 0.167 · 10³ + 3 · 10² + 7 - 0.167 · 0³ - 3 · 0² - 7
Δs = 467
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sqrt((x^(2)-1)^(2))=x^(2)-1
The algebraic expression √((x²-1)²) simplifies to x²-1
How to simply an algebraic expression?
An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.
Given: sqrt((x^(2)-1)^(2))=x^(2)-1
√((x²-1)²)
The square root will cancel out the square:
Thus, √((x²-1)²) = x²-1
Therefore, √((x²-1)²) simplifies to x²-1
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Sheelu bought a scooter for Rs. 55000. While selling the value of the scooter decreased to Rs. 50600. Find the percentage of decrease in the value of the scooter.
Answer:
8%
Step-by-step explanation:
1. Subtract:
55000 - 50600 = 4400
2. Divide:
4400/55000 = 0.08
Pedro vive cerca del bosque, el terreno de su propiedad ocupa 15 metros en total, su casa ocupa sólo 6 metros, tiene un huerto el cual ocupa 4 metros y el resto es un espacio donde puede disfrutar de la naturaleza ahí encuentra algunas clases de musgos que le dan un aspecto maravilloso al bosque.” ● Representa con fracciones el espacio que ocupa la casa, el espacio que ocupa el huerto y deduce qué fracción representa el resto del terreno, a lado de cada fracción realiza la representación gráfica de cada una, usando las herramientas como tablas o insertar formas en PowerPoint.
El espacio que ocupa la casa sería 6/15, el espacio que ocupa el huerto sería 4/15 y el espacio restante del terreno sería 5/15.
¿Cómo representar las fracciones del terreno?Para representar en forma de fracciones el área de los diferentes espacios del terreno de Pedro debemos tener en cuenta que el total tiene 15 metros. Adicionalmente, cuando representamos una fracción estamos informando cuántas unidades de un número x de unidades estamos utilizando. Por ejemplo, en este caso del total (15 metros) del terreno que tiene Pedro, él esta utilizando 6 metros para su casa. Esta fracción se representaría así:
6 / 15
Por otra parte, la fracción para representar el área del huerto de Pedro debe seguir los mismos lineamientos que la anterior, es decir en el numerador (número de la parte de arriba) ponemos el número de unidades que utilizamos y en el denominador (número de la parte de abajo) ponemos el número total de unidades disponibles. Entonces la fracción del huerto sería:
4 / 15
Por ultimo, para saber cuántas unidades quedan disponibles del terreno de Pedro, debemos restarle al total de terreno la cantidad de espacio que usamos:
15 - 4 - 6 = 5
De acuerdo con lo anterior, el espacio disponible serían 5 metros, que expresado en fraccionarios sería:
5 / 15
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An audio cable is 14.1 dm long. How long is the cable in meters?
Answer: 1.41 meters
Step-by-step explanation:
14.1 decimeters to meters
Decimeters are 10 times smaller than meters, so you divide the value by 10 to get meters
14.1/10 = 1.41
1.41 meters
What is function definition with example?
A function is defined as a relation between a set of inputs having one output each.
Say, there is an element x in the sets of input, now it can be paired with no more than one y in the sets of output. We should note that the same y can be paired with different x's, but not the reverse. All linear equations, with the exception of vertical and horizontal lines, are functions.
The function is generally written as "f(x)" where x is the input value.
let us take an example-
f(x) = x/2
here, f(x) is a function because each input "x" has a single output "x/2":
• f(2) = 1
• f(5) = 2.5
• f(−12) = −6
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What is the value of t??
1.4t - 0.4 ( t - 3.1 ) = 5.8
Please explain step by step on how I could get this answer!
1.4t - 0.4(t-3.1)=5.8
Combine terms in paratheses
1.4t - 0.4t + 1.24 = 5.8
Combine t's
(1)t + 1.24 = 5.8
Subtract 1.24 over
t = 4.54please help me answer this question
Answer:
this 1
Step-by-step explanation:
same doubt pease any help
A rectangle is placed around a semicircle as shown below. The width of the rectangle is 4 yd. Find the area of the shaded region.
Use the value 3.14 for pi, and do not round your answer. Be sure to include the correct unit in your answer.
The area of the shaded region is calculated as: 6.88 yd²
How to Find the Area of a Shaded Region?The area of the shaded region in the diagram = area of rectangle - area of semicircle.
Given the following:
Width of rectangle = 4 ydRadius of the semicircle (r) = 4 ydLength of the rectangle = 2(4) = 8 ydArea of the semicircle = 1/2(πr²) = 1/2 × 3.14 × 4² = 25.12 yd²
Area of the rectangle = length × width = 8 × 4 = 32 yd²
The area of the shaded region = 32 - 25.12 = 6.88 yd²
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5. Julia is playing a computer game. To enter a new quest she has
to pay a "tax" of 2.5 points, but she expects to gain 75 points.
For each quest, how many points can she gain overall?
The number of points gained overall by Julia playing the game is 30 point
How to determine the number of points gained overall?From the question, we have the following parameters that can be used in our computation:
Tax paid for a new quest = 2.5 points
Total points gained playing the game = 75 points
The above parameters can be represented as
The number of points gained overall = Total points gained playing the game/Tax paid for a new quest
Substitute the known values in the above equation, so, we have the following representation
The number of points gained overall = 75/2.5
Express as a correct fraction
So, we have the following representation
The number of points gained overall = 750/25
Evaluate the quotients
So, we have the following representation
The number of points gained overall = 30
Hence, the number of points gained overall =is30
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please I need help on question 6
The value of the variable x and the measures of each side of the triangle ΔDEF found using the definition of an isosceles triangle are;
x = 9
DE = 13
EF = 28
DF = 28
What is an isosceles triangle?An isosceles triangle is a triangle that has two angles in the triangle that are congruent and two congruent sides.
The specified parameters are;
∠D is congruent to ∠E in triangle ΔDEF
The length of the segments of ΔDEF are;
DE = x + 4
EF = 4·x - 8
DF = 7·x - 35
The (base) angles ∠D and ∠F of ΔDEF are congruent, therefore, ΔDEF is an isosceles triangle (definition)
Therefore;
EF = DF (Definition of an isosceles triangle)
4·x - 8 = 7·x - 35
7·x - 4·x = 3·x = 35 - 8 = 27
3·x = 27
x = 27 ÷ 3 = 9
x = 9
DE = x + 4
Therefore;
DE = 9 + 4 = 13
EF = 4·x - 8
Therefore;
EF = 4 × 9 - 8 = 28
DF = 7·x - 35
Therefore;
DF = 7 × 9 - 35 = 28
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A rectangular paperboard measuring 21 in long and 16 in wide has a semicircle cut out of it, as shown below.
Find the area of the paperboard that remains. Use the value 3.14 for pi, and do not round your answer. Be sure to include the correct unit in your answer.
The area of the paperboard remaining after a semicircle is cut out of it is 235.52 in².
What is area?The area is the amount of space within the perimeter of a 2D shape.
To calculate the area of the rectangular board that remain, we use the formula below.
Formula:
A' = lw-[πr²/2]............. Equation 1Where:
A' = Area of the paperboard leftl = Length of the paperboardw = width of the paperboardr = Radius of the semi circleFrom the question,
Given:
l = 21 inw = 16 inr = 16/2 in = 8 inπ = 3.14Substitute these values into equation 1
A' = (21×16)-(3.14×8²/2)A' = 336-100.48A' = 235.52 in²Hence, the area of the paperbaord left is 235.52 in².
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Find the area of the shaded region as a simplified expression 5x + 3 * 2x
Answer:11x
Step-by-step explanation:
If m<1 = 128, then m<8=
Answer:
m<8=1024
Step-by-step explanation:
Since they are asking for m<8, we do 128*8=1024.
The equation of a parabola is y = a(x - 1)^2 + k and the points (2, 6.5) and (-1, -1) lie on the parabola. Determine the maximum value of the parabola.
The maximum value of the parabola is represented by y-vertex whose value is 9.
What is a Quadratic Function?
The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.
For solving a quadratic function you should find the discriminant: Δ=b²-4ac . And after that you should apply the discriminant in the formula:[tex]x=\frac{-b\pm\sqrt{\Delta} }{2a}[/tex] .
The question gives a quadratic equation and two points, but you do not know some coefficients. Then, you should find the unknown coefficients and after that, you should find the y-vertex of the parabola ([tex]y_v=\frac{-{\Delta} }{4a}[/tex]).
For finding the coefficients, you should solve the system of equations.
y = a(x - 1)² + k -> points (2, 6.5) and (-1, -1), thus
6.5=a(2-1)² + k (1)
-1=a(-1-1)² + k (2)
Simplifying the equations
6.5=a(1)² + k ( 1 )
-1=a(-2)² + k (2)
6.5=a+ k ( 1 )
-1=4a+ k (2)
Multiply equation 1 by -1
-6.5=-a- k ( 1 )
-1=4a+ k (2)
Sum equations 1 and 2
-7.5=3a
a= -2.5
If a= -2.5, from equation 1, you have
-6.5=-a- k
-6.5=-(-2.5)- k
-6.5=2.5- k
k=2.5+6.5
k=9
Then , the parabola equation is y= -2.5 (x-1)² +9. You can rewrite it as:
y=-2.5(x²-2x+1)+9
y= -2.5x²+5x-2.5+9
y= -2.5x²+5x+6.5
Find y-vertex[tex]y_v=\frac{-{\Delta} }{4a}=y_v=\frac{-{(b^2-4ac)} }{4a}=\frac{-{(5^2-4*(-2.5)*(6.5))} }{4*(-2.5)}=\frac{-90}{-10} =9[/tex]
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The box-and-whisker plots below (sometimes called boxplots) summarize the noon temperatures for each city.
Use the box-and-whisker plots to answer the questions.
Comparing the box-and-whisker plots for both data of each city, we have:
a. City B had more noon temperatures above 76°F
b. Both had the same interquartile range.
c. City B had a larger median noon temperature
d. City A had the largest noon temperature.
How to Analyze a Box-and-whisker Plot?The box-and-whisker plot has the following values it displays about a data distribution:
Minimum value: This is the value at the beginning of the left whisker.Lower quartile (Q1): This is indicated by the beginning of the edge of the box, 25% of the data are below this point.Median value: the line that divides the box is the median value which is 50% of the data.Upper quartile (Q3): This is indicated by the end of the edge of the box, 75% of the data are below this point.Maximum value: This is the largest data point and is located at the end of the right whisker.Interquartile range = Q3 - Q1
Analyzing the box-and-whisker plots given above, we have the following to conclude:
a. City B had more noon temperatures above 76°F because about more than 50% of the data are above 76°F.
b. Interquartile range for City A = Q3 - Q1 = 75 - 68 = 7
Interquartile range for City B = Q3 - Q1 = 80 - 73 = 7
Both had the same interquartile range.
c. Median for City A = 70
Median for City B = 78
City B had a larger median noon temperature
d. City A had the largest noon temperature of 85.
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8+[8+(−1⋅(−3)−4)]÷(−7)
Answer:
8 + [8 + (-1*(-3)-4)]÷(-7) = 7/1 = 7
Hope this helped answer your question!
Answer:
7
Step by Step Explanation:
The cost of a cheese pizza is $11.99 plus $0.45 for each additional topping, t. Write an inequality that can be used to represent the cost of a pizza that is at most $16. What is the most number of toppings that a pizza can have and still be at most $16?
Answer: 11.99 + 0.45t ≤ 16 The most toppings you can have is 8
Step-by-step explanation:
11.99 + 0.45 is a basic cheese pizza plus one topping
11.99 + 0.45t represents a pizza plus an undefined amount of toppings
11.99 + 0.45t ≤ 16 The cost of the pizza has to be 16$ or less
Subtract 11.99 from each side
0.45t ≤ 4.01
Divide both sides by 0.45
t ≤ 8.9111
You can't have a partial number of toppings, and 9 is too much, so we round down to 8.
A model rocket is shot straight up from the roof of a school. The height, h, in meters, after t seconds can be approximated by h(t)=-5t2+22t+15. Answer the following questions algebraically, showing all of your work
How long does it take for the rocket to pass a window that is 10m above the ground? (hint: make h=10, group like terms, then solve the quadratic equation)
Answer: [tex]\frac{11+\sqrt{146}}{5}[/tex] seconds
Step-by-step explanation:
[tex]10=-5t^2 +22t+15\\\\5t^2 -22t-5=0\\\\t=\frac{22 \pm \sqrt{(-22)^2 -4(5)(-5)}}{2(5)}\\\\t=\frac{11+\sqrt{146}}{5} \text{ } (t > 0)[/tex]
Some people are saying it is possible to use the Law of Cosines to solve a triangle if given only three angles, and some are saying it is not possible. Which is it?
Hence, yes we can solve the triangle with the help of Law of Cosines.
What is trigonometry?
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Here given that,
Some people are saying it is possible to use the Law of Cosines to solve a triangle if given only three angles, and some are saying it is not possible.
Yes, with the help of Law of Cosines we can solve the triangle and the formula for it is
[tex]c^2=a^2+b^2-2abcos(C)[/tex]
where, [tex]a,b,c[/tex] are the side lengths of the triangle and [tex]C[/tex] is the angle.
Hence, yes we can solve the triangle with the help of Law of Cosines.
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Cole and Maggie play table tennis. Maggie has won 4 more games than Cole. Is it possible for Cole to have won 13 games if the sum of the games Cole and Maggie have won together is 30?
*
1 point
Yes; Cole could have won 13 games because 2x + 4 = 30.
Yes; Cole could have won 13 games because 13 + 4 is less than 30.
No; Cole could not have won 13 games because 2x + 13 ≠ 30.
No; Cole could not have won 13 games because 2x + 4 ≠ 30
The answer to this Question is A we can use basic knowledge from linear equations to find the answer
What is Linear Equation?
Linear Equation is a equation in which degree of variables is 1 only
Yes the given case is possible only under some conditions that we can define as follows and as given in Linear Equations from Options
together cole and maggie have won 30 games and we are also given that out of those 30 maggie has won 4 games
we should closely see at Linear Equations given in Options.
therefore cole has won 26 games which is more than 13
Hence the answer to the Question is Yes
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A magician makes potions by combining maple syrup from a magical maple tree with ordinary water. The magician starts with a large supply of two potions: a red potion, which is 50% magical syrup by volume (and the rest is just water), and blue potion, which is 10% magical syrup by volume. (Perhaps you're wondering how the same syrup can produce both red and blue potions. That's why it's magic syrup!)
(a) Find the amount of red potion (in mL) that must be added to 200 mL of blue potion in order to produce potion that is 30% magical syrup by volume.
(b) Find the amounts of red potion and blue potion (in mL) that can be combined in order to produce 150 mL of a potion that is 30% magical syrup by volume.
(c) Does there exist a combination of red potion and blue potion that can produce a potion that is 20% magical syrup by volume?
Answer:
Step-by-step explanation:
its a
What does m<2 mean in geometry?
Answer: I hope this is helpful mark me brainlist if this apply to you
Step-by-step explanation:
The square meter, also called the meter squared, is the International System of Units (SI) unit of area. The symbol for square meters is m2. Less formally, square meter is sometimes abbreviated as sq m.A metre square is a square with sides one metre in length – it refers to the shape and the side length, not the area. By contrast, a square metre is an area and can be any shape.The basic unit of length is the meter and is denoted as. In geometry, can be used as a variable to denote a line and can be used to name a point. In algebra, denotes the slope of a line in the equation y = m x + c .
A car is traveling at a rate of 20 meters per second. What is the car's rate in kilometers per hour? How many kilometers will the car travel in 2 hours? Do not round your answers.
Rate:
Distance traveled in 2 hours:
Answer:
Rate = 72 km per hour
Distance traveled in 2 hours = 144 km
Step-by-step explanation:
The car speed is given as 20 meters per second
There are 3600 seconds in an hour
So in 1 hour the car would travel 20 x 3600 = 72,000 meters. This is equivalent to 72,000 meters per hour
There are 1000 meters in a kilometer
So, in terms of kilometers, the car would travel 72,000/1000 = 72 km i one hour. This is equivalent to a speed of 72 km per hour
In 2 hours the car would travel 72 x 2 = 144 km
Can someone help me please? I would really appreciate the person to help me.
The system of linear equations have variable unique solutions, infinitely many solutions and no solutions.
System of Linear EquationIn algebra, a system of equations comprises two or more equations and seeks common solutions to the equations. "A system of linear equations is a set of equations which are satisfied by the same set of variables."
A system of equations as discussed above is a set of equations that seek a common solution for the variables included.
1.
y = -2x + 3 ...eq(i)
y = 1/2x - 7 ...eq(ii)
The solutions to the linear equations (x,y) are (4, -5)
2.
y = 2x - 7 ...eq(i)
y = 5x + 5 ...eq(ii)
The solutions to the linear equations (x,y) are (-4, -15)
3.
3y = -12x + 6 ...eq(i)
y = -4x + 2 ...eq(ii)
The linear equations (x, y) have infinitely many solutions
4.
y = -2x + 3 ...eq(i)
y = 2x - 1 ...eq(ii)
The linear equations (x,y) have solutions of (1, 1)
5.
y = 5x + 4 ...eq(i)
y = 5x - 2 ...eq(ii)
The linear equations have no solutions
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What is Incentre of triangle ABC?
The Incenter of triangle ABC is I = (ax1+bx2+cx3 / a+b+c , ay1+by2+cy3 / a+b+c).
Given:
Let I be the incenter of triangle ABC.
Let A(x1,y1) ,B(x2,y2) and C(x3,y3) are vertices.
Let a,b and c are lengths of the sides AB,BC and AC.
we know that:
Incenter I = (ax1+bx2+cx3 / a+b+c , ay1+by2+cy3 / a+b+c)
we can find a, b and c values using the distance formula between the vertices.
AB = a = [tex]\sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]
BC = b = [tex]\sqrt{(x3-x2)^2 + (y3-y2)^2}[/tex]
AC = c = [tex]\sqrt{(x3-x1)^2 + (y3-y1)^2}[/tex]
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Which symbol is represent function?
The value of a function f at an element x of X, denoted by the symbol f(x), is regarded to as the picture of x as per f or the value of f implemented to the input x.
In the given question we have to define which symbol is represent function.
The notation f: X→Y denotes a function, its domain, and its codomain. The value of a function f at an element x of X, denoted by the symbol f(x), is regarded to as the picture of x as per f or the value of f implemented to the input x.
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How do you match equivalent expressions?
To match equivalent expression is the fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.
In mathematics, equivalent fractions are those with the same denominator and differing numerators.
According to equivalent fractions, two or more fractions are considered to be equal if both provide the same fraction following simplification. Let's imagine that two fractions, a/b and c/d, were simplified to provide comparable fractions, e/f. In this case, the two fractions are equal to one another.
For instance, if we simplify 5/15, we get a fraction that is equal to 1/3, which is equal to 5/15.
We have to find how do we match equivalent expression.
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Is the exponential function 5 x?
It is Growing Exponential function because the base is greater than 1 and the exponent has a positive sign.
What is exponential decay function?
A exponential decay is a function that, as the name implies, decays exponentially. So it decays fast at the beginning and slower as the value of the variable increases.
[tex]y=5^x[/tex]
It is a function called "Exponential function". The base determines the growth or decay of the function.
If base > 1, then the function grows, otherwise if base is between 0 and 1, the function decays.
Here, the base is positive and it's not 1 or 0.
If we have
[tex]y=5^{-x}[/tex]
this function can be rewritten in this way:
[tex]y=(1/5)^x[/tex]
Here, base between 0 and 1, the function decays
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