The polynomial 1 / 10 x² + 10 - 3x in standard form is 1 / 10 x² - 3x + 10.
How to represent polynomial in standard form?The standard form of a polynomial is expressed by writing the highest degree of terms first then the next degree and so on.
Standard form simply refers to the format of a polynomial expression where the terms are arranged by decreasing order of degree. Where the degree is determined by the exponent value of the variable of each term.
Therefore, let's rewrite the expression in standard form.
1 / 10 x² + 10 - 3x
Hence, in standard form,
1 / 10 x² - 3x + 10
learn more on standard form here: https://brainly.com/question/7037256
#SPJ1
if y varies jointly with x and z and y=-60 when x=-5 and z=4, find y when x=4 and z=-3
The value y is -36.
What is proportionality?Proportionality is the property of two variables being in a multiplicative relation to a constant.
Given that, y varies jointly with x and z and y=-60 when x=-5 and z=4,
y ∝ xz
Let k be the Proportionality constant,
y = kxz
-60 = k*4*-5
k = 3
When x = 4 and z = -3
y = 3*4*-3
y = -36
Hence, The value y is -36.
For more references on Proportionality, click;
https://brainly.com/question/22620356
#SPJ1
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.
Learn more about box-and-whisker plot on:
https://brainly.com/question/12343132
#SPJ1
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.
Learn more about area here: https://brainly.com/question/25092270
#SPJ1
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
To learn more about the exponential decay function from the given link
brainly.com/question/19599469
#SPJ4
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
Aprenda más sobre fraccionarios en: https://brainly.com/question/24249348
#SPJ1
PLSSSSSSS HELPPPPPPPPP
Answer:
undefined
Step-by-step explanation:
since all the x are zero it’s undefined and when all y is zero it’s 0
Hopes this helps please mark brainliest
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 .
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:
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.
To learn more about points of triangle refer here
https://brainly.com/question/10273861
#SPJ4
Find the area of the shaded region as a simplified expression 5x + 3 * 2x
Answer:11x
Step-by-step explanation:
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]
Learn more about the triangle here:
https://brainly.com/question/2773823
#SPJ4
How do you find the equidistant point of a triangle?
The equidistant point of the triangle is point O , which is shown below.
In the question ,
we have to find the equidistant point in the triangle ,
We know that the equidistant point from the vertices of the triangle is the circumcenter ,
let the circumcenter be point O .
The perpendicular bisectors of the given triangle ABC are AC and BC that intersect at point O .
We have to prove that point O lies on the perpendicular bisector of AB and it is equidistant from A , B and C .
So ,we draw OA ,OB and OC .
we know that any point on perpendicular bisector of a segment is equidistant from endpoints of the segment.
that means , OA = OC and OC = OB .
which means OA = OB .
we also know that any point that is equidistant from end points of a segment lies on its perpendicular bisector.
So, we can say that point O is on the perpendicular bisector of AB .
and
Since OA = OB = OC , the point O is equidistant from A , B and C .
Therefore , the equidistant point of the triangle is the circumcenter (point O) .
Learn more about Circumcenter here
https://brainly.com/question/2520846
#SPJ4
A water line enters a house 2.0m below ground. A smaller diameter pipe carries water to a faucet in the house. Water flows at 2.0m in the main line and 7.0m out of the second-floor faucet. Take the density of water to be 1.0 ×10^-3 ^3 If the pressure in the line is 2.00 × 10^5 and the pressure at the faucet is 1.40 × 10^5 , how far above ground is the faucet?
The difference in pressure between the main line and the second floor is 91,100 Pa.
How to calculate difference in pressure between main line and second floor ?Bernoulli's theorem states that a drop in fluid pressure is connected with an increase in fluid velocity if the fluid flows horizontally so that there is no change in gravitational potential energy.
On the basis of the idea of energy conservation, Bernoulli's principle is explained. According to this law, the total amount of mechanical energy in a fluid travelling along a streamline will be the same at every point along that streamline in a steady flow.
Given ,
The settings provided;
The main line's water speed is 2.0 m/s,
The second floor's water speed is 7.0 m/s,
The water's density is 1.0 x 103 kg/m3.
The following formula can be used to compute the pressure difference between the main line and the second level using Bernoulli's equation:
[tex]p_1+1/2pv2/1+pgh1+ = p2+1/2pv2/2+pgh_2[/tex]
[tex]p1- p2 = 1/2pv2/2 - 1/2pv2/1 + pgh2 - pgh1[/tex]
[tex]p1 - p2 = 1/2p(v2/2 - v 2/1) + pg (h2- h1)[/tex]
p1 - p2 = 1/2(1000)(7² - 2²) + (1000 ×9.8)(5 - (-2))
p1 - p2 = 91100 pa
Thus, the difference in pressure between the main line and the second floor is 91,100 Pa.
The complete question is : A water line enters a house 2.0 m below ground. A smaller diameter pipe carries water to a faucet 5.0 m above ground, on the second floor. Water flows at 2.0 m/s in the main line and at 7.0 m/s on the second floor. Take the density of water to be 1.0 × 103 kg/m 3 . The difference in pressure between the main line and the second floor is _______.
To learn more about Bernoulli's equation refer to :
https://brainly.com/question/14082066
#SPJ4
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]
Learn more about the quadratic function here:
brainly.com/question/1497716
#SPJ1
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
Read more about expression at
https://brainly.com/question/4344214
#SPJ1
A person drives 120 kilometers in 2 hours. The distance traveled is proportional to the time taken. If the distance driven, in kilometers, is represented by d and the time taken, in hours, is represented by t, which equation could represent the relationship between d and t?
The equation that could represent the relationship between [d] and [t] is d = 60t.
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
We have a person drives 120 kilometers in 2 hours. The distance traveled is proportional to the time taken.
We can write the equation that could represent the relationship between [d] and [t] with the help of the equation of a straight line.
y = mx + c
for c = 0
y = mx
m = 120/2
m = 60
So -
y = 60t
or
d = 60t
Therefore, the equation that could represent the relationship between [d] and [t] is d = 60t.
To solve more questions on straight lines, visit the link below-
brainly.com/question/20400984
#SPJ1
How do you rewrite equivalent expressions?
To rewrite equivalent expression is the fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.
We know that,
The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.
It's crucial to understand the concept of multiplicity in order to correctly count without mentioning exceptions (for example, double roots counted twice). Thus, "counted with multiplicity" is used.
This can be highlighted by counting the number of different elements, as in "the number of separate roots," if multiplicity is disregarded. However, multiplicity is always taken into account when a set (as opposed to a multiset) is established, therefore the word "different" is not necessary.
To learn more about fraction visit: https://brainly.com/question/10354322
#SPJ4
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.
What property describes the number sentence of 6 0 6?
The property that defines the number sentence 6 + 0 = 6 is Additive Identity Property.
Given,
6 + 0 = 6
We have to find the property that defines the number sentence;
Additive Identity Property;
Additive identity property says that if zero is added to any real number, the resultant would be the same real number.
Here,
6 + 0 = 6
In this instance, we have added 0 to a real number (6) and have received back the same real number (6).
That is,
Additive Identity Property is the property that defines the number sentence 6 + 0 = 6
Learn more about Additive Identity property here;
https://brainly.com/question/112508
#SPJ4
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
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.
To learn more about function link is here
brainly.com/question/5975436
#SPJ4
Is centroid and Circumcentre same?
No, the centroid and Circumcentre are not same but it is same in equilateral triangle.
The intersection of a triangle's perpendicular bisectors is called the circumcenter.A triangle's circumcenter is a location that is equally spaced from each of its vertices.The centroid of a triangle is the location where its medians connect.
Triangle's centroid is always within it. The centroid of a triangle is its center of gravity in physical terms. If the triangle is evenly distributed around the plane's surface and you want to balance it by supporting it at only one point, you must do it near the center of gravity.Are the circumcenter and centroid at the same location? In the case of an equilateral triangle, they will both be.
Therefore, the centroid and Circumcentre are not same but it is same in equilateral triangle.
To learn more about circumcenter click here:
brainly.com/question/16276899
#SPJ4
graph the system of equations below on a piece of paper. what is the solution y=x-1 y=3x+1
The intersection of these lines is the answer to the given system of equations. → (-1, -2)
Given the system of equations,
y = x - 1
y = 3x + 1
Now, equating both the given equations,
x - 1 = 3x + 1
3x - x = -2
2x = -2
x = -1
From, y = x - 1
y = -1 - 1
y = -2
The answer to the given system of equations is located at the intersection of these lines.
⇒ (-1, -2)
To learn more about equations click here:
brainly.com/question/10413253
#SPJ4
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 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 = 4.54A 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
Learn more about the area of shaded region on:
https://brainly.com/question/14989383
#SPJ1
What is the length of 1 ton AC?
The length of 1 on AC is 54.6 cm.
Given:
Let x be the length
we know that,
AC dimensions = 54.6 * 175.7 * 85.6 cm
It is the volume = l * b * h
Volume :
Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.
Length :
Length is defined as the measurement or extent of something from end to end.
Breadth :
The breadth of something is the distance between its two sides.
On comparing both
Length l = 54.6 cm
Breadth b = 175.7 cm
Height h = 85.6 cm
Therefore the length of 1 on AC is 54.6 cm.
Learn more about the length here:
https://brainly.com/question/8552546
#SPJ4
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
Read more about Functions:
brainly.com/question/22340031
#SPJ4
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
Learn more on system of linear equation here;
https://brainly.com/question/13729904
#SPJ1