Answer: The measure of the third side of a triangle, when the measures of the other two sides are 13 in and 27 in, must be greater than the difference between the measures of the other two sides (which is 27 in - 13 in = 14 in) and less than the sum of the measures of the other two sides (which is 27 in + 13 in = 40 in).
This is because according to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So the measure of the third side must be between the difference of the two given sides and the sum of the two given sides.
Therefore the range of the measure of the third side of a triangle with side lengths 13 in and 27 in is:
(14 in < x < 40 in)
or
[x > 14 in and x < 40 in].
It is also important to note that any value of x within this range will produce a valid triangle, however any value less than 14 in or greater than 40 in will not.
Step-by-step explanation:
The function f(x) = -0.5x^2 + 32.5x - 375 gives a company's profit (or loss) in thousands of dollars, based on what it charges for it's product, x in dollars. If the product is too cheap, the company will not make enough money. If it is too expensive, it will not sell well. A company "breaks even" when it makes enough money to cover it's costs, but hasn't yet made a profit. To break even or make money, how much should the company charge for it's product?
To break even or make money, the company should charge at least $_____________ for it's product but no more than $___________
Using the quadratic function for the company to break even the company should charge at least $ 15 for it's product but no more than $ 50.
What is a quadratic function?A quadratic function is an equation in which the highest power of the unknown is 2.
How to find the amount of money the company should charge to break even?Since we have the function f(x) = -0.5x² + 32.5x - 375, to determine the value of x at which the company breaks even, we equate f(x) to zero and solve for x.
So, f(x) = 0
⇒ -0.5x² + 32.5x - 375 = 0
So, using the quadratic formula, we solve for x
so, [tex]x = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}[/tex]
where
a = -0.5, b = 32.5 and c = -375So, substituting the values of the variables into the equation, we have that
[tex]x = \frac{-32.5 +/- \sqrt{(32.5)^{2} - 4\times(-0.5)\times(-375)} }{2\times(-0.5)}\\= \frac{-32.5 +/- \sqrt{1056.25 - 750} }{-1}\\= \frac{-32.5 +/- \sqrt{306.25} }{-1}\\= \frac{-32.5 +/- 17.5 }{-1} \\x = \frac{-32.5 - 17.5 }{-1} or x = = \frac{-32.5 + 17.5 }{-1} \\x = \frac{-50}{-1} or x = \frac{-15}{-1} \\x = 50 or x = 15[/tex]
So, for the company to break even the company should charge at least $ 15 for it's product but no more than $ 50.
Learn more about quadratic function here:
https://brainly.com/question/28955205
#SPJ1
A stadium brought in an average revenue of $11,000 per night for a professional sports tournament. Total receipts for the
period of time the tournament took place was $132,000. This means the tournament took place throughout how many days?
a) 5
b) 7
c) 12
d) 14
A stadium brought in an average revenue of $11,000 per night for a professional sports tournament. Total receipts for the period of time the tournament took place was $132,000. This means the tournament took place throughout is 12 days
How to find the number of members ?
When the teachers joined the members of the chess club for a tournament, the number of members that Alan counted was 31 people which means that the number of members in the chess club would be this number, less the number of teachers.
A stadium brought in an average revenue of $11,000 per night for a professional sports tournament.
Total receipts for the period of time the tournament took place was $132,000.
This means the tournament took place throughout how many days?
since total divide by per night is equal to number of days
now 132000/11000= 12
learn more about of average here
https://brainly.com/question/30170976
#SPJ4
rewrite the following polynomial in standard form
Polynomial [tex]$-1+x^3-\frac{1}{3} x^3$[/tex] and its conventional form, [tex]x^5-\frac{x^2}{3}-1$$[/tex] , are both used.
How did you write the polynomial in standard form?[tex]$$-1+x^5-\frac{1}{3} x^2=x^5-\frac{x^2}{3}-1$$[/tex]
steps
[tex]$$-1+x^5-\frac{1}{3} x^2$$[/tex]
[tex]\begin{aligned}& \frac{1}{3} x^2=\frac{x^2}{3} \\& =-1+x^5-\frac{x^2}{3}\end{aligned}[/tex]
rephrase in proper grammar
[tex]=x^5-\frac{x^2}{3}-1$$[/tex]
The term "polynomial" refers to a mathematical statement of one or more algebraic terms in which the variables are all of non-negative integer powers. Variables, fixed values, and exponents are all present in the terms. The degree 'n' standard form polynomial is Standard form is one method of expressing a polynomial. You must consider each term's degree in order to write any polynomial in standard form.
Next, list each phrase in order of degree, left to right, highest to lowest. An expression that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables is said to be a polynomial. Variables, which are sometimes known as indeterminates, and coefficients make up a polynomial.
To learn more about Polynomial refer to :
https://brainly.com/question/1600696
#SPJ1
what must be included in a algebriac expression?
Answer:
Algebraic expressions include at least one variable and at least one operation (addition, subtraction, multiplication, division). For example, 2(x + 8y) is an algebraic expression.
Step-by-step explanation:
From a 200-foot observation tower on the beach, a man sights a whale in difficulty. The angle of depression of the whale is 7 degrees. How far is the whale from the shoreline?
Whale is 1628.87 feet far from the shoreline.
What is angle of depression?The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.
Given,
Height of the tower = 200 feet
Angle of depression = 7°
Distance of whale from the shore line = x = AB = ?
In the figure
tan 7° = BC/AB = 200/AB
0.1228 = 200/AB
AB = 1628.87 feet = x
Distance of whale from the shoreline = 1628.87 feet.
Hence, Whale and shoreline are 1628.87 feet far from each other.
Learn more about angle of depression here:
https://brainly.com/question/13514202
#SPJ1
Please help me with my classwork
Answer:(b)7m^4
Step-by-step explanation:
56m^8/8m^4
is can be said as
(7m^4 )(8m^4)/8m^4
8m^4 from both numerator and as well as denominator cancels so the final answer is 7m^4(7 m to the power 4)
If XV =27-2x and VZ =3x+2, find VZ and XZ
If XV =27-2x and VZ =3x+2, then the diagonal of parallelogram XZ = 34 units and VZ = 17 units.
What is a parallelogram?
A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size.
The length of line XV = 27 - 2x.
The length of line VZ = 3x + 2.
According to the properties of a parallelogram the diagonals bisect each other .
Hence, XV = VZ.
Equating the expressions -
27 - 2x = 3x + 2
-2x - 3x = 2 - 27
-5x = -25
x = 5
The value of line XV = 27 - 2x
27 - 2(5)
27 - 10
17 units
The value of line VZ = 3x + 2
3(5) + 2
15 + 2
17 units
The value of line XZ = XV + VZ
17 + 17
34 units
Therefore, the value of VZ = 17 units and value of XZ = 34 units.
To learn more about parallelogram from the given link
https://brainly.com/question/970600
#SPJ1
Carter A charges $15 per person and $100 to set up tables. Carter B charges $20 per person and $50 to set up tables. Graph a system of equations. For what number of guests will the cost of Carter A be the same as the cost of Carter B? What is the cost for that number of guests?
PLEASE HELP AS SOON AS YOU SEE THIS!!!
Answer:
x=10 guests and $250
Step-by-step explanation:
Cater A=15x+100
Cater B=20x+50
2x+50=15x+100
5x=50
x=10
i need help with my math, can someone tell me yes or no for each one?
yes there is no work show below
Consider this system of equations 2/3 x + 3/5 y =12 (equation A) 5/2y - 3x = 6 (equations B)
The values of x and y that are solutions to the system of simultaneous equations are; y = 573/25 and x = 17.1
How to solve the system of linear equations?We are given the simultaneous equations;
²/₃x + ³/₅y = 12 -----(eq A)
⁵/₂y - 3x = 6 ------(eq B)
Multiply eq A by 9 and eq B by 2 to get;
6x + ²⁷/₅y = 108 -----(eq C)
5y - 6x = 12 ------(eq D)
Add eq C to eq D to get;
5y + ²⁷/₅y = 120
Multiply through by 5 to get;
25y + 27 = 600
25y = 600 - 27
25y = 573
y = 573/25
Thus;
5(573/25) - 6x = 12
6x = 5(573/25) - 12
6x = 102.6
x = 17.1
Read more about system of linear equations at; https://brainly.com/question/14323743
#SPJ1
Answer this following question to revive 10 points
Answer:
2x^7
Step-by-step explanation:
To simplify this expression, there are two steps. You have to act as though the exponents are whole numbers and add them together to combine like terms.
[tex]2x^4 \times x^3\\= 2x^{4+3}\\= 2x^7[/tex]
Hope this helps!
I need help with the problem on the photo. It’s in French so angines who can read French please tell me the answer.
Answer:
Step-by-step explanation:
Karine De Marchand is 54 years
Complete the table below for the equation y=1/2x-1.
Why pixel value is 255?
The value 255 in pixels means the code for the image is white. Therefore, any image with 255 pixels means it is white color.
Pixel values are the numerical values that make up the matrix in which images are stored in computers. The byte image, the most popular pixel format, stores this number as an 8-bit integer with a possible value range of 0 to 255.
Normally, zero and 255 are considered to be black and white, respectively. The many colors of gray are composed of values in between. This has the tremendous benefit of allowing computers to operate with color values that can be stored in a tidy number of bytes.
It is represented in 8 bits because 2⁸ equals 256 (from 0 to 255).
To know more about pixels:
https://brainly.com/question/3486094
#SPJ4
Describe the power function f(x)=x^5. What does it look like? Where does it cross the x- and y-axis?
f(x) = x⁵ – 8x⁴ + 16x³ at x = 4, does not cross the x-axis. at x = 0, crosses the x-axis. This relates to the x-axis end behavior of a graph of a function.
What is meant by Function?A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output.A function, which generates one output from a single input, is an illustration of a rule. The photographer is Alex Federspiel.Y=X2 is an illustration of this. You only get one output for y if you enter anything for x. The fact that x is the input value leads us to say that y is a function of x.An input is connected to an output by a function. It resembles a device with an input and an output.Let's now find the roots of this function;
f(x) = x⁵ - 8x⁴ + 16x³
Let's factorize it first to get;
f(x) = x³(x² – 8x + 16)(x² – 8x + 16) is a perfect square trinomial and can be expressed as (x – 4)(x - 4).
Thus; f(x) = x³ (x – 4)(x - 4)
C) Since we have found the factorized form to be;
f(x) = x³ (x – 4)(x - 4)
The roots are at f(x) = 0;
The roots are; x³ = 0; (x – 4) = 0 ; (x - 4) = 0
This indicates that x=0 and x=4 are f(xroots. )'s x = 4
As a result, the graph will touch the x-axis but not the repeated root of 4, which indicates that the graph has a repeated root.
D) The graph will cross at x = 0 because it is a root and does not cross at x = 4.
To learn more about Function, refer to:
https://brainly.com/question/11624077
#SPJ1
Write the function g(x)=Asin(Bx)+C that results from the given transformation of f(x)=sin(x).
The function f(x) is stretched vertically by a factor of 3 and horizontally by a factor of 12 and is translated down 5 units to obtain the function g(x).
Question 1
What is the value of A, the amplitude of the function?
Enter your answer in the box.
The amplitude of a sine or cosine function is the vertical stretch or compression factor of the function. In this case, the function f(x) = sin(x) has been stretched vertically by a factor of 3. Therefore, the amplitude of the function g(x) is A = 3.
The function g(x) = 3sin(12x) + (-5)
What is the y-intercept of Y =- 10?
The y-intercept of Y = - 10 is -10.
If we draw the graph of the linear equation y = mx + c. The result is a line with m as the slope, and c as the y-intercept. This form of the linear equation y = mx + c is called the slope-intercept form, and the values of m and c are real numbers.
The slope, m, of the line represents the steepness of a line. This is also termed a gradient, sometimes. The y-intercept, b, represents the y-coordinate of the point where the graph of the line intersects the y-axis.
Now, if we equate the standard slope-intercept form of the equation with the given equation, we get
y = mx + c
y = - 10 = 0x -10
m = 0 and c = -10
As we know the c is the y-intercept which is equal to -10.
To know more about slope-intercept form, here
https://brainly.com/question/29146348
#SPJ4
A time of 10.4 seconds is given to the nearest 0.1 of a second complete the error interval
The result for the error interval has already been rounded to the nearest integer, which is 4.8.
Define the term error interval?The accuracy thresholds that apply that whenever a number has now been rounded or shortened are known as error intervals. In other words, they represent the range of values which a number may have taken had it not been rounded off or truncated.The numbers 10.3 and 10.5 are below and above, respectively (to 1 decimal place)
For the lower bound, we need to look halfway between 10.3 and 10.4 and for the upper bound, we need to look halfway between 10.4 and 10.5.
For the number to be rounded to 10.4 with one decimal point, it has to be between 10.35 and 10.45.
An inequality can be used to describe this.
We use the or equal symbol because 10.35 should round to 10.4.We simply utilize the less than sign because 10.45 would just not round to 10.5.10.35 ≤ x < 10.45
Thus, the error interval with the lower bound and upper bound are: 10.35 ≤ x < 10.45.
To know more about the error interval, here
https://brainly.com/question/28791883
#SPJ1
What is obtuse triangle Class 7?
A triangle whose any one of the angles is an obtuse angle or more than 90°, then it is called an obtuse-angled triangle or obtuse triangle.
What is obtuse in math?Less than 90 degrees is the acute angle measurement. Right angles are 90 degrees in length. Angles that are obtuse are more than 90 degrees. Isosceles (two equal sides and two equal angles) or scalene are two possible types of obtuse triangles (no equal sides or angles). This indicates that every angle is less than 90 degrees. A triangle with two angles that are less than 90 degrees and one angle that is 90 degrees (acute angles). A triangle is said to have an obtuse angle if one of the inner angles is greater than 90 degrees. If one of the angles of an obtuse triangle is greater than 90°, then the total of the other two angles is also less than 90°.To learn more about obtuse refer to:
https://brainly.com/question/30193837
#SPJ4
Evaluate the integral. (Use C for the constant of integration). integral t/t^4 + 5 dt
The value of integral is [tex]\frac{1}{2 \sqrt{5}} \tan ^{-1}\left(\frac{t^2}{\sqrt{5}}\right)+C$$[/tex]
The Integral is [tex]$$\int \frac{t}{t^4+5} d t$$[/tex]
Indefinite integrals are not defined using the upper and lower limits. The indefinite integrals represent the family of the given function whose derivatives are f, and it returns a function of the independent variable.
The integration denotes the summation of discrete data. The integral is calculated to find the functions which will describe the area, displacement, volume, that occurs due to a collection of small data, which cannot be measured singularly.“Integral is based on a limiting procedure which approximates the area of a curvilinear region by breaking the region into thin vertical slabs.Let [tex]$t^2=u= > t d t=\frac{d u}{2}$[/tex]
The above Integral becomes
[tex]$\frac{1}{2} \int \frac{1}{u^2+(\sqrt{5})^2} d u=\frac{1}{2 \sqrt{5}} \tan ^{-1}\left(\frac{u}{\sqrt{5}}\right)+C$$[/tex]
Substitute u In terms of t
[tex]$$\int \frac{t}{t^4+5} d t=\frac{1}{2 \sqrt{5}} \tan ^{-1}\left(\frac{t^2}{\sqrt{5}}\right)+C$$[/tex]
Therefore, the value of integral is [tex]\frac{1}{2 \sqrt{5}} \tan ^{-1}\left(\frac{t^2}{\sqrt{5}}\right)+C$$[/tex].
For more such questions on Integral
https://brainly.com/question/22008756
#SPJ4
How many is two pairs?
Answer:4 individuals
Step-by-step explanation:
Two pairs refers to 2 sets of two things. In general terms, a pair refers to two items and when you have two of them, it would be two sets of two things, or simply "four items".
For example, two pairs of socks would be four socks.
Mr. Sullivan makes $24,000 a year working at the school. He pays $7,700 in taxes. What percent of his income does he pay in taxes? (I’ll give branliest.)
The percentage of his income that he pays in taxes would be = 32%
What are taxes?Taxes is defined as the amount that is paid to the government by working class individuals as a way of generating internal revenue for the country.
The total amount of money made by Mr. Sullivan = $24,000
The amount of tax paid for the wedges = $7,700
The percentage of the income paid as tax would be calculated as;
= 7700/24000 × 100
= 770000/24000
= 32.01
= 32%
Learn more about percentage here:
https://brainly.com/question/24304697
#SPJ1
Can someone help me with these pls
Answer:
12.375 hours
Step-by-step explanation:
We know that car travel
400 miles = 5.5 hours
900 miles = ?
We take 900 times 5.5, then divide by 400 and get 12.375 hours
So, the car take 12.375 hours to travel 900 miles
Answer:
12.375
Step-by-step explanation:
400+400+100=900miles
5.5+5.5=11
5.5÷4=1.375
11+1.375=12.375
X- 2.6 =5. Help me plsss
Answer: x=7.6
Step-by-step explanation:
x-2.6=5
Step 1: Move 2.6 to another side of the equation with addition
X-2.6+2.6=5+2.6
X=7.6
Check your answer!
7.6-2.6=5 Correct!
Answer:
x = 7.6
Step-by-step explanation:
x - 2.6 = 5
x = 5 + 2.6
x = 7.6
--------------------------
check7.6 - 2.6 = 5
5 = 5
the answer is goodI don’t know how to solve this I sent a picture of it
Answer:
4y
Step-by-step explanation:
You want to simplify the expression (12x²y)/(3x²).
SimplifyWhen reducing any fractions, common factors in the numerator and denominator are cancelled. Here, the factor 3x² in the numerator is cancelled by the same factor in the denominator.
[tex]\dfrac{12x^2y}{3x^2}=\dfrac{(3x^2)(4y)}{(3x^2)}=\boxed{4y}[/tex]
What are longitudes for Class 7?
Longitudes: The vertical lines running north-south, join the two poles. They are called the meridians of longitude. They are spaced farthest apart at the equator and converge at a point at each pole.
Horizontal lines called latitudes are used to measure distances north or south of the equator. Vertical lines known as longitudes are used to determine the west or east of the meridian in Greenwich, England. Latitude and longitude work together to help cartographers, geographers, and others find specific locations on the globe.
What is the uses of latitude?
Any location's distance from the equator may be determined using its latitude, which is based on its degree. We can locate any point on Earth using longitude and latitude. The GPS or Global Positioning System uses these coordinates.
The grid system that enables us to locate absolute or precise places on the surface of the Earth is made up of latitude and longitude. Latitude and longitude can be used to pinpoint certain locations. Landmark identification also benefits from knowledge of latitude and longitude.
To know m ore about longitude refer to:
https://brainly.com/question/13492273
#SPJ4
A certain store is selling packages of 10 pencils and 4 pens for back to school . The store manger wants to make a larger package in the same ratio . If the larger package has 10 pens , how many penclis are in the larger package ?
If a certain store is selling packages of 10 pencils and 4 pens for back to school . The number of pencils that are in the larger package is 25 pencils.
How to find the number of pencils ?First step is to find the number of pencils per pen
Number of pencils per pen = 10 / 4
Number of pencils per pen = 2. 5
Now let find the number of pencils that are in the larger package
Number of pencils = Number of pens x Pencils per pen
Number of pencils = 10 x 2.5
Number of pencils = 25 pencils
Therefore we can conclude that the number of pencils is 25 pencils.
Learn more about number of pencils here:https://brainly.com/question/26677581
#SPJ1
8. LaTrenda and Osman both play in the school band.
LaTrenda finds out that the trumpet produces sounds
around 88 decibels and the saxophone produces
sounds around 75 decibels. LaTrenda is worried about
whether or not playing all the instruments in the band
together will damage her hearing. Osman claims that
88 +75 decibels would be 163 decibels. which is very
dangerous to hearing. LaTrenda thinks that it might
make more sense to add the intensities of the sounds
of the two instruments played together and then
calculate the number of decibels. Who do you think is
correct? Explain and show your reasoning.
Sound decibel are not additive because humans listen to sound logarithmically and LaTrenda is correct
What is sound intensity of the two instrumentOsman is not correct in his claim that 88 + 75 decibels would be 163 decibels. The decibel unit is not an additive unit, meaning that when you add the decibel levels of two different sound sources, you do not simply add the decibel levels.
Instead, adding the decibel levels of two different sound sources together would give you the total sound pressure level (SPL) of the combined sound.
To calculate the SPL of the combined sound, you would need to add the intensities of the two sounds and then calculate the decibel level of the combined sound using the formula:
SPL (dB) = 10 log10 (I1/I0) + 10 log10 (I2/I0)
Where I1 and I2 are the intensities of the two sound sources and I0 is the reference intensity, which is the threshold of human hearing.
It would make more sense to add the intensities of the two sounds and then calculate the number of decibels, because the human ear perceives loudness of sounds logarithmically, not linearly.
So, LaTrenda would be correct in this scenario.
Learn more on sound intensity here;
https://brainly.com/question/14349601
#SPJ1
Use the equation y =5/2
* to complete the table.
The solutions for the given equation are (0, 0), (1, 2.5), (2, 5) and (3, 7.5).
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is y=5/2 x.
Substitute x=0, 1, 2, 3, 4,......
When x=0
y=0
When x=1
y=5/2=2.5
When x=2
y=5
When x=3
y=7.5
Therefore, the solutions for the given equation are (0, 0), (1, 2.5), (2, 5) and (3, 7.5).
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ1
"Your question is incomplete, probably the complete question/missing part is:"
Use the equation y=5/2 x to complete the table. Is y proportional to x? Explain why or why not.
An open box i to be contructed from a quare piece of heet metal by removing a quare of ide 5 feet from each corner and turning up the edge. If the box i to hold 605 cubic feet, what hould be the dimenion of the heet metal?
An open box is to be constructed from a square area piece of sheet metal, then the dimension of the sheet metal is,
[tex]l = 5 feet[/tex] , [tex]b = 5 feet[/tex] , [tex]h = 24.2 feet[/tex]
Given that,
An open box length [tex]l[/tex] = 5 feet
An open box breadth b = 5 feet
An open box height = h
An open box area = 605 cubic feet
A square is a four-sided polygon which has it's all sides equal in length and the measure of the angles are 90 degrees. The shape of the square is such as, if it is cut by a plane from the center, then both the halves are symmetrical. Each half of the square then looks like a rectangle with opposite sides equal.
Area = [tex]l * b * h[/tex] (Equation - 1)
So,
We can substitute l , b , h values in the equation - 1,
605 = 5 * 5 * h
605 = 25 * h
605/25 = h
24.2 = h
Therefore,
An open box is to be constructed from a square area piece of sheet metal, then the dimension of the sheet metal is,
[tex]l = 5 feet[/tex] , [tex]b = 5 feet[/tex] , [tex]h = 24.2 feet[/tex]
To learn more about Square area problems visit :
brainly.com/question/29380588
#SPJ4