7)
The ordered pairs are:
(-4, -2), (-2, 1), (0, -1), (-3, 0), and (-3,2)
Domain = {-4, -3, -2, 0}
Range = {-2, -1, 0, 1, 2}
A function must map every element of the domain to a unique number in the range
But here -3 is mapped to 0 and 2.
Hence it is not a function
8)
The ordered pairs are:
(-2, 3), (-1,-1), (0,-1), (1,-3), (3, 1)
Domain = {-2, -1, 0, 1, 3}
Range = {-3, -1, 1, 3}
In this case, every element of the domain is mapped to a unique
ut -The ordered pairs are:
Solve each equation by using the square root property. X^2–6x+9=4
We have the following:
[tex]\begin{gathered} x^2-6x+9=4 \\ \end{gathered}[/tex]solving by the square root property
[tex]\begin{gathered} x^2-6x+9=4 \\ x^2-6x+9-9=4-9 \\ x^2-6x=-5 \\ x^2+2ax+a^2=\mleft(x+a\mright)^2 \\ 2ax=-6x \\ 2a=-6\rightarrow a=-3 \\ x^2-6x+(-3)^2=-5+(-3)^2 \\ (x-3)^2=-5+(-3)^2 \\ (x-3)^2=-5+9 \\ x-3=\pm\sqrt[]{4} \\ x=\sqrt[]{4}+3=2+3=5 \\ x=-\sqrt[]{4}+3=-2+3=1 \end{gathered}[/tex][tex]y = \frac{1}{3} x + 15[/tex]what is the answer
The slope of the given equation is ,
[tex]m=\frac{1}{3}[/tex]Slope of perellel line will also be same = 1/3 ,
The equation of perellel line is ,
[tex]\begin{gathered} y-0=\frac{1}{3}(x-6) \\ y=\frac{1}{3}x-2 \end{gathered}[/tex]A farmer has 1,416 feet of fencing available to enclose a rectangle area bordering a river. No fencing is required along the river. Let x represent the length of the side of the rectangular enclosure that is perpendicular A(x)= Find the dimensions that will maximize the area. The length of the side rectangle perpendicular to the river is and the length of the side of the rectangle parallel to the river is.What is the maximum area?
The dimensions that will maximize the area are x = 354 ft and y = 708 ft
The length of the side rectangle perpendicular to the river is 354 ft
The length of the side of the rectangle parallel to the river is 708 ft
The maximum area = 250632 ft²
Explanation:Given:
The length of the fencing = 1416 ft
The length of the side rectangle perpendicular to the river = x
To find:
The dimensions that will maximize the area
To determine the dimensions, we will make an illustration of the given information:
let the length o the rectangle parallel to the river = y
Length of the for the enclosed area = Perimeter of the enclosed area
Perimeter of the enclosed area = x + x = y = 2x + y
[tex]1416=2x+y\text{ . . .\lparen1\rparen}[/tex]Area of the rectangle = length × width
length = y, width = x
let the Area of the rectangle = A(x)
[tex]A(x)\text{ = xy . . . \lparen2\rparen}[/tex]To get the expression for A(x), we will make y the subject of the formula in equation (1):
y = 1416 - 2x
substitute for y in equation (2):
[tex]\begin{gathered} A(x)\text{ = x\lparen1416 - 2x\rparen} \\ \\ A(x)\text{ = 14166x - 2x}^2 \end{gathered}[/tex]To get the maximum dimension, we will differentiate with respect to x:
[tex]\begin{gathered} A^{\prime}(x)\text{ = 1416 - 4x} \\ \\ At\text{ maximum, A'\lparen x\rparen = 0:} \\ 1416\text{ - 4x = 0} \\ 1416\text{ = 4x} \\ x\text{ = }\frac{1416}{4} \\ x\text{ = 354} \end{gathered}[/tex]substitute for x in equation (1):
[tex]\begin{gathered} 1416\text{ = 2\lparen354\rparen + y} \\ 1416\text{ - 708 = y} \\ y\text{ = 708} \end{gathered}[/tex]The dimensions that will maximize the area are x = 354 ft and y = 708 ft
The length of the side rectangle perpendicular to the river is 354 ft
The length of the side of the rectangle parallel to the river is 708 ft
The maximum area = 354 × 708
The maximum area = 250632 ft²
1 - The Le Mans car race is a 24-hgur race. The longest distance erertraveled by a car in the race is 3,315 miles. What is the distancerounded to the nearest ten?2- The longest river in the world is the Nile. It is 4,184 miles long.What is the length of the Nile River rounded to the nearesthundred miles?3- Frank rounds 846,025 to the nearest hundred thousand and to the nearest ten thousand.Part A What is 846,025 rounded to the nearest hundred thousand?Part B What is 846,025 rounded to the nearest ten thousand?Part C Which rounded number is greater? Explain.
1. To find the nearest ten of 3315.
Since 15 is midway between 10 and 20.
So, the nearest ten of 3315 is 3320.
2. To find the nearest hundred miles of 4,184 miles:
184 is closest to 200.
Hence, the nearest hundred miles of 4,200 miles.
3.
A) To find the nearest hundred thousand of 846,025:
846,025 is closest to 800,000.
Hence, nearest hundred thousand of 846,025 is 800,000.
B) To find the nearest ten thousand of 846,025:
46,025 is closest to 50,000.
Hence, nearest ten thousand of 846,025 is 850,000.
C) Comparing the results of Part A and Part B,
The rounded number of Part B is greater.
Find the absolute value of | 2x+ z | + 2y x = 2.1, y = 3, z = -4.2
6
Explanations:The given absolute value expression is:
| 2x+ z | + 2ySubstitute x = 2.1, y = 3, z = -4.2 into the given expression:
[tex]|2(2.1)+(-4.2)|+2(3)[/tex]This can be simplifed as:
[tex]|2(2.1)-4.2|+6[/tex][tex]|4.2-4.2|+6[/tex]Since |4.2-4.2| = 0, the expression above becomes:
0 + 6
= 6
Therefore, the absolute value of the expression, after simplification, is 6
A pie shop bakes a certain amount of pies each week. 150 of those pies are apple pies. These apple pies makes up 40 percent of the total pies. How many pies does the shop make each week?
The number of apple pies made each week is 375
Here, we want to know the total number of pies made per week
Let the total number of pies be p
From the question, 40% of p is 150
Thus, we have it that;
[tex]\begin{gathered} 40\text{ \% of p = 150 } \\ \frac{40}{100}\times\text{ p = 150} \\ 40p\text{ = 100}\times150 \\ \\ p\text{ = }\frac{100\times150}{40} \\ p\text{ = 375} \end{gathered}[/tex]Which integer represents this scenario? a fish grows 4 inches a) -4" b) 4” 6.NS.5
as it is about growth, the integer is positive, therefore
answer is b) 4"
Math Lab A - Section 203B Notebook Home Insert Draw View Class Notebook U abe А. = = A Styles ☆ ? The table shows the average mass, in kilograms, of different sizes of cars and trucks. Size Small Car Average Mass (kilograms) 1,354 1,985 Large Car Large Truck 2,460 Part A To the nearest hundred, how much greater is the mass of a large truck than the mass of a small car? Fill in the blanks to answer the question. To the nearest hundred, a large truck has a mass of kilograms, and a small car has a mass of kilograms. So, a large truck has a mass about kilograms greater than a small car.
Given:
Round the mass of the large car to the nearest thousand.
Because 1985 is between 1,000 and 2,000 and closer to 2,000 ,the number should round up to 2,000.
Option D is the correct answer.
simplify the expression tan (3 x+ 2pi) as the tangent of a single angle
tan(3x)
Explanation
[tex]\tan (3x+2\pi)[/tex]Step 1
remember some property
[tex]\tan (a+b)=\frac{\tan a+\tan b}{1-\tan a\tan b}[/tex]then
[tex]\begin{gathered} \tan (3x+2\pi)=\frac{\tan 3x+\tan 2\pi}{1-\tan 3x\tan 2\pi}\text{ Equation(1)} \\ \tan \text{ 2}\pi=0 \\ so \\ \tan (3x+2\pi)=\frac{\tan 3x+0}{1-\tan 3x\cdot0}\text{ } \\ \tan (3x+2\pi)=\frac{\tan \text{ 3x}}{1-0}=\frac{\tan \text{ 3x}}{1} \\ \tan (3x+2\pi)=\tan (3x) \end{gathered}[/tex]I hope this helps you
Use the box method to distribute and simplify (-3x – 3)(5 + 4x²). Drag and drop the terms to the correct locations of the table.
Looking at the diagram, the box method has already been applied. The simplified answer would be gotten by adding up each term in the boxes while taking into consideration, the signs of each term. It becomes
- 15x - 15 - 12x^2 - 12x^3
Rearranging the terms in descending order of the exponents, it becomes
- 12x^3 - 12x^2 - 15x - 15 15x - 15 - 12x
Solve the inequality. Graph the solution on the number line and then give the answer in interval notation.Interval notation for the above graph in inequality is______
Answer:
[tex](-∞,4)[/tex]Step-by-step explanation:
To solve the following inequality, use inverse operations.
[tex]\begin{gathered} -8x-4>-36 \\ -8x>-32 \\ x<\frac{-32}{-8} \\ x<4 \\ \text{ Interval notation:} \\ (-∞,4) \end{gathered}[/tex]Now, for the number line representing this inequality:
Let the random variable x be the number of rooms in a randomly chosen owner- occupied housing unit in a certain city. The distribution for the units is given below.
(a)
Since X can only assume whole values, it is a discrete random variable.
(b)
The sum of all probabilities in the table must be equal to 1, so we have:
[tex]\begin{gathered} 0.07+0.22+0.41+0.2+0.05+0.03+0.01+P(10)=1\\ \\ 0.99+P(10)=1\\ \\ P(10)=1-0.99\\ \\ P(10)=0.01 \end{gathered}[/tex](c)
The values of x smaller than 5 in the table are 3 and 4, so we have:
[tex]P(X<5)=P(3)+P(4)=0.07+0.22=0.29[/tex](d)
For x between 4 and 6, we have:
[tex]P(4\leq x\leq6)=P(4)+P(5)+P(6)=0.22+0.41+0.2=0.83[/tex](e)
Looking at the table, for x = 3 we have:
[tex]P(3)=0.07[/tex]10 Natalie uses a 15% off coupon when she buys a camera. The original price of the camera is $45.00. How much money does Natalie save by using the coupon.?
Given data:
The given discount through coupon is d=15%.
The original price of camera is c=$45.00.
The discount on the given amount is,
[tex]\begin{gathered} d=(\frac{15}{100})(45) \\ =6.75 \end{gathered}[/tex]Thus, the amount saved is $6.75.
which of the following equations is a direct variation equation that has the ordered pairs 12.5, 5 as a solutiona. y=7.5xb. y=x-7.5c. x=y+7.5d. y=2.5x e. y= -2.5x f. (2/5)x
The ordered pair given is 12.5, 5
This means that
When x = 12.5, y = 5
Looking at the given equations, if we substitute the values of x and y, the correct option would be C
The equation is expressed as
x = y + 7.5
By substituting, it becomes
12.5 = 5 + 7.5
12.5 = 12.5
The correct option is C
I need help with this trigonometric function I will upload a photo
For us to be able to determine the distance along an arc on the surface of the earth, we will be using the following formula:
[tex]\text{ S = r}\theta[/tex]Where,
S = arc length
r = radius (radius of the earth)
θ = central angle (in radian)
Given:
r = 3960 miles
θ = 48 mins.
a.) Let's convert the given measure of the central angle to radian.
[tex]\theta=48mins.\text{ = (48 mins.) x }\frac{1^{\circ}}{(60\text{ mins.})}\text{ = }\frac{48}{60}(1^{\circ})[/tex][tex]\theta\text{ = }\frac{4}{5}^{\circ}[/tex][tex]\text{ }\theta_{radian}\text{ = }\theta_{degrees}\text{ x }\frac{\pi}{180^{\circ}}[/tex][tex]\text{ }\theta_{radian}\text{ = }\frac{4}{5}\text{ x }\frac{\pi}{180}\text{ = }\frac{4\pi}{900}\text{ = }\frac{\pi}{225}\text{ radians}[/tex]b.) Let's now determine the distance (arc length).
[tex]\text{ S = r}\theta[/tex][tex]\text{ S = (3960)(}\frac{\pi}{225}\text{ ) = }\frac{3960\pi}{225}\text{ miles = 17.6}\pi\text{ miles = 55.2920307 }\approx\text{ 55.292 miles}[/tex]Therefore, the answer is 55.292 miles.
The United States Pentagon building is modeled on the coordinate plane as regular pentagon ABThe vertices of the pentagon are A(-7.42,2.42), B(0,7.88),C(7.42,2.42),D(4.605,-6.35), and E(-4.605-6.35) what is the approximate perimeter in feet of the us pentagon building
Given,
The coordinates of the vertices of the pentagon is,
A(-7.42,2.42), B(0,7.88), C(7.42,2.42),D(4.605,-6.35), and E(-4.605-6.35)
Required
The approximate perimeter of the pentagon.
The perimeter of the pentagon is calculated as,
The length of side AB is,
[tex]AB=\sqrt{(-7.42-0)^2+(2.42-7.88)^2}=\sqrt{84.868}=9.2124[/tex]The length of side BC is,
[tex]AB=\sqrt{(7.42-0)^2+(2.42-7.88)^2}=\sqrt{84.868}=9.2124[/tex]The length of side CD is,
[tex]CD=\sqrt{(4.605-7.42)^2+(-6.35-2.42)^2}=\sqrt{84.8371}=9.211[/tex]The length of DE is,
[tex]DE=9.21[/tex]The length of AE is,
[tex]CD=\sqrt{(4.605-7.42)^2+(-6.35-2.42)^2}=\sqrt{84.8371}=9.211[/tex]The perimeter of the pentagon is,
[tex]Perimeter=9.2124+9.2124+9.211+9.211+9.21=46.0568[/tex]Hence, the perimeter of the pantagon is 46.0568.
In the front of a building there are three doors each to be painted
a different color from 10 different available colors. How many color
arrangements for the doors are there?
In this case, the order doesn't matter and the colors cant be repeated.
Now, we need to use the permutation formula:
[tex]P(n,r)=\frac{n!}{(n-r)!}[/tex]Where n represents the total different available colors and r is equal to
the number of doors.
Replacing on the permutation formula:
[tex]P(10,3)=\frac{10!}{(10-3)!}[/tex][tex]P(10,3)=\frac{10!}{7!}[/tex][tex]P(10,3)=\frac{10x9x8x7!}{7!}[/tex][tex]P(10,3)=10x9x8![/tex]Then
[tex]P(10,3)=\frac{10x9x8x7!}{7!}[/tex][tex]P(10,3)=720[/tex]Hence, there are 720 possible arrangements for the doors.
Pleasr help fast it's due today 1. Consider the surface area of the following pyramid.224 am4 am4 am2.24 cm4 cm3 cm4 cm4 cm3 cm13 cm4 cm4 cm3 cm4 cm4 cm3 cm(a) Calculate the total surface area of the pyramid. Show your work.
Given data:
The given figure of square pyramid.
The expresssion for the total surface area is,
[tex]\begin{gathered} \text{TSA}=(3\text{ cm)(3 cm)+4}\times\frac{1}{2}(3\text{ cm)(}2.24\text{ cm)} \\ =9cm^2+2(3\text{ cm)(2.24 cm)} \\ =22.44cm^2 \end{gathered}[/tex]Thus, the total surface area of the given pyramid is 22.44 sq-cm.
2/7 in reduced terms
2/7 is in reduced terms already
no simplification can be made over this fraction.
hope it is clear
by noon the temperature in Buffalo had risen to 18 degrees farenheit what was the temperature there at noon Buffalo is a - 9
If the temperature of buffalo rised 18 degrees means that it is an addition between the 2 temperatures
[tex]-9+18=9[/tex]the temperature at noon is 9°F
A college had 5,000 students in 2018. The number of students decreased by 10% in 2019 andanother 5% in 2020. How many students did the college have in 2020? (1 point)
Okay, here we have this:
Inicially we have 5000 students, let's calculate how many were left in 2019:
Students in 2019=5000*0.9
Students in 2019=4500
Now, let's finally calculate how many were left in 2020:
Students in 2020=4500*0.95
Students in 2020=4275
Finally in 2020 they were 4275 students
Max exercise 4 hrs during each 7 day week. At this rate, how many hours do he exercise in 35 days?
We know that Max exercises 4 hours during each 7-day-week.
After 35 days (5 weeks), the number of hours would be
[tex]4\cdot5=20[/tex]Max would exercise 20 hours after 35 days.Generalize Two data sets have the same number of values. The first data set has a mean of 7.2 and a standard deviation of 1.25. The second data set has a mean of 7.2 and a standard deviation of 2.5. Which data set is more spread out?
ANSWER
The second data set is more spread out
EXPLANATION
The standard deviation measures the spread of a data distribution. The more spread out a data distribution is, the greater its standard deviation.
In this problem, the second data set has twice the standard deviation of the first data set, so it's more spread out.
5x + 4y = 12Step 1 of 2: Determine the missing coordinate in the ordered pair (0) so that it will satisfy the given equation,
Answer:
Explanations:
Given the equation;
[tex]5x+4y=12[/tex]In order to get the missing coordinate in the ordered pair (0, ?), we will substitute x = 0 into the equation and get the corresponding y-value as shown:
[tex]\begin{gathered} 5(0)+4y=12 \\ 0+4y=12 \\ 4y=12 \end{gathered}[/tex]Divide both sides of the equation by 4;
[tex]\begin{gathered} \frac{4y}{4}=\frac{12}{4} \\ y=3 \end{gathered}[/tex]Therefore, the missing coordinate will be 3 to have (0, 3)
If f(5)=3, write an ordered pair that must be on the graph of y = f(x + 1) + 2
(4, 5)
Explanations:The given function is:
y = f(x + 1) + 2
There are many ordered pairs that can be on the graph of y = f(x + 1) + 2, but with the information given will can look for one of them.
Let x = 4
y = f(x + 1) + 2
y = f(4 + 1) + 2
y = f(5) + 2
Since it is given that f(5) = 3, the equation above can be simplified to get the value of y.
y = f(5) + 2
y = 3 + 2
y = 5
Therefore, an ordered pair that must be on the graph of y = f(x+1) + 2 is (4, 5)
Can you show me how to solve this and graph?
The points (x,y) whose values satisfy the equation -5y=13 belong to the graph of that equation.
First, isolate y by dividing both sides of the equation by -5 and simplifying:
[tex]\begin{gathered} -5y=13 \\ \Rightarrow\frac{-5y}{-5}=\frac{13}{-5} \\ \Rightarrow y=-\frac{13}{5} \end{gathered}[/tex]Then, the points (x,y) belon to the graph of the equation -5y=13 whenever the value of y is -13/5, regardless of the value of x. Then, choose two different values of x to find two points that belong to the graph. For example, x=0 and x=2. Then, this two points belong to the graph:
[tex]\begin{gathered} (0,-\frac{13}{5}) \\ (2,-\frac{13}{5}) \end{gathered}[/tex]Notice that -13/5=-2.6,
Plot the points (0,-2.6) and (2,-2.6) in a coordinate plane:
Since the given equation is linear, the graph of the equation is a straight line. We can draw a straight line between any two points given. Draw a line between (0,-2.6) and (2,-2.6) to find the graph of the equation -5y=13:
Mary is 4 years older than Sue. If the sum of their ages is 16. How would you set up the equations?
Answer:
A. x=y-4, x+y=16
C. x=y-4, x+y=16
Explanation:
• Let Sue's age = x
Mary is 4 years older than Sue, therefore:
• Mary's age, y = x+4
[tex]\begin{gathered} y=x+4 \\ \implies x=y-4 \end{gathered}[/tex]Next, the sum of their ages is 16. This gives:
[tex]x+y=16[/tex]Therefore, the equation is:
[tex]\begin{gathered} x=y-4 \\ x+y=16 \end{gathered}[/tex]The correct choices are A and C.
IQ is normally distributed with a mean of 100 and a standard deviation of 15.a) Suppose one individual is randomly chosen. Find the probability that this person has an IQ greater than 95.Write your answer in percent form. Round to the nearest tenth of a percent.P(10 greater than 95) =%b) Suppose one individual is randomly chosen. Find the probability that this person has an IQ less than 125.Write your answer in percent form. Round to the nearest tenth of a percent.P(IQ less than 125) =%c) In a sample of 800 people, how many people would have an IQ less than 110?peopled) In a sample of 800 people, how many people would have an IQ greater than 140?peopleCheck Answer
To answer this questions we need to remember the standard score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where x is the value we are looking for, mu si the mean and sigma is the standard deviation.
a.
We need the probability:
[tex]P(IQ>95)[/tex]using the standard score this is equivalent to:
[tex]\begin{gathered} P(IQ>95)=P(z>\frac{95-100}{15}) \\ =P(z>-0.3333) \end{gathered}[/tex]Using a normal distribution table we have:
[tex]P(z>-0.3333)=0.6306[/tex]Therefore the probability to select a person with more than 95 IQ points is 63.1%.
b.
Following the same reasoning as before we have:
[tex]\begin{gathered} P(IQ<125)=P(z<\frac{125-100}{15}) \\ =P(z<1.6667) \\ =0.9522 \end{gathered}[/tex]Therefore the probability to select a person with less than 125 IQ points is 95.2%
c.
To find how many people of this sample have more less than 110 points we need to find that probability:
[tex]\begin{gathered} P(IQ<110)=P(z<\frac{100-110}{15}) \\ =P(z<-0.666) \\ =0.7475 \end{gathered}[/tex]Multiplying this value with the sample size we have
[tex](800)(0.7475)=598[/tex]Therefore 598 people will have an IQ less than 110.
d.
By the same reasoning as before we have:
[tex]\begin{gathered} P(IQ>140)=P(z>\frac{140-100}{15}) \\ =P(z>2.6667) \\ =0.0038 \end{gathered}[/tex]Multiplying this value with the sample size we have
[tex](800)(0.0038)=3[/tex]Therefore 3 people will have an IQ greater than 140.
Find the distance of a wheel where the radius is 10 feet and it gives 15 rotations. How many inches did the wheel travel in those 15 rotations?
We will find the distance after 15 rotations by multiplying the perimeter of the circumference by 15, that is:
[tex]d=15(2\pi r)\Rightarrow d=30\pi(10)\Rightarrow d=300\pi\Rightarrow d\approx941.48[/tex]From this, we have that the wheel traveled approximately 941.48 feet.
NO LINKS!! Use the method of substitution to solve the system. (If there's no solution, enter no solution). Part 7z
Answer:
(-3, 4)(5, 0)=====================
Given systemx + 2y = 5 x² + y² = 25Rearrange the first equationx = 5 - 2y Substitute the value of x into second equation(5 - 2y)² + y² = 254y² - 20y + 25 + y² = 255y² - 20y = 0y² - 4y = 0y(y - 4) = 0y = 0 and y = 4Find the value of xy = 0 ⇒ x = 5 - 2*0 = 5y = 4 ⇒ x = 5 - 2*4 = -3Answer:
[tex](x,y)=\left(\; \boxed{-3,4} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{5,0} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}\;x+2y=5\\x^2+y^2=25\end{cases}[/tex]
To solve by the method of substitution, rearrange the first equation to make x the subject:
[tex]\implies x=5-2y[/tex]
Substitute the found expression for x into the second equation and rearrange so that the equation equals zero:
[tex]\begin{aligned}x=5-2y \implies (5-2y)^2+y^2&=25\\25-20y+4y^2+y^2&=25\\5y^2-20y+25&=25\\5y^2-20y&=0\end{aligned}[/tex]
Factor the equation:
[tex]\begin{aligned}5y^2-20y&=0\\5y(y-4)&=0\end{aligned}[/tex]
Apply the zero-product property and solve for y:
[tex]5y=0 \implies y=0[/tex]
[tex]y-4=0 \implies y=4[/tex]
Substitute the found values of y into the first equation and solve for x:
[tex]\begin{aligned}y=0 \implies x+2(0)&=5\\x&=5\end{aligned}[/tex]
[tex]\begin{aligned}y=4 \implies x+2(4)&=5\\x+8&=5\\x&=-3\end{aligned}[/tex]
Therefore, the solutions are:
[tex](x,y)=\left(\; \boxed{-3,4} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{5,0} \; \right)\quad \textsf{(larger $x$-value)}[/tex]