Answers
The roots are those values that make a function or polynomial take a zero value. The roots are also the intersection points with the x-axis. In the case of a quadratic equation you can use the quadratic formula to find its roots:
[tex]\begin{gathered} ax^2+bx+c=y\Rightarrow\text{ Quadratic equation in standard form} \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\Rightarrow\text{ Quadratic formula} \end{gathered}[/tex]So, in this case, you have
[tex]\begin{gathered} y=x^2-6x+9 \\ a=1 \\ b=-6 \\ c=9 \end{gathered}[/tex][tex]\begin{gathered} x=\frac{-(-6)\pm\sqrt[]{(-6)^2-4(1)(9)}}{2(1)} \\ x=\frac{6\pm\sqrt[]{36-36}}{2} \\ x=\frac{6\pm0}{2} \\ x=\frac{6}{2} \\ x=3 \end{gathered}[/tex]As you can see, this function only has one root, at x = 3.
You can see this in the graph of the function:
Related Questions
2. The area of the arena is 2160 in.2 a) Will the arena fit on the rug? Show your work and explain your answer below. b) If the length of the arena is 60 inches, what is the width? c) If the arena fits, and is placed exactly in the middle of the rug, how much standing room on the rug could a drive have? Use your measurements from above to help you. ? 3. If 15 robots can fit on the arena floor at one time, how much space does each robot take up?
Answers
Answers:
2a. The arena will fit on the rug
b. Width = 36 in
c. Standing room: 4 in
3. 144 in²
Explanation:
2. Part a.
First, we need to convert the measures of the rug to inches, so taking into account that 1 ft = 12 in, we get
Length = 6 ft x 12 in/ 1ft = 72 in
Width = 4 ft x 12 in/ 1 ft = 48 in
Then, the area of the rug will be
Area = Length x Width
Area = 72 in x 48 in
Area = 3456 in²
Therefore, the area of the arena, which is 2160 in² is lower than the area of the rug. It means that the area will fit on the rug.
Part b.
The area of the arena is equal to
Area = Length x Width
To find the width of the area, we need to solve the equation for the width, so
Width = Area/Length
So, replacing Area = 2160 in² and Length = 60 in, we get
Width = 2160 in² / 60 in
Width = 36 in
Therefore, the width of the area is 36 in.
Part c.
The measures that we get from parts a and b can be represented as
Therefore, the missing length can be calculated as:
(48 in - 36 in)/2 = 12 in/ 2 = 6 in
Therefore, a drive will have 6 in of standing room.
3.
Finally, to know how much space each robot take up, we need to divide the area of the arena by 15, so
2160 in²/ 15 = 144 in²
Therefore, each robot take 144 in²
Use the formula for n^P_r to evaluate the following expression.
Answers
Use the following formula:
[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]Then, for 11P6:
[tex]\begin{gathered} _{11}P_6=\frac{11!}{(11-6)!}=\frac{11!}{5!}=\frac{5!\cdot6\cdot7\cdot8\cdot9\cdot10\cdot11}{5!} \\ _{11}P_6=6\cdot7\cdot8\cdot9\cdot10\cdot11=332640 \end{gathered}[/tex]Hence, the result is 332640
Please answer part a and b questions are in the picture
Answers
Part A
we have that
A(4) ----> looking at the graph
A(4) means----> population in the year 1994
so
A(4)----> less than 2 million
and
B(4) -----> greater than 2 million
therefore
the answer Part a is option B
Part B
there is only one value of t where A(t)=B(t)
the value of t is 6 (the year 1996)
Given the following information about events A, B, and C, determine which pairs of events, if any, are independent andwhich pairs are mutually exclusive.
Answers
Let's begin by identifying key information given to us:
[tex]\begin{gathered} P(A)=0.39 \\ P(B)=0.42 \\ P(C)=0.19 \\ P(A|B)=0 \\ P(C|B)=0.19 \\ P(A|C)=0.39 \end{gathered}[/tex]When two events A and B are independent we have it thus:
[tex]undefined[/tex]In AUVW, VW = UV and mZU = 74º. Find mZV.
Answers
We will find the measure of angle V as follows:
*From theorem we have that angles that are opposite to congruent sides are congruent. So, Angle W will also have a measure o 74°. Now, we also have that the sum of all internal angles of a triangle add 180°, so the following is true:
[tex]U+V+W=180\Rightarrow74+V+74=180[/tex]Now, we solve for V:
[tex]\Rightarrow V=32[/tex]So, the measure of angle V is 32°.
For each set of three side lengths in the table, determine how many unique triangles can be formed. Select the appropriate circle in each row.
Answers
The first one the 3 sides are equal to 1, this mean that it is a equilater triangle, so it is possible to made exactly one unique triangle.
now for the other triangles we will add the two shortest sides of the triangle, and if they are more than the greater side of the triangle, then it will be a unique triangle, if not there will be more than one triangle
for the second one:
[tex]3+4=7>5[/tex]so the second one have exactly one unique triangle.
for the number 3:
[tex]5+10=15=15[/tex]So in this case there is none unique triangles.
for the number 4:
[tex]6+16=22<26[/tex]So in this case there is none unique triangles.
and for the number 5:
[tex]10+50=60>55[/tex]So we hace exactly one unique triangle.
given the tableau, circle the pivot and explain how you found it
Answers
The equations are
[tex]2x_1+3x_2+6x_3+S_2=22[/tex][tex]3x_1+5x_2+3x_3+S_1=20_{}[/tex][tex]-3x_2-1x_3+S_1+Z\text{ = 24}[/tex]The smallest negative number is the pivot column
so the smallest negative number is -3 and hence the pivot column is
3
5
-3
The row pivot hence = 5
so pivot will be (x= -3 and S = 5)
The price of Stock A at 9 A.M. was $15.21. Since then, the price has been increasing at the rate of $0.07 each hour. At noon the price of Stock B was $15.96. It begins to decrease at the rate of $0.15 each hour. If the two rates continue, in how many hours will the prices of the two stocks be the same?
Answers
The price of the two stocks will be same in 1 hours .
in the question ,
it is given that
the price of the stock A at 9 A.M is $15.21
price increases at the rate of 0.07 each hour .
so the price of the stock A at 12 P.M. is 15.21 + 0.21 = $15.42
and the price of the stock A after x hours from 12 P.M. is given by the equation
stock A = 15.42 + 0.07(x)
the price of stock B at 12 P.M. is $15.96
price decreases at the rate of 0.15 each hour .
the price of the stock B after x hours from 12 P.M. is given by the equation
stock B = 15.96 - 0.15(x)
since the price of the two stocks is same , we equate both the equations .
15.42 + 0.07(x) = 15.96 - 0.15(x)
15.42 + 0.07x = 15.96 - 0.15x
0.15x + 0.07x = 15.42 - 15.21
0.22x = 0.21
x = 0.9545
x ≈ 1
Therefore , The price of the two stocks will be same in 1 hours .
Learn more about Equations here
https://brainly.com/question/18724762
#SPJ1
Write a word problem to fit the following rates: 72 tokens/12 games, ◾️ tokens/10 games
Answers
We have to write a word problem using,
• 72 tokens/12 games
,• tokens/10 games
We can first give an information related to 72 tokens PER 12 games.
Then we can ask "how many tokens" per 10 games.
Let us devise a word problem.
The local game center sells tokens to play online games. Jeremy used 72 token to play 12 online games. At this rate, how many token would Jeremy use to play 10 online games?
The above problem uses both the information provided.
Graph the inequality on a number line
Answers
Hope this helps :)
during happy hour appetizers are at 30% off how much would each appetize your cost show the original price your math and discounted price
Answers
EXPLANATION
Let's see the facts:
Appetizers = 30%
The discount price is given by the following equation:
Discount percentage=
Could you send me a screenshot of the question for better understanding, please?
An ice cream truck began its daily route with 95 gallons of ice cream. The truck driver sold 58% of the ice cream. How many gallons of ice cream were sold? round to nearest gallon
Answers
Start making the percentage as a fraction
[tex]\begin{gathered} 58\text{\%}=\frac{58}{100} \\ \end{gathered}[/tex]multiply the fraction by the total of the daily routine
[tex]95\cdot\frac{58}{100}=55.1\approx55gallons[/tex]Sofia ordered sushi for a company meeting. They change plans and increase how many people
will be at the meeting, so they need at least 100 pieces of sushi in total.
Sofia had already ordered and paid for 24 pieces of sushi, so she needs to order additional sushi.
The sushi comes in rolls, and each roll contains 12 pieces and costs $8.
Let R represent the number of additional rolls that Sofia orders.
1) Which inequality describes this scenario?
Choose 1 answer:
B
12 + 24R ≤ 100
12+24R 100
24+12R 100
24+12R 100
Answers
Answer:
24 + 12R ≥ 100Step-by-step explanation:
List the conditions as per question:
Number of pieces of sushi ordered = 24,Number of pieces required in total at least 100,Number of rolls to be ordered = R,Each roll contains = 12 pieces.Inequality to represent the total number of pieces of sushi is:
24 pieces and R rolls of 12 pieces to get at least 100 pieces, or 24 + 12R ≥ 100Which equation represents a line that passes through the two points in thetable?O A. y+3= (x+3)OB. y-3-(x-3)O G. y+3=(x+3)C.OD.y-3-(x-3)X36y35
Answers
The first step is to choose one option and rewrite it in the explicit form
I will choose the second option:
[tex]y-3=\frac{2}{3}(x-3)[/tex][tex]y=\frac{2}{3}(x-3)+3[/tex][tex]y=\frac{2}{3}x-2+3[/tex][tex]y=\frac{2}{3}x+1[/tex]Now replace the x points in the equation to verify if it satisfies their respective value in y
For x=3
[tex]y=\frac{2}{3}(3)+1=\frac{6}{3}+1=2+1=3[/tex]For x=3 satisfy y=3
Now x=6
[tex]y=\frac{2}{3}(6)+1=\frac{12}{3}+1=4+1=5[/tex]For x=6 satisfy y=5
So the answer is b.
I'm graphing and I need to find out how mutch it costs for 4.5 inches of the construction. and the construction is $25.50 per inch
Answers
You have to determine the cost for 4.5 inches of the construction using the graph.
The height is on the y-axis, and the cost is on the x-axis.
First, locate 4.5 in the y-axis, which is the value in the midpoint between 4 and 5.
Draw a horizontal line until you intersect with the line, then draw a vertical line from the function until the x-axis:
The line crosses the x-axis at the midpoint between values 102 and 127.5 to determine the value at this point you have to average both costs:
[tex]\frac{127.5+102}{2}=\frac{229.5}{2}=114.75[/tex]The cost of 4.5 inches of construction is $114.5
I solved the attached equation as 7000 but it seems to ask for a “solution set” did I answer properly?
Answers
The solution set does have only one element: {7000}
Find the perimeter of the rectangle. Write your answer in scientific notation.Area = 5.612 times 10^14 cm squared9.2 times 10^7cm is one side of the perimeter
Answers
Answer: Perimeter = 1.962 x 10^8 cm
Explanation:
The first step is to calculate the width of the rectangle. Recall,
Area = length x width
width = Area /length
From the information given,
Area = 5.612 times 10^14 cm squared
Length = 9.2 times 10^7cm
Thus,
width = 5.612 times 10^14 /9.2 times 10^7
width = 6.1 x 10^6
The formula for calculating the perimeter is
Perimeter = 2(length + width)
Thus,
Perimeter = 2(9.2 x 10^7 + 6.1 x 10^6)
Perimeter = 1.962 x 10^8 cm
A vase is in the shape of a cone. The height is 12 inches and the diameter is 4.4 inches.
What is the lateral surface area to the nearest tenth of a square inch?
O
O
24.3 square inches
149.1 square inches
168.6 square inches
99.5 square inches
Answers
84.27 square inch is the lateral surface area of cone.
Define lateral surface area.All of an object's sides, excluding its base and top, are considered its lateral surface. The size of the lateral surface is referred to as its area. This must be distinguished from the total surface area, which consists of the base and top areas as well as the lateral surface area. A figure's lateral area consists solely of the non-base faces. The lateral surface area of several forms, such as a cuboid, cube, cylinder, cone, and sphere, is discussed in this article.
Given,
Height = 12 inches
Diameter = 4.4 inches
Radius = 2.2 inches
Lateral surface area:
πr√h² + r²
3.14 × 2.2 √(12)² + (2.2)²
3.14 × 2.2 √144 + 4.84
3.14 × 2.2 √148.84
3.14 × 2.2(12.2)
3.14 × 26.84
84.27
84.27 square inch is the lateral surface area of cone.
To learn more about lateral surface area, visit:
https://brainly.com/question/14001755
#SPJ13
Use the functions f(x) = 8x + 11 and g(x) = 4x² + 7x - 2 to evaluate the following:a. f(8) =b. f(-8)=c. g(6) =d. g(-7)=e. g(a) =
Answers
Given:
f(x) = 8x + 11
g(x) = 4x² + 7x - 2
We are asked to evaluate using the following:
(a) f(8)
f(8) = 8(8) + 11
f(8) = 64 + 11
f(8) = 75
(b) f(-8)
f(-8) = 8(-8) + 11
f(-8) = -64 + 11
f(-8) = -53
(c) g(6)
g(6) = 4(6)² + 7(6) - 2
g(6) = 4(36) + 42 - 2
g(6) = 144 + 42 - 2
g(6) = 184
(d) g(-7)
g(-7) = 4(-7)² + 7(-7) - 2
g(-7) = 4(49) - 49 - 2
g(-7) = 196 - 49 - 2
g(-7) = 145
(e) g(a)
g(a) = 4(a)² + 7(a) - 2
g(a) = 4a² + 7a - 2
What is the intermediate step in the form (x+a)^2=b(x+a)
2
=b as a result of completing the square for the following equation?
x^2+6x+19=4x
Answers
The intermediate step in the form (x + a)² = b when you solve the given quadratic equation by using completing the square method is (x + (√3 - 2)/2)² = 77/4.
The standard form of a quadratic equation.In Mathematics, the standard form of a quadratic equation is given by:
ax² + bx + c = 0.
In this exercise, you're required to determine the intermediate step in the form (x + a)² = b when you solve the given quadratic equation by using completing the square method. Therefore, we would re-write the quadratic equation by subtracting 19 from both sides as follows:
x² + 6x + 19 = 4x
x² + 6x + 19 - 19 = 4x - 19
x² + 6x = 4x - 19
x² + 6x - 4x = 19
x² + 2x = 19
In order to complete the square, we would have to add (half the coefficient of the x- term)² to both sides of the quadratic equation as follows:
x² + 2x + (1/2)² = 19 + (1/2)²
x² + 2x + 1/4 = 19 + 1/4
(x + (√3 - 2)/2)² = 77/4
Read more on completing the square here: https://brainly.com/question/11398876
#SPJ1
Complete Question:
What is the intermediate step in the form (x + a)² = b as a result of completing the square for the following equation?
x² + 6x + 19 = 4x
find the coordinates of point P that lies on the line segment MQ, M(-9,-5) , Q(3,5), and partitions the segment at a ratio of 2 to 5
Answers
Write a equation that passes through the points (2,5) (-3,5)
Answers
Line equation: y = 5
Slope: 0
Intercept: 5
Formule:
. Equation : y = mx + b
. Slope: m = () / ()
Write 0.000000000054 in scientific notation
Answers
Answer:
5.4 × 10^-11
Step-by-step explanation:
Which statement describes how the reasonable domain
compares to the mathematical domain?
Answers
A statement which best describes how the reasonable domain compares to the mathematical domain is that: C. the mathematical domain includes all real numbers, while the reasonable domain includes only real numbers greater than 2.
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values or numbers to a function and the domain of any graph comprises all the input numerical values or numbers which are primarily shown on the x-axis.
Next, we would evaluate the function which represents the perimeter of this rectangle by substituting the value of 2 as follows:
f(w) = 6w – 8
f(2) = 6(2) – 8
f(2) = 12 – 8
f(2) = 4.
For the length of this rectangle, we have:
Length = 2w - 4
Length = 2(2) - 4
Length = 4 - 4
Length = 0
Therefore, the width of this rectangle must be real numbers that are greater than 2.
Read more on domain here: brainly.com/question/17003159
#SPJ1
Complete Question:
A rectangle has a length that is equal to 4 less than twice the width. The function for the perimeter depending on the width can be expressed with the function f(w) = 6w – 8, where w is the width of the rectangle in centimeters.
Which statement describes how the reasonable domain compares to the mathematical domain?
Both the mathematical and reasonable domains include only positive real numbers.
Both the mathematical and reasonable domains include only positive whole numbers.
The mathematical domain includes all real numbers, while the reasonable domain includes only real numbers greater than 2.
The mathematical domain includes all real numbers, while the reasonable domain includes only whole numbers greater than 2.
Hi, I always have a hard time with these, the whole question is in the picture.
Answers
we have that
x1 ----> number of cars with a 7,000 gal capacity
x2 ---> number of cats with a 14,000 gal capacity
x3 ---> number of cars with a 28,000 gal capacity
so
7000x1+14000x2+28000x3=462000
using a 3x3 system of equations solver
the solution is
x1=-2s-4t+66
x2=s
x3=t
The answer is option B
Find the midpoint for the line segment whose endpoints are (-10,11) and (-1,-15).
Answers
Answer:
( -11/2, -2)
Step-by-step explanation:
Finding the midpoint
To find the x coordinate of the midpoint, add the x coordinates of the endpoints and then divide by 2
(-10+-1)/2 = -11/2
To find the y coordinate of the midpoint, add the y coordinates of the endpoints and then divide by 2
(11+-15)/2 = -4/2 = -2
The mid point is ( -11/2, -2)
Rosa receives money from her relatives every year on her birthday. Last year, she received a total of $350. This year, she received $441. What is the percent of increase in Rosa’s annual birthday money?
Answers
Answer:
26%
Step-by-step explanation:
use a online percentage calculator
What is the equation of the line that passes through the point (8,-6) and has a
slope of o?
Answers
The equation is y = -6
Triangle FGH is similar to triangle IJK. Find the measure of side JK. Round youranswer to the nearest tenth if necessary.
Answers
Let x be the measure of JK so we get that
[tex]\frac{23}{5}=\frac{x}{3.5}\rightarrow x=3.5\cdot\frac{23}{5}=16.1[/tex]writing equations in slope-intercept form common core algebra 1question 1
Answers
The equation of the line in the slope-intercept form is y = mx + b, where "m" is the slope and "b" is the y-intercept.
"b" is the point (0, yi).
"m" can be found using 2 points P₁ (x₁, y₁) and P₂ (x₂, y₂), according to the formula below:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, to solve this question, follow the steps below.
(a) First graph
Step 01: Find the y-intercept and another point in the graph.
To find the points in the graph, choose a x-value and find its corresponding y-value.
Choosing x = 0, y = 2.
P₁ = (0, 2).
Choosing x = -3, y = -2.
P₂ = (-3, -2).
Step 02: