Answer
Option A is correct.
Slope = 0
Explanation
For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For this question,
(x₁, y₁) and (x₂, y₂) are (2, 1) and (0, 1)
x₁ = 2
y₁ = 1
x₂ = 0
y₂ = 1
[tex]\text{Slope = }\frac{1-1}{1-2}=\frac{0}{-1}=0[/tex]Hope this Helps!!!
Write the sum of 5x^2+2x-10 and 2x^3+6 as a polynomial in standard form
Given polynomials:
[tex]\begin{gathered} 5x^2\text{ + 2x - 10} \\ 2x^2\text{ + 6 } \end{gathered}[/tex]The sum of the polynomials is:
[tex]=\text{ 5x}^2\text{ + 2x - 10 + \lparen2x}^2\text{ + 6\rparen}[/tex]Simplifying the sum:
[tex]\begin{gathered} =\text{ 5x}^2\text{ + 2x - 10 + 2x}^2\text{ + 6} \\ Collect\text{ like terms} \\ \text{ = 5x}^2\text{ + 2x}^2\text{ + 2x - 10 + 6} \\ =\text{ 7x}^2\text{ + 2x - 4} \end{gathered}[/tex]Hence,the sum of the polynomials in standard form is:
[tex]=\text{ 7x}^2\text{ + 2x - 4}[/tex]m/5+9=11 what does m Stand for?
we have the expression
(m/5)+9=11
solve for m
that means
isolate the variable m
step 1
multiply by 5 both sides
5*(m/5)+5*9=5*11
m+45=55
step 2
subtract 45 both sides
m+45-45=55-45
m=10In a class of 29 students, 19 are female and 14 have an A in the class. There are 8students who are male and do not have an A in the class. What is the probability thata student does not have an A given that the student is female?
SOLUTION
The total number of females =
[tex]19[/tex]if 14 have an A in the class, the number of students without A is:
[tex]29-14=15[/tex]8 male students do not have an A, therefore the number of female students without an A is:
[tex]15-8=7[/tex]The probability that a student does not have an A given that the student is female can be calculated thus:
[tex]\frac{\text{Total number of female students without an A}}{Total\text{ number of female students in the class}}[/tex][tex]\frac{7}{19}[/tex]Evaluate Indicated Function!f(x) = x^2 - 1g(x) = x - 2
Given the following functions
[tex]\begin{gathered} f(x)=x^2-1 \\ g(x)=x-2 \end{gathered}[/tex]We want to evaluate
[tex](f+g)(t-4)[/tex]First, let's create this composition of functions. Since it is a sum, we just need to add them together.
[tex](f+g)(x)=f(x)+g(x)=x^2-1+x-2=x^2+x-3[/tex]Now, to evaluate at t - 4, we just need to substitute our variable for t - 4.
[tex]\begin{gathered} (f+g)(t-4)=(t-4)^2+(t-4)-3 \\ =t^2-8t+16+t-4-3 \\ =t^2-7t+9 \end{gathered}[/tex]And this is our final answer.
[tex](f+g)(t-4)=t^2-7t+9[/tex]Find the x-intercepts of y = 4x2 - 15x - 4.4 and 1/4-21 and 10-1/4 and 4No x-intercepts exist.
Explanation
[tex]y=4x^2-15x-4.[/tex]We can find the x-intercepts of the function by plotting the graph.
Answer: -1/4 and 4
RedGoldKitsBeadsBeads12015210075360454403058060Part BUse the drop-down menus to complete the rule for each bead colonRed: Add Choose...Gold: AddChoose...
Part B)
As the problem says, for each bead kit we have 20 red beads and 15 gold beads.
Then, the rule for each beads is
Red: add 20
Gold: add 15
Mr.Palacios delivers newspapers. He can deliver 60 papers in 3/4 of an hour. At this rate how may newspaper will Mr.Palacios deliver in 2 1/4 hours?
Given Data:
Total number of newspapers delivered is 3/4 hour is: 60
Let Mr.Palacios delivers 'x' number of newspaper in 2 1/4 hours.
The expression to calculate the total number of the newspaper delivered in 2 1/4 hour is,
[tex]\begin{gathered} \frac{x}{2\frac{1}{4}}=\frac{60}{\frac{3}{4}} \\ x=(2\frac{1}{4})\times(\frac{60}{3}\times4) \\ x=(\frac{2\times4+1}{4})\times(20\times4) \\ x=(\frac{9}{4})\times80 \\ x=2.25\times80 \\ x=180 \end{gathered}[/tex]Thus, Mr.Palocios delivers 180 newspapers in 2 1/4 hours.
I was a little confused on what to do or where to start, could you help?
Our approach is to determine the equation of the function and when we do, we can substitute as appropriate.
[tex]\begin{gathered} \text{ At x = 4, y = 12} \\ \frac{y}{x}=\frac{12}{4}=3 \\ y=3x \end{gathered}[/tex]Now we have established a relationship between x and y.
[tex]\begin{gathered} \text{ When y = 6,} \\ 6=3x \\ \text{ Divide both sides by 3 to get:} \\ x=2 \end{gathered}[/tex][tex]\begin{gathered} \text{ When x = 6,} \\ y=3(6)=18 \\ y=18 \end{gathered}[/tex]We can confirm these values by tracing downwards to 2 when y = 6
In the same way, we can trace leftward to 18 when x = 6
A student bought a calculator and a textbook for a course in algebra. He told his friend that the total cost was $170(without tax) and thatthe calculator cost $30 more than thrice the cost of the textbook. What was the cost of each item? Let x = the cost of a calculator andy = the cost of the textbook. The corresponding modeling system isx + y = 170Solve the system by using the method ofx = 3y + 30substitution.
Given:
x + y = 170.........Equation 1
x = 3y + 30........Equation 2
Asked: Find the value of x and y.
Solution:
First, let's find he value of y.
[tex]\begin{gathered} x+y=170\text{ }\Rightarrow Eqn\text{ 1} \\ x=3y+30\text{ }\Rightarrow Eqn\text{ 2} \\ We\text{ will substitute equation 2 to equation 1.} \\ 3y+30+y=170\text{ } \\ 4y+30=170 \\ 4y=170-30 \\ 4y=140 \\ \frac{4y}{4}=\frac{140}{4} \\ y=35 \end{gathered}[/tex]Now, for the value of x, let's substitute y to the second equation.
[tex]\begin{gathered} x=3y+30\text{ }\Rightarrow Eqn\text{ 2} \\ x=3(35)+30\text{ } \\ x=105+30 \\ x=135 \end{gathered}[/tex]ANSWER: (135, 35)
x = 135
y = 35
2 3 Year months A 7 months B 3 months © 8 months D 9 months
In order to fill the blank space, consider that 1 year = 12 months
Then, you have:
(2/3) · 12 months = 24/3 months = 8 months
C) 8 months
can someone help me find the y= mx +b of this equation
The given coordinates are (0,-2) and (-5,-3). The line equation is,
y = mx + b
Here, m is the slope and b is the y-intercept.
The slope can be calculated as,
[tex]m=\frac{y2-y1}{x2-x1}=\frac{-3+2}{-5}=\frac{1}{5}[/tex]Now to calculate b, let us take the point (0,-2) and 1/5 as m,
[tex]\begin{gathered} -2=0\times\frac{1}{5}+b \\ b=-2 \end{gathered}[/tex]Therefore the equation of the line is,
[tex]y=\frac{1}{5}x-2[/tex]Caleb is painting and this figure the Shaded area represents the part of the picture that has painted blue. what is the area of the blue part of Caleb's picture
The above rough sketch repressents the shaded area of the mural and the shaded part is a rectangle.
Area of a shaded mural = Length x Breadth
[tex]\begin{gathered} \text{Length}=\text{ }\frac{6}{8}m \\ \text{Breadth}=\frac{4}{8}m \\ \text{area of the shaded mural = }\frac{6}{8}\times\frac{4}{8}=\frac{24}{64}=\frac{3}{8}m^2 \end{gathered}[/tex]Hence, the shaded area (blue) of the mural is deduced above.
I don’t know how to solve this I need help please
Since the path of Grant is a line segment, the first step to solve the exercise is to find the slope of the line segment. For this, we can use the following formula:
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where m is the slope of the line, and} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are two points through the line passes} \end{gathered}[/tex]As we can see in the graph, the line segment passes through the points (8,0) and (-4,6). Then, we have:
[tex]\begin{gathered} (x_1,y_1)=(8,0) \\ (x_2,y_2)=(-4,6) \\ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{6-0}{-4-8} \\ m=\frac{6}{-12} \\ \text{ Simplify} \\ m=\frac{1\cdot6}{-2\cdot6} \\ m=-\frac{1}{2} \end{gathered}[/tex]Now that we have the slope of the line segment and a point which it passes, we can use the point-slope formula:
[tex]y-y_1=m(x-x_1)\Rightarrow\text{ Point-slope formula}[/tex][tex]y-0=-\frac{1}{2}(x-8)[/tex]Finally, we solve for y the above equation:
[tex]\begin{gathered} y=-\frac{1}{2}(x-8) \\ \text{ Apply the distributive property} \\ y=-\frac{1}{2}\cdot x-\frac{1}{2}\cdot-8 \\ y=-\frac{x}{2}+\frac{1}{2}\cdot8 \\ y=-\frac{x}{2}+\frac{8}{2} \\ y=-\frac{x}{2}+4 \\ \text{ Reorder} \\ y=4-\frac{x}{2} \end{gathered}[/tex]Therefore, the equation that represents the path of Grant is:
[tex]$$\boldsymbol{y=4-\frac{x}{2}}$$[/tex]Complete the end behavior statement for the function shown above. Asx→−∞, f(x)→
Given
The function
[tex]f(x)=\frac{12x^5}{3x^5}[/tex]To find the end behavior of the function.
Explanation:
It is given that,
[tex]f(x)=\frac{12x^5}{3x^5}[/tex]That implies,
[tex]\begin{gathered} \lim_{x\to-\infty}f(x)=\lim_{x\to-\infty}(\frac{12x^5}{3x^5}) \\ =\lim_{x\to-\infty}(\frac{12}{3}) \\ =\lim_{x\to-\infty}(4) \\ =4 \end{gathered}[/tex]Hence,
[tex]As\text{ }x\rightarrow-\infty,f(x)\rightarrow4[/tex]How do I solve this?Farmer Ed has 1500 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If farmer Ed does not fence the side along the river what is the largest area that can be in enclosed?
We need to find the maximum (Vertex of the function)
Let:
L = Length = 1500 - 2x
W = Width = x
The area is given by:
[tex]\begin{gathered} A=W\cdot L \\ A=x(1500-2x) \\ A=1500x-2x^2 \\ A(x)=1500x-2x^2 \end{gathered}[/tex]We can find the maximum using the following formula:
[tex]\begin{gathered} xm=-\frac{b}{2a} \\ where \\ a=-2 \\ b=1500 \\ so\colon \\ xm=-\frac{(1500)}{2(-2)}=\frac{1500}{4}=375 \end{gathered}[/tex]Evaluate the area for the value we found previously:
[tex]A(375)=-2(375)^2+1500(375)=-281250+562500=281250[/tex]The largest area that can be enclosed is 281250m²
You are getting your carpet cleaned. You have three bedrooms (9x10, 10x12 and 11x16), a living (14x16 ) , and dining room (14x14 ) Modernistic Carpet Cleaning will do 3 rooms for $ 270 and then charge $0.60/sq ft. If you put your 3 biggest rooms in the 3 rooms for $270" deal and then pay $0.60/ sq. ft. for the rest , how much will you pay?
Answer:
$396
Explanation:
First, determine the area of all the rooms:
• Area of Bedroom 1 = 9x10 = 90 sq.ft.
,• Area of Bedroom 2 = 10x12 = 120 sq.ft.
,• Area of Bedroom 3 = 11 x 16 = 176 sq.ft.
,• Area of the living room = 14x16 = 224 sq.ft.
,• Area of the dining room = 14x14 = 196 sq.ft.
Thus, the three biggest rooms are bedroom 3, living room and the dining room.
• The total area of the other two rooms = 90+120 = 210 sq.ft.
Since the cost for the rest is $0.60/ sq. ft.:
[tex]\begin{gathered} \text{Total Cost}=270+0.60(210) \\ =270+126 \\ =\$396 \end{gathered}[/tex]You will pay a total of $396.
You wish to buy a $330,000 home. The mortgage company offers you a 30-year loan with a 3.6 percent APR. What are the monthly payments? Assumezero down payment.O $1,423.93O $1,500.33O $1,469.91O $1,578.11
Step 1
Given; You wish to buy a $330,000 home. The mortgage company offers you a 30-
year loan with a 3.6 percent APR.
Required; What are the monthly payments? Assume
zero down payment.
Step 2
[tex][/tex]Examine the following step function. Open circle at (negative 1, 0) connected by a line to closed circle at (0, 0). Open circle at (0, 1) connected by a line to a closed circle at (1, 1). Pattern continues.© 2018 StrongMind. Created using GeoGebra. Which statements are true?Select all that apply.
From the given graph, let's select the correct statements.
Here, since the open dots are on the left and the closed dots are on the right, the function can be said to be a ceiling function.
Ceiling functions are functions which give the smallest value which is greater than or equal to the specified value on the number line.
Therefore, the correct statements are:
• 1. It is a ceiling function.
• 2. Any decimal or fraction rounds to the least integer that is greater than x.
ANSWER:
• B. It is a ceiling function.
• C. Any decimal or fraction rounds to the least integer that is greater than x.
R is the midpoint of line segment of PQ. PR is 3x + 6 and RQ is 5x - 2.Find the followingX:PR:RO:PQ:
Let's draw a diagram to represent the given problem.
If R is midpoint then PR and RQ are equal by definition of midpoint. So, we can express the following equation.
[tex]\begin{gathered} PR=RQ \\ 3x+6=5x-2 \end{gathered}[/tex]Then, we solve for x. First, we subtract 5x on each side.
[tex]\begin{gathered} 3x-5x+6=5x-5x-2 \\ -2x+6=-2 \end{gathered}[/tex]Now, we subtract 6 on each side.
[tex]\begin{gathered} -2x+6-6=-2-6 \\ -2x=-8 \end{gathered}[/tex]At last, we divide the equation by -2.
[tex]\begin{gathered} \frac{-2x}{-2}=\frac{-8}{-2} \\ x=4 \end{gathered}[/tex]The solution for x is 4.We use this value to find PR and RQ.
[tex]PR=3x+6=3(4)+6=12+6=18=RQ[/tex]Then, we find PQ.
[tex]PQ=18+18=36[/tex]Therefore, PR and RQ are equal to 18 units, and PQ is equal to 36 units.Last year during the July 4th holiday, Americans ate about 150,000,000 hot dogs. Over the entire year, Americans ate a total of about 2 x 10^10. Compute how many times greater the total number of hot dogs eaten by Americans last year was than the number of hot dogs eaten during the 4th of July holiday. Round your answer to the nearest one. times greater than the number of The total number of hot dogs eaten by Americans last year was blank hot dogs eaten during the July 4th holiday.
July 4th quantity: 150,000,000 = 1.5 x 10^9
Entire year quantity: 2 x 10^10 = 2,000,000,000
2,000,000,000 - 150,000,000 = 2 thousand millions - 150 millions =
one thousand, eith hundred fifty millions
2,000,000,000 - 150,000,000 = 1,850,000,000
1,850,000,000 = 1.85x10^10
Americans eated 1,850,000,000 = 1.85x10^10 more hotdogs over the entire year than they eated on the 4th of July
2,000,000,000/150,000,000 = 13.33
Americans eated 13.33 times more hotdogs over the entire year than in the 4th of July
Write the equation of the line that passes through the point (-7, -1) and isperpendicular to x = -3y+6. Write your answer in slope-intercept form y = mx + b
If two lines are perpendicular, the multiplication of the slopes is equal to -1.
So, the line x = -3y + 6 can be written as:
[tex]\begin{gathered} x=-3y+6 \\ x-6=-3y \\ \frac{x-6}{-3}=y \\ \frac{-1}{3}x+2=y \end{gathered}[/tex]So, the slope is -1/3. It means that the slope of the perpendicular line is:
[tex]\begin{gathered} \frac{-1}{3}\cdot m=-1 \\ -m=-3 \\ m=3 \end{gathered}[/tex]Then, with a point (x1, y1) and a slope m, we can find the equation of the line as:
[tex]y-y_1=m(x-x_1)[/tex]Replacing, m by 3 and (x1, y1) by (-7,-1), we get:
[tex]\begin{gathered} y-(-1)=3(x-(-7)) \\ y+1=3(x+7) \\ y+1=3x+21 \\ y=3x+21-1 \\ y=3x+20 \end{gathered}[/tex]Answer: y = 3x + 20
Benadryl is a medicine used to treat runny noses, itching, and other cold and allergy symptoms. Ittakes an average of two to three days for the active ingredient of Benadryl, diphenhydramine, to leave the body. The formula below represents the amount, A, of diphenhydramine left in the body,measured in mg, t hours after taking 50 mg of the medicine.A = 50 (0.9217)^tA) How long does it take for the body to eliminate half of the initial amount of Benadryl? Solve thisalgebraically. Round decimal to two places.
We have to replace A= 25 mg in the equation and solve for t. Doing so, we have:
[tex]\begin{gathered} 25=50(0.9217)^t\text{ } \\ 0.5=(0.9217)^t\text{ (Dividing by 50 on both sides of the equation)} \end{gathered}[/tex][tex]\begin{gathered} \log _5(0.5)=\log _5(0.9217)^t(\text{ Taking the logarithm base 5 of both sides of the equation)} \\ \log _5(0.5)=t\cdot\log _5(0.9217)\text{ (Using the power rule of logarithms)} \\ -0.431=t\cdot(-0.0507)\text{ (Finding the logarithms for each case)} \\ 8.50=t\text{ (Dividing by }-0.0507\text{ on both sides of the equation)} \end{gathered}[/tex]The answer is 8.50 hours (Rounding to two decimal places)
Given that events A and B are independent with P(A)=0.9P(A)=0.9 and P(B)=0.71P(B)=0.71, determine the value of P(A\cap B)P(A∩B), rounding to the nearest thousandth, if necessary.
Remember that
If A and B are independent events, then
P(A∩B)=P(A)*P(B)
substitute given values
P(A∩B)=(0.9)*(0.71)=0.639
therefore
The answer is 0.639translate this phrase into an algebraic expression 59 Less than twice a number use the variable n to represent the unknown number
To write the given phrase as an algebraic expression you can identify what does each part of the phrase mean:
59 less than: You have to substract 59 to the other part of the phrase
twice a number: as the number is n, twice a number is 2n
Then, you get the next algebraic expression:
[tex]2n-59[/tex]is 6xy^5z monomial or not
To be a monomial an expresion needs to have just 1 term, the terms in a math expression are separated by a + or a -
Then, even if the term has two or more variables as given: A exponential expression with a term with different variables
[tex]6xy^{5z}[/tex]It is just one term. It is a monomialA jet leaves a runway whose bearing is N 36°E from the control tower. After flying 4 miles, the jet turns 90° and flies on a bearing of S 54°E for 5 miles. At that time, what is the bearing of the jet from the control tower?
The initial bearing is N 36° E. Then, the jet turns 90° after 4 miles and flies on a bearing of S 54° E for 5 miles. The diagram of the problem is:
To solve this, we need to know the angle x. First of all, we calculate the distance traveled vertically and horizontally in the first part:
[tex]\begin{gathered} x_1=4\cdot\sin 36\degree \\ y_1=4\cdot\cos 36\degree \end{gathered}[/tex]Now, for the second part:
[tex]\begin{gathered} x_2=5\sin 54\degree \\ y_2=5\cos 54\degree \end{gathered}[/tex]As we can see from the figure, the jet first travels to the NE and then to the SE, so the horizontal net distance is the sum of the two parts, and the vertical net distance is the subtraction:
[tex]\begin{gathered} x=x_1+x_2=4\sin 36\degree+5\sin 54\degree\approx6.3962^{} \\ y=y_1-y_2=4\cos 36\degree-^{}5\cos 54\degree\approx0.2971 \end{gathered}[/tex]The angle of the final position and the horizontal line is given by:
[tex]\theta=\tan ^{-1}(\frac{0.2971}{6.3962})=2.6594\degree\approx3\degree[/tex]The complement of this angle is the angle we are looking for, that is:
[tex]90\degree-3\degree=87\degree[/tex]Since the first angle is positive, then our direction will be NE, then the bearing of the jet from the control tower will be:
[tex]N87\degree E[/tex]Which integer represents this scenario? an elevator goes down 3 floors a) -3 b) 3 6.NS.5
Answer : -3
Since, the elevattor is going down the floor
This means its decreasing from the its original height
An elevetor goes down 3 floors = -3
Epitaxian is a cutting edge technology company based in Texas. The company has just finisheddeveloping a prototype of a product it is calling the X-13. According to the company'sdocumentation, the X-13 must be operated in a room that is kept at a temperature of 18.1 °F.What is this temperature in degrees Celsius (°C)?Use the given formulas as necessary, and round your answer to the nearest tenth of a degree.°CX2?Formulas:C11599|5F=(F-32)C+32 I need help with this math problem.
Solution
- The formula for converting from Fahrenheit to Celsius is given below:
[tex]\begin{gathered} (f-32)\degree F\times\frac{5}{9}=Y\degree C \\ where, \\ Y=Celsius\text{ temperature} \\ f=Fahrenheit\text{ temperature} \end{gathered}[/tex]- Thus, we can solve the question as follows:
[tex]\begin{gathered} f=18.1\degree F \\ \\ \therefore Y=(18.1-32)\times\frac{5}{9} \\ \\ Y=-7.7222...\degree\approx-7.7\degree\text{ \lparen To the nearest tenth of a degree\rparen} \end{gathered}[/tex]Final Answer
The answer is -7.7 degree Celsius
a car is traveling at a speed of 80 miles per hour. what is the car speed in kilometers per hour? how many kilometer will the car travel in 3 hours, assume that 1 mile is equal to 1.6 kilometers. do not round.
The car is travelling at speed of 80miles per hour.
since it is given that 1 mile=1.6km
To convert 80 miles per hour into kilometer per hour.
multiply 80 by 1.6
[tex]\begin{gathered} 80\text{ miles per hour=80}\times1.6\text{ kilometer per hour} \\ 80\text{ miles per hour=80}\times128\text{ kilometer per hour} \end{gathered}[/tex]128 km per hour.
The expression for the distance is :
[tex]\text{Distance}=\text{speed}\times Time[/tex]For distance at time t=3,
subtitute speed=128km/hr
time=3 hr
[tex]\begin{gathered} \text{Distance}=128\times3 \\ \text{Distance}=384\operatorname{km} \end{gathered}[/tex]The car travel 384km in 3 hours.
f(x) = x to graph g(x) = |x - 4
Using the parent function as reference, and according to the expression for g(x), to graph this function you need to do a vertical translation down 4 units.
It means, if the parent function had a y intercept of 0, now g(x) will have a y intercept of -4.
The graph will look like this: