Solution
- In order to solve the question, we need to understand the rules guiding the translation of graphs. This rule is given below:
[tex]\begin{gathered} f(x)\to f(x+h) \\ \text{ If h is positive, then, the graph is shifted to the left} \\ \text{ If h is negative, then, the graph is shifted to the right} \end{gathered}[/tex]- The question given to us has h = 8. This means that h is positive, therefore, the graph of f(x) must be shifted to the left by 8 units
Final Answer
The answer is "Shifted Left" (OPTION B)
I need this done in 20 minutes please and thank you
An isosceles triangle in the one that has 2 equal sides, means that it also has two equal angles
this means that:
[tex]\begin{gathered} ifJK=KL \\ \text{then,}\measuredangle KJL=\measuredangle KLJ \\ \end{gathered}[/tex]using the properties of the triangle
[tex]\begin{gathered} \measuredangle KJL+\measuredangle KLJ+\measuredangle JKL=180 \\ 2\cdot\measuredangle KLJ+\measuredangle JKL=180 \\ 2\cdot34+\measuredangle JKL=180 \\ \measuredangle JKL=180-68 \\ \measuredangle JKL=112 \end{gathered}[/tex]5.Given the sample triangle below and the conditions a=3, c = _51, find:cot(A).
Depending on the angle we are analyzing on the right triangle, each side of it takes a different name. In this case, we are going to name them depending on the angle A. Then,
a: opposite side (to A)
b: adjacent side
c: hypotenuse
STEP 2: formula for cot(A)We know that the formula for cot(A) is:
[tex]\cot (A)=\frac{\text{adjacent}}{\text{opposite}}[/tex]Replacing it with a and b:
[tex]\begin{gathered} \cot (A)=\frac{\text{adjacent}}{\text{opposite}} \\ \downarrow \\ \cot (A)=\frac{b}{a} \end{gathered}[/tex]Since a = 3:
[tex]\cot (A)=\frac{b}{3}[/tex]STEP 3: finding bWe have an expression for cot(A) but we do not know its exact value yet. First we have to find the value of b to find it out.
We do this using the Pythagorean Theorem. Its formula is given by the equation:
[tex]c^2=a^2+b^2[/tex]Since
a = 3
and
c = √51
Then,
[tex]\begin{gathered} c^2=a^2+b^2 \\ \downarrow \\ \sqrt[]{51}^2=3^2+b^2 \\ 51=9+b^2 \end{gathered}[/tex]solving the equation for b:
[tex]\begin{gathered} 51=9+b^2 \\ \downarrow\text{ taking 9 to the left} \\ 51-9=b^2 \\ 42=b^2 \\ \downarrow square\text{ root of both sides} \\ \sqrt{42}=\sqrt{b^2}=b \\ \sqrt[]{42}=b \end{gathered}[/tex]Then,
b= √42
Therefore, the equation for cot(A) is:
[tex]\begin{gathered} \cot (A)=\frac{b}{3} \\ \downarrow \\ \cot (A)=\frac{\sqrt[]{42}}{3} \end{gathered}[/tex]Answer: Dthe number of people with the flu during the epidemic is a function,f, of the number of days,d, since the epidemic began. The equation began. The equation f(d)= 50*(3/2)^d defines f.How quickly is the flu spreading? or what is the exponential growth factor?
We have that the general exponential formula is:
[tex]f(x)=a\cdot b^x[/tex]In this case, we have:
[tex]f(d)=50\cdot(\frac{3}{2})^d[/tex]the term b on the exponential formula is also known as the growth factor. Therefore, in this case the growth factor is b=3/2
Line segments, AB,BC,CD,DA create the quadrilateral graphed on the coordinate grid above. The equations for two of the four line segments are given below. Use the equations of the line segments to answer the questions that follow. AB: y = -x + 1 BC: y = -3x + 11
The equations of the line segments are,
[tex]\begin{gathered} AB\colon y=\frac{1}{3}x+1 \\ BC\colon y=-3x+11 \end{gathered}[/tex]Calculate the equations of CD and AD.
The equation of line Cd is,
[tex]\begin{gathered} (y-(-3))=\frac{-1+3}{4+2}(x+2) \\ y+3=\frac{1}{3}(x+2) \\ 3y=x-7 \end{gathered}[/tex]The equation of the line AD is,
[tex]\begin{gathered} y-0=\frac{-3-0}{-2+3}(x+3) \\ y=-3x-9 \end{gathered}[/tex]1)If two lines are parallel slope will be equal and perpendicular product of slope will be -1.
From the equation, the slope of AB is 1/3
From the equation, the slope of Cd is 1/3.
So, they are parallel.
2)The slope of AB is 1/3.
The slope of BC is -3.
The product of two slopes is -1. Therefore, AB is perpendicular to BC.
3) The slope of AB is 1/3 and slope of AD is -3. Since, the product is -1, they are perpendicular.
Another pair of line segments that are perpendicular to each other is AB and AD.
HELPPPP ME PLEASE I NEED TO KNOW THE ANDWER ASAP
Given the figure in the attached image.
The polygon has 4 sides, and all the four sides are equal.
but the four angles are not given to be equal.
Therefore, the polygon shown in the figure is a Rhombus
There are 6000 students at Mountain High School, and 1/4 of these students are seniors. If 2/3 of the seniors are in favor of the school forming a debate team and 1/5 of the remaining students (not seniors) are also in favor of forming a debate team how many students do not favor this idea?
hello
tp solve this question, let's get the data out
we have a total of 6000 students. 1/4 of the students are seniors, let's find the numbers of seniors in the school
the number of senior students are
[tex]\frac{1}{4}\times6000=1500[/tex]we have 1500 seniors in the school.
we can find the seniors in support of a debate team by multiplying 2/3 by 1500
[tex]\frac{2}{3}\times1500=1000[/tex]now we know that 1000 students are in support of the debate team. let's subtract the numbers of students in support of debate team from numbers of seniors in the schoolto giveus the numbers of seniors that are not in support of debate team.
[tex]1500-1000=500[/tex]500 seniors from the school are not in support of a debate team.
Also note that 1/5 of the remaining students are not in support of the debate team.
which would be
[tex]\begin{gathered} 6000-1500=4500 \\ \frac{1}{5}\times4500=900 \end{gathered}[/tex]now, we can add the numbers of seniors that are not in support of a debate team plus number of remaining students not in support of a debate team
[tex]500+900=1400[/tex]from the calculationabove, a total of 1400 students are not in support of the idea
An electronics store makes a profit of $59 for everystandard DVD player sold and $69 for every portableDVD player sold. The manager's target is to make atleast $345 a day on sales from standard and portableDVD players. Write an inequality that represents thenumbers of both kinds of DVD players that can besold to reach or beat the sales target. Let s representthe number of standard DVD players sold and prepresent the number of portable DVD players sold.Then graph the inequality.
The profit on one standard DVD player is $59 and on one portable DVD player is $69.
If there are s number of standard DVD player then total profit on standard DVD players is $59s. Simillarly total profit on portable DVD players is $69p.
The total profit on DVD player shoul be at least $345, which means total profit on DVD players is $345 or more than $345.
The linear inequalty for total profit is,
[tex]59s+69p\ge345[/tex]The graph of the linear inequality is,
In graph, lines pointing away the origin represent the region for the equation.
h(x) = 3a + 410-8-h612-X10-8-668-2-2-10Select the correct answer from each drop-down menu.Function h is alwaysThe function'sis located at (0,5), and there is noThe function isfor all values of x.
We are given the following exponential function.
[tex]h(x)=3^x+4_{}[/tex]The function h(x) is always increasing as can be seen in the given graph.
The y-intercept of a graph is the point where the function intersects/crosses the y-axis.
As you can see from the graph, the graph intersects the y-axis at the point (0, 5)
Therefore, the function's y-intercept is located at (0, 5)
The x-intercept of a graph is the point where the function intersects/crosses the x-axis.
As you can see from the graph, the graph does not intersect the x-axis at any point.
Therefore, there is no x-intercept.
Notice that the graph of the function h(x) is always positive for all values of x.
Answer:
Step-by-step explanation:
Nicole wants to use his 18% employee discount to buy a video game that is priced at $69.99. A 6.5% sales tax is applied to the discounted price. What will be the total cost of the video game, including the sales tax?
Given:
The discount rate, D=18%.
The mared price, M=$69.99.
The sales tax percentage on discounted price, s=6.5%.
The discounted price is,
[tex]\begin{gathered} C=\frac{(100-D)}{100}\times M \\ C=\frac{100-18}{100}\times69.99 \\ C=57.39 \end{gathered}[/tex]The sales tax on the discounted price is,
[tex]\begin{gathered} S=\frac{s}{100}\times C \\ S=\frac{6.5}{100}\times57.39 \\ S=3.73 \end{gathered}[/tex]The total cost of the video game including the sales tax is,
[tex]\begin{gathered} T=C+S \\ T=57.39+3.73 \\ T=61.12 \end{gathered}[/tex]Therefore, the total cost of the video game including the sales tax is $61.12.
The image point of A after a translation left 2 units and down 5 units is the pointB(-8, -11). Determine the coordinates of the pre-image point A.Submit Answer
Let the coordinates of the pre-image which is point A be (x,y)
The point after the translation left 2 units and down 5 units is B(-8, -11)
To get the x coordinate
we were tolt that the point was move 2 units left
So this implies x = -8+2 = -6
To get the y coordinates, we wre told that the point was moved down 5 units
This implies y = -11+ 5 = -6
Therefore, the coordinates of the pre-image point A is (-6, -6)
find the value of expression if d = 10 and c= 5, 5d + c + 2
Laying down my n buffer is concerned after receiving her weekly paycheck she believes that her deductions for social security,Medicare,and federal income ta withholding (fit) may be incorrect Larsen is paid a salary of 4330 she is married filling jointly and prior to this payroll check has total earnings of 140,460 what are the correct deductions for social security Medicare and fit assume a rate of 6.3% on 142,809 for social security and 1.45% for Medicare
Correct deduction for social security Medicare and fit at 6.3% = 8,996.967
Correct deduction for Medicare at rate of 1.45% = 2,070.731
What is Medicare?Medicare is defined as a type of health insurance that reduces the fees incurred by an individual following the reception of health services.
After deductions the total earning = 140,460
The correct deduction for social security, Medicare and fit at the rate of 6.3% of 142,809;
= 6.3/100 × 142,809
= 899696.7/100
= 8,996.967
The correct deduction for Medicare at the rate of 1.45%;
= 1.45/100 × 142,809
= 207,073.05/100
= 2,070.731.
Learn more about Medicare here:
https://brainly.com/question/24304697
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I need help on my practice sheet. needs to be simplified
then
[tex]\begin{gathered} \frac{x+6}{3x}\times\frac{3(x-6)}{(x+6)(x-6)} \\ \frac{x+6}{3x}\times\frac{3}{x+6} \\ \frac{(x+6)\times3}{3x\times(x+6)} \\ \frac{3}{3x} \\ \frac{1}{x} \end{gathered}[/tex]answer: 1/x
The endpoints of the line are (0, 5) and (6, 4). Find the slope of the line.
Solution:
Given the endpoints of the line;
[tex](0,5),(6,4)[/tex]The slope, m of the line is;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ \text{ Where }x_1=0,y_1=5,x_2=6,y_2=4 \end{gathered}[/tex]Thus;
[tex]\begin{gathered} m=\frac{4-5}{6-6} \\ \\ m=-\frac{1}{6} \end{gathered}[/tex]CORRECT ANSWER:
[tex]-\frac{1}{6}[/tex]Your $8800 investment grows to $15600 over the course of 5 years compounded quarterly. What interest rate did you receive on your investment? (Write your answer with at least four decimal points) Your interest rate is r =
Given:
The initial amount is $8800.
The Future value is $15600.
Number of year = 5 years compounded quarterly .
The interest rate is calculated as,
[tex]\begin{gathered} FV=P(1+\frac{r}{4})^{4\times n} \\ 15600=8800(1+\frac{r}{4})^{4\times5} \\ \frac{39}{22}=(1+\frac{r}{4})^{20} \\ \sqrt[20]{\frac{39}{22}}=1+\frac{r}{4} \\ \frac{r}{4}=\sqrt[20]{\frac{39}{22}}^{}-1 \\ r=4(\sqrt[20]{\frac{39}{22}}-1) \\ r=0.1162 \end{gathered}[/tex]Answer: the interest rate is 0.1162.
I would like some help on how to solve this problem!(please and thank you)
Answer
GH is congruent to JH and FH is congruent to HI. ∠GHF should be congruent to ∠JHI by Vertical Angles Theorem. Since GH is congruent to JH, ∠GHF is congruent ∠JHI, and FH is congruent is congruent to HI, ΔGHF is congruent ΔJHI, by SAS. Then one can assume that FG is congruent to IJ by CPCTC.
Given parallelogram ABCD, diagonals AC and BD intersect at point E. AE=2x, BE=y+10, CE=x+2 and DE=4y−8. Find the length of AC.A. 8B. 6C. 2D. 4
Answer:
the length of the diagonal AC is;
[tex]8[/tex]Explanation:
Given the parallelogram ABCD, diagonals AC and BD intersect at point E.
[tex]\begin{gathered} AE=2x \\ CE=x+2 \\ BE=y+10 \\ DE=4y+8 \end{gathered}[/tex]Recall that the diagonals of a parallelogram bisect each other;
So;
[tex]AE=CE[/tex]substituting AE and CE;
[tex]\begin{gathered} 2x=x+2 \\ 2x-x=2 \\ x=2 \end{gathered}[/tex]To calculate the length of AC;
[tex]\begin{gathered} AC=2x+x+2=3x+2 \\ since\text{ x=2} \\ AC=3x+2=3(2)+2 \\ AC=6+2 \\ AC=8 \end{gathered}[/tex]Therefore, the length of the diagonal AC is;
[tex]8[/tex]a gate that is 5 ft tall casts a shadow 9 ft long the house behind the gate cast a shadow of 54 ft how about how many feet tall is the house
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
gate:
hg = 5 ft
shadow = 9ft
house
hh = ?
shadow = 54 ft
Step 02:
We must apply the theorem of thales.
[tex]\frac{hg}{hh}=\frac{shadow\text{ gate}}{\text{shadow house}}[/tex][tex]\frac{5ft}{hh}=\frac{9ft}{54\text{ ft}}[/tex]hh * 9 ft = 5 ft * 54 ft
hh = (5 ft * 54 ft ) / 9 ft
hh = 270 ft ² / 9 ft = 30 ft
The answer is:
The house is 30ft tall.
Find the surface area of a right cone with diameter 30 in. and slant height 8 in.Your answerEXTRA CREDIT: Find the surface area of the figure below. Round to the nearesttenth, if necessary.10 in?
Answer:
Surface area = 1084 in²
Step-by-step explanation:
To find the surface area of a right cone, we can use the following formula:
[tex]\boxed{{Area = \pi r^2 + \pi rl}}[/tex],
where:
• r = radius
• l = slant height.
In the question, we are told that the diameter of the cone is 30 in. Therefore its radius is (30 ÷ 2 = ) 15 in. We are also told that its height is 8 in.
Using this information and the formula above, we can calculate the surface area of the cone:
Surface area = [tex]\pi \times (15)^2 + \pi \times 15 \times 8[/tex]
= [tex]345 \pi[/tex]
[tex]\approx[/tex] 1084 in²
Word Problems: Define your variable, write and solve the equation. 9. You have $75 to spend at the grocery store. You get $23 in change. How much money do you spend? Define your variable: Equation: Answer:
ANSWER
Variable : how much money was spent (x)
Equation: x + 23 = 75
Answer: $52
EXPLANATION
Let the variable (amount of money spent) be x.
Initially, you had $75 and you spend some money (x) and you are left with $23 in change.
This means that the sum of the money you spent and the change you received is $75.
That is:
x + 23 = 75
That is the equation.
To find how much money you spent, we have to find the value of x by collecting like terms:
=> x = 75 - 23
x = $52
You spent $52.
A rectangular athletic field is twice as long as it is wide if the perimeter of the athletic field is 360 yards what are its dimensions. The width isThe length is
Step 1. We will start by making a diagram of the situation.
Since the length of the rectangle is twice the width, if we call the width x, then the length will be 2x as shown in the diagram:
Step 2. One thing that we know about the rectangle is its perimeter:
[tex]\text{Perimeter}\longrightarrow360\text{yd}[/tex]This perimeter has to be the result of the sum of all of the sides of the rectangle:
[tex]x+x+2x+2x=360[/tex]Step 3. Solve the previous equation for x.
In order to solve for x, the first step is to combine the like terms on the left-hand side:
[tex]6x=360[/tex]The second step to solve for x is to divide both sides of the equation by 6:
[tex]\frac{6x}{6}=\frac{360}{6}[/tex]Simplifying:
[tex]x=60[/tex]Step 4. Remember from the diagram from step 1, that x was the width of the rectangle:
[tex]\text{width}\longrightarrow x\longrightarrow60yd[/tex]and the length was 2x, so we multiply the result for the with by 2:
[tex]\text{length}\longrightarrow2x=2(60)=120\longrightarrow120yd[/tex]And these are the values for the width and the length.
Answer:
The width is 60yd
The length is 120yd
Find the set A n Φ.U = {1, 2, 3, 4, 5, 6, 7, 8, 9)A = 2, 3, 8, 9)Selectthe correct choice below and, if necessary, fill in the
Answer
Option B is the correct answer.
A n Φ = {}
A n Φ is the empty set.
Explanation
We are told to find the intersection between set A and the empty set Φ.
The intersection of two sets refers to the elements that belong to the two sets, that is, the elements that they both have in common.
Set A = (2, 3, 8, 9)
Set Φ = {}
What the elements of set A and set Φ (an empty set) have in common is nothing.
Hence, the intersection of set A and set Φ is an empty set.
A n Φ = {}
Hope this Helps!!!
66. WORKER EFFICIENCY An efficiency study of the morning shift at a certain factory indicates that an average worker who arrives on the job at 8:00 A.M. will have assembled f(x) = -x³ + 6x² + 15x television sets x hours later. How many sets will such a worker have assembled by 10:00 A.M.? [Hint: At 10:00 A.M., x = 2.] b. Ilow many sets will such a worker assemble between 9:00 and 10:00 A.M.?
Step-by-step explanation:
use differential calculus
20 P1: a For two events, A and B.P(B) -0.5, P(AB) -0.4 andPAB) = 0.4.Calculatei PAB)ii P(A)ili P(AUB)iv P(AB)(8 marks)b Determine, with a reason, whetherevents A and B are independent ornot.(2 marks)probabilityStatistics and
We have two events A and B.
We know that:
P(B) = 0.5
P(A|B) = 0.4
P(A∩B') = 0.4
i) We have to calculate P(A∩B).
We can relate P(A∩B) with the other probabilities knowing that:
[tex](A\cap B)\cup(A\cap B^{\prime})=A[/tex]So we can write:
[tex]P(A\cap B)+P(A\cap B^{\prime})=P(A)[/tex]We know P(A∩B') but we don't know P(A), so this approach is not useful in this case.
We can try with the conditional probability relating P(A∩B) as:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]In this case, we can use this to calculate P(A∩B) as:
[tex]\begin{gathered} P(A\cap B)=P(A|B)P(B) \\ P(A\cap B)=0.4*0.5 \\ P(A\cap B)=0.2 \end{gathered}[/tex]ii) We have to calculate P(A) now.
We can use the first equation we derive to calculate it:
[tex]\begin{gathered} P(A)=P(A\cap B)+P(A\cap B^{\prime}) \\ P(A)=0.2+0.4 \\ P(A)=0.6 \end{gathered}[/tex]iii) We have to calculate P(A∪B).
We can use the expression:
[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ P(A\cup B)=0.6+0.4-0.2 \\ P(A\cup B)=0.8 \end{gathered}[/tex]iv. We can now calculate P(A|B') as:
[tex]\begin{gathered} P(A)=P(A|B)+P(A|B^{\prime}) \\ P(A|B^{\prime})=P(A)-P(A|B) \\ P(A|B^{\prime})=0.6-0.4 \\ P(A|B^{\prime})=0.2 \end{gathered}[/tex]b) We now have to find if A and B are independent events.
To do that we have to verify this conditions:
[tex]\begin{gathered} 1)P(A|B)=P(A) \\ 2)P(B|A)=P(B) \\ 3)P(A\cap B)=P(A)*P(B) \end{gathered}[/tex]We can check for the first condition, as we already know the value:
[tex]\begin{gathered} P(A|B)=0.4 \\ P(A)=0.6 \\ =>P(A|B)P(A) \end{gathered}[/tex]Then, the events are not independent.
Answer:
i) P(A∩B) = 0.2
ii) P(A) = 0.6
iii) P(A∪B) = 0.8
iv) P(A|B') = 0.2
b) The events are not independent.
Suppose that the velocity v (t) (in meters per second) of a sky diver falling near the Earth’s surface is given by the following exponential function, where time t is the time after diving measured in seconds.
The equation of the velocity is given by the exponential:
[tex]v(t)=53-53e^{-0.24t}[/tex]Let us say that the sky driver's velocity will be 47 m/s at t₁. Then, using the expression above:
[tex]\begin{gathered} v(t_1)=47 \\ 53-53e^{-0.24t_1}=47 \end{gathered}[/tex]Solving for t₁:
[tex]\begin{gathered} \frac{53-47}{53}=e^{-0.24t_1} \\ \ln (\frac{6}{53})=-0.24t_1 \\ t_1=9.1s \end{gathered}[/tex]WHAT IS THE CHEAPEST UNIT RATE??? 10 donuts for 13.00 or 1 dozen donuts for 12.00
Step 1: Let's review the information provided to us to answer the question correctly:
• Option 1: 10 donuts for 13.00
,• Option 2: 1 dozen donuts for 12.00
Step 2: Let's calculate the price of a donut in each option, as follows:
• One donut Option 1 = 13/10 = 1.30, this means the price of an individual donut is $ 1.30
,• One donut Option 2 = 12/12 = 1, this means the price of an individual donut is $ 1
Step 3: Twitch Beast 8 will decide what is the cheapest unit rate based on the calculations we did on Step 2
Find the point slope Slope= 7Passing through (6,1)
The point-slope form of a line always has the form:
[tex]y-y_0=m\cdot(x-x_0)[/tex]"m" represents the slope of the line; in our case, the statement of the problem says that
[tex]m=7[/tex]Besides, (x_0, y_0) is a point of the line. By the statement of the problem (again), we can choose:
[tex]x_0=6,y_0=1[/tex]Then, the point-slope form becomes:
[tex]y-1=7\cdot(x-6)[/tex]if a driver drive at aconstant rate of 38 miles per hour how long would it take the driver to drive 209 mile
In order to calculate how long would it take to drive 209 miles, we just need to divide this total amount of miles by the speed of the driver.
So we have:
[tex]\text{time}=\frac{209}{38}=5.5[/tex]So it would take 5.5 hours (5 hours and 30 minutes).
Rabbit's run: distance (meters) time (minutes) way 800 1 900 5 1107.5 20 1524 32.5
Answer:
Notice that:
[tex]\begin{gathered} \frac{800}{1}=800, \\ \frac{900}{5}=180, \\ \frac{1107.5}{20}=\frac{443}{8}, \\ \frac{1524}{32.5}=\frac{3048}{65}. \end{gathered}[/tex]Since all reduced fractions are different, the distance traveled by the rabbit and the time are not proportional.
On the planet Alaber, there are 15 dubbles to every 13 rews. If farmer Mimstoon has 100 rews on his frent farm, how many dubbles are on the farm?
You have that on planet Alaber, there are 15 dubbles to every 13 rews. This proportion can be wrtten as 15:13, or 15/13.
In order to calculate how many dubbles are on the farm, while there are 100 rews. You use the previous ratio and proceed as follow:
15/13 = x/100 where x is the unknown number of dubbles
This is because the ratio between dubbles and rews must be the same.
You solve the previous equation as follow:
15/13=x/100 multiply both sides by 100 to cancel the denomitaro 100 right side
15/13(100) = x/100(100)
1500/13 = x
In order to write the previous result as a mixed number you divide numerator and denominator:
1500 | 13
143 115
70
65
5
Then, x = 1500/13 is also equal to:
x = 115 13/5
This means there are approximately 115 dubbles for 100 rews
