I need help with question 4, I've included the prior answers from questions 1, 2 and 3 to help you. I've also included what the previous questions were so you have some context of the situation. Although, I think you only need the answers from part C ( which is the graph I've including) to answer question 4
Answers
We are asked to determine the equation of the midline for the periodic function. This can be seen below.
Explanation
Using the parameters from the graph, the function can be expressed as;
[tex]y=(100sinx)+150[/tex]The graph that contains the equation of the midline can be seen below.
Therefore, the equation of the midline is
Answer:
[tex]y=150[/tex]
Related Questions
The prices of cell phone cases in a store are normally distributed.The mean of the prices is $22.90,and the standard deviation is $4.90.If you want to look at the bottom 45% of cases in terms of price,what is the cutoff price so that 45% of all cases are priced below that amount?
Answers
Given:
Mean = 22.90
Standard Deviation = 4.90
Find the cutoff price so that 45% of all cases are priced below that amount.
To solve this problem, the first thing we need to do is to find the z-score for 45% or 0.45.
The z-score for 0.45 is -0.126.
Now, to find the cutoff price or the "score", we will use the following equation
[tex]z=\frac{x-\mu}{\sigma}[/tex]Where:
z = z-score
x = score
μ = mean
σ = standard deviation
We are looking for the "x"
Derive the formula and substitute the given data.
[tex]z=\frac{x-\mu}{\sigma}[/tex][tex]\sigma z=x-\mu[/tex][tex]x=z\sigma+\mu[/tex][tex]x=(-0.126)(4.90)+22.90[/tex][tex]x=22.28[/tex]We got a value of 22.28 for our score, therefore, the cutoff price must be $22.28.
True or false: if the determinant is 0, then the system has no solution?
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If the determinat of a matrix is 0, then the linear system of equations it represents has no solution.
Then, the statement is true.
Four gallons of gasoline cost $17.56. What is the price per gallon?
Answers
write a relationship between the cost and the amount of gasoline
[tex]\begin{gathered} 4gal\Rightarrow17.56 \\ 1gal\Rightarrow x \end{gathered}[/tex]solve for the x
[tex]\begin{gathered} x=\frac{1gal\cdot17.56}{4gal} \\ x=4.39 \end{gathered}[/tex]the price per gallon is $4.39
Fiona is playing Fetch with her dog she is standing at the coordinate points (7, -5) when she throws the stick, it lands at the coordinate point (-1, 10). How far did Fiona throw the stick
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Answer:
Fiona threw the stick 17 units far
Explanation:
To know how far Fiona threw the stick, we find the distance between the given coordinate points, (7, -5) and (-1, 10)
The formula for the distance between two coordinate points is:
[tex]D=\sqrt[\square]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Here,
[tex]\begin{gathered} x_1=7 \\ y_1=-5 \\ x_2=-1 \\ y_2=10 \end{gathered}[/tex]Now,
[tex]\begin{gathered} D=\sqrt[]{(-1-7)^2+(10-(-5))^2} \\ =\sqrt[\square]{(-8)^2+(15)^2} \\ =\sqrt[\square]{64+225} \\ =\sqrt[\square]{289} \\ =17 \end{gathered}[/tex]Therefore, Fiona threw the stick 17 units far
Write a formula for the function obtained when the graph is shifted as described. When typing exponents use the carrot key ^ by pressing SHIFT and 6. For example x squared can be typed as x^2. Do not put spaces between your characters and remember to use parentheses in the appropriate places!f(x)=x^3 is shifted up 3 unit and to the left 7 units.The new equations f(x)=Answer
Answers
Given the function
[tex]f(x)=x^3[/tex]We are asked to shift the function up 3 units and to the left 7 units.
Explanation
1) To shift upwards, we will add outside of the argument
2) To shift to the left, we will add inside of the argument
Therefore;
[tex]x^3\rightarrow(x+7)^3+3[/tex]Answer:
[tex]f(x)=(x+7)^3+3[/tex]Is position on an x or y axis
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Usually, time is the independent variable, so it goes in the x-axis.
Position is similar to distance, and spedd is the rate of variation of position or distance. All of these three are usually graphed in the y-axis, as they depend on time.
Anjali's Bikes rents bikes for $15 plus $7per hour. Aliyah paid $57 to rent a bike.For how many hours did she rent the bike?
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From the question;
Anjali's Bikes rents bikes for $15 plus $7 per hour.
Let h represent the number of hours she rent the bike;
the total amount she will pay for h hours is;
[tex]T=15+7h[/tex]Given that; Aliyah paid $57 to rent a bike.
T = $57
The equation becomes;
[tex]T=15+7h[/tex]Write a equation of a line in slope intercept form that is perpendicular to the line y= [tex] \frac{1}{4} x[/tex]and crosses through the point (-3, -2)
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Here, we want to write the equation of a line that passes through the given point and is perpendicular to the given line
When two lines are perpendicular to each other, what this mean is that the product of their slopes are equal to -1
Generally, the equation of a straight line can be written in the form;
[tex]y\text{ = mx + b}[/tex]where m is the slope of the line and b is the y-intercept of the given line
Now from the given equation, we can see that the coefficient of x is 1/4. What this mean is that the slope of the line is 1/4 (the line's y-intercept is zero)
We can then proceed from here to get the slope of the second line
Mathematically, since the two lines are perpendicular;
[tex]m_{1\text{ }\times\text{ }}m_2\text{ = -1}[/tex]Thus;
[tex]\begin{gathered} \frac{1}{4}\text{ }\times m_2\text{ = -1 } \\ \\ m_2\text{ = -1 }\times\text{ 4 = -4} \end{gathered}[/tex]This shows that the slope of the second line is -4
We can write the equation of the second line as;
[tex]y\text{ = -4x + c}[/tex]To completely write the equation of the second line, we need to get the value of c
To do this, we substitute the coordinates of the point that lies on the line
The point we are given is (-3,-2)
So in this case, we substitute the value x = -3 and y = -2
Thus, we have;
-2 = -4(-3) + c
-2 = 12 + c
c = -2 -12
c = -14
About 1% of the population has a particular genetic mutation. 100 people are randomly selected.Find the standard deviation for the number of people with the genetic mutation in such groups of 100. (Remeber that standard deviation should be rounded to one more decimal place than the raw data, in this case 1 decimal place is necessary.)
Answers
ANSWER:
1.0
STEP-BY-STEP EXPLANATION:
Given:
p = 1% = 0.01
q = 1 - p = 1 - 0.01 = 0.99
n = 100
The standard deviation is calculated using the following formula:
[tex]\begin{gathered} \sigma=\sqrt{n\cdot p\cdot q} \\ \\ \text{ We replace each value and obtain the standard deviation:} \\ \\ \sigma=\sqrt{100\cdot0.01\cdot0.99} \\ \\ \sigma=\sqrt{0.99} \\ \\ \sigma=0.99498 \\ \\ \sigma=0.995\rightarrow1\text{ decimal place}\rightarrow1.0 \end{gathered}[/tex]Therefore, the standard deviation is equal to 1.0
The ratio of the quantities of sugar and flour needed to bake a cake is 2:5. What is the quantity of sugar needed for a cake, if 750 grams of flour are used to bake it?
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The quantity of sugar needed for a cake, if 750 grams of flour are used to bake it is 300 grams.
What is ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them.
In this case, the ratio of the quantities of sugar and flour needed to bake a cake is 2:5.
The quantity of sugar needed is illustrated by x.
This will be:
2/5 = x/750
Cross multiply
5x = 2 × 750
5x = 1500
Divide
x = 1500/5
x = 300
The sugar needed is 300 grams.
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Perform the operations and simplify the final answer if possible
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Answer:
-23
Explanation:
To perform the operations, we first need to solve the operations in parenthesis, then the power, and finally, the sum.
So, the expression is equal to:
2 - (4 - 9)²
2 - (-5)²
2 - (25)
2 - 25
-23
Therefore, the answer is -23
108A) 54B) 60C) 68D) 72BCNote: Figure not drawn to scale.In the figure above, lines and m are paralleland BD bisects ZABC. What is the value of x?
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Given the shown figure:
lines l and m are parallel
So, m∠A = m∠ABC
Because the alternative angles are congruent
So, m∠ABC = 108°
And BD bisects the m∠ABC
So, m∠CBD = 1/2 * m∠ABC = 1/2 * 108 = 54°
As the lines l and m are parallel
So, m∠CBD = m∠D = x
So, the answer will be x = 54
The answer will be A) 54
aSuppose you want to buy a new car that costs $32,600. You have no cash-only your old car, which is worth $5000 as a trade-in. The dealer says theinterest rate is 5% add-on for 4 years. Find the monthly paymentThe monthly payment is $(Type an integer or decimal rounded to the nearest cent as needed.)
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Given:
Cost of a new car = $32,600
Trade-in old car cost = $5,000
Rate, r = 5% or 0.05
Time, t = 4 years
Asked: Find the monthly payment.
Solution:
[tex]PMT=\frac{P_O(\frac{r}{n})}{(1-(1+\frac{r}{n})^{-nt})}[/tex]where:
PMT = Loan Payment
Po = Loan Amount
r = Annual Interest Rate
n = Number of Compounds per year
t = Length of the Loan in years
Now that we have the formula, we will substitute the values.
Po = $32,600 - $5,000 = $27,600
r = 5% or 0.05
n = 12 (There are 12 months in 1 year)
t = 4 years
[tex]\begin{gathered} PMT=\frac{P_O(\frac{r}{n})}{(1-(1+\frac{r}{n})^{-nt})} \\ PMT=\frac{27600(\frac{0.05}{12})}{(1-(1+\frac{0.05}{12})^{-12\cdot4})} \\ PMT=\frac{115}{(1-0.8190710169^{})} \\ PMT=\frac{115}{0.1809289831} \\ PMT=635.6085026 \end{gathered}[/tex]ANSWER:
The monthly payment is $636. (Rounded to the nearest cent.)
an unusually shaped section of a park is to be paved. this section is drawn to scale below. the length of a single grid segment is 1 m.
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Since the length of a single grid square is 1m, then its area is:
[tex]A=1m\times1m=1m^2\text{.}[/tex]Now, to compute the area of the given section we will use the following diagram.
To compute the area of each triangle we will use the following formula for the area of a triangle:
[tex]\begin{gathered} A=\frac{bh}{2}, \\ \text{where b is the base of the triangle and h is its height.} \end{gathered}[/tex]And to compute the area of the rectangle we will use the following formula:
[tex]\begin{gathered} A=bh, \\ \text{where b is the base of the rectangle and h is its height.} \end{gathered}[/tex]Therefore the area of triangle A is:
[tex]A_A=\frac{6m\cdot2m}{2}=6m^2\text{.}[/tex]The area of triangle B is:
[tex]A_B=\frac{4m\cdot2m}{2}=4m^2\text{.}[/tex]The area of triangle C is:
[tex]A_C=\frac{3m\cdot1m}{2}=1.5m^2\text{.}[/tex]The area of triangle D is:
[tex]A_D=\frac{5m\cdot1m}{2}=2.5m^2\text{.}[/tex]The area of rectangle E is:
[tex]A_E=12m^2\text{.}[/tex]Finally, the area of the given section is:
[tex]\begin{gathered} A=A_A+A_B+A_C+A_D+A_E \\ =6m^2+4m^2+1.5m^2+2.5m^2+12m^2=26m^2\text{.} \end{gathered}[/tex]Answer:
The area of a single grid square is:
[tex]1m^2\text{.}[/tex]The approximate area of the section that will be paved is:
[tex]26m^2\text{.}[/tex]
In ABC, AB = 10 and BC = 5. Which expression is always true?
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Using the Triangle inequality:
In every triangle the sum of the lengths of any two sides is always greater than the length of the remaining side, so:
[tex]\begin{gathered} AB+BC>AC \\ so\colon \\ 5Find the mode of each set of data.21, 12, 12, 30, 36, 34, 40, 22
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The mode of a set of data is the value that appears the most number of times in the set.
So, checking this set, we have:
21: one time
12: two times
30: one time
36: one time
34: one time
40: one time
22: one time
So the mode of this set is 12.
Use the standard deviation values of the two samples to find the standard deviation of the sample mean differences.Sample Standard Deviationred box 3.868blue box 2.933
Answers
Given:
The standard deviation are given as,
[tex]\begin{gathered} \sigma_{m_1}=\text{ 3.868} \\ \sigma_{m_2}\text{ = 2.933} \\ \end{gathered}[/tex]Required:
The standard deviation of the sample mean differences.
Explanation:
The formula for the deviation of the sample mean difference is given as,
[tex]\begin{gathered} \sigma_{m_1}-\text{ }\sigma_{m_2}\text{ = }\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}} \\ \end{gathered}[/tex]Substituting the values in the above formula,
[tex]\begin{gathered} \sigma_{m_1}-\text{ }\sigma_{m_2}\text{ = }\sqrt{\frac{3.868^2}{n_1}+\frac{2.933^2}{n_2}} \\ \sigma_{m_1}-\text{ }\sigma_{m_2}\text{ = }\sqrt{\frac{14.9614}{n_1}+\frac{8.6025}{n_2}} \end{gathered}[/tex]Answer:
Thus the required answer is,
[tex]\sigma_{m_1}-\text{\sigma}_{m_2}=\sqrt{\frac{\text{14.9614}}{n_1}+\frac{\text{8.6025}}{n_2}}[/tex]
use the given actual and magnified lengths to determine which of the following insects were looked at using the same magnifying glass (with the same scale factor)
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Grasshoper
Actual: 2 in
Magnified: 15 in
The scale factor is given by:
[tex]k=\frac{15}{2}=7.5[/tex]Black beetle
Actual: 0.6 in
Magnified: 4.2 in
The scale factor is:
[tex]k=\frac{4.2}{0.6}=7[/tex]Honybee
Actual: 5/8 in
Magnified: 75/16 in
The scale factor is:
[tex]k=\frac{\frac{75}{16}}{\frac{5}{8}}=\frac{75\cdot8}{16\cdot5}=\frac{600}{80}=\frac{15}{2}=7.5[/tex]Monarch butterfly
Actual: 3.9 in
Magnified: 29.25 in
The scale factor is:
[tex]k=\frac{29.25}{3.9}=\frac{15}{2}=7.5[/tex]Answer:
Grasshoper, Honybee and Monarch butterfly have the same factor scale = 7.5
Black beetle has a factor scale = 7
The count in a bacteria culture was 800 after 15 minutes and 1000 after 30 minutes. Assuming the count grows exponentiallyA)What was the initial size of the culture? B)Find the doubling period. C)Find the population after 60 minutes. D)When will the population reach 13000.
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Answer:
A) The initial size o the culture is 640
B) The doubling period is 47 minutes
C) The population after 60 minutes is 1563
D) The population will reach 13000 after 3 hours 22 minutes
Explanation:
The form of an exponential grow model is:
[tex]S=Pb^t[/tex]Where:
S is the population after t hours
P is the initial population
b is the base of the exponent
t is the time, in hours
We know that after 15 minutes, the population was 800. 15 minutes is a quarter of an hour. Thus, t = 1/4, S = 800:
[tex]800=Pb^{\frac{1}{4}}[/tex]Also, we know that after 30 minutes, the population was 1000. Thus, t = 1/2, S = 1000
[tex]1000=Pb^{\frac{1}{2}}[/tex]Then, we have a system of equations:
[tex]\begin{cases}800=Pb^{\frac{1}{4}}{} \\ 1000=Pb^{\frac{1}{2}}{}\end{cases}[/tex]We can solve the first equation for P:
[tex]\begin{gathered} 800=Pb^{\frac{1}{4}} \\ P=\frac{800}{b^{\frac{1}{4}}} \end{gathered}[/tex]And substitute in the other equation:
[tex]1000=\frac{800}{b^{\frac{1}{4}}}b^{\frac{1}{2}}[/tex]And solve:
[tex]\frac{1000}{800}=\frac{b^{\frac{1}{2}}}{b^{\frac{1}{4}}}[/tex][tex]\begin{gathered} \frac{5}{4}=b^{\frac{1}{2}-\frac{1}{4}} \\ . \\ \frac{5}{4}=b^{\frac{1}{4}} \end{gathered}[/tex][tex]\begin{gathered} b=(\frac{5}{4})^4 \\ . \\ b=\frac{625}{256} \end{gathered}[/tex]Now, we can find the initial population P:
[tex]P=\frac{800}{(\frac{625}{256})^4}=\frac{800}{\frac{5}{4}}=\frac{800\cdot4}{5}=640[/tex]The initial population is 640
To find the doubling period, we want that the population equal to twice the initial population:
[tex]S=2P[/tex]Then, since we know the equation, we can write:
[tex]2P=P(\frac{625}{256})^t[/tex]Then:
[tex]\begin{gathered} \frac{2P}{P}=(\frac{625}{256})^t \\ . \\ 2=(\frac{625}{256})^t \\ \ln(2)=t\ln(\frac{625}{256}) \\ . \\ \frac{\ln(2)}{\ln(\frac{625}{256})}=t \\ . \\ t\approx0.7765 \end{gathered}[/tex]If an hour is 60 minutes:
[tex]60\cdot0.7765=46.59\approx47\text{ }minutes[/tex]To find the population after 60 minutes, we use t = 1 hour and we want to find S:
[tex]\begin{gathered} S=640(\frac{625}{256})^1 \\ . \\ S=640\cdot\frac{625}{256}=1562.5 \end{gathered}[/tex]To find when the population is 13000, then we use S = 13000 and solve for t:
[tex]\begin{gathered} 13000=640(\frac{625}{256})^t \\ . \\ \frac{13000}{640}=(\frac{625}{256})^t \\ . \\ \frac{325}{16}=(\frac{625}{256})^t \\ . \\ \ln(\frac{325}{16})=t\ln(\frac{625}{256})^ \\ . \\ t=\frac{\ln(\frac{325}{16})}{\ln(\frac{625}{256})}\approx3.373 \\ \\ \end{gathered}[/tex]We have 3 full hours and 0.373. Since one hour is 60 minutes:
[tex]60\cdot0.373\approx22[/tex]The population reach 13000 after 3 hours 22 minutes
I need help with this question please (just question 10, not the one below)
Answers
Let the cost of each packet of cheese is $x
Let the cost of each burger $y
Calvin bought 5 packets of cheese and 3 burgers for $29.99
Mathematically we can write
[tex]5x+3y=29.99\text{ ..(1)}[/tex]Alex bought 3 packets of cheese and 7 burgers for $32.71
Mathematically we can write
[tex]3x+7y=32.71\text{ ..(2)}[/tex]Now we have to solve equations (1) and (2) for x and y
Now 7*(1)-3*(2) implies
[tex]7\times(1)-3\times(2)\Rightarrow35x+21y-9x-21x=209.93-98.13\Rightarrow26x=111.8\Rightarrow x=\frac{111.8}{26}\Rightarrow x=4.30[/tex]Hence the price of each packets of cheese is $4.30
The distance from Becca’s house to Liz’s house is 13 kilometers. Approximately how many miles does Becca live from Liz? Use the conversion factor shown below.
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Data:
13 km
Convert to miles
(1 km is equal to 0.6214 miles)
[tex]13\operatorname{km}\cdot\frac{0.6214mi}{1\operatorname{km}}=8.078mi[/tex](1 mile is equal to 1.6093km)
[tex]13\operatorname{km}\cdot\frac{1mi}{1.6093\operatorname{km}}=8.078mi[/tex]Then, Becca lives 8.078 miles (aprroximately 8.1 miles) from LizExpress the following ratio in simplest form 39:10
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ok
If we have
[tex]\text{ }\frac{39}{10}[/tex]It was not possible to simplify it anymore so the answer will be the same.
It is not possible to implify it because the are no common fators between 39 and |0.
what is the value of f(0)=
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SOLUTION:
Case:
Given:
Required:
Method:
Step 1:
Step 2:
Step 3:
Final answer:
a landscaper is hired to take care of the lawn and shrubs around the house. the landscaper claims that the relationship between the number of hours worked and the total work fee is proportional. the fee for 4 hours of work is $140.
which of the following combinations of values for the landscapers work hours and total work fee support the claim that the relationship between the two values is proportional?
A. 3 hours for $105 B. 3.5 hours for $120 C. 4.75 hours for $166.25 D. 5.5 hours for $190 E. 6.25 hours for $210.25 F. 7.5 hours for $262.50
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The two combinations that shows that the landscapers work hours and total work fee are proportional are: 3 hours for $105 and 7.5 hours for $262.50(option A and F)
What is direct proportion?Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value. It is represented by the proportional symbol.
Direct proportion is given by y= kx, where k is the constant and y and x are the variables.
If x represents the landscapers work hours and y represents the total work fee.
y= kx
when y = $140 and x= 4hours
k= 140/4= 35
therefore when x= 3 then y= 3×35=105
similarly when x= 7.5, y= 35×7.5=262.50
Only option A and F obeys the proportional relationship.
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In the diagram of ABCD shown below, 'BA is drawn from vertex B to point A on DC, such that BC & BA.Аa.b.What kind of triangle is AABD? Explain.hat kind of triangle is ADBC? Explain.
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We have the following information from the picture:
mmWe have that:
m m m
m m
Therefore, the angles in triangle ABD are m < D = 30, m< DAB = 120, and m < B = 30.
We need now to find the angles of the triangle ABC to find the rest of the angles.
In triangle ABC, we need to find the
Then, we can draw this as follows:
According to the angles, the triangle ABC is an Obtuse Triangle because it has an obtuse angle (
The triangle DBC is a right triangle because it has a right angle (
Part 2 out of 2If you plan to cancel your internet service after 11 months, which is the cheaper option
Answers
m = number of months
Option 1 cost = 35 + 20m
Option 2 cost = 25m
Part 1: If the cost is equal for both otpions, then we can write: 35 + 20m = 25m, solving for m:
5m = 35 ==> m = 35/5 = 7
m = 7
In month 7, the cost is 35 + 20(7) = 35 + 140 = 175
Part 2:
Option1 cost when m = 11: 35 + 20(11) = 35 + 220 = 255
Option2 cost when m = 11: 25(11) = 275
Option 2 costs more than option 1, so Option 1 is cheaper
You poured 1/4 of the juice from a 2-liter bottle while serving guests at a party. How much juice, in liters, is still left in the bottle?
How much juice was used?
How much is left?
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Answer:
1.5 litters is left and 0.5 litters was used
Step-by-step explanation:
2 litters divided by 4 = 0.5 litters and you can do the rest of the math if needed
A. Substitute the x-values shown to the right into y = xand y = |x| to find several points on their graphs. Usethe probe to check your work.
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For the function y=x we just have to replace the values in the table for the x so:
[tex]\begin{gathered} -3\to x=-3 \\ -2\to x=-2 \\ -1\to x=-1 \\ 0\to x=0 \\ 1\to x=1 \\ 2\to x=2 \\ 3\to x=3 \end{gathered}[/tex]and for y = |x| we have to change all the negative values for positive:
[tex]\begin{gathered} -3\to\mleft|x\mright|=3 \\ -2\to|x|=2 \\ -1\to|x|=1 \\ 0\to|x|=0 \\ 1\to|x|=1 \\ 2\to|x|=2 \\ 3\to|x|=3 \end{gathered}[/tex]I have a triangle and diamond on an equation which is =1.05so I am asking am I suppose to divide by 2 to get the answer?
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Let,
T = Triangle
S = Semi Circle
R = Star
D = Diamond
Given:
a.) 4 Triangles = 2 Semi Circle + 2 Star → 4T = 2S + 2R
b.) 1 Triangle + 1 Diamond = 1.05 → 1T + 1D = 1.05
c.) 1 Star + 1 Semi Circle = 0.525 → 1R + 1S = 0.525
d.) Diamond = ?
For us to be able to determine the value of the diamond, we must be able to determine the value of the Triangle.
For us to get it, we will be using first the equation at a and c.
4T = 2S + 2R
1R + 1S = 0.525
We get,
2S + 2R = 2(1S + 1R)
2S + 2R = 2(0.525)
2S + 2R = 1.05
Let's now get the value of the triangle,
4T = 2S + 2R
4T = 1.05
T = 1.05/4
T = 0.2625 (Value per triangle)
Let's now determine the value of the DIAMOND.
1 Triangle + 1 Diamond = 1.05 → 1T + 1D = 1.05
1T + 1D = 1.05
1(0.2625) + 1D = 1.05
0.2625 + 1D = 1.05
1D = 1.05 - 0.2625
1D = D = 0.7875
ANSWER: The value of the diamond is 0.7875
Which expression is equivalent to75a7b"40213,9 ? Assume a=1 and C=0.
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we have the expression
[tex]\sqrt[3]{\frac{75a^7b^4}{40a^{(13)}c^9}}[/tex]Remember that
[tex]\frac{75}{40}=\frac{15}{8}=\frac{15}{2^3}[/tex][tex]\frac{a^7}{a^{(13)}}=\frac{1}{a^6}[/tex]substitute
[tex]\sqrt[3]{\frac{75a^7b^4}{40a^{(13)}c^9}}=\sqrt[3]{\frac{15b^4}{2^3a^6c^9}}[/tex]we have that
[tex]2^3a^6c^9=(2a^2c^3)^3[/tex]substitute
[tex]\sqrt[3]{\frac{15b^4}{2^3a^6c^9}}=\frac{\sqrt[3]{15b^4}}{(2a^2c^3)}=b\frac{\sqrt[3]{15b^{}}}{(2a^2c^3)}[/tex]answer is the second option