Answer:
Below in bold.
Step-by-step explanation:
Standard form is Ax + By = C
where A, B and C are integers and A must be positive.
So the first 2 are already in standard form but the last 2 can be converted to standard form by multiplying each term by -1:
-12x+3y=27
= -1*-12x + -1*3y = -1*27
12x - 3y = -27 is the answer.
The last one is:
24x + 12y = -60.
25. Jen ran x miles last week and 18 miles
this week. Write an expression to represent
the total number of miles Jen ran over the
last two weeks.
Solve: If she ran 34 miles over the last two
weeks, how many did she run last week?
Answer:
Step-by-step explanation:
If Jen ran 34 miles over the last 2 weeks and only 18 miles the second week, she would've had to have run 16 miles the first week.
34= 18+x
I hope this helps!
HELPPPPPPPPPPPPPPPPPPP!
Answer: Real, equal, rational.
Step-by-step explanation:
[tex]-x^2-8x-16=0\\-(x^2+8x+16)=0\\Multiply \ the\ left \ and\ right \ sides\ of\ the\ equation\ by \ -1:\\x^2+8x+16=0\\x^2+2*x*4+4^2=0\\(x+4)^2=0\\x+4=0\\x=-4.[/tex]
An airplane is heading due north at 700 kph, and a wind blows at 60 kph in the direction s 45° e. what is the plane’s ground speed?
We can infer and logically deduce that airplane’s ground speed is equal to 658.94 kph.
Given the following data:
Airplane speed = 700 kph.Wind speed = 60 kph.Angle = 45° due East.What is speed?Speed can be defined as the distance covered by an object per unit of time. Thus, speed can be measured in kilometer per hour (kph).
Mathematically, speed can be calculated by using this formula;
Speed = distance/time
How to calculate the plane’s ground speed?In order to calculate the airplane’s ground speed, we would apply the law of cosine:
C² = A² + D² - 2(A)(D)cosθ
Substituting the given parameters into the formula, we have;
C² = 700² + 60² - 2(700)(60)cos45
C² = 434,203.03
C = √434,203.03
C = 658.94 kph.
In conclusion, we can infer and logically deduce that airplane’s ground speed is equal to 658.94 kph.
Read more on cosine law here: brainly.com/question/11000638
#SPJ1
PLEASE HELP!!!!!! I CAN’T UNDERSTAND!!!! How to do this one
The coefficient of t²s⁵ in the expansion of (2t + s)⁷ is d. 84
What is binomial expansion?Binomial expansion is the expansion of two term expressions such as (a + b)ⁿ where n is a rational number.
What is Pascal's triangle?Pascal's triangle is atriangle used in determining the coefficients of a binomial expansion.
What is the coefficient of t²s⁵ in the expansion of (2t + s)⁷?
The general term for the expansion (a + b)ⁿ = ∑ⁿCₓaˣbⁿ⁻ˣ.
So, each term is ⁿCₓaˣbⁿ⁻ˣ.
Comparing (a + b)ⁿ with (2t + s)⁷,
a = 2t, b = s and n = 7.So, its general term is ⁿCₓ(2t)ˣsⁿ⁻ˣ = ⁷Cₓ(2t)ˣsⁿ⁻ˣ
= ⁷Cₓ(2)ˣtˣsⁿ⁻ˣ
So, the coefficient term is ⁷Cₓ(2)ˣ
Now for the term t²s⁵, x = 2.
So, the coeficient term is ⁷Cₓ(2)ˣ = ⁷C₂(2)²
= 7!/2!(7 - 2)! × 4
= 7!/2!5! × 4
= 7 × 6 × 5!/(2! × 5!) × 4
= 7 × 6/2 × 4
= 7 × 3 × 4
= 84
So, the coefficient of t²s⁵ in the expansion of (2t + s)⁷ is d. 84
Learn more about binomial expansion here:
https://brainly.com/question/25086608
#SPJ1
identify all values of that make the equation true.
Please explain them as step by step !!
Thank you!!
Part a
[tex]\frac{2x+1}{x}=\frac{1}{x-2}\\\\(2x+1)(x-2)=x\\\\2x^2 -3x-2=x\\\\2x^2 - 4x-2=0\\\\x^2 - 2x-1=0\\\\x=\frac{2 \pm \sqrt{8}}{2}\\\\x=1 \pm \sqrt{2}[/tex]
Part C
[tex]\frac{x+3}{1-x}=\frac{x+1}{x+2}\\\\(x+3)(x+2)=(1-x)(x+1)\\\\x^2 +5x+6=-x^2 +1\\\\2x^2 + 5x+5=0\\\\x=\frac{-5 \pm \sqrt{-15}}{4}\\\\x=\frac{-5 \pm i\sqrt{15}}{4}[/tex]
Match the graph of the function with the function rule.
y = 3 • 2x
y = 2 • 3x
y = 1 • 3x
y = 4 • 3x
By applying the definition of exponential function, we find that the function f(x) = 3 · 2ˣ match with the graph of the picture. (Correct choice: A)
What is the equation behind the exponential curve seen in the graph?In this question we have the graph of a exponential function, whose expression have to be found based on the definition of exponential function:
y = a · bˣ (1)
Where:
a - Initial value of the exponetial function.b - Base of the exponential function.x - Independent variabley - Dependent variableNow we find the values for a and b:
Initial value (x = 0, y = 3)
3 = a · b⁰
a = 3
Base of the exponential function (x = 1, a = 3, y = 6)
6 = 3 · a
a = 6 / 3
a = 2
By applying the definition of exponential function, we find that the function f(x) = 3 · 2ˣ match with the graph of the picture. (Correct choice: A)
To learn more on exponential functions: https://brainly.com/question/11487261
#SPJ1
I found this proof by induction that all people in canada are the same height, i was wondering what is the incorrect step?
Step 1: In any group that consists of just one person, everybody in the group has the same age, because after all there is only one person!
Step 2: Therefore, statement S(1) is true.
Step 3: The next stage in the induction argument is to prove that, whenever S(n) is true for one number (say n=k), it is also true for the next number (that is, n = k+1).
Step 4: We can do this by (1) assuming that, in every group of k people, everyone has the same age; then (2) deducing from it that, in every group of k+1 people, everyone has the same age.
Step 5: Let G be an arbitrary group of k+1 people; we just need to show that every member of G has the same age.
Step 6: To do this, we just need to show that, if P and Q are any members of G, then they have the same age.
Step 7: Consider everybody in G except P. These people form a group of k people, so they must all have the same age (since we are assuming that, in any group of k people, everyone has the same age).
Step 8: Consider everybody in G except Q. Again, they form a group of k people, so they must all have the same age.
Step 9: Let R be someone else in G other than P or Q.
Step 10: Since Q and R each belong to the group considered in step 7, they are the same age.
Step 11: Since P and R each belong to the group considered in step 8, they are the same age.
Step 12: Since Q and R are the same age, and P and R are the same age, it follows that P and Q are the same age.
Step 13: We have now seen that, if we consider any two people P and Q in G, they have the same age. It follows that everyone in G has the same age.
Step 14: The proof is now complete: we have shown that the statement is true for n=1, and we have shown that whenever it is true for n=k it is also true for n=k+1, so by induction it is true for all n.
The incorrect step in the induction that all people in Canada are the same height is; Step 9
How to prove Mathematical Induction?The principle of mathematical induction as follows:
For example, we have a set of natural numbers. Now, suppose that 1 is in the set. Now, we assume that anytime n is in the set, n + 1 is also in the set. Therefore we can say that every natural number is in the set.
The wrong step in the given mathematical Induction is Step 9. This is because;
We might not be to see anyone else in the arbitrary group G other than groups P or Q!
Recall that G is a group of k + 1 people. Thus, provided that k > 1, k + 1 > 2 and that a third person R in G does not exist, then the rest of the proof will work.
The steps above proves that;
S(k) = S(k + 1), for every k > 1.
Thus, we can also say that if S(2) is true, then it equally means S(3) is true and so on till infinity.
From our induction process written so far, we have see that S(1) was true. However, our induction step in the question does not show us that that S(1) = S(2) = true.
So: Thus, from the induction I have done It shows that S(1) not imply S(2) and as a result the proof is fallacious.
Read more about Mathematical Induction at; https://brainly.com/question/24672369
#SPJ1
Now say you invest the $7,500 and the highest interest rate you can find is 4.5% compounded annually, but you would have to leave the investment in the account for a minimum of 4 years. If you decide to wait 4 years to buy the car, how much more money will you have to save to buy a car at the $9,500 price? Use the compound interest formula A = P (1 + i)n. (Round final answer to the nearest cent, but otherwise don’t round any intermediate values)
The amount of money that you will have to save to buy a car at the $9,500 price is $556.11 ($9,500 - $8,943.89).
How is the amount of money needed determined?The amount of money needed can be determined by calculating the future value of $7,500 invested at 4.5% for 4 years.
Then, the result, which is the future value, $8,943.89, is deducted from the $9,500 price, to determine the additional savings required.
The future value of an investment can be calculated using the future value formula, A = P (1 + i)^n.
Where:
A = future value
P = Present value of investment
i = interest rate
n = number of periods.
The future value can also be determined using an online finance calculator, as follows.
Data and Calculations:N (# of periods) = 4 years
I/Y (Interest per year) = 4.5%
PV (Present Value) = $7,500
PMT (Periodic Payment) = $0
Results:
FV = $8,943.89
Total Interest = $1,443.89
Thus, the amount of money that you will have to save to buy a car at the $9,500 price is $556.11.
Learn more about future value calculations at https://brainly.com/question/24703884
#SPJ1
Use the binomial series to find the maclaurin series for the function. f(x) = 4 1 x
Answer:
We note that,
x/³√(1+x²) dx = (3/4) d/dx (1+x²)²ᐟ³
now we can use binomial series on (1+x²)²ᐟ³
(1+x²)²ᐟ³ = ( 1+2x²/3+((2/3)*(2/3 -1)/2) x⁴ + ((2/3)*(2/3 -1)(2/3–2)/6) x⁶ +o(x⁶) =
= 1 + 2x²/3 - x⁴/9 +4x⁶/81 +o(x⁶)
The last step is to differentiate,
x/³√(1+x²) dx = (3/4) d/dx (1+x²)²ᐟ³
= (3/4) d/dx (1 + 2x²/3 - x⁴/9 +4x⁶/81 +o(x⁶) )
= (3/4) ( 0 + (4/3)x - 4/9 x³ + 24x⁵/81 + o(x⁵))
= x - x³/3 + 2x⁵/9 + o(x⁵)
The complete Question is- How do I find the Maclaurin series using binomial series in the function f(x) = x/³√1+x^2?
Learn more about binomial series here:
https://brainly.com/question/14004514
#SPJ4
pls help me with this
Answer:
Step-by-step explanation:
9. the set containing all objects or elements and of which all other sets are subsets.
10. complement --> the amount in only one of teh sets
intersection --> the amount in both sets
11. 14 or -14
13. 46 1/2
14. 2 31/120
15. 1100% profit
16. 1200 gm
17. cube root of 7?
18. 6000 per year
The height of a soccer ball that is kicked from the ground can
be approximated by the function: y = -16x² + 48x, where y is the height of
the soccer ball in feet x seconds after it is kicked.
Find the time, in seconds, it takes from the moment the soccer ball is kicked until it
returns to the ground.
The time, in seconds, it takes from the moment the soccer ball is kicked until it returns to the ground is 3 seconds
How to determine the time to hit the ground?The function is given as:
y = -16x^2 + 48x
When the ball hits the ground, we have
y = 0
Substitute the known values in the above equation
-16x^2 + 48x = 0
Factor out -16x
-16x(x - 3) = 0
Divide through by -16x
x - 3 = 0
Add 3 to both sides
x = 3
Hence, the time, in seconds, it takes from the moment the soccer ball is kicked until it returns to the ground is 3 seconds
Read more about quadratic functions at:
https://brainly.com/question/8992769
#SPJ1
Instructions: Find the surface area of each figure. Round your answers to the nearest tenth, if necessary.
The surface area of the given figure is 288 km²
Calculating surface areaFrom the question, we are to determine the surface area of the figure
The given figure is a square-base pyramid
Surface area of the pyramid = (10×10) + 4× 1/2(10×9.4)
Surface area of the pyramid = (100) + 2(94)
Surface area of the pyramid = 100 + 188
Surface area of the pyramid = 288 km²
Hence, the surface area of the given figure is 288 km²
Learn more on Calculating surface area here: https://brainly.com/question/22744289
#SPJ1
In the year 2018, it was estimated that approximately 28,000 Floridians were homeless. A social worker estimates that 78% of these people were age 18 and up. In the distribution of ages of homeless Floridians, an 18 year old would be considered what percentile
At 22nd percentile in the distribution of ages of homeless Floridians, an 18 year old would be considered.
Given that 78% of the ages are greater than or equal to 18 years. Hence.
18 years will be (100 - 78)th percentile
i.e. 22nd percentile.
Historically, policymakers and practitioners at every level of government have focused special attention on specific subpopulations.
Decision-makers are often concerned about children and young people due to their vulnerability. People in families with children make up 30 percent of the homeless population. Unaccompanied youth (under age 25) account for six percent of the larger group.
Finally, due to their service to our country, veterans are often analyzed separately from the larger group. They represent only six percent of people experiencing homelessness.
Learn more about homeless here
https://brainly.com/question/9784214
#SPJ4
11. Find the value of x. x=______
Answer: x = 3.5
Step-by-Step Solution:
Let us first label the figure.
Let the Triangle be ABC with a line DE || BC.
Now, in ∆ABC,
DE || BC (given)
=> AD/DB = AE/EC (by B.P.T)
Substituting the given values,
AD/DB = AE/EC
2/4 = x/7
1/2 = x/7
2x = 7
x = 7/2
=> x = 3.5
Therefore, x = 3.5
Use a right-hand sum with 4
intervals to approximate the area
under f(x) = 4 - x² between
x = 0 and x = 2.
Answer:
17 / 4
Step-by-step explanation:
To find the right sum, you need to....
Step #1: Find Δx
Step #2: Find [tex]x_k[/tex]
Step #3 Make the right-hand sum equation: ∑[tex]^n_{k=1}f(x_k)[/tex]Δx
Step #4: Solve the right-hand sum equation
If Hiawatha held his bow 1.5 m off the ground and shot the arrow at a 45° angle with an initial velocity of 40 m/s, then the arrow’s height (in meters) off the ground can be modeled by the equation h(t)=−9.8t2+28t+1.5.
The arrow hits the top of a 3 meters tall wigwam at 0.054 seconds
How to determine the time to reach 3 meters?The complete question is added as an attachment
The function is given as:
[tex]h(t) = -9.8t^2 + 28t + 1.5[/tex]
Set the height to 3
[tex]-9.8t^2 + 28t + 1.5 = 3[/tex]
Subtract 3 from both sides
[tex]-9.8t^2 + 28t - 1.5 = 0[/tex]
Apply the following quadratic formula
[tex]t = \frac{-b \pm \sqrt{b^2- 4ac}}{2a}[/tex]
So, we have:
[tex]t = \frac{-28 \pm \sqrt{28^2- 4*-9.8*-1.5}}{2*-9.8}[/tex]
This gives
[tex]t = \frac{-28 \pm \sqrt{725.2}}{-19.6}[/tex]
This gives
[tex]t = \frac{-28 \pm 26.93}{-19.6}[/tex]
Expand
[tex]t = \frac{-28 + 26.93}{-19.6}[/tex] and [tex]t = \frac{-28 - 26.93}{-19.6}[/tex]
This gives
t = 0.054 and t = 2.80
0.054 is less than 2.80
This means that the arrow hits the top of a 3 meter tall wigwam at 0.054 seconds
Read more about quadratic functions at
https://brainly.com/question/27958964
#SPJ1
Which equation represents the function? f(x)=−1/2x+4 f begin argument x end argument equals negative fraction 1 over 2 end fraction x plus 4 f(x)=2x+12 f begin argument x end argument equals 2 x plus 1 half f(x)=4x−2 f begin argument x end argument equals 4 x minus 2 f(x)=−2x+4
The equation that represents the function is y = -x - 1
How to determine the equation of the function?The complete question is added as an attachment
From the table of values, we have the following points
(x, y) = (-1,0) and (0,-1)
Calculate the slope (m) using
m = (y2 - y1)/(x2 - x1)
Substitute the known values in the above equation
m = (-1 -0)/(0 + 1)
Evaluate the exponent
m = -1
The equation is then calculated as:
y = mx + c
This gives
y = -x + c
Using the point (0,-1), we have:
0 = 1 + c
Solve for c
c = -1
So, we have
y = -x - 1
Hence, the equation that represents the function is y = -x - 1
Read more about linear functions at:
https://brainly.com/question/1884491
#SPJ1
What is the volume of a square pyramid that is 8 feet tall with base edges of 3 feet?
8 ft
3 ft
3 ft
Prepare a grid with magic number 30. You can choose any set of numbers in sequence but the numbers should not be repeated.
The grid of numbers with a row and column sum of 30 is
3 15 12
17 11 2
10 4 16
How to prepare the grid?The grid in the question has a row sum and column sum of 15
The question implies that we create a similar grid with a row sum and column sum of 30
Represent the grid as follows:
a b c
d e f
g h j
So, we have the following sum of rows
a + b + c = 30
d + e + f = 30
g + h + j = 30
And, we have the following sum of rows
a + d + g = 30
b + e + h = 30
c + f + j = 30
Using trial by error, we have:
3 + 15+ 12 = 30
17 + 11 + 2 = 30
10 + 4 + 16 = 30
When the columns are added, we have
3 + 17 + 10 = 30
15 + 11 + 4 = 30
12 + 2 + 16 = 30
Hence, the grid of numbers is
3 15 12
17 11 2
10 4 16
Read more about number grid at:
https://brainly.com/question/4727909
#SPJ1
3 tons of sawdust cost $5,700.00. What is the price per pound?
$
Answer:
$0.95/lb
Step-by-step explanation:
1 ton = 2000 lb
3 tons = 3 × 1 ton = 3 × 2000 lb = 6000 lb
$5700/(6000 lb) = $0.95/lb
Answer: $0.95/lb
Step-by-step explanation:
3 tons = 6000 pounds
Therefore, using ratio and proportion rules,
6000/5,700 = 1/x
x = 5700/6000 = 0.95
The price is $0.95, or 95 cents per pound.
5. In a recent year, the population of Springfield, Illinois was one hundred
sixteen thousand, four hundred eighty-two. Write this number in standard
form. Show your work in the space below. Remember to check your solution
Answer: 16482
Step-by-step explanation:
Let's divide the number into three parts:
sixteen thousand | four hundred |eighty-two
A thousand is 1000, so sixteen thousand should be 16000.
A hundred is 100, so four hundred should be 400.
Eighty-two is just 82.
Let's add all of these:
[tex]16000+400+82=16482[/tex]
What type of number is -√/81?
Choose all answers that apply:
A. whole number
B. integer
C. rational
D. irrational
Answer:
Step-by-step explanation:
integer and rational
find the total surface area and volume, then multiply by 0.0004
The Total surface area of the rectangular prism = 168 in.²
The Volume of the rectangular prism = 108 in.³
What is the Total Surface Area of a Rectangular Prism?The total surface area of a rectangular prism is given as: SA = 2(wl + hl + hw), where:
w = width of the rectangular prism
h = height of the rectangular prism
l = length of the rectangular prism
What is the Volume of a Rectangular Prism?The volume of a rectangular prism = l × w × h
Find the Total surface area of the rectangular prism:
Length (l) = 9 in.
Width (w) = 2 in.
Height (h) = 6 in.
Total surface area of the rectangular prism = 2(wl+hl+hw) = 2·(2·9+6·9+6·2) = 168 in.²
Find the volume of the rectangular prism:
Length (l) = 9 in.
Width (w) = 2 in.
Height (h) = 6 in.
Volume of the rectangular prism = l × w × h = 9 × 2 × 6
Volume of the rectangular prism = 108 in.³
Learn more about the rectangular prism on:
https://brainly.com/question/1015291
#SPJ1
There is a balcony that forms part of a circle around a stage, and they need to put up a safety railing. How long of a railing do they need if the radius of the circle is 40 feet, and the arc takes up 45°? Use 3.14 for pi.
A sector is a part of a circle that is formed by two radii, and an arc. So that the length of the safety railing required is 31.4 feet.
A sector is a part of a circle that is formed by two radii, and an arc, thus forming a central angle.
Thus the required length of safety railing can be considered as the arc of the sector.
So that;
length of an arc = (θ / [tex]360^{o}[/tex]) * 2[tex]\pi[/tex]r
where θ is the measure of the central angle of the sector, and r is the radius of the sector.
From the given question, θ = 45°, and r = 40 feet.
So that,
length of the safety railing = (45° / [tex]360^{o}[/tex]) * 2 * 3.14 * 40
= 0.125 * 2* 3.14* 40
length of safety railing = 31.4
Therefore, the length of the safety railing required is 31.4 feet.
For more clarifications on the length of an arc, visit: https://brainly.com/question/2005046
#SPJ1
The marked price of a mobile set is Rs 9,600 and 40% discount is allowed to make 20% profit. By what percent is the discount to be reduced to increase the profit by 10%?
Answer:
5%
Step-by-step explanation:
price after discount :
9 600 - 9 600×40%
= 5760
Original price (price without profit) :
let x be the original price of the device.
x + x × 20% = 5760
Then
x = (5 760×100)÷120
= 4 800
Original price increased by 30% :
4 800 + 4 800×30%
= 6 240
the discount needed to increase the profit by 10% :
[(9 600-6 240)÷9 600]×100
= 35%
Then
to increase the profit by 10% ,we have to reduce
the percent of discount to :
40% - 35%
= 5%
Adam’s house is 2 centimeters from juan’s house on a map. if each centimeter on the map represents 6 kilometers, how far apart are the two houses? startfraction 1 over 12 endfraction kilometer one-third kilometer 3 kilometers 12 kilometers
Juan's home is about 12 kilometers from Adam's.
What are measurements in math's?In the study of mathematics and science, measurement is the fundamental idea. By quantifying an object's or event's qualities, we can compare them to those of other objects or occurrences. When discussing the division of a quantity, the phrase "measurement" is most frequently employed.
According to the given information:The distance between Adam's and Juan's residences on the map in centimeters is simply multiplied by the number of kilometers that each centimeter on the map represents, which in this case is 6, to determine how far Adam's house is from Juan's.
2 * 6 = 12
Which is our response.
Juan's home is about 12 kilometers from Adam's.
To know more about measurements visit:
https://brainly.com/question/1311417
#SPJ4
I will give you 10 pts if you teach me
Answer:
time required = 26 min
Step-by-step explanation:
To solve this, let's first list all the given information, and change the units to millimeters (mm) if required (because the discharge rate is given in mm/s):
○ diameter of pipe = 64 mm ⇒ radius = 32 mm
○ water discharge rate = 2.05 mm/s
○ diameter of tank = 7.6 cm = 76 mm ⇒ radius = 38 mm
○ height of tank = 2.3 m = 2300 mm.
Now, let's calculate the cross-sectional area of the pipe:
Area = πr²
⇒ π × (32 mm)²
⇒ 1024π mm²
Next, we have to calculate the volume of water transferred from the pipe to the tank per second. To do that, we have to multiply the pipe's cross-sectional area and the discharge rate of the water:
Volume transferred = 1024π mm² × 2.05 mm/s
⇒ 6594.83 mm³/s
Now. let's find the volume of the cylindrical tank using the formula:
Volume = π × r² × h
⇒ π × (38)² × 2300
⇒ 10433857 mm³
We know that 6594.83 mm³ of water is transferred to the tank every second, so to fill up 10433857 mm³ with water,
time required = [tex]\frac{10433857 \space\ mm^3}{6594.83\space\ mm^3/s}[/tex]
⇒ 1582.12 s
⇒ 1582.13 ÷ 60
≅ 26 min
Answer:
26 minutes
Step-by-step explanation:
The rate of filling the tank matches the rate of discharge from the pipe. Each rate is the ratio of volume to time. Volume is jointly proportional to the square of the diameter and the height.
VolumeFor some constant of proportionality k, the volume of discharge in 60 seconds from the pipe is ...
V = k·d²·h . . . . d = diameter; h = rate×time
V = k(0.64 dm)²(0.0205 dm/s × 60 s) = k·0.503808 dm³
For the tank, the height (h) is the actual height of the tank. The volume of the tank is ...
V = k(0.76 dm)²(23 dm) = k·13.2848 dm³
ProportionThen the proportion involving (inverse) rates is ...
time/volume = (fill time)/(k·13.2848 dm³) = (1 min)/(k·0.503808 dm³)
fill time = 13.2848/0.503808 min ≈ 26.369
__
Additional comments
1 dm = 100 mm = 10 cm = 0.1 m
1 dm³ = 1 liter, though we don't actually need to know that here.
We have used 1 decimeter (dm) as the length unit to keep the numbers in a reasonable range. We have worked out the rate numbers, but that isn't really necessary (see attached).
__
The value of k is π/4 ≈ 0.785398. We don't need to know that because the values of k cancel when we solve the proportion.
100 POINTS HELP EXPERTS PLEAASE!
The graph shows the functions f(x), p(x), and g(x):
Graph of function g of x is y is equal to 2 multiplied by 0.85 to the power of x. The straight line f of x joins ordered pairs minus 7, 3 and minus 3, minus 2 and is extended on both sides. The straight line p of x joins the ordered pairs 4, 1 and minus 3, minus 2 and is extended on both sides.
Part A: What is the solution to the pair of equations represented by p(x) and f(x)? (4 points)
Part B: Write any two solutions for f(x). (4 points)
Part C: What is the solution to the equation p(x) = g(x)? Justify your answer. (6 points)
Answer:
A) (-3, -2)
B) (-7, 3) and (-3, -2)
C) (4.074, 1.032)
Step-by-step explanation:
An ordered pair is a solution to an equation if it satisfies the equation — makes it true. The given points are solutions to the functions whose graphs pass through those points.
Part A.The function p(x) is defined to pass through points (4, 1) and (-3, -2).
The function f(x) is defined to pass through points (-7, 3) and (-3, -2).
These function definitions have point (-3, -2) in common.
(-3, -2) is the solution to the equation p(x) = f(x).
Part B.The function f(x) is defined to pass through points (-7, 3) and (-3, -2).
Two solutions to f(x) are (-7, 3) and (-3, -2).
We could identify other solutions, (1, -7) for example, but there is no need since the problem statement already gives us two solutions.
Part C.The solution to the equation p(x) = g(x) can be read from the graph as approximately (4.074, 1.032). This is close to the point (4, 1) that is used to define p(x). With some refinement (iteration), we can show the irrational solution is closer to ...
(4.07369423957, 1.03158324553)
Answer:
A) (-3, -2)
B) (1, -7) and (5, -12)
C) (4, 1) to the nearest whole number
Step-by-step explanation:
Function g(x):
[tex]g(x)=2(0.85)^x[/tex]
Function f(x) (straight line):
Given ordered pairs:
Let (x₁, y₁) = (-7, 3)Let (x₂, y₂) = (-3, -2)Calculate the slope of the straight line:
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-3}{-3-(-7)}=-\dfrac{5}{4}[/tex]
Using the Point-slope form of linear equation:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-3=-\dfrac{5}{4}(x-(-7))[/tex]
[tex]\implies y=-\dfrac{5}{4}x-\dfrac{23}{4}[/tex]
[tex]\implies f(x)=-\dfrac{5}{4}x-\dfrac{23}{4}[/tex]
Function p(x) (straight line):
Given ordered pairs:
Let (x₁, y₁) = (4, 1)Let (x₂, y₂) = (-3, -2)Calculate the slope of the straight line:
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-1}{-3-4}=\dfrac{3}{7}[/tex]
Using the Point-slope form of linear equation:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-1=\dfrac{3}{7}(x-4)[/tex]
[tex]\implies y=\dfrac{3}{7}x-\dfrac{5}{7}[/tex]
[tex]\implies p(x)=\dfrac{3}{7}x-\dfrac{5}{7}[/tex]
Part AWe have been given two ordered pairs for function f(x) and function p(x).
One of those ordered pairs is the same for both functions.
The solution to a pair of equations is their point(s) of intersection.
Therefore, as both functions pass through (-3, -2), this is their point of intersection and therefore the solution.
Part BThe solutions for f(x) are any points on the line of the function f(x).
To find any two points, substitute values of x into the found equation for f(x):
[tex]\implies f(1)=-\dfrac{5}{4}(1)-\dfrac{23}{4}=-7[/tex]
[tex]\implies f(5)=-\dfrac{5}{4}(5)-\dfrac{23}{4}=-12[/tex]
Therefore, two solutions are (1, -7) and (5, -12).
Part C
The solution to p(x) = g(x) is where the two graphs intersect. From inspection of the graphs, p(x) intersects g(x) at approximately (4, 1).
Therefore, the approximate solution to p(x) = g(x) is (4, 1).
To prove this, substitute x = 4 into the equations for p(x) and g(x):
[tex]\implies p(4)=\dfrac{3}{7}(4)-\dfrac{5}{7}=1[/tex]
[tex]\implies g(4)=2(0.85)^4=1.0440125=1.0\:(\sf nearest\:tenth)[/tex]
The actual solution to p(x) = g(x) is (4.074, 1.032) to three decimal places, which can be found by equating the functions and solving for x using a numerical method such as iteration.
View picture for question
By using properties of right triangles and trigonometric functions, we conclude that the length of the side BC is 19 units.
How to find the length of a side in a system of three triangles
In this problem we can use trigonometric functions to determine the length of the side BC in three steps:
Step 1
BE = AB/tan 60°
BE = 19√2 /4
Step 2
BD = BE/cos 45°
BD = 19/2
Step 3
BC = BD/sin 30°
BC = 19
To learn more on trigonometric functions: https://brainly.com/question/6904750
#SPJ1
Which of the following represents the series in summation notation?
−2 + 4 − 8 + 16 − 32 + 64 − 128.
Answer:
ummation of n=1 to n=7 (-2)^n
Step-by-step explanation:
summation of n=1 to n=7 (-2)^n
