Answer:
Non-Homogeneous Recurrence Relation and Particular Solutions
A recurrence relation is called non-homogeneous if it is in the form. Fn=AFn−1+BFn−2+f(n) where f(n)≠0.
In ABC, m<2=70 and m
The measure of the third angle in the ΔABC is 70 degrees
Complete questionIn ΔABC, m∠2 = 70 and m∠1 = 40, find the measure of all third angle of ΔABC.
How to determine the third angle?The given parameters are:
m∠2 = 70
m∠1 = 40
The sum of angles in a triangle is:
m∠1 + m∠2 + m∠3 = 180
So, we have:
70 + 40 + m∠3 = 180
Subtract 110 from both sides
m∠3 = 70
Hence, the measure of the third angle in the ΔABC is 70 degrees
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Rewrite, using the distributive
property (Algebra 1)
Answer:
[tex]24m + 32[/tex]
Step-by-step explanation:
[tex]8(3m + 4) = 24m + 32[/tex]
A candle burns down at the rate of 0.5 inches per hour. The original height of the candle was 8 inches.
Part A: Write a list of 6 ordered pairs to show the height of the candle in inches (y) as a function of time in hours (x) from the first hour after it started burning. For example, the point (0, 8) would represent a height of 8 inches after 0 hours. Explain how you obtained the ordered pairs. (5 points)
Part B: Is this relation a function? Justify your answer using the list of ordered pairs you created in Part A. (2 points)
Part C: If the rate at which the candle burned was 0.4 inches per hour instead of 0.5 inches per hour, would the relation be a function? Explain your answer using input and output values. (3 points)
The ordered pairs are (0,8), (1, 7.5), (2, 7), (3,6.5), (4, 6) and (5, 5.5)
How to determine the ordered pairs?The given parameters are:
Initial height, h = 8 inches
Rate = 0.5 inches per hour
The height of the candle at x hour is:
y = Initial - rate * x
This gives
y = 8 - 0.5x
Set x = 0 to 5
y = 8 - 0.5(0) = 8
y = 8 - 0.5(1) = 7.5
y = 8 - 0.5(2) = 7
y = 8 - 0.5(3) = 6.5
y = 8 - 0.5(4) = 6
y = 8 - 0.5(5) = 5.5
So, the ordered pairs are (0,8), (1, 7.5), (2, 7), (3,6.5), (4, 6) and (5, 5.5)
Is the relation a function?In (a), we have:
y = 8 - 0.5x
The above is a linear relation.
All linear relations are functions
Hence, the relation is a function.
Would a new relation be a function?
We have
Initial height, h = 8 inches
New rate = 0.4 inches per hour
The height of the candle at x hour is:
y = Initial - rate * x
This gives
y = 8 - 0.4x
The above is a linear relation.
All linear relations are functions
Hence, the new relation is also a function.
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The Scooter Company manufactures and sells electric scooters. Each scooter cost $150 to produce, and the company has a fixed cost of $2,000. The Scooter Company earns a total revenue that can be determined by the function R(x) = 400x − 2x2, where x represents each electric scooter sold. Which of the following functions represents the Scooter Company's total profit?
−2x2 − 150x − 2,000
−2x2 + 250x − 2,000
−2x2 + 150x − 1,600
−300x3 − 4,000x2 + 60,000x + 800,000
The function that represents the Scooter Company's total profit is given by:
P(x) = -2x² + 250x - 2,000.
How to calculate the profit function?The profit function is calculated by the revenue function subtracted by the cost function, hence:
P(x) = R(x) - C(x).
In this problem, we have that:
The revenue function is: R(x) = 400x - 2x².The cost function is: X(x) = 150x + 2000.Hence the profit function is:
P(x) = R(x) - C(x).
P(x) = 400x - 2x² - (150x + 2000).
P(x) = -2x² + 250x - 2,000.
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HELP ME !!!!!!! Which of the following best describes a single fixed point that is the same
distance from the parabola as the directrix is from the parabola?
A. center
B. vertex
C. focus
D. locus
Answer:
C. Focus
.............
Triangle U S T is shown. Angle U S T is 100 degrees. The length of U S is 9, the length of S T is 10, and the length of U T is s.
Which equation correctly uses the law of cosines to solve for the length s?
92 = s2 + 102 – 2(s)(10)cos(100°)
9 = s + 10 – 2(s)(10)cos(100°)
102 = s2 + 100 – 2(s)(10)cos(100°)
s2 = 92 + 102 – 2(9)(10)cos(100°)
By solving through law of cosines the length s can be written as [tex]s^{2} =9^{2} +10^{2} -2*9*10cos(100)[/tex].
Given the length of US is 9, the length of ST is 10 and the length of UT is s and the angle UST is 100 degrees.
According to law of cosines a length can be written as [tex]c^{2} =a^{2} +b^{2} -2abcos g[/tex]
where c is the side opposite to the given angle and a and b are other sides , g is the angle given.
[tex]s^{2} =9^{2} +10^{2} -2*9*10cos(100)[/tex]
where s is the length of the side opposite to the angle given, the length of other sides are 9 and 10 where the angle is 100.
Hence the fourth option is correct which is s^{2} =9^{2} +10^{2} -2*9*10cos(100).
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Answer:
its D
Step-by-step explanation: ed 2023
How do you solve 32-34?
Answer:
32. {-4, 1, 2, 12}
33. {2, 6, 9, 31, 65}
34. No
Step-by-step explanation:
32. The domain of a relation is the set that contains all the x-coordinates of all the ordered pairs of the relation.
domain = {-4, 1, 2, 12}
33. The range of a relation is the set that contains all the y-coordinates of all the ordered pairs of the relation.
range = {2, 6, 9, 31, 65}
34. No since the same number, 2, appears twice as an x-coordinate. In a function, no two ordered pairs can have the same x-coordinate.
Please answer all four of the questions please I will mark u brainliest
Answer:
1: 8 ft
2: 10 cm
3: c is approximately 127.2 or exactly equal to 90 * sqrt(2)
4: sqrt(133)
Step-by-step explanation:
(1) Kevin tries to climb a wall with a ladder. The length of a ladder is 17 feet and it reaches only 15 feet up the wall. What is the distance between the base of the ladder and the wall? :
Here you can use the Pythagorean Theorem to find the length of the base.
the equation is a^2 + b^2 = c^2 where c is the hypotenuse. In this case 17 is the hypotenuse which is c, 15 is a or b it doesn't really matter where you put it.
a^2 + (15)^2 = 17^2
a^2 + 225= 289
a^2 = 64
a = 8
(2) In a right triangle, if the length of one leg is 8 cm and the length of the other leg is 5 cm, what is the length of the hypotenuse? :
The same formula can be used except you don't have to move anything around.
8^2 + 6^2 = c^2
64 + 36 = c^2
100 = c^2
10 = c
10 cm
A baseball field is a square with sides of length 90 feet. What is the shortest distance between the first base and the third base?:
So if you look at the image provided, the shortest distance is just a straight line, but more specifically that straight line forms two triangles with the same lengths, That line is the hypotenuse so you can use the same equation as the previous equations
90^2 + 90^2 = c^2
16,200 = c^2
c is approximately 127.2 or exactly equal to 90 * sqrt(2)
(4) How far up a wall will a 13-meter ladder reach, if the foot of the ladder is 6 meters away from the base of the wall?:
6^2 + b^2 = 13^2
36 + b^2 = 169
b^2 = 133
b = sqrt(133)
Which of the following is most likely the next step in the series?
⠀⠀
The next step in the series is choice D.
Answer:
D
Step-by-step explanation:
if we define the diagrams in terms of their rows and columns, then
1st : 2 by 1
2nd : 3 by 2
3rd : 4 by 3
note that the rows and columns both increase by 1
then the next likely diagram is
5 by 4 , that is diagram D
A variable is normally distributed with mean 6 and standard 2 deviation .
a. Find the percentage of all possible values of the variable that lie between 5 and 9.
b. Find the percentage of all possible values of the variable that exceed 1.
c. Find the percentage of all possible values of the variable that are less than 4.
The normal distribution is also known as the Gaussian distribution. The percentage of all possible values of the variable that are less than 4 is 15.87%.
What is a normal distribution?
The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.
A.) The percentage of all possible values of the variable that lie between 5 and 9.
P(5<X<9) = P(X<9) - P(5<X)
= P(z<1.5) - P(-0.5<z)
= 0.9332 - 0.3085
= 0.6247
= 62.47%
B.) The percentage of all possible values of the variable that exceed 1.
P(X>1) = 1 - P(X<-2.5)
= 1-0.0062
= 0.9938
= 99.38%
C.) The percentage of all possible values of the variable that are less than 4.
P(X<4) = P(X <4)
= P(z<-1)
= 0.1587
= 15.87%
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63, 58, 57, 71, 54, 60 Calculate the coefficient of variation for the following data
Answer:
The coefficient of variation (CV)= 9.83
Step-by-step explanation:
look at the attachment above ☝️
Change a Relation to Make It a Function The relation R is shown below as a list of ordered pairs. R = { (1, 4), (1, 3), (-1, 3), (2, 15) } Which ordered pairs prevent this relation from being a function? (1, 4) and (1, 3), because they have the same x-value (1, 3) and (–1, 3), because they have the same y-value
Answer: (1,4) and (1,3) because the have the same x-value
Step-by-step explanation:
A function is defined so that for each input (known as the domain), there is no more than one output (known as the range).
The number of wrecks at a certain intersection varies directly as the number of cars that travel through the intersection. If there are 31 wrecks when 1,085 cars have traveled through the intersection, how many cars have passed through the intersection after 7 wrecks?
The number of cars that have passed through the intersection after 7 wrecks is 1/5 cars
Direct variationNumber of wrecks = wNumber of cars = cw = k × c
31 = k × 1,085
31 = 1,085k
k = 1085/31
k = 35
If w = 7
w = k × c
7 = 35 × c
7 = 35c
c = 7/35
c = 1/5 car
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If g(x) = 2^x were shifted 7 units to the right and 3 units down, what would be the new equation?
H(x) = 4(x - 7)^2 - 19
Hope you find it usefull
A polynomial-function has −5+√3 as a root. Which of the following must also be a root of the function?
O-5-√√3
0 -5+√√√31
05-√√√31
0 5+√√31
Answer:
First option.
Step-by-step explanation:
In the diagram, DG = 12, GF = 4, EH = 9, and HF = 3.
Triangle D E F is shown. Line G H is drawn parallel to side D E within the triangle to form triangle G F H. The length of D G is 12, the length of G F is 4, the length of E H is 9, and the length of H F is 3.
To prove that △DFE ~ △GFH by the SAS similarity theorem, it can be stated that StartFraction D F Over G F EndFraction = StartFraction E F Over H F EndFraction and
∠DFE is 4 times greater than ∠GFH.
∠FHG is One-fourth the measure of ∠FED.
∠DFE is congruent to ∠GFH.
∠FHG is congruent to ∠EFD.
To prove that △DFE ~ △GFH by SAS similarity theorem, then option C. ∠DFE is congruent to ∠GFH is appropriate. So that: [tex]\dfrac{DF}{GF}[/tex] =[tex]\dfrac{EF}{HF}[/tex] and ∠DFE is congruent to ∠GFH.The correct answer is option C.
The image of the triangle is attached with the answer below:-
What is congruency?The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.
Given ΔDEF as shown in the diagram attached to this answer, the following can be observed:
By comparing ΔDEF and ΔGFH
DF = DG + GF
= 12 + 4
DF = 16
Also,
EF = EH + HF
= 9 + 3
EF = 12
Comparing the sides of ΔDEF and ΔGFH, we have;
[tex]\dfrac{DF}{GF}[/tex] = [tex]\dfrac{EF}{HF}[/tex]
[tex]\dfrac{16}{4}=\dfrac{12}{3}[/tex]
4 = 4
Thus, the two triangles have similar sides.
Comparing the included angle <DFE and <GFH, then;
∠DFE is congruent to ∠GFH
Therefore, to prove that △DFE ~ △GFH by the SAS similarity theorem;
[tex]\dfrac{DF}{GF}[/tex] =[tex]\dfrac{EF}{HF}[/tex] and ∠DFE is congruent to ∠GFH.
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Answer:
C
Step-by-step explanation:
Edg
I will give BRAINLIEST! ANSWER FOR 30 Points !!!!
Pleasee look at picture
What is the frequency of the tangent function represented in the graph below?
Answer CHOICES:
1 , 4 , 3 , 2
Answer:
The answer is 3
Step-by-step explanation:
You can see that it recurs faster than usual for a tan curve so 1 is eliminated and it cant be 2 or 4 because it isnt recurring equally.
Please give brainliestThe points (2,3) and (5,9) are on the line. What is the equation of the line
The equation of the line is y = 3x +3 .
What is a Straight Line Equation ?A straight line equation is that can be represented by y = mx +c , where m is the slope and c is the intercept on y axis.
The points given are (2,3) and (5,9)
m = (9-3)/(5-2) = 3
m = 3
Therefore the equation becomes
y = 3x +c
Te equation is given by
(y-y₁) = m(x-x₁)
y-3 = 3(x - 2)
y-3 = 3x -6
y = 3x +3
Therefore the equation of the line is y = 3x +3 .
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What are the approximate area and circumference, respectively, of a circle with a diameter of 30 inches?
Solution:
[tex]\searrow[/tex]
Detailed explanation:
Here we need to find both the circumference and the area of a circle whose diameter is 30 in.
///\\\///\\\///\\\///\\\///\\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\\////\\\\////\\\\///\\\///\\\///\\\///
⚜ Circumference ⚜
This is the formula that we use for the circumference. [tex]\large\texttt{$C=\pi d$}[/tex].
Here, C is the circumference,
[tex]\pi[/tex] is pi, *
d is the diameter
_____________
* The number pi is an irrational number. This means that no matter how hard we try, we cannot write this number as a fraction. The reason for that is: The number pi has never-ending digits after its decimal point.
To avoid getting never-ending numbers, we will use 3.14 for pi.
_____________
Alright, so now we just stick in the values.
[tex]\boldsymbol{C=3.14\cdot30}[/tex]
[tex]\boldsymbol{C=94.2\:inches}[/tex]
The circumference is successfully calculated.
///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\////\\\\///\\\///\\\///\\\//\\//\/\/\/\//\///\\//
⚜ Area ⚜
This is the formula we will use to work out the area.
[tex]---\mapsto\boldsymbol{A=\pi r^2}[/tex]
Here,
A denotes the area
[tex]\pi[/tex] denotes pi
r denotes the radius (30/2=15, because the diameter is always two times the radius)
[tex]\large\boldsymbol{\therefore,\;the\;radius\;is\;15}[/tex]
Once again, it's just a matter of sticking in the values.
[tex]---\mapsto\boldsymbol{A=3.14\cdot15^2}[/tex]
NB:Remember the Order of Operations!
P.E.M.D.A.S.
P=Parentheses
This operation tells us to evaluate all expressions in the parentheses first, if any are present.
E=Exponents
This one tells us to evaluate all expressions with exponents, if any are present.
M=Multiplication | D=Division
Unlike the two operations above, these two are completely interchangeable.
A=Addition | S=Subtraction
Like M and D, A and S are interchangeable.
_________________
Now let's simplify... According to P.E.M.D.A.S., we should square 15 first.
[tex]---\mapsto\boldsymbol{A=3.14\cdot225}[/tex]
Now, we need to multiply.
[tex]---\mapsto\boldsymbol{A=706.5\;square\;inches}[/tex]
Turkey sandwiches cost $2.50 and veggie wraps cost $3.50 at a snack stand. Ben has sold no more than $30 worth of turkey sandwiches and veggie wraps in the first hour of business. Let x represent the number of turkey sandwiches and y represent the number of veggie wraps. The inequality 2.50x+3.50y30 represents the food sales in the first hour.
If Ben has sold 4 veggie wraps, what is the maximum number of turkey sandwiches Ben could have sold?
The maximum number of turkey sandwiches Ben sold is 6.
What is the maximum number of turkey sandwiches Ben sold?Given this equation : 2.50x + 3.50y ≤ $30
If y is 4, take the following steps in order to determine the value of x:
Substitute for y in the above equation:
2.50x + (3.50 x 4) ≤ $30
2.50x + 14 ≤ $30
2.50x ≤ $30 - 14
2.50x ≤ $16
x ≤ 6.4
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Answer:
6
Step-by-step explanation:
(3x + 2y = 7
(7x-2y = 3
What is the reason for statement 7 in the given proof? A. definition of midpoint B. definition of slope C. Parallel lines have equal slopes. D. using point-slope formula
The reason is using point slope formula.
The photo attached given below:
what is point slope formula?The equation of a straight line in the form y − y1 = m(x − x1) where m is the slope of the line and (x1, y1) are the coordinates of a given point on the line — compare slope-intercept form.
Now, we have to find the slope of AE, BF and CD.
We have to done this with help of coordinates.
So, we have to use point slope formula to find the slope of AE, BF and CD.
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A bakery sold 27 mocha cupcakes in a day, which was 9% of the total number of
cupcakes sold that day. How many total cupcakes did the bakery sell that day?
Answer:
300 cupcakes
Step-by-step explanation:
[tex]27 = .09c[/tex]
[tex]c = \frac{27}{.09} = \frac{2700}{9} = 300[/tex]
In total, the bakery sold 300 cupcakes on a certain day.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, A bakery sold 27 mocha cupcakes in a day, which was 9% of the total number of cupcakes sold that day.
let, 'x' be the total number of cupcakes sold that day.
Therefore, 9% of 'x' is 27 which is,
(9/100)×x = 27.
0.09x = 27.
x = 27/0.09.
x = 300.
So, The number of cupcakes sold that day is 300.
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Help me with this question please!! :)
Answer: 20/63
Step-by-step explanation:
The probability that the first marble is red is 16/28.The probability that the second marble is red is 15/27.Multiplying these probabilities, we get (16/28)(15/27) = 20/63
3x+7-6=(8/7)-0
Value of x?
Answer:
[tex]\boxed{\sf x = \dfrac{1}{21}}[/tex]
Explanation:
[tex]\rightarrow \sf 3x+7-6= \dfrac{8}{7} - 0[/tex]
simplify the following
[tex]\rightarrow \sf 3x+1= \dfrac{8}{7}[/tex]
subtract 1 from both sides
[tex]\rightarrow \sf 3x+ 1 -1= \dfrac{8}{7} - 1[/tex]
simplify the following
[tex]\rightarrow \sf 3x= \dfrac{1}{7}[/tex]
multiply both sides by 1/3
[tex]\rightarrow \sf 3x \cdot \dfrac{1}{3}= \dfrac{1}{7}\cdot \dfrac{1}{3}[/tex]
simplify the following
[tex]\rightarrow \sf x = \dfrac{1}{21}[/tex]
[tex]3x + 7 - 6 = \frac{8}{7} - 0 \\ \\ 3x + 1 = \frac{8}{7} \\ \\ 3x = \frac{8}{7} - 1 \\ \\ 3x = \frac{ 8 - 7}{7} \\ \\ 3x = \frac{1}{7} \\ \\ x = \frac{1}{7 \times 3} \\ \\ x = \frac{1}{21} .[/tex]
Evaluate
3(x+4)(x+1)
HP for x = 4.
(x+2)(x-2)
Answer:
120
Step-by-step explanation:
3(x+4)(x+1)
3((4)+4) ((4)+1)
(12 + 12)(4+1)
(24)(5)
120
If you need the other function, here:
(4+2)(4-2)
6(2)
12
Answer:
below
Step-by-step explanation:
3×x=12
3×4=12
3(x+4)=12+12+12+3=39
If the center of a circle is at (5,-7)
and its radius is 6, complete its
equation:
The equation is:
(x-5)^2+(y-(-7))^2=36
I hope it helps!
Answer: [tex]\boldsymbol{(x - 5)^2 + (y + 7)^2 = 36}[/tex]
=========================================
Work Shown:
[tex](h,k) = (5,-7) = \text{center}\\\\r = 6 = \text{radius}\\\\(x - h)^2 + (y - k)^2 = r^2\\\\(x - 5)^2 + (y - (-7))^2 = 6^2\\\\\boldsymbol{(x - 5)^2 + (y + 7)^2 = 36}\\\\[/tex]
The graph of the quadratic function f(x) = - 1/2 x ^ 2 + 3 is shown. Describe the end behavior of the function.
In the last three years Frederic’s basketball team win 40 more games than they lost
Answer:
Wht is the total matches they played?
Dan Barker, the chief engineer, told Ms. Silva that the company is currently making 150 units of Model Diamond per batch and 245 units of Model Gold per batch. He suggests doubling the batch sizes to cut the number of setups in half, thereby reducing the setup cost by 50 percent. Compute the cost per unit for each product if Ms. Silva adopts his suggestion.
The cost per unit for each product is given as:
x ≈ 0.0067; and
y ≈ 0.0041. See explanation below.
What is the cost per unit for each product?Given that the current production:
Model Diamond (Md) - 150 UnitsModel Gold (Mg) - 245 UnitsCurrent cost of production is given as:
Current Total Cost = 150y + 245x where;
if doubling the batch sizes will reduce the cost per unit by 50% then the new cost equation will be:
Thus, New Total Cost of production = (150 x 2) (y/2) + (245 x 2) (x/2)
= (300)(y/2) + (490) (x/2)
Since we are looking for the cost per unit of each product:
f(x) = 300 * (x/2)..........Unit cost of Model Gold
If we make x subject of the formula, then we arrive at:
1/300 = x/2
x = (1/300) * 2
x = 0.00666666666
x ≈ 0.0067
f(x) = 490* (x/2)
If we make y subject of the formula, then we arrive at:
i/490 = y/2
y = (1/490) * 2
y = 0.00408163265306122448979591836735
y ≈ 0.0041
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