[tex]\begin{cases} x-2y=3\\ 2x+4y=6 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{x-2y=3}\implies x=2y+3 \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{2(\underset{x}{2y+3})+4y=6}\implies 4y+6+4y=6\implies 8y+6=6 \\\\\\ 8y=0\implies y=\cfrac{0}{8}\implies \boxed{y=0}\hspace{5em}\stackrel{2(0)+3}{\boxed{x=3}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (3~~,~~0)~\hfill[/tex]
Isaac purchased a new car in 2004 for $16, 900. The value of the car has been depreciating exponentially at a constant rate. If the value of the car was $1,400 in the year 2012, then what would be the predicted value of the car in the year 2017, to the nearest dollar?
The value of the car in the year of 2017 would be of:
$295.
How to obtain the value of the car in 2017?A decaying exponential function is given as follows:
y = a(1 - r)^x.
In which:
a is the initial value.r is the decay rate, as a decimal.The initial value for this problem is of:
a = 16900.
After 8 years, the value was of 1400, hence the decay rate is obtained as follows:
16900(1 - r)^8 = 1400
(1 - r)^8 = 1400/16900
((1 - r)^8)^1/8 = (1400/16900)^1/8
1 - r = 0.73245368177
Hence the function is:
y = 16900(0.73245368177)^x.
2017 is 13 years after 2004, hence the value would be of:
y = 16900(0.73245368177)^13
y = $295.
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4) Find the 12th term in the sequence -2, 6, -18, 54, ...
A. f(n) = 2,048
OB. f(n)=512
C. f(n) = 354,294
D. f(n) = 781,250
The 12th term in the sequence is (c) f(n) = 354294
How to determine the 12th term in the sequence?From the question, we have the following parameters that can be used in our computation:
The definition of the function is given as
-2, 6, -18, 54, ...
The above definitions imply that we simply multiply -3 to the previous term to get the current term
Using the above as a guide,
so, we have the following representation
f(n) = -2(-3)^n-1
Where
-2 is the first term and -3 is the common ratio
For the 12th term, we have
f(n) = -2(-3)^11
Evaluate
f(n) = 354294
Hence, the 12th term is (c) f(n) = 354294
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The volume of 10 drops of a liquid is 0.1 fluid ounces.
What is the volume of 100 drops?
Answer:
1 fluid ounce
Step-by-step explanation:
if 10 drops is equal to 0.1 fl and we multiply 10 by 10 to get 100, we have to multiply 0.1 by 10 as well, which is 1 fluid ounce.
You have $80 in your bank account. Each week you plan to deposit $9 from your allowance and $25 from your paycheck. The equation b = 80+(25+9)w gives the amount b in your account after w weeks how many weeks from now will you have $245 in your bank account
Answer:
165/34
Step-by-step explanation:
245=80+(25+9)w We subtract 80 from each side and simplify
165=(34)w Divide each side by 34
165/34 = w
A daycare charges a base fee of 333 dollars plus 0. 500. 500, point, 50 dollars per minute for late (after closing time) pick-ups. Albin had to pay 10. 5010. 5010, point, 50 dollars for a late pick-up. Albin uses the equation, 10. 50=0. 50a+310. 50=0. 50a+310, point, 50, equals, 0, point, 50, a, plus, 3 to represent the situation
It means Albin was 15 minutes late to a pickup.
a represents the Number of Minutes Late, (a=15 in this case)
Now, According to the question:
A daycare charges a base fee of 333 dollars plus 0. 500. 500, point, 50 dollars per minute for late (after closing time) pick-ups.
Albin had to pay 10. 5010. 5010, point, 50 dollars for a late pick-up.
Albin uses the equation,
10.50 = 0.50a+3
0.50a = 10.50-3
0.50a = 7.50
a = 7.50/0.5
a= 15
Hence, It means Albin was 15 minutes late to a pickup.
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Sally has a swimming pool that needs to be drained. Her pool holds
9,774.5 gallons of water and will need to drain completely in 9.1 hours.
What is the change in the water level per hour for Sally's swimming
pool? Round your answer to the nearest hundredth.
The required change in the water level per hour for Sally's swimming pool is 1074 gallons.
What is rate change per hour?Rate of change is equal to (Change in completed assignments) / (Change in hours) Change in rate = (6-3) / (2-1) Change in rate = (3) / (1) The change rate is 3/1, or 3 assignments every hour. The rate of change is 3.0, or three assignments are completed every hour when time is measured in hours.
According to question:We have,
Her pool holds 9,774.5 gallons of water and will need to drain completely in 9.1 hours.
Number of gallons per hour are
gallons per hour = 9,774.5/9.1
gallons per hour = 1074 approx
Thus, required number of gallons per hours 1074.
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Convert 9y^2+72y=72=6x-x^2 to standard form.
A) (x-3)^2/81 + (y-4)^2/ 9=1
B) (x+3)^2/81+(y+4)^2/9=1
C) (x-3)^2/81 + (y+4)^2/9=1
D) doesnt matter the answer is C
The standard form of the equation 9y^2+72y=72=6x-x^2 will be x-3)^2/81 + (y+4)^2/9=1.
Imagine that you are collaborating on a math assignment with students Andrea and Susan. To represent a word problem, you are looking for an equation. You each work on the problem independently, then compare your solutions. The formula 2x - y = -1 was created by you. The formula y = 2x + 1 was created by Andrea. Susan's final solution was the equation y - 3 = 2(x - 1).The given equation is :
[tex]x^{2} + 9y^{2} -6x +72 y = 72[/tex]
[tex]x (x-6) +9y (y+6) = 72[/tex] +1 +36
x(x-6) / 109 + 9y(y+6) / 109 = 1
Thus, by simplifying above equation
(x-3)^2/81 + (y+4)^2/9=1
In this case, Option C is correct.
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Answer:
C) (x-3)^2/81 + (y+4)^2/9=1
Step-by-step explanation:
Can someone help me with this please?
Answer:
Scalene Triangle
Step-by-step explanation:
Right triangles have 90 degree angles. Isosceles triangles have 2 equal sides. While, equilateral triangles have 3 equal sides.
in the equation 3(x-1)=2x+c, for what value of c will x = 3? Explain your reasoning
Brainliest Answer
By algebra properties, the value of variable c for linear equation 3 · (x - 1) = 2 · x + c such that x = 3 is equal to 0.
How to solve a linear equationIn this problem we need to find the value of a variable c such that the following system of linear equations exists:
3 · (x - 1) = 2 · x + c
x = 3
First, substitute x in the first equation:
3 · (3 - 1) = 2 · 3 + c
Second, simplify and clear the resulting expression:
3 · 2 = 6 + c
6 = 6 + c
c + 6 = 6
c = 0
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is the given value a root of the equation or not?
1. 8x-4= 2; 3
2. 4y + 5 = y-7; -4
Answer: To check if a given value is a root of the equation 8x-4 = 2, we can substitute the value into the equation and see if it makes the equation true.
When we substitute 3 for x in the equation 8x-4=2, we get 8(3)-4=2, which simplifies to 24-4=2, which is not true. So, 3 is not a root of the equation.
To check if a given value is a root of the equation 4y + 5 = y-7, we can substitute the value into the equation and see if it makes the equation true.
When we substitute -4 for y in the equation 4y + 5 = y-7, we get 4(-4) + 5 = -4-7, which simplifies to -16+5=-11=-4-7, which is true. So, -4 is a root of the equation.
Step-by-step explanation:
write a description of each inequality
-5a+3>1
show work
Answer:
Step-by-step explain
You have to solve for 5a
A scooter costs a retailer $75, but it sells for $125 at the local store. What is the percent markup? Be sure to round to the nearest hundreth.
Answer = ___%
The percent markup for the scooter that costs a retailer $75 but sells for $125 at the local store is 66.67%.
What is the markup?The markup is the additional price added to the cost of an item for retail sales.
Markups are usually expressed in percentages.
To express the markup in percent determine the difference between the retail price and the cost price. Then divide the difference by the cost price and multiply by 100.
The cost price of the scooter = $75
The selling price of the scooter = $125
The markup in dollars = $50 ($125 - $75)
The markup percent = 66.67% ($50/$75 x 100)
Thus, the scooter was marked-up at 66.67%.
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Put the numbers in order from smallest to largest.
50.57
150
15.2
5.899
Answer:
Smallest to Largest =
5.899, 15.2, 50.57, and 150
Step-by-step explanation:
I hope this helps you out :D
seaview high school currently has 1,206 students and the town is predicting that they will receive 7 new students each year springtown high school currently had 1,074 students and the town is predicting that they will receive 19 new students each year how many years will it take for the schools to have the same number of students
The number of years that will take for the schools to have the same number of students is given as follows:
11 years.
How to define the linear functions?The number of students in each school is modeled by linear functions in slope-intercept format, as follows:
y = mx + b.
In which:
m is the slope, representing the yearly change.b is the intercept, representing the initial amount of students in each school.The functions for this problem are given as follows:
Seaview: Se(t) = 1206 + 7t.Springtown: Sp(t) = 1074 + 19t.They will have the same number of students when:
Sp(t) = Se(t).
Hence:
1074 + 19t = 1206 + 7t
12t = 132
t = 132/12
t = 11 years.
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in how many ways can i distribute $6$ identical gummy bears and $6$ identical chocolates to $4$ students, if each student must receive exactly $3$ pieces of candy?
If we divide the candy according to numbers rather than type, I can give 4 pupils 6 identical chocolates and 6 identical gummy bears, ensuring that each student will get exactly 3 pieces of candy.
We have to find in how many ways I can distribute 6 identical gummy bears and 6 identical chocolates to 4 students, if each student must receive exactly 3 pieces of candy.
Gummy Bear = 6
Chocolates = 6
Total numbers of candy = Gummy bear + Chocolates
Total numbers of candy = 6 + 6
Total numbers of candy = 12
We have to distribute the tablet in between 4 students. So each student must receive exactly 3 pieces of candy if we distribute the candy by the numbers not their type.
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The trajectory of a golf ball hit from a tee on the ground at an angle of 50 degrees with an initial speed of 60 meters per second can be modeled by the parabola f(x) = 1. 19x − 0. 0033x2, where the x-axis is the ground. Find the height of the highest point of the trajectory and the horizontal distance the golf ball travels before hitting the ground.
PLEASE HELP!
The height of the highest point of the trajectory and the horizontal distance the golf ball travels before hitting the ground will be 360 .6 meters
Apparently, x is the distance from the place where the ball is impacted on the ground.
The ball's horizontal speed, given by s, can be calculated using the equation cos(50) = s/60, where s = 38.5 mps.
Size is represented by f(x). The highest point of the parabola would be at -b/2a = -1.19/-.0066 = 180.3 metres, meaning the ball has moved 180.3 metres.
Input 107.28 metres into the formula to find the height.
In order to calculate the distance travelled, the ball must be on the ground, hence f(x) = 0.
-.0033x^2 + 1.19x = 0
x*(-.0033x + 1.19) = 0
x= 1.19/.0033 = 360 .6 meters
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A pizza company charges $60 for 12 pizzas.
Using the above situation write a complete answer for the following questions.
li) Write the ratio
iii) Write the unit rate or m
iv)write the equation(y=Mx)
v) create a table from the above question
Answer:
Step-by-step explanation:
ii) ratio = 60:12 = 5:1
iii) unit rate is 5
iv) 60 = 12M
Aplicación de expresions algebraica
En la vida m cotidiana
Answer:
Aprende a leer expresiones algebraicas y comprende conceptos como variable, coeficiente u operador, entre otros.
Step-by-step explanation:
Ejemplo: la mitad de un número “x” si x= 8 x/2= 8/2= +4
How many terms are in the following Algebraic Expression? -
(7 x 6) + 8
Answer: 3
Step-by-step explanation: First you have to do 7 times 6 which is 42. Then you add 8 and get 50!
est scores for students on an easy test. approximately symmetric b) the numbers of hours of television watched by a large, typical group of americans. approximately symmetric c) the heights of a large, typical group of ad
Symmetry is a way of measuring the shape of a data set. It is defined as the similarity between the upper and lower halves of a distribution.
A symmetric distribution is one where the data is equally distributed around a central point. To calculate this, you need to subtract the mean (the average of the values) from each data point and then divide by the standard deviation (the measure of how much the data is spread out). The formula for symmetry is: (x-mean)/standard deviation. An example of a symmetric distribution would be the scores of a group of students on an easy test. If the mean score was 70 and the standard deviation was 10, then any score between 60 and 80 would be considered symmetric.
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Find the perimeter of the
polygon if ZB = ZD.
D
A
10.5 cm
12.5 cm
C
B
11.5 cm
P = [?] cm
Perimeter of Regular Polygon = 92cm (Number of sides) x (Side length of a polygon) units
What is Perimeter of Polygon?The total length of a polygon's boundary is calculated as the polygon's perimeter. Due to the fact that polygons are closed plane shapes, their perimeters likewise reside in a two-dimensional plane. A polygon's perimeter is always measured in linear distances such as metres, centimetres, inches, feet, etc.
Based on the length of its sides, we can classify a polygon as either regular or irregular. The formula for several well-known polygons' perimeter is as follows:
A triangle's perimeter is equal to its three side lengths, a, b, and c.
A rectangle's perimeter equals 2 (length + width).
We first determine whether the given polygon is a regular polygon or an irregular polygon before computing the perimeter of the polygon. The polygon's perimeter is then determined using the proper Formula
Therefore, the formula to find the perimeter of a regular polygon is: Perimeter of regular polygon = (number of sides) × (length of one side)
From the given diagram;
Perimeter of the polygon = AB + BC+ CD + DA
Perimeter of the polygon = 10.5 + 11.5 + 12.5 + 11.5 + 11.5 + 12.5 + 11.5 + 10.5
Perimeter of the polygon = 22 + 24 + 24 + 22
Perimeter of the polygon = 46 + 46
Perimeter of the polygon = 92cm
Hence the Perimeter of the polygon is 92cm
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you have built a regression model to predict future crops of tomato based on a range of growing conditions. the model seems to fit well to the training data, but when any new data is tested it performs very poorly. how would you typically describe a model where this occurs?
That regression model is described as overfitting. The model has identified specific data points in the data that are not universal.
A regression model, which provides a function, describes the relationship between one or more independent variables and a response, dependent, or target variable. To explain the relationship between height and weight, for instance, a linear regression model might be utilized.
Regression analysis is the foundation for many forecasts and evaluations of the effects on target variables. Regression models are widely employed in research to support claims about fuel economy, the causes of pollution, or the effects of screen time on learning.
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Use the figure to write a two-column proof.
Given: PSUR is a rectangle.
PQ=TU
Prove: QS=RT
*THE QUESTION IN THE PHOTO IS JUST NUMBER 10
Answer:Given Prove
PSUR is a rectangle QS = RT
PQ = TU
Proof:
Since PSUR is a rectangle, we know that opposite sides are parallel.
Therefore, PQ and TU are parallel.
Also, PSUR is a rectangle, so the angles P and R are right angles.
Therefore, angles Q and S are also right angles.
Since PQ and TU are parallel, and angles Q and S are right angles, we know that QS and RT are corresponding angles.
Therefore, QS=RT
QED.
Step-by-step explanation:
HELP HELL GELP
HELPFBDNAKAKIWKW
Part 6
What is the mean absolute deviation for Doctor As data set on contacts? What is the mean absolute deviation for Doctor Bs data set on contacts
Write a sentence comparing these two data sets using their mean absolute deviations.
There is more variability on glasses of doctor B's dataset than the glasses of doctor A's dataset
Now, According to the question:
The doctors' mean absolute deviation on glasses
The dataset of doctor A is given as:
643 634 670 658 636 624 641 655 649 629
The dataset of doctor B is given as:
651 625 622 624 631 621 653 647 646 646
Using a statistical calculator, we have:
Doctor A
Doctor A: Mean Absolute Deviation (MAD) = 11.28
Doctor B: Mean Absolute Deviation (MAD) = 12
Hence, the mean absolute deviation is 11.28 for Doctor A’s and 12 for Doctor B’s data set on glasses
The variation of the two data
In a dataset, the larger the mean absolute deviations value, the larger the variation.
By comparison, 12 is greater than 11.28
Hence, there is more variability on glasses of doctor B's dataset than the glasses of doctor A's dataset
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The given question is incomplete, complete question is:
What is the mean absolute deviation for Doctor A’s data set on glasses? What is the mean absolute deviation for Doctor B’s data set on glasses? Write a sentence comparing the variation of the two data sets using their mean absolute deviations.
Doctor A Doctor B
Corrective Lenses Glasses Contacts Corrective Lenses Glasses Contacts
745 643 102 763 651 112
726 634 92 736 625 111
769 670 99 735 622 113
765 658 107 759 624 135
756 636 120 748 631 117
742 624 118 756 621 135
757 641 116 765 653 112
748 655 93 761 647 114
770 649 121 768 646 122
738 629 109 761 646 115
If f(x)=3x, g(x)=x+4 , and h(x)=x2−1 , find g[h(0)]
the value of function g[h(0)] at x = 0 is 3.
What is Function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
Given that,the functions f(x) = 3x, g(x) = x + 4 , and h(x) = x² − 1
Since,
G(h(x)) = x² - 1 +4
G(h(x)) = x² + 3
Thus at x = 0
G(h(0)) = 0² + 3
G(h(0)) = 3
therefore, the value of function g[h(0)] at x = 0 is 3.
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what is the lowest value of the rangee of the function shown on the graph? -♾️, -2, 0, 3
The correct option is -2. The range of function is found to be minimum is -2.
Explain the term minima of the function?The highest and smallest values of a function, respectively, can either be found inside a specific range or across the entire domain. They are sometimes referred to as the function's extrema. The plural forms of a function's maximum and minimum are called maxima and minima, respectively. Let's first examine the function's local maximum and minimal values before delving further into maxima and minima.A function's global minimum is its lowest value across the entire function's range, whereas a localized minimum is its lowest value within a specific local area.
From the given graph of the function:
To get the lowest point of the range of the function, check the value where graph is turning.
This, shows the minima of the function which is -2 at x = 3.
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The complete question is attached-
Find the length of the prism
The length of the rectangular prism is 4/5x.
What is a rectangular prism?
Six faces make up the three-dimensional shape of a rectangular prism (two at the top and bottom and four are lateral faces). The prism has rectangular shapes on each of its faces. There are therefore three sets of identical faces in this picture. A cuboid is another name for a rectangular prism because of its shape.
We know that Volume of a rectangular prism is a product of length, height and width.
We are given volume as (7/x)-(3/5x).
The width(w) is 2/x and the height(h) is 4/x
Using the formula, we get
⇒ V = lwh
⇒ (7/x)-(3/5x) = l * (2/x) * (4/x)
⇒ l = [(7/x)-(3/5x)] / [(2/x) * (4/x)]
⇒ l = (32/5x) /(8/x^2)
⇒ l = 4/5x
Hence, the length of the rectangular prism is 4/5x.
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Garrick is building a swimming pool. He wants the length to be at least 20 feet, but the perimeter cannot exceed 100 feet. What are the 2 resulting equations out of this question?
The 2 resulting inequality equations out of this question are;
L ≥ 20 ft
(L + W) ≤ 50
How to express inequality equations?The formula for the perimeter of a rectangle is expressed as;
Perimeter = 2(Length + Width)
We are told that the length has to be at least 20 feet, which means it must not be lesser than 20 feet. Thus;
L ≥ 20 ft
Now, we are told that the perimeter cannot exceed 100 feet. Thus;
2(L + W) ≤ 100
Solving that by dividing both sides by 2 gives;
(L + W) ≤ 50
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The following games are played with 8 cards: the four kings and the four aces. The dealer fans the cards with their back to you and asks you to take one, but not to look at it. He tells you that you will win a prize if your chosen card is an ace. There are two versions of what happens next.
In version 1, he closes up the remaining 7 cards, shuffles them and reveals to you the top card face up on the table which turns out randomly to be the King of Spades. He then deals the next card face down on the table. He then offers you the chance to trade the card you hold for the face-down card that was just dealt. So you have two choices: stay or switch. What are your chances of winning under each choice?
In version 1, if you choose to stay with the card you have initially chosen, your chances of winning are 1 in 8, since you have a 1 in 8 chance of having selected an ace initially.
If you choose to switch, your chances of winning are 7 in 8, since the card you are switching to is randomly selected from the remaining 7 cards, 4 of which are aces. However, if the card you have initially chosen is an ace, you should stay with it since you have already won the prize. If it is not an ace, it may be beneficial to switch as you have a higher chance of getting an ace with the face-down card.
In either case, the dealer has a 7-in-8 chance of winning since he has access to all the cards and can choose the card to be revealed at random. This means that he has a higher chance of winning than the player does. Overall, the game is quite balanced in terms of the chances of winning for either the player or the dealer.
The dealer has an advantage due to knowing the cards and being able to select the card to be revealed, but the player still has a chance of winning depending on their decision to switch or stay with their initial selection.
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