The value of x in the given equation x² = 9 is x = ± 3.
In x² = 9, we need to remove the power of 2 in order to separate just x.
This implies finding the square root √x² which is equal to x.
However, there are 2 possible answers to any square root, a positive or a negative answer.
x = √9
x = ± 3
0r we can solve this equation by the splitting method.
Rearrange the equation
x² = 9
(x - 3)(x + 3) = 0
On solving, we get
x = +3 and x = -3
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You are deciding a social hall that will seat no more than 1600 people. You want at least 500 seats to be priced at $20 each, and at least 800 seats to be priced at $30 each. Those investing in the social hall would also like to bring in at least $2800 in revenue from the ticket sales. Let X represent the number of $20 seats, and let Y represent the number of $30 seats. Which system of inequalities represents this situation?
x ≥ 0
y ≥ 0
x + y ≥ 1600
20x + 30y ≤ 2800
x ≥ 500
y ≥ 800
x + y ≤ 1600
20x + 30y ≥ 2800
x ≥ 800
y ≥ 500
x + y ≤ 1600
20x + 30y ≤ 2800
x ≥ 500
y ≥ 800
x + y ≤ 1600
20x + 30y ≤ 2800
Answer: Option B
Just trust me that its right.
If the growth rate of bacteria at any time t is proportional to the number present at t and triples in 1 week
If the growth rate of bacteria at any time is proportional to the number of bacteria present at t then the population after 20 weeks will be 403.42[tex]x_{0}[/tex] in which [tex]x_{0}[/tex] is the initial population.
Given that the growth rate of bacteria at any time t is proportional to the number present at t and triples in 1 week.
We are required to find the number of bacteria present after 10 weeks.
let the number of bacteria present at t is x.
So,
dx/dt∝x
dx/dt=kx
1/x dx=k dt
Now integrate both sides.
[tex]\int\limits {1/x} \, dx[/tex]=[tex]\int\limits{k} \, dt[/tex]
log x=kt+log c----------1
Put t=0
log [tex]x_{0}[/tex]=0 +log c ([tex]x_{0}[/tex] shows the population in beginning)
Cancelling log from both sides.
c=[tex]x_{0}[/tex]
So put c=[tex]x_{0}[/tex] in 1
log x=kt+log [tex]x_{0}[/tex]
log x=log [tex]e^{kt}[/tex]+log [tex]x_{0}[/tex]
log x=log [tex]e^{kt}x_{0}[/tex]
x=[tex]e^{kt}x_{0}[/tex]
We have been given that the population triples in a week so we have to put the value of x=2[tex]x_{0}[/tex] and t=1 to get the value of k.
2[tex]x_{0}[/tex]=[tex]e^{k} x_{0}[/tex]
2=[tex]e^{k}[/tex]
log 2=k
We have to now put the value of t=20 and k=log 2 ,to get the population after 20 weeks.
x=[tex]e^{20log 2}[/tex][tex]x_{0}[/tex]
x=[tex]e^{0.30*2}[/tex][tex]x_{0}[/tex]
x=[tex]e^{6}x_{0}[/tex]
x=403.42[tex]x_{0}[/tex]
If the growth rate of bacteria at any time is proportional to the number of bacteria present at t then the population after 20 weeks will be 403.42[tex]x_{0}[/tex] in which [tex]x_{0}[/tex] is the initial population.
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The given question is incomplete as the question incudes the following:
Calculate the population after 20 weeks.
Identify which property you would use first to solve the following equation.
3(2y+5) = 8y - 23
Answer:
Distributive property
Step-by-step explanation:
In order to solve this equation we first need to distribute 3 into 2y+5, we use the distributive property to do this.
25 POINTS!!!!
The graph of f(x) = (0.5)x is replaced by the graph of g(x) = (0.5)x − k. If g(x) is obtained by shifting f(x) down by 7 units, the value of k is ________??
The answer is k = 7.
As the graph has been shifted down 7 units, the translation can be represented as :
g(x) = f(x) - 7
(0.5)x - k = (0.5)x - 7
k = 7
A family needs to build fencing around their rectangular home and square swimming pool, depicted below.
A rectangle labeled home has its right side labeled (2 + 5 x) yards and its bottom side labeled (3 + 10 x) yards. The square, labeled pool, is smaller than the rectangle. One of its sides is labeled (2x) yards.
The total amount of fencing they need can be written as x + 10.
If x = 5;
The family needs yards of fencing for their home.
The family needs yards of fencing for their pool.
The total amount of fencing they need = 38x + 10.
Perimeter for the rectangular fencing of the home = 160 yards
Perimeter for the square fencing of the pool = 40 yards
What is the Perimeter of a Rectangle and a Square?Perimeter of a rectangle = 2(length + width)
Perimeter of a square = 4(side length).
Perimeter for the rectangular fencing of the home = 2(3 + 10x + 2 + 5x) = 2(15x + 5) = 30x + 10
Perimeter for the square fencing of the pool = 4(2x) = 8x
The total amount of fencing they need = 30x + 10 + 8x = 38x + 10.
If x = 5, then:
Perimeter for the rectangular fencing of the home = 30x + 10 = 30(5) + 10 = 160 yards
Perimeter for the square fencing of the pool = 4(2x) = 8x = 8(5) = 40 yards.
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Answer:
38
160
40
Step-by-step explanation:
The length of tr is 17 units. what are the lengths of sv and qt? sv = units qt = units
Applying the properties of kite, the measures are: SV = 41 units; QT = 21 units.
What is a kite?A kite is a quadrilateral that has 2 pairs of congruent adjacent sides, and has two diagonals where the longest one bisects the shorter one and divides it into equal segments.
The diagram given is a kite. Where TR = 17 units. Thus we would solve for x using the equation as shown below:
TR = RV [congruent adjacent sides of the kite]
Plug in the values
17 = 3x + 2
17 - 2 = 3x
15 = 3x
15/3 = x
x = 5
SV = TS = 9x - 4 [congruent adjacent sides of the kite]
Plug in the value of x
SV = 9(5) - 4
SV = 41 units
The length of segment QT is 41 units.
QT = QV = 4x + 1 [congruent adjacent sides of the kite]
Plug in the value of x
QT = 4(5) + 1
QT = 21 units
The length of segment QT is: 21 units.
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Answer:
SV: 41
QT:21
Step-by-step explanation:
determine which two of the three given triangles are similar. Find the scale factor for the pair
Answer:
Triangles MNP and QRS
Step-by-step explanation:
This is due to each corresponding line follows the same ratio of 1.5:1
e.g.
NP=6
RS=4
6:4
1.5:1
You can verify this by dividing 6 by 4 (6/4) which is 1.5
The leaning Tower of Pisa was completed in 1372 and makes 86 degree angle with the ground. The tower is 50 meters tall, measured vertically from the ground to the highest point. If you were to climb to the top then accidentally drop your keys, where would you start looking for them? question 5
Answer:
you would look for them 3.5 meters away from the base
Step-by-step explanation:
so u do tan 86 =50/x
and u solve from there
Which classification best represents a triangle with side lengths 10 in., 12 in., and 15 in.?
acute, because 102+122>152
acute, because 122+152>102
obtuse, because 102+122>152
obtuse, because 122+152>102
Answer:
Option (1)
Step-by-step explanation:
See attached image.
The given measures form a acute angle triangle.
What is an obtuse angle triangle?An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees. In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°.
Given that, a triangle with side lengths 10 in., 12 in., and 15 in.
We know that,
a²+b²=c² then triangle will be right angled
a²+b²>c² then triangle will be acute angled
a²+b²><c² then triangle will be obtuse angled
Here, a=10 inches, b=12 inches and c=15 inches
10²+12²>15²
100+144>225
244>225
Therefore, the given measures form a acute angle triangle.
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Which of the following are factor pairs for 12?
1. 1 and 12
2. 2 and 4
3. 2 and 6
3. 3 and 4
4. 3 and 5
NEED ANSWER QUICK PLEASE!!
Answer:
FACTOR pairs are a set of two integers that when multiplied together gives a particular product.FACTOR pairs of 12 are :1 and 12 because 1 x 12 = 122 and 6 because 2 x 6 =123 and 4 because 3 x 4 = 12Hope you understandHope this helps.Good luck ✅.Find the equation of the line perpendicular to 2x+3y-6=0 and passing through (-1,1)
Answer: [tex]y-1=\frac{3}{2}(x+1)[/tex]
Step-by-step explanation:
[tex]2x+3y-6=0\\\\3y=-2x+6\\\\y=-\frac{2}{3}x+2[/tex]
So, the slope of the given line is -2/3, meaning the slope of the line we want to find is 3/2.
Substituting into point-slope form, we get the equation of the line is
[tex]y-1=\frac{3}{2}(x+1)[/tex]
Volume=
Help me please!! Asap thanks so much
The volume of the oblique cylinder is 6867.18 cubic units
How to determine the volume?The given parameters are:
Height = 27
Radius = 9
The volume is calculated as:
[tex]V = \pi r^2 h[/tex]
So, we have:
[tex]V = 3.14 * 9^2 * 27[/tex]
Evaluate
V = 6867.18
Hence, the volume of the oblique cylinder is 6867.18 cubic units
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.
7-9p≥7 or 2p - 9> 11
Answer:
2p-9>
Step-by-step explanation:
Select the correct answer from the drop-down menu.
Jaden and his family are using a map to drive down to Napa Valley. On the map, the distance is given by the equation c = 1.3m, where c is the number of centimeters on the map and m is the corresponding real-world distance in miles.
If they cover a distance of 18 miles, that would mean a distance of
centimeters on the map.
Answer:
13.846153846
Step-by-step explanation:
Its easy Just 18:1.3=13.846153846
1. Factor and simplify: cos² xcsc² x-cos²xcot² x
Answer:
Cos² x
Step-by-step explanation:
Trigonometry:[tex]\sf Cos^2 \ x *Csc^2 \ x-Cos^2 \ x *Cot^2 \ x = Cos^2 \ x (Csc^2 \ x - Cot^2 \ x)[/tex]
[tex]\sf = Cos^2 \ x \left(\dfrac{1}{Sin^2 \ x} - \dfrac{Cos^2 \ x}{Sin^2 \ x}\right)\\\\= Cos^2 \ x \left(\dfrac{1-Cos^2 \ x}{Sin^2 \ x}\right)\\\\\boxed{\bf Indentity: \ 1 - Cos^2 \ x = Sin^2 \ x}\\\\\\= Cos^2 \ x \left(\dfrac{Sin^2 \ x}{Sin^2 \ x}\right)\\\\= Cos^2 \ x[/tex]
Which is the completely factored form of 12x4 + 39x3 + 9x2?
3x2(x – 3)(4x – 1)
3x2(x + 3)(4x + 1)
3x(x + 3)(4x + 1)
3x(x – 3)(4x + 1)
Answer:
The second option, 3x^2(x+3)(4x+1)
Step-by-step explanation:
Factor out the common term, which is 3x^2
This then becomes 3x^2(4x^2+13x+3)
Factor the inside term and it becomes
(3x^2)(x+3)(4x+1)
calculate problems one and two.
Answer:
Question 1) 2/3
Question 2) -3
Step-by-step explanation:
Question 1)
The formula of a slope is (increase in y)/(increase in x), so in the graph, all we need to do is find two precise points and look at the distance difference.
1. The two points that I've found were (0,3) and (3,5). The change in y is 3 --> 5, which is 2. The change in x is 0 --> 3, which is 3.
2. The slope will be 2/3.
Question 2)
In this question, we can consider n as x and f(n) as y.
1. The two points I chose were (4, -31) and (7,-40). The change in y is -31 --> -40, which is -9. The change in x is 4 --> 7, which is 3.
2. The slope will be -9/3.
3. -9/3 can be simplified to -3 since we can divide both the numerator and the denominator by 3.
4. The final slope will be -3.
Rebecca filled 28 glasses with orange juice for a camp breakfast. if each glass holds 1 cup of juice, how many quarts of orange juice did rebecca use?
The number of quarts of orange juice did Rebecca use is 7
Given that 28 glasses with orange juice are filled for a camp breakfast
Each glass holds 1 cup of juice
We need to find the number of quarts of orange juice did Rebecca use
We know that a quarts has 4 cups
We need to calculate the quarts from 28 glasses
Let the number of the quarts be x
So the equation formed is
4x = 28
Where x is number of quarts and 28 are the number of glasses
x = 7
Hence the number of quarts is 7
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The value of a company’s stock is represented by the expression x2 – 2y and the company’s purchases are modeled by 2x 5y. the company’s goal is to maintain a stock value of at least $5,000, while keeping the purchases below $1,000. which system of inequalities represents this scenario? x2 – 2y > 5000 2x 5y < 1000 x2 – 2y > 5000 2x 5y ≤ 1000 x2 – 2y ≥ 5000 2x 5y < 1000 x2 – 2y ≤ 5000 2x 5y ≤ 1000
Answer:
answer is (c)
May it help you
Option C. The inequality can then be written as x² - 2y ≥ 5000 and 2x + 5y <1000
How to write the inequality
Stock = x² - 2y
Purchase = 2x + 5y
Stock is said to be at least 5000 dollars. We can write this as
x² - 2y ≥ 5000
Then the purchase is said to be below 1000. This is written as 2x + 5y <1000
The inequality can then be written as x² - 2y ≥ 5000 and 2x + 5y <1000
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What comes next in the following series?
The next number in the series is 30.
What is series?It should be noted that series simply means the operation of adding values together in a data set.
In this case, it can be seen that the numbers are interchangeable between 30 and 31.
In this case, since 31 was the last number, the next number will be 30.
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What are the roots of the polynomial equation x superscript 4 baseline x squared = 4 x cubed minus 12 x 12? use a graphing calculator and a system of equations. round noninteger roots to the nearest hundredth.
The roots of the polynomial equation are -1.73, 1.73 and 0
How to determine the roots?The polynomial equation is given as:
[tex]x^4 + x^2 = 4x^3 - 12x + 12[/tex]
Next, we split the equation as follows:
[tex]y = x^4 + x^2[/tex]
[tex]y= 4x^3 - 12x + 12[/tex]
Next, we plot the equations on a graphing calculator
From the graph, we have the x-coordinates of the intersection points to be:
x = -1.73, 1.73 and 0
Hence, the roots of the polynomial equation are -1.73, 1.73 and 0
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5 Jack works as a part-time waiter. He earns $60 per weekday and $98 per day on weekends. (a) On a particular week, he works from Tuesday to Sunday. How much was he paid for that week? (b) Find his average wage rate per day.
Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Yeony2202, tysm for the help!
These two should be the points as then 2 points will remain on both sides
Slope
m=(7+2)/6+6m=9/12m=3/4Equation in point slope form
y+2=3/4(x+6)y=3/4x+6-2y=3/4x+4When x=-15
y=3/4(-15)+4y=-45/4+4y=(-45+16)/4y=--29/4Just above 7
Determine S9 of the series where a=6 and r=2
Hi
arithmetic serie mean that to change from a rank to an other, you add "r"
So : if 6 is S1, and 2 is pace,
then you need 8 hops to go from S1 to S9.
so you 'r going to add the reason 8 times.
so : S9 = 6 + 8 * 2 = 6 + 16 = 22
conclusion : S9 = 22
4. (06.02 MC)
Write an equation of a line that passes through the point (7,3) and is parallel to the line y =
y=-3x+3.0
x + 3. (5 points)
Answer:
Step-by-step explanation:
Givens
Line: y = 3x + 3
Point: (7,3)
Discussion
The easiest variation on line problems is one like this one. The reason is that all you need do is read the slope of the given line.
m = 3 of the given line. Also the slope of the new line.
What you have so far is
y = 3x + b
The point is used to find b -- the y intercept.
x = 7
y = 3
You are not given this, but what you want to think is that when x = 7, y = 3
Substitute into the new equation
3 = 3*7 + b
3 = 21 + b Subtract 21 from both sides.
3 - 21 = 21-21 + b
- 18 = b
Answer
y = 3x - 18
Answer:
-2/3x+23/3
Step-by-step explanation:
y= mx+c
where
m is the slope c is the y-intercept.
1-getting the slope:
we are given that the line we are looking for is parallel to the line
y=-2/3x+3
this means that the slope of the two lines are equal . comparing the general formula with the given line , we would find that the slope of the given lines -2/3.this means that the slope of the lines we are looking for is also -2/3
The equation of the line now becomes:y=-2/3x+c
2-getting the value of c
to get the value of c, we will use a point that belongs to the line (7,3),substitute in the equation and solve for c as follows:
y=-2/3x+c
3=(-2/3)(7)+c
3=-14/3+c
c=3+14/3
c=23/3
Based on the above, the equation of the line we are looking for is:
y=-2/3x+23/3
A sample of college students was asked how much they spent monthly on cell phone plans. approximate the standard deviation for the
cost.
monthly cell phone plan cost (5)
number of students
10.00-19.99
7
20.00-29.99
20
30.00-39.99
28
40.00-49.99
12
50.00-59.99
7
The mean and the standard deviation of the following data are 35.75 and 11.6765 respectively.
First, we'll find the mean (X) of the data:
[tex]X =\dfrac{(\sum x \times f) } {\sum f}[/tex]
So, the approximate standard deviation for the monthly cell phone plan cost is 9.87.
The mean is given by
[tex]\mu =\frac{\sum xf}{\sum f}[/tex]
Where x is the midpoint of the class and f is the frequency.
The calculation of mean and the standard deviation is shown in the below table:
Hence, the mean is calculated as:
mean is [tex]\mu =\frac{2359.67}{66}[/tex]
=35.75
The standard deviation is calculated as:
Standard deviation =[tex]\sigma[/tex] =[tex]\sqrt{\Dfrac{\sum f(x-\bar{x})^2}{n-1}}[/tex]
=[tex]\sqrt{\dfrac{8862.12121}{65}}[/tex]
=11.6765
Thus, the mean and the standard deviation are 35.75 and 11.6765 respectively.
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The table of standard deviation is attached below.
Drag the tiles to the correct boxes to complete the pairs.
Match the descriptions of cross sections of three-dimensional figures to their corresponding shapes.
Answer:
B, C, A
Step-by-step explanation:
Don't really know how to explain this.
What is the perimeter of the given quadrilateral?
y
0000
20 units
10 units
50 units
25 units
A
D
B
C
Answer:
20 units
Step-by-step explanation:
As you know that the quadrilateral is a square, you’ll just have to find the length of one side and multiply it by four. We can count and see that one side is 5 units.
5 * 4 = 20 units
You can also add the length of each of the four sides.
5 + 5 + 5 + 5 = 20
Hope that helps you! Please let me know if you need more help with this question. Have a great day!
Please help with these problems having trouble!!
The function f(x) is vertically compressed to form g(x) while the function f(x) is vertically compressed and then reflected across the x-axis to form h(x)
How to compare both functions?The functions are given as
f(x) =x^2
g(x) =3x^2
h(x) = -3x^2
Substitute f(x) =x^2 in g(x) =3x^2 and h(x) = -3x^2
g(x) =3f(x)
h(x) = -3f(x)
This means that the function f(x) is vertically compressed to form g(x)
Also, the function f(x) is vertically compressed and then reflected across the x-axis to form h(x)
See attachment for the functions g(x) and h(x)
Also, functions f(x) and g(x) have the same domain and range
While functions f(x) and h(x) have the same domain but different range
The complete table is:
x -2 -1 0 1 2
g(x) 12 3 0 3 12
h(x) -12 -3 0 -3 -12
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Find the perimeter of a parallelogram with corner points at (2,1), (4,5), (7,5), and (5,1)
Perimeter =
THANK YOU SO MUCHHH
Answer:
14 units
Step-by-step explanation:
Oops, I was solving for the area in the picture. You can still use the picture to find the perimeter. When I change the shape into a rectangle, you can see that the top and bottom lengths are 3 and the side lengths are 4. 3+3+4+4=14