Find all critical points for the function
4x + 6
x² + x + 1
on (-∞, ∞) and then list them (separated by commas) in the box below.
List of critical points:
f(x) =
Answers
Answer: [tex]\frac{-3+\sqrt{7}}{2}, \ \frac{-3-\sqrt{7}}{2}[/tex]
========================================================
Explanation:
Let
g(x) = 4x+6h(x) = x^2+x+1Each derivative is,
g ' (x) = 4h ' (x) = 2x+1which will be useful in the next section.
--------------
[tex]f(\text{x}) = \frac{4\text{x}+6}{\text{x}^2+\text{x}+1} = \frac{g(\text{x})}{h(\text{x})}\\\\f(\text{x}) = \frac{g(\text{x})}{h(\text{x})}\\\\[/tex]
Apply the derivative with respect to x. We'll use the quotient rule.
[tex]f(\text{x}) = \frac{g(\text{x})}{h(\text{x})}\\\\\\f'(\text{x}) = \frac{g'(\text{x})h(\text{x})-g(\text{x})h'(\text{x})}{\big[h(\text{x})\big]^2}\\\\\\f'(\text{x}) = \frac{4(\text{x}^2+\text{x}+1)-(4\text{x}+6)(2\text{x}+1)}{(\text{x}^2+\text{x}+1)^2}\\\\[/tex]
The critical value(s) occur when either...
f ' (x) = 0f ' (x) doesn't exist, when x is in the domain of f(x)The first criteria will be handled in the next section.
The second criteria is handled in the section after that.
-------------------------
f ' (x) is in the format A/B. It means f ' (x) = 0 leads to A/B = 0 and A = 0.
We set the numerator equal to zero and solve for x.
[tex]4(\text{x}^2+\text{x}+1)-(4\text{x}+6)(2\text{x}+1) = 0\\\\4(\text{x}^2+\text{x}+1)-(8\text{x}^2+16\text{x}+6) = 0\\\\4\text{x}^2+4\text{x}+4-8\text{x}^2-16\text{x}-6 = 0\\\\-4\text{x}^2-12\text{x}-2 = 0\\\\-2(2\text{x}^2+6\text{x}+1) = 0\\\\2\text{x}^2+6\text{x}+1 = 0\\\\[/tex]
From here we use the quadratic formula.
Plug in a = 2, b = 6, c = 1.
[tex]\text{x} = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\text{x} = \frac{-6\pm\sqrt{(6)^2-4(2)(1)}}{2(2)}\\\\\text{x} = \frac{-6\pm\sqrt{28}}{4}\\\\\text{x} = \frac{-6\pm2\sqrt{7}}{4}\\\\\text{x} = \frac{2(-3\pm\sqrt{7})}{4}\\\\\text{x} = \frac{-3\pm\sqrt{7}}{2}\\\\\text{x} = \frac{-3+\sqrt{7}}{2} \text{ or } \text{x} = \frac{-3-\sqrt{7}}{2}\\\\[/tex]
If x is equal to either of those values, then f ' (x) = 0 would be the case. Therefore, these are the critical points of f(x).
There may be other critical values. We'll still need to check the second criteria.
-------------------------
f ' (x) doesn't exist when we divide by zero.
Set the denominator equal to 0 and solve for x.
[tex](\text{x}^2+\text{x}+1)^2 = 0\\\\\text{x}^2+\text{x}+1 = 0\\\\[/tex]
Plug a = 1, b = 1, c = 1 into the quadratic formula.
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-1\pm\sqrt{(1)^2-4(1)(1)}}{2(1)}\\\\x = \frac{-1\pm\sqrt{-3}}{2}\\\\[/tex]
We have a negative number as the discriminant, which leads to complex number solutions in the form a+bi where [tex]i = \sqrt{-1}[/tex]
Therefore, there aren't any real number values for x that lead [tex](\text{x}^2+\text{x}+1)^2[/tex] to be zero.
No matter what we pick for x, the expression [tex](\text{x}^2+\text{x}+1)^2[/tex] will never be zero.
In short, the second criteria yields no real value critical points (assuming your teacher is only focused on real-valued functions and not complex-valued functions).
-------------------------
Summary:
The first criteria f ' (x) = 0 led to [tex]\text{x} = \frac{-3+\sqrt{7}}{2} \text{ or } \text{x} = \frac{-3-\sqrt{7}}{2}[/tex] as the critical valuesThe second criteria, f ' (x) doesn't exist where x is in the domain of f(x), leads to no critical values (assuming your teacher is not focusing on complex-valued functions).Therefore, the only critical values are [tex]\text{x} = \frac{-3+\sqrt{7}}{2} \text{ or } \text{x} = \frac{-3-\sqrt{7}}{2}[/tex]
-------------------------
Extra info:
A critical value is where a local/absolute min, a local/absolute max, or a saddle point would be at this x value. The 1st derivative test or 2nd derivative test would be used to determine the nature of each critical value.
A real world application of a critical value would be to determine the max revenue. Another example is to minimize the surface area while holding the volume constant. Linear regression relies on a similar concept.
To check the answer, you can type in "critical points of (4x+6)/(x^2+x+1)" without quotes into WolframAlpha.
Related Questions
Solve g−17≥17 . Graph the solution.
Answers
The inequality expression g - 17 ≥ 17 when solved has a solution of g ≥ 34
How to solve the given inequalityGiven the inequality expression
g - 17 ≥ 17
To solve the inequality g - 17 ≥ 17, we need to isolate the variable g on one side of the inequality.
We can do this by adding 17 to both sides of the inequality:
g - 17 + 17 ≥ 17 + 17
Simplifying, we get:
g ≥ 34
So the solution to the inequality is all values of g that are greater than or equal to 34.
We can graph this solution on a number line by placing a closed circle at 34 and shading to the right, to indicate that any value greater than or equal to 34 satisfies the inequality.
The graph looks like this the attached figure
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The ratio of men to women at the picnic is 4:5,if there are 819 people, how many men are there in the picnic
Answers
Answer:
819/5 is the correct answer that I think
HELP ASAP PLEASE!!!!!!!!
Answers
The inverse function of f(x) = (x + 5)² on the domain x >= -5 is given as follows:
[tex]f^{-1}(x) = \sqrt{x} - 5[/tex]
The domain of the inverse function is given as follows:
x >= 0.
How to obtain the inverse function?The function for this problem is defined as follows:
f(x) = (x + 5)² on the domain x >= -5.
The range of the function is y >= 0, as the vertex is at (-5,0) and the function is increasing over it's domain, hence the domain of the inverse function, which is the range of the original function, is given as follows:
x >= 0.
To obtain the inverse function, wee exchange x and y in the definition of the function, and then isolate y, hence:
x = (y + 5)²
[tex]y + 5 = \sqrt{x}[/tex]
[tex]y = \sqrt{x} - 5[/tex]
[tex]f^{-1}(x) = \sqrt{x} - 5[/tex]
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Which shows the best estimate of the quotient of 523 +67?
O between 7 and 8
O between 8 and 9
O between 70 and 80
O between 80 and 90
Answers
Help please !!
The volume of a fixed amount of a gas varies directly as the temperature 7 and inversely as the pressure P. Suppose that I'-70 cm³ when 7-420 kelvin
kg
kg
and P-18-
Find the temperature when
is 60 cm and P-7
X
Answers
Answer:
First question:
We can start by setting up the formula that relates the volume V, temperature T, and pressure P:
V = k * (T/P)
where k is a constant of proportionality. We can solve for k by plugging in the given values for V, T, and P:
70 = k * (420/18)
Simplifying the right side of the equation, we get:
70 = k * 23.3333
Dividing both sides by 23.3333, we get:
k = 3
Now we can use this value of k to find the temperature T when V is 60 cm and P is 7:
60 = 3 * (T/7)
Simplifying the equation, we get:
T/7 = 20
Multiplying both sides by 7, we get:
T = 140
Therefore, the temperature when V is 60 cm and P is 7 is 140 kelvin.
Second question: We can start by using the formula that relates the time (T), distance (D), and speed (S):
D = S * T
Since the distance between the two cities is constant, we can set the distances for the two cars to be equal:
35 * 9 = 21 * T
Simplifying the right side of the equation, we get:
315 = 21T
Dividing both sides by 21, we get:
T = 15
Therefore, the trip takes 15 hours for a car moving at 21 mph.
Hopefully this helps you! I'm sorry if it wrong. If you need more help, ask me! :]
In a quadrilateral ABCD, AB is parallel to DC, and AD is parallel to BC. Find the perimeter of △COD if the diagonals of the quadrilateral intersect each other at point O and AC=40 in, BD=50 in, AB=25in.
Answers
Answer:
Step-by-step explanation:
In quadrilateral ABCD, we have:
AB is parallel to DC
AD is parallel to BC
AC = 40 in (given)
BD = 50 in (given)
AB = 25 in (given)
We can use the fact that opposite sides of a parallelogram are equal in length to find the length of CD:
CD = AB = 25 in
Next, we can use the fact that the diagonals of a quadrilateral bisect each other to find the length of AO and OC:
AO = BO = BD/2 = 50/2 = 25 in
OC = OD = AC/2 = 40/2 = 20 in
Now we can use the triangle inequality to find the perimeter of triangle COD:
CO + OD + CD > OC
CO + 20 + 25 > 20
CO + 45 > 20
CO > -25
CO + OC > CO
CO + 20 > 0
CO > -20
CO + CD > OD
CO + 25 > 20
CO > -5
Therefore, the possible range of values for CO is:
-20 < CO < -5
However, since lengths cannot be negative, we can take the absolute value of CO to get:
5 < CO < 20
So the perimeter of triangle COD is:
CO + OD + CD = CO + 20 + 25 = CO + 45
Substituting the possible range of values for CO, we get:
5 + 45 < CO + 45 < 20 + 45
50 < CO + 45 < 65
So the perimeter of triangle COD is between 50 in and 65 in.
Therefore, the perimeter of triangle COD is between 50 in and 65 in, but the exact value depends on the length of CO, which is between 5 in and 20 in.
Factor completely.
9 - 25x2
Answers
Answer:
-41 is the ANS.
Step-by-step explanation:
9-25*2
9-50
-41
Round the decimal number to the nearest tenth: 285.429 can you show steps?
Answers
"To round the decimal number 285.429 to the nearest tenth, we need to look at the digit in the hundredths place, which is 2.
If the digit in the hundredths place is 5 or greater, we round up the digit in the tenths place. If it is less than 5, we leave the digit in the tenths place as it is.
In this case, the digit in the hundredths place is 2, which is less than 5. Therefore, we leave the digit in the tenths place as it is, which is 2.
So, rounding 285.429 to the nearest tenth gives us:
285.4
Therefore, the rounded value of the decimal number 285.429 to the nearest tenth is 285.4." (ChatGPT, 2023)
Question 1
Find the unpaid balance, new interest, and purchasing power on the credit card after the minimum monthly payment is made. The interest charge for unpaid balances is 18% per year.
Credit Card Balance = $5000
Credit Limit = $5000
Minimum Payment = $125.00
Answers
Assuming that there are no other transactions or fees on the credit card, here's how to calculate the unpaid balance, new interest, and purchasing power on the credit card after the minimum monthly payment is made:
1.) Unpaid Balance: The unpaid balance is the amount of the credit card balance that remains after making the minimum monthly payment. In this case, the minimum monthly payment is $125, so the unpaid balance would be:
$5000 - $125 = $4875
2.) Interest Charge: The interest charge for unpaid balances is 18% per year. To calculate the monthly interest rate, divide the annual rate by 12:
18% / 12 = 1.5%
3.) To calculate the interest charge for the month, multiply the unpaid balance by the monthly interest rate:
$4875 x 1.5% = $73.13
So the new interest charge for the month is $73.13.
4.) Purchasing Power: Purchasing power refers to the amount of credit that is available on the credit card after making the minimum monthly payment and accounting for any interest charges. To calculate the purchasing power, subtract the unpaid balance and interest charge from the credit limit:
$5000 - $4875 - $73.13 = $51.87
So the purchasing power on the credit card after the minimum monthly payment is made is $51.87.
If sin 0 = -2/3which of the following are possible?
Answers
Is sin (θ) = - 2/ 3, the options that are possible include:
A) sec(θ) = -3/2 and tan(θ) = 2/√5C) cos(θ) = -(√5)/3 and tan(θ) = 2/√5How to find the possible expressions?Since sec(θ) is negative, cos(θ) is also negative (sec(θ) = 1/cos(θ)). This means θ is in the second or third quadrant, but since sin(θ) is negative, θ must be in the third quadrant. Now let's check if the given tan(θ) value is correct:
tan(θ) = sin(θ)/cos(θ)
Since we already know that cos(θ) is negative, we have cos(θ) = -(√5)/3.
Now calculate tan(θ):
tan(θ) = (-2/3) / (-(√5)/3) = 2/√5
The given values in option A are correct.
cos(θ) = -(√5)/3 and tan(θ) = 2/√5
These are the same as in option A. So, this option is also possible.
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Evaluate the given expression and show the steps, please.
Answers
Answer:
80
Step-by-step explanation:
The variable "n" is not defined, but rather "k" is used in the summation. Assuming that "n" was meant to be "k", the expression should be:
s4 = ∑ k=1 to 4 of 2(3^(k-1))
To evaluate this expression, we need to substitute each value of k from 1 to 4 into the expression 2(3^(k-1)), and then sum up the results.
Starting with k = 1:
2(3^(1-1)) = 2(3^0) = 2(1) = 2
Moving on to k = 2:
2(3^(2-1)) = 2(3^1) = 2(3) = 6
Next, k = 3:
2(3^(3-1)) = 2(3^2) = 2(9) = 18
Finally, k = 4:
2(3^(4-1)) = 2(3^3) = 2(27) = 54
Now we add up these four results:
s4 = 2 + 6 + 18 + 54 = 80
Therefore, the value of s4 is 80.
2074 Set B Q.No. 17 The compound interest on a certain sum at a certain rate is Rs. 204 in 2 years and simple interest at the same rate is Rs. 300 in 3 years. Find the sum and the rate of interest.
Answers
Answer:
Answer equals 2500 according to the question
a) Copy and complete the table below for the graph of y = 2x.
21=33 9 1 2
1-4-2 A
b) The lines y = x and y = 2x are shown on the axis below.
Write down one similarity and one difference between these lines.
f y-20 У=2
5-
4-
3-
1-
654-32-18 1 23 45 6*
1-2
--3・
-4・
-5
-6-
Answers
x y
0 0
1 2
2 4
3 6
4 8
5 10
b) One similarity between the lines y = x and y = 2x is that they both pass through the origin (0,0). This means that when x = 0, y = 0 for both lines.
One difference between the lines is their steepness or slope. The slope of y = x is 1, which means that for every 1 unit increase in x, there is a 1 unit increase in y. The slope of y = 2x is 2, which means that for every 1 unit increase in x, there is a 2 unit increase in y. This means that the line y = 2x is steeper than the line y = x.
What will be the reminder. When 362*461*2761will be divided by 6
Answers
The remainder when 362 is divided by 6 is 2 (362 ÷ 6 = 60, with a remainder of 2).
The remainder when 461 is divided by 6 is 5 (461 ÷ 6 = 76, with a remainder of 5).
The remainder when 2761 is divided by 6 is 1 (2761 ÷ 6 = 460, with a remainder of 1).
Multiplying these remainders together, we get:
2 x 5 x 1 = 10
Therefore, the remainder when 362 x 461 x 2761 is divided by 6 is 10.
Answer:
10
Step-by-step explanation:
362/6 = 60R2
461/6 = 76R5
2761/6 = 460R1
2x5x1 = 10
complete the table based on the pattern you see
Answers
The figures to complete the table, based on the pattern, would be 6. 20, 7.00.
How to complete the table ?To complete the table, you need to find the common difference between the values in B which is :
= 4. 6 - 3. 8 = 5. 4 - 4. 6
= 0. 80 = 0. 80
The next two values would therefore be :
= 5. 4 + 0. 80 = 6. 20 + 0. 80
= 6. 20 = 7. 00
The complete table then is :
A - 5, 6, 7, 8, 9
B- 3.8, 4.6, 5.4, 6. 20, 7. 00
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The full question is:
Complete the table based on the pattern you see:
A- 5, 6, 7, 8, 9
B- 3.8, 4.6, 5.4, ____, ____,
Helppp ! , Use substitution to solve each system of equation and must show checks !!!
Answers
Collect terms
3x = 9
Divide by 3
X= 3
____________________
Plug 3 for x
Y= 2•3
Y= 6
——————————————
Check:
{ 6 = 2•3
{ 5•3-6 = 9
{ 6 = 6
{ 9 = 9
Solution:
( X, Y ) = ( 3, 6 )
This graph shows how the time required to complete an online shopping transaction is related to the number of products being purchased.
y
x
10
20
30
40
50
60
70
80
90
100
10
20
30
40
50
60
70
80
90
100
0
Time (seconds)
Products being purchased
Online shopping
What is the rate of change?
Write your answer as a decimal or integer.
seconds per product
Answers
Answer:
1 product
Step-by-step explanation:
Given the equation that shows how the time required to complete an online shopping transaction is related to the number of products being purchased as;
t = 24p + 27
t represents the time required to complete the transaction
p is the product purchased
If it takes 51 seconds to complete a transaction, to get the amount of product purchased, we will substitute t = 51 into the expression and find p as shown;
51 = 24p + 27
Substract 27 from both sides
51-27 = 24p + 27 - 27
24 = 24p
24p= 24
p = 24/24
p = 1
Hence only 1 product is being purchased
A cylinder has a volume of 1 and one third in3 and a radius of one third in. What is the height of a cylinder? Approximate using pi equals 22 over 7.
42 over 6 inches
42 over 9 inches
42 over 11 inches
42 over 22 inches
Answers
The height of the cylinder is approximately 42/11 inches. The answer is option C.
What is the formula for the volume of the cylinder?
The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.
We are given that the volume of the cylinder is 1 and one-third in^3 and the radius is one-third in. Substituting these values into the formula, we get:
1 and one-third = 4/3
V = π(1/3)²h = 4/3
Simplifying the equation, we get:
h = (4/3) / (π(1/3)²) = (4/3) / (π/9) = (4/3) * (9/π) = 12/π
Approximating π as 22/7, we get:
h ≈ (12/π) ≈ (12/(22/7)) = 42/11 inches
Therefore, the height of the cylinder is approximately 42/11 inches. The answer is option C.
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Find exact values for the following:
Answers
Answer:
-sqrt(2)
-sqrt(2)
1
1
Step-by-step explanation:
se the equations shown in the table below to answer the following question.
Equation A -2x -6y=36 -4r
Equation B 2(3x-3y)=36
Equation C 4r-6y+36=-2r
Which two of the three equations create a system of equations with no solution?
Explain how you determined your answer.
Respond in the space provided.
Answers
Quadrilateral ABCD is shown.
-5
A
3
N
6
2
5-
3-
2-
1-
10
-1-
-24
-3-
-4-
-5-
A
B
(a) Work out the coordinates of C when ABCD is
Rotated 900 clockwise about 0
then
translated by
1 2
3
D
с
4
5
[2 marks]
Answers
Answer:
C'(-5, -2)
Step-by-step explanation:
You want the coordinates of point C(4, 1) after rotation 90° CW about the origin and translation by (-6, 2).
RotationThe transformation accomplished by rotation 90° clockwise is ...
(x, y) ⇒ (y, -x)
TranslationThe translation by (-6, 2) adds those values to the coordinates:
(x, y) ⇒ (x -6, y +2)
Both transformationsCombined, the transformations give you ...
(x, y) ⇒ (y -6, -x +2)
C(4, 1) ⇒ C'(1 -6, -4 +2) = C'(-5, -2)
The coordinates of C after the transformation(s) are (-5, -2).
At Brian’s Bookstore, 0.3 of the shelves hold mysteries, 25% of the shelves hold travel books, and 7/20 of the shelves hold children’s books. Which type of book covers the most shelf space in the store? Explain how you arrived at your answer
Answers
Answer:
Childrens books
Step-by-step explanation:
What is a fraction?A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.
To solve for which type of book covers the most space, we need to first convert 25% from a percentage to a fraction.
What is a percentage?A percentage is a ratio, or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.
If percentages are fractions of 100, then 25% as a fraction would look like this:
25% = [tex]\frac{25}{100}[/tex]We can do the same to 0.3, although it isn't a percentage.
0.3 = 0.30 = [tex]\frac{30}{100}[/tex]Now, we need to convert the fractions ([tex]\frac{25}{100}[/tex], [tex]\frac{30}{100}[/tex], [tex]\frac{7}{20}[/tex]) to have a common denominator.
What is a common denominator?A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.
To make [tex]\frac{7}{20}[/tex] have a denominator of 100, we can multiply the 20 by 5 to get 100.
7 × 5 = 4520 × 5 = 100Now the fraction is [tex]\frac{35}{100}[/tex].
The three fractions given are:
[tex]\frac{30}{100}[/tex] (Mystery books)[tex]\frac{25}{100}[/tex] (Travel books)and [tex]\frac{35}{100}[/tex] (Children books)The larges given fraction is [tex]\frac{35}{100}[/tex] meaning that the children's books cover the most shelf space in the store.
julia needs to make 500 hamburgers for the a school function... hamburger patties are sold in packets of 12
how many packets of patties should she buy ?
Answers
Julia needs to buy 42 packets of patties to make 500 hamburgers for the school function
What is an equation?An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.
Hamburger patties are sold in packets of 12. Let x represent the number of packet of patties to be bought to make 500 hamburgers. Hence:
12x = 500
x = 500/12
x = 41.67
x≅ 42
Julia needs to buy 42 packets
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simplify 1/2-1/x-y+2/(x-y)
Answers
Answer: x^2-xy-2x^2y+2xy^2+2x+2y over 2x(x - y)
Step-by-step explanation:
because im that guy
Kareem is considering buying a guitar priced at $179.99 He has $200 cash with him. He uses predict whether he has enough money.
Add 10% and 1%
The current HST rate is 13%
a) Round the price of the guitar to a convenient
amount:
b) What is 10% of the rounded price
c) What is 1% of the rounded price
d) How many 1%s do you need?
e) What is the estimated tax?
f) Add the estimated tax to the rounded price.
Does Kareem have enough money with him? YES OR NO
Answers
Using the concept of percentage, we can deduce that Kareem does not have enough money with him
Does Kareem have enough money with him?To solve the questions given, we need to apply the concept of percentage on some.
a) Rounding the price of the guitar to a convenient amount, we get $180.
b) 10% of the rounded price is: 0.1 x $180 = $18.
c) 1% of the rounded price is: 0.01 x $180 = $1.80.
d) To get the estimated tax, we need to multiply the rounded price by the HST rate: 0.13 x $180 = $23.40. Dividing this by $1.80, we get approximately 13.
e) The estimated tax is $23.40.
f) Adding the estimated tax to the rounded price, we get $180 + $23.40 = $203.40.
Since Kareem has $200 cash with him, he does not have enough money to buy the guitar at the estimated price of $203.40. Therefore, the answer is NO.
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Factorise 3-6x I don’t know how to do it
Answers
Answer:
Step-by-step explanation:
-3(2x-1)
Step by step
3 - 6x is your expression
You want to factor out any number or variable that can be divided into any number or variable in the term
3 is divisible by 3 and 6 is divisible by 3 so 3 goes outside the parentheses
x is NOT divisible in 3 although it is in 6x
It has to work with every part of the term so x cannot be factored out
3 ( )
Now divide the two parts of your term by 3 and put your answer in the parentheses
3/3 - 6x/3
3 ( 1 - 2x )
You can check your work by distribution
3 ( 1 - 2x )
3 - 6x
This was your original expression! Problem solved
Image shows 2 joined rectangular prisms. One is 10 in. in length, 6 in. in height, and 3 in. in width. The second is 4 in. in length, 3 in. in width, and 6 in. in height. Which expressions can be added to find the volume of the solid figure? A. 10 × 3 and 10 × 6 B. 10 × 3 × 6 and 4 × 3 × 6 C. 10 × 4 and 3 × 6 D. 10 × 3 × 3 and 10 × 3 × 6
Answers
The correct option to determine the value of volume of solid figure is: B. 10 × 3 × 6 and 4 × 3 × 6.
Explain about the rectangular prisms?One of the three-dimensional shapes that can be created with six pairs with parallel lines is a rectangular prism. Three-dimensional shapes in this category include cubes and cuboids. Prisms come in a variety of classifications based on the base.
Volume of rectangular prism = length * width * height
rectangular prism A:
length = 10 in.
Width = 3 in.
height = 6 in.
rectangular prism B:
length = 4 in.
Width = 3 in.
height = 6 in.
Thus,
volume of the solid = volume of rectangular prism A + volume of rectangular prism A
volume of the solid = 10*3*6 + 4*3*6
Thus, the correct option to determine the value of volume of the solid figure is: B. 10 × 3 × 6 and 4 × 3 × 6.
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Philip and Laura want to build a pool in their backyard. The length and width of the pool can be represented by the equation f(x)=(x-3)(5x+2) feet. What is the area of Philip and Laura’s pool? You must show your work and include your units.
Answers
Answer:
5x^2 - 19x + 15
Step-by-step explanation:
We must multiply the pool's length and width to determine its area. We can factor the equation f(x)=(x-3)(5x+2) to determine the length and width:
f(x) = (x-3)(5x+2)
f(x) = 5x^2 - 13x - 6
One of the parameters is the pool's length (x-3), while the other is its breadth (5x+2). We multiply these two elements to determine the area:
Area is length times width (x-3)
(5x+2)
By extending this statement using FOIL (First, Outer, Inner, Last), we may make it simpler:
Area is equal to 5x^2 - 13x - 6x + 15
Area: 5x^2 - 19x + 15
The pool at Philip and Laura's home is therefore 5x^2 - 19x + 15 square feet in size. We are unable to establish the precise square footage of the pool because we were not given a specific figure for x.
what is 19/100,also written into decimals
Answers
19/100 into decimals is 0,19
To solve this, we must knowTo write a fraction based on 10/100/1000... you must move the decimal point to the left the number of times equivalent to the number of zeros in the base.
In this case, base 100 has two zeros. Then move two squares to the left.
[tex]\begin{array}{l}\bf 19\\\sf {0}{,}\!\overset{\overset{2}{\curvearrowleft}}{1}\!\overset{\overset{1}{\curvearrowleft}}{9}\\\\\bf \dfrac{19}{100}=0{,}19\end{array}[/tex]
Did you see how easy the conversion was under these circumstances?
If you have any question about this solution, you can ask me in the comments :)
Consider the equation: x2 18x +72 = 0
A) First, use the "completing the square" process to write this equation in the form (x + D)² =
and enter your results below.
x² 18x+72=0 is equivalent to:
=
Preview left side of eqn:
B) Solve your equation and enter your answers below as a list of numbers, separated with a com
where necessary.
Answer(s): 6,12
Answers
Using square process method, we can get the values of x to be 12 and 6.
Define square process?The formula a (x + m)2 + n = a (x + m)2 + n is the simplest to remember while learning how to complete the square technique.
The following formulas can be used to compute m and n in this situation: m = b/2a and n = c - (b2/4a).
From the question,
x² - 18x + 72= 0
⇒ x² - 18x = -72
Complete the square by adding the half of the square of the coefficient of x to both sides of the expression as shown:
⇒ x² - 18x + (18/2) ² = -72 + (18/2) ²
⇒ x² - 18x + 9² = -72 + 81
⇒ (x-9) ² = 9
⇒ x-9 = ± 3
So, values of x are:
x = 3 + 9
= 12
x = -3 + 9
= 6
Therefore, the values of x are 12 and 6.
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