O POLYNOMIAL AND RATIONAL FUNCTIONSFinding the maximum or minimum of a quadratic function
Given
The function,
[tex]g(x)=x^2+4x[/tex]To find:
The maximum or minimum value of the function, and where does it occur.
Explanation:
It is given that,
[tex]g(x)=x^2+4x[/tex]That implies,
Set g(x)=y.
Then,
[tex]\begin{gathered} y=x^2+4x \\ y=(x+2)^2-4 \\ y+4=(x+2)^2 \end{gathered}[/tex]Here, a=1>0.
Then, the parabola opens up.
And, k is the minimum functional value, it occurs when x = h.
Therefore,
1) g(x) has a minimum value.
2) g(x)'s minimum value is -4.
3) And it occurs at x = -2.
how do I solve 9-2x=35
In order to solve the expression:
[tex]9-2x=35[/tex]We operate inn such a manner that x is left alone, that is:
[tex]9-2x=35\Rightarrow9=35+2x\Rightarrow9-35=2x[/tex][tex]\Rightarrow-26=2x\Rightarrow-13=x[/tex]We have our expression 9 - 2x = 35.
In order to solve for x, we try and leave x alone, that is, we sustract 9 from both sides of the operation:
9 - 9 - 2x = 35 -9 => -2x =26
Now that we have this, we proceed to eliminate -2 from the side of x, for that we divide both sides by -2, that is:
(-2/-2)x=(26/-2) => x = -13
Find the total surface area of the following cone. leave your answers in terms of PI
Given
height of cone = 4cm
Base radius of cone = 3cm
Find
TSA of cone
Explanation
[tex]l=\sqrt{4^2+3^2}=\sqrt{16+9}=5[/tex]We know that TSA of cone is
[tex]\begin{gathered} TSA=\pi r(r+l) \\ =\pi(3)(3+5) \\ =\pi(3)(8) \\ =24\pi cm^2 \end{gathered}[/tex]Final Answer
[tex]TSA=24\pi cm^2[/tex]The angel pitch of a roof is safest when measuring between 18 - 27. According to these guidelines, is the roof pictured in the image safe? I cannot figure out where to start with this question nor how to solve it.
we know that
YZ=RV+VQ ----> by addition segments postulate
substitute given values
30=RV+15
so
RV=30-15=15 ft
that means
Point V is the midpoint of the segment RQ
triangle RPQ is an isosceles triangle
mFind out the value of angle x
tan(x)=4/15 ------> by TOA
x=tan^-1(4/15)
x=14.93 degrees
The angle x is not between 18 - 27
therefore
The roof Is not safeSolve the equation p + 7 = −15 for p. −22 22 −8 8 need help
An equation is a collection of variables and constants. The value of p for the given equation p + 7 = −15 is p = -22 so option (A) is correct.
What is the equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
The equation must be constrained with some constraints.
As per the given equation,
p + 7 = -15
Subtract both sides by 7
p + 7 - 7 = -15 - 7
p + 0 = -22
p = -22
Hence "An equation is a collection of variables and constants. The value of p for the given equation p + 7 = −15 is p = -22 so option (A) is correct".
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Which of (3, 5), (4, 6), (5, 7), and (6, 8) are solutions to y = x + 2?
O(3, 5) and (4, 6)
O(4, 6) and (5, 7)
Onone
O all
All of them would be the answer.
What is the basic component of solving an equation?The left side and right side of every equation should be equal. It is essential that both parties are on an even playing field. An equation must contain the following elements: coefficients, variables, operators, constants, terms, expressions, and an equals sign. Any one, some, or all of these terms may circle the equal sign in an equation.
Rule of Thumb for Equation Solving:
Remove parentheses from each side of the equation and combine similar phrases to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.Here, we will put the values of x and y coordinates in the equations:
5=3+2
6=4+2
7=5+2
8=6+2
Hence, the right and left side of the equation is equal.
Thus, all of them are correct answers. It would just be all of them.
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is when you multiply with any number with a negative or possitive the asnwer is also suppossd to also have a negative and possitive . Also will i get the answer wrong if i dont put any of the sighn ?
If we mutiply a positive number with a positive or negative sign we get the answer as number with sign.
[tex]eg\colon5\times(+1)=5,5\times(-1)=-5[/tex]If we mutiply a negative number with sign the answer will be,
[tex]eg\colon(-5)\times(+1)=-5,)-5\times(-1)=5_{}[/tex]Thus, if we mutiply a negative to a positive number the sign gets reversed.
2. Invasive weed species can grow quickly. One variety grows up to 1.65 ft per day.
I NEED HELP .How fast in inches per minute can this weed grow? Show your work using the correct conversion factors and make sure all conversion factors are labeled with appropriate units. You should have more than one conversion factor shown.
Invasive weed grows at a rate of 0.0011 ft per minute a day
In the above question, it is given as
Invasive weed grows really fast and the rate of its growth is being provided as follows
The rate at which the weed is growing a day is = 1.65 ft
We need to find the, rate at which this weed is growing per minute
So, to do this, we'll find the growth in 1 min
In 24 hours growth is = 1.65 ft
Conversion factors
We know, 1 hour = 60 minutes
In 1 min growth is = [tex]\frac{1.65}{24 . 60}[/tex]
Here, we have multiplied with 60 in the denominator to convert hours into minutes
After solving the fraction we'll get
Growth in 1 min of the weed = 0.0011 ft
Hence, Invasive weed grows at a rate of 0.0011 ft per minute a day
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please break down 145 + 216 with the hundreds tens and ones.
Step 1:
Sum the numbers
[tex]145+216=361[/tex]Step 2:
Express the number in Hundreds, Tens, and Ones
3 has a value of 300
6 has a value of 60
1 has a value of 1
Therefore, to express 361 in hundreds, tens and ones
Most cars depreciate in value as they age. A specific model car purchased for $14 995depreciates by 28% per year. The function that models it value over time
(a)
Graphing the function from x = 0 to x = 10:
b)
Evaluate the function for x = 5
[tex]\begin{gathered} V\left(5\right)=14995\left(0.72\right)^5 \\ V\left(5\right)\approx2901.41 \end{gathered}[/tex]Answer:
$2901.41
c)
Let's solve the following inequality:
[tex]V\left(x\right)<1000[/tex]so:
[tex]\begin{gathered} \left(0.72\right)^x<\frac{1000}{14995} \\ x<\frac{1}{ln\left(0.72\right)}*ln\left(\frac{1000}{14995}\right? \\ x>8.2 \end{gathered}[/tex]Approximately after 8.2 years.
d)
[tex]4300=14995\left(y\right)^5[/tex]Let's solve the previous equation in order to find the rate y:
[tex]\begin{gathered} y^5=\frac{4300}{14995} \\ y=\sqrt[5]{\frac{4300}{14995}} \\ y\approx0.78 \end{gathered}[/tex]The depreciation rate is approximately:
[tex]0.78[/tex]It depreciates 22% per year
- The simple interest equation is I = Prt, where I is the interest
-
earned, P is the principal investment, and t is the amount of time
(in years).
Use the formula to solve the problem: If a $5,000 investment earns
$1,57 interest over 18 years, what is the annual interest rate?
% (enter your answer as a percent and do not round)
T=
The rate of the given amount 0.001744%
What is Simple Interest?
Simple interest is a quick and easy way to calculate interest on a loan. Simple interest is the daily interest rate multiplied by the principal multiplied by the number of days until the next payment.
Given,
Principal = $5000
Interest = $157
Time = 18years
The formula for simple interest:
I = P x R x T
157 = 5000 x R x 18
R = 157 / 5000 x 18
R =0.001744%
Hence, the annual rate of interest is 0.001744%
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Which equation represents a proportional relationship between x and y?
A.y=0.25x+1.25
B.y=4x
C.y=14x−2
D.y=23x−23
y=4x equation represents a proportional relationship between x and y.
Form the question
Only B doesn't have constant
y=4x
x=y/4
So option 2 is correct.
The formula y=kx y = k x can be used to describe a proportional relationship, where k is the constant ratio.
y = k x, where is the proportionality constant, is the equation that depicts a proportional relationship, or a line. Find k and create the equation by using k = y x from a table or graph. Tables, diagrams, and equations can all be used to depict proportional relationships.
The graph of a straight line through the origin with a slope equal to the unit rate can be used to depict a relationship where two quantities are related proportionally. is equal to k, where k is the unit rate, for each point (x, y) on the graph.
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(a) Rewrite as a logarithmic equation.e^y=2(b) Rewrite as an exponential equation.In x=9
Let's rewrite it the first one
[tex]e^y=2[/tex][tex]\begin{gathered} \log _ee^y=\log _e2 \\ y=\log _e2 \end{gathered}[/tex]When we apply, log on both sides. We have the logarithm of a power equal to its exponent that is why we have y on the left side.
Rewriting the second one:
[tex]\begin{gathered} \ln (x)=9 \\ \log _ex=9 \\ x=e^9 \end{gathered}[/tex]Since the Natural Logarithm is log in the base "e" we can say that x is equal to e raised to 9
Your lunch in the hospital cadet cost $6.50. Based on working 50weeks per year , how much will you spend on your lunch per year?
Answer:
Step-by-step explanation:
if they are working 7 days a week, lunch will cost $2,275
hope this helped :)
M) Point K is the midpoint of JL. JK = 6x + 9 andKL = 5x + 12. Find JK.1) 272) 303) 18
Answer:
The right option is 1) 27
Explanation:
According to the given data we have the following:
K is the midpoint of JL.
JK = 6x + 9
KL = 5x + 12
K is the midpoint of JL, hence, JL=JK+KL
So, to find JK we would equal JK with KL
So, 6x + 9=5x + 12
6x-5x=12-9
x=3
Therefore, JK=6(3)+9
JK=18+9
JK=27
Therefore, the right option is 1) 27
f(x)=4x^{2}-8x-5 f(x)=4x 2 −8x−5 \text{Find }f(-7) Find f(−7)
The value of given quadratic equation at -7 is 247.
What is quadratic equation?
The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of:
ax² + bx + c = 0
where x is the unknown variable and a, b and c are the constant terms.
given ,f(x) = [tex]4x^{2} -8x-5[/tex] to find f(-7)
f(-7)= 4(49)-8(-7)-5
=196+56-5
=247
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Find the solution of each equation if the replacement set is 10 11 12 13
If we replace with 10:
[tex]\frac{10}{5}=2[/tex][tex]2=2[/tex]10 is a solution.
Let's try with 11:
[tex]\frac{11}{5}=2[/tex][tex]2.2\ne2[/tex]11 is not a solution.
WIth 12:
[tex]\frac{12}{5}=2[/tex][tex]2.4\ne2[/tex]12 is not a solution
WIth 13
[tex]\frac{13}{5}=2[/tex][tex]2.6\ne2[/tex]13 is not a solution.
Therefore, the solution to this equation is 10
If a linear function has no restrictions, the domain of the function is
The Domain of the linear function with no restriction is (-∞,∞)
What is a linear function?A linear function is of the form f(x) = ax+ b, where a and b are constants , x is independent variable and the graph of such function is a straight line.
Domain of f is the set of all values of x for which function f is defined.
Given that the linear function has no restrictions , means the values of the function can be from anywhere of real line.
-∞ < f(x) < ∞
⇒ -∞ < ax+ b < ∞ , where a≠0
⇒ -∞- b < ax+ b-b < ∞ -b
⇒ -∞ < ax < ∞ ( adding or subtracting anything from infinity does not
make any difference)
⇒ -∞ < x < ∞
Thus the domain of the linear function which has no restriction is (-∞,∞)
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Store A charges $10.00 for a pack of hotdogs and $8.00 for a pack of hotdog buns. Store B charges $11.00 for a pack of hotdogs and $7.50 for a pack of hotdog buns. Suppose you buy x packs of hotdogs and y packs of hotdog buns at both stores. You end up spend $80.00 at store A and $81.50 at store B. Which system of equations represents the total amount of money you spent on hotdogs and hotdog buns at each store?
Taking into account the definition of a system of linear equations, the system of equations that represents the total amount of money you spent on hotdogs and hotdog buns at each store is
10x + 8y= 80
11x + 7.50y= 81.50
System of linear equationsA system of linear equations is a set of linear equations that have more than one unknown, appear in several but not necessarily all of the equations, and are related by the equations.
In the systems of equations, the values of the unknowns must be found, with which when replacing, they must give the solution proposed in both equations.
System of equation in this caseIn this case, a system of linear equations must be proposed taking into account that:
"x" is the packs of hotdogs buns at both stores."y" is the packs of hotdog buns at both stores.You know that:
Store A charges $10.00 for a pack of hotdogs and $8.00 for a pack of hotdog buns. You end up spend $80.00 at store A.Store B charges $11.00 for a pack of hotdogs and $7.50 for a pack of hotdog buns.You end up spend $81.50 at store B.The system of equations to be solved is
10x + 8y= 80
11x + 7.50y= 81.50
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Please help me!! The question is in the attachment!!
Using it's concept, the probabilities are given as follows:
b) P(B|C) = 0.1429.
c) P(not A|B) = 0.8.
What is a probability?The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
For item b, the conditional probability can be written as follows:
P(B|C) = P(B and C)/P(C).
From the diagram, we have that:
P(B and C) = P(5) = 0.05.P(C) = P(5) + P(6) = 0.05 + 0.3 = 0.35.Hence:
P(B|C) = 0.05/0.35 = 0.1429.
For item c, the conditional probability is:
P(not A|B) = P(not A and B)/P(B).
From the diagram, these probabilities are:
P(not A and B) = P(4) + P(5) = 0.15 + 0.05 = 0.20.P(B) = P(3) + P(4) + P(5) = 0.05 + 0.15 + 0.05 = 0.25.Hence:
P(not A|B) = 0.20/0.25 = 0.8.
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20Which equation, when paired with the equation below, will create a system of equations with infinitelymany solutions?3x - 8y = -5A. 3x+ 8y = -5B.6x+ 16y = -10C.6x- 16y = -10D. -8x+ 3y = 5
ANSWER
C. 6x - 16y = -10
EXPLANATION
An equation or a pair of equations has infinite solutions when all numbers are solutions of the equation(s).
The left and right hand side of the equation(s) are the same.
So, we have to look for the equation such that the case happens.
To do that, we have to simply look for an equation that is identical to the given equation:
3x - 8y = -5
By observing keenly, we see that the identical one is:
6x - 16y = -10
Divide both sides by 2, we have that:
3x - 8y = -5
Let us try to solve these equations:
3x - 8y = -5
3x - 8y = -5
Subtract the second from the first:
3x - 8y = -5
- (3x - 8y = -5)
0 + 0 = 0
=> 0 = 0
We see that both sides are identical.
So, the answer is option C.
Can anyone put on these on a table
y=4x-7 and y + x =6
Answer:
4x_7+x=6 4x_x=7+6 3x=13 x=13÷3
-r + 23 = -7r+ 3(2r + 8)
Ned help solving….Please help
The equation has no solution.
How to find the solution of the given equation?
-r + 23 = -7r + 3(2r + 8)
Applying distributive property A(B+C) = AB+AC
⇒ -r + 23 = -7r + 6r + 24
Combining like terms,
⇒ 7r - 6r -r = 24 - 23
⇒ 7r - 7 r = 1
⇒ 0 = 1
L.H.S ≠ R.H.S
Since the two sides are unequal , there is no solution.
What is the distributive property ?
In mathematics, the rule governing addition and multiplication operations is known as distributive law or distributive property.It is shown as A(B+C) = AB+AC.This law makes it simple to demonstrate that multiplying a sum of numbers by a certain number after adding multiple numbers has the same result as multiplying each number by the same amount independently before adding the results. It claims that multiplying a collection of significant two or three digit numbers will produce the same result as partitioning, multiplying, and adding the numbers individually.To learn more about distributive property, refer:
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Find the y-intercept of line on the graph.
Answer:
the y intercept is -3. it is -3 because it goes through the point (0,-3)
The next nine births at a hospital all being girls
Answer:
There is a chance it could happen. Rare occurrence though.
Step-by-step explanation:
A combined total of $41,000 is invested in two bonds that pay 6% and 7% simple interest. The annual interest is $2,700.00. How much is invested in each bond?
Answer
Amount invested at 6% interest = 17,000
Explanation
The simple interest on an invested principal (P), at a rate, R, for a period of time, T, is given by
Simple Interest = (PRT/100)
Let the amount invested at 6% be x
Let the amount invested at 7% be y
Sum of these amounts is $41,000
x + y = 41000
Simple Interest on x for 1 year
SI = (x × 6 × 1/100) = 0.06x
Simple interest on y for 1 year
SI = (y × 7 × 1/10) = 0.07y
Sum of annual interest = $2,700
0.06x + 0.07y = 2700
Now, we have a simultaneous equation
x + y = 41000
0.06x + 0.07y = 2700
Solving this simultaneously,
x = 17,000
y = 24,000
Hope this Helps!!!
What is the concentration of hydrogen ions in a solution with a pH of 2?
When pH is 2, the hydrogen ion concentration in [tex]litre^{-1}[/tex] is [tex]10^{-2}[/tex]
What is pH?The pH value of water indicates how acidic or basic it is. The negative log of the hydrogen ion concentration is defined as pH. The pH scale starts from 0 and ends at 14. A pH of 7 is considered neutral because pure water has a pH of exactly 7. Acidic values are less than 7; basic or alkaline values are greater than 7.
Given that,
pH = 2 for HCl acid
We know that,
The relation between concentration of acid and pH is,
pH = -log[[tex]H^{+}[/tex]]
2 = -log[[tex]H^{+}[/tex]]
[tex][H^{+} ][/tex] = [tex]10^{-2}[/tex]
Hence, the hydrogen ion concentration in a solution with a pH of 2 is [tex]10^{-2}[/tex].
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15. In circle A, SQ = 12 and AT = 8. Find AR.AR =AR
We have to find the length of AR.
It will be the same as the length of AS, as they are both radius of the circle:
[tex]AR=AS[/tex]AS is the hypotenuse of a right triangle with legs AT and TS.
Also, TS has half the length of SQ, so we have:
[tex]TS=\frac{1}{2}SQ=\frac{1}{2}\cdot12=6[/tex]We then can calculate AS as:
[tex]\begin{gathered} AS^2=TS^2+AT^2 \\ AS^2=6^2+8^2 \\ AS^2=36+64 \\ AS^2=100 \\ AS=\sqrt[]{100} \\ AS=10 \\ \Rightarrow AR=10 \end{gathered}[/tex]Answer: AR = 10
A coffee shop collected the following information regarding purchases from 110 of its customers. 67 purchased coffee. 41 purchased donuts. 19 purchased coffee and donuts. Complete parts a) through c) . a) Of those surveyed, how many purchased only coffee? (Type a whole number.)
We have the next information
Let X be the number of customer purchased coffee
Let Y be the number of customer pwho urchased donuts
X∩Y Then is the number of customers who purchased both coffee and donuts
X∪Y is the number of customers who purchased both coffee or donuts
The number of customers who purchase only coffee is
[tex]67-19=48[/tex]48 customers purchased only coffee
The number of customers who purchase only donuts is
[tex]41-19=22[/tex]22 customers purchased only donuts
In order to know how many customers did not purchase either of these items
First we will calculate the customers that purchase something
[tex]67+41-19=89[/tex]then we know that the total number of customers is 110
[tex]110-89=21[/tex]21 customers did not purchase either of these items
Determine the equation of the line that passes through the point (1/7,1) and is parallel to the line −4y−3x=−3
SOLUTIONS
The parallel line will be of form
[tex]m_1=m_2[/tex]the equation of the line that passes through the point (1/7,1) and is parallel to the line −4y−3x=−3
[tex]\begin{gathered} -4y-3x=-3 \\ -4y=3x-3 \\ y=\frac{3x}{-4}-\frac{3}{-4} \\ y=-\frac{3}{4}x+\frac{3}{4} \\ y=mx+c \\ m_1=-\frac{3}{4} \end{gathered}[/tex]The equation of the line parallel to point(1/7 , 1)
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ x_1=\frac{1}{7},y_1=1 \\ y-1=-\frac{3}{4}(x-\frac{1}{7}) \\ y-1=-\frac{3}{4}x+\frac{3}{28} \\ y=-\frac{3}{4}x+\frac{3}{28}+1 \\ multiply\text{ through by 28} \\ 28y=-21x+3+28 \\ 28y=-21x+31 \end{gathered}[/tex]