Answer:
x=2 x=-1
Step-by-step explanation:
f(x) = x^2 - X - 2
0= x^2 -x-2
Factor
0 =(x-2)(x+1)
Using the zero product property
x-2 =0 x+1 =0
x=2 x=-1
Answer:
x=2, -1
Step-by-step explanation:
Hi there!
We want to find the zeros of this function: f(x)=x²-x-2
The zeros are the values of x that will make f(x)=0
So that means in order to find the zeros, set f(x) as 0
In that case,
x²-x-2=0
Now let's solve the quadratic equation
We can do it by factoring
-x is the sum of two numbers, while -2 is the product of those two same numbers
Now think: which two numbers add up to -1, but multiply to get -2?
Those numbers are -2 and 1
Now factor the polynomial by FOIL:
(x-2)(x+1)=0
Split and solve
x-2=0
x=2
x+1=0
x=-1
The zeros are x=2, -1
Hope this helps!
I need help answering this ASAP
Answer:
"D"
if you multiply by Conjugate
the denominator would end up A^2 - b^2
the answer has 25 - 10x
that is D
Step-by-step explanation:
During a particularly dry growing season in a southern state, farmers noticed that there is a delicate balance between the number of seeds that are planted per square foot and the yield of the crop in pounds per square foot. The yields were the smallest when the number of seeds per square foot was either very small or very large.
What is the explanatory variable for this relationship?
yield of the crop
location of the farm
precipitation for the growing season
number of seeds planted per square foot
I think it's (D).
number of seeds planted per sf
Answer:
The guy above me is correct
Step-by-step explanation:
2022
Answer:
number of seeds planted per square foot
Step-by-step explanation:
response is the yield explained by how many seeds are planted
The difference between two positive integers is 7 and the sum of their squares is 949. What are the numbers?
Answer:
25 and 18
Step-by-step explanation:
Let's say that the first number is x and the second one is y.
First, the difference between them is 7, so x-y=7
Next, the sum of their squares is 949, so x²+y² = 949
We have
x-y=7
x²+y²=949
One thing we can do to solve this problem is to solve for x in the first equation, plug that into the second equation, and go from there
Adding y to both sides in the first equation, we have
x = 7 + y
Plugging that into the second equation for x, we have
(7+y)²+ y² = 949
expand
(7+y)(7+y) + y² = 949
49 + y² + 7y + 7y + y² = 949
combine like terms
2y² +14y + 49 = 949
subtract 949 from both sides to put this in the form of a quadratic equation
2y² + 14y - 900 = 0
divide both sides by 2
y² + 7y - 450 = 0
To factor this, we want to find 2 numbers that add up to 7 and multiply to -450.
The factors of 450 are as follows:
1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450.
Note that we want to find two numbers with a difference of 7, as one will have to be negative for the multiplication to end up at -450. Two numbers that stand out are 18 and 25. To make them add up to 7, 18 can be negative. We therefore have
y² + 25y - 18y - 450 = 0
y(y+25) - 18(y+25) = 0
(y-18)(y+25) = 0
Solving for 0,
y-18 = 0
add 18 to both sides
y=18
y+25 = 0
subtract 25 from both sides
y= -25
As the question states "two positive integers", this means that y must be positive, so y = 18. We know x-y=7, so
x-18 = 7
add 18 to both sides to isolate x
x = 25
find the sum 38+39+40+41...+114+115
It seems like you want to find the sum of 38 to 115:
[tex] \displaystyle \large{38 + 39 + 40 + 41 + ... + 114 + 115}[/tex]
If we notice, this is arithmetic series or the sum of arithmetic sequences.
To find the sum of the sequences, there are three types of formulas but I will demonstrate only one and the best for this problem.
[tex] \displaystyle \large{S_n = \frac{n(a_1+a_n) }{2} }[/tex]
This formula only applies to the sequences that have the common difference = 1.
Given that a1 = first term of sequence/series, n = number of terms and a_n = last term
We know the first term which is 38 and the last term is 115. The problem here is the number of sequences.
To find the n, you can use the following formula.
[tex] \displaystyle \large{n = (a_n - a_1) + 1}[/tex]
Substitute an = 115 and a1 = 38 in the formula of finding n.
[tex] \displaystyle \large{n = (115 - 38) + 1} \\ \displaystyle \large{n = (77) + 1} \\ \displaystyle \large{n = 78}[/tex]
Therefore the number of sequences is 78.
Then we substitute an = 115, a1 = 38 and n = 78 in the sum formula.
[tex] \displaystyle \large{S_{78} = \frac{78(38+115) }{2} } \\ \displaystyle \large{S_{78} = \frac{39(38+115) }{1} } \\ \displaystyle \large{S_{78} = 39(153) } \\ \displaystyle \large \boxed{S_{78} = 5967}[/tex]
Hence, the sum is 5967.
Which equation does the graph of the systems of equations solve?
two linear functions intersecting at 3, negative 2
−one thirdx + 3 = x − 1
one thirdx − 3 = −x + 1
−one thirdx + 3 = −x − 1
one thirdx + 3 = x − 1
Answer:
-1/3x+3 = x-1
Step-by-step explanation:
The solution is (3,-2)
Check and see if the point solves the equation
-1/3x+3 = x-1
-1/3(3) +3 = 3-1
-1+3 = 3-1
2=2 yes
Answer:
C
Step-by-step explanation:
what is the absolute value of -5/9
Answer:
5/9
Step-by-step explanation:
In short, the absolute value of a number turns that number into a positive value no matter what. Here is a small representation:
Negative -> Positive
Positive -> Positive
Since we are working with a negative value, it will turn positive.
Best of Luck!
At a time hours after taking a tablet, the rate at which a drug is being eliminated r(t)= 50 (e^-01t - e^-0.20t)is mg/hr. Assuming that all the drug is eventually eliminated, calculate the original dose.
Answer:
2500 mg
Step-by-step explanation:
Since r(t) is the rate at which the drug is being eliminated, we integrate r(t) with t from 0 to ∞ to find the original dose of drug, m. Since all of the drug will be eliminated at time t = ∞.
Since r(t) = 50 (e^-01t - e^-0.20t)
m = ∫₀⁰⁰50 (e^-01t - e^-0.20t)
= 50∫₀⁰⁰(e^-01t - e^-0.20t)
= 50[∫₀⁰⁰e^-01t - ∫₀⁰⁰e^-0.20t]
= 50([e^-01t/-0.01]₀⁰⁰ - [e^-0.20t/-0.02]₀⁰⁰)
= 50(1/-0.01[e^-01(∞) - e^-01(0)] - {1/-0.02[e^-0.02(∞) - e^-0.02(0)]})
= 50(1/-0.01[e^-(∞) - e^-(0)] - {1/-0.02[e^-(∞) - e^-(0)]})
= 50(1/-0.01[0 - 1] - {1/-0.02[0 - 1]})
= 50(1/-0.01[- 1] - {1/-0.02[- 1]})
= 50(1/0.01 - 1/0.02)
= 50(100 - 50)
= 50(50)
= 2500 mg
Use the discriminant to determine the number of solutions to the quadratic equation −40m2+10m−1=0
From the analysis of the discriminant, you obtain that the quadratic function has no real solutions.
In first place, you must know that the roots or solutions of a quadratic function are those values of x for which the expression is 0. This is the values of x such that y = 0. That is, f (x) = 0.
Being the quadratic function f (x)=a*x² + b*x + c, then the solution must be when: 0 =a*x² + b*x + c
The solutions of a quadratic equation can be calculated with the quadratic formula:
[tex]Solutions=\frac{-b+-\sqrt{b^{2} -4*a*c} }{2*a}[/tex]
The discriminant is the part of the quadratic formula under the square root, that is, b² - 4*a*c
The discriminant can be positive, zero or negative and this determines how many solutions (or roots) there are for the given quadratic equation.
If the discriminant:
is positive: the quadratic function has two different real solutions. equal to zero: the quadratic function has a real solution. is negative: none of the solutions are real numbers. That is, it has no real solutions.In this case, a= -40, b=10 and c= -1. Then, replacing in the discriminant expression:
discriminant= 10² -4*(-40)*(-1)
Solving:
discriminant= 100 - 160
discriminant= -60
The discriminant is negative, so the quadratic function has no real solutions.
Một miếng đất hình chữ nhật có chu vi 80 mét.Nếu kéo dài thêm 8 mét nữa thì diện tích tăng thêm là 72 mét vuông.Tính chiều dài và chiều rộng hình chữ nhật ban đầu ?
Answer:
Step-by-step explanation:
(D+R) = 80:2 = 40
D = 40-R
(D+8) * R = 72X
Thay D=40-R
(40-R+8)*R = 72X
R=1.55, D=38.45
Jupiter orbits the sun at a rate of 8 miles per second. How far does Jupitertravel in one day? Tip: There are 86400 seconds in a day.
Answer:
Jupiter travels 691200 miles a day
Step-by-step explanation:
I just did 86400 x 8
Plz give brainliest
Solve this inequality: x+ 4< 16
Answer:
x < 12
Step-by-step explanation:
subtract 4 from both sides:
x + 4 < 16
- 4 -4
x < 12
Answer:
x<4
Step-by-step explanation:
x+4 <16
x < 16
4
x<4
I hope this will help you
Will give brainliest
mplete the equation describing how
x and y are related.
Х
0 1
2
3
4
Y -1 3 7
11 15
y = 4x + [? ]
Enter the answer that belongs in [?]
Answer:
y = 4x + -1
Step-by-step explanation:
clearly seen.
Suppose that a population begins at a size of 100 and grows continuously at a rate of 200% per year. Give the formula for calculating the size of that population after t years.
A) A = 100 + te^2
B) A = 100 + e^2t
C) A = 100e^2t
D) A = 100 + 2e^t
Answer:
D)
Step-by-step explanation: Im not so sure ok i sorry if Im wrong
what is the volume of the container
What is the value of 2 in 9,274
Answer:
200
Step-by-step explanation:
4 is in the ones place so 4 just 4
7 is in the tens place so it is 70
2 is the hundreds place so 200
9 is in the thousands place so 9.000
Rewrite 3.16 as a fraction (the 6 is repeating)c
[tex]3\frac{16}{99} = \dfrac{313}{99}= 3.161616161616.....[/tex]
Please help me to find this answer
Answer:
37
Step-by-step explanation:
Tan(B) = 6/8
B= arctan(3/4)=37
(-2x) (x-3) answer please
Answer:
−2x^2+6x
Explanation:
You just have to distribute meaning you have to multiply -2x to the equation.
I want to know how to solve this equation
Answer:
the last two answers are the only correct ones
Hello I'm new can anyone help me with this question?
Thank you so much! <3 xoxo
Find the value of x in each case:
9514 1404 393
Answer:
x = 45°
Step-by-step explanation:
The triangle interior angle at I will be the supplement of the angle marked 2x. The triangle interior angle at G will be equal to x, the alternate interior angle with respect to transversal GI crossing the parallel lines.
The angle marked 3x is the sum of these "remote" interior angles:
3x = 180 -2x +x
4x = 180 . . . . . . . . . add x; next, divide by 4
x = 180/4 = 45 . . . . . degrees
x = 45°
Does the function ƒ(x) = (1∕2) + 25 represent exponential growth, decay, or neither?
A) Exponential growth
B) Impossible to determine with the information given.
C) Neither
D) Exponential decay
Answer:
A) Exponential growth
Step-by-step explanation:
The profit earned by a hot dog stand is a linear function of the number of hot dogs sold. It costs the owner $48 dollars each morning for the day’s supply of hot dogs, buns and mustard, but he earns $2 profit for each hot dog sold. Which equation represents y, the profit earned by the hot dog stand for x hot dogs sold? y=48x−2 y=48x+2 y=2x−48 y=2x+48
Answer:
c. y=2x−48
Explanation:
It is telling us that it costs $48 each morning to buy the day's supply of hot dogs, so we must subtract that from our pay, and it will be our y intercept
It also says he earns $2 per hot dog, so that will be our slope (rate of change)
Hope it helps! :]
y = 2x - 48 equation represents the profit earned by the x hot dog sold.
What is linear equation?A linear equation is an algebraic expression in which highest power of the given variable is equals to one.
Given that, the profit earned by a hot dog stand is a linear function of the number of hot dogs sold.
It costs the owner $48 dollars each morning for the day’s supply of hot dogs, buns and mustard, but he earns $2 profit for each hot dog sold.
We need to establish an equation that represents the total profit,
According to the question,
x represents the number of hot dogs sold
y represents the total profit earned
Cost required for supply = $48
Profit on each hot dog sold = $2
As per the condition given, the required linear equation is =
y = 2x - 48
Hence, y = 2x - 48 equation represents the profit earned by the x hot dog sold.
Learn more about linear equation here :
brainly.com/question/11897796
#SPJ7
The sum of the interior angles of a regular nonagon (9-gon) is equal to
The sum of the interior angles is 1260°
Question 3 plz show ALL STEPS
Answer:
7,0, -1 and -2
Step-by-step explanation:
Just substitute the values,
a. f(g(7))=f(-1) [g(7)=-1 given]
=7 [f(-1)=7 given]
b.f(g(-1))=f(3)=0 [g(-1)=3 Given]
c.g(f(-1))=g(7)=-1 [f(-1)=7 given]
d.g(f(7))=g(5)=-2 [f(7)=g(5) given]
In Waterville, the average daily rainfall in July is 10 mm with a standard deviation of 1.5 mm. Assume that this data is normally distributed. How many days in July would you expect the daily rainfall to be more than 11.5 mm
Answer:
You should expect 5 days in July with daily rainfall of more than 11.5 mm.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
In Waterville, the average daily rainfall in July is 10 mm with a standard deviation of 1.5 mm.
This means that [tex]\mu = 10, \sigma = 1.5[/tex]
Proportion of days with the daily rainfall above 11.5 mm.
1 subtracted by the p-value of Z when X = 11.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{11.5 - 10}{1.5}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.84.
1 - 0.84 = 0.16.
How many days in July would you expect the daily rainfall to be more than 11.5 mm?
July has 31 days, so this is 0.16 of 31.
0.16*31 = 4.96, rounding to the nearest whole number, 5.
You should expect 5 days in July with daily rainfall of more than 11.5 mm.
Which expression is equivalent to (b^n)m?
Step-by-step explanation:
By the law of exponent :
(a^n)^m=a^n×m
Option C
b^n×m is the correct answer...
hope it helps
Which of the following show the factored equivalent of
f(x) = (2x^2 +7x + 3)(x - 3) and its zeros?
Answer:
the answer is "D"
(2x+1)(x+3)(x-3) //// -3,-.5,3
Step-by-step explanation:
Factored Form: y= (2x+1)(x+3)(x-3)
Answer:
D
Step-by-step explanation:
[tex]f(x) = (2x^2 +7x + 3)(x - 3)[/tex] is factored into: [tex]f(x)= (2x+1)(x+3)(x-3)[/tex]
That takes out the choices B and C.
The roots are -0.5, 3, and -3.
Therefore, the answer is D.
I hope this helps!
pls ❤ and mark brainliest pls!
In the picture below, which lines are lines of symmetry for the figure?
A. none
B. 1, 2, and 3
C. 1 and 3
D. 2 and 4
Answer:
i gues none... bcuz its irregular symmetry shape
Answer:
1 because it takes a full rotation to get back to a symmetrical shape. or 2 because it is the same halfway around.
The lines shown below are parallel. If the green line has a slope of 5, what is a
the slope of the red line?
Answer:
A. 5
Step-by-step explanation:
Parallel lines have the same slope.
Answer:
5
Step-by-step explanation:
