Answers
Answer:
The horizontal distance is 5
Explanation:
The zeros of a function f(x) are the values of x which:
\(f(x)=0\)In this case, we have the function:
\(-x^2+x+6\)We want to find the zeros:
\(-x^2+x+6=0\)Now, we can use the quadratic formula:
\(x_{1,2}=\frac{-1\pm\sqrt{1^2-4(-1)6}}{2(-1)}\)\(x_{1,2}=\frac{-1\pm\sqrt{1+4\cdot6}}{-2}\)\(x_{1,2}=\frac{1\pm\sqrt{1+24}}{2}\)\(x_{1,2}=\frac{1\pm\sqrt{25}}{2}\)\(x_{1,2}=\frac{1\pm5}{2}\)Then:
\(\begin{gathered} x_1=\frac{1+5}{2}=\frac{6}{2}=3 \\ \end{gathered}\)\(x_2=\frac{1-5}{2}=\frac{-4}{2}=-2\)The two roots are x = -2 and x = 3
To find the distance, we take the absolute value of the difference:
\(Distance=|-2-3|=|-5|=5\)The distance is 5
Related Questions
In class, we developed the formula
(a) Use the formula (using appropriate substitutions) to find the closed form for ∑2
= 2
(b) Use the formula in the notes for ∑
= 13 to find the closed form expression form for
∑
= 3 (assume a ≥ 1 and a ≤ b)
(c) In class, we developed the formula
Use this formula and some algebra to derive a closed form for the sum ∑
= 0( ― 1)2 ― 1
(d) Test your closed form solution in (c) to find the value of ∑3
= 0( ― 1)2 ― 1 and see if
it matches the manual computation of the 4 terms of the sum.
Answers
(a) The closed form for ∑2 is 2.
(b) The closed form expression for ∑3 is 24.
(c) The closed form for the sum ∑n = 0(― 1)² ― 1 is n(1 - n) / 2.
(d) The value of -3 matches the manual computation of the four terms.
Our closed form solution is correct.
To find the closed form for ∑2, we can use the formula for the sum of the first n terms of an arithmetic series:
∑2 = n(a + l) / 2
In this case, a = 2 (the first term) and l = 2 (the last term) since we are summing a series of 2's.
We also know that there is only one term, so n = 1.
Substituting these values into the formula, we have:
∑2 = 1(2 + 2) / 2
= 4 / 2
= 2
The formula for the sum of the first n terms of an arithmetic series is:
∑n = n(a + l) / 2
In this case, we have a = 3 (the first term), l = 13 (the last term), and n = 3 (the number of terms).
Substituting these values into the formula, we get:
∑3 = 3(3 + 13) / 2
= 3(16) / 2
= 48 / 2
= 24
The formula we developed in class is:
∑n = n(a + a + (n - 1)d) / 2
In this case, we have a = 0 (the first term) and d = -1 (the common difference).
Substituting these values into the formula, we get:
∑n = n(0 + 0 + (n - 1)(-1)) / 2
= n(0 - n + 1) / 2
= n(1 - n) / 2
To test the closed form solution for ∑3 = 0(― 1)² ― 1, we substitute n = 3 into the closed form expression we derived in part (c):
∑3 = 3(1 - 3) / 2
= 3(-2) / 2
= -6 / 2
= -3
Now, let's manually compute the sum of the first four terms of ∑3 = 0(― 1)² ― 1:
0(― 1)² ― 1 + 1(― 1)² ― 1 + 2(― 1)² ― 1 + 3(― 1)² ― 1
= 0 - 1 - 2 - 3
= -6
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Ryan enjoys flying a kite on the beachWhich is the closest to the length of the string?
Answers
EXPLANATION
Let's see the facts:
Adjacent leg= 100 feet
Angle= 57 degrees
The closest to the length is given by the Pythagorean Theorem as shown as follows:
\(\cos \text{ }\alpha=\frac{\text{adjacent cathetus}}{\text{Hypotenuse}}\)Replacing terms:
\(\cos 57=\frac{100}{x}\)Isolating x:
\(x=\frac{100}{\cos 57}=183.6\)So, the answer is 183.6 feet OPTION B
Point Bis on line segment AC.Given AB 4. - 6, AC = 2x + 10, and
BC = 4, determine the numerical length of AC.
Answer: AC
Submit Answer
attempt
Answers
Answer:
5
Step-by-step explanation:
the equation of straight line passing through the point (2,3)&perpendicular to the line 4x-3y=10 is
Answers
Answer:
4y = -3x +18
Step-by-step explanation:
Let's get the gradient from this line equation first.
4x-3y=10
4x-10=3y
Y= 4/3x -10/3
The gradient is 4/3.
For a line perpendicular to another line.
M*M'= -1
M= -/(4/3)
M = -3/4
So the gradient to be used is -3/4
Formula for solving is
(Y-y1)/(x-x1)= M
X1= 2
Y1= 3
M = -3/4
(Y-y1)/(x-x1)= M
(Y-3)/(x-2)= -3/4
4(y-3)= -3(x-2)
4y -12 = -3x +6
4y = -3x +18
Prove that if n is an odd integer, then n^2 + 1 is an even integer.
Answers
n^2 will still give you an odd integer, but if you add one it will be an even integer
1a)Due to the fuel scarcity in Japan the cost of a phone rises from 4500Naira to 5500 find the increment in price = (1b)Use the information above to find the percentage increase in price = (2) The discount of 10% was given to a customer and she paid 3,000Naira for an article, find the marked price = (3) 30 crates of eggs was bought by a distributor at 30 Naira each, she was given a commission of 4% on a crate. How much commission did she get ? = (4) A dealer sells articles worth 49000 Naira and get a commission of 7% calculate his commission = (5) A dealer wanted to buy an article for Naira39.28kobo,but the marketed price for the article is Naira44.48kobo. How much discount did the customer request for? = (6) A trader appealed to buy an article for 225.00Naira but the marketed price for the article is 245.00 Naira what percent of discount did the trader request for ? = (7) Am agent was given a commission of 3% on a house he sold for 33.00Naira . How much commission did the agent get ? = (8) A company increases the salary of all employees by 5% of their salaries. If an employee earns 250Naira a month what is his new salary ? = (9) A man gives a discount of 5% on the fridge he bought for 55.00Naira. Find the marketed price of the fridge.= (10) A trader demanded a discount of 55.00Naira ok the goods she bought for 845.00Naira . What is the marketed price and the percentage discount ? =.
Answers
Answer:
1a) Increment in price = 5500 - 4500 = 1000 Naira
1b) Percentage increase in price = (increment in price / old price) x 100%
= (1000 / 4500) x 100%
= 22.22%
2) Marked price = selling price / (1 - discount percentage)
= 3000 / (1 - 0.1)
= 3333.33 Naira
3) Total cost of 30 crates of eggs = 30 x 30 = 900 Naira
Commission = (4/100) x 900
= 36 Naira
4) Commission = (7/100) x 49000
= 3430 Naira
5) Discount = marked price - selling price
= 44.48 - 39.28
= 5.20 Naira
6) Discount = (245 - 225) / 245 x 100%
= 8.16%
7) Commission = (3/100) x 33
= 0.99 Naira
8) New salary = old salary + 5% of old salary
= 250 + (5/100) x 250
= 262.50 Naira
9) Marketed price = selling price / (1 - discount percentage)
= 55 / (1 - 0.05)
= 57.89 Naira
10) Marketed price = selling price + discount
= 845 + 55
= 900 Naira
Percentage discount = (discount / marked price) x 100%
= (55 / 900) x 100%
= 6.11%
Step-by-step explanation:
(pls pls help!!) Calculate each value for ⊙P.
=
Area of shaded factor = (fraction) ft
Area of unshaded factor = (fraction) ft
Answers
The area of the shaded sector is 575π/9 square units.
The area of the unshaded sector is 325π/9 square units
What is the area of the sectors?
The value of the angle subtended by the unshaded sector is 130⁰ the value of the angle subtended by the shaded sector is 230⁰.
To find the area of a sector with radius 10 units and angle 230⁰, we can again use the same formula:
Area of sector = (angle/360) x πr^2
Substituting the values given in the formula, we get:
Area of sector = (230/360) x π(10)²
= (23/36) x 100π
= 575π/9 square units
To find the area of a sector with radius 10 units and angle 130⁰, we can use the formula:
Area of sector = (angle/360) x πr^2
Substituting the values given in the formula, we get:
Area of sector = (130/360) x π(10)^2
= (13/36) x 100π
= 325π/9 square units
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Write an equation in point slope form of the line passes through the point (9,0) and has a slope of m=-3
Just so if won't get DELETED
Answers
Step-by-step explanation:
hey it' s me probably my new account
Fin the Interquartile Range
4|1 2 3 5 5 6
5|1 1 8 8 8 9
6|0 0 0 1 2 5
7|1 1
Answers
The interquartile range of the stem and leaf plot is 6.
What is the interquartile range?The table given is a stem and leaf plot. A stem and leaf plot is a table that divides a number into a stem and a leaf. The stem is the tens digit and the leaf is the unit digit.
The interquartile range is the difference between the third quartile and the first quartile.
Third quartile = 3/4(n + 1) = 61
First quartile = 1/4 x (n + 1) = 55
Interquartile range = 61 - 55 = 6
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Determine whether 81a^2 − 25z^6 is a difference of two squares. If so, factor it. If not, explain why.
(9a − 5z^3)(9a − 5z^3)
(9a + 5z^3)(9a − 5z^3)
(9a − 5z^6)(9a + 5z^6)
It is not a difference of squares because −25z^6 is not a perfect square.
Answers
The given polynomial 81a² − 25z⁶ is not a difference of two squares because −25z⁶ is not a perfect square.
We can see that 81a² is a perfect square because it is equal to (9a)². However, 25z⁶ is not a perfect square because it can't be written as the square of a single term.
Therefore, we cannot factor 81a² − 25z⁶ into the difference of two squares.
\( \: \: \: \)
The vertices of a rectangle are listed below.
I(6,8), J(6, -1), K(-6, -1), L(-6, 8)
What is the area of the rectangle?
Answers
Answer:
please find attached pdf
Step-by-step explanation:
reduce 90/135 plss answer
Answers
Answer: 2 over 3
Step-by-step explanation: The GCF of 90 and 135 is 45. So,
divide 90 by 45 = 2
divide 135 by 45 = 3
Answer: 2/3
11 players are going to practice in the batting cage. how many different orders are possible
Answers
Answer:
Step-by-step explanation:
With your team, create a piecewise-defined function with at least three “pieces.” The function does not need to be a step-function with horizontal line segments, but it needs to meet the definition of a function. Make a table and a graph for your function, and write an equation for each part. Be sure to state the domain for each part, as well as the domain for the whole function.
Answers
On solving the provided question we can say that The following is the data table of the function.
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
here,
the provided functions that can be formed are
x -infinity < x < -10
f(x) = 2x + 10 -10 < x < 10
4X - 10 10 < x < infinty
The following is the data table of the function.
x y
-20 -20
-15 -15
-10 -10
-5 0
0 10
5 20
10 30
15 50
20 70
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An example of the piecewise defined function is: \(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output.
A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or range.
Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
The following is the data table of the function.
x y
-20 -20
-15 -15
-10 -10
-5 0
0 10
5 20
10 30
15 50
20 70
The provided functions that can be formed are
\(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)
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Kathryn deposits 100 into an account at the beginning of each 4-year period for 40 years. The account credits interest at an annual effective interest rate of i. The accumulated amount in the account at the end of 40 years is X, which is 5 times the accumulated amount in the account at the end of 20 years. Find X
Answers
Answer:
X=6.195
Attached please find equation.
Step-by-step explanation:
Let 1+i∗=(1+i)4 so that the calculation using annuity
{1, √2, √√3, 2, √5, ...}
need help knowing the sequence and the 3 next terms
Answers
Answer:
3, 2√2, √7
Step-by-step explanation:
compute the square roots of the next three prime numbers:
√7
√11
√13
Therefore, the next three terms of the sequence are:
{1, √2, √3, 2, √5, √7, √11, √13}
chatgpt
chat
At a certain gas station, 40% of the customers use regular gas (A1), 35% use plus gas (A2), and 25% use premium (A3). Of those customers using regular gas, only 20% fill their tanks (event B). Of those customers using plus, 40% fill their tanks, whereas of those using premium, 50% fill their tanks.
Consider the following information on credit card usage.
1. 70% of all regular fill-up customers use a credit card.
2. 50% of all regular non-fill-up customers use a credit card.
3. 60% of all plus fill-up customers use a credit card.
4. 50% of all plus non-fill-up customers use a credit card.
5. 50% of all premium fill-up customers use a credit card.
a) What is the probability that the next customer will requestplus gas and fill their tank?
b) What is the probability that the next customer fills thetank?
c) If the next customer fills the tank, what is the probabilitythat the regular gas is requested? Plus? Premium
Answers
Answer:
a.)
P( A₂ ∩ B ) = P(B | A₂) × P(A₂)
P( A₂ ∩ B ) = 0.40 × 0.35
P( A₂ ∩ B ) = 0.14
b.)
P(B) = P( A₁ ∩ B ) + P( A₂ ∩ B ) + P( A₃ ∩ B )
P(B) = 0.08 + 0.14 + 0.125
P(B) = 0.345
c.)
For regular gas:
P(A₁ | B) = P( A₁ ∩ B ) / P(B)
P(A₁ | B) = 0.08 / 0.345
P(A₁ | B) = 0.232
For plus gas:
P(A₂ | B) = P( A₂ ∩ B ) / P(B)
P(A₂ | B) = 0.14 / 0.345
P(A₂ | B) = 0.406
For premium gas:
P(A₃ | B) = P( A₃ ∩ B ) / P(B)
P(A₃ | B) = 0.125 / 0.345
P(A₃ | B) = 0.362
Step-by-step explanation:
We are given the following information
40% of the customers use regular gas (A2)
P(A₁) = 0.40
35% use plus gas (A2)
P(A₂) = 0.35
25% use premium (A3)
P(A₃) = 0.25
Of those customers using regular gas, only 20% fill their tanks (event B).
P(B | A₁) = 0.20
Of those customers using plus, 40% fill their tanks
P(B | A₂) = 0.40
Whereas of those using premium, 50% fill their tanks.
P(B | A₃) = 0.5
a) What is the probability that the next customer will request plus gas and fill their tank?
We are asked to find P(A₂ ∩ B) = ?
Recall that Multiplicative law of probability is given by
P( A₂ ∩ B ) = P(B | A₂) × P(A₂)
P( A₂ ∩ B ) = 0.40 × 0.35
P( A₂ ∩ B ) = 0.14
b) What is the probability that the next customer fills the tank?
We are asked to find P(B) = ?
P(B) = P( A₁ ∩ B ) + P( A₂ ∩ B ) + P( A₃ ∩ B )
P( A₂ ∩ B ) is already calculated, we need to calculate
P( A₁ ∩ B ) and P( A₃ ∩ B )
So,
P( A₁ ∩ B ) = P(B | A₁) × P(A₁)
P( A₁ ∩ B ) = 0.20 × 0.40
P( A₁ ∩ B ) = 0.08
P( A₃ ∩ B ) = P(B | A₃) × P(A₃)
P( A₃ ∩ B ) = 0.50 × 0.25
P( A₃ ∩ B ) = 0.125
Finally,
P(B) = P( A₁ ∩ B ) + P( A₂ ∩ B ) + P( A₃ ∩ B )
P(B) = 0.08 + 0.14 + 0.125
P(B) = 0.345
c) If the next customer fills the tank, what is the probability that the regular gas is requested? Plus? Premium
For regular gas:
P(A₁ | B) = P( A₁ ∩ B ) / P(B)
P(A₁ | B) = 0.08 / 0.345
P(A₁ | B) = 0.232
For plus gas:
P(A₂ | B) = P( A₂ ∩ B ) / P(B)
P(A₂ | B) = 0.14 / 0.345
P(A₂ | B) = 0.406
For premium gas:
P(A₃ | B) = P( A₃ ∩ B ) / P(B)
P(A₃ | B) = 0.125 / 0.345
P(A₃ | B) = 0.362
5.
The width of a rectangle is one foot more than a third of the length. If the
perimeter is 42 feet, what is the width? What is the length?
Answers
2l + 2w.
So, by plugging in our values of the length and width, we can easily find an answer:
length = L
width = 1 + L ( 1/3 )
2 ( L ) + 2 ( L ( 1/3 + 1 ) = 42
2l + 2/3( L ) + 2 = 42
8/3 ( L ) = 40
L = 40 * 3/8
L = 15
Therefore, the length is 15 and the width is 6.
LOTS OF POINTS PLEASEE HELP
Answers
Answer:
i) x = 0.25 and 1.25
ii) x = -0.5 and 1.5
Step-by-step explanation:
Given that y = 4x² - 4x - 1. So for question 1, you can let y = 0, then see which x-value did the curve touches 0 at y-axis.
Same for question 2.
ii) -0.5 and 1.5
Work out value x, give answer to 1 decimal place
Answers
Answer:
x ≈ 44.6°
Step-by-step explanation:
perimeter of a perfect circle: 2πr = 2π(9) = 18π
perimeter of the circle arc : 25 - 2(9) = 7
The central angle in a full circle is 360 degrees. In the segment of the circle is x degrees. The value of x is obtained using proportionality.
\( \frac{360}{x} = \frac{18\pi}{7} \\ \\ x = \frac{7 \times 360}{18\pi} = 44.56\)
what is the Y intercept of function g if g(x)=2f(x)+1? a. 0,3 b.0,2 c 0,1 d 0,-1
Answers
Answer:
d
Step-by-step explanation:
The y- intercept is where the graph crosses the y- axis
The graph crosses the y- axis at (0, 1 ) ← y- intercept
Estimate 6,976 + 3,983 + 13,560 by first rounding each number to the nearest thousand.
Answers
Answer:
Step-by-step explanation:
The thousand mark is the 4th number when going from right to left. So it would be the {6},976. When it comes to rounding, you go "5 and above, give it a shove, 4 and below, let it go. 6,976 rounded to the nearest thousand is 7,000, 3,983 rounded to the nearest thousand is 4,000, 13,560 rounded is 14,000.
7,000 + 4,000+ 14,000 = 25,000
What is the approximate value of θ if tan θ = 7/9
Answers
Answer:
37.9°-----------------------
Taking the inverse tangent (arctan) of the given ratio 7/9.
Use a calculator or trigonometric table to find:
θ ≈ arctan(7/9)The approximate value of θ is 37.9°.
write 0.125 as a simplest fraction and percent.
Answers
Answer:
12½% 0.125 1/8
Step-by-step explanation:
Which of the following is not a property of a rectangle?
O A) All sides are congruent.
B) Diagonals bisect each other.
C) All angles are congruent.
D) Diagonals are congruent.
Answers
Answer:
A
Step-by-step explanation:
Congruent means equal and not all the sides of a rectangle are equal
Find the surface area of this triangular promise correct unit
Answers
The surface area of the triangular prism would be =324,000cm²
How to calculate the triangular surface area of the given prism?To calculate the surface area of the triangular prism the formula that should be given would be as follows:
Surface area of triangular prism;
Surface area of triangular prism;= bh+(b1+b2+b3)l
where:
base length = 20cm
height = 15cm
length = 18cm
SA = 20×15(20+15+25)×18
= 300×60×18
= 324,000cm²
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plz help ill mark you brainliest
Answers
Answer:
cos 30= 0.1542
tan 48= 1.2001
sin 79= -0.4441
plz mark brainliest
You can fill a 15-gallon tank of gas for $35.25 or buy gas for $2.55/gal. Which a better deal and why?
Answers
Answer:
The 15-gallon tank of gas for $35.25 is a better deal
Step-by-step explanation:
First we need to find the unit rate for the 15 gallon tank of gas for $35.25 so we divide 35.25 by 15 which equals 2.35. $2.35 is cheaper than the $2.55/gal which makes the 15-gallon tank of gas for $35.25 a better deal.
Can someone please explain to me how to solve the problem? I need to know how to complete it more than just the answer. Thanks!
A plane is flying at an altitude of 13,000 ft, where the temperature is -2 degrees F. The nearby airport, at an altitude of 2,000ft, is reporting precipitation. If the temperature increases 2.1 degrees F for every 1000-ft decrease in altitude, will the precipitation at the airport be rain or snow? Assume that rain changes to snow at 32 degrees F.
Is the precipitation at the airport rain or snow?
Answers
9514 1404 393
Answer:
snow
Step-by-step explanation:
The relationship between temperature and altitude is given as ...
T = -2 +((13000 -a)/1000)×2.1
We can put a=2000 into this equation to find the temperature at that altitude.
T = -2 +((13000 -2000)/1000)×2.1 = -2 +11(2.1) = -2 +23.1 = 21.1
The airport temperature of 21.1 °F is below 32 °F, so we expect the precipitation to be snow.
i need help with this
Answers
you wanna add up all of the values and then subtract by how much was taken out (0.20)