Write a quadratic equation in a such that the sum of its roots is -8 and the product
of its roots is -15
The equation is x^2-8 x-15=0.
What is equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."
Given, sum of the roots of a quadratic equation is 8 and their product is 15 We know that the quadratic equation is given as [tex]$\mathrm{x}^2-$[/tex](Sum of the roots) [tex]$\mathrm{x}+$[/tex] (product of the roots)[tex]$=0$[/tex] [tex]$\Rightarrow x^2-8 x-15=0$[/tex]
Hence, the equation is x^2-8 x-15=0.
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Answer:
x² +8x -15 = 0
Step-by-step explanation:
You want a quadratic such that the sum of the roots is -8 and their product is -15.
CoefficientsWhen the roots of a quadratic are p and q, its factored form is ...
(x -p)(x -q) = 0
The expanded form of this is ...
x² -(p+q)x +pq = 0
That is, the coefficient of x is the opposite of the sum of the roots, and the constant is the product of the roots.
ApplicationHere, we want the sum of roots to be -8, so the x-coefficient will be the opposite of that: 8. The constant will be the product of the roots: -15. That makes the desired quadratic be ...
x² +8x -15 = 0
__
Additional comment
The attachment shows the quadratic, its roots, and their sum and product.
A survey of 2000 subscribers to a certain news paper revealed that 1800 people subscribe to the daily morning edition and 1000 subscribe to both the daily and the sunday editions. how many subscribe to the Sunday edition? how many subscribe to the Sunday edition only?
1200 people subscribed Sunday edition and 200 people subscribed only sunday edition.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that A survey of 2000 subscribers to a certain news paper revealed that 1800 people subscribe to the daily morning edition
And 1000 subscribe to both the daily and the sunday editions.
Let x denote the number who subscribe to the Sunday edition.
Then the addition rule with overlap tells us that is;
1800 + x – 1000 = 2000
800 + x = 2000
x = 1200
so, 1500 subscribe to the Sunday edition and 1200 – 1000 = 200 subscribe to the Sunday edition only.
Hence, 1200 people subscribed Sunday edition and 200 people subscribed only sunday edition.
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Alexa has $900 in a savings account that earns 2% annually. The interest is not compounded. How much will she have in total in 5 years? Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answer:
Alex will have a total of $990 in 5 years.
Step-by-step explanation:
Using the formula [tex]i=prt[/tex] we get [tex]i=900[/tex] × [tex]0.2[/tex] × [tex]5[/tex] which equals 90
[tex]900 + 90 = 990[/tex]
trying to find the arc length of the arc for the polar curve r=8cosθ between 0 and π4
Answer:
Step-by-step explanation:
To find the arc length of the polar curve r = 8cosθ between 0 and π/4, we can use the formula for arc length:
L = ∫a^b √(r^2 + (dr/dθ)^2) dθ
Substituting in the values for r and dθ, we get:
L = ∫0^(π/4) √(8^2cos^2θ + (-8sinθ)^2) dθ
= ∫0^(π/4) √(64cos^2θ + 64sin^2θ) dθ
= ∫0^(π/4) √(64) dθ
= ∫0^(π/4) 8 dθ
= 8(π/4 - 0)
= 8π/4
= 2π
Therefore, the arc length of the polar curve r = 8cosθ between 0 and π/4 is 2π.
On July , the billing date, Marvin Zug had a balance due of $265.72 on his credit card. His card charges an interest rate of 1.25% per month. The transactions he made are to the right.
a) Find the finance charge on August , using the previous balance method.
b) Find the new balance on August 7.
(see photo)
Answer:
475$
Step-by-step explanation:
Andrea started out the day with 2 quects and sold some each hour. Lee started the day with 12 quects and sold some each hour. The graph below represents the number of quects each person has after x hours. Estimate the number of quects each person will have when they have the same amount.
Each person will have 3 quects when they have the same amount
How to estimate the number of quects each person will have when they have the same amount?
Given that:
Andrea started out the day with 2 quects and sold some each hour. Lee started the day with 12 quects and sold some each hour.
The equation of a line is of the form y = mx+c
where m is the slope and c is the y-intercept
For Lee
y =mx+c
c = 12
m = 12-8/0-1 = 4/( -1) = -4
y = -4x+12
For Andrea
y =mx+c
c = 2
m = 2-1/0-1.5 = 1/(-1.5) = -2/3
y = -2/3 x + 2
At the same amount y = -4x+12 is equal to y = -2/3 x + 2. Thus:
-4x+12 = -2/3 x + 2
4x-2/3 x = 12-2
10/3 x = 10
10x = 30
x = 30/10 = 3
Therefore, at 3 quects each person will have when they have the same amount
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If y varies inversely as x2 and y=38 when x=18, find y if x=20.
The required value of y for the given inverse relation is 30.78
What is the inverse variation?
Inverse variation occurs when one variable varies inversely with respect to another. It represents the inverse relationship between two quantities are two quantities.
In mathematics, inverse variation refers to the relationships between variables that are expressed as y = k/x, where x and y are two variables and k is a constant value. It states that if the value of one quantity rises, the value of the other quantity falls.
Given, y varies inversely as [tex]x^{2}[/tex]
That is, y∝ 1/ [tex]x^{2}[/tex]
or, y = k/ [tex]x^{2}[/tex]
or, [tex]x^{2}[/tex]y = k
And, y=38 when x=18
Then, [tex]18^{2}[/tex]*38 = k
k = 12312
Now, if x=20 then y=?
[tex]x^{2}[/tex]y = 12312
or, [tex]20^{2}[/tex]*y = 12312
or, 400y = 12312
or, y = 12312/400 = 30.78
Hence, the required value of y is 30.78
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You have a student who says the sum of 3/4 and 5/6 is 4/5. Do you agree with them? Explain and solve this problem. Draw a model and explain how to solve this problem. Explain why we need common denominators.
The sum of 3/4 and 4/5 is 31/20 and To divide the common denominators by the individual denominators without using fractions or decimals, we need common denominators or the LCM of the two denominators.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, are two fractions 3/4 and 4.5 and their sum is,
= 3/4 + 4/5.
= (15 + 16)/20.
= 31/20.
So, the answer of the student is wrong.
We need common denominators or LCM of the two denominators so that we can divide the common denominators by the individual denominators without having fractions or decimals.
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At the July 1980 Olympics, the record for the women's shot put was 22.41 meters, which was 5.09 meters less than double the 1948 Olympic winning distance. What was the women's winning shot put distance in the 1948 Olympics?
The revenue, R(x), of producing and selling x Awesome Hearing Aids is modeled by the function: R(x) = -3x^2 +53x
a. How many hearing aids need to be produced and sold in order to maximize the revenue? Round to the nearest whole number. ______ hearing aids must be produced and sold to maximize revenue.
b. What is the revenue? Use the fraction from (a) then round answer to the nearest dollar. The maximum revenue is $ ________.
Answer:
9 ; $234
Step-by-step explanation:
the maximum revenue is the vertex of the parabola
a) -53/(2*-3)
-53/-6
53/6
8.833333
9
b
-3(53/6)^2 + 53(53/6)
-3(2809/36) + 2809/6
-2809/12 + 2809/6
(-2809 + 5618)/12
2809/12
234.083333
234
Part of your job as manager is to count the cash for the daily bank deposit. When you count thecash, you have 47 ones, 22 fives, 9 tens and 17 twenties. You also have 67 pennies, 12 nickels, 9dimes and 15 quarters. What is the total amount of the deposit?
Answer:
$592.92
Step-by-step explanation:
Part of your job as manager is to count the cash for the daily bank deposit. When you count the cash, you have 47 ones, 22 fives, 9 tens and 17 twenties. You also have 67 pennies, 12 nickels, 9dimes and 15 quarters. What is the total amount of the deposit?
47 ones = $47
22 fives = $110
9 tens = $90
17 twenties = $340
67 pennies = $0.67
12 nickels = $ 0.60
9 dimes = $0.90
15 quarters = $3.75
$47 + $110 + $90 + $340 + $0.67 + $ 0.60 + $0.90 + $3.75 = $592.92
Mackenzie is trying to find the height of a radio antenna on the roof of a local
building. She stands at a horizontal distance of 29 meters from the building. The
angle of elevation from her eyes to the roof (point A) is 24°, and the angle of
elevation from her eyes to the top of the antenna (point B) is 32°. If her eyes are 1.71
meters from the ground, find the height of the antenna (the distance from point A to
point B). Round your answer to the nearest meter if necessary.
The antenna's height is determined to be 10 m using right triangle relations.
What are the relations in a right triangle?Following are the relationships in a right triangle:
The sine of an angle is equal to the length of the hypotenuse divided by the length of the side opposite the angle.
The cosine of an angle is equal to the neighboring side's length divided by the hypotenuse's length.
The tangent of an angle is calculated by dividing the length of the angle's adjacent side by its opposite side.
So, n this case, the side opposite to the 17o angle is the vertical height from her eyes to the top of the antenna, and the next side is the horizontal distance of 29 m, then:
tan 17° = h/29
h = 29 tan 17°
h = 8.87
Including eye height:
h = 8.87 + 1.51 = 10.38 m.
The antenna is 10 meters tall, rounded to the nearest meter.
Therefore, the antenna's height is determined to be 10 m using right triangle relations.
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What is the image of (7, 8) after a reflection over the line y = -x?
Answer:
If you connect the 2 dots it will give a X image.Both lines will cross each other forming the X
What is the y-intercept of the
grouph of the line whose equation is
y = -2/5 x +4?
Answer:
b = 4
Step-by-step explanation:
y = mx + b represents the equation of a line
m represents the slope
b represents the y-intercept
Based on what we're given, we could determine that 4 is our y-intercept or b.
Ethan and his children went into a grocery store and he bought $6 worth of apples and bananas. Each apple costs $0.75 and each banana costs $0.30. He bought a total of 14 apples and bananas altogether. Determine the number of apples, x,x, and the number of bananas, y,y, that Ethan bought.
The number of apples x will be 10 and the number of bananas y will be 4.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Ethan and his children went into a grocery store and he bought $6 worth of apples and bananas. Each apple costs $0.75 and each banana costs $0.30. He bought a total of 14 apples and bananas altogether.
The number of apples and bananas will be calculated as,
0.75x +0.30y = 6
x + y = 14 or x = 14 - y
0.75(14-y) = 0.30y = 6
10.5-0.75y + 0.30y = 6
y = 10
x = 14 - y
x = 14 - 10 = 4
Therefore, the number of apples x will be 10 and the number of bananas y will be 4.
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If an object is dropped from a height of 85 feet, the function h(t) = -16t2 +85 gives the height
of the object after t seconds. Approximately, when will the object hit the ground?
Answer:
Step-by-step explanation: h(t)=-16t2+85
Let h(t)=0 to find when the object will hit the ground
0=-16t2+85
Solve for t=?
We need to get t term on its own
Take 85 from both sides
0-85=-16t2+85-85
-85=-16t2
To get t term on its own
Divide both sides by -16
-85/-16=-16t2/-16
5.3=t2
We have to solve for t squared that means we must take the square root of both sides
the square root of 5.3=gives + or - 2.3 seconds we can't have negative time so discard -2.3 seconds
Find the value.
4³ =
A
12
с
B
81
64
Answer: 64
Step-by-step explanation:
43 = (4)(4)(4)
=64
OR
4x4x4=64
eg=72. if ef = 4x-3 and fg = 6x+9 then x+?
The value of x has been solved as 6.4
How to solve for xWe would have EG = EF + FG
where EG = 70
EF = 4x-3
FG = 6x+9
We would have to put these values in the equation that we have above, such that we would have, To the respective variables, connect the related terms:
70 = (4x-3) + (6x+9)
Separate the x variable. Because of the equal symbol, everything you do on one side also affects the other.
Open the brackets
70 = 4x + 6x -3 + 9
70 = 10x + 6
70 - 6 = 10x
64 = 10x
divide through by 10
x = 64 / 10
x = 6.4
Hence the value of x would be given as 6.4
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can someone help me quick? don’t just put the answer, explain it please
Step-by-step explanation:
Riders must be at least 48 inches. "At least" means greater than or equal to. Therefore, the inequality is:
h ≥ 48
To graph this, we draw a solid dot at the 48 mark (because it can equal 48) and an arrow to the right (because it can be greater than 48).
Help me plssss I dead don’t get this asap
Answer:
i don't know but its not B or D and my guess is A
Step-by-step explanation:
What is the complete factorization of the polynomial below?
x³-2x²+x-2
A. (x-2)(x + 1)(x-1)
B. (x + 2)(x + 1)(x-1)
C. (x + 2)(x-1)(x-1)
D. (x-2)(x-1)(x-1)
Answer:
(x-2)(x^2+1)
do not exist the answer, so check your question
Step-by-step explanation:
(x^3-2x^2)+(x-2) = x^2(x-2)+(x-2)
= (x-2)(x^2+1)
If cos(θ)=-1/4 and θ is in the 3rd quadrant, find the exact value for
sin(θ).
Consider the graph of the function.
Which best represents the graph of the function?
Responses
f(x)=x−8−−−−√+2
f
(
x
)
The equation of the function represented by the graph is (d) g(x) = √(x + 9) - 1
How to describe the transformed equation from the parent function?From the question, we have the graph that can be used in our computation:
The parent function of the graph is a square root function
This is represented as
f(x) = √x
First, we have the transformation to be:
The function is translated left by 9 units
Next, we have:
The function is translated down by 1 unit
Mathematically, this can be represented as
g(x) = f(x - 9) - 1
When represented as an equation, it is
g(x) = √(x + 9) - 1
Hence, the transformation is (d) g(x) = √(x + 9) - 1
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WILL GIVE BRAINLY, BUT WILL REPORT NONSENSE ANSWERS...
Why doesn't the following function have a hole at x=2, the function is 3x(x-2)/(x-2)(x-2)?
Answer:
This is because the function is an exception - it is a special type of function called a Separatrix Separation Function.
Step-by-step explanation:
The Separatrix Separation Function theorem helps us prove through complex conjugates the reason why there is no hole at x =2.
Work out the area of this triangle.
8 cm
11 cm
13 cm
Answer:
44
Step-by-step explanation:
BxH/2=Area
8x11=88
88/2=44
area=44
14,032.8/ 1,000 this is my q and a i nedd this to colm
Answer: 14.0328
Step-by-step explanation:
Answer: 14.032
Step-by-step explanation: you just have to move the decimal point
Drag and drop the range of each data set into the boxes.
Answer:
Data set 1: 20
Data set 2: 25
Step-by-step explanation:
Range is where you take the lowest value and subtract it from the highest value. So with data set 1, the highest number is 40 and the lowest is 20.cSo 40-20=20. Answer 20. Then with data set number 2, the highest number is 60 and the lowest is 35. So 60-35=25. Answer 25.
I hope this helps!!!
A person standing close to the edge on top of a 48-foot building throws a ball vertically upward.
The quadratic function
h(t) = 16t+52t + 48 models the ball's height about the ground, h(t) in feet, t seconds after it was thrown. What is the maximum height of the ball? (Write the answer to the nearest hundredth)
After solving, the maximum height of the ball is 90.25 feet.
In the given question,
A person standing close to the edge on top of a 48-foot building throws a ball vertically upward.
The quadratic function
h(t) = -16t^2+52t + 48 models the ball's height about the ground, h(t) in feet, t seconds after it was thrown.
We have to find the maximum height of the ball.
Height is given that;
h(t) = -16t^2+52t + 48
Now comparing the given equation by the standard equation ax^2+bx+c=0
Here b = 52, a = -16
For maximum height put t= -b/2a
t = -52/2(-16)
t = 52/32
t = 1.625
Maximum height
h(1.625) = -16(1.625)^2+52(1.625) + 48
h(1.625) = -42.25+ 84.5 + 48
h(1.625) = 90.25 feet
The maximum height of the ball is 90.25 feet.
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Which relation is a function?
Answer:
i think A is a function because when you search what it looks like it looks kind of like A so i am sure it is A
Step-by-step explanation:
Systolic blood pressure for a group of women is normally distributed, with a mean of 115 and a standard deviation of 9. Find the probability that a woman selected at random has the following blood pressures. (Round your answers to four decimal places.) (a) greater than 130 (b) less than 108 (c) between 108 and 122
The probability that the blood pressure of woman is more than 130 by given normal distribution is 0.9505
What is z-value?
The standard score in statistics is the amount of standard deviations that a raw score deviates from or exceeds the mean of the phenomenon being observed or assessed. Standard scores are positive for raw scores above the mean.
We are given a normal distribution with a mean value 115 and standard deviation 9
And we are asked to find the probability that a woman selected at random has blood pressure greater than 130
We first find the z-value
z= (x-μ)/σ
z= (130-115)/9
z= 15/9
z= 1.6666
Now the corresponding value is
Probability is 0.95
Hence the probability is 95%
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