-Polynomial Functions-Write and solve a system of equations to find the quadratic function with the given zeros and y-intercept. Write rational coefficients as reduced fractions.
Answers
We We SOLUTION
Given the question in the image tab, the following are the solution steps to get the quadratic functions
Step 1: Write the zeroes and the y-intercept
\(\begin{gathered} \text{roots}=\text{zeroes}=-1\text{ and 5} \\ (x,y)=(0,3),\text{ y-intercept=3} \end{gathered}\)Step 2: Write the general factored form formula
\(f(x)=a(x-r_1)(x-r_2)\)Step 3: Get the value of a using the zeroes and the points written in step 1
\(\begin{gathered} f(x)=a(x-(-1))(x-5) \\ f(x)=a(x+1)(x-5) \\ \operatorname{Re}call\text{ that x=0 and y=3} \\ 3=a(0+1)(0-5) \\ 3=a(1)(-5) \\ 3=-5a \\ a=-\frac{3}{5} \end{gathered}\)Step 4: Write the quadratic function for the system using the formula in step 2
\(f(x)=-\frac{3}{5}(x+1)(x-5)\)Hence, the quadratic function with the given zeroes and y-intercept in a reduced fraction form will be:
\(f(x)=-\frac{3}{5}(x+1)(x-5)\)Related Questions
A copy machine makes 84 copies in 3 minutes and 30 seconds, how many copies does it make per minute.
Answers
Answer:
24
Step-by-step explanation:
3 minutes and 30 seconds = 3.5 minutes
84/3.5 = 24copies/minute
Last week, a chocolate shop sold 9 ounces of white chocolate. It sold 9 9/10 times as much milk chocolate as white chocolate. How many ounces of milk chocolate did the shop sell?
please answer asap
Answers
Solving the Question
We're given:
9 ounces of white chocolate sold\(9\dfrac{9}{10}\) times as much milk chocolate as white chocolate soldIf the shop sold " \(9\dfrac{9}{10}\) times as much milk chocolate as white chocolate", we must multiply \(9\dfrac{9}{10}\) by the amount of white chocolate sold to find the amount of milk chocolate sold.
Multiply \(9\dfrac{9}{10}\) by 9 ounces:
\(9\dfrac{9}{10}\times9\)
Convert the fraction into an improper fraction:
\(=\dfrac{99}{10}\times9\)
Multiply:
\(=\dfrac{891}{10}\)
AnswerThe shop sold \(\dfrac{891}{10}\) ounces of milk chocolate.
How much interest must you deposit in an account to earn $400 per year at 2% simple interest?
Answers
time is measured in seconds
(c) If a plane travels at x-110 mph for 3.5 hr, write an expression that represents the distance traveled. The expression that represents the distance traveled is mi. X
Answers
Answer:
Step-by-step explanation:
The distance traveled by the plane can be represented by the expression: distance = speed x time
In this case, the speed of the plane is given as x-110 mph and the time it travels is 3.5 hours.
So the expression for the distance traveled is:
distance = (x-110) * 3.5 miles
This expression represents the distance traveled in miles. The variable x represents the speed of the plane in mph.
(4x-7)
(3x+12)
Angle?
Answers
I'm assuming you mean factorise, in this case the answer is 12x²+27x-84
If you mean find out what x is, x=\(\frac{7}{4}\) and x=-4
Question content area top
Part 1
A new bank customer with $ wants to open a money market account. The bank is offering a simple interest rate of %.
a. How much interest will the customer earn in years?
Answers
years will be, $ 660
Step-by-step explanation:
Given:
Principle = $3000
Interest rate = 1.1 %
Time = 20 years
Now we have to determine the simple interest.
Formula used:
S.I = PRI
100
where,
P = principle
R = interest rate
T= time
S.I = simple interest
Now put all the given values in the above formula, we get:
5.1 =
_ ($3000)x1.1x(20)
100
S.I = $660
Thus, the interest customer earn in 20 years will be, $ 660
Let A be a 3 X 4 matrix. If
b = a1 + a2 + a3 + a4
then what can you conclude about the number of solutions of the linear system Ax=b?
Explain.
Answers
Answer:
Let A be a 3 X 4 matrix. If
b = a1 + a2 + a3 + a4
then what can you conclude about the number of solutions of the linear system Ax=b?
Explain.
The system has infinitely many solutions
Step-by-step explanation:
Since b= a1 + a2 + a3+ a4 if it follows that x= (1,1,1,1)^T is a solution to the equation Ax = b.
Since the matrix contains 3 rows there can be 3 nonzero rows and consequently
3 lead variables at most after we compute the row echelon form of the matrix
At least of the variables is free variables is free variable.
The system has infinitely many solutions
Sam is going to paint the outside of a cylindrical grain silo. He only needs to paint the lateral surface and roof.
If the radius of the roof is x feet and the silo is y feet high, which expression represents the surface area Sam needs to paint?
a. 2πxy
b. πx^2 + 2πxy
c. 2πx^2 + 2πxy^2
d. 2πx^2 + 2πxy
Answers
The surface area Sam needs to paint on the cylinder is πx² + 2πxy i.e. B.
What exactly is a cylinder?
In geometry, a cylinder is one of the fundamental 3d forms with two parallel circular bases at a distance. A curving surface connects the two circular bases at a predetermined distance from the centre. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases. One real-world example of a cylinder is an LPG gas-cylinder.
Because the cylinder is a three-dimensional form, it has two primary properties: surface area and volume. The cylinder's total surface area (TSA) is equal to the sum of its curved surface area and the area of its two circular bases.
The volume of a three-dimensional cylinder is the space it occupies (V).
TSA=2πr²+2πrh, where r is the radius and h is the height.
Now,
Given that the radius of the roof is x feet and the silo is y feet high
Area of roof=πx² and
curved surface area=2πxy
then the surface area Sam needs to paint=πx²+2πxy
Hence,
The surface area Sam needs to paint on the cylinder is
πx² + 2πxy.
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What is the y-intercept of y= 2/3x+2
1.(2,3)
2.(3,2)
3.(0,2)
4.(-3,0)
Answers
Which of the the coordinates is equal to sin (4pi/5) ?
A) x-coordinate of point A
B) y-coordinate of point A
C) x-coordinate of point B
D) y-coordinate of point B
E) x-coordinate of point C
F) y-coordinate of point C
Answers
Answer:
Step-by-step explanation:
π/2 < 4π/5 < π
4π/5 is in Quadrant II
sin(4π/5) = y-coordinate of A
The coordinates is equal to sin(4π/5) = y-coordinate of A.
We need to find the coordinates is equal to sin (4pi/5).
Which trigonometric functions are positive in which quadrant?In first quadrant (0 < θ < π/2), all six trigonometric functions are positive.
In second quadrant(π/2 < θ < π), only sin and cosec are positive.
In the third quadrant (π < θ < 3π/2), only tangent and cotangent are positive.
In fourth (3π/2 < θ < 2π = 0), only cos and sec are positive.
Then, we have π/2 < 4π/5 < π
So, 4π/5 is in Quadrant II
Hence, the coordinates is equal to sin(4π/5) = y-coordinate of A.
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which is the correct answer?
Answers
Step-by-step explanation:
Step 3 is incorrect, it should be x - 4 + x = x(x - 3).
x - 4 + x = x(x - 3)
2x - 4 = x² - 3x
x² - 5x + 4 = 0
(x - 4)(x - 1) = 0
x = 4 or x = 1.
x = 4 is rejected as 1 / (x - 4) will become 1 / 0 which is undefined.
=> x = 1.
Given that a+b = 10 and a square - b square = 40 find the value of a-b
Answers
Answer:
the value of a - b is 4.
Step-by-step explanation:
We have been given the following two equations:
a + b = 10 ------------(1)
a² - b² = 40 -------(2)
We can factor the left-hand side of equation (2) using the difference of squares identity:
(a + b)(a - b) = 40
Substituting equation (1) into this equation, we get:
10(a - b) = 40
Dividing both sides by 10, we get:
a - b = 4
Therefore, the value of a - b is 4.
Step-by-step explanation:
if I understand this correctly :
a + b = 10
a² - b² = 40
(a² - b²) = (a + b)(a - b) = 40
10(a - b) = 40
(a - b) = 4
Which division problem is represented with this model?
Responses
15÷2
1 fifth divided by 2
15÷6
1 fifth divided by 6
16÷2
1 over 6 end fraction divided by 2
12÷5
1 half divided by 5
Answers
Answer:
C.
Step-by-step explanation:
We have five unshaded, 1 half of unshaded, and 1 shaded, Thus, It will be showed as \(\frac{1}{6}\) ➗ \(2\)
9. CONSTRUCT AN ARGUMENT Determine
if the following statement is true or false.
Construct an argument to defend your
response.
Proportions can only be used to solve
problems where the smaller values are
known and a larger value is unknown.
Answers
Answer:
Step-by-step explanation:
The correct answer is true. If you know that the relationship between quantities is proportional, you can use proportions to find missing quantities.
13. Pls help thank you
No work necessary
A, B, C, or, D ?
Answers
Answer: C
Step-by-step explanation:
Try These questions out and I’ll give you brainliest
Answers
The expressions are simplified to;
1. 72n² + 63n
2. 18t - 18t²
3. -18b² - 18b
4. -56r - 21r²
5. -6m + 9m²
What are algebraic expressions?Algebraic expressions are simply described as expressions that are known to consist of coefficients of variables, variables, constants, terms, and factors.
These algebraic expressions are also made up of mathematical or arithmetic operations.
These operations are;
BracketParenthesesAdditionMultiplicationDivisionSubtractionFrom the information given, we have;
1. -9n (-8n -7)
expand the bracket
72n² + 63n
2. -2t(-9 + 9t)
expand the bracket
18t - 18t²
3. -3b(6b + 6)
expand the bracket
-18b² - 18b
4. -7r(8 + 3r)
expand the bracket
-56r - 21r²
5. 3m(-2 + 3m)
expand the bracket
-6m + 9m²
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0 Mark this and return
Answers
The equations that can be used to find the length of the rectangular room are:
y² - 5y = 750
750 - y(y - 5) = 0
(y + 25)(y – 30) = 0
What is the Area of a Rectangular Room?Area of a rectangular room = length × width.
Given the following:
Length of the rectangular room = y ft
Width of the rectangular room = y - 5 ft
Area = 750 square ft
Therefore:
750 = y(y - 5)
750 - y(y - 5) = 0
y² - 5y = 750
Expand
y² - 5y - 750 = 0
Factorizing the equation, we would have:
(y + 25)(y – 30) = 0
We can then find value of y, which is y = -25 or y = 30.
Therefore, the equations we can use are:
y² - 5y = 750
750 - y(y - 5) = 0
(y + 25)(y – 30) = 0
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CAN SOMEONE HELP WITH THIS QUESTION?✨
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The percentage error in the density of metal will be 3.4%.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that the density of the metal in the handbook is 4.018 g/mL and the measured value of the density is 4.16 g/mL.
The percentage error will be calculated as:-
Percentage = [ ( 4.16 - 4.018 ) / 4.16 ] x 100
Percentage = 0.034x 100
Percentage = 3.4%
Hence, the percentage error will be 3.4% for the densities.
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A person's Body Mass Index (BMI) is a measure of the amount of fat in their body. The relationship between antioxidant food consumption per day in cups and the BMI of an individual is modeled by the following line of best fit: \(y=-1.2x+26\) . Interpret the slope and intercept of the trend line within the context of the data.
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NO LINKS ALLOWED!
Answers
Answer:
The slope of -1.2 means that for each cup of antioxidant a person consumes per day, it's BMI decreases by 1.2.
The intercept of 26 means that a person that does not consume any cup of antioxidant food a day should have an BMI around 26.
Step-by-step explanation:
Line of best fit:
\(y = -1.2x + 26\)
Slope:
The slope is the number that multiplies x, that is, -1.2. The slope of -1.2 means that for each cup of antioxidant food a person consumes per day, it's BMI decreases by 1.2.
Intercept:
Value of y when x = 0, that is, 26. The intercept of 26 means that a person that does not consume any cup of antioxidant food a day should have an BMI around 26.
Answer:
the slope is -1.2 and the intercept is 26.
Step-by-step explanation:
our line's equation is y= -1.2x + 26
In the equation y = mx + b, m is the slope and b is the y-intercept. So in this equation, look for where the numbers are placed and that it what you get.
Mr. and mrs. Brown bought a new kitchen table for $450. It was 75% of the original price. Determine the original price of the kitchen table.
Answers
Answer:
$600
Step-by-step explanation:
To find the original price, divide the cost by 0.75
450/0.75
= 600
So, the original price was $600
Answer: $600
Step by Step explaination:
Solve for c
X=
4
X Х
8
9
Answers
Answer:
C is 356
Step-by-step explanation:
Two increased by the product of a number and 7 is at most -29
Answers
The number that satisfies the equation is x = -31/7. This means that if we increase two by the product of a number and 7, the result is at most -29 if the number is -31/7.
The expression we need to solve is "Two increased by the product of a number and 7 is at most -29". We can express this as 2 + x × 7 ≤ -29 where x is the number we need to find.In order to solve this equation, we need to start by isolating the variable x. We can subtract 2 from both sides of the equation to get x × 7 ≤ -31. Then, we divide both sides of the equation by 7 to get x ≤ -31/7.Therefore, the number that satisfies the equation is x = -31/7. This means that if we increase two by the product of a number and 7, the result is at most -29 if the number is -31/7.
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The number that satisfies the equation is x = -31/7. This means that if we increase two by the product of a number and 7, the result is at most -29 if the number is -31/7.
The expression we need to solve is "Two increased by the product of a number and 7 is at most -29". We can express this as 2 + x × 7 ≤ -29 where x is the number we need to find.In order to solve this equation, we need to start by isolating the variable x. We can subtract 2 from both sides of the equation to get x × 7 ≤ -31. Then, we divide both sides of the equation by 7 to get x ≤ -31/7.Therefore, the number that satisfies the equation is x = -31/7. This means that if we two by the product of a number and 7, the result is at most -29 if the number is -31/7.
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the number can be divided by the least common multiple of 3 and 5
the hundreds digit is 2
the sum of all three digits is 12
Answers
9514 1404 393
Answer:
255
Step-by-step explanation:
If the sum of digits is 12, the number is divisible by 3. If the number ends in 0 or 5, it is divisible by 5. So, we're looking for ...
2x0 . . . where x is a digit and 2+x+0 = 12 . . . . . . not possible
2x5 . . . where x is a digit and 2+x+5 = 12 . . . . true for x=5
The number is 255.
You bought some new fish and need the tank ready. You fill the tank with water and start running the filter system.You check the temperature of the water after 2 hours and notice the water is 78 degrees Fahrenheit. You need the temperature to be at 72 degrees Fahrenheit. after three additional hours and the water temperature is at so, you add the fish. What was the temperature when you first filled the tank?
Answers
Answer:
82 degrees
Step-by-step explanation:
It took 3 hours for it to go from 78 to 72.
Which is a rate of -2 degrees per hour
We want to know what the temperature was two hours before it was 78 degrees so we'd do 78 - (-2) which is 82
carla bought 42 tomato plants.she planted them in 7 rows .how many plants are in each row?
Answers
Answer:
6 plants.
Step-by-step explanation:
42 = total.
7 = rows
42 divided by 7 = 6 plants in each row
If carla bought 42 tomato plants. she planted them in 7 rows then there are 6 plants in each row.
What is Division?A division is a process of splitting a specific amount into equal parts.
Given that carla bought 42 tomato plants
Carla planted them in 7 rows
We need to find the number of plants in each row.
The total number of plants=42
Number of rows=7
Number of plants in each row we get by dividing 42 by 7 which means we are splitting 42 to 7 equal parts
42/7
6
So 6 plants in each row
Hence, if carla bought 42 tomato plants. she planted them in 7 rows then there are 6 plants in each row.
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PLEASE HELP! I JUST NEED TO KNOW HOW YOU SOLVE THIS!!! SEE ATTACHED!!! WILL MARK YOU BRAINLIEST!!! Surface Area
Answers
The surface area of the complex solid is 530 square yards.
How to determine the surface area of a complex solid
In this problem we need to determine the surface area of the complex solid, that is, the sum of the area of all faces of the solid. The area formulas required to find the surface area is:
A = w · h
Where:
A - Area, in square yards.w - Width, in yardsh - Height, in yards.The surface area of the complex solid is:
A = 2 · (11 yd) · (3 yd) + 2 · (4 yd)² + (12 yd) · (11 yd) + (12 yd) · (3 yd) + (12 yd) · (7 yd) + 2 · (4 yd) · (12 yd) + (12 yd) · (7 yd)
A = 66 yd² + 32 yd² + 132 yd² + 36 yd² + 84 yd² + 96 yd² + 84 yd²
A = 530 yd²
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Malcolm has $50 gift card to a local car wash and order is the ultimate car wash each visit is $8.95
Answers
The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.
The correct answer choice is option B.
How much cheaper is the car washes Malcolm orders than the car washes Martha's order?Malcolm's gift card = $50.
Cost Malcolm's car wash per visit = $7
Martha's gift card = $180
Cost Martha's car wash per visit = Difference between gift card balance of first and second visit
= $180 - $160
= $20
How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7
= $13
Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13
The complete question is attached in the diagram.
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A bag of color tiles contains 2 red, 1 blue, 1 green, and 4 yellow. Sean reaches in and draws one
tile without replacing it. He then draws a second tile and a third tile without replacing them. Which
of the following combinations is a possible draw?
F:red,blue,blue G:red,green,green H:yellow,blue,green J:blue,blue,green
Answers
Answer:
H
Step-by-step explanation:
Since there is 4 yellows, 1 green, and 1 blue, there is no way you could draw 2 blues or 2 greens. Therefore, F, G, and J are immediately eliminated. The only answer left is H, and it makes sense. H is the answer.
Answer:
H: yellow, blue, green
Step-by-step explanation:
F: red, blue, blue = cannot be true as there is 1 blue tile in bag and it cannot be drawn twice without replacing first draw.
G: red, green, green = cannot be true because 1 original green tile in bag cannot be drawn twice
J: blue,blue, green = cannot be true for same reason; 1 original blue tile cannot be drawn twice without replacement.
6x -8=16 solve equation
Answers
Answer:
x = 4
Step-by-step explanation:
6x - 8 = 16 (add 8 to both sides)
6x = 24 (divide by 6 on both sides)
x = 4
Brainliest, please :)
Step-by-step explanation:
6x=16+8
6x=24
6x/6=24/6
x=4
so the answer is 4
The graph shows the distance traveled by an Olympic-level sprinter over time during a race.
Find the slope of the line, and complete the sentences below.
100 meter race graph of a diagonal line on a coordinate plane going up and to the right with Time in seconds on the x axis and Distance in meters on the y axis. The line begins at the origin and passes through the point 2 comma 20.
The slope of the line is
Choose...4,10,20,2
. The slope represents
Choose...the distance the sprinter runs, the sprinter's speed in seconds per meter, the sprinter's speed in meters per seconds, the time the sprinter runs
.
Answers
The slope of the line is 10. The slope represents the sprinter's speed in meters per seconds.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Given:
From the graph,
we interpreted two points (2, 20) and (4, 40)
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
m = (40 - 20) / (4-2)
m = 20 / 2
m = 10 meter per second
Therefore, the slope is 10.
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