We want to get a quadratic equation by knowing its tangent line at a point. Remember that the tangent line is given by the derivative of the equation.
We will find that the parabola is:
y = 3*x^2 - 4*x
We start with the tangent line:
y₂ = 8*x - 12
The slope of this tangent line is equal to the derivative of our parabola evaluated in x = 2.
Our parabola is y = a*x^2 + b*x
Derivating we get:
y' = 2*a*x + b
Then we have:
2*a*2 + b = 8
And we also know that our parabola passes through the point (2, 4), then we must have:
4 = a*2^2 + b*2
Then we have a system of equations:
2*a*2 + b = 8
4 = a*2^2 + b*2
First we can simplify the equations:
4*a + b = 8
4 = 4*a + 2*b
We can isolate 4*a in the first equation to get:
4*a = 8 - b
Now we can replace it in the second equation:
4 = (8 - b) + 2*b
4 = 8 + b
4 - 8 = b
-4 = b
Now that we know the value of b, we can use
4*a = 8 - b
4*a = 8 + 4 = 12
a = 12/4 = 3
Then the equation of the parabola is:
y = 3*x^2 - 4*x
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Drag the correct tiles that match.?
best estimate of 48% of 60
The point A(-3,5) and the point B(1,-15) lie on the line L. Find the equation of the line L.
The equation of the line L is : y = -5x - 10..or 5x + y = -10
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
where (x₁, y₁) and (x₂, y₂) are the two points that you are trying to find the slope between.
Given; The point A(-3,5) and the point B(1,-15) lie on the line L.
The slope = (-15 - 5) / (1 - (-3)
= -20/4
m = -5
Therefore, y = mx + b
The slope(m) = -5
Now use either of ur points...(-3,5)...x = -3 and y = 5
Thus, we subtract and find b, the y value,
5 = -5(-3) + b
5 = 15 + b
5 - 15 = b
-10 = b
Thus the equation is : y = -5x - 10..or 5x + y = -10
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What set of 3 numbers have GCF of 3
3x + 8 = -x + 20 What is x?
What is the equation of the circle shown in the graph
The equation of the circle will be x² + (y + 3)² = 4. Then the correct option is C.
What is an equation of a circle?A circle can be characterized by its center's location and its radius's length.
Let the center of the considered circle be at the (h,k) coordinate.
Let the radius of the circle be 'r' units.
Then, the equation of that circle would be:
(x - h)² + (y - k)² = r²
The center of the circle is at (0, -3) and the radius of the circle is 2 units. Then the equation of the circle will be
(x - 0)² + (y - (-3))² = 2²
x² + (y + 3)² = 4
Then the correct option is C.
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What are the steps to solve for: 1/5(x+5)=1/4(x-3)+1
What is the slope of the line passing through points A(−18,24) and B(16,−8)?
Enter your answer as a ratio, in simplest form, like this: 42/53
Write 9/4 as a decimal. Round to three decimal places
The fraction 9/4 can be written as a decimal by performing the division, resulting in 2.25. As this is already to three decimal places, the answer is 2.250.
Explanation:To write the fraction 9/4 as a decimal, you simply need to perform the division operation. Dividing 9 by 4 will give you the decimal. Using a calculator or long division, the result is 2.25.
However, your question asks for the answer to be rounded to three decimal places. Since 2.25 already falls within that criteria, there's no need for further rounding. Therefore, 9/4 as a decimal, rounded to three decimal places, is 2.250.
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Each beehive on larsons honey farm usually produces 85 pounds if honey per year. About how many pounds of honey wil 10 to 3power hives produce in a year
A rectangular soccer field is twice as long as it is wide. If the perimeter of a soccer field is 300 yards, what are the fields's dimensions?
14,560,000 in standard form ?
Answer:
In the US: 14,560,000
In Britain: 1.456×10⁷
Step-by-step explanation:
On the European side of the Atlantic, "standard form" for a number is the form called "scientifc notation" on the American side of the Atlantic.
If a well pumps at a rate of 8.4 gal per minute how long would it take to fill the tank described above
To calculate the time it takes to fill a tank using a well pump that pumps at 8.4 gallons per minute, divide the tank's volume (in gallons) by the pump's output rate (8.4 gallons per minute). For example, for a tank with a volume of 84 gallons, it would take about 10 minutes to fill.
Explanation:The time it takes to fill the tank with a well pump pumping at a rate of 8.4 gallons per minute depends on the size of the tank, which wasn't specified in your question. However, to calculate this, you would use the formula: Time = Volume / Rate. If 'Volume' is the size of your tank in gallons and 'Rate' is the rate the well pump can pump water in gallons per minute (8.4 in this case), you would divide the 'Volume' by the 'Rate' to get the time it would take to fill the tank in minutes.
For example, if your tank has a volume of 84 gallons, using our formula: Time = Volume / Rate, it would translate to Time = 84 / 8.4. This gives us a duration of 10 minutes.
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james has 14,500 g of sand in his sandbox. he brings hike another 7,400 g of sand from the beach to add to his sandbox
After the addition of sand in the sandbox the total amount of sand in the sandbox will be equal to 21900 grams.
What are arithmetic operations?The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.
They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.
As per the given information in the question,
Total amount of sand in the sandbox = 14,500 grams
Then, James adds 7400 grams more to the sandbox.
So,
The total amount of sand in the sandbox will be,
= 14500 + 7400
= 21900 grams.
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Your questions seem incomplete, so the complete question may be:
Jim has 19,700 g of sand in his sandbox. He brings home another 6,300 g of sand from the beach to add to his sandbox.
How many kilograms of sand does Jim have in his sandbox now?
A function of the form f(x) = mx + b, where m and b are real numbers, is called a _____ function.
The the function represented by f(x) = mx + b is called a linear function.
What is the equation for a straight line?A straight line can be written in the form of equation as, y = mx + c.
Two straight lines intersect each other only at one point.
When two straight lines are parallel to each other the angle between them is zero.
The given function is as below,
f(x) = mx + b
This function is equivalent to the point-slope function of a straight line where m represents the slope of the line and c is the y-intercept.
The degree of the given function is one.
Thus, it is a linear function.
Hence, a function of the form f(x) = mx + b, where m and b are real numbers, is called a linear function.
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How do you write 314,207 in standard form?
a sixth grade class has 12 boys and 24 girls consider this statement: <br />for every two boys there are 4 girls do you agree with this statement?
a central angle θ of a circle with radius 16 inches subtends an arc of 19.36 inches. find θ
The required measure of the angle Ф is given as Ф = 69.36°.
As mentioned in the question, a central angle θ of a circle with a radius of 16 inches subtends an arc of 19.36 inches.
What are the angles?Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
here,
Angle = [arc/radius] 180/π
Substitute the values in the above equation,
Ф = [19.36/16]180/3.14
Ф = 69.36°
Thus, The required measure of the angle Ф is given as Ф = 69.36°.
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Mr. Johnson used 80 meters of fencing to enclose a rectangular garden.
The length of the garden is 25 meters.
How wide is the garden?
A) 25
B) 15
C) 30
D) 50
25*2 = 50
80-50 =30
30 /2 = 15
Answer is B
Which equation best represents the graph shown above?
Y=-(x+1)^2-1
Y=(x-1)^2
Y=(x+1)^2
Y=-(x-1)^2+1
The square root of -108
what is 3/5 x +1.4y=2/5
The given equation is a linear equation in standard form. It can be solved for 'y' by isolating 'y' on one side. The resulting 'y' expression represents a straight line in a 2D coordinate system.
Explanation:The equation 3/5 x + 1.4 y = 2/5 is a linear equation in the standard form a*x + b*y = c. In this equation, 'x' and 'y' are variables, '3/5' is the coefficient of 'x', '1.4' is the coefficient of 'y', and '2/5' is a constant.
To solve this equation, we can neatly isolate 'y' by subtracting '3/5 x' from both sides of the equation which would give us 1.4*y = -3/5*x+2/5. Then, we could further simplify by dividing both sides by '1.4', giving the equation for 'y' in terms of 'x'.
Note that this equation represents a straight line in a coordinate system. The value of 'x' and 'y' would depend on the specific problem's constraints or where this line intersects with another line in a system of linear equations.
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Jackrabbits are capable of reaching speeds up to 40 miles per hour. How fast is this in feet per second? (Round to the nearest whole number.)
5,280 feet = 1 mile
40 x 5280 = 211200 feet per hour
211200 / 3600 = 58.666 = 59 feet per second
If the decimal form for a unit fraction is a repeating decimal is it possible for a multiple of that fraction to have a decimal form that is not a repeating decimal
Answer:
If a unit fraction has a repeating decimal, its multiples will also have repeating decimals. Division by the same divisor generates the same repeating pattern. Thus, multiples cannot avoid repetition.
Explanation:
If the decimal form for a unit fraction (a fraction where the numerator is 1) is a repeating decimal, then its reciprocal (the fraction obtained by flipping the numerator and denominator) will also be a repeating decimal. This is a consequence of the way division works.
For example, if [tex]\( \frac{1}{3} \)[/tex] is a repeating decimal (0.333...), then [tex]\( \frac{3}{1} \)[/tex] (which is [tex]\( 3 \times \frac{1}{3} \)[/tex] ) will also be a repeating decimal because dividing 3 by 1 will result in the same repeating pattern.
So, no matter how you multiply a unit fraction that has a repeating decimal representation, the resulting decimal will still be repeating. Therefore, it is not possible for a multiple of that fraction to have a decimal form that is not a repeating decimal.
Selena's family took a road trip. The first day they traveled 462 miles in 7 hours. They continued at the same rate on the second day and traveled for 4 hours. How far did they travel in all?
what is square root of 8 plus square root of 50 minus square root of 72
Answer:
1.41421356237 making it a terminating decimal.
Step-by-step explanation:
2.82842712475
+
7.07106781187
-
8.48528137424
Simplified Answer
1.4 or 1.41
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What is 8.61×10−8 in decimal form?
A.0.000000861
B.0.0000000861
C.8,610,000
D.861,000,000
Answer:
B. 0.0000000861
Step-by-step explanation:
The exponent of -8 tells you the leading digit (8) goes in the 8th spot to the right of the decimal point. The number is ...
[tex]0.0000\,0008\,61[/tex]
The ray XZ is the angle bisector of ∠WXY and m∠WXY = 105°. Enter m∠WXZ. The measure of ∠WXZ is
Answer:
∠WXZ = 52.5
Step-by-step explanation:
Angle Bisector is the line that divides that angle into two equal parts.
Hence, Ray XZ divide the ∠WXY into two equal parts.
⇒ [tex]\angle WXZ = \frac{1}{2} \angle WXY [/tex]
∴ [tex]\angle WXZ =\frac{1}{2}\times105^{\circ}=52.5[/tex]
⇒ ∠WXZ = 52.5
An angle bisector divides an angle into two equal parts.
The measure of [tex]\angle WXZ[/tex] is [tex]52.5^o[/tex]
Given that:
[tex]XZ \to[/tex] Bisector of [tex]\angle WXY[/tex]
[tex]\angle WXY = 105^o[/tex]
This means that:
[tex]\angle WXY = 2 \times \angle WXZ[/tex]
So, we have:
[tex]105^o = 2 \times \angle WXZ[/tex]
Divide both sides by 2
[tex]52.5^o = \angle WXZ[/tex]
Rewrite as:
[tex]\angle WXZ = 52.5^o[/tex]
Hence, the measure of [tex]\angle WXZ[/tex] is [tex]52.5^o[/tex]
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a student worked 5 days/week and 8h/day. he earned $300/week. What was his hourly rate of pay?
5 days x 8 hours per day = 40 hours total
300/40 = $7.50 per hour
The hourly rate for students will be $7.5 per hour.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
For example = 2 + 8 + 9
Subtraction = Minus of any two or more numbers with each other called subtraction.
For example = 4 - 8
Division = divide any two numbers or variable called division.
For example 4/8
Multiplication = to multiply any two or more numbers or variables called multiplication.
For example 5 × 7.
Given,
Number of days working in one week = 5 days
Number of hours working in one day = 8 hour
So,
A number of hour working in one week = 5 × 8 = 40 hours.
Now
Hourly rate of pay = Earning per week/number of hours working per week
Hourly rate of pay = 300/40 = $7.5.
Hence "The hourly rate for students will be $7.5 per hour".
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Which set of numbers can represent the side lengths, in centimeters, of a right triangle?
A. 8,12,15
B. 10,24,26
C. 12,20,25
D. 15,18,20
Answer:
B is the correct answer , B. 10,24,26
Step-by-step explanation: