Where does the normal line to the parabola y = x − x2 at the point (1, 0) intersect the parabola a second time?
The normal line to the parabola [tex]y=x-x^2[/tex] at the point [tex](1,0)[/tex] intersect it second time at the point [tex](-1,-2)[/tex].
The given equation is:
[tex]y = x-x^2[/tex]at point,
[tex](1,0)[/tex]then,
→ [tex]y' = 1-2x[/tex]
So, at (1,0),
→ [tex]y' = 1-2\times 1[/tex]
[tex]= -1[/tex]
Since,
This is the slope of the tangent, we take its negative reciprocal to get the slope of normal:
= [tex]-\frac{1}{(-1)}[/tex]
= [tex]1[/tex]
The normal line has slope 1 and goes through (1,0):
→ [tex]y-0=1(x-1)[/tex]
→ [tex]y = x-1[/tex]
We want to know where this intersects [tex]y = x-x^2[/tex], we get
→ [tex]x-1=x-x^2[/tex]
→ [tex]x^2=1[/tex]
→ [tex]x = \pm 1[/tex]
hence,
The point corresponding to (1,0) is the one we started with, so we want x=-1:
→ [tex]x = -1[/tex]
→ [tex]y = x-x^2[/tex]
By substituting the value of "x", we get
→ [tex]= -1-1[/tex]
→ [tex]= -1[/tex]
Thus the answer above is right.
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how do you know when to rewrite square trinomials and difference of squares as separate factors
Recognizing the specific forms of square trinomials and the difference of squares allows you to rewrite them as separate factors, simplifying algebraic expressions and facilitating further mathematical operations.
Knowing when to rewrite square trinomials and the difference of squares as separate factors depends on the algebraic expression you are dealing with. Let's consider each case separately.
1. Square Trinomials:
- Square trinomials have the form [tex]\(a^2 + 2ab + b^2\) or \(a^2 - 2ab + b^2\)[/tex], where(a) and (b) are algebraic expressions.
- These trinomials can be factored into the square of a binomial: [tex]\((a + b)^2\) or \((a - b)^2\).[/tex]
- You should rewrite a square trinomial as separate factors when you encounter an expression that matches the form of a perfect square trinomial. Recognizing this pattern allows you to simplify the expression.
2. Difference of Squares:
- The difference of squares has the form [tex]\(a^2 - b^2\),[/tex] where (a) and (b) are algebraic expressions.
- This expression can be factored into the product of conjugates: [tex]\((a + b)(a - b)\).[/tex]
- You should rewrite a difference of squares as separate factors when you have an expression in the form [tex]\(a^2 - b^2\)[/tex]. Recognizing this pattern helps you simplify and factor the expression efficiently.
Formula for volume and surface area of a cylinder and explain why
Read the following statement: x + 6 = 6 + x. This statement demonstrates:
the substitution property.
the reflexive property.
the symmetric property.
the transitive property.
The statement x + 6 = 6 + x demonstrates the symmetric property of equality.
Explanation:The given statement x + 6 = 6 + x represents the symmetric property.
The symmetric property of equality states that if a = b, then b = a. In this case, both sides of the equation are the same, with x and 6 appearing in different orders. Thus, the equation satisfies the symmetric property.
For example, if we let x = 2, the equation becomes 2 + 6 = 6 + 2, which is true.
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yo, can someone give me an algebraic expression with work that equals 3? & it also has to include addition & multiplication.
Determine the interest rate in order to Dublin investment in nine years assuming interest is compounded continuously
Divide 6 feet 6 inches by 5
Final answer:
To divide 6 feet 6 inches by 5, convert the length to inches, divide by 5, then convert back to feet and inches, resulting in 1 foot 3 inches per section.
Explanation:
To divide 6 feet 6 inches by 5, first convert the entire length to inches. Since there are 12 inches in 1 foot, 6 feet equals 72 inches (6 feet x 12 inches/foot). Adding the additional 6 inches gives us a total of 78 inches. Now, divide 78 inches by 5 to find the length of each section.
78 inches ÷ 5 = 15.6 inches per section.
To convert this back to feet and inches, remember that there are 12 inches in a foot. Therefore, 15 inches is 1 foot 3 inches, and the remaining 0.6 inches can be expressed as a fraction of an inch (0.6 x 12 = 7.2, which is approximately 7 inches). So, each section is 1 foot 3 inches.
A carnival game allows a group of players to each draw and keep a marble from a bag. The bag contains 5 gold marbles, 25 silver marbles, and 70 red marbles.
A player wins a large prize for drawing a gold marble and a small prize for drawing a silver marble. There is no prize for drawing a red marble.
At the start of the game, the probability of winning a large prize is 0.05 and the probability of winning a small prize is 0.25.
1. Suppose that the first player draws a silver marble and wins a small prize. What is the probability that the second player will also win a small prize?
2. If a group of four plays the game one at a time and everyone wins a small prize, which player had the greatest probability of winning a large prize?
3. How could the game be made fair for each player? That is, how could you change the game so that each player has an equal chance of winning a prize?
Can someone please help me solve 91
Identify the function that best models the data.
AB is tangent to circle O at B. what is the length of the radius r? Round to the nearest tenth. Look at image attached.
A circle is a curve sketched out by a point moving in a plane. The radius of the given circle is 8.4 units. The correct option is D.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
In a circle, a tangent is always perpendicular to the radius of the circle. Therefore, in the given figure the triangle formed will be a right angled triangle.
Now, in a right angle triangle, using the Pythagoras theorem the relation between the different sides of the triangle can be written as,
AO² = AB² + OB²
(9.8)² = 5² + r²
96.04 = 25 + r²
r² = 96.04 - 25
r² = 71.04
r = √(71.04)
r = 8.4
Hence, the radius of the given circle is 8.4 units.
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WHAT IS 50% OF 9? ROUND TO THE NEAREST HUNDRETH
Kit folds a bandana diagonally before tying it around her head. The side length of the bandana is 16 in. About how long is the diagonal?
The length of the diagonal of Kit's bandana tied around her head is approximately 22.63 inches long.
Kit folds a bandana diagonally.
To find the length of the diagonal (hypotenuse of a right triangle), we can use the Pythagorean theorem.
The bandana side length (a) is 16 in.
Let x be the length of the diagonal.
Using a^2 + a^2 = x^2, we get 16^2 + 16^2 = x^2. Solving this gives x ≈ 22.63 in.
Can someone help me out please ? Thanks!
In the triangle below, b = _____. If necessary, round your answer to two decimal places.
Answer: The value of b is approximately 54.94 .
Explanation:
In the given figure two angles are given and according to the angle sum property the sum of interior angles of a triangle is 180 degree.
[tex]\angle A+\angle B+\angle C=180[/tex]
[tex]42+\angle B+41.5=180[/tex]
[tex]\angle B=180-83.5[/tex]
[tex]\angle B=96.5[/tex]
According to the law of sine,
[tex]\frac{a}{\sin A} =\frac{b}{\sin B} =\frac{c}{\sin C}[/tex]
From given figure, [tex]\angle A=42,a=37[/tex]
[tex]\frac{37}{\sin (42^{\circ})}= \frac{b}{\sin (96.5^{\circ})}[/tex]
[tex]\frac{37}{0,66913} =\frac{b}{0.99357}[/tex]
[tex]b=54.94018[/tex]
[tex]b\approx 54.94[/tex]
Therefore, the value of b is 54.94.
Determine the number of possible triangles, ABC, that can be formed given B = 45°, b = 4, and c = 5.
Answer:
2
Step-by-step explanation:
this is right trust
(15 POINTS) A card is drawn from a deck of 52. What is the probability of drawing either a diamond or a seven?
A) 6/13
B) 17/52
C) 19/52
D) 4/13
Answer:
The correct answer is 4/13
Step-by-step explanation:
The events "drawing a diamond or a seven" are inclusive events since there is a seven of diamonds. Follow the rule for inclusive events.
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
Hope this helps! :)
Find the value of x.
A.
25
B.
32.5
C.
37.5
D.
65
Answer: The correct option is (A) 25.
Step-by-step explanation: We are given to find the value of x from the figure shown.
From the figure, we note that there are two parallel lines and a transversal.
Also, the angles with measurements (x + 40)° and (3x - 10)° are corresponding angles.
Since the measures of two corresponding angles are equal, so we must have
[tex](x+40)^\circ=(3x-10)^\circ\\\\\Rightarrow x+40=3x-10\\\\\Rightarrow 3x-x=40+10\\\\\Rightarrow 2x=50\\\\\Rightarrow x=\dfrac{50}{2}\\\\\Rightarrow x=25.[/tex]
Thus, the required value of x is 25.
Option (A) is CORRECT.
The table below shows the number of students in a school who like tacos and/or pizza:
Like Tacos Do Not Like Tacos Total
Like Pizza 57 13 70
Do Not Like Pizza 12 15 27
Total 69 28 97
What is the relative frequency, by row, of students who like both tacos and pizza?
0.18
0.46
0.81
0.83
Answer:
Relative frequency, by row, of students who like both tacos and pizza is:
0.81
Step-by-step explanation:
Like Tacos Do Not Like Tacos Total
Like Pizza 57 13 70
Do Not Like Pizza 12 15 27
Total 69 28 97
The relative frequency by row is calculated as the ratio of the frequency of the required field to the total frequency of that row
Hence, relative frequency, by row, of students who like both tacos and pizza is:
57/70
=0.81
Joe multiplies a number by 4, adds 1, and then divides by 3, getting a result of 7. sue divides the same original number by 3, adds 1, and multiplies by 4. what result does she get? express your answer as a common fraction.
Sue divides the initial number (which is 20/3 in this case) by 3, adds 1, and then multiplies by 4. Simplifying this we find her result to be 80/9 or 8 8/9.
Explanation:Let's denote the initial number as 'x'. If Joe multiplies 'x' by 4, adds 1 and then divides by 3, getting 7, we can say that (4x+1)/3 = 7. Solving this equation, we find that x = 20/3.
Now let's apply this value to Sue's operations. Sue divides the initial number (which is 20/3) by 3, adds 1, and then multiplies by 4. Therefore, Sue's result is 4*((20/3)/3 + 1). Simplifying this expression, we obtain that Sue's result is 80/9 or 8 8/9.
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Need help. Thank you
How do I find the linear equation for y=4x-5
Mia's perents said that she can use a space in the yard that measures. 13 feet long by 9 feet wide for her wildflower garden. What is the area of the garden
The area of 13 feet long by 9 feet wide wildflower garden is 117 square feet.
Use the concept of a rectangle defined as:
Rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from a square in that its opposite sides are equal in length.
To find the area of her garden,
Multiply the length and width of the space.
In this case,
the length is 13 feet and the width is 9 feet.
So, the area of Mia's garden would be,
13 feet x 9 feet = 117 square feet.
Hence,
The area of the garden is 117 square feet.
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77+14 is the same as blank +11
A right triangle has leg lengths of x units and 3(x + 1) units. Its hypotenuse measures 25 units. Find the leg lengths. URGENT! Brainliest to the best answer!
the gas tank on a car holds 16.6 gallons. If the car goes 332 miles on a single tank how many miles per gallon does the car get
A 18 miles
B 20 miles
C 17 miles
D 19 miles
(as with any math question I ask I would also like an explanation of why the answer is what it is//how you get the answer so I am able to do it on my own the next time)
The car gets 20 miles per gallon.
Explanation:To find the miles per gallon the car gets, we need to divide the total miles driven by the number of gallons of gas used. In this case, the car goes 332 miles on a single tank, and the gas tank holds 16.6 gallons. So, the miles per gallon can be calculated as:
Miles per gallon = Total miles driven / Number of gallons used
Miles per gallon = 332 miles / 16.6 gallons
Miles per gallon = 20 miles
Therefore, the car gets 20 miles per gallon.
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Solve the system by the elimination method.
x + y - 6 = 0
x - y - 8 = 0
When you eliminate y , what is the resulting equation?
Answer: 2x = 14
Step-by-step explanation:
Solving the equation us in elimination method,
x + y - 6 = 0...1
x - y - 8 = 0...2
From 1,
x+y = 6...3
x-y = 8...4
To eliminate y, we will add equation 3 and 4 since both the signs attached to y are different.
2x=6+8
2x = 14 (This will be the resulting equation)
To get the variables x, we will divide both sides of the resulting equation by 2
x = 14/2
x = 7
Substituting x = 7 into eqn 3
7 + y = 6
y = -1
A bird's nest is on top of a power pole that is 30 feet tall. The bird is above the nest and the angle formed from the nest to the bird is 25°. The horizontal distance from the bird to the pole is 100 feet. Approximately how far is the bird above the ground?
Help identify!!!! ADB
The value of angle ADB in the triangle ADB is determined as m∠ ADB = 95⁰. (Option A).
How to calculate angle ADB?
The value of angle ADB is calculated by applying intersecting chord theorem and principle of sum of angles in a triangle.
The intersecting chord theorem states that the angle at tangent is half of the arc angle of the two intersecting chords.
So the value of angle A is calculated as follows;
m ∠ BAC = ¹/₂ x arc BC
m ∠ BAC = ¹/₂ x 110
m ∠ BAC = 55
The value of angle ADB is calculated as follows;
m ∠ ABD + m ∠ ADB + m ∠ BAD = 180 (sum of angles in a triangle)
30 + m ∠ ADB + 55 = 180
m ∠ ADB + 85 = 180
m ∠ ADB = 180 - 85
m ∠ ADB = 95⁰
Calculate the average rate of change for the graphed sequence from n = 2 to n = 4. graphed sequence showing point 1, negative 3, point 2, negative 3.5, point 3, negative 6.75, point 4, negative 10.125, point 5, negative 15.1875, and point 6, negative 22.78125
I believe the given sequence is in the tabular form of:
n value
1 - 3
2 - 3.5
3 - 6.75
4 - 10.125
5 - 15.1875
6 - 22.78125
Now to find for the average rate of change from n1 = 2 to n2 = 4, we simply have to use the formula:
average rate of change = (value2 – value1) / (n2 – n1)
Substituting:
average rate of change = (- 10.125 – (-3.5)) / (4 – 2)
average rate of change = (- 6.625) / (2)
average rate of change = -3.3125
Therefore the average rate of change from n=2 to n=4 is -3.3125.
Answer:
B or −3.3125
Step-by-step explanation:
flex point 2023