Final answer:
Equations of lines that intersect a parabola at distinct points can vary, but typically involve conditions based on the slope and y-intercept relative to the vertex of the parabola. For two points, a non-tangent linear equation; for one point, a tangent with slope equal to the parabola's derivative at the intersection; for no points, the line lies entirely outside the parabola's path.
Explanation:
To find equations of lines intersecting the parabola y = x² at different points, we consider three cases:
(a) The line intersects the parabola at two points. This is a secant line and can be represented by a linear equation like y = mx + b, where m is not equal to 2a for any x-coordinate of the intersection points (since 2a is the derivative of the parabola at the point (a, a²), where it would be tangent).(b) The line intersects the parabola at one point. This is a tangent line and can be represented by a linear equation like y = mx + b, where m = 2a is the slope of the tangent at the point of tangency (a, a²).(c) The line does not intersect the parabola, meaning it is either above all points of the parabola for positive y-values or below for negative y-values. Such a line might have an equation like y = mx + b with b > a² for positive y-values or b < 0 for negative y-values when m < 2a for any x-coordinate.All lines can be represented by the general linear equation y = a + bx + cx², which is the equation of a parabola only if c ≠ 0.
Can the following question be considered a statistical question and why or why not? Do students at Bryan Middle School exercise?
Answer:
this is a multiple choice question with 4 answers
Yes, it specifies the population
No, it does not specify the population
Yes, it anticipates enough variability in responses
No, it does not anticipate enough variability in responses
I think the answer is.......... (Drum roll please)........... D.
Step-by-step explanation:
There is not any variability in this question it is just a yes or no question. If the question was "How long does an average person exercise for "
4. One-half of Heather's age two years from now plus one-third of her age three years ago is twenty years. How old is she now?
x = the age of Heather
One half of Heather's age two years from now plus one-third of her age three years ago is twenty years
(x + 2)/2 + (x - 3)/3 = 20
by solving the equation we find
x = 24 years
The number of girls, g, in a room is four more than two times the number of boys, b. Half of the number of girls in the room minus the number of boys is 2. The equations below represent the situation.
Answer:
A
Step-by-step explanation:
A segment with endpoints X (6, 2) and Y (- 1, - 3) is rotated 90º about the origin. What are the coordinates of X Prime and Y Prime?
A segment with endpoints X (6, 2) and Y (- 1, - 3) when rotated 90 degrees about the origin will result in new endpoints X' (-2, 6) and Y' (3, -1).
Explanation:This problem deals with the concept of point rotation in a 2D coordinate plane around the origin. When any point (X, Y) is rotated 90 degrees counter-clockwise about the origin, the new position, let's say (X', Y'), can be calculated by using the formulas X' = -Y and Y' = X. Therefore, applying these rotations to the points X(6,2) and Y(-1,-3), we get X'(-2, 6) and Y' (3, -1). So, the endpoints X Prime and Y Prime of the rotated segment are (-2, 6) and (3, -1) respectively.
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After rotating a 90-degree rotation about the origin, the coordinates of X (6, 2) and Y (-1, -3) transform to X' (-2, 6) and Y' (3, -1) respectively.
Explanation:When a point (x, y) is rotated 90º counterclockwise about the origin, it transforms to (-y, x). Let's apply this rule to the endpoints X (6, 2) and Y (-1, -3).
The coordinates of X prime would be (-2, 6) that is, (-y, x).
The coordinates of Y prime would be (3, -1) that is, (-y, x).
Thus, the transformed coordinates for X and Y would be (-2, 6) and (3, -1) respectively after a 90-degree rotation about the origin.
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What is a correct first step in solving the inequality-4(3_5×)>_6×+9?
In a circle whose radius is 4cm find the arc length intercepted by 30 degree angle
As per the radius and given angle the length of the arc will be equal to 2.09 cm.
What is an expression?If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.
The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. In order to include terms in an expression, a mathematical operation like reduction, addition, multiplication, or division is used.
As per the given information in the question,
Radius, r = 4 cm
Angle, θ = 30°
The formula for an arc's length is stated as:
= 2πr(θ ÷ 360)
So,
The length of arc = 2π(4)(30/360)
The length of the arc = 2.09 cm.
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Liam uses checks and a debit card, but does it not always right all the transactions and his checkbook register. He has lost track of his checkbook balance. Liam looks up the "available balance" using online banking, and write it on the next line as his new checkbook balance available to spend. What is wrong with Liam's method
Answer:
All of the above is the answer
Step-by-step explanation:
Any please help me :) because this is due tomorrow
7.1 + 16.04 – .2 = ?
Solve for x. x/3≤−6
Answer:
Hence, the value of x is [tex]x\leq -18[/tex]
Step-by-step explanation:
Consider the provided inequity.
[tex]\frac{x}{3}\leq -6[/tex]
We need to solve the above inequity of x.
Multiply both the side by 3.
[tex]3\times\frac{x}{3}\leq 3\times -6[/tex]
[tex]x\leq -18[/tex]
Hence, the value of x is [tex]x\leq -18[/tex]
Brad makes his own snack mix using whole grain cereal and mixed nuts. One batch of his recipe makes 6 cups of snack mix. Brad uses 3 times as much cereal as mixed nuts. The system below can be used to find the number of cups of cereal and number of cups of mixed nuts Brad uses to make one batch of snack mix.
Which describes the ingredients Brad uses to make one batch of snack mix?
Answer:
The answer is 4.5 cups of cereal and 1.5 cups of mixed nuts
Step-by-step explanation:
Let 'c' be the number of cups of cereal.
Let 'n' be the number of cups of mixed nuts.
One batch of his recipe makes 6 cups of snack mix, so equation becomes:
[tex]c+ n=6[/tex] ..... (1)
Also given that Brad uses 3 times as much cereal as mixed nuts, so equation becomes:
[tex]c=3n[/tex] ......(2)
Substituting (2) in (1)
[tex]3n+n=6[/tex]
=> [tex]4n=6[/tex]
=> [tex]n=1.5[/tex]
Since c = 3n, then
[tex]c=3*1.5=4.5[/tex]
So, the answer is 4.5 cups of cereal and 1.5 cups of mixed nuts.
What is the edge length of a cube with the volume of 1,000 cubic feet.
Jessica has two strings. the first string measures 80 cm and the second string measures 64cm. she wants to cut the strings into equal lengths. of the least number of strings equal length is 16 what is the length of each string
The perimeter of a parallelogram is 72 meters. The width of the parallelogram is 4 meters less than its length. Find the length and the width of the parallelogram
Answer:
Length is 20 meters and width is 16 meters.
Step-by-step explanation:
Given: Perimeter of parallelogram is 72 meters.
Width of the parallelogram is 4 meters less than its length.
To find: Length and width of the parallelogram.
Solution: Let the length of the parallelogram be x meters. So, width of the parallelogram is [tex]x-4[/tex] meters.
As per question,
[tex]x+x+x-4+x-4=72[/tex]
[tex]4x-8=72[/tex]
[tex]4x=72+8[/tex]
[tex]4x=80[/tex]
[tex]x=\frac{80}{4}[/tex]
[tex]x=20[/tex]
Hence, length of the parallelogram is 20 meters, and width of the parallelogram is [tex]20-4=16[/tex] meters.
Ted weighs twice as much as Julie. Mike weighs three times as much as Julie. Together, Ted, Mike, and Julie weigh 210 lbs. What is the weight of each person?
The length of a rectangle is 3 inches less than 4 times the width. If the perimeter is 55 inches, what is the width of the rectangle?
The width of the rectangle is 6.1 in.
What is a rectangle?That parallelogram in which adjacent sides are perpendicular to each other is called a rectangle.
Perimeter of the rectangle = 2(L + W) unit
WE have been given that length of a rectangle is 3 inches less than 4 times the width.
Length = 4x-3
width = x
If the perimeter is 55 inches, then
Perimeter of the rectangle = 2(L + W) unit
55= 2(4x-3 +x)
55 = 2(5x-3)
27.5 = 5x-3
27.5+3 = 5x
30.5/5 = x
6.1=x
Thus, Width is 6.1 in
The length (4 x 6.1 -3) = 21.4
Hence, the width of the rectangle is 6.1 in.
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3x - 24= -6 solve for x
Consider the equation 5x+10=30 and 5(x+10)=30 Do they have the same solution? Why or why not?
These two equations do not have the same solution. x = 4 for the first equation and x = -4 for the second equation.
Why are both equation different?In the equation 5x + 10 = 30, we are adding 10 to the product of 5 and x. To find x, we can first subtract 10 from both sides of the equation to get 5x = 20. Then we divide both sides of the equation by 5 to solve for x, giving us x = 4.
5x + 10 = 30
5x = 30 - 10
5x = 20
x = 20/5 = 4
In the equation 5(x + 10) = 30, we are first adding x and 10 together, then multiplying the result by 5. To solve for x, we can start by dividing both sides of the equation by 5 to get x + 10 = 6. Then we subtract 10 from both sides to solve for x, giving us x = -4.
5(x + 10) = 30,
5x + 50 = 30
5x = 30 - 50
5x = -20
x = -20/5 = -4
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Is 5.78778778 a rational or irrational number? Explain
The number 5.78778778 is a rational number because it has a repeating decimal pattern that can be expressed as the fraction 573/99.
The number 5.78778778 is a rational number. Rational numbers are those that can be expressed as a fraction where both the numerator and the denominator are integers.
In this case, the number 5.78778778 has a repeating decimal pattern, which is a hallmark of rational numbers.
We can convert this repeating decimal into a fraction by setting it equal to a variable, say x, subtracting a shifted version of x to isolate the repeating part, and then solving for x to find its fractional equivalent.
If we perform this process, we can turn 5.78778778... into a fraction. For example:
→ Let x = 5.78778778...
→ Multiply both sides of the equation by 100 to shift the decimal two places: 100x = 578.78778778...
→ Subtract the original x from this new equation: (100x - x) = (578.78778778... - 5.78778778...)
→ This simplifies to 99x = 573
→ Divide both sides by 99 to solve for x: x = 573/99
→ This fraction represents the decimal number 5.78778778..., confirming it is rational.
What is 8.63 repeating as a fraction?
1. Find a counterexample.
If two angles are complementary, then they are not congruent.
Complementary angles are angles that add up to 90 degrees but may not have the same measure. A counterexample to the statement would be two angles that are complementary but not congruent.
Explanation:Complementary angles are angles that add up to 90 degrees. Congruent angles are angles that have the same measure.
A counterexample is a situation where the statement is false. In this case, a counterexample would be two angles that are complementary but not congruent.
For example, let's consider a 45-degree angle and a 45-degree angle. These angles are complementary because their sum is 90 degrees. However, they are not congruent because they have different measures.
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Gabrielle's age is three times Mikhail's age. The sum of their ages is 32 . What is Mikhail's age?
g + m = 32
g = 3m
3m + m = 32
4m = 32
m = 32/4
m = 8 (Mikhail's age)
g = 3m
g = 3(8)
g = 24 (Gabrielle's age)
how can you discover a person's age by year?:To find out a person's age, all you need is that person's 12 months of beginning. After this, all you want to do now's subtract the beginning 12 months from the continuing modern year and you will have the age. this can help you to calculate the age from the date of delivery. Age= 2020- 1966 = 54.
How do you calculate age in mm dd yyyy?Your age in the total range of days is calculated as a variety of years, x, with twelve months = 365x plus. a number of years, y, with three hundred and sixty-six days = 366y plus. a number of days in the remaining partial yr.
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Plz help! Convert 6/9 into fractions with a denominater of 27 A. 6/7 B.21/27 C. 9/27 D.18/27
Mario purchases a prepaid phone plan for $50. Each minute he uses costs $0.13. How many minutes can Mario talk on this plan? Write an inequality that represents this problem and solve the inequality
Final answer:
Mario can talk for up to 384 minutes on his $50 prepaid phone plan. We use the inequality 0.13m ≤ 50 and solve for m to find the maximum number of whole minutes Mario can use.
Explanation:
To solve this problem, we need to set up an inequality that represents the constraints of Mario's prepaid phone plan budget. The inequality will help us determine the maximum number of minutes Mario can talk on this plan.
Let's use m to represent the number of minutes Mario can talk. We know that each minute of talk time costs $0.13, and Mario's prepaid plan is $50. Our inequality should reflect the fact that the total cost of talking m minutes cannot exceed his budget of $50.
The inequality will look like this:
0.13m ≤ 50
To solve for m, we divide both sides of the inequality by 0.13:
m ≤ 50 / 0.13
When we calculate 50 divided by 0.13, we get approximately 384.6154. Since Mario cannot talk for a partial minute on his prepaid plan, we round this number down to the nearest whole minute, which is 384 minutes.
Therefore, Mario can talk for up to 384 minutes on his prepaid phone plan.
To find the number of minutes Mario can talk on the prepaid phone plan, we can set up an inequality: 0.13x <= 50. Solving this inequality, we find that Mario can talk for a maximum of 384 minutes.
Explanation:To find the number of minutes Mario can talk on the prepaid phone plan, we can set up an inequality based on the cost. Let x represent the number of minutes. The cost of the phone plan is $50, and each minute costs $0.13. So, the inequality is: 0.13x <= 50. To solve this inequality, we divide both sides by 0.13 to isolate x and find: x <= 50 / 0.13. Using long division or a calculator, we can find that x is approximately 384.61, but since we can't have a fraction of a minute, the maximum number of minutes Mario can talk on this plan is 384 minutes.
Amanda drove 355 miles using 17 gallons of gas. At this rate how many gallons of gas would she need to drive 284 miles?
When is it helpful to round the quotient to the nearest hundredths?
8.0 × 105 + 6.0 × 107 = A. 14,000,000,000,000 B. 140,000,000 C. 60,800,000 D. 68,000,000
Write the point-slope form of the equation of the horizontal line that passes through the point (2, 1). Pease show how!
The function L = 0.8T2 models the relationship between L, the length in feet of a pendulum, and T, the period in seconds of the pendulum. Which value is closest to the period in seconds for a pendulum that is 30 ft long?
A) 5.4 s
B) 4.9 s
C) 6.8 s
D) 6.1 s
Please help A.S.A.P
Final answer:
Using the formula L = 0.8T², we find that a pendulum 30 ft long has a period of approximately 6.1 seconds, which corresponds to Option D.
Explanation:
The question is about finding the period, T, in seconds for a pendulum that is 30 ft long, using the formula L = 0.8T2. First, to solve for T given that L = 30, we rearrange the equation to T = √(L/0.8). Plugging in L = 30, we have T = √(30/0.8), which simplifies to T = √(37.5).
Calculating further, we find T ≈ 6.12 seconds. Therefore, the answer closest to the period in seconds for a pendulum that is 30 ft long is 6.1 seconds (Option D).
Three (6‐sided) dice are thrown what is the probability that the same number appears on all three dice?