The equation of a parabola with a vertical axis and vertex (h, k) is given by:
(x - h)² = 4p(y - k)
How to explain the equationIn the equation, where p is the distance from the vertex to the focus (and also the distance from the vertex to the directrix).
If the vertex is at the origin (h=0, k=0), then the equation simplifies to:
x² = 4py
where p is still the distance from the vertex to the focus (and also the distance from the vertex to the directrix).
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At 12.30 p.m, a car overtook a van along an expressway. The car and the van were travelling at
average speeds of 90Km/h and 70 Km/h respectively. After 1/2 hour the speed of the car
was reduced by 10 km/h. How far apart were the two vehicles at 2 .00 p.m?
PLEASE HELP (1 point)
Let X be a continuous random variable with probability
distribution represented by the graph below.
Find P (X≤2).
f(x)
The probability P (X≤2). from the probability distribution is 1/3
Evaluating the probability from the probability distributionA continuous random variable is a type of random variable that can take on any value within a specific range, often an infinite range.
It has a probability distribution function that describes the probability of the variable taking on certain values within that range.
This means that
P (X≤2) = the f(x) value
From the graph, we have
P (X≤2) = 1/3
Hence, teh value is 1/3
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What is the definition of perpendicular lines?
1.two lines that intersect in a way that forms right angles
2.two lines that intersect in a way that cuts both lines in half
3.two lines that intersect in a way that they share more than one common point
4.two lines that intersect in a way that forms two congruent angles
Answer:
Step-by-step explanation:
The correct definition of perpendicular lines is option 1: "Two lines that intersect in a way that forms right angles."
When two lines intersect to form four right angles (90-degree angles), they are said to be perpendicular to each other. The point at which the lines intersect is called the point of intersection.
Therefore, option 1 is the correct definitation of perpendicular lines.
Answer: 1. Two lines that intersect in a way that forms right angles.
Step-by-step explanation:
Hope this helped! :)
Given cards with the letters A, B,
C, and D, how many different
orders can you place the four
cards?
Find the endpoints of the latus rectum of the parabola below.
Select the correct answer below:
(x + 3)² = -20(y + 1)
The endpoints of the latus rectum of the parabola equation is : f. The endpoints of the latus rectum are (-6, 9) and (-6, -15).
What is the latus rectum?Standard form of the equation of a parabola =y (x - h)² = 4p(y - k)
Where:
(h, k) = vertex
4p = distance between the vertex and focus
Comparing this with (x + 3)² = -20(y + 1) will gives us
(x + 3)² = -20(y + 1)
= (x - (-3))² = -20(y - (-1))
The vertex of the parabola is = (-3, -1)
4p = -20
p = -20/4
p = -5
The line that is perpendicular to the axis of symmetry (line y = -1) and passes through the focus (-3, -6) is known as the latus rectum of a parabola. The line y = - 6—the focus—and the directrix are separated by a distance of 4p = 20.
The vertex which is located at (-3, -1) is the latus rectum's midway. The latus rectum tend to has a length of 20 and passes through the points (-3, -1). Its endpoints must be located on the line x = -3 since it is perpendicular to the axis of symmetry.
The endpoints of the latus rectum are:
(-3, -1 - 10) = (-3, -11) and (-3, -1 + 10) = (-3, 9).
Therefore, the correct option is f.
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Chandra needs to make 3 gallons of punch how many cups of strawberry are needed
The number of cups of frozen strawberries that are needed to make 3 gallons of punch is equal to 48 cups.
How to solveIn this exercise, you're required to determine the number of cups of frozen strawberries that are needed to make 3 gallons of punch.
Thus, we would apply direct proportion.
Note: There are 16 cups of frozen strawberries in a gallon.
By direct proportion:
16 cups = 1 gallon
X cups = 3 gallons
Cross-multiplying, we have:
X = 16 × 3
X = 48 cups of frozen strawberries.
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15 POINTS! HELP PLEASE ASAP!!
Answer:
C
Step-by-step explanation:
The equation is:
y = [tex]\frac{1}{4}[/tex]x - 8
If you plug in the x and y value from the table, you find they are solutions to the equation.
(36,1)
y = [tex]\frac{1}{4}[/tex]x - 8 Substitute in 36 for x and 1 for y
1 = [tex]\frac{1}{4}[/tex](36) - 8
1 = 9 - 8
1 = 1
You can do the same thing for all of the other points on the table.
Helping in the name of Jesus.
What’s x+2(7-x)=12 but like this ( , )
The solution to the equation x + 2(7 - x) = 12 is x = 2.
What is the solution to the given equation?Given the equation in the question:
x + 2(7 - x ) = 12
To solve the equation, you need to use algebraic techniques to isolate the variable x on one side of the equation.
x + 2(7 - x) = 12
Apply distributive property
x + 2×7 + 2×-x = 12
x + 14 - 2x = 12
Combine like terms by subtracting 14 from both sides:
x - 2x = 12 - 14
-x = -2
Solve for x by dividing both sides by -1:
-x/-1 = -2/-1
x = 2
Therefore, the value of x is 2.
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A stainless steel patio heater is a square pyramid. The length of one side of the base is 22.8 in. The slant height of the pyramid is 89.8 in. What is the height of the pyramid?
The height of the pyramid formed by the patio heater is 89.07 inches
What is an equation?An equation is an expression that shows how numbers and variables using mathematical operators.
Pythagoras theorem shows the relationship between the sides of a right angled triangle.
To find the height (h) of the pyramid. A right angled is form with base (b) = side of square / 2 = 22.8 / 2 = 11.4 in
Slant height (S) = 89.8 in
Using Pythagoras:
S² = h² + b²
89.8² = h² + 11.4²
h = 89.07 inches
The height of the pyramid is 89.07 inches
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Yellow light: When the light turns yellow, should you stop or go through it? A recent study of driver behavior defined the "indecision zone" as the period when
a vehicle is between 2.5 and 5.5 seconds away from an intersection. At the first intersection studied, 127 vehicles were observed to encounter a yellow light in
the indecision zone, and 24 of them ran the red light. At the second intersection, 164 vehicles entered the intersection in the indecision zone, and 29 ran the red
light. Let p denote the proportion of red light runners at the first intersection. Can you conclude that the proportion of red light runners differs between the two
intersections? Use the a=0.01 level of significance.
Answer:
Step-by-step explanation:
To test the null hypothesis that the proportion of red light runners is the same at both intersections, we can use a two-sample z-test for proportions.
Let p1 be the proportion of red light runners at the first intersection, and p2 be the proportion of red light runners at the second intersection. We want to test the null hypothesis:
H0: p1 = p2
against the alternative hypothesis:
Ha: p1 ≠ p2
We can use the following formula to calculate the test statistic:
z = (p1 - p2) / sqrt(p_hat * (1 - p_hat) * (1/n1 + 1/n2))
where p_hat = (x1 + x2) / (n1 + n2) is the pooled sample proportion, and x1 and x2 are the number of red light runners at the two intersections, and n1 and n2 are the sample sizes.
For the first intersection, we have x1 = 24 and n1 = 127. For the second intersection, we have x2 = 29 and n2 = 164.
The pooled sample proportion is:
p_hat = (x1 + x2) / (n1 + n2) = (24 + 29) / (127 + 164) = 0.167
The test statistic is:
z = (p1 - p2) / sqrt(p_hat * (1 - p_hat) * (1/n1 + 1/n2)) = (0.189 - 0.177) / sqrt(0.167 * (1 - 0.167) * (1/127 + 1/164)) = 0.99
Using a standard normal distribution table, we can find that the probability of getting a z-value of 0.99 or greater is 0.160. Since this is greater than the significance level of 0.01, we fail to reject the null hypothesis.
Therefore, we cannot conclude that the proportion of red light runners differs between the two intersections.
Suppose that the functions and are defined as follows.
The value of the function f/g is (x - 1) / (x + 8)
Let's start by writing out the functions we are given:
f(x) = 4 / (x + 8)
g(x) = x / (x - 1)
To find f/g, we need to divide f(x) by g(x). We can do this by multiplying f(x) by the reciprocal of g(x), which is (x - 1) / x. Multiplying f(x) by this reciprocal gives us:
f(x) * (x - 1) / x = 4 / (x + 8) * (x - 1) / x
To simplify this expression, we can first find a common denominator for the two fractions on the right-hand side:
4 / (x + 8) * (x - 1) / x = 4(x - 1) / x(x + 8)
Now we can simplify this expression by canceling out any common factors in the numerator and denominator. In this case, we can cancel out a factor of 4 and a factor of (x - 1):
4(x - 1) / x(x + 8) = (x - 1) / (x + 8)
Therefore, the quotient of f(x) and g(x), or f/g, is:
f/g = (x - 1) / (x + 8)
We can interpret this expression as a new function, h(x), where h(x) = f(x) / g(x) = (x - 1) / (x + 8). This new function takes a value of x and returns the ratio of f(x) to g(x) at that value.
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College Level Trigonometry Question!
The force parallel to the incline that would be required to hold the monolith on this causeway is 32, 120.52 Newtons.
How to find the force ?The formula for finding the force parallel to the incline:
= mass of the monolith x acceleration due to gravity x sin( slope angle )
Mass in kg :
= 57 tons x 1000
= 57, 000 kg
Force parallel to the incline:
= 57, 000 kg x 9. 81 m/s² * sin ( 1.4 degrees )
= 57, 000 kg x 9.81 m/s² x sin ( 0.0244 radians )
= 32, 120.52 Newtons
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what is the graphed line of the equation 2x + 3y = -6
The graphed line of the equation is attached 2x + 3y = -6
What is linear equation?A linear equation is an expression that consists of a single power of the variable(s) in which it contains. This formulation can be impeccably illustrated in the following way:
ax + b = 0
The given equation 2x + 3y = -6 can be rearranged to get
y = -2/3x - 2
The x variables is plugged in to solve for y and used for the table of values for the graph
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a 10 x 10 x 10 cub is painter red on all faces and then cut into ten 10 x 10 x 1 slices each slice is then cut into twenty five 2 x 2 x 1 blocks how many of the 250 blocks have exactly on face painted red
There are exactly 250 blocks with exactly one face painted red.
What is cube ?
A cube is a three-dimensional solid shape with six square faces of equal size that meet at 90-degree angles. It is a special case of a rectangular prism, where all of the edges have the same length.
When the 10 x 10 x 10 cube is painted red on all faces, it means that all of the 1000 unit cubes inside the large cube are red.
When the cube is cut into ten 10 x 10 x 1 slices, each slice will contain 100 unit cubes. When each slice is cut into twenty-five 2 x 2 x 1 blocks, each block will contain 4 unit cubes.
Therefore, each 2 x 2 x 1 block will come from 4 unit cubes, and each unit cube will contribute to 4 different blocks.
To count the number of blocks with exactly one face painted red, we can focus on the blocks that have a red face on the bottom (or top) and three unpainted faces on the other sides. Each such block will correspond to one of the 100 unit cubes in a slice, and there are 10 slices, so there are 1000 such blocks in total.
However, each of these blocks has four unit cubes, so we need to divide by 4 to get the number of blocks. Therefore, the answer is:
1000 ÷ 4 = 250
Therefore, there are exactly 250 blocks with exactly one face painted red.
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in the figure below, m JKM=106 degrees, m LKM=66, and KN bisects LKM. Find m JKN
The value of angle JKN is 73°.
Given that the m ∠JKM = 106 degrees, m ∠LKM = 66, and KN bisects LKM.
So we need to find the value of ∠JKN,
So, using the angles addition postulate,
∠LKM = ∠LKN + ∠MKN
Therefore,
∠LKN = 66/2 [definition of bisector]
∠LKN = 33°
Again, using the angles addition postulate,
∠JKM = ∠JKL + ∠LKM
∠JKL = 106 - 66
∠JKL = 40°
Therefore,
∠JKN = ∠JKL + ∠LKN
∠JKN = 40 + 33
∠JKN = 73°
Hence, the value of angle JKN is 73°.
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What is the quotient of 100 ÷ 7.50
Answer:
13.3333333333 or 13.3
Step-by-step explanation:
yeah :3
area of traingle is what if square root 6 in height iand base is square root 24
The area of the triangle that has height of √6 and a base of √24 is calculated as: 6 square units.
How to Find the Area of a Triangle?The area of a triangle = 1/2 * b * h, where:
h is the height of the triangle, and
b is the base length of the triangle.
Given the following:
Height of triangle = √6
Base length of the triangle = √24
Plug in the values:
Area of triangle = 1/2 * √24 * √6
= (√24 * √6) / 2
= √144 / 2
= 12/2
Area of triangle = 6 square units.
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If a cylinder has a height of 5 inches and a radius of 3 inches, which equation can be used to find V, the volume of the cylinder in cubic inches?
The equation to find the volume of the cylinder is: V = 45π cubic inches.
What is cubic inches?The volume of things or containers is often measured in cubic inches in the United States. It is the amount of area that a cube with one inch sides takes up. A cubic inch is about equal to 16.387 millilitres or 0.016387064 litres. The displacement of an engine—a measurement of the total amount of air and fuel the engine can compress into its cylinders—is frequently discussed in terms of cubic inches.
According to given information:The formula to find the volume of a cylinder is:
V = πr²h
Where V is the volume, r is the radius, and h is the height.
Substituting the values given in the problem, we get:
V = π(3²)(5)
V = π(9)(5)
V = 45π
Therefore, the equation to find the volume of the cylinder is:
V = 45π cubic inches.
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if (-8,3) lies on the circle and its Center is (-4,3) find the radius
If (-8,3) lies on the circle and its Center is (-4,3) then, the radius of the circle is 4.
We know that the center of the circle is (-4, 3). Let's call the radius of the circle "r".
The distance between the center of the circle and the point (-8, 3) on the circle is equal to the radius "r".
Using the distance formula, we can find the distance between these two points;
d =√[(x2 - x1)² + (y2 - y1)²]
d = √[(-8 - (-4))² + (3 - 3)²]
d = √[(-8 + 4)² + 0²]
d = √[4²]
d = 4
Since the distance between the center of the circle and the point on the circle is equal to the radius, we have;
r = d = 4
Therefore, the radius of the circle is 4.
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The point (3,b) lies on the circle with radius 8 and center (−2,−1). What are the possible values of b
The point (3,b) can lie on the circle with radius 8 and center (-2,-1) for values of b equal to -1 + √39 and -1 - √39.
We know that the circle with radius 8 and center (-2,-1) has the equation:
(x + 2)² + (y + 1)² = 8²
Substituting x = 3 and y = b, we get:
(3 + 2)² + (b + 1)² = 8²
Simplifying, we get:
25 + (b + 1)² = 64
(b + 1)² = 39
Taking the square root of both sides, we get:
b + 1 = ± √39
Therefore, the possible values of b are:
b = -1 ± √39
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suppose that the function G is defined for all real numbers as follows. Find g(-5), g(-2) and g(-1)
If "function-g" defined for all real numbers as g(x) = x² + 6, then the value of g(-5) = 31, g(-2) = 10 and g(-1) = 7.
In mathematics, a function is generally denoted by a symbol such as "f" or "g", and its definition is given by an equation or formula that specifies the relationship between the input and output values.
The function "g" is given as : g(x) = x² + 6;, which is defined for all "real-numbers",
So, to find g(-5), g(-2), and g(-1), we simply substitute these values of x into the function "g" and simplify the resulting expressions:
⇒ g(-5) = (-5)² + 6 = 25 + 6 = 31,
⇒ g(-2) = (-2)² + 6 = 4 + 6 = 10,
⇒ g(-1) = (-1)² + 6 = 1 + 6 = 7.
Therefore, g(-5) = 31, g(-2) = 10, and g(-1) = 7.
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The given question is incomplete, the complete question is
Suppose that the function G is defined for all real numbers as g(x) = x² + 6. Find g(-5), g(-2) and g(-1).
Which function is represented by the graph?
A f(x) = -12x + 6f(x) = - 1 2 x + 6
B f(x) = 12x + 6f(x) = 1 2 x + 6
C f(x) = -2x + 6f(x) = -2x + 6
D f(x) = 2x + 6
Answer:
B
Step-by-step explanation:
Notice that all y-intercepts are the same (doesn't give a clue to the answer).
The line has a downward slant as you move from left to right, so the slope is negative (eliminating A & C as answers).
Determine the actual slope by identifying the y-intercept and x-intercept, and calculate Rise over Run:
Rise = -6 (goes from +6 to 0)
Run = +12
-6/12 = -1/2
Help please quickly calculus
Her next step in obtaining the area of the triangle is replacing the numeric values of h and y into the area formula.
How to obtain the area of a triangle?The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:
A = 0.5bh.
The dimensions for this problem are given as follows:
Base of b = y.Height of h.Hence the formula is:
A = 0.5yh.
Hence the actual values of y and h must be inserted into the formula to obtain the area of the triangle.
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find cooordinates of point of interection
11x-6y=2
-8x+5y=3
Answer:
To find the coordinates of the point of intersection of the given equations, we need to solve the system of equations simultaneously. We can use the elimination method to do this:
11x - 6y = 2 (multiply both sides by 5)
-8x + 5y = 3 (multiply both sides by 11)
55x - 30y = 10
-88x + 55y = 33
Adding the two equations, we get:
-33x + 25y = 43
Solving for y, we get:
y = (33x + 43)/25
Substituting this expression for y into either of the original equations and simplifying, we get:
x = -1/7
Substituting this value of x into the equation for y, we get:
y = 1/35
Therefore, the coordinates of the point of intersection are (-1/7, 1/35).
Determine any horizontal or slant asymptotes of the rational function: f(X)= 3x^2-x/2x^2-1
The horizontal asymptote is y = 3/2, and the slant asymptote is y = x/2.
How to express the asymptoteWe need to compare the degrees of the numerator and denominator.
The degree of the numerator is 2, and the degree of the denominator is also 2. Therefore, the horizontal asymptote is given by the ratio of the leading coefficients, which is 3/2. The horizontal asymptote is y = 3/2
Furthermore, f(x) = 3/2 + x/(2x² - 1)
This expression shows that the function has a slant asymptote given by the line: y = x/2
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Carl is buying a shirt that costs $24.00. It is on sale for 50% off. what will the price of the shirt be?
A. 19.00
B. 50.00
C. 12.00
D. 14.00
Please help I’ll give brainly if you explain :)
Answer: C
Step-by-step explanation:
We need to turn 50% into a fraction first to make it easier,
50% is equal to 1/2 because 50/100 is simplified to 1/2.
Now let's multiply!
24 x 1/2 = 24/2 = 12/1 = 12
Solve the equation x2 = 8.
x = 4
x = ±4
x = 8‾√
x = ±8‾√
Answer:
Step-by-step explanation:
x^2 = 8
x=+-√8
On their farm, Adam’s family maintains a storage that can hold 14.3 cubic yards (yd3) of grain. Use the fact that 1 yard is approximately equal to 0.9144 m to convert this volume to m3. Round your answer to the nearest hundredth. Do not type the units in the space below.
The storage can hold approximately 10.94 cubic meters of grain.
Unit conversion:
Unit conversion is the process of converting a quantity expressed in one set of units to an equivalent quantity expressed in another set of units. For example, converting a length from feet to meters, or converting a temperature from Celsius to Fahrenheit.
To convert cubic yards to cubic meters, multiply the given volume in cubic yards by this conversion factor to obtain the equivalent volume in cubic meters.
Here we have
Adam’s family maintains storage that can hold 14.3 yd³ of grain.
Given that 1 yard is approximately equal to 0.9144 meters
To convert cubic yards (yd³) to cubic meters (m³),
Use the conversion factor:
1 yd³ = (0.9144 m)³
So, we can convert 14.3 cubic yards of grain to cubic meters as follows:
14.3 yd³ x (0.9144 m/yd)³ ≈ 10.94 m³
Rounding this answer to the nearest hundredth gives us:
10.94 m³ rounded to the nearest hundredth = 10.94 m³
Therefore,
The storage can hold approximately 10.94 cubic meters of grain.
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HELP ASAPPPP I NEED HELP
Answer:
137 yd2
Step-by-step explanation:
is y=-x directly proportional or non proportional
Answer: Directly proportional.
Step-by-step explanation:
y = -x is directly proportional for a few reasons.
➜ The graph of this equation is a straight line, so all the ratios of points are equal.
➜ The constant of proportionality (k) is equal to -1.
➜ This line intersects the graph at the origin (0, 0).
➜ See the graph below.