Answer:
a ≥ -5
Step-by-step explanation:
Think like this is a number line
--------------------------------------------------------------------------------------------------------
-6 -5 -4 -3 -2 -1 0 1 2 3 4
and all the inequality says is for it to be bigger than -6 so than is -5, -4, -3, -2 -1, 0,1 and so on. So the answer is a>-6 or a≥-5
What quadrant does (-a,b) belong
Coordinate (-a , b ) belongs to second quadrant.
What is a Quadrant?The axes (x-axis and y-axis) of a two-dimensional Cartesian plane system divide the plane into four infinite regions called quadrants. The horizontal line or x-axis and vertical line or y-axis intersect each other at the right angle. The intersection of two lines is known to be the reference point. All the measurement is done by taking this point as the reference (or starting point) in the coordinate system.
"A quadrant is simply defined as the region of a cartesian plane formed when the x-axis and y-axis intersect each other."
Given, Coordinate ≡ (-a , b)
1st Quadrant: The upper right-hand corner of the graph is the first quadrant. In this quadrant the values of x and y both are positive.
2nd Quadrant: The upper left-hand corner of the graph is the second quadrant. In this quadrant, the value of x is negative whereas the value of y is positive.
3rd Quadrant: The lower left-hand corner of the graph is the third quadrant. It contains the negative values of both x and y.
4th Quadrant: Finally, the fourth quarter is at the lower right-hand corner, which has a positive value of x and a negative value of y.
Hence, by the above observation, given coordinate (-a, b) belongs to the 2nd quadrant.
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Examine the graph of the function. The graph of a line that contains points (negative 1, 7), (0, 5), and (2, 1). © 2017 StrongMind. Created using GeoGebra. What is the initial value of the function? Enter your answer as a number, like this: 42
The initial value of the function is equal to 5.
How to determine the initial value of the function?In order to determine the initial value of the function, we would have to find the slope from line graph and then write the required equation based on the data points contained in the table by using the slope-intercept form.
Mathematically, the slope-intercept form of a line is modeled by this mathematical equation:
y = mx + c
Where:
m represents the slope.x and y are the data points.c represents the y-intercept or initial value.Next, we would determine the slope of the data points as follows;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (5 - 7)/(0 + 1)
Slope, m = -2/1
Slope, m = -2.
At point (0, 5), an equation of this line can be calculated in slope-intercept form as follows:
Note: The y-intercept or initial value is equal to 5.
y = mx + c
y = -2x + 5
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CAN SOMEONE PLS HELP WITH THIS QUESTION ILL GIVE 20 POINTS
To fix their problem, a consumer is requesting a phone call,... I'll get a notification as soon as you respond.
How high is the ball after one second?The ball's height is 86 feet after one second. h=176t-16t2 calculates the height of a ball in feet after t seconds.
How much time did the ball take to hit the ground When the ball lands, its height (h) is 0 feet. You launch a ball into the air with an initial vertical velocity of 32 feet per second while standing at a height of 5 feet.
Calculate the maximum height of the ball using the vertical motion model, which is h = -16t2 + vt + s, where v is the initial velocity in feet/second and s is the height in feet.
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Seth built a wooden step stool out of two rectangular prisms and two cubes. Before fastening the components together, he stained each component to give it its final color.
To completely stain the bottom rectangular prism, Seth had to cover
square inches of wood. For one of the cubes to be completely stained, he had to cover
square inches of wood. To completely stain the top rectangular prism, he had to cover
square inches of wood.
Once the stool was fastened together, he applied a coat of sealant to all exposed surfaces of the stool, including the bottom, to cover a total of
square inches.
To complete stain the bottom rectangular prism, he needs to cover 624 square inches.
What is surface area?A solid object's surface area is a measurement of the overall space that the object's surface takes up.
Given that:
Bottom rectangular prism:
Length = 22 in
Width = 8 in
Height = 6 in
The surface area of the rectangular prism is:
SA = 2( lh + wh + lw)
SA = 2((22)(6) + (8)(6) + (22)(6))
SA= 624 square inches.
To complete stain the bottom rectangular prism, he needs to cover 624 square inches.
Square:
Side = 4 in
The surface area of the cube is:
[tex]SA = 6a^2[/tex]
[tex]SA = 6 (4)^2\\\\SA= 96[/tex]square inches.
To completely stain two squares, he needs to cover 96 * 2 = 196 square inches.
Top rectangular prism:
Length = 18 in
Width = 5 in
Height = 2 in
The surface area of the rectangular prism is:
SA = 2( lh + wh + lw)
SA = 2((18)(2) + (5)(2) + (18)(5))
SA = 136 square inches
Hence to completely stain top rectangular prism, he needs to cover 136 square inches.
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Pythagorean theorem and its converse
problem 3:
leg:16
leg:x
hypo:27
problem 4:
leg:12.8
leg:5.3
hypo:x
problem 5
18 <--------->
`20
x'
The missing measures, using the Pythagorean Theorem, are given as follows:
3. Leg x = 21.75.
4. Hypotenuse x = 13.85.
What is the Pythagorean Theorem?The Pythagorean Theorem states that length of the hypotenuse squared is equals to the sum of each of the sides of the triangle squared.
For item 3, we have that the leg x is missing, while another leg and the hypotenuse are given, meaning that the relation is of:
x² + 16² = 27²
Hence:
x² = 27² - 16²
[tex]x = \sqrt{27^2 - 16^2}[/tex]
x = 21.75.
For item 4, we are given two legs and want to find the hypotenuse, hence the relation is given as follows:
x² = 12.8² + 5.3²
[tex]x = \sqrt{12.8^2 + 5.3^2}[/tex]
x = 13.85.
As for item 5, there is not enough information to answer, but the procedure should be the same.
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What is the probability that all the members of your mathematics class have different birthdays? What is the probability that there is a birthday coincidence in the group?
Supposing a band of 20 members, we have that the probabilities are given as follows:
All have different birthdays: 0.9466 = 94.66%.There is a birthday coincidence: 0.0534 = 5.34%.What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The parameter values for this problem are given as follows:
n = 20, as the band has 20 members.p = 1/365, as the year has 365 days, hence the probability of a person having a given day as a birthday is of 1/365.The probability that all members have different birthdays is of P(X = 0), hence:
P(X = 0) = (1 - 1/365)^20 = 0.9466.
Hence the probability that there is a birthday coincidence is of:
P(X > 0) = 1 - P(X = 0) = 1 - 0.9466 = 0.0534.
Missing InformationThis problem is incomplete, hence we suppose a band of 20 members.
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solve the inequality and explain how
Answer:
B. (see attached)
Step-by-step explanation:
You want the solution and graph of the inequality |x+3| > 2.
SolutionThe inequality resolves to two inequalities with different domain definitions:
|x +3| > 2
When the argument is negative, (x+3) < 0, this is ...
-(x +3) > 2
-x -3 > 2 . . . . . . eliminate parentheses
x +3 < -2 . . . . . . multiply by -1
x < -5 . . . . . . . . . subtract 3; consistent with the domain definition
When the argument is positive, (x+3) > 0, this is ...
x +3 > 2
x > -1 . . . . . . . . subtract 3
-1 < x . . . . . . . . same thing using the < symbol
These differing solution sets do not overlap, but elements of either set are solutions to the inequality. The appropriate conjunction is "OR":
solution: x < -5 or -1 < x
The graph is attached.
__
Additional comment
We like to use the < or ≤ symbols when expressing the solution to an inequality. That way, the relation of the variable to the boundary value is the same as its relation on a number line. Solution values are left of -5 or right of -1:
x < -5 or -1 < x
It helps provide a check that the graph is properly drawn.
The inequality can be rewritten as ...
|x -(-3)| > 2
which can be interpreted as saying the positive distance from x to -3 is more than 2. This tells you the graph will have two disjoint branches, and the appropriate conjunction is OR.
If the problem were different, and the inequality were ...
|x -(-3)| < 2
it would be telling you the solution values have a distance less than 2 from -3. They will be in one continuous band from -5 to -1, so the appropriate conjunction is AND. The solution in this case is usually written as a compound inequality with no conjunction: -5 < x < -1. (Note the use of < symbols puts the variable value in the middle, between the boundary values, as in graph D.)
You invest $300 at 4% interest, compounded every year. What will your balance be after 5 years? (Remember, the formula is A = P(1 + r)t. ) A. $365. 00 B. $350. 96 C. $364. 65 D. $382. 88
Therefore , the solution of the given problem of interest rate comes out to be the amount after 5 years is A ≈ 364.996.
Define interest rate.With the help of an interest rate, you can determine how much borrowing will cost you and how much saving will yield. As a result, the interest rate is the cost of borrowing money and, if you're a borrower, it's expressed as a percentage of the total loan amount. An amount, expressed as a percentage of the loan amount, that a borrower is required to pay to a lender as interest during the term of a loan.
Here,
Given : Principal amount : $300
rate of interest : 4%
and time =5 years
Thus , to find the amount after 5 years as compounded
We use , the formula:
=> A = P
=> A =
=> A =
=> A ≈ 364.996
Therefore , the solution of the given problem of percentage comes out to be the amount after 5 years is A ≈ 364.996.
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The amount after 5 years with compound interest rate is option(A) = $365. 00.
What is called interest rate?The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal, or the loaned amount. Typically, a loan's interest rate is expressed as an annual percentage rate, or APR (APR).
A savings account or certificate of deposit earnings at a bank or credit union may also be subject to an interest rate (CD). The interest received on these deposit accounts is measured in annual percentage yields (APY).
Given : Principal amount : $300
rate of interest : 4% (compounded yearly)
time =5 years
Thus , to find the amount after 5 years as compounded we use , the formula:
=> A = P(1 + r/100)^t.
=> A = $300 (1 +4/100)^5
=> A = $300 (104/100)^5
=> A = $300 (1.04)^5
=> A = $300 * 1.2167
=> A = $365.00
The amount after 5 years with compound interest rate is option(A) = $365. 00.
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How do you know if there are 2 real solutions?
For Quadratic equation, It is possible to know if there are 2 real solutions by examining the discriminant that is [tex]b^2-4ac[/tex] of the equation [tex]ax^2+bx+c[/tex].
What do you mean by a solution?In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.
What are ideal and real solutions?In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.
discriminant : [tex]b^2-4ac[/tex]
if [tex]b^2-4ac[/tex] is positive, Both solutions are real.
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Find all the real and complex solutions of the polynomial equation. Be sure to show ALL work (4 points):
The real and complex solutions of the polynomial equation are 2,-3i and 3i
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
The given polynomial is x³-2x²+9x-18
Factor out x² from x³-2x² which becomes x²(x-2)
Factor out 9 from 9x-18 which becomes 9(x-2)
x³-2x²+9x-18
x²(x-2)+9(x-2)
Factor out common term x-2
( x²+9)(x-2)=0
x²+9=0
x=-3i and 3i
x-2=0
x=2
Hence, the real and complex solutions of the polynomial equation are 2,-3i and 3i
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A vegetable store sold 3 fewer tons of vegetables on the first day than on the second, and on the third day it sold 5 9 of the amount sold in the first two days. How many tons of vegetables did the store sell on each of the days if it sold a total of 98 tons of vegetables on those three days
On solving the provided question, we can say that by equation
30 tons of veggies were sold on the first day, 33 tons on the second day, and 35 tons on the third day.
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
x = amount (ton) of vegetables sold on day one; y = amount (ton) of vegetables sold on day two. Z = the amount of vegetables sold on the third day (in tons).
[tex]x=y-3\\z=(5/9)*(x+y)\\x+y+z=98\\x+y+[(5/9)*(x+y)]=98\\ 9x+9y+5x+5y=882\\14x+14y=882\\x=y-3\\14x+14y=882[/tex]
solution
[tex]x=30\\y=33\\x+y+z=98---- > z=98-(x+y)---- > z=98-63--- > 35[/tex]
30 tons of veggies were sold on the first day, 33 tons on the second day, and 35 tons on the third day.
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A rectangle and a _________ are quadrilaterals with four right angles.
Answer:
A rectangle and a square are quadrilaterals with four right angles.
Step-by-step explanation:
Hope it helps! =D
what if 5464x43214x-532
Answer:
-1.256165295×10×10×10×10×10×10×10×10×10×10×10
Step-by-step explanation:
negative changes everything
6x - 4y = 8 ; x
Solve for indicated value
Solved equation is, x = 4/3 + 2y/3
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
here we have,
Write equation
6x - 4y = 8
Then,
Solve for x
Add 4y to both sides: 6x = 8 + 4y
Divide both sides by 6: x = 8/6 + 4y/6
Simplify: x = 4/3 + 2y/3
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How do you do a simple random sample on a calculator?
Using the calculator there are various methods according to the calculator we used and the approach we follow, Basic answer is to select N and generate random number.
What do you mean by random sampling?Random sampling is a method of selecting a sample from a population in such a way that each member of the population has an equal probability of being selected. This ensures that the sample is representative of the population, and reduces bias in the sampling process. In simple random sampling, a random sample is drawn from a larger population by using random number generators, tables of random numbers, or other methods that ensure that each member of the population has an equal chance of being selected.
What are samples?A sample is a portion or a subset of a population that is selected for the purpose of studying characteristics of the population. The sample is used to make inferences or conclusions about the population from which it was drawn. The sample is usually smaller in size than the population, and it is selected through a process called sampling. The process of sampling is used to select a sample that is representative of the population, meaning that the sample has similar characteristics as the population.
Define the population size (N) and the sample size (n) that you want to obtain.
Use the calculator's random number generator to generate a random number between 1 and N. This will be the first element of your sample.
Repeat step 2 to generate the remaining elements of the sample, making sure that each element is different from the previous ones.
Record the elements of the sample, which are the random numbers that have been generated.
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How do you find the base and height of an isosceles triangle?
The base and height of an isosceles triangle can be found by using the Pythagorean theorem.The hypotenuse is also the base of the triangle.
First, you need to determine the length of the two sides that are equal, which are referred to as the "legs" of the triangle. Then, use the Pythagorean theorem to find the length of the hypotenuse, which is the longest side of the triangle.
Once you have determined the length of the hypotenuse, the height of the triangle can be found using the formula, h = √(b^2 - (l/2)^2). In this formula, b is the length of the hypotenuse, and l is the length of the legs.
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Kelvin and Lewie each design surveys in order to determine the average number of people who buy food at the mall. Kelvin surveys every other person leaving the food area. Lewie surveys every fifth person leaving the mall main entrance. Which set of survey results is most likely to show biased results for people who buy food at the mall
The set of survey results that is most likely to show biased results for people who buy food at the mall is Lewie's survey.
Lewie's survey samples only every fifth person leaving the mall's main entrance, which means that it only captures a small percentage of the total number of mall visitors. Additionally, by only surveying people leaving the main entrance, Lewie's survey may not capture people who enter and exit the mall through other entrances or exits and may also miss those who don't leave the mall after buying food. As a result, Lewie's survey may not accurately represent the total number of people who buy food at the mall and may lead to biased results.
On the other hand, Kelvin's survey samples every other person leaving the food area. This method captures a larger percentage of the total number of people who buy food at the mall and is more likely to provide a more accurate representation of the total number of people who buy food at the mall.
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Answer:
A. Kelvin’s because he surveyed people leaving an area where food is sold
Step-by-step explanation:
The student is expected to determine the value of a collection of coins and bills. Which of the following is an example of a clear learning goal for the Texas Essential Knowledge and Skills (TEKS) skill stated above
With an accuracy of within $0.01, the student will be able to recognize
and determine the total worth of a given assortment of coins and bills, including pennies, nickels, dimes, quarters, half-dollars, and dollar bills.
TEKS stands for Texas Essential Knowledge and Skills. It is a set of state standards for public schools in Texas, that outline what students should know and be able to do in each grade level and subject area. The standards cover subjects such as English language arts, mathematics, science, social studies, and languages other than English.
The TEKS are used to guide the development of curriculum and instruction in Texas schools.
The clear learning goal for the Texas Essential Knowledge and Skills (TEKS) skill of determining the value of a collection of coins and bills could be: "The student will be able to accurately identify and calculate the total value of a given collection of coins and bills, including pennies, nickels, dimes, quarters, half-dollars, and dollar bills, to within $0.01."
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Are isosceles triangles always 180?
No, isosceles triangles are not always 180 degrees. The sum of the interior angles of an isosceles triangle is 180 degrees, but the individual angles can be different.
Isosceles triangles do not necessarily have a 180-degree angle. Any triangle with two equal sides is said to be isosceles. Any triangle's internal angles add up to 180 degrees. An isosceles triangle's individual angles can change depending on how long its sides are, though. An isosceles triangle, for instance, might have a third side that is longer or shorter than the other two sides if the first two sides are equal. The size of the inner angles will be impacted by this. As a result, an isosceles triangle need not have angles that are 180 degrees. An isosceles triangle has interior angles that add up to 180 degrees, but the individual angles might vary.
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Octagon ABCDEFGH with side lengthsABCDEFGII 10 and BC=DE FG = HA= 11 isformed by removing 6-8-10 triangles from the corners of a 23 x 27 rectanglewith side AH on a short side of the rectangle, as shown. Let J be the midpointof AH, and partition the octagon into 7 triangles by drawing segments JB,JC, JD, JE, JF, and JG. Find the area of the convex polygon whosevertices are the centroids of these 7 triangles.
Area of the convex polygon whose vertices are the centroids of these 7 triangles is 184.
What is a convex polygon?
A polygon that forms the edge of a convex set is said to be convex polygon. This indicates that the union of the interior and the boundary of the polygon has the line segment connecting two points of the polygon.
Given,
AB = CD = EF = GH = 10
BC = DE = FG = HA = 11
Triangles of side length 6,8,10 is cut from corners 23×27 rectangle.
Using the above information, we marked the position of A,B,C,D,E,F,G,H and J, taking the upper left corner of rectangle as origin.
The centroid of a triangle can be found using the formula,
Centroid = [tex](\frac{x_{1} + x_{2}+x_{3}}{3} , \frac{y_{1} +y_{2}+y_{3}}{3})[/tex]
For ΔJAB,
[tex]C_{1}[/tex] = (8/3 , -35/6)
For ΔJBC,
[tex]C_{2}[/tex] = ( 9 , -23/6)
For ΔJCD,
[tex]C_{3}[/tex] = ( 46/3, -35/6)
For ΔJDE,
[tex]C_{4}[/tex] = ( 18 , -23/2)
Area of convex polygon = [tex]\frac{1}{2} [x_{1} y_{2} + x_{2}y_{3}+.........+x_{n}y_{1}] - [y_{1}x_{2}+y_{2}x_{3}+......+y_{n}x_{1}][/tex]
From figure we find the area of C₁C₂C₃C₄C₈, where C₈ = (8/3 , -23/2)
Area =
[tex]\frac{1}{2} [8/3 (-23/6 )+ 9(-35/6)+46/3(-23/2)+18(-23/2)+8/3(-35/6)] - [(-35/9)9+(-23/6)46/3+(-35/6)18+(-23/2)8/3+(-23/2)8/3][/tex]
= 184 / 2
Therefore total area of convex polygon = 2 × 184/2 = 184 sq. units
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How do you find the slope of a line example?
The easiest way to find the slope of a line is converting the line equation into the slope-intercept form.
There are 3 forms of line equations:
- slope intercept form, the equation is given by:
y = mx + b
Where:
m = slope
- point slope form, the equation is given by:
y − y₁ = m (x - x₁)
Where:
m = slope
- standard form: Ax + By = C
The easiest way to find the slope of a line is to convert it into a slope-intercept form.
Example:
Line equation in standard form:
2x + 4y = 6
We will convert it into slope-intercept form.
4y = -2x + 6
y = (-2/4) x + 6
y = (-1/2) x + 6
Hence, the slope is (-1/2)
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A car uses 1 liter of gas every 12 kilometers. How many meters can the car travel on 3 liters of gas
Answer: 360,000
Step-by-step explanation: First you would convert 12 kilometers to meters, which is 120,000. Then multiply that by 3. You get 360,000 meters. Therefore, the car can travel 360,000 meters on liters of gas.
You want to ride your bike down the street to your friend's house, which is 340 meters from your house. The trip takes you 68 seconds from start to finish. How fast are you traveling on your bike?
The speed of the Bike is 5 meters per second
What is speed?Speed is a scalar quantity that describes how fast an object is moving . It is defined as the distance an object travels divided by the time it takes to travel that distance. The units of speed are typically meters per second (m/s) or kilometers per hour (km/h).
To find out how fast you are traveling on your bike, you can use the formula:
Speed = [tex]\frac{Distance}{Time}[/tex]
In this case, the distance is 340 meters and the time is 68 seconds. So, you can plug these values into the formula and get:
Speed = 340 meters / 68 seconds
Speed = [tex]\frac{340 meters}{68 seconds}[/tex] = 5 meters per second
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Choose all of the equations that represent a parabola with the focus (3,9) and the vertex (3, 6).
A. 12y = x² - 6x+81
B. 24y=x²-12x + 72
C. 24y=x² - 6x + 225
D. (x-3)2 24 (-9)
E. (x-3)² = 12 (y – 6)
F. (x-9)² = 24 (y - 3)
(x-3)² = 12 (y – 6) is the equation for a parabola with the vertex (3, 6) and focus (3, 9) in it.
what is parabola ?A parabola is a U-shaped plane curve in which every point is situated at an equal distance from both the focus, a fixed point, and the directrix, a fixed line. The topic of conic sections includes parabola as a key component, and all related parabola topics are discussed. a plane curve produced by a point shifting such that its separation from a fixed point equals its separation from a fixed line: junction of a plane parallel to an element of a right circular cone with the cone. : a bowl-shaped object (such as an antenna or microphone reflector)
given
focus (3,9) and the vertex (3, 6)
general equation of parabola = (x - h)2 = 4a (y - k)
a = |y2 - y1| = | 9 - 6 |
a = 3
so
(x - 3 )[tex]^{2}[/tex] = 4 * 3 ( y - 6 )
= [tex](x-3)^{2} = 12 ( y - 6 )[/tex]
(x-3)² = 12 (y – 6) is the equation for a parabola with the vertex (3, 6) and focus (3, 9) in it.
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Please help me find the shaded area!
Answer:
216
Step-by-step explanation:
first multiply 4by6 to get that area we will call that a
then 12 by 20 to get that area we will call that b
the shaded area is a's area minus B's area
(12*20)-(4*6)
240-24
216
Answer:
216 in²
Step-by-step explanation:
(12)(20) - (4)(6) = 240 - 24 = 216
Is 0 in a closed interval?
So the only boundary point of [0,∞) and (0,∞) is 0 itself. It is in [0,∞), so that set is closed. It is not in (0,∞), so that set is open.
In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between. Other examples of intervals are the set of numbers such that 0 < x < 1, the set of all real numbers
the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton (set of one element).
Real intervals play an important role in the theory of integration, because they are the simplest sets whose "length" (or "measure" or "size") is easy to define. The concept of measure can then be extended to more complicated sets of real numbers, leading to the Borel measure and eventually to the Lebesgue measure.
Intervals are central to interval arithmetic, a general numerical computing technique that automatically provides guaranteed enclosures for arbitrary formulas, even in the presence of uncertainties, mathematical approximations, and arithmetic roundoff.
So the only boundary point of [0,∞) and (0,∞) is 0 itself. It is in [0,∞), so that set is closed. It is not in (0,∞), so that set is open.
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answer this question for me.
The angle measure of m∠CAF = 23°.
What is an angle measure?When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
Given:
The angle measures,
m∠EBG = 23°
m∠CAE = 52°
From the figure,
m∠EBG = m∠FAE = 23°
So, from the figure,
m∠CAE = m∠CAF + m∠FAE
Substituting the angle measures,
52 = m∠CAF + 23
m∠CAF = 52 - 23
m∠CAF = 22°
Therefore, 23° is the angle measure of m∠CAF.
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Emmet had c caramels. Then his sister took 5 of the caramels. Write an expression that shows the number of caramels Emmet has left.
Answer:
C - 5
Step-by-step explanation:
We know
Emmet had c caramels
His sister took 5 caramels, that means subtract 5, so the equation is
c - 5
On the way home, Mark rode the first six miles of the trip in 30 minutes to stop at the ice cream shop. What was his speed in miles per hour
The speed of Mark riding the bike is 16 miles/hour. If you know how far something has travelled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance * time.
What are time, distance, and speed?Speed tells us how quickly or slowly an object is moving. While distance, as the name suggests, refers to the amount of space between two points, time refers to the period of time separating two events.
Given,
Distance travelled= 6 miles
time taken = 30 minute =0.5 hour
[tex]speed = distance/time\\speed=8/0.5\\speed= 16 miles/hour[/tex]
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Is a 45 45 triangle isosceles?
Yes, a 45 45 triangle is an isosceles triangle, meaning that two of its sides are equal in length.
A 45 45 triangle is a triangle in which two of its angles are 45 degrees. This type of triangle is also known as an isosceles triangle because it has two sides of equal length. To determine whether a triangle is isosceles, we need to measure the lengths of its sides. In a 45 45 triangle, both sides are equal in length as the angles are equal. Therefore, a 45 45 triangle is an isosceles triangle. The triangle also has two acute angles (less than 90 degrees) and one obtuse angle (greater than 90 degrees). This type of triangle is a special type of triangle and is often used in geometry and trigonometry.
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