A quadratic graph is a type of parabolic graph that can be represented by the equation y = ax^2 + bx + c, where a, b, and c are constants and x is the variable. The graph of this equation is a parabola that opens either up or down, depending on the value of a.
The equation y = x^2 + 2x - 3 is an example of a quadratic graph. It can be written in the standard form of a quadratic equation as y = x^2 + 2x - 3, where a = 1, b = 2 and c = -3.
The x^2 term in the equation is known as the quadratic term, and it is responsible for the parabolic shape of the graph. The x term and the constant term, 2x and -3, respectively, determine the location of the vertex and the direction of the parabola.
The vertex of the parabola is the point where the parabola changes direction. It can be found by using the formula x = -b/2a, which in this case is x = -2/2 = -1 and y = f(-1) = -1.
The graph of y = x^2 + 2x - 3 is a parabola that opens upwards and the vertex of the parabola is (-1,-1)
In summary, a quadratic graph is a parabolic graph represented by the equation y = ax^2 + bx + c, where a, b, and c are constants. The x^2 term gives the parabolic shape to the graph, the x term and the constant term determine the vertex and the direction of the parabola respectively.
Determine the range of the following graph:
Answer:
-1 ≤ y ≤ 6
[-1, 6]
Step-by-step explanation:
The y coordinates of all points on the graph are from -1 to 6, so the range is:
-1 ≤ y ≤ 6
[-1, 6]
At a baseball game, a vender sold a combined total of 135 sodas and hot dogs. The number of sodas sold was two times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
Answer:
vendor sold 90 sodas and 45 hot dogs
Step-by-step explanation:
Let x = number of sodas sold
Let y = number of hot dogs sold
We have x = 2y (1)
( The number of sodas sold was two times the number of hot dogs sold)
We also have x + y = 135 (2)
( sold a combined total of 135 sodas and hot dogs.)
Substituting x = 2y we get
2y + y = 135
3y = 135
y = 135/3
y = 45
Therefore x = 135 - 45
x = 90
Therefore vendor sold 90 sodas and 45 hot dogs
what is the mean number of cakes jenny bakes in a month. Numbers of cake are 100, 200, 300, 400, 500, 600, 700
Answer:
400
Step-by-step explanation:
[tex]100 + 200 + 300 + 400 + 500 + 600 + 700 = 2800 [/tex]
There are 7 numbers ( No. of cakes in a month)
Therefore, we should divide it by sum of the cakes
[tex]2800 \div 7 = 400[/tex]
SO MEAN NUMBER IS 400//
3. expressing the binomial coefficients in terms of factorials and simplifying algebraically, show that (a) nr
Expressing the binomial coefficients in terms of factorials and simplifying algebraically. we have proved that
[tex]$\left(\begin{array}{l}n \\ r\end{array}\right) = \dfrac{n-r+1}{r} \cdot \left(\begin{array}{c}n \\ r-1\end{array}\right)[/tex]
What is binomial coefficients?The binomial coefficient [tex]\left(\begin{array}{l}n \\ k\end{array}\right)[/tex] is the number of ways of picking k unordered outcomes from n possibilities, also known as a combination or combinatorial number. The symbols [tex]_nC_k[/tex] and [tex]\left(\begin{array}{l}n \\ k\end{array}\right)[/tex] are used to denote a binomial coefficient, and are sometimes read as "n choose k."
[tex]$$In general, $\left(\begin{array}{l}n \\ r\end{array}\right) \neq\left(\begin{array}{c}n \\ r-1\end{array}\right)$To solve (a), simply expand LHS.$$\left(\begin{array}{l}n \\r\end{array}\right)=\frac{n !}{r ! \cdot(n-r) !}=\frac{n !}{r \cdot(r-1) ! \cdot(n-r) !}$$Multiply numerator and denominator by $(n-r+1)$, then,$$\left(\begin{array}{l}n \\r\end{array}\right)=\frac{n-r+1}{r} \cdot \frac{n !}{(r-1) ! \cdot(n-r+1) !}=\frac{n-r+1}{r} \cdot\left(\begin{array}{c}n \\r-1\end{array}\right)$$[/tex]
Thus, Expressing the binomial coefficients in terms of factorials and simplifying algebraically. we have proved that
[tex]$\left(\begin{array}{l}n \\ r\end{array}\right) = \dfrac{n-r+1}{r} \cdot \left(\begin{array}{c}n \\ r-1\end{array}\right)[/tex]
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Full question:
Expressing the binomial coefficients in terms of factorials and simplifying algebraically, show that:
(a) [tex]$\left(\begin{array}{l}n \\ r\end{array}\right) = \dfrac{n-r+1}{r} \cdot \left(\begin{array}{c}n \\ r-1\end{array}\right)[/tex]
otherwise, x is possible but uncertain, and 0 < p(x) < 1. in the die example, the probabilities of each of the six outcomes are equally likely (so long as the die is fairly balanced), so p(1)
The probability of rolling an odd number on a fair six-sided die is P(odd) = (1/6) + (1/6) + (1/6) = 3/6 = 1/2. This is because there are three odd numbers (1, 3, and 5) out of the six possible outcomes, and they are each equally likely to occur.
The probability of rolling a number divisible by 3 on a fair six-sided die is P (divisible by 3) = (1/6) + (1/6) = 2/6 = 1/3. This is because there are two numbers (3 and 6) out of the six possible outcomes that are divisible by 3, and they are each equally likely to occur.
It's important to note that in both of these examples, we are assuming that the die is fair and unbiased, which means that each of the six possible outcomes has an equal chance of occurring. If the die is not fair, the probabilities of each outcome could be different.
Complete question:
More probability Aa Aa An event's probability measures the likelihood of its occurrence. The probability that an event X occurs is between 0 and 1, inclusive, and is denoted by P(X). If it is impossible for X to occur, then P(X) Rolling a standard six-sided die, the probability of rolling a 7 is zero, P(7)-0. If X is the set of all possible outcomes in the experiment, then X is certain to occur and P(X)1 In the die example, X could be that an integer is rolled, which must occur, and thus P(integer)-1 Otherwise, X is possible but uncertain, and 0<P(X) 1. In the die example, the probabilities of each of the six outcomes are equally likely (so long as the die is fairly balanced), so P(1)-P(2)-P(3)-P(4) = P(5)-P(6)- 1/3. If possible, you want to identify all the possible outcomes, called the If you are rolling a 1/6). fair die, your outcomes range from 1 to 6, with equal probability (P The probability of rolling an odd number is the probability of rolling a number divisible by 3 is
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40,512 rounded to the nearest thousand
Answer: 41,000
Step-by-step explanation:
If the hundreds column 5 or more than it rounds up if it is lower it rounds down
3 bottle of water of wine and four bottled water costs N450 if each bottle water cost 35 naira how much is spent on the wine
Answer:
N103. 33
Step-by-step explanation:
let the cost of bottle of water be represented by B
Let the cost of wine be represented by W
3×W + 4×B =N450
3W+4B=450....(1)
one bottle of water(B)Costs N35
3W+ 4(N35)= N450
3W + 140=450
collect the.like terms
3W= 450-140
3W = 310
divide through by 3
W= N103.33
If the function h(x) goes
through the point (−5, 7),
then the function −h(x)
must go through what
point?
Answer: (-5, -7)
Multiply the y coordinate by -1. Keep the x coordinate the same. The point (-5,7) reflects over the x axis to land on (-5,-7)
The reason why we multiply by -1 is because [tex]\text{y} = \text{h}(\text{x})[/tex], so [tex]-\text{y} = -\text{h}(\text{x})[/tex]
Answer:
(-5,-7)
................
how many 1/4 are in 3 inches
Answer:
12 inches
Step-by-step explanation:
3 inches / (1 / 4) = 12 inches
HELP!! Quadrilateral ABCD is inscribed in circle P. Complete the following.
The measures of the angles are (a) 180-C, and 180-A (b) 180 (c) 180 and supplementary.
What is a cyclic quadrilateral?You should understand that cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle
For better understanding note the following
Opposite angles of a cyclic quadrilateral are supplementaryopposite angles of a cyclic quadrilateral = 180 degrees(a) m<A = 180 - m<C
m<C = 180 - m<A
(b) m<A + m<C = 180 .......... (opposite angles are supplementary)
(c) m<A + m <C = 180 (Sum of opposite angles = 180⁰)
(d) <A and <C are supplementary angles
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Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) f(x)=x [-/1 Points]. Find the most generat antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) r(θ)=sec(θ)tan(θ)−5e θ3. [-/1 Points] Find 1. f(x)=(x)=1+2 x ,f(4)=24
4. [-/1 Points] 4.9.061 A paricle is moving with the given gata. Find the position of the particle.
1. The antiderivative would be x.
2. The antiderivative would be sec(θ)tan(θ)−5e^(θ^3).
3. The antiderivative would be 1+2x.
What is the antiderivative of the function?
An antiderivative of a function is a function whose derivative is equal to the original function. It is also known as an indefinite integral of a function with respect to its variable. The process of finding an antiderivative is called integration.
1. The most general antiderivative of the function f(x)=x is F(x) = (1/2)x^2 + C, where C is the constant of the antiderivative. To check this, we can differentiate F(x) using the power rule for derivatives and see if we get back f(x) = x: d/dx [(1/2)x^2 + C] = d/dx (1/2)x^2 + d/dx C = x
2. The most general antiderivative of the function r(θ)=sec(θ)tan(θ)−5e^(θ^3) is R(θ)=∫sec(θ)tan(θ)−5e^(θ^3) dθ = -ln(cos(θ))+5e^(θ^3)/3+C, where C is the constant of the antiderivative. To check this, we can differentiate R(θ) using the rules of integration by substitution, and see if we get back r(θ) = sec(θ)tan(θ)−5e^(θ^3): d/dθ [-ln(cos(θ))+5e^(θ^3)/3+C] = sec(θ)tan(θ)−5e^(θ^3)
3. The most general antiderivative of the function f(x)=1+2x is F(x) = x+x^2 + C, where C is the constant of the antiderivative. To check this, we can differentiate F(x) using the power rule for derivatives and see if we get back f(x) = 1+2x: d/dx (x+x^2 + C) = d/dx x+d/dx x^2 + d/dx C = 1+2x
Hence,
1. The antiderivative would be x.
2. The antiderivative would be sec(θ)tan(θ)−5e^(θ^3).
3. The antiderivative would be 1+2x.
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x² - 2x - y² + 4y-3 , x² + 2x - y² + 8y-15 find hcf
To find the highest common factor (HCF) of two polynomials, we can use the Euclidean algorithm or the method of factoring the polynomials and comparing their common factors.
The first polynomial is x² - 2x - y² + 4y-3 and the second polynomial is x² + 2x - y² + 8y-15
x² - y² is common in both polynomials, let's factor it out.
x² - y² = (x-y)(x+y)
so the first polynomial can be written as (x-y)(x+y) - 2x + 4y - 3
and the second polynomial can be written as (x-y)(x+y) + 2x + 8y - 15
So the HCF of these two polynomials is (x-y)(x+y)
It is important to note that the HCF of polynomials is not unique, there can be more than one factorization.
what is 5 less than 4 times 7
Answer:
-31
Step-by-step explanation:
Let's put this into an equation:
[tex]4-5 *7[/tex]
Note that 5 less than 4 means I take 5 AWAY from 4, not 5-4.
Most people would go about this straight across, doing 4-5, -1, and then times 7 which would be -7.
BUT if there are no parentheses around 4-5, we do 5 times 7 first.
Why? In PEMDAS or order of operations, you multiply before subtracting.
That means I do 5 times 7 first. That is 35.
Now I subtract 4-35. That is -31.
There are 36 tables set up for the
annual pancake breakfast. Each table
is 8 feet long. The students plan
to cover each table with a paper
tablecloth that extends an extra
4 inches over each end so they can
tape it underneath. What is the total
length of paper needed to cover all
the tables?
The total length of paper needed to cover all the tables is equal to 10 tables multiplied by 104 inches per table, which is equal to 1040 inches.
What is Pythagorean theorem?According to the Pythagorean theorem, the hypotenuse's square length is equal to the sum of the squares of the two legs' lengths in a right triangle. The formula for this is a2 + b2 = c2, where a and b represent the lengths of the two legs, respectively, and c represents the length of the hypotenuse.
The theory used in this question is the Pythagorean theorem.
Number of tables:
Let's say there are 10 tables.
Length of each table plus 8 inches:
Each table is 8 feet long, which is equal to 96 inches. The extra 8 inches makes it 104 inches per table.
Total length of paper needed:
The total length of paper needed to cover all the tables is equal to 10 tables multiplied by 104 inches per table, which is equal to 1040 inches.
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The stem & leaf diagram shows the
number of emails received by Colin
each day.
8016
9 2 3 5 6 7789
10 0 1 2 3 4
11 1 3
12 3 8
Key:
10 3 means 103 emails
Find the median.
To find the median of the data set, we first need to arrange the data in numerical order. We can do this by grouping the digits in the stem & leaf diagram according to the key:
8016
92 35 67
100 124 34
113
123 8
Then we will arrange them in order as: 8016 92 35 67 100 124 34 113 123 8
To find the median we have to identify the middle value of the data set, considering that we have 12 data points. The middle value is the 7th value in the set which is 100, therefore the median is 100.
can you help me solve this? it says I have to prove, using statements and reasons, (ASA traingle congruence)
Richard is incorrect, As if two angles are same then the 3rd angle must be same too using angle sum property and therefore ΔJFH ≅ ΔJGH with AAA congruency.
What is the congruent triangle?Two triangles are congruent if they have the same shape and size. Congruent triangles have all corresponding angles and sides congruent, meaning they are equal in measure.
A triangle can be shown to be congruent to another triangle by using one or more of the following criteria:
SSS (Side-Side-Side) Congruence: If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
SAS (Side-Angle-Side) Congruence: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
ASA (Angle-Side-Angle) Congruence: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
HL (Hypotenuse-Leg) Congruence: If the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.
Richard is incorrect, As if two angles are same then the 3rd angle must be same too using angle sum of property and therefore ΔJFH ≅ ΔJGH
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Is (1 5/2) a solution ?
Answer:
No!
Step-by-step explanation:
(1 5/2)
is a mixed fraction so you will change it to proper fraction.
the solution is
=7/2 or 3.5
You will multiple two by one and add by five given 7/2.
9(7h−4k)+10k−5(6k−7h)
Answer:
98h - 56k----------------------------
Given expression:
9(7h - 4k) + 10k - 5(6k - 7h)Simplify it in steps below:
9(7h - 4k) + 10k - 5(6k - 7h) = Given 9(7h) - 9(4k) + 10k - 5(6k) + 5(7h) = Distribute63h - 36k + 10k - 30k + 35h = Simplifyh(63 + 35) - k(36 - 10 + 30) = Collect like terms98h - 56k AnswerAnswer:
[tex] \sf \: 98h - 56k [/tex]
Step-by-step explanation:
Given expression,
→ 9(7h - 4k) + 10k - 5(6k - 7h)
Let's simplify the expression,
→ 9(7h - 4k) + 10k - 5(6k - 7h)
→ 63h - 36k + 10k - 30k + 35h
→ (63h + 35h) + (-36k + 10k - 30k)
→ (98h) + (-56k)
→ 98h - 56k
Hence, answer is 98h - 56k.
A long year-end status report for work is 127 pages long. You need to print 18 copies for a meeting next week. How much is the paper going to cost for those reports? Paper is sold in reams (500 pages) for $3.77 each.
$
Answer:
$18.85
Step-by-step explanation:
1. 127*18 = 2286 pages.
2. 2286/500 = 4.6 (approx.)
3. You need to buy 5 reams of paper 500 pages each.
It will cost 5*$3.77 = $18.85
Find the area of the shaded region shown below and choose the appropriate result.
92 Square inches is the area of the shaded region shown below
What is Area?The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.
Given a rectangle, that has a length of 12 inches and 9-inch width
Since,
Area = length * width
Area of the given triangle = 12 * 9
Area of the given triangle = 108 square inch
There is also one square inside this rectangle of side 4 inch
Since the area of square = side * side
Thus in our case,
Area of square = 4 * 4 = 16 square inch
As we can see in the figure:
Area of shaded region = complete area of rectangle - area of square
Area of shaded region = 108 - 16
Area of shaded region = 92 square inch
Therefore, The area of the shaded region is 92 Square inches.
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Complete question:
Someone help me on this please
Least-cost planning methodology (LCPM), sometimes known as "least-cost planning" (LCP), is a relatively new strategy used by economists to make logical decisions about investments in transportation and other urban infrastructure projects.
What does the term "cost least" mean?Least Cost refers to the lowest cost; in Example 1.Least-cost planning methodology (LCPM), sometimes known as "least-cost planning" (LCP), is a relatively new strategy used by economists to make logical decisions about investments in transportation and other urban infrastructure projects. It is founded on a cost-benefit analysis.A contract is awarded to the company that submitted the lowest financial proposal among those that passed the technical review via the "Least-Cost Selection" (LCS) procedure, which is based on a two-step consecutive evaluation.Least-cost planning methodology (LCPM), sometimes known as "least-cost planning" (LCP), is a relatively new strategy used by economists to make logical decisions about investments in transportation and other urban infrastructure projects.The complete question is,
What is a project's least cost?
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The given points lies on the terminal side of an angle (θ)in standard position. Find the values of six trig functions of (θ).(2,−4).
The values of six trig functions are:
sinθ=− √5/5, cosθ=2√5/5, tanθ=-1/2, cot θ=−2, secθ=√5/2, cscθ=−√5
The relationship between the angles and sides of a triangle is given by these trig functions.
There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).
The point's coordinates are:
x=2, y=−4
To calculate the functions we have to calculate the distance between the point and the origin:
r=√x²+y²=√2²+(−4)²=√16+4=√20
r=2√5
Now we can calculate the functions:
sinθ=y/r=−2/2√5=−√5/5
cosθ=x/r=4/2√5=2/√5=2√5/5
tanθ=y/x=−2/4=−1/2
cotθ=x/y=4/−2=−2
secθ=r/x=2√5/4=√5/2
cscθ=r/y=2/√5−2=−√5.
Hence, the values of trig functions are calculated.
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Find two consecutive whole numbers that square root of 32 lies between
Answer:
5 and 6
Step-by-step explanation:
sqrt of 32= 4sqrt2 = 5.656
given 1 is congruent to 2 prove. p is parallel to q
Answer:
Step-by-step explanation:
Given : ∠1 ≅ ∠2
To prove : p║q
Solution :
In the figure attached,
Statements Reasons
1). m∠1 ≅ m∠2 1). Given
2) m∠1 ≅ m∠3 2). Vertical angles
3) m∠2 ≅ m∠3 3). Transitive property of congruence of the angles
4). Line p║q 4). Corr
An open box is to be constructed from a square piece of sheet metal by removing a square of side 3 feet from each corner and turning up the edges. If the box is to hold 300 cubic feet, what should be the dimensions of the sheet metal?
If an open box is to be constructed from a square piece of sheet metal by removing a square of side 3 feet from each corner and turning up the edges. the dimensions of the sheet metal is 16 feet.
How to find the dimension?Let x represent the dimension of the sheet metal
So,
Volume =3×(x-2×3)×(x-2×3) = 300
Volume =3×(x-6)×(x-6) = 300
(x -6)² = 300/3 = 100
x-6 = √100 =10
x = 10 +6
x = 16 feet
Therefore the dimensions of the sheet metal is 16 feet
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tell me what spending and saving habits you have learned from your parents, guardians, family and friends. what will you do the same in your adult life and what will you change?
I learned to save for the future and spend responsibly. In my adult life I will continue to save and be mindful of my spending habits. I will change my attitude towards money and become more frugal.
How can I save money for the future?Saving money for the future requires discipline and dedication. One of the easiest ways to start saving is to create a budget and stick to it. Make sure to include a line item for savings in your budget and allocate a specific amount each month to save.
Additionally, set up automatic transfers from your checking account to your savings account to ensure money is put into savings each month. It's also important to find ways to minimize expenses. Cutting back on eating out, reducing your cell phone bill, and shopping for discounts are all great ways to save money.
Finally, look into investing your money in stocks, bonds, and other investments to help your savings grow. Saving money for the future takes time, but it is possible with the right strategies.
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write about how to solve 8 divided by 5
Answer: 1⅗
Step-by-step explanation: We can write 8 divided by 5 as 8/5.
As 8/5 is an improper fraction, when we divide 8 by 5, we get 1 as quotient and 3 as remainder.
To convert an improper fraction into a mixed fraction, we take quotient 1 as a whole part and in the fractional part remainder 1 as the numerator, and divisor 5 as the denominator.
The GCF of 5 and 1 is 1. So, divide both the numerator and denominator by the GCF to simplify and convert it to a mixed fraction.
Thus, 8 divided by 5 as a fraction in simplest form is 1⅗.
Convert mixed number into an improper fraction 2 1/8
Answer:
[tex]\frac{17}{8}[/tex]
Step-by-step explanation:
[tex]2\frac{1}{8} = (2*8)+1 =17= \frac{17}{8}[/tex]
Answer:
17/8
Step-by-step explanation:
Scenario: Given sphere_radius and pi, compute the volume of a sphere and assign to sphere_volume. Volume of sphere = (4.0 / 3.0) π r^3
Sample output with input: 1.0 Sphere volume: 4.19
The volume of the sphere = (4.0 / 3.0) π r^3.
What is the volume of the sphere?
The quantity of space occupied within a sphere is referred to as its volume. Every point on the surface of the sphere is equally spaced from its center, making it a three-dimensional round solid object. The fixed point and fixed distance are referred to as the sphere's center and radius, respectively.
Here, we have
The volume program in Python, where comments are used to explain each line is as follows
#This initializes pi to 3.142
pi= 3.142
#This gets input for the radius
sphere_radius = float(input("Radius: "))
#This calculates the sphere volume
sphere_volume = (4.0 / 3.0) * sphere_radius**3
#This prints the sphere volume
print(sphere_volume)
Hence, the volume of the sphere = (4.0 / 3.0) π r^3.
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I Need help please….
The distance between two points on a line segment .
What is the formula for graph length?Learn how to use the distance formula to calculate the distance between two points, which is an application of the Pythagorean theorem. To calculate the distance between any two points, we may rewrite the Pythagorean theorem as d=((x 2-x 1)2+(y 2-y 1)2). Sal Khan and the CK-12 Foundation created it.
A line segment is delimited by two separate points on a line in geometry. A line segment is a section of a line that links two locations. A line has no endpoints and stretches in both directions indefinitely, but a line segment has two defined or definite endpoints.
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