A straight line has a gradient of 4 and passes through the point (2,9).
Work out the equation of the line.
Give your answer in the form y = mx + c, where m and c are integers or
fractions in their simplest forms.
Answers
The equation of the given line passes through the point (2,9) y = 4x + 1.
What exactly is the slope of a line?The slope of a line indicates its steepness. The slope is determined mathematically as "increase over run" (change in y divided by change in x).
A line equation is defined as:The conventional form of a line equation is ax + by + c = 0. Here, the coefficients are a and b, the variables are x and y, and the constant term is c. It is a one-degree equation with variables x and y. The coordinates of both the point on the line that appears in the coordinate plane are represented by the values of x and y.
According to the given data:m = 4
equation of the line = y = mx + c
substituting the value of m = 4
y = 4x + c
the point (2,9):
putting the points in the line of the equation:
x = 2
y = 9
So,
y = mx + c
9 = 4 * 2 + c
9 = 8 + c
c = 1
The equation of the given line y = 4x + 1.
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Answer:
y=4x+1
Step-by-step explanation:
y-y1=m(x-x1)
y-9=4(x-2)
y=4x-8+9
y=4x+1
Related Questions
Use the Integral Test to determine whether the series is convergent or divergent. ∑n=1[infinity](4n+4)31 Evaluate the following integral ∫1[infinity](4x+4)31dx Since the integral finite, the series is
Answers
Integral Test:
The integral test is used to check the convergence of an infinite series. According to the integral test, a series converges if and only if the corresponding improper integral converges. If the improper integral diverges, then the series also diverges.
Use the Integral Test to determine whether the series is convergent or divergent. \(∑n=1[infinity](4n+4)31\) For Integral test, Firstly, we need to find the integral of the given series i.e.\(∫1[infinity](4x+4)31dx∫(4x+4)31dx\)
\(=∫4(x+1)31dx
=4∫(x+1)31dx\) Now, to solve the integral, we can use substitution method.
Let (\(x+1)
= t → dx
= dt4∫(x+1)31dx
=4∫t31dt\) Now integrating by using the formula\(∫xn dx= xn+1/n+1+ C4∫(x+1)31\)
\(dx=4∫t31dt
=4* t32/32+C
= 4*(x+1)32/32+C
=4*(x+1)32/32∣11
=4/32+4/32\)
=1/4 We now have the value of integral which is finite, so we can conclude that the given series also converges.
Thus, the series is convergent. Evaluate the following integral \(∫1[infinity](4x+4)31dx∫(4x+4)31dx
=∫4(x+1)31dxLet (4x+4)
= t → dx
= dt4∫(x+1)31dx
=4∫t31dt4∫t31dt
= 4* t32/32+C
= 4*(x+1)32/32∣11
=4/32+4/32
=1/4\)
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Explain this words in form of trigonometry graphs
1.Period
2.Amplitude
3.Range
4.maximium y-value
5.manimum y-value
Answers
Amplitude: is the vertical distance between the midline and one of the extremum points.
Period: is the distance between two consecutive maximum points or two consecutive minimum points (these distances must be equal). HOPE THIS HELPS!
The equation for the circle below is x2 + y2 = 16. What is the length of the
circle's radius?
Answers
Answer:
e) 4
Step-by-step explanation:
This is the form of a circle. Use this form to determine the center and radius of the circle.
(x−h)^2+(y−k)^2=r^2
r=4
h=0
k=0
Given a hash table T with 25 slots that stores 2000 elements, the load factor α for T is __________a)80b)0.0125c)8000d)1.25
Answers
The load factor α for the given hash table T is 80.
The load factor of a hash table is defined as the ratio of the number of elements stored in the table to the number of slots in the table. In this case, we are given that the hash table T has 25 slots and stores 2000 elements.
Therefore, the load factor α can be calculated as follows:
α = number of elements / number of slots
= 2000 / 25
= 80
Therefore, the load factor α for the given hash table T is 80. This means that on average, each slot in the hash table contains 80 elements. A high load factor can cause performance issues such as increased collisions and slower access times, so it is important to choose an appropriate number of slots when designing a hash table.
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Draw the cross-sectional effect diagrams for the beam whose loading condition is given in the figure ({N}, {T}, {M})
Answers
A cross-sectional effect diagram, also known as an axial force-shear force-bending moment diagram or simply an internal force diagram, is a graphical representation that shows the distribution of internal forces (axial force, shear force, and bending moment) along the length of a structural member, such as a beam or column.
To draw the cross-sectional effect diagrams for the beam whose loading condition is given in the figure, we need to follow these steps:
Step 1: Identify the type of loadingFor this question, the loading conditions are {N}, {T}, {M}. So, the loading types are axial force, shear force, and bending moment.
Step 2: Draw the cross-sectional diagram of the beam. We need to draw the diagram of the cross-section of the beam in the direction of the forces acting on the beam. In this case, it will be a rectangular beam.
Step 3: Draw the effect diagrams After drawing the cross-sectional diagram, we need to draw the effect diagrams for each loading condition.
The effect diagrams are as follows: 1. Axial force diagram (N):In this case, the axial force is positive (+) which means it is a tensile force. 2. Shear force diagram (T):The shear force is negative (-) from x = 0 to x = 1, which means the shear force is acting downward. It is zero at x = 1 and then becomes positive (+) from x = 1 to x = 2, which means the shear force is acting upward. 3. Bending moment diagram (M):The bending moment is zero at x = 0, becomes negative (-) from x = 0 to x = 1, reaches a minimum at x = 1, and then becomes positive (+) from x = 1 to x = 2.
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Laura must choose a number between 67 and 113 that is a multiple of 3, 6, and 9. Write all the numbers that she could choose. If there is more than one
number, separate them with commas.
Answers
Answer:
72, 90, 108
Step-by-step explanation:
7th GRADE MATH hellp
Answers
Answer:
I took 5 minutes to think this through, hope I'm right cause been a long time since my brain killed me over this one question. I believe the answer to this is B, cause the students might of gotten two chances to get picked so I'll stick with B. So sorry if I'm wrong. 3 students 2 chances... yea it's B.
Step-by-step explanation:
Find the orthogonal complement S⊥.
S is the subspace of R5 consisting of all vectors whose third and fourth components are zero
Answers
The orthogonal complement S is the set of all vectors orthogonal to the subspace S in R5 whose third and fourth components are zero. To find S, we need to find vectors such that vu = 0 for all u in S using the dot product. The orthogonal complement S has dimension three and a basis for it is f1, f2, f3, where f1 = (1,-1,0,0,0) f2 = (0,0,1,0,0) f3 = (0,0,0,1,0).
Let's begin by defining the orthogonal complement S⊥, which is the set of all vectors orthogonal to the subspace S in question. The subspace S is defined as the set of all vectors in R5 whose third and fourth components are zero. Let's go through the steps to find S⊥.
Step 1: Determine the dimensions of S The dimension of the subspace S is two. This is because the subspace consists of vectors whose third and fourth components are zero. Therefore, only the first, second, fifth components are nonzero, making up a 3D subspace. Since S is a subspace of R5, the remaining two components can also take any value and thus the dimension of S is 2.
Step 2: Determine a basis for S To determine a basis for S, we can use the fact that the subspace is defined as all vectors whose third and fourth components are zero.
Therefore, a basis for S is given by {e1, e2}, where e1 = (1,0,0,0,0) and e2 = (0,1,0,0,0).
Step 3: Find the orthogonal complement S⊥ To find S⊥, we need to find all vectors orthogonal to S. This means we need to find vectors v such that v⋅u = 0 for all u in S. To do this, we can use the dot product: v⋅u = v1u1 + v2u2 + v3u3 + v4u4 + v5u5= v1u1 + v2u2 + v5u5We want this to be zero for all u in S. This implies:v1 + v2 = 0 andv5 = 0Therefore, S⊥ is given by the set of all vectors in R5 of the form (a,-a,b,c,0), where a, b, and c are arbitrary constants. The orthogonal complement S⊥ has dimension three, and a basis for it is {f1, f2, f3}, where:f1 = (1,-1,0,0,0)f2 = (0,0,1,0,0)f3 = (0,0,0,1,0)The above result gives us a complete characterization of S⊥.
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Please help me with this math problem
Answers
Answer:
18vw²y^9 + 24v^6w^5
= 6vw²( 3y^9 + 4v^5w³)
Hope this helps.
Answer:
6vw^2(3y^9 + 4v^5w^3)
Step-by-step explanation:
If you were to multiply the equation 6vw^2(3y^9 + 4v^5w^3) then the result would be
18vw^2y^9 + 24v^6w^5
Hope this helps!
find the value of x
Answers
Answer:
4√5
Step-by-step explanation:
Use Pythagorean theorem
a^2=21^2-19^2
a^2=441-19^2
a^2=441-361
a^2=80
a= √80
simplify
A department in a company has 10 members: 7 males and 3 females. To gain greater insight into the employee's views of various benefits, the human resources office plans to form a focus group from members of this department, four departmental members will be selected at random from the department's members. What is the probability that the focus group will have two males and two females? a. 0.22 b. something else c. 0.38 d. 0.3
e. 0.44
Answers
Thus, the probability that the focus group will have two males and two females is 0.3.
To determine the total number of possible ways to select four members from a department of 10. This is known as the sample space and is calculated using the combination formula, which is:
n C r = n! / r! (n - r)!
where n is the total number of individuals (in this case, 10) and r is the number of individuals being selected (in this case, 4).
So, the sample space for selecting four members from a department of 10 is:
10 C 4 = 10! / 4! (10 - 4)! = 210
Next, we need to determine the number of ways to select two males and two females from a department with 7 males and 3 females.
This is calculated using the multiplication principle, which states that the total number of ways to perform a sequence of events is equal to the product of the number of ways to perform each individual event.
So, the number of ways to select two males and two females from a department with 7 males and 3 females is:
(7 C 2) x (3 C 2) = 21 x 3 = 63
Finally, we can calculate the probability of selecting a focus group with two males and two females by dividing the number of ways to select two males and two females by the total number of possible ways to select four members:
63 / 210 = 0.3
Therefore, the probability that the focus group will have two males and two females is 0.3. The answer is d.
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What is the measure of angle Z?
Answers
Answer:
sum of exterior angles of polygon = 360°
therefore,
z = 360 - (105+145)
z = 360 - 250
z = 110°
Can someone explain how to do this?
Answers
Answer: ok ima try my best
the numbers that's in the {} are the umbers you put in for x so
10+10=22 is false
12+10=22 is true
in the x columns you put in the numbers
in the columns with the (x+10=22) you input the number for x so just rewrite it
then you answer if its the answer or not
Step-by-step explanation:
10+10=22 is false
12+10=22 is true < this one is the only one that's true the rest are false
i hope this helps
is the complex vector space of polynomials consist of complex-valued functions of a complex variable?
Answers
The complex vector space of polynomials is a vector space over complex number fields and is composed of complex-valued functions of a complex variable.
A vector represents a mathematical entity with both magnitude and direction. When the vector elements are generally complex numerals, then the column space is referred to as complex. The set of polynomials in such a vector space generates the space over the domain of complex numbers by combining extra polynomials that are each specified portion and by multiplying each coefficient by the scalar.
In this vector space, the polynomials are vectors whereas the complex numerals are scalars. These requirements for the space are in addition also catered by this space, like the associativity and commutativity of vector addition, the presence of additive inverses, the distributivity of scalar multiplication over vector addition, and the existence of a neutral element with respect to vector addition.
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for (i = 1; i <= n; i *= 2) { for (j = 1; j <= i; j *= 2) { // 9 assignment instructions }Analyze the following programs and show their time complexity functions and big-O notations. please show big-O proofs.
Answers
The time complexity functions and big-O notations of the program is O(log n)
Let's analyze the time complexity of the code using mathematical terms.
The outer loop runs log n times, where n is the input size, because i doubles in each iteration until it reaches n. Therefore, the time complexity of the outer loop is O(log n).
For each iteration of the outer loop, the inner loop runs log i times. Since i doubles in each iteration of the outer loop, the number of iterations of the inner loop is 1, 2, 4, 8, ..., i.
The total number of iterations of the inner loop is the sum of the geometric series 1 + 2 + 4 + ... + n/2 + n. This series sums up to 2n - 1, which is O(n).
Therefore, the overall time complexity of the code is the product of the time complexity of the outer and inner loops, which is O(n log n).
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Two angles of a triangle are in the ratio of 2:3 if the third angle is 50 degree find the other two angles
Answers
Answer:
52° & 78°Step-by-step explanation
Two angles of a triangle are in the ratio of 2:3 if the third angle is 50 degree find the other two angles
the sum of the interior angles in a triangle is 180°
so
180 - 50 = 130°
130 : 5 = 26° (unit)
26 * 2 = 52°
26 * 3 = 78°
--------------
check
50 + 52 + 78 = 180°------------
2 : 3 = 52 : 780.66666666666 = 0.66666666666The answer is good
100 POINTS AND BRAINLIEST
What is the rule for the function that is graphed?
y = 2 x + 2
y = 3 x + 2
y = 2 x
y = x – 2
Answers
Answer:
Y=2x+2
and tbh it's simple for most people
Step-by-step explanation:
Hope it helps
Answer:
y = 2 x + 2
Step-by-step explanation:
I did the assignment, so I hope it helps (A like helps me if you have time)
if two secants of a circle are ____ then they cut off congruent arcs
Answers
Answer: Parallel
Step-by-step explanation:
if two secanys of a circle are made them they cut off congruent arcs
Estimate the amount of the tip by rounding the bill to the nearest dollar before calculating.
20% tip on a bill of $13.48
The amount of the tip is approximately $
Answers
need an answer please asap!
Answers
Answer:
Step-by-step explanation:
(A). The quadrilateral ABCD is a trapezoid.
(B). A = 36 units²
910 in scientific notation
Answers
910 is 9.1 × 10^2 in scientific notation
Fractions 7/8+ 1/5
Evaluate the expression shown below and write your answer as a fraction in simplest form
Answers
The simplest form of fraction of the given terms is 43/40.
According to the statement
we have to find that the simplest form of the fraction by evaluating.
So, For this purpose, we know that the
A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole.
The given expression is
7/8+ 1/5
Now, to solve it take a LCM of it then
35+8/40
Now solve the term then the equation become
43/40.
Now, The simple form of the fraction become the 43/40.
So, The simplest form of fraction of the given terms is 43/40.
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Please only answer if you know how :)
create a drawing that includes at least {ONE} of each of the
following. Be creative in your drawing making the scene work together to create one cohesive picture.
Label each structure on your drawing.
Point
Line
Segment
Ray
Plane
Acute angle
Obtuse angle
Straight angle
Complementary angles
Supplementary angles
Adjacent angles
Non‐adjacent angles
Alternate interior angles
Alternate exterior angles
Consecutive interior angles
Consecutive exterior angles
A regular polygon
An irregular polygon
Equilateral triangle
Isosceles triangle
Scalene triangle
Acute triangle
Obtuse triangle
Right triangle
Equiangular triangle
Square
Rectangle
Trapezoid
Kite
Parallelogram
Rhombus
Answers
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
2. Is 7,580 divisible by 2 3 9 10 Explain your reasoning for your choices. 3. Is 113,724 divisible by 2 3 5 6 9 Explain your reasoning for your choices.
Answers
Answer:
7580is divisible by only 2& 10
113, 724 is divisible by 2
translate: 6 less than twice a number
Answers
Answer:
2x-6
Step-by-step explanation:
twice a number is
\(2\times x\\\\=2x\)
6 less than twice a number is
6 less than 2x and that is
\(2x-6\)
1/4 + 3 = ??
What’s the answer??
Answers
Answer:
3.25
Step-by-step explanation:
divide then add 3
Answer:
3 1/4 or 13/4
Step-by-step explanation:
is the theoretical or the experimental probability greater for the coin landing on tails?
Answers
Mr. Tanaka is loading his boat with many identical 45-pound boxes. Mr. Tanaka weighs 190 pounds. The boat can carry at most 1,000 pounds. If each box is fully-filled, how many boxes can he load on the boat?
Write an inequality that represents this situation.
Answers
Answer:
there should be 14, 45 pound boxes
Step-by-step explanation:
1000-190= 810
810/45=14 boxes
Someone plzz help it’s urgent!!
Answers
Answer:
hope it helps..
Step-by-step explanation:
If this helped please comment..
A group of friends wants to go to the amusement park. They have no more than $70
to spend on parking and admission. Parking is $5.50, and tickets cost $35.25 per
person, including tax. Which inequality can be used to determine p, the maximum
number of people who can go to the amusement park?
Answers
The maximum amount of people that can go is 1
Answer: 35.25p + 5.5 ≤ 70