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.

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

\(2x-6\)

Answer:

Step-by-step explanation:

(A). The quadrilateral ABCD is a trapezoid.

(B). A = 36 units²

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

Answer: Parallel

Step-by-step explanation:

if two secanys of a circle are made them they cut off congruent arcs

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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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:

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

Answer:

sum of exterior angles of polygon = 360°

therefore,

z = 360 - (105+145)

z = 360 - 250

z = 110°

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

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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Answer:

7580is divisible by only 2& 10

113, 724 is divisible by 2

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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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

Answer: 35.25p + 5.5 ≤ 70

910 is 9.1 × 10^2 in scientific notation

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)

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!

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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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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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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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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Answer:

72, 90, 108

Step-by-step explanation:

Answer:

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

------------

The answer is good

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.\(∫1[infinity]​(4x+4)31​dx∫(4x+4)31dx\)

\(=∫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)31​dx∫(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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Answer:

there should be 14, 45 pound boxes

Step-by-step explanation:

1000-190= 810

810/45=14 boxes

Answer:

hope it helps..

Step-by-step explanation:

If this helped please comment..

Answer:

3.25

Step-by-step explanation:

divide then add 3

Answer:

3 1/4 or 13/4

Step-by-step explanation: