-6y+6x=0 written in standrad form

The equation is given as y = 4x - 3 , where the slope is m = 4

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The value of term 1 = 1 square

The value of term 2 = 5 suqres

The value of term 3 = 9 squares

So , the increment in the number of squares is 4

Let the first point be P ( 1 , 1 )

Let the second point be Q ( 2 , 5 )

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 5 - 1 ) / ( 2 - 1 )

Slope m = 4

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 1 = 4 ( x - 1 )

On simplifying the equation , we get

y - 1 = 4x - 4

Adding 1 on both sides of the equation , we get

y = 4x - 3

Therefore , the value of y is 4x - 3

when x = 1 . y = 4 - 3 = 1

when x = 2 , y = 4 ( 2 ) - 3 = 8 - 3 = 5

Hence , the equation of line is y = 4x - 3

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22 MB in 5 seconds

how many MB per second

divide the 5 out

22/5 = 4.4 MBPS

30 MB in 6 seconds

30/6 = 5 MBPS

5 MBPS > 4.4 MBPS

No, they aren't equivalent because one is greater than the other.

Hope this helps,

- Jeron :- )

Answer: (a) The equation 2x^2 + 4x + 3 = k has real roots if and only if its discriminant, which is 4^2 - 4(2)(3), is nonnegative. The discriminant is equal to 0, so the equation has real roots if and only if k = 3.

(b) For the equation f(x) = kx^2 + kx + 1 to have real roots, its discriminant, which is 1 - 4k, must be nonnegative. This gives us k >= 1/4. The range of values of k for which the equation has real roots is k >= 1/4.

(c) When k = -2, the equation f(x) = -2x^2 - 2x + 1 = 0. Solving this equation using the quadratic formula, we get x = (-1 ± √(1 + 8))/4. So, the roots are x = (-1 ± √(9))/4 = (-1 ± 3)/4 = 1/2, -2.

The probability that the item will be defective is 0.017, the probability that an item selected at random is defective is 0.018 and the probability that an item is produced by machine D is 0.25

Using the formula of probability distribution to solve the given problem;

6: The probability that the item will be defective is the sum of the probabilities of a defective item from each machine:

(1% * 30%) + (1.5% * 30%) + (3% * 15%) + (2% * 25%) = 0.017

So the answer is b

7: If an item is selected at random and found to be defective, the probability that it was produced by machine A is the probability of a defective item from machine A divided by the overall probability of a defective item:

(1% * 30%) / 0.017  = 0.018

The answer is option a

8: The probability that the item was produced by machine D is the probability of a non-defective item from machine D divided by the overall probability of a non-defective item:

(25% * 98%) / (100% - 0.017) = 0.25 * 0.98 / 0.895 = 0.25

So the answer is (d) 0.253

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The perimeter of the triangle is 16+8√2 feet.

The perimeter of any two-dimensional figure is defined as the distance around the figure. The formula for a closed shape figure's perimeter is typically equal to the length of the figure's outer line.

The perimeter of a triangle will therefore be equal to the sum of its three sides. Consequently, if a triangle has sides a, b, and c,

Here, a= 8 feet

b=  8 feet

c= 8√2 (length of a leg * √2= 8*√2)

Perimeter= Sum of all three sides of the triangle

Perimeter = a + b + c

Perimeter= 8+ 8 +8√2

Perimeter=  16+8√2 feet.

16+8√2 feet is the perimeter of the triangular garden.

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The value of x in expression is -1/8.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

(3+4x-2)4 2/7=0

(3+4x-2)16/7=0

48+64x-32=0

x=-1/8

Therefore, the answer of given algebra problem will be -1/8.

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Answer: If Ken brought 8 liters of water for everyone to share and they drank 5 liters of it, then the remaining amount of water they have is 8 - 5 = 3 liters.

Step-by-step explanation:

If the surface of the area of a cylinder is 372π square centimeters. Then the height of the cylinder is 31 centimeters.

Let r be the radius and h be the height of the cylinder. Then the surface area of the cylinder will be given as,

SA = 2πrh square units

The surface of the area of a cylinder is 372π square centimeters the radius is 6 cm. Then the height of the cylinder is given as,

SA = 2πrh

372π = 2π x 6 x h

h = 372 / 12

h = 31 centimeters

The height of the cylinder is 31 centimeters.

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The requried, given system of equations y=x+3 and 3x-3y=9 has no common solution.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,

From the first equation, we can solve for y:

y = x + 3

Substitute y = x + 3 into the second equation:

3x - 3(x + 3) = 9

Simplify the right side:

3x - 3x - 9 = 9

-9 = 9 (inconsistent)

Since the equation -9 = 9 is inconsistent, the system of equations has no solution, which means that there are no values of x and y that make both equations true at the same time. It implies the system of equations has no solution.

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The sequences of translations, rotations, and reflections bthat would take polygon P to polygon Q will be:

C Translate so that Ais taken to J. Then reflect over line BA

E Reflect over line BAand then translate by directed line segment BA.

A function is translated when it is moved from where it was before. In geometry, a function that moves an object a specific distance is referred to as translation. Nothing else is done to change the object.

It is not scaled, reflected, rotated, or refracted. Every point of the object must be translated by the same amount and in the same direction.

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Answer:

x = 12

y = 11

Step-by-step explanation:

It's a parallelogram, so opposite sides are equal.

4x + 10 = 58

4x = 58 - 10 = 48

x = 48/4 = 12

10y - 6 = 104

10y = 104 + 6 = 110

y = 110/10 = 11

Answer:

The surface area of the label is 28 squared inches.

Step-by-step explanation:

The dimensions of juice box are length=2 inches, breadth=1.5 inches and height= 4 inches.

The lateral surface area of a cuboid is given by 2(length+breadth)×height.

Now, lateral surface area of juice box = 2(2+1.5)×4

= 2×3.5×4

= 28 squared inches

Answer:

28 square inches

Step-by-step explanation:

         The label covers the lateral surface area of the box.

  l = 2 in ;  w = 1.5 in ; h = 4 in

    [tex]\boxed{\text{\bf lateral surface area of cuboidal box = 2h*(l +w)}}[/tex]

                                                                      [tex]\sf = 2*4 *( 2 +1.5)\\\\= 2 * 4 * 3.5\\\\ = 28 \ in^2[/tex]

The students divided the number ‘n’ by 3 instead of dividing (n-5) by 3.

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here: Given, Scott solve the equation Winnie, Texas, working realize they made a mistake identify Scott era wrote an algebraic expression for “5 less than a number n divided by 3” as (n/3) - 5.

We have to find the error made by the students.

5 less than a number n = n - 5

5 less than a number n divided by 3 = (n - 5)/3

Correct expression = (n - 5)/3

Expression written by student = (n/3) - 5

Therefore, the students divided the number ‘n’ by 3 instead of dividing (n-5) by 3.

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What’s the Error? A Scott solve the equation Winnie, Texas, working realize they made a mistake identify Scott era wrote an algebraic expression for “5 less than a number n divided by 3” as (n/3) - 5. What error did the they make?

Answer:

first convert 2mins to seconds

60sec=1 min

which is 2×60=120sec

then70/120sec=0.583

convert 50mis to sec

5×60=300sec

so therefore 300sec×0.583=174.9words

HOPE IT HELPS

Answer: 175 words

Step-by-step explanation:

First start out by dividing how many amount (5 min) you are looking for by the amount (2 min) that we already know.

5 / 2  = 2.5

This gives us the key to finding our final answer.

Use this new number (2.5) and multiply it by 70 to get our answer.

70 x 2.5 = 175

Answer:

4

Step-by-step explanation:

18 = 3x + 6

18 - 6 = 3x

12=3x

12/3 = x

4 = x

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Answer:

y + 7 = -1/2 ( x - 17)

Step-by-step explanation:

y-y₁=m(x-x₁)

[tex]x_{1\\} = 17[/tex]

[tex]y_{1}[/tex] = -7

y - (-7) = -1/2(x - 17)

y + 7 = -1/2(x -17)

Answer:

To turn -5/7 and 8 into a quadratic equation, we first need to convert 8 into an equation by adding 8 to both sides. The equation becomes: -5/7 = x^2 + 8. Then, we can expand the right side into a complete square, using the formula (b/2)^2. The equation becomes:

-5/7 = (x^2 + 8) + (4/2)^2

-5/7 = x^2 + 8 + 4

-5/7 = x^2 + 12

Finally, we can rearrange the equation to make the right side equal to 0, and then factor it. The final equation is:

x^2 + 12 + 5/7 = 0

x^2 + 12 + 5/7 = (x + 6/√7)(x + 6/√7) = 0

Step-by-step explanation:

In the first step, we added 8 to both sides to make the equation -5/7 = x^2 + 8. In the next step, we added 4 to the right side to complete the square. The purpose of completing the square is to get a perfect square on the right side, which will make it easier to factor the equation.

Next, we rearranged the equation to make the right side equal to 0, so that we can factor the equation. The equation x^2 + 12 + 5/7 = 0 can be factored as (x + 6/√7)(x + 6/√7) = 0, where (x + 6/√7) is a binomial that satisfies the equation.

The counterexample proves that the converse of the theorem is not always true, and we have to be careful when making statements about limit points and convergence of sequences.

A sequence is a set of numbers that are generated one after the other in a specific pattern.

The theorem states that if a sequence converges, it will have exactly one limit point. In other words, if a sequence is getting closer and closer to a certain number, there will be only one number that it approaches. This is a fundamental idea in mathematics, and it is important to understand why it is true.

To prove this theorem, let's consider a sequence (a_n) that converges to a limit L. If there were two different limit points, say L1 and L2, then there would be a contradiction. This is because by definition, the sequence (a_n) would be getting closer and closer to L1 and L2 at the same time, which is not possible. Hence, it must be true that the sequence (a_n) has exactly one limit point, L.

The converse of this theorem is not always true. In other words, just because a sequence has exactly one limit point, it doesn't necessarily mean that it converges to that limit. To see why this is the case, let's consider the following sequence:

(2, 3, 4, 5, 6, ...)

In this sequence, the limit point is 6. However, the sequence does not converge to 6 because it is not getting closer and closer to 6 as it goes on. Instead, it is increasing by 1 with each term, and therefore it does not converge.

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Charlie's utility function is given by U(A, B) = AB, where A is the number of apples he consumes and B is the number of bananas he consumes. The price of apples is $1, and the price of bananas is $2.

If Charlie's income is $120, he has a budget constraint given by:

1A + 2B = 120

To maximize his utility subject to this budget constraint, Charlie must use his income to purchase the combination of apples and bananas that gives him the greatest value of U(A, B).

The solution to this problem can be found by using the method of Lagrange multipliers. From the budget constraint, we can solve for A in terms of B:

A = 120 - 2B

Substituting this into the utility function, we have:

U(B) = (120 - 2B)B = 120B - 2B^2

To maximize U(B), we must find the value of B that maximizes this expression. Taking the derivative of U(B) with respect to B and setting it equal to zero, we find that:

dU/dB = 120 - 4B = 0

Solving for B, we find that:

B = 30

Thus, if Charlie chose the bundle that maximizes his utility subject to his budget constraint, he would consume 30 units of bananas. The answer is therefore a. 30.

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Answer:

Step-by-step explanation:

Answer:

The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²vvvThe diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²v

Step-by-step explanation:

its E and A

Answer:

The solutions to the inequality are B, E, and F: 25, 36, and 9.

Step-by-step explanation:

The solutions to the inequality √x < 10 are the values of x that make the inequality true when plugged in. To find these values, we can square both sides of the inequality:

√x < 10

x < 10^2 = 100

So, the values of x that make the inequality true are those that are less than 100. The options that satisfy this condition are:

A. 100 (not a solution)

B. 25 (solution)

C. -100 (not a solution)

D. 105 (not a solution)

E. 36 (solution)

F. 9 (solution)

a) The area of Tina's kitchen is 44.8625 square meters. b) Tina cost $2520 to buy flooring for her kitchen floor.

a) To work out the area of Tina's kitchen in square meters, we need to divide the area in square centimeters by 10,000, which is the number of square centimeters in a square meter:

Area = length x width = 925 cm x 485 cm = [tex]448,625 cm^2[/tex]

Area in square meters =[tex]448,625 cm^2 / 10,000 cm^2/m^2 = 44.8625 m^2[/tex]

b) To find how many whole square meters of flooring Tina needs, we round the area of the kitchen up to the nearest whole number:

Area in square meters rounded up = ceil(44.8625) = [tex]45 m^2[/tex]

The cost of the flooring is $56 per square meter, so Tina pays:

Total cost = [tex]45 m^2 * $56/m^2 = $2520[/tex]

To use inverse operations to check this answer, we can divide the total cost by the cost per square meter to get the number of square meters, and then multiply by the cost per square meter to check that we get back to the total cost:

Number of square meters =[tex]$2520 / $56/m^2 = 45 m^2[/tex]

Total cost = [tex]45 m^2 x $56/m^2 = $2520[/tex] (same as the original answer)

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Graph the Trapezoid PQRS with vertices P(-6, 2), Q(-2, -1), R(-2, -3), and S(-6, -6). Reflect in the line x=1.

The preimage's point corresponds to the image's points in the following way:

P(-6, 2) → P'(6, 2)

Q(-2, -1) → Q' (2, -1)

R(-2, -3) → R'(2, -3)

S(-6, -6) → S'(6, -6)

                                       (x,y)→(−x,y)

A trapezoid, commonly referred to as a trapezium, is a quadrilateral or a polygon with four sides. It has a set of parallel opposing sides and a set of non-parallel sides. The bases and legs of the trapezoid are known as the parallel and non-parallel sides, respectively.

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the given function  y = 3(4)ˣ, is an exponential function.

The opposite of an exponential function is a logarithmic function. A log function and an exponential function both use the same base. An exponent is a logarithm. f(x) = bx is how the exponential function is expressed. The formula for the logarithmic function is f(x) = log base b of x.

Given a function y = 3(4)ˣ

An exponential function is defined by the formula f(x) = a, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

The exponential function is an important mathematical function which is of the form

f(x) = aˣ

therefore, we can say that the given function is an exponential function.

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The distances traveled by the car are given as follows:

Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:

v = d/t.

The parameters for this problem are given as follows:

v = 1.15 km/min, t = 1 min.

Hence the equation for the distance in km after t minutes is given as follows:

d = 1.15t.

Then after 3 minutes, the distance is of:

d = 1.15 x 3 = 3.45 km.

After 5 minutes, the distance is of:

d = 1.15 x 5 = 5.75 km.

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Answer:

Both C and D are equations for the two given points.

Step-by-step explanation:

A. Y+2=0.5(x-3)  NO

 (-3,-5):  -5+2 = 0.5(-3-3);   -3 = 0.5(-6);   -3 = -3  YES

 (3,2):     2+2 = 0.5(3-3):   4 = 0.5(0);   4 = 0   NO

B. Y-5=0.5(x-3)  NO

(-3,-5):  -5-5=0.5(-3-3);  -10 = -3   NO

(3,-2):  -2-5=0.5(3-3);   -7 = 0       NO

C. Y+5=0.5(x+3)   YES

(-3,-5):  -5+5=0.5(-3+3);  0 = 0    YES

(3,-2):   -2+5=0.5(3+3);  3 = 3      YES

D. Y=0.5x-3.5   YES

(-3,-5):  -5 = 0.5(-3)-3.5;  -5 = -5 YES

(3,-2):  -2 = 0.5(3)-3.5;  -2 = 1.5 - 3.5   YES

Answer:

12% of the items in the group are red and have stripes.

Step-by-step explanation:

Aassume that there is 100 items, 40 items red.

In the 40 items, 30% are striped.

40×(30/100)=12%

12% of the items in the group are red and have stripes. This is found by multiplying the proportion of red items (40%) by the proportion of these red items that also have stripes (30%).

We are given that 40% of items in a group are red. This is represented as 40/100, or 0.40. The question mentions that out of these red items, 30% also have stripes. This can be represented as 30/100, or 0.30. The question requires us to find out what percentage of the total items in the group are red and have stripes. To find this, we multiply 0.30 (the proportion of red items that are striped) by 0.40 (the proportion of items that are red).

So, 0.30 x 0.40 = 0.12 or 12%.

Therefore, 12% of the items in the group are red and have stripes.

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The amount that the salesperson will earn in commission from selling the couch is $ 27. 23.

The amount the sale of the couch by the store would get it is $ 467. 77.

The commission on the couch can be found by the formula :

= Selling price of couch x Commission to salesperson

= 495 x 5 . 5 %

= $ 27. 23

The money the store will get from the sale of the couch to Lin and her dad is:

= Selling price of couch - Commission to salesperson

= 495 - 27. 23

= $ 467 . 77

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The full question is:

Lin is shopping for a couch with her dad and heard him ask the salesperson “how much is your commission?” The salesperson says that her commission is 5 1/2% of the selling price.

A.How much commission will the salesperson earn by selling a couch for $495?

B.How much money will the store get from the sale of the couch?