Write the equation of the line in fully simplified slope-intercept form.

The expression 10ax + 14ay + 15bx + 21by has a coefficient of (2a + 3b)

as a factor.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, An expression 10ax + 14ay + 15bx + 21by.

The given expression is in 4 variables namely a, b, x and y we'll combine the x and y terms in the expression.

Now, 10ax + 15bx + 14ay + 21by.

= 5x(2a + 3b) + 7y(2a + 3b).

= (2a + 3b)(5x + 7y)

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Step-by-step explanation:

10y(3/5y) = 3×10y / 5y = 3×2 = 6

since this is not one of the answer options, you must have mistyped something.

probably the real problem is

10y((3/5)y) = 2y×3 × y = 6y²

the 3rd answer option is correct.

Answer:

19°

Step-by-step explanation:

m<A + m<B + m<C = 180°

a + 17° + 49° + 5a = 180°

6a + 66° = 180°

6a = 114°

a = 19°

Answer:

The future value of an investment is calculated by using the formula:

$FV = PV(1 + r/n)^{nt}$

where $FV$ is the future value, $PV$ is the present value (the initial investment), $r$ is the interest rate, $n$ is the number of times the interest is compounded per year, and $t$ is the number of years the investment is held.

In this case, we have $PV = 1743$, $r = 5.45% = 0.0545$, $n = 2$, and $t = 2$. Plugging these values into the formula, we get:

$FV = 1743(1 + 0.0545/2)^{2 \cdot 2} = 1743(1 + 0.0273)^{4}$

Now we can calculate the future value by raising $1 + 0.0273$ to the power of 4:

$FV = 1743(1.0273)^{4} \approx \boxed{1956}$

Note that we rounded the result to the nearest cent.

Step-by-step explanation:

Answer:

1:5

Step-by-step explanation:

The solution of the inequality will be;

⇒ x > 5

And, The solution is shown on number line.

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ - 2/5x < - 2

Now,

Solve the inequality as;

⇒ - 2/5x < - 2

⇒ - 2x < - 2 × 5

⇒ - 2x < - 10

Multiply by - 1,

⇒ 2x > 10

⇒ x > 5

Thus, The solution of the inequality = x > 5

And, The solution is shown on number line in figure.

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it would be inconsistent. Meaning it won't have a solution

The stated statement indicates that the takt time is 5.38 minutes for each section.

Takt time is calculated as the amount of manufacturing time that is available divided by the volume of orders. Takt time, for instance, is two minutes if a factory makes widgets for 480 minutes a day and clients need 240 widgets per day. Similar to this, the takt time is one week if clients desire two new goods per month.

Takt time depends on client demand and the amount of time that is available, and for many items, it is always changing as the demand from the market shifts. Takt time is unaffected by system changes, although cycle time is affected.

Available hours are 7 * 60 minutes, which is 420 minutes.

No. of parts = 78 units

Available time for work / No of parts = Takt time

               = 420/ 78

               = 5.38 minutes per part

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So our goal is to determine the mean test score, which we don't know, we know to raw scores, we know one raw score is 38 that's one standard deviation below the mean, which by definition of a Z score that Z equals negative one. one

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Answer:

Step-by-step explanation:

A vending machine

The user puts in money, punches a specific button, and a specific item drops into the output slot. (The function rule is the product price. The input is the money combined with the selected button. The output is the product, sometimes delivered along with coins in change, if the user has entered more money than required by the function rule.)

Answer: it is mean to state a real world relationship that consisted a state of a input and output

Step-by-step #hopethishelps

By using determinant, it can be calculated that-

det(C) = 8

det(D) = 9

What is a determinant?

Determinant of a square matrix is equal to the product of the elements of a square matrix and their cofactors.

Here,

det(A) = -8

The matrix C is obtained from A by swapping the second and third rows

We know if the rows and columns of a matrix are swapped then the value of the determinant of the new matrix changes in sign only

So det(C) = 8

Now,

det(A) = 9

We know that the value of determinant remain unchanged on adding any combination row or column

Matrix D is obtained from A by adding 2 times the fourth row to the first

det(D) = 9

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The required values of x and y are x = 2 and y = 11.

We have been given that parallelogram PQRS which has:

PT = ​y, TR = 5x+​1, QT = 2​y, TS = 6x+10

We know that the diagonals of a parallelogram bisect each other.

So, PT = TR and QT = TS

Substitute the values and we have a system of equations:

y = 5x + ​1    ....(i)

2y = 6x + 10 ....(ii)

Substitute the value of the equation y = 5x + ​1 in equation (ii), and solve for x

2(5x + ​1) = 6x + 10

10x + 2 = 6x + 10

10x - 6x = 10 - 2

4x = 8

x = 8/4

x = 2

Substitute the value of x = 2 in equation (i), and solve for y

y = 5(2) + ​1

y = 10 + 1

y = 11

Therefore, the required values of x and y are x = 2 and y = 11.

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The Equation of the Line in Standard form is 4x - y = 3

What is Slope of a Line?

The slope formula is used to compute the inclination or steepness of a line. The slope of the lines is calculated using the x and y coordinates of the lines. It is the ratio of the y-axis change to the x-axis change.

Solution:

Slope of the Line passing through the points (1, 1), (2, 5)

is

m = 5-1/2-1 = 4

Equation of the line = (y - y1) = m(x - x1)

y - 1 = 4(x - 1)

y - 1 = 4x - 4

4x - y = 3

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B

Step-by-step explanation:

Answer:

Slope is undefined. { Infinity }

Step-by-step explanation:

Formula we use,

→ Slope(m) = (y2 - y1)/(x2 - x1)

Now required slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (8 + 12)/(17 - 17)

→ m = 20/0

→ [ m = 0 ]

Hence, the slope is undefined.

The slope of the line passing through the points ( 17 , -12 ) and ( 17 , 8 ) is undefined

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 of line be represented as A

Now , the value of A is

Let the first point be P ( 17 , -12 )

Let the second point be Q ( 17 , 8 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 8 - ( -12 ) ) / ( 17 - 17 )

On simplifying the equation , we get

Slope m = ( 8 + 12 ) / 0

Slope m = 20 / 0

So , the slope is undefined

Hence , the slope of the line is m = undefined

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To evaluate the integral, you will need to define the limits of integration and use appropriate coordinate systems for the given area.

And the area is given as   [tex]I_{xy} =\int \limits \int \limits {(y^2 - x^2)} \,dm[/tex]

What is direct integration?

Direct integration is a method of finding the moment of inertia of a body or a region about a given axis by directly integrating the product of the mass of each infinitesimal element of the body or region and the square of its distance from the axis.

To determine the product of inertia of a given area with respect to the x and y axes, you will need to first define the area and its mass distribution. Then, you can use the following formula for the product of inertia:

[tex]I_{xy} =\int \limits \int \limits {(y^2 - x^2)} \,dm[/tex]

Where Ixy is the product of inertia, y is the distance from the y-axis, x is the distance from the x-axis, and dm is the mass of an infinitesimal element of the area.

Hence, To evaluate this integral, you will need to define the limits of integration and use appropriate coordinate systems for the given area.

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Answer:

2 and -5 (B & E)

Step-by-step explanation:

Factor the equation into

(x-2) (x+5)

Thus the zeros are 2 and -5

x=2 and x=-5 are the solutions of the quadratic equation x² + 3x-10 = 0

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The given quadratic equation is x² + 3x-10 = 0

We have to find the solutions of the quadratic equation

x² + 3x-10 = 0

Let us factorize the given equation

x² +5x-2x-10=0

x(x+5)-2(x+5)=0

(x-2)(x+5)=0

Now equate both the terms with zero to find the solutions

x=2 and x=-5

Hence, x=2 and x=-5 are the solutions of the quadratic equation x² + 3x-10 = 0

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After solving the equation, we can conclude that Callie should rent the bicycle for a maximum of 3 hours.

The equals sign is indeed a symbol used in mathematical formulas to denote the equality of two reactions.

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.

For example, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.

So, according to the given information, form the equation as follows:

12x + 10 = 45

Where x is the number of hours Callie rents the cycle.

Now, calculate for x as follows:

12x + 10 = 45

12x = 45 - 10

12x = 35

x = 35/12

x = 2.91

Rounding off: 3

Therefore, after solving the equation, we can conclude that Callie should rent the bicycle for a maximum of 3 hours.

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Complete question:

Callie is on vacation and wants to rent a bicycle to explore the town. She pays a $10 flat fee and then $12 per hour for the rental.

If Callie has $45 to spend, what is the greatest number of full hours she can rent the bicycle?

Answer: x = 52, y = 128, z = 52

Step-by-step explanation:

Answer:

(12,1)

Step-by-step explanation:

Before the transformation, Point B is at (-8,1).

When it will be reflected, it will be at (8,1)

Then, it shifts 4 points to the right, and so it will be at (12,1)

The annual percentage rate of the investment account is of:

14.1%.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

The effective annual interest rate is given as follows:

[tex]E = \left(1 + \frac{r}{n}\right)^n[/tex]

In this problem we have a semi-annual compounding, hence:

n = 2.

The effective rate was of 14.6%, hence E = 1.146, and thus the interest rate is obtained as follows:

[tex]E = \left(1 + \frac{r}{n}\right)^n[/tex]

[tex]1.146 = \left(1 + \frac{r}{2}\right)^2[/tex]

1 + 0.5r = 1.0705 (applying to square root to both sides).

0.5r = 0.0705

r = 0.0705/0.5

r = 0.141 = 14.1%.

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Mike charged for each shirt is $2.49, each pair of slacks is $5.99 and each sports coat is $7.99.

What is system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system.

Let

Price of shirts = x

Price of slacks = y

Price of sports = z

From the given information,

3x + y = $13.46         ..(1)

7x + 3y + z = $43.39         ..(2)

5x + 2z = $28.43        ..(3)

From equation (1), y = 13.46 - 3x

From equation (3),  z = (28.43 - 5x) / 2

Plug the value of x and z in equation (2)

7x + 3(13.46 - 3x) +(28.43 - 5x)/2 = 43.39

7x + 40.38 - 9x + 14.22 - 2.5x = 43.39

-4.5x +54.6 = 43.39

4.5x = 54.6 - 43.39

4.5x = 11.21

x = 2.49

Plug x = 2.49 in equation (1)

3(2.49) + y = 13.46

2.47 + y = 13.46

y = 5.99

Plug x = 2.49 in equation (3),

5(2.49) + 2z = 28.43

12.45 + 2z = 28.43

2z = 15.98

z = 7.99

Hence, Mike charged for each shirt is $2.49, each pair of slacks is $5.99 and each sports coat is $7.99.

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The graph represents the situation Allison purchases lemons for $0.75 each.

The ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane is known as slope of line.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

From the given graph, we can take two points (4, 3) and (8, 6) to find the slope.

Let us plug in the values in formula of slope.

m=6-3/8-4

m=3/4

m=0.75

Hence, Allison purchases lemons for $0.75 each is represented by the given graph.

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The best interpretation of the slope of the linear regression equation is given as follows:

For each increase of one degree of latitude, the average low temperature decreases by 0.70 degrees Fahrenheit.

The slope represents the rate of change of the output variable relative to the input variable of a linear relation.

Hence, it can be said that the slope states by how much the output variable y changes when the input variable x is increased by 1.

The variables in this problem are given as follows:

The negative slope of -0.7 means that for each increase of one degree of latitude, the average low temperature decreases by 0.70 degrees Fahrenheit.

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Answer:

B

Step-by-step explanation:

Answer: e

Step-by-step explanation:

4+6= 10 and then divide by 50 and add 25 so 0.2+25+25.02 so then subtract 4 so about 21 or 21.02

It'll take you 3 hours to reach your destination.

The population of the city after eight years is 35,125,731,743

Population growth is the increase in the number of people in a population or dispersed group. The expression P(t) = P(o)(1+r)^t can be used to determine the growth rate of a population.

Where P(t) is the population at a particular time

P(o) is the initial population , t is the time and r is the growth rate.

Here the growth rate has been given, but we are to find p(t).

P(t) = 330,000(1+3.25)⁸

P(t) = 330,000(4.25)⁸

P(t) = 330,000× 106441.61

P(t) = 35,125,731,743( nearest billion)

Therefore the population of the city after 8years is 35,125,731,743

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The value of x is 9.

The value of y is 5.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Two triangles in a composite triangle.

We see that,

m∠UST = m∠STR

This means,

x + 4 = 13

x = 13 - 4

x = 9

The sum of the angles in a triangle is 180 degrees.

One triangle is an equilateral triangle.

All three angles are equal.

This means,

The angle has to be 60°.

m∠UTR + m∠URT + m∠TUR = 180

3m = 180

m = 60

Now,

m∠URS = 180

m∠URT + m∠SRT = 180

60 + m∠SRT = 180

m∠SRT = 120

The isosceles triangle has two equal angles.

m∠RTS = m∠RST

m∠SRT + m∠RTS + m∠RST = 180

120 + 6y + 6y = 180

12y = 180 - 120

12y = 60

y = 5

Thus,

The value of x and y are 9 and 5.

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Answer:

Hope the picture will help you

Answer:

Step-by-step explanation:

(0,-9)