A srtaight line l has the equation of 2y-6x=-8 what is the gradient of l

Answer:

Cost of each Computer is $225 and Cost of each Printer is $150.

Step-by-step explanation:

Let the cost of the Computers be 'x'.

Let the cost of Printer be 'y'.

Given:

If he buys three computers and one printer, the cost is $825.

framing in equation form we get;

[tex]3x+y =825 \ \ \ \ \ equation\ 1[/tex]

Also Given:

if he buys 4 computers and 2 printers, the cost is $1200.

framing in equation form we get;

[tex]4x+2y =1200 \ \ \ \ \ equation\ 2[/tex]

Now Multiplying equation 1 by 2 we get;

[tex]2(3x+y)=825\times 2\\\\6x+2y=1650 \ \ \ \ \ equation\ 3[/tex]

Now Subtracting equation 2 from equation 3 we get;

[tex](6x+2y)- (4x+2y) = 1650-1200\\\\6x+2y-4x-2y = 450\\\\2x=450\\\\x=\frac{450}{2} =\$225[/tex]

Now Substituting the value of x in equation 1 we get;

[tex]3x+y=825\\\\3\times 225+y=825\\\\675+y =825\\\\y = 825 -675\\\\y = \$150[/tex]

Hence Cost of each Computer is $225 and Cost of each Printer is $150.

Answer:

Cost of each Computer is $225 and Cost of each Printer is $150.

Answer:

(3,-8)

(2,-10)

Step-by-step explanation:

we have

[tex]10x + 4y < 12[/tex] ----> inequality A

[tex]8x- 3y > 20[/tex] ----> inequality B

we know that

If a point is a solution of the system of inequalities, then the point must satisfy both inequalities (makes true both inequalities)

Verify  all the points

Substitute the value of x and the value of y of each point in both inequalities  

Case 1) point (3,-8)    

For x=3, y=-8

inequality A

[tex]10(3) + 4(-8) < 12[/tex]

[tex]-2 < 12[/tex] ----> is true

inequality B

[tex]8(3)- 3(-8) > 20[/tex]

[tex]48 > 20[/tex] ---> is true

therefore

The point is a solution of the system of linear inequalities

Case 2) point (2,5)    

For x=2, y=5

inequality A

[tex]10(2) + 4(5) < 12[/tex]

[tex]40 < 12[/tex] ----> is not true

therefore

The point is not a solution of the system of linear inequalities

Case 3) point (-5,1)    

For x=-5, y=1

inequality A

[tex]10(-5) + 4(1) < 12[/tex]

[tex]-46 < 12[/tex] ----> is true

inequality B

[tex]8(-5)- 3(1) > 20[/tex]

[tex]-43 > 20[/tex] ---> is not true

therefore

The point is not a solution of the system of linear inequalities

Case 4) point (10,3)    

For x=10, y=3

inequality A

[tex]10(10) + 4(3) < 12[/tex]

[tex]112 < 12[/tex] ----> is not true

therefore

The point is not a solution of the system of linear inequalities

Case 5) point (2,-10)    

For x=2, y=-10

inequality A

[tex]10(2) + 4(-10) < 12[/tex]

[tex]-20 < 12[/tex] ----> is true

inequality B

[tex]8(2)- 3(-10) > 20[/tex]

[tex]46 > 20[/tex] ---> is true

therefore

The point is a solution of the system of linear inequalities

see the attached figure to better understand the problem

If a ordered pair is a solution of the system , then the ordered pair must lie in the shaded area of the solution set

Answer:

(3,-8)(2,-10)

Step-by-step explanation:

Answer:

Only option D is correct as a dilation by a scale factor of 1/2 with the origin as the center of dilation would transform the object which would still be similar to the original figure, but it would no longer be congruent to the original figure due to reduction in size due to a dilation by a scale factor of 1/2.

Step-by-step explanation:

When we transform a certain shape, we normally associate the original shape as 'object', while the transformed shape is associated as "image',

If any shape like triangle, parallelogram or any other certain quadrilateral is rotated, reflected or translated, it wold preserve the same size. Hence, the resulting transformed image would be similar and also called 'congruent' to the original object.

But, if any shape like triangle, parallelogram or any other certain quadrilateral is enlarged or resized, it would certainly change in size. Therefore, the resulting transformed image would still be considered as similar, but it would no longer congruent to the original object.

Hence, when two transformation are performed on a figure in the coordinates plane. The first transformation is a translation 8 units to the left. A dilation by a scale factor of 1/2 with the origin as the center of dilation would transform the object which would still be similar to the original figure, but it would no longer be congruent to the original figure due to reduction in size due to a dilation by a scale factor of 1/2.

In all other cases, like a clockwise rotation of 90 degrees about the center, A clockwise rotation of 180 degrees about the center and a dilation by a scale factor of 1 with the origin as the center of a dilation would not not alter the size of the shape, and the resulting transformed image would be similar as well as called 'congruent' to the original object.

Hence, only option D is correct as a dilation by a scale factor of 1/2 with the origin as the center of dilation would transform the object which would still be similar to the original figure, but it would no longer be congruent to the original figure due to reduction in size due to a dilation by a scale factor of 1/2.

Therefore, only option D is correct.

Keywords: dilation, transformation

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The Sedona transformation that will result in an image that is similar to, but not congruent to the original figure is D. A dilation by a scale factor of 1/2 with the origin as the center of dilation.

To get an image that is similar but not congruent to the original figure, we shall perform a transformation that changes the size of the figure while keeping the same shape.

This is because when a figure is translated 8 units to the left, its position changes, but its size and shape remain the same.

A dilation by a scale factor of 1/2 with the origin as the center of dilation means the image would be reduced to half of its original size while maintaining the same shape.

This transformation results in a figure that is similar but not congruent to the original figure, as it has the same shape but a different size.

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Answer:D

Step-by-step explanation:

Hey there!

First, set up an exponential equation that represents the rate at which your original amount, 1000, gains interest:

y = 1000(1.24)^x

Y represents the value after X years. 1.24 represents the rate at which the money gains interest, 1 + 0.24 (your 24% interest rate in decimal form). 1000 is your original amount.

Now, set this equation equal to 64000, graph y = 64000 and y = 1000(1.24)^x on a graphing calculator, and see where the two equations intersect in order to solve for x.

They intersect when x is about 19.334, as seen in the graph below (it is very zoomed in so that you can see where the two functions intersect). Therefore, it will be about 19 years after the year in which you deposited the 1000 dollars before the money is worth 64000 dollars.

Answer:

(5,1)

Step-by-step explanation:

A vertex is where two or more curves, lines, or edges meet

The function p(x) is obtained by subtracting g(x) from f(x)

The rule of p(x) is p(x) = 5.5 x - 50

Step-by-step explanation:

A drill team is raising money by holding a car wash

We need to describe how can you use f(x) and g(x) to obtain a function p(x) that gives the team's profit for washing x cars, and then write a rule for p(x)

∵ The team earns $6.00 for each car washed

∵ f(x) represent the team's total earning for washing x cars

- Equate f(x) by the product of x and 6

∴ f(x) = 6 x

∵ The team's expenses include $50.00 for advertising plus $0.50

    in materials for each car washed

∵ g(x) represent the team's total expenses for washing x cars

- Equate g(x) by the sum of 50 and the product of 0.5 and x

∴ g(x) = 50 + 0.5 x

The profit = total earning - total expenses

∵ f(x) is the total earning for washing x cars

∵ g(x) is the total expenses for washing x cars

∵ p(x) represents the team's profit for washing x cars

- Subtract g(x) from f(x) and equate the difference by p(x)

∴ p(x) = f(x) - g(x)

The function p(x) is obtained by subtracting g(x) from f(x)

∵ f(x) = 6 x

∵ g(x) = 50 + 0.5 x

∴ p(x) = 6 x - (50 + 0.5 x)

- Simplify the right hand side

∴ p(x) = 6 x - 50 - 0.5 x

- Add the like term

∴ p(x) = 5.5 x - 50

The rule of p(x) is p(x) = 5.5 x - 50

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Answer:

0.800 is the answer. If you want an explanation let me know.

Step-by-step explanation:

Answer:

Therefore the value of [tex]x=31\°[/tex]

Step-by-step explanation:

Given:

m∠ A = 56°

m∠ B = 75°

m∠ ACD = x°

To Find:

x = ?

Solution:

In Δ ABC

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

Here,

The opposite interior angles are angle A and angle B.

An exterior angle of a triangle is angle ACD which is x°

∴ [tex]m\angle A +m\angle B=m\angle ACD\\[/tex]...Exterior angle property of Δ

Substituting the values we get

[tex]56+75=x\\\\\therefore x=131\°[/tex]

Therefore the value of [tex]x=31\°[/tex]

Answer:

Total bikes and cars are 260

Step-by-step explanation:

Cars: [tex]n_{cars}185[/tex]

Bikes: [tex]n_{bikes}=n_{cars}-113=72[/tex]

Total: [tex]n_{total}=n_{bikes}+n_{cars}=257[/tex]

Rounding to the nearest ten: 260

Answer:

  B, C

Step-by-step explanation:

The solution space is the area to the right of the X where the lines cross. Only points B and C are in that space. Point E is on the line, but the line is not included in the solution space.

_____

The lines are drawn as though the inequality were an equation. The solution space is above the first line (which has negative slope) because y > ... indicates the solution is values of y above (>) the line.

The solution space is below the second line, which has positive slope, because y < ... indicates the solution is values of y below (<) the line.

Answer:

225.5

Step-by-step explanation:

220 + (2.5% × 220) =

220 + 2.5% × 220 =

(1 + 2.5%) × 220 =

(100% + 2.5%) × 220 =

102.5% × 220 =

102.5 ÷ 100 × 220 =

102.5 × 220 ÷ 100 =

22,550 ÷ 100 =

225.5

Answer:

225.5

Step-by-step explanation:

So, you would start by doing

220 times 2.5% that would equal 5.5

Then you would add

220 + 5.5 = 225.5

Therefore your answer will be 225.5

Answer:

The domain is the interval [5,∞)

Step-by-step explanation:

we have

[tex]y = \sqrt{x-5}-1[/tex]

we know that

The radicand (number under a radical) must be greater than or equal to zero

so

[tex]x-5\geq 0[/tex]

solve for x

Adds 5 both sides

[tex]x-5+5\geq 0+5[/tex]

[tex]x\geq 5[/tex]

therefore

The domain is the interval [5,∞)

All real numbers greater than or equal to 5

Answer:

x >= 5

Step-by-step explanation:

Edge 2021

Answer:

Step-by-step explanation:

Given that the percentage of physicians who are women is 27.9%. In a survey of physicians employed by a large  university health system,

45 of 120 randomly selected physicians were women.

Sample size n = 120

Sample proportion p = [tex]\frac{45}{120} \\=0.375[/tex]

H0: p = 0.279

Ha: p >0.279

(Two tailed test at 5% significance level)

p difference = 0.096

STd error of p assuming H0 true

= [tex]\sqrt{\frac{pq}{n} } \\=\sqrt{\frac{0.279(0.721}{120} } \\=0.041[/tex]

Test statistic Z = [tex]\frac{0.096}{0.041} \\=2.345[/tex]

Z critical value one tailed is 1.645

Since Z statistic > 1.645 we reject H0

There is evidence to conclude that the proportion of women physicians at the university health system exceeds

27.9%

Answer: [tex]4\ feet[/tex]

Step-by-step explanation:

The exercise provides you the following Quadratic function:

[tex]h(t)=4+60t-16t^2[/tex]

Then, based on the information given in the exercise, you can conclude that, when the ball strikes the bat, the time in seconds is the following:

[tex]t=0[/tex]

Therefore, in order to calculate the height in feet of the ball when it strikes the bat, you need to subsititute [tex]t=0[/tex] into the function and    then evaluate.

Then, you get this result:

 [tex]h(0)=4+60(0)-16(0)^2\\\\h(0)=4+0-0\\\\h(0)=4[/tex]

Answer:

P'(7, - 8 )

Step-by-step explanation:

Given the translation rule

(x, y ) → (x + 4, y - 3 )

This means add 4 to the original x- coordinate and subtract 3 from the original y- coordinate, thus

P(3, - 5 ) → P'(3 + 4, - 5 - 3 ) → P'(7, - 8 )

Let...

1st number=x

2nd number=x+2

3rd number=x+4

4th number=x+6

x+x+2+x+4+x+6=200

4x=188

x=47

x+6=53

answer: 53

Answer: about 1

Step-by-step explanation:

Bc 1 mil minutes are 1.902 of a year

Answer:

d) $498.75

Step-by-step explanation:

Given:

Fixed expenses = $475

Expense raised by = 5%

We need to find updated Total Fixed Expenses.

Amount of expense raised is equal to Percentile expense raised multiply by Fixed expenses and then Divided by 100.

framing in equation form we get;

Amount of expense = [tex]\frac{5}{100}\times 475 = \$23.75[/tex]

Now Updated Total Fixed expense will be equal to sum of Fixed expenses and Amount of expense raised.

framing in equation form we get;

Updated Total Fixed expense = $475 + $23.75 = $498.75

Hence The updated Total fixed expenses will be $498.75.

Answer:498.75

Step-by-step explanation:

Hope it helped

Answer:

Step-by-step explanation:

Dilation can be compared with zooming some image according to the given scale.

The vertices of VWXY is given by (-1, -1), (-1, 2), (2, -1), (2, 2) respectively.

Since the given scale is 4, to get the vertices of V'W'X'Y' we need to multiply the co-ordinates by 4.

The desired co-ordinates will be (-4, -4), (-4, 8), (8, -4), (8, 8) respectively.

Answer:

The salesperson will earn total commission of $ 445 .

Step-by-step explanation:

The salesperson gets 5% commission for first $2500, and 8% for above that.

So, for sale of $ 6500, the salesperson will earn commission,

$ [tex](2500 \times \frac {5}{100} + (6500 - 2500) \times \frac {8}{100})[/tex]

= $ [tex](125 + (4000) \times \frac {8}{100})[/tex]

= $ (125 + 320)

= $ 445

Answer:

Step-by-step explanation:

21% more then 5/11...

5/11 + 21% of 5/11 = 5/11 + 0.21(5/11) = 5/11 + (21/100 * 5/11) =

5/11 + 21/220 = 11/20 <===

Firstly, we converted the fraction 5/11 to its decimal equivalent, which is approximately 0.4545. Then, we calculated a number that is 121% of 0.4545 (because 21% more than the original number means we have to count the original number plus the additional 21%). The calculation gave us approximately 0.5499.

To answer this question, we can firstly calculate the equivalent decimal of 5/11. This can be done either by manual calculation or using a calculator. Dividing 5 by 11, we get approximately 0.4545.

Next, it's important to understand what the question is asking. When it asks what number is 21% more than a given number, it's essentially asking you to calculate a number that is 121% of the given number. Why? Because the original number (100%) plus the additional 21% gives you a total of 121%.

Once you know this, you simply multiply the given number (0.4545) by 1.21 (the decimal equivalent of 121%). And finally, multiplying 0.4545 by 1.21, we get approximately 0.5499. That is your final answer: The number that is 21% more than 5/11 is approximately 0.5499.

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Answer:

xy = 1

Step-by-step explanation:

Given

[tex]x+y=\dfrac{1}{x}+\dfrac{1}{y}\\ \\x+y\neq 0[/tex]

Simplify the first expression:

[tex]x+y=\dfrac{1}{x}+\dfrac{1}{y}\\ \\x+y=\dfrac{y+x}{xy}\ [\text{Add fractions in the left side}]\\ \\1=\dfrac{1}{xy}\ [\text{Divide by }x+y \ (\text{it can be done since})\ x+y\neq 0]\\ \\xy=1\ [\text{Cross multiply}][/tex]

Answer:

(0,0)

Step-by-step explanation:

(0, 3) + 4 = (0,7)

(0, 7) - 7 = (0,0)

Answer:

x = -2

y = 3

Step-by-step explanation:

Write the system the following way:

4x + 5y = 7

-3x +y  = 9

we need to eliminate one unknown by multiplying one equation for a suitable number in such a way that when we add the equations one unknown is eliminated.

If we multiply the second eq. by -5 the y is eliminated

4x + 5y = 7

15x -5y = -45

add the equations

19x = -38 ===> x = -38/19 ===> x = -2

Now replace this value in any equation to get y. For example, in 1st one.

4(-2) + 5y = 7 ===> -8 +5y = 7 ===> 5y = 7+8 ===> 5y = 15 ===> y = 15/5 ===>

y=3

The value of f(5) is 49.1

Step-by-step explanation:

To find f(x) from f'(x) use the integration

f(x) = ∫ f'(x)

1. Find The integration of f'(x) with the constant term

2. Substitute x by 1 and f(x) by π to find the constant term

3. Write the differential function f(x) and substitute x by 5 to find f(5)

∵ f'(x) =  + 6

- Change the root to fraction power

∵  =

∴ f'(x) =  + 6

∴ f(x) = ∫  + 6

- In integration add the power by 1 and divide the coefficient by the

 new power and insert x with the constant term

∴ f(x) =  + 6x + c

- c is the constant of integration

∵

∴ f(x) =   + 6x + c

- To find c substitute x by 1 and f(x) by π

∴ π =   + 6(1) + c

∴ π =  + 6 + c

∴ π = 6.4 + c

- Subtract 6.4 from both sides

∴ c = - 3.2584

∴ f(x) =   + 6x - 3.2584

To find f(5) Substitute x by 5

∵ x = 5

∴ f(5) =   + 6(5) - 3.2584

∴ f(5) = 49.1

Answer:

AB = 5 units

Step-by-step explanation:

Given that:

So the the length in units of the line segment that connects vertex A and vertex B is the length of line AB. So we have the following formula:

AB = [tex]\sqrt{(x2-x1)^{2} + (y2-y1)^{2} }[/tex]

<=> AB = [tex]\sqrt{(1-1)^{2} +(4-(-1))^{2} }[/tex]

<=> AB = 5 units

Hope it will find you well.

The question relates to finding the distance between two points in a coordinate system. The length of the line segment connecting vertex A (1,-1) and vertex B (1,4) of the triangle ABC can be calculated using the distance formula, which yields a result of 5 units.

The subject of your question is geometry, specifically the concept of distance between two points in a coordinate system. In finding the length of the line segment that connects vertex A (1,-1) and vertex B (1,4), you can use the distance formula based on Pythagorean theorem.

The distance formula is d = sqrt [(x2 - x1)² + (y2 - y1)²]. In this case, x1 = 1, x2 = 1, y1 = -1 and y2 = 4.

Substituting these values, we have d = sqrt [(1 - 1)² + (4 - (-1))²] = sqrt [0 + 25], hence d = sqrt [25] = 5 units.

Therefore, the length of the line segment connecting vertex A (1, -1) and vertex B (1, 4) is 5 units.

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Final answer:

The midpoint of the line segment with endpoints C(6,-8) and D(-4,10) is calculated to be at (1, 1) by averaging the x and y coordinates of the endpoints.

Explanation:

The midpoint of a line segment with endpoints C(6,-8) and D(-4,10) can be found by averaging the x-coordinates and the y-coordinates of the two endpoints. To do this, add together the x-coordinates, 6 and -4, and divide by 2 to find the x-coordinate of the midpoint. Add together the y-coordinates, -8 and 10, and divide by 2 to find the y-coordinate of the midpoint.

The calculations are as follows:
x-coordinate: (6 + (-4)) / 2 = 1
y-coordinate: (-8 + 10) / 2 = 1

Therefore, the midpoint of CD is (1, 1).

Answer:

12

Step-by-step explanation:

simplify: 15 + -3

combine: 15 + -3 = 12

The numerical expression 15-3 is equal to 12.

A numerical expression is a mathematical phrase containing only numbers and operational symbols (such as +, -, *, /) without any variables. It represents a specific value when the numbers are replaced with actual values. For example, "3 + 5 * 2" is a numerical expression that evaluates to 13.

The numerical expression 15-3 can be solved by subtracting 3 from 15. You can start with the number 15 and subtract 3 to get the result.

15 - 3 = 12

So, the numerical expression 15-3 is equal to 12.

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There are 168 sweets altogether

Richard, Henry and Gavin share some sweets in the ratio 5 : 4 : 3

Let "5a" be the share of Richard

Let "4a" be the share of Henry

Let "3a" be the share of Gavin

Richard gets 70 sweets

share of Richard = 70

5a = 70

To find: number of sweets altogether

number of sweets altogether = share of richard + share of henry + share of gavin

number of sweets altogether = 5a + 4a + 3a

number of sweets altogether = 12a = 12(14) = 168

Thus there are 168 sweets altogether