Finding Coordinates of a Translation
Triangle XYZ has coordinates X(2, 4), Y(-3, 4), and Z(-3,1). If the triangle is translated using the rule
(x, y) → (x - 2, y + 1), what are the coordinates of Y'?
Y'(-5,5)
OY'(0,5)
Y'(-5,2)
Y'(-1,3)

Answer:

The diffrence written in simple expression form is 40/63

Step-by-step explanation:

To solve for the difference normally you have to subtract your own subscription from that of your friends,

Let's perform this operation step wise

Now your subscription is

(7w = 6)

w=6/7

Your friends own is

( 9w = 2)

w=2/9

So the difference in simple form is

6/7-2/9

The LCM is 63 I.E 9*7=63

=54-14/63

=40/63

Answer: 13.7

Step-by-step explanation:

The total distance Carlo travelled form his house to Kelvin's house to the game store and back to his house is 13.7 km.

Using the distance formula, we can caulate the distance he rode from his house to Kelvin's house and then to the video game store.

Therefore,

d = √(y₂ - y₁)²+(x₂- x₁)²

Hence,

(0, 0)(2.5, 6)

Distance from his house to Kelvin's house = √(6- 0)²+(2.5 - 0)²

Distance from his house to Kelvin's house = √36 + 6.25 = 6.5 km

Therefore,

(2.5, 6)(2.5, 2)

Distance from Kelvin's house to game store =  √(2- 6)²+(2-5 - 2.5)²

Distance from Kelvin's house to game store = √16  = 4 km

Hence,

Total distance travelled = 6.5 + 4 + 3.2 = 13.7 km

learn more distance here: https://brainly.com/question/14656247

Answer:

20 checks

Step-by-step explanation:

Answer:

2 pounds of turkey?

Step-by-step explanation:

Margot will therefore need 3 pounds of turkey to make 4 liters of her turkey chili.

To find out how many pounds of turkey Margot will need to make 4 times her turkey chili recipe for 1 liter, we first identify the amount needed for 1 liter based on the given ratio, and then multiply that amount by 4.

Margot uses 1/2 pounds of turkey for 2/3 liters of turkey chili. If we need to find out the amount for 1 liter, we can set up a proportion:

1/2 pounds turkey / (2/3 liters) = x pounds turkey / 1 liter

We cross multiply to solve for x:

(1/2) * 1 = x * (2/3)

Now we solve for x:

x = (1/2) * (3/2)

x = 3/4 pounds of turkey for 1 liter of chili

For 4 liters of chili (4 times the recipe), we would multiply:

4 * (3/4 pounds) = 3 pounds of turkey

Answer:

y = -1/3x -3

Step-by-step explanation:

-2x - 6y = 18

We want to solve for y since the slope intercept form is y =mx+b where m is the slope and b is the y intercept

Add 2x to each side

-2x-6y +2x = 2x+18

-6y = 2x+18

Divide each side by -6

-6y/-6 = 2x/-6 + 18/-6

y = -1/3x -3

This is in slope intercept form with the slope -1/3 and the y intercept -3

Answer:

[tex]y = - \frac{x }{ 3} - 3[/tex]

Step-by-step explanation:

-2x - y = 18

Add 2x to both sides.

-6y = 2x + 18

divide both sides by -6.

[tex]y = \frac{2x + 18}{ - 6} [/tex]

divide 2x + 18 by 6

[tex]y = - \frac{x }{ 3} - 3[/tex]

Answer:

3 1/5 ft

Step-by-step explanation:

We can set up a proportion:

[tex]\frac{1}{2\frac{2}{7} } =\frac{1\frac{2}{5} }{x}[/tex] , where x is how long the pants are in real life

Cross multiply:

x = (2 2/7) * (1 2/5)

It's easier if we have improper fractions, so convert the mixed numbers into improper fractions:

2 2/7 = 16/7

1 2/5 = 7/5

Now, put these back in:

x = (16/7) * (7/5) = 16/5 = 3 1/5

Thus, in real life, the pants would be 3 1/5 ft long.

Hope this helps!

Answer:

3⅕ ft

Step-by-step explanation:

1 in --> 2 2/7 ft

2 2/7 = 16/7

1 2/5 in = 7/5 in

7/5 × 16/7 = 16/5 ft

3 1/5 ft

Answer:

The Length , width and height of solid are 4 feet , 3 feet and 7 feet respectively.

Step-by-step explanation:

Let the width of rectangular solid be x

We are given that the length of the container must be one meter longer than the width

So, Length of solid = x+1

We are also given that height must be one meter greater than twice the width

So, Height of solid = 2x+1

So, Volume of solid = [tex]Length \times Width \times height[/tex]

Volume of solid = [tex](x+1) \times x \times (2x+1)[/tex]

Volume of solid =[tex](x^2+x)(2x+1)[/tex]

Volume of solid =[tex]2x^3+x^2+2x^2+x=2x^3+3x^2+x[/tex]

We are given that  a rectangular solid must have a volume of 84 cubic meters

So, [tex]2x^3+3x^2+x=84\\2x^3+3x^2+x-84=0\\(x-3)(2x^2+9x-28)=0\\[/tex]

On equating

x-3=0

x=3

So, Length of solid = x+1=3+1 = 4 feet

Height of solid = 2x+1 =2(3)+1=7 feet

Width of solid = 3 feet

Hence The Length , width and height of solid are 4 feet , 3 feet and 7 feet respectively.

The volume of a rectangular solid shipping container = 84 cubic meters

The width of the container = 3m

The length of the container = (x + 1) = (3+1) = 4m

The height of the container = (2x + 1) = (2 x 3 + 1) = 7m

Given:

The volume of a rectangular solid shipping container = 84 cubic meters

Let: The width of the container be x

The length of the container must be one meter longer than the width.

So, The length of the container be (x + 1)

The height must be one meter greater than twice the width.

So, The height of the container be (2x + 1)

To find the dimensions of the container

The Volume of the container = Length x Width x Height

[tex]84=x(x+1)(2x+1)[/tex]

[tex]84=(x^{2} +x)(2x+1)[/tex]

[tex]84=2x^{3} +3x^{2} +x[/tex]

[tex]2x^{3} +3x^{2} +x-84=0\\(x-3)(2x^{2} +9x+28)=0\\x-3=0\\x=3[/tex]

So, The width of the container = 3m

The length of the container = (x + 1) = (3+1) = 4m

The height of the container = (2x + 1) = (2 x 3 + 1) = 7m

For more information:

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Step-by-step explanation:

[tex]1+1=2 \\

2+2=4 \\

57-2+5=60 \\

7000+3+67+90=7160[/tex]

Answer:

7160

Step-by-step explanation:

1+1=2

2+2=4

5x7-2+5=5x7+3

7000+3+67+90+7160

Answer:

39.6x +26.4

Step-by-step explanation:

The area of a rectangle is given by

A = l*w

A = 13.2 * (3x+2)

Distribute

    39.6x +26.4

Answer: A

Step-by-step explanation:

Answer:

a = -1  b = -9   c = -20

x1 = [--9 +- (sq root -9^2 - 4 * -1 * -20)] / 2 * -1

x1 = 9 +sq root (81 - 80) / -2

x1 = [9 + 1 ] / -2

x1 = -5

x2 = 9 -sq root (81 - 80) / -2

x2 = 8 / -2

x2 = -4

Step-by-step explanation:

Answer:

54 = median

48 = 1st quartile

69 = 3rd quartile

21 = interquartile

Hope this helped!!  :)

Answer:

54 = median

48 = 1st quartile

69 = 3rd quartile

Step-by-step explanation:

Answer: The value of k = 0.9031

Step-by-step explanation: The equation for calculating the number of hits has been given as y = 4060ekt, where y is the number of hits and t is the number of months the website has been operating.

The values for y and t has been determined already as given, (y = 11000 and t = 3) therefore we can substitute for the known values in order to calculate the value of the unknown, k.

y = 4060kt

11000 = 4060 x 3k

11000/(4060 x 3) = k

11000/12180 = k

0.9031198 = k

Rounded to four decimal places,

k = 0.9031

Answer: (x+3)2 + (y+5)2 =36

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

Step-by-step explanation:

For right triangles, we can use the Pythagorean theorem. This means that a2+b2 = c2. In this problem, a and b are the given side lengths of the triangle. This means that a=b=13. To solve this problem, we plug in 13 to the equation above and solve for c.  

132 + 132 = c2

169+169 = c2

338 = c2

square root(338) = c

c = 18.38

Answer:18.38

Step-by-step

13^2 +13^2=338

square root 338

=18.38

Answer:

[tex]V(x) = 4x^3 - 54x^2 + 180x[/tex]  

Step-by-step explanation:

We are given the following in the question:

A rectangular piece of cardboard of side 15 inches by 12 inches is cut in such that a square is cut from each corner.

Let x be the side of this square cut. When it was folded to make the box.

The height of box =

[tex]x\text{ inches}[/tex]

The length becomes

[tex](15-2x)\text{ inches}[/tex]

The width becomes

[tex](12-2x)\text{ inches}[/tex]

Volume of box =

[tex]V =l\times w\times h[/tex]

Putting values, we get

[tex]V(x) = (15-2x)(12-2x)x\\V(x) = (180-30x-24x+4x^2)(x)\\V(x) = (4x^2 - 54x + 180)(x)\\V(x) = 4x^3 - 54x^2 + 180x[/tex]

is the required polynomial for volume of box formed.

Answer: Y-intercept: When the car doesn’t move...

Relative max or min: The most efficient...

Increasing or decreasing interval: As the car accelerates...

Step-by-step explanation:

The parameters are matched and shown below..

The [y] - intercept of a graph is the point where the graph cuts the [y] axis.

We have a curve that models the fuel efficiency of a certain car as a function of the car's speed.

The [y] - intercept of the graph would be at y = 0. This point represents the situation when the car does not have any fuel to move.

The increasing or decreasing value represents as car accelerates towards 55 Km/hr, it gets more efficient.

The relative maximum value represents that the most efficient the car can get is 20 Km/litre.

Therefore, the parameters are matched and shown above.

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Answer:

$45 more

(but honestly I think I would spend longer mowing their lawns to try and make some more profit)

Step-by-step explanation:

Mr. Smith requires 4 1/2 hours.

Mrs Jones requires 7 1/2 hours.

7 - 4 = 3

3 * 15 = $45

To find the difference in charges between Mrs. Jones and Mr. Smith for mowing lawns, calculate the total amount charged by Ryan for each lawn and subtract the amount charged for Mr. Smith from the amount charged for Mrs. Jones. The difference in charges is $22.50.

The question asks how much more Ryan would charge Mrs. Jones than Mr. Smith for mowing lawns.

To find the answer, we need to calculate the total amount charged by Ryan for each lawn and then subtract the amount charged for Mr. Smith from the amount charged for Mrs. Jones.

For Mr. Smith's lawn, the given information is that it takes 2 hours to mow. So, the total amount charged would be y = 15 * 2 = $30.

For Mrs. Jones' lawn, it takes 3.5 hours to mow. So, the total amount charged would be -

y = 15 * 3.5 = $52.50.

To find the difference in charges between Mrs. Jones and Mr. Smith, we subtract $30 from $52.50.

The difference is $22.50.

Answer:

(x,y)=(2,-3)

Step-by-step explanation:

6x+2y=6

7x+3y=5

Multiply both sides by 3

18x+6y=18

7x+3y=5

Multiply both sides by -2

18x+6y=18

-14x-6y=-10

Eliminate one variable by adding the equations

4x=8

x=2

Substitute the value of x to get y

6(2)+2y=6

y=-3

x=2

y=-3

The solution to the system of equations 6x+2y=6 and 7x+3y=5 is x = 2 and y = -3.

The solution to the system of equations 6x+2y=6 and 7x+3y=5 involves finding the values of x and y that satisfy both equations simultaneously.

First, let's multiply:

3(6x + 2y) = 3(6)
=> 18x + 6y = 18

2(7x + 3y) = 2(5)
=> 14x + 6y = 10

Next, we subtract the second equation from the first:

18x + 6y - (14x + 6y) = 18 - 10

4x = 8

x = 2

Now that we have the value of x, we can substitute it back into either of the original equations to find the value of y. For instance, substituting x into the first original equation:

6(2) + 2y = 6

12 + 2y = 6

2y = 6 - 12

2y = -6

y = -3

The solution to the system of equations is x = 2 and y = -3.

Answer:

[tex]log(10a)[/tex]

Step-by-step explanation:

[tex]log(a\sqrt{44})+log(a \sqrt275)-log(11a)[/tex]

We can simplify this using these log laws:

[tex]log(a)+log(b)=log(ab)\\log(a)-log(b)=log(\frac{a}{b})[/tex]

[tex]log(\frac{a^2\sqrt{44} \sqrt{275}}{11a})[/tex]

We also have laws to simplify square roots

[tex]\sqrt{a}*\sqrt{b} = \sqrt{ab}[/tex]

So this becomes

[tex]log(\frac{a^2\sqrt{12100}}{11a})[/tex]

[tex]\sqrt{12100} = 110[/tex]

so this becomes

[tex]log(\frac{110a^2}{11a})=log(10a)[/tex]

Step-by-step explanation:

A (the first one)

.............

The upside down U means intersection, which would be the area the two circles overlap.

X’ and y’ would be opposite, so the area not in x or y.

The area would be outside the circles

The answer would be picture b

Answer:

Step-by-step explanation:

you would find the slope by doing the change in y over the change in x. in your case, the change in y is 11 and the change in x is -11.

Answer:

Slope formula is y2-y1 over x2-x1

Once you find the slope you are going to need to put it into point slope form which is y-y1=m(x-x1)

Step-by-step explanation:

9-(-2) divided by -3-8 is 11 over -11 which your slope is -1 m=-1

Then you use the point slope formula

y-(-2)=-1(x-8)

Then solve algebraically

Y+2=-1x+8

-2. -2

Y=-1x+6 , that is in slope-intercept form your m which is your slope is -1 and your b which is your y intercept is 6

So basically your answer is slope(m) which is -1.. hope this helps!!

Answer:

0.0545454545455

Step-by-step explanation:

Answer:

3/9 or 33.33%

Step-by-step explanation:

there are 9 total cans and 3 pink cans. So, that'd be 3/9 or 33.33%

hope this helps!

Answer:

1/3

Step-by-step explanation:

Start with y: [tex]y[/tex]

Subtract 4: [tex]y-4[/tex]

Multiply by 9: [tex]9(y-4)=9y-36[/tex]

Answer:

[tex]9(y - 4) \\ = 9y - 36[/tex]

Step-by-step explanation:

[tex]start \: \: \: \: \: \: \: \: \: \: = y \\ subtract \: = y - 4 \\ times \: \: 9 \: \: \: = 9(y - 4) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 9y - 36[/tex]

Answer:

6.5 units

Step-by-step explanation:

In circle with center O, AB is diameter.

[tex] \therefore m\angle ACB = 90°\\[/tex]

(Angle inscribed in a semicircle)

[tex] \therefore \: in\: \triangle ABC, \:AB \: is\: hypotenuse \\[/tex]

By Pythagorean theorem:

[tex]AB = \sqrt{ {12}^{2} + {5}^{2} } \\ = \sqrt{144 + 25} \\ = \sqrt{169} \\ AB \: = 13 \\ r = \frac{13}{2} = 6.5 \: units[/tex]

Answer:

[tex]500,500\text{ and }500\sqrt{2}[/tex] feet

Step-by-step explanation:

GIVEN: The boundary of a field is a right triangle with a straight stream along its hypotenuse and with fences along its other two sides.

TO FIND: Find the dimensions of the field with maximum area that can be enclosed with [tex]1000[/tex] feet of fencing.

SOLUTION:

Let the other two sides of triangle be [tex]x[/tex] and [tex]y[/tex]

such that,   [tex]x+y=1000 \implies x=1000-y[/tex]

Area of triangle [tex]A=\frac{1}{2}\times base\times height=\frac{1}{2}\times x\times y[/tex]

Area of triangle[tex]A=\frac{1}{2}\times(1000-y)\times y=\frac{(1000y-y^2)}{2}[/tex]

to maximize area, put [tex]\frac{d\ A}{d\ y}=0[/tex]

[tex]\implies 500-y=0[/tex]

[tex]\implies y=500\text{ feet}[/tex]

other side [tex]x=1000-y=500\text{ feet}[/tex]

[tex]\text{hypotenuse}^2=x^2+y^2[/tex]

                   [tex]=500^2+500^2\implies \text{hypotenuse}=500\sqrt{2}[/tex]

dimension of triangle are [tex]500,500\text{ and }500\sqrt{2}[/tex] feet

The problem is solved by using the optimization strategy in mathematics. The maximum area of the field is obtained when the triangular field is an isosceles right triangle with base 500 ft and the hypotenuse side 250 ft each.

This problem involves optimization in mathematics. In a right triangle with hypotenuse (h) and other two sides as base (b) and height (h), we know that the hypotenuse is the longest side. The Pythagorean theorem applies which states that h² = b² + h².

Given that the total length of the fences is 1000 ft, we know that b + h + h = 1000. We then solve for h and substitute it into the area formula, A = 1/2 bh. We get a quadratic function upon simplification, and we maximize the function to get the base and the height.

Using the strategy of setting the derivative equal to zero, the dimensions that maximize the area are found to be base b = 500 ft and the two equal sides h = 250 ft each which form the hypotenuse. Therefore, the field will have it's maximum area when it's a isosceles right triangle.

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Answer:

[TeX] (x+\frac{17}{2})^{2}=\frac{269}{4} [/TeX]

Step-by-step explanation:

Given the expression:

[TeX] x^2+17x=-5 [/TeX]

To complete the square,

First Step: Identify the Coefficient of x.

Coefficient of x=17

Second Step: Divide the coefficient of x by 2.

Third Step: Square your result from the second step.

This gives:

[TeX] (\frac{17}{2})^{2}[/TeX]

Fourth Step: Add your result to both sides if the equation.

[TeX] x^2+17x+(\frac{17}{2})^{2}=-5+(\frac{17}{2})^{2} [/TeX]

Fifth Step:Express the left hand side as a square

[TeX] (x+\frac{17}{2})^{2}=-5+(\frac{17}{2})^{2} [/TeX]

Sixth Step:Simplify the Right Hand Side

[TeX] (x+\frac{17}{2})^{2}=\frac{269}{4} [/TeX]

These are the values that make an equivalent number sentence.

Answer:

the domain is anything with the x-axis and range the y-axis

Answer:

Domain- is the set of all possible x-values or "input" for the function that gets you to the "output" or y-values. Range- is the difference between the highest and the lowest values.

Step-by-step explanation: