A polygon is shown on the graph:

A polygon is shown on a coordinate plane. Vertex A is located at 2 comma negative 1, vertex B is located at 1 comma negative 4, vertex C is located at 3 comma negative 5, vertex D is located at 5 comma negative 3.

If the polygon is translated 3 units down and 4 units left, what will the coordinates of the new image be? Use prime notation in expressing the new coordinates.

Answer:

a) The equation of the arch is [tex]y = -10\cdot x^{2}[/tex].

b) The height of the arch from the ground is 810 feet.

Step-by-step explanation:

Statement is incomplete. Complete statement is:

An archway in front of a school is in the shape of a parabola. The top of the arch is the vertex (0,0). The school seal is at the focus, 2.5 feet below the vertex, and the arch is 18 feet wide at the ground.

Write an equation  that represents the arch.

What is the height from the top of the arch to the  ground?

a) Write an equation that represents the arch.

According to the statement, the archway is a vertical downward parabola. From Analytical Geometry we know that parabolas are represented by the following equation in standard form:

[tex]y-k = 4\cdot p\cdot (x-h)^{2}[/tex] (Eq. 1)

Where:

[tex]p[/tex] - Distance between vertex and focus, measured in feet.

[tex]x[/tex] - Independent variable, measured in feet.

[tex]y[/tex] - Dependent variable, measured in feet.

[tex]h[/tex], [tex]k[/tex] - Coordinates of the vertex, measured in feet.

If we know that [tex]p = -2.5\,ft[/tex], [tex]h = 0\,ft[/tex] and [tex]k = 0\,ft[/tex], then the equation that represents the arch:

[tex]y = -10\cdot x^{2}[/tex]

The equation of the arch is [tex]y = -10\cdot x^{2}[/tex].

b) What is the height from the top of the arch to the  ground?

Given that parabola is a symmetrical curve, we determine the vertical position at the base of the arch ([tex]x = 9\,ft[/tex]):

[tex]y_{min} = -10\cdot (9\,ft)^{2}[/tex]

[tex]y_{min} = -810\,ft[/tex]

Then, the height of the arch from the ground is given by this difference:

[tex]h = 0\,ft-(-810\,ft)[/tex]

[tex]h = 810\,ft[/tex]

The height of the arch from the ground is 810 feet.

Answer 6.

Step-by-step explanation:

Answer:

A.) 1

Step-by-step explanation:

A trapezoid only has one pair of parallel sides.

Answer:

X = 64/19

y equals -2/19

z =9/19

Step-by-step explanation:

its very hard to type in the explanation but I know the answer is right trust me I do a level maths

Answer:

Audrey needs to collect 3 more coins.

Step-by-step explanation:

Since she already scored 53 points, we have to find out how many more points she needs to score 97.

So, 97-53=45 points.

The problem says that each coin Audrey collects is worth 22 points. Therefore, 45 divided by 22= 2 remainder 1. However, if she only collects two more coins, Audrey will only have 96 points in total, not 97.

So, add another coin to make 3.

Answer:

[tex]m=-3[/tex]

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Simply plug in the 2 coordinates into the slope formula to find slope m:

[tex]m=\frac{5-(-1)}{-5-(-3)}[/tex]

[tex]m=\frac{5+1}{-5+3}[/tex]

[tex]m=\frac{6}{-2}[/tex]

[tex]m=-3[/tex]

Answer:

it is SAS

Step-by-step explanation:

side angle side

triangle JKL is congruent to triangle JML

because they have two equal sides:

JL whitch is common in both of them and ML equal to KL

and the included angles are equal.

Answer:

Budget A

Step-by-step explanation:

Total monthly budget is;

T = Rent cost + Personal Items cost + Entertainment cost +Savings cost

For budget A;

T_A = $200 + $120 + $100 + $250

T_A = $670

For budget B:

T_B = $200 + $120 + $300 + $50 = $670

Foe budget C;

T_C = $200 + $120 + $200 + $150

T_C = $670

For budget D;

T_D = $200 + $120 + $325 + $25 = $670

We can see the total budget for all is $670.

Her rent and personal expenses have fixed amounts. Thus, the only ones that can vary are Entertainment cost and Savings cost.

Now, in all the budgets, budget A has the highest savings which is $250.

Thus, we can say it's the best budget to help her meet her goals as it still provides $100 for even entertainment which she loves with her friends.

Answer:

budget A

Step-by-step explanation:

Answer:

900

Step-by-step explanation:

Answer:

1+1=78993939939

Step-by-step explanation:

1x1= 0 (-_<)

Answer:

x = -2

Step-by-step explanation:

That's really it, since it's a vertical line.

Answer:

The equation of vertical line, parallel to y-axis is

x + k=0

Here, the line passes through the point (–2,–9)

So, –2 + k = 0

=> k = 2

The required equation be, x + 2 = 0

Answer:

N = 18

Step-by-step explanation:

Answer:

18/4

Step-by-step explanation:

Answer:

Neptune is 45 million so 1 million difference

Answer:

9

Step-by-step explanation:

Answer:

x=9

Step-by-step explanation:

set up a proportion

10/15 = 6/x

(or 12/18 = 6/x)

cross multiply:

10x = 90

x=9

Answer:

20666.6?

Step-by-step explanation:

3100/3= 1033.33

1033.33*20

20666.6

Answer:

EF = 11

JK = 32

Step-by-step explanation:

Because the average of  10 and 12 is 11, therefore that would be the answer, since EF has a slite angle, finding the average of the largest side length and the opposite side would be the best way to find it.

Because the average of 28 and 36 is 32 your answer would be 32, this is from adding both lengths on LJ, which is 12 and 24, I added them to get 36, then found the average, the average was 36,  meaning that this was your answer.

Answer:

4 bags.

Step-by-step explanation:

1/10 is already good, but you need to multiply 2/5 by 2 to get 4/10, and then it's self-explanatory from there

Answer:

11 weeks

Step-by-step explanation:

Kiaya has $376 but can only withdraw $276 before being charged by the bank.

First I subtracted the $100 she can't spend from $376.

-She has a total of $276 she can spend without being charged.

Next, I divided $276 by $25 (the amount she withdraws every week)

- The total is 11.04

This means she has 11 Weeks before she will have to pay the fee.

Hope I helped you out!! :)

Answer:

250.890

Step-by-step explanation:

Answer:

12 times.

Step-by-step explanation:

If she swims three times a week, then you need to find how many weeks make up 28 days. 28/7= 4 weeks. Since she swims three times a week, you multiple that by the amount of weeks, which is four. You get that she swims 12 times in 28 days.

Answer:

slope is -4

Step-by-step explanation:

To find the slope with points, you do (y2-y1)/(x2-x1)

4-(-8)=12

0-3=-3

12/-3=-4

Answer:I think you make somthing like i think task one would be lets say (Av)task two would be like(Bx) and it would all end out like this C

Av+Bx=C

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

Area of ΔABC = 10 square units

Step-by-step explanation:

Distance between the two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is represented by,

d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Length of AB = [tex]\sqrt{(-4-2)^2+(-6+8)^2}[/tex]

                      = [tex]\sqrt{36+4}[/tex]

                      = [tex]2\sqrt{10}[/tex]

Length of CD = [tex]\sqrt{(-6+7)^2+(-2+5)^2}[/tex]

                      = [tex]\sqrt{1+9}[/tex]

                      = [tex]\sqrt{10}[/tex]

Area of a triangle ABC will be represented by the formula,

Area = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

        = [tex]\frac{1}{2}(AB)(CD)[/tex]

        = [tex]\frac{1}{2}(2\sqrt{10})(\sqrt{10})[/tex]

        = 10 square units

Answer:

10 square units

Step-by-step explanation:

Answer:

Sowy but try Mathwa y

Step-by-step explanation:

Answer:

5(2.2y+3.4)=5(y-2)+6y has no solution

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The third one down.

32.1y+3.1+2.4y-8.2=34.5y-5.1

Combine like terms

34.5y + 3.1 - 8.2 = 34.5y - 5.1

34.5y - 5.1 = 34.5y - 5.1              y can be anything

===========================

Remove the brackets from D

11y + 17 = 5y - 10 + 6y

11y + 17 = 11y - 10

This gives 17 = - 10 which of course is nonsense.

D has no solution.

Answer:225

Step-by-step explanation:

Answer:

eiffel tower - 984ft

leaning tower of pisa - 180

Step-by-step explanation:

2x+804=1164

   -804    -804

2x = 360

divide both sides by 2

x = 180

eiffel - 180 + 804

pisa - 180