Help! Geometry project parabolas part 3

Help! Geometry Project Parabolas Part 3

Answers

Answer 1

Answer:

\((x-2)^2=4(y+5)\)

Step-by-step explanation:

Standard form of a parabola with a vertical axis of symmetry

\(\large\boxed{(x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0}\)

\(\textsf{Vertex}=(h, k)\)

\(\textsf{Focus}=(h,k+p)\)

\(\textsf{Directrix}:y=(k-p)\)

\(\textsf{Axis of symmetry}:x=h\)

If p > 0, the parabola opens upwards.

If p < 0, the parabola opens downwards.

From inspection of the given graph:

Vertex = (2, -5)Focus = (2, -4)Directrix: y = -6Axis of symmetry: x = 2

Therefore:

h = 2k = -5k + p = -4  ⇒  -5 + p = -4  ⇒  p = 1k - p = -6  ⇒  -5 - p = -6  ⇒  p = 1

Substitute the found values of h, k and p into the formula:

\(\implies (x-2)^2=4(1)(y-(-5))\)

\(\implies (x-2)^2=4(y+5)\)

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Related Questions

Patty measured a house and its lot and made a scale drawing. In real life, the front patio is 14 meters wide. It is 2 cm wide in the drawing. 1 cm is equal to how many meters?

Answers

7cm just divide by 2

Can somebody plz help figure out the rest of the answers thanks ! :D (make sure u do them correclty)

WILL MARK BRAINLIEST WHOEVER ANSWERS FIRST :DD

Can somebody plz help figure out the rest of the answers thanks ! :D (make sure u do them correclty)

Answers

Answer:

Step-by-step explanation:

3. 3

4. 5

5. 6

Answer:
3) 7z = 21 = 3
4) 5m = 25 = 5
5) 8n = 48 = 6
You can always a calculator!!

Which fraction is equal to 0.54 REPEATING ?
A.27/50
B.49/90
C.6/11
D.5/4

Answers

Step-by-step explanation:

the fraction that is equal to 0.54 repeating is A.27/50

Find the missing side length of the right triangle 5in 15in

Answers

The answer is 15 because

AB is parallel to ED.

ACD and BCE are straight lines.

AB = 8 cm

AC = 4.8cm

BC = 6.4cm

ED = 20 cm

Work out the length of BE.​

AB is parallel to ED.ACD and BCE are straight lines.AB = 8 cmAC = 4.8cmBC = 6.4cmED = 20 cmWork out the

Answers

Answer:

BE = 22.4 cm

Step-by-step explanation:

Δ CAB and Δ CDE are similar , then ratios of corresponding sides are equal, that is

\(\frac{CB}{CE}\) = \(\frac{AB}{DE}\) , substitute values

\(\frac{6.4}{CE}\) = \(\frac{8}{20}\) ( cross- multiply )

8 CE = 128 ( divide both sides by 8 )

CE = 16 cm

Then

BE = BC + CE = 6.4 + 16 = 22.4 cm

assume that x has a normal distribution with the given mean and a standard deviation. find the indicated probability. (round your answer to four decimal places.) = 102, = 15, find p(111 ≤ x ≤ 126)

Answers

The probability of x is between 111 and 126 is 0.2195 or 21.95%.

We are given that the variable x has a normal distribution with a mean (μ) of 102 and a standard deviation (σ) of 15. We need to find the probability of x being between 111 and 126, that is P(111 ≤ x ≤ 126).

We can standardize the values using the z-score formula:

z = (x - μ) / σ

For x = 111:

z = (111 - 102) / 15 = 0.6

For x = 126:

z = (126 - 102) / 15 = 1.6

Using a standard normal distribution table or calculator, we can find the probabilities associated with these z-values.

P(z ≤ 0.6) = 0.7257

P(z ≤ 1.6) = 0.9452

Then, the probability we need to find is the difference between these probabilities:

P(111 ≤ x ≤ 126) = P(0.6 ≤ z ≤ 1.6)

= P(z ≤ 1.6) - P(z ≤ 0.6)

= 0.9452 - 0.7257

= 0.2195

Therefore, the probability of x being between 111 and 126 is 0.2195 or 21.95%.


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The probability of a measure between 111 and 126 is given as follows:

0.2195 = 21.95%.

How to obtain probabilities using the normal distribution?

We first must use the z-score formula, as follows:

\(Z = \frac{X - \mu}{\sigma}\)

In which:

X is the measure.\(\mu\) is the population mean.\(\sigma\) is the population standard deviation.

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, and can be positive(above the mean) or negative(below the mean).

The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure represented by X in the distribution.

The mean and the standard deviation for this problem are given as follows:

\(\mu = 102, \sigma = 15\)

The probability is the p-value of Z when X = 126 subtracted by the p-value of Z when X = 111, hence:

Z = (126 - 102)/15

Z = 1.6

Z = 1.6 has a p-value of 0.9452.

Z = (111 - 102)/15

Z = 0.6

Z = 0.6 has a p-value of 0.7257.

Hence:

0.9452 - 0.7257 = 0.2195 = 21.95%.

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find the two values of k for which y ( x ) = e k x is a solution of the differential equation y ' ' − 14 y ' 40 y = 0 . smaller value = larger value =

Answers

The given differential equation is: y'' − 14y' + 40y = 0. To find the two values of k for which y(x) = ekx is a solution of the differential equation, we first differentiate y(x) twice. We get y'(x) = ekxk and y''(x) = ekxk2. Now we substitute these values in the differential equation and get;ekxk2 − 14ekxk + 40ekxk = 0ekxk [k2 − 14k + 40] = 0k2 − 14k + 40 = 0Solving this quadratic equation gives us;k = 7 ± √9.

The two values of k are; Smaller value = 7 − √9Larger value = 7 + √9Now we need to simplify this further. We know that √9 = 3Therefore,Smaller value = 7 − 3 = 4Larger value = 7 + 3 = 10Therefore, the two values of k for which y(x) = ekx is a solution of the differential equation y'' − 14y' + 40y = 0 are 4 and 10. The smaller value is 4 and the larger value is 10.

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please solve:
3.15=X-6.85

Answers

Answer:

X=10

Step-by-step explanation:

Answer:

x=10

Step-by-step explanation:

3.15+6.85 is 10 so x is 10

Qd=95−4P
Qs=5+P

a. What is Qd if P=5 ? b. What is P if Qs=20 ? β=9 c. If Qd=Qs, solve for P.

Answers

P = 90 is the solution for the given equation.

Given: Qd=95−4

PQs=5+P

To find Qd if P=5:

Put P = 5 in the equation

Qd=95−4P

Qd = 95 - 4 x 5

Qd = 75

So, Qd = 75.

To find P if Qs = 20:

Put Qs = 20 in the equation

Qs = 5 + PP

= Qs - 5P

= 20 - 5P

= 15

So, P = 15.

To solve Qd=Qs, substitute Qd and Qs with their respective values.

Qd = Qs

95 - 4P = 5 + P

Subtract P from both sides.

95 - 4P - P = 5

Add 4P to both sides.

95 - P = 5

Subtract 95 from both sides.

- P = - 90

Divide both sides by - 1.

P = 90

Thus, P = 90 is the solution for the given equation.

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can someone solve n/7-12=5n+5 step by step pls

Answers

Answer:

n=-7/2 I hate asking for things but can i have brainliest im trying to rank up.

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

n/7−12=5n+5

1/7n+−12=5n+5

1/7n−12=5n+5

Step 2: Subtract 5n from both sides.

1/7n−12−5n=5n+5−5n

-34/7n−12=5

Step 3: Add 12 to both sides.

-34/7n−12+12=5+12

-34/7n=17

Step 4: Multiply both sides by 7/(-34).

(7/-34)*(-34/7n)=(7/34)*(17)

suppose a research firm conducted a survey to determine the mean amount steady smokers spend on cigarettes during a week. a sample of 120 steady smokers revealed that the population mean is $20. the population standard deviation is $5. what is the probability that a sample of 120 steady smokers spend between $19 and $21?

Answers

Using the Z-table, we can determine the probability that a sample of 120 steady smokers spend between $19 and $21 is 0.986.

We have given that,

A sample is consider as survay to determine mean unt of steady smokers.

sample size (n) = 120

sample mean (X-bar ) = $20

standard deviations of sample (s) = $5

confidence interval is (19,21)

firstly we find the Z-Score value for given sample , C.I = X-bar +- Z(s/√n)

=> either 19 = 20 + Z(5/√120) or

21 = 20-Z(5/√220)

=> either Z = -0.456 or Z = 1/0.456

=> -2.19<Z<2.19

Using the either two tailed test or Z-table we can easily calculate the value of Probability.

the value of P( - 2.19<Z<2.19) is 0.986 ~ 0.99

Hence, the required probability is 0.986

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what is the graph of linear inequality 2y>x-2

Answers

Answer:

Please refer to the attached graph for the graph of linear inequality:

\(2y>x-2\)

Step-by-step explanation:

Method to draw graph of inequality:

1. First of all replace the inequality sign with equality.

Now the equation is:

\(2y=x-2\)

Now, find point and plot them.

Let us put x = 0, we get y = -1. So one point is (0, -1)

Let us put y = 0, we get x = 2. So one point is (2,0)

Now, plot both the point and join with straight line on xy coordinate axis.

2. Now, try to find a random point and put in the inequality.

If the point satisfies the inequality shade the region moving from the line towards that point.

For example:

Taking a point (4, 2)

Putting in the inequality:

\(8 > 2-2 \\8>0\)

So, (4, 2) satisfies the inequality.

Now, shade the region moving from the line towards the point (4,2).

We get the shaded region as shown in the attached figure in the answer area.

what is the graph of linear inequality 2y&gt;x-2

Inequalities are used to represent expressions of unequal values

The linear inequality is given as:

\(2y > x - 2\)

Divide through by 2

\(y > 0.5x - 1\)

The above linear inequality means that:

The inequality has a dotted lineThe upper part is shadedThe slope of the line is 0.5The y-intercept is -1

See attachment for the graph of \(2y > x - 2\)

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what is the graph of linear inequality 2y&gt;x-2

Find the value of x that makes 25x^2 + 70x + c a perfect square trinomial

Answers

The value of x that makes 25x^2 + 70x + c a perfect square trinomial is c = 1225.

To make the quadratic expression 25x^2 + 70x + c a perfect square trinomial, we need to determine the value of c.

A perfect square trinomial can be written in the form (ax + b)^2, where a is the coefficient of the x^2 term and b is half the coefficient of the x term.

In this case, a = 25, so b = (1/2)(70) = 35.

Expanding (ax + b)^2, we have:

(25x + 35)^2 = 25x^2 + 2(25)(35)x + 35^2

= 25x^2 + 70x + 1225.

Comparing this with the given quadratic expression 25x^2 + 70x + c, we can see that c = 1225.

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find all values of x such that (6, x, −11) and (5, x, x) are orthogonal. (enter your answers as a comma-separated list.)x = ___

Answers

The values x such that (6, x, −11) and (5, x, x) are orthogonal is 6,5.

The orthogonal vectors have dot product to be zero. Thus, the formula to be used is -

a . b = a1b1 + a2b2 + a3b3, where a1, a2 and a3 are components a vector and b1, b2 and be are components of b vector.

Keep the values in formula -

a . b = 6(5) + x² + (-11)x

a . b = 30 + x² - 11x = 0

So, x² - 11x + 30 = 0

x(x - 6) - 5(x - 6) = 0

(x - 6) (x - 5) = 0

So, the value of x is 6,5.

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use a model for security purposes a jewelry company prints a hidden watermark on the logo of its official documents. the watermark is a chord located 0.7 cm from the center of a circular ring that has a 2.5 cm radius. to the nearest tenth, what is the length of the chord?

Answers

The length of the chord located 0.7 cm from the centre of a circular ring with a 2.5 cm radius is approximately 3.5 cm.

To calculate the length of the chord, we can use the following formula:

Chord Length = 2 x √(r^2 - d^2)

Where r is the radius of the circular ring and d is the distance between the chord and the centre of the circle.

In this case, r = 2.5 cm and d = 0.7 cm. Plugging these values into the formula, we get:

Chord Length = 2 x √(2.5^2 - 0.7^2) ≈ 3.5 cm (rounded to the nearest tenth)

Therefore, the length of the chord is approximately 3.5 cm. This hidden watermark technique is a simple but effective security measure that can help prevent counterfeiting or tampering with important documents. By incorporating a unique and difficult-to-replicate watermark, the jewellery company can protect its brand identity and ensure the authenticity of its official documents.

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the periodic transfer of a portion of the cost of an intangible asset to expense is referred to as

Answers

The periodic transfer of a portion of the cost of an intangible asset to expense is known as amortization. This is the process of spreading the cost of an intangible asset over its useful life, similar to how depreciation is used for tangible assets like buildings and equipment.

Intangible assets, such as patents, copyrights, and trademarks, do not have a physical existence but still have value to the company. Amortization recognizes the decline in value of these assets over time and helps to accurately reflect their impact on the company's financial statements.

The amount of amortization each period is calculated by dividing the cost of the asset by its estimated useful life. It is important for companies to track and properly account for their intangible assets, including amortization, as it can have a significant impact on their financial statements and overall financial health.

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I need help solving the following question...

I need help solving the following question...

Answers

Answer: -10, 2

Step-by-step explanation:

To find the next two numbers, we first need to determine the pattern. We can see that the next number is the result of the previous number divided by -5. This tells us we need to divide 50 by -5 and that solution by -5 also.

50÷(-5)=-10

-10÷(-5)=2

Now, we know the next two numbers are -10 and 2.

Answer:

-10 and 2

Step-by-step explanation:

To find the next two numbers, you have to find what operation is being applied to the given numbers. If we look at the numbers, we can see that the absolute value is getting smaller, which means they are decreasing. However, they are decreasing at an even rate, meaning that the numbers are being divided rather than subtracted. So, let's find what number 1250 was divided by to equal -250:

1250/x = -250

Multiply both sides by x to isolate it:

1250 = -250x

Divide both sides by -250 to isolate x:

-5 = x

Each number in the pattern is divided by -5 to find the next number in the pattern. Now that we know this, we can find the next two numbers:

50/-5 = -10

-10 is one of the numbers.

-10/-5 = 2

2 is the other number.

Hope this helps :)

If two angles are supplement tart, it means they

Answers

Answer:

are equal to 180 degrees

Step-by-step explanation:

sat scores in one state is normally distributed with a mean of 1403 and a standard deviation of 200. Suppose we randomly pick 32 SAT scores from that state. a) Find the probability that one of the scores in the sample is greater than 1484. P(X > 1484) = b) Find the probability that the average of the scores for the sample of 48 scores is greater than 1484 P(X > 1484) = Round each answer to at least 4 decimal places.

Answers

The probability that one of the scores in the sample is less than 1484 is 0.2437 .

a)Given that mean u = 1403

standard deviation σ = 200

sample size n = 32

P(x>1484) = P(X-u/σ > 1484-1403/200)

                = P (z > 0.405)

P(x>1484) = 0.2437 .

hence the probability that one score is greater than 1484 is 0.405 .

b) Now we have to find the average of the scores of 48 samples.

P(x>1484)

= P(x-μ/ σ/√n> 1484-1403 /200/√48)

= P(z>2.805.)

Now we will use the normal distribution table to calculate the p value to be 0.002516.

p-value = 0.0025

Normal distributions are very crucial to statistics because not only they are commonly used in the natural and social sciences but also to describe real-valued random variables with uncertain distributions.

They are important in part because of the central limit theorem. This claim states that, in some cases, the average of many samples (observations) of a random process with infinite mean and variance is itself a random variable, whose distribution tends to become normal as the number of samples increases.

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Beth needs 16 cups of milk to make mango milk shakes for her friends. If 1 pint is equal to 2 cups, how many pints of milk should Beth buy?

Answers

They will need 8 cups/pints for the milk shakes

If 13% is lost by selling goods for Rs 1475, what would be the loss or gain if the goods are sold for Rs 1615?

Answers

Given:

Loss percent is 13%.

Selling price = 1475

To find:

The loss or gain if the goods are sold for Rs.1615?

Solution:

Let x be the cost price of goods.

Loss percent is 13% and selling price is 1475.

\(1475=x-\dfrac{13}{100}x\)

\(1475=x-0.13x\)

\(1475=0.87x\)

\(\dfrac{1475}{0.87}=x\)

\(1695.4023=x\)

\(x\approx 1695.40\)

The cost price of goods is 1695.40.

We need to find the loss or gain if the goods are sold for Rs.1615.

Cost price is greater than the selling price because 1695.40 > 1615. It means , it is a loss.

\(Loss=CP-SP\)

\(Loss=1695.40-1615\)

\(Loss=80.40\)

The loss percent is

\(Loss\%=\dfrac{Loss}{C.P}\times 100\)

\(Loss\%=\dfrac{80.40}{1695.40}\times 100\)

\(Loss\%\approx 4.74\%\)

Therefore, the loss is 80.40 and the loss percent is about 4.74%.

HELP ME PLEASE I NEED HELP ASAP JUST SOLVE THE EQUATION

HELP ME PLEASE I NEED HELP ASAP JUST SOLVE THE EQUATION

Answers

Answer:

x=18

Step-by-step explanation:

I hope this helps I just did mental math so im not sure

You need to provide a clear and detailed solution for the following questions: Question 1 [20 pts]: a) [5 pts]: Verify that the differential equation is exact: (-y8 sin(x)+7x6y³)dx+(8y cos(x)+3x7y²)dy = 0. b) [15 pts]: Find the general solution to the above differential equation. Question 2 [20 pts]: a) [15 pts]: Solve the following linear system in detailed, by using Gauss-Jordan elimination: x-3y- 5z = 2 2x + 5y-z = 1 x + 3y - 3z = -5 b) [5 pts] Is the system homogeneous and consistent? What about the solution type ? Is it unique ? Question 3 [20 pts]: Let -3x - 6y=k² + 3k - 18 -6x-3y=k²-9k +18 Question 3 [20 pts]: Let -3x - 6y=k² + 3k - 18 -6x - 3y = k² - 9k + 18 be a system of equations. a) [5 pts]: If the system is homogeneous, what is the value(s) for k? b) [15 pts]: Solve the homogeneous system. Is the solution trivial? Is the solution unique ?

Answers

To verify if the given differential equation is exact, we check if the partial derivative of the coefficient of dx with respect to y is equal to the partial derivative of the coefficient of dy with respect to x.

[Question 1]

a) To verify the exactness of the given differential equation, we compute the partial derivatives of the coefficients: ∂/∂y (-y^8 sin(x) + 7x^6y^3) = -8y^7 sin(x) + 21x^6y^2 and ∂/∂x (8y cos(x) + 3x^7y^2) = 8y cos(x) + 21x^6y^2. Since these partial derivatives are equal, the equation is exact.

b) To find the general solution, we integrate the coefficient of dx with respect to x while treating y as a constant, which gives -y^8 sin(x) + 7/2x^7y^3 + C(y). Then, we integrate the coefficient of dy with respect to y while treating x as a constant, resulting in 4y^2 cos(x) + x^7y^3 + D(x). Combining these results, the general solution is given by -y^8 sin(x) + 7/2x^7y^3 + C(y) + 4y^2 cos(x) + x^7y^3 + D(x) = C(y) + D(x).

[Question 2]

a) By performing row operations on the augmented matrix, we find the values of x, y, and z as x = -8/11, y = -11/22, and z = -1/22.

b) The system is consistent as it has a solution. Since it has a unique solution for x, y, and z, the solution type is unique.

[Question 3]

a) To make the system homogeneous, we set the right side of each equation equal to zero. By equating -3x - 6y to zero, we obtain k^2 + 3k - 18 = 0. Solving this quadratic equation gives us the values for k as k = 3 and k = -6.

b) By substituting k = 0 into the equations and applying Gaussian elimination, we can find the solution to the homogeneous system. The solution may be trivial (all variables are zero) or nontrivial (at least one variable is nonzero). The uniqueness of the solution depends on the results obtained from the Gaussian elimination process.

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\(\\ jn j j j\)

Answers

Answer:

glhIblzikdjbgjdzgbobrgbzoerbgoernbs

Step-by-step explanation:

ur welcome ;)

Answer:

njjjj

Step-by-step explanation:

one sixth of a number is 9 algebraic expression​

Answers

Answer:

x= 54

Step-by-step explanation:

let the number be (x)

so One sixth of x will be 9

numerically,

1/6 × (x) =9

x= 9×6

x= 54

Given ↓The verbal phrase → one-sixth of a number is 9To find ↓The algebraic expression of the verbal phraseCalculations ↓

One-sixth can be written as \(^1/_6\)

now, let the number be y

so one-sixth of y is written as

\(^1/_6~y~=~9\)

If it's necessary to solve for y, consult the [Solving for y] section of this ans ↓

[Solving for y]

First we need to get rid of the fraction, one-sixth.

since in mathematics we can't just terminate fractions without altering the equation/expression itself, we need to perform an operation.

the first one is multiplication; we will multiply both sides of the equation by 6 (the denominator of the fraction)

\(^1/_6*6~y~=~9~*~6}\)

On the left-hand side the 6's cancel, and we're left with

1 y = 9 * 6

Or

y = 9* 6

Which simplifies to :

y = 54

"A bakery sells vanilla cupcakes and mocha cupcakes. It sold 286 vanilla cupcakes in a day. 35% of the cupcakes sold that day were mocha. How many total cupcakes did the bakery sell that day?" PLS HELP

Answers

Answer:

386 cupcakes in total

Step-by-step explanation:

convert 35% to a decimal

0.35 x 286 = 100.1

100.1 + 286 = 386

"use
integration by substitution to evalute these problems. show work
1. Evaluate the integral S ""S 2. Evaluate the integral cos(t) dt. sin² (t) + 1 ex 3. Evaluate the integral - dx. ex + 1 √In(x) + 73 X dx."

Answers

1. Evaluate the integral S
Let u = 1 + 3x²,

then du = 6x dx.

Therefore, x dx = 1/6 du.

Integral can be rewritten as:
S = ∫ (x / (1 + 3x²)) dx.
Let u = 1 + 3x²,

then du = 6x dx.

Therefore, x dx = 1/6 du.

The integral can be rewritten as:

S = ∫ 1/u du S

= ln |u| + C,

where C is a constant.

S = ln |1 + 3x²| + C,

where C is a constant.

2. Evaluate the integral cos(t) dt. sin² (t) + 1
Let u = sin(t),

then du = cos(t) dt.

Therefore, cos(t) dt = du. Integral can be rewritten as:
∫ cos(t) / (sin²(t) + 1) dt.
Let u = sin(t),

then du = cos(t) dt.

Therefore, cos(t) dt = du. Integral can be rewritten as:
∫ du / (u² + 1).
The solution is given as arctan(u) + C,

where C is a constant. Substituting u back, the solution is:
∫ cos(t) / (sin²(t) + 1) dt

= arctan(sin(t)) + C,

where C is a constant.

3. Evaluate the integral - dx. ex + 1 √In(x) + 73 X dx.
Let u = ln(x),

then du = (1 / x) dx.

Therefore, dx = x du. Integral can be rewritten as:
∫ -du / (e^u + 1) √(u + 73).
Let u = ln(x),

then du = (1 / x) dx.

Therefore, dx = x du. Integral can be rewritten as:
∫ -du / (e^u + 1) √(u + 73).
Let v = √(u + 73),

then dv = (1 / 2) (1 / √(u + 73)) du.

Therefore, du = 2v √(u + 73) dv. Substituting, we get:
∫ -2v dv / ((e^u + 1) v)

= -2 ∫ dv / (e^u + 1).
The solution is given as -2 ln |e^u + 1| + C,

where C is a constant. Substituting u and v back, the solution is:
∫ -dx / (ex + 1) √(ln(x) + 73 x)

= -2 ln |e^(ln(x)) + 1| + C

= -2 ln |x + 1| + C,

where C is a constant.

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0.25 , 0.5 , 0.375 , 2.5 , 0.125 in asending order ..​

Answers

0.125 is the CLOSEST to 0 while 2.5 is the FARTHEST. Using this as a guide, the order is: 0.125, 0.25, 0.375, 0.5, 2.5. Hope this helped :)

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Justin spent a total of $15 ice skating. He rented ice skates for $4.50 and skated for 3 hours. Write an equation to determine the cost per hour, h, to ice skate. ​

Answers

Answer:

3h+4.50=15

We know that she skates for 3 hours, but we don't know the cost per hour so is the "h". He pays a start up $4.50 for the ice skates. And he spend $15 in total for ice skating.

Hopefully that helps. Have a great night! Or day!

Help me please answer all thanks

Help me please answer all thanks

Answers

The coordinates are 3,3

Answer:

the coordinates are (3,3)

Step-by-step explanation:

hope I helped!!

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