The system of conics has two solutions.

(x−4)^2 + (y+1)^2 = 9
(x−4)^2/9 + (y+1)^2/81 = 1

What are the solutions to this system of conics?

30

Answer: Where is the figure??

Answer:

I think it this one but picture would help...

Angle DBC and angle BDA form a pair of vertical angles, not a pair of alternate interior angles, which are congruent.  

The distance apart of the two guy wire is 187.7 metres

The distance apart of the two wires can be found using trigonometric ratios.

Therefore,

tan ∅ = opposite / adjacent

Therefore,

tan 13 = 27 / x

x = 27 / tan 13 = 27 / 0.23086819112 = 117.391304348

tan 21 = 27 / y

y = 27 / tan 21

y = 70.338144115

Therefore,

distance apart of the guy wire = 117.391304348 + 70.338144115 = 187.728144115 = 187.7 metres

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Answer:

14.7, because 5x + 90 + 16.5 =180

so 180-90-16.5=5x

x= 14.7

Expand the binomials.

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

Now let \(x=1\) and \(y=\sin(A)\).

Answer:

....

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

If this figure is a rhombus, then the two sides have to be equal:

3x+9=8x-1

Move like terms to one side (note that when you move it, the sign flips. Ex: - becomes +)

3x-8x=-9-1

-5x=-10

Divide both sides by -5

x=2

Answer:

Equations:

a + b = 19

a = b + 2

a = Money that spent Laura

b = Money that spent Laureen

then:

(b+2) + b = 19

2b + 2 = 19

2b = 19-2

2b = 17

b = 17/2

b = 8.5

a = b + 2

a = 8.5 + 2

a = 10.5

Check:

10.5 + 8.5 = 19

All the three statements "f(n) = O(g(n))"," g(n) = Ω(f(n))","f(n) = Θ(g(n))" are false as the given functions f(n) and g(n) do not satisfy the conditions required for the Big O and Big Omega notation.

We have the following two functions:

f(n) = (n^2 - 8)(n - 1)

g(n) = n^2

Now, let's analyze each statement:

1. Statement: f(n) = O(g(n))

To check if this statement is true, we need to determine if there exist constants c and n0 such that f(n) ≤ c * g(n) for all n ≥ n0.

Expanding f(n), we get f(n) = n^3 - 9n^2 + 8n - 8.

Comparing f(n) and g(n), we can see that f(n) grows faster than g(n) as n approaches infinity. Therefore, f(n) is not bounded by g(n), making the statement false.

2. Statement: g(n) = Ω(f(n))

To check if this statement is true, we need to determine if there exist constants c and n0 such that g(n) ≥ c * f(n) for all n ≥ n0.

Since f(n) grows faster than g(n), we cannot find such constants c and n0. Therefore, the statement is false.

3. Statement: f(n) = Θ(g(n))

To check if this statement is true, both f(n) = O(g(n)) and g(n) = O(f(n)) must hold.

Since neither f(n) = O(g(n)) nor g(n) = O(f(n)), the statement is false.

In conclusion, all three statements are false.

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Complete question:

Consider the following functions:

f(n) = (n^2 - 8)(n - 1)

g(n) = n^2

Evaluate the validity of the following statements:

1. Statement: f(n) = O(g(n))

2. Statement: g(n) = Ω(f(n))

3. Statement: f(n) = Θ(g(n))

For each statement, determine whether it is true or false, providing reasoning and evidence to support your answer.

Step-by-step explanation:

just as the graph shows.

no trick or hidden meaning or whatever.

#1

0 seconds to 5 seconds.

0 meters to 3 meters.

traveled 3-0 = 3 meters in 5-0=5 seconds

#2

0 seconds to 8 seconds.

0 meters to 5 meters.

traveled 5-0=5 meters in 8-0=8 seconds.

Answer:

n<5

Step-by-step explanation:

6(3+n)<48

Step 1: Simplify both sides of the inequality.

6n+18<48

Step 2: Subtract 18 from both sides.

6n+18−18<48−18

6n<30

Step 3: Divide both sides by 6.

6n /6 < 30 /6

n<5

Answer: The answer is C. 5

Step-by-step explanation:

Just took the test on edg.

Answer:

96π mm^3

Step-by-step explanation:

πr^2*h = formula

π4^2*6 = 16π(6) = 96π mm^3

Answer:

\(\Longrightarrow: \boxed{\sf{96\pi }}\)

Step-by-step explanation:

You must use the volume of this cylinder formula to solve the volume of this cylinder.

Volume of this cylinder formula:

\(\Longrightarrow: \sf{\pi r^2*h}\)

\(\Longrightarrow\sf{\pi 4^2*6}\)

Use the order of operations.

PEMDAS stands for:

First, solve exponents.

4²=4*4=16

16*6

Multiply.

16*6=96

\(\Longrightarrow: \boxed{\sf{96\pi}}\)

I hope this helps! Let me know if you have any questions.

The solution of the system of equation is (-7, -2).

The system of the equations;

\(\rm y^2 + x^2 = 53 \\\\y -x = 5\)

From equation 1

\(\rm y -x=5\\\\y = 5+x\)

Substitute the value of y in equation 1

\(\rm y^2+x^2=53\\\\(5+x)^2+x^2=53\\\\25+x^2+10x+x^2=53\\\\2x^2+10x+25-53=0\\\\2 x^2 + 10x - 28 = 0 \\\\Divide \ by \ 2 \ both \ side \ the \ equation\\\\x^2 + 5x - 14 = 0\\\\x^2-7x+2x-14=0\\\\x(x-7) + 2(x-7) =0\\\\(x-7) \ (x+2)=0\\\\x-7=0 \ \ x = 7\\\\x +2 =0 \ \ x=-2\)

The value of x= 2 is rejected because x = 2 not satisfy the equation.

Substitute 2 for the value of x in equation II

y − x = 5

y – 2 = 5

y = 5 +2

y = 7 (x =2, y =7) … Not included in the options

If x = -7

Substitute the value of x = -7 in the equation

\(\rm y -x=5\\\\y - (-7)=5\\\\y +7= 5\\\\y = 5-7\\\\y = -2\)

Hence, the solution of the system of equation is (-7, -2).

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Answer:

The equation y = 10x + 5 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

The equation y = 10x + 5 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.Slope (m) = 10

The equation y = 10x + 5 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.Slope (m) = 10Y-intercept (b) = 5

The equation y = 10x + 5 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.Slope (m) = 10Y-intercept (b) = 5The slope represents the rate of change of the monthly rate with respect to the fee to join. For every increase of $1 in the fee to join, the monthly rate increases by $10.

The equation y = 10x + 5 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.Slope (m) = 10Y-intercept (b) = 5The slope represents the rate of change of the monthly rate with respect to the fee to join. For every increase of $1 in the fee to join, the monthly rate increases by $10.The y-intercept represents the initial cost of joining the gym. It is the amount that the gym charges even if the fee to join is $0. In this case, the gym charges $5 to join.

Answer:

$4752  was collected during that time

Answer:

$4752 was made in the 2 hour time period.

Hope this helps :)

Step-by-step explanation:

12 * 396 = 4752

Answer:

Y'(-5, 5)

Step-by-step explanation:

To find the coordinates of Y' after the translation, we apply the given rule to the coordinates of point Y(-3, 4).

Using the translation rule (x, y) → (x - 2, y + 1), we can substitute the coordinates of Y(-3, 4) into the rule:

x' = x - 2 = -3 - 2 = -5

y' = y + 1 = 4 + 1 = 5

Therefore, the coordinates of Y' are (-5, 5).

Answer:

199.5

Step-by-step explanation:

i know because I added it up

The measure of each angle is 34.1° and 55.9°

complementary angles are angles that gives 90° when added to together.

if the first angle is x and the other complementary angle is y,

then x+y=90

x= y-21.8

representing y-21.8 for x in equation x+y=90

y+ y-21.8= 90°

2y= 111.8

y= 55.9°

and x= 34.1°

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Amanda would use 3 planks of lengths 3 feet, 5 feet, and 6 feet.

To determine which planks Amanda should use to build the triangular-shaped kennel:

Therefore, Amanda would use 3 planks of lengths 3 feet, 5 feet, and 6 feet.

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The mean speed of the cars is 52.77 mph

To calculate the mean, you multiply each speed value by its corresponding frequency, sum up these products, and then divide by the total number of cars:

Mean = (38 × 19 + 45×12 + 55×12 + 65 × 12 + 75 × 9) / (19 + 12 + 12 + 12 + 9)

Calculating this expression gives:

Mean = (722 + 540 + 660 + 780 + 675) / 64

Mean = 3377 / 64

Mean ≈ 52.77 (rounded to two decimal places)

Therefore, the mean speed of the cars is approximately 52.77 mph.

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The highway speeds of cars are summarized in the frequency distribution below. Find the mean of the frequency distribution. Round your answer to one more decimal place than is present in the original data values.

Speed (eph) / Cars

38−39 / 19  

40⋅49/12

50−59/12

60−69/12

79−79/9

Answer:

622.27

Step-by-step explanation:

- $87.45 + (- $24.76) + (-17.29) = $-129.5

$143.87 + $348.90 = $492.77

492.77 - (-129.5) = 622.27

The test statistic for the sample is approximately 3.295. The p-value for this sample is approximately 0.0006. The p-value is less than the significance level of 0.01. Therefore, based on the test statistic and p-value, the decision is to reject the null hypothesis.

To test the claim that the population mean (μ) is greater than 89.5 at a significance level of α = 0.01, we can perform a one-sample t-test. Since the population standard deviation (σ) is unknown, we will use the sample standard deviation (SD = 10.6) as an estimate.

The test statistic for this sample is calculated using the formula:

t = (M - μ) / (SD / √n)

Plugging in the values from the problem, we have:

t = (91.6 - 89.5) / (10.6 / √300) ≈ 3.295

The p-value for this sample can be found by comparing the test statistic to the t-distribution with n - 1 degrees of freedom. Since the alternative hypothesis is μ > 89.5, we are interested in the right-tail area.

Using statistical software or a t-table, we find that the p-value associated with a t-statistic of 3.295 and 299 degrees of freedom is approximately 0.0006.

Comparing the p-value to the significance level (α = 0.01), we can see that the p-value (0.0006) is less than α. Therefore, the p-value is less than or equal to α.

This test statistic leads to a decision to reject the null hypothesis. In other words, there is sufficient evidence to support the claim that the population mean is greater than 89.5 at a significance level of 0.01.

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The answers are =

a. Gradient: 1

Y-intercept: (0, 3)

b. Gradient: -3

Y-intercept: (0, 4)

c. Gradient: -5

Y-intercept: (0, -2)

d. Gradient: 4

Y-intercept: (0, -3)

To find the gradient and the y-intercept for each line, let's examine each equation:

1) Formula: y = x + 3

Gradient: Since x has a coefficient of 1, the gradient is also 1.

Y-intercept: Since the constant term is 3, the line's y-intercept is at (0, 3).

2) Formula: y = -3x + 4

Gradient: The gradient is -3 because the coefficient of x is -3.

Y-intercept: The line crosses the y-axis at (0, 4) since the constant term is 4.

3) Formula: y = -5x - 2

Gradient: The gradient is -5 because the coefficient of x is -5.

Y-intercept: The line crosses the y-axis at (0, -2) since the constant term is -2.

5) Formula: y = 4x - 3

Gradient: The gradient is 4 because the coefficient of x is 4.

Y-intercept: Since the constant term is -3, the line's y-intercept is at (0, -3).

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Answer:

\(\boxed {12x + 2}\)

Step-by-step explanation:

Solve the following expression:

\(4(3x + 2) - 6\)

-Use Distributive Property:

\(4(3x + 2) - 6\)

\(12x + 8 - 6\)

-Combine like terms:

\(12x + 8 - 6\)

\(\boxed {12x + 2}\)

Answer:

\(12x+2\)

Step-by-step explanation:

The first step is to distribute the 4 to the parenthesis. This turns the equation into:

\((12x+8)-6\)

We can remove the parenthesis now. Also, now we combine like terms. There are no other variables in the equation, so we leave the 12x alone. Combine the +8 and the -6 to get +2. This leaves the equation at:

\(12x+2\)

Answer:

Q = 108°

R = 72°

Step-by-step explanation:

Quadrilateral means this is a four-sided shape. Parallelogram means that both sets of opposite side are parallel, so all the angles are either equal or add up to 180° (supplementary)

The order of the letters matters bc PQRS means that you go along an edge from P to Q, but you have to go thru the middle of the shape to get from P to R. So P and Q add up to 180°.

P + Q = 180°

72° + Q = 180°

Q = 108°

Opposite from each other, across the middle of the shape, P and R are equal.

P = R = 72°

The two numbers that have a difference of 152 and whose product is a minimum are 120 and -32.  To find these numbers, we can set up an equation. Let's call the larger number x and the smaller number y. Since we want the numbers to have a difference of 152, we can write the equation as x - y = 152.

To find the product, we can multiply the two numbers together. So the equation for the product is xy.

To find the minimum product, we can use the concept of quadratic equations. The product xy can be expressed as x(x - 152) or -y(y - 152). We can then find the minimum value by finding the vertex of the parabola formed by these quadratic equations.

Using calculus, we can find that the vertex occurs at x = 76 and y = -76. Therefore, the two numbers are 76 and -76, which have a difference of 152.

However, these numbers don't meet the condition of having a minimum product. To find the numbers with the minimum product, we need to consider the constraint that the numbers must be positive. The closest positive numbers to 76 and -76 are 120 and -32, respectively. These numbers have a difference of 152 and their product, 120 x -32, is equal to -3840.

Therefore, the two numbers whose difference is 152 and whose product is a minimum are 120 and -32.

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The centroid of a triangle divides the triangle in 1/3 and 2/3.

The length of NM is 6 units

The given parameters are:

IM = 18

KN = 4

HL = 15

The centroid of the triangle divides line IM to NM and NI, where NM < NI

So, we have:

\(\mathbf{NM = \frac 13 \times IM}\)

This gives

\(\mathbf{NM = \frac 13 \times 18}\)

Expand

\(\mathbf{NM = 6}\)

Hence, the length of NM is 6 units

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Yes, irrational numbers such as π are included in the domain of the function f(x) = 7.

The domain of a function is the set of all possible input values (x) for which the function is defined. In the case of the function f(x) = 7, the output value (y) is always equal to 7, regardless of the input value.

Since every real number, including irrational numbers like π, can be an input value for f(x) = 7, the domain of this function is the set of all real numbers, which includes both rational and irrational numbers. Therefore, π is included in the domain of the function f(x) = 7.

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Answer:

Extraneous solutions are values that we get when solving equations that aren't really solutions to the equation.

Step-by-step explanation: None