solve the simultaneous equation :

x² + y² = 18
x + 2 = - 3x

Two lines represented by the following equations are perpendicular to each other. Explanation is given below.

Those lines that are perpendicular to each other that means create an angle of 90° at intersecting point are perpendicular lines.

We have the equations:

a)6x²-5xy-6y² = 0

b) x²-y²+x+y=0

c) x² - y² = 0​

The above lines are the product of two separate lines.

To prove that the two lines represented by the following equations are perpendicular to each other:

We have drawn the graphs of all the three equations.

The attached images are equation 1, equation 2, equation 3 are in the order of a, b and c.

And we can clearly see that the lines are perpendicular.

The general formula of the equation,

ah²+ 2hk + bk² = 0.

When a+b = 0,

Then the lines are perpendicular.

The sum of the coefficients of order 2 variable is zero.

a). 6 - 6 = 0

b). 1-1 = 0

c). 1-1 = 0

Therefore, the proof is given above.

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Answer:

y = x + 9 ==> x + (-y) = -9

y = -6x - 5 ==> 6x + y = -5

y = 2/3x + 1​ ==> 2x/3 + (-y) = -1

Step-by-step explanation:

y = x + 9  ==> isolate the constant 9

**Don't subtract x on both sides as x has to be positive**

y - 9 = x ==> keep x positive by subtracting 9 on both sides

-9 = x - y  ==> subtract y on both sides to isolate the constant

x + (-y) = -9  ==> make the equation in the form of ax + by = c

y = -6x - 5  ==> isolate the constant -5

y + 6x = -5  ==> isolate -5 by adding 6x on both sides, making x positive

6x + y = -5  ==> make the equation in the form of ax + by = c

y = 2x/3 + 1​  ==> isolate the constant 9

**Don't subtract 2x/3 on both sides as x has to be positive**

y - 1 = 2x/3 ==> keep x positive by subtracting 1 on both sides

-1 = 2x/3 - y  ==> subtract y on both sides to isolate the constant

2x/3 + (-y) = -1  ==> make the equation in the form of ax + by = c

Yes, it is possible to construct a triangle with the given sides 6cm 5 cm and 9 cm.

As given in the question,

Let the triangle with the given side length be ΔABC.

Measure of the side length is equal to :

Side Length 1 ( AB ) = 6cm

Side Length 2 ( BC ) = 5cm

Side Length 3 ( CA ) = 9cm

To construct a triangle following property should satisfied:

Sum of the two side length is always greater than the third side.

AB + BC

= 6cm + 5cm

= 11cm > 9cm

BC + CA

= 5cm + 9cm

= 14cm > 6cm

CA + AB

= 9cm + 6cm

= 15cm > 5cm

Here the required condition to construct a triangle is satisfied.

Therefore, yes it is possible to construct a triangle with the given sides measure .

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The image of the point (-8, 0) after a rotation of 270 degrees counterclockwise is (0,8).

What is rotation?

The term "rotation" refers to an object moving in a circle around its center. Different forms can be rotated at an angle around the centre. A rotation is a map in mathematics. The term "rotation group of a unique space" refers to all rotations that revolve around a fixed point and form a group beneath a structure. With respect to three-dimensional shapes, we can turn or rotate the elements about an endless number of fictitious axes.

Here When rotating a point 270 degrees counterclockwise about the origin our point A( x , y) becomes A'(y,-x). Then

=> (x , y) = (-8,0)

Now 270 degrees counter clockwise rotation then,

=> (y,-x) = (0,-(-8))

=> (y,-x)=(0,8)

Hence the image of the point (-8, 0) after a rotation of 270 degrees counterclockwise is (0,8).

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Answer:

2x^2 + 8x + 3 in 2( x + 2 )^2 + q form is 2( x + 2 )^2 - 5

The equation of the circle with center (3, 2) and point (1, 1) is:

(x - 3)² + (y - 2)² = 5.

The equation of a circle with center (h, k) and radius r is given by the equation: (x - h)² + (y - k)² = r²

To find the equation of the circle with center (3, 2) and a point on the circle (1, 1), we first need to find the radius of the circle. We can use the distance formula to find the distance between the center and the point on the circle:

r = √((1 - 3)² + (1 - 2)²) = √((-2)² + (-1)²) = √5

So the radius of the circle is √5

Now we can substitute the center and radius into the equation of a circle:

(x - 3)² + (y - 2)² = (√5)²

Simplifying, we get:

(x - 3)² + (y - 2)² = 5

So the equation of the circle with center (3, 2) and point (1, 1) is:

(x - 3)² + (y - 2)² = 5.

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The distance between Cardwell and Claremont if they are 4.5 inches apart on the map will be 150 miles.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

If a road map has a scale of 3 inches to 100 miles.

Then the scale factor is given as,

Sclar factor = 100 / 3

Sclar factor = 33.33 miles per inch

Then the distance between Cardwell and Claremont if they are 4.5 inches apart on the map will be given as,

Distance = 33.33 x 4.5

Distance = 150 miles

The distance between Cardwell and Claremont if they are 4.5 inches apart on the map will be 150 miles.

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The answer reads "40," is the correct response to the earlier question.

What is median ?

The value of the middle observation found after the data are arranged in ascending order is referred to as the median of the data. In many cases, it is challenging to take all of the facts into account when representing something, and in these cases, median is helpful. The median is one of the simple to compute statistical summary metrics. The median is also known as the place average since it uses the data that is in the centre of a sequence to determine its value.

There are data of 9 students and we need to arrange them in ascending order to find our answer.

So, the arrangement looks like the following:

⇒ 25, 35, 45, 50, 60, 80, 90, 95, 100

We are aware that

In all cases, the middle value is the median.

Therefore, it is safe to say that the Median of the aforementioned arrangement is 60.

Hence, Median of the numbers on the left of the median is 60=35+45/2 = 40

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Answer: y=25x+80

Step-by-step explanation:

Step-by-step explanation:

f(x) = 0.5 ∛(x − 4) − 5

As x approaches ∞:

f(∞) = 0.5 ∛(∞ − 4) − 5

f(∞) = 0.5 ∛(∞) − 5

f(∞) = 0.5 (∞) − 5

f(∞) = ∞ − 5

f(∞) = ∞

As x approaches -∞

f(-∞) = 0.5 ∛(-∞ − 4) − 5

f(-∞) = 0.5 ∛(-∞) − 5

f(-∞) = 0.5 (-∞) − 5

f(-∞) = -∞ − 5

f(-∞) = -∞

P=(m+nmx2​+nx1​​,m+nmy2​+ny1​​). The formula can be derived by constructing two similar right triangles, as shown below. Their hypotenuses are along the line segment and are in the ratio m : n m:n m:n.

What is the segment ratio formula?

P=(m+nmx2​+nx1​​,m+nmy2​+ny1​​). The formula can be derived by constructing two similar right triangles, as shown below. Their hypotenuses are along the line segment and are in the ratio m : n m:n m:n.

A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.

Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.

Given ratios are 2:1 and 3:1

we can write it as 2/1 and 3/1.

The lcm of 2 and 3 is 6.

Multiply denominator of both ratio with 6, we get

2/6 and 3/6 And we can see both the ratios are not equal.

Hence, there are not equivalent ratios.

4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2

11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)

3:1 and 9:3 are equivalent ratios ------> is true

because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3

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Answer:

Step-by-step explanation:

Anything raised to the power of 0 equals 1, so we have 1 raised to the power of -3. That's the same thing as

[tex]\frac{1}{1^3}[/tex] which is just 1. The answer is 1.

Answer: 2x + 3y + 1

Step-by-step explanation:

That is your answer

Please give brainliest

The translation in y = (x + 3)² is of 3 units to the left. The correct option is the last one.

For a general function y = f(x), we define a horizontal translation of N units as:

g(x) = f(x + N)

Here the original function is y = x² and the translated one is:

y = (x + 3)²

So we just added 3 on the argument, so this is a shift of 3 units to the left, the correct option is the last one.

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Answer: m angle3 = 3x - 7 = 3(14) - 7 = 37 degrees

Step-by-step explanation:

Since angles 3 and 9 are complementary, their measures add up to 90 degrees. So, we can set up the equation:

m angle3 + m angle9 = 90

We can substitute in the given values for the measures of each angle:

(3x - 7) + (4x - 1) = 90

Solving for x:

7x - 8 = 90

7x = 98

x = 14

The most effective way to use her 4 hours of study time to get the highest possibility or probability of test scores would be to spend 4 hours working on multiple-choice problems and 0 hours reviewing lecture notes.

From the information given, it is clear that working on multiple-choice problems is the most effective way to improve her test score. Therefore, the highest possibility or probability of test scores would be achieved by spending the most time working on multiple-choice problems.

The available time for studying is 4 hours, so the maximum time that can be spent working on multiple-choice problems is 4 hours. If she spends 4 hours working on multiple-choice problems, she will not have any time left to review lecture notes.

So, the most effective way to use her 4 hours of study time to get the highest possible test score would be to spend 4 hours working on multiple-choice problems and 0 hours reviewing lecture notes.

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The customer rented the car for 8 days.

The total amount paid by the customer, $138, is made up of the initial fee and the daily fee multiplied by the number of days the car was rented.

We can set up the equation as:

138 = 42 + 12x (where x is the number of days the car was rented)

To find the number of days, we can subtract the initial fee from both sides of the equation:

138 - 42 = 12x

96 = 12x

Then we can divide both sides by 12 to solve for x:

x = 8

So the customer rented the car for 8 days.

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12 cups of water should be mixed to 6 scoops of fruit mix and the unit rate is 0.5 scoops per cup

Unit rate is the ratio of two different units, with denominator as 1. For example, kilometer/hour, meter/sec, miles/hour, salary/month, etc. Arithmetic is probably the most basic and ancient branch of mathematics and is quite commonly used in our day-to-day life.

Given here: Ryan is making a fruit drink. The directions say to mix 3 cups of water with 1 1/2 scoops of powdered fruit mix.

Thus the ratio of the number of cups of water to scoops of powdered fruit mix is equal to 3:3/2=2:1

∴ With 6 scoops of fruit mix we will be required to mix 12 cups of water.

Again unit rate ( scoops of fruit mix / cup of water)= 1.5/3

                                                                                   =0.5 scoops/cup of water

The unit rate means the number of scoops that are required to be mixed with  a cup of water.

Hence, 12 cups of water should be mixed to 6 scoops of fruit mix and the unit rate is 0.5 scoops per cup

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The length of the median of the trapezoid is 12.

The area of a trapezoid is given by the formula (1/2)h(b1+b2), where h is the height and b1 and b2 are the lengths of the bases. We know that the area is 60, the height is 5 and b1 = b2 + 4.

So, we can write the equation as follows:

(1/2) * 5 * (b1 + b2) = 60

To find the length of the median of a trapezoid, we need to find the length of the mid-segment. The mid-segment of a trapezoid connects the midpoints of the non-parallel sides. The length of the midsegment is the average of the lengths of the bases.

So, the length of the median is (b1 + b2) / 2.

We can substitute the value of the area to find the lengths of the bases and then use that to find the length of the median.

(1/2) * 5 * (b1 + b2) = 60

(1/2) * 5 * (b1 + b2) = 60

b1 + b2 = 24

b1 = b2 + 4

b2 = 24 - b1

b1 = (24 - b1) + 4

b1 = 24 - b1 + 4

b1 = 28 - b1

b1 = 28 - (24 - b1)

b1 = 4 + b1

b1 = b2 + 4

b1 = b1

So, the lengths of the bases are equal to 14 and 10.

Length of median = (14 + 10) / 2 = 12.

Therefore, The length of the median of the trapezoid is 12.

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The explanation of each of the term are defined below.

The order of each reactant is known as the reaction orders in a rate law describe the mathematical dependence of the rate on reactant concentrations.

The term rate law expression in math is defined as the expression in which reaction rate is given in terms of molar concentration of reactants with each term raised to some power in which may or may not be same as the stoichiometric coefficient of the reacting species in a balanced chemical equation.

The term overall order of the reaction is known as  the sum of orders for each reactant.

Finally value of the rate constant means the rate constant is temperature dependent.

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The required Confidence interval for the given data is CI = 0.6 - 0.7 ± 1.96[tex]\sqrt{\frac{0.6(1-0.6)}{50}+\frac{0.7((1-0.7)}{50} }[/tex].

Hypothesis testing is a methodical process for determining whether research study findings are consistent with a specific idea that pertains to a population. To evaluate a hypothesis about a population, hypothesis testing uses sample data.

We have,

x1 = 30,  x2 = 35

n1 = 50, n2 = 50

p1 = x1/n1 = 30/50 = 0.6

p2 = x2/n2 = 35/50 = 0.7

Then,

at α= 0.05, the critical value taken by table of z

Zc = 1.96

CI =[tex]P_{1}-P_{2}[/tex] ±[tex]\sqrt{\frac{P_{1}(1-P_{1})}{n_{1}}+\frac{P_{2}((1-P_{2})}{n_{2}} }[/tex]

CI = 0.6 - 0.7 ± 1.96 [tex]\sqrt{\frac{0.6(1-0.6)}{50}+\frac{0.7((1-0.7)}{50} }[/tex]

This is our needed answer,So option (D) is correct.

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The rate of change of the surface area of the sphere is 1903784*pi cubic inches^2 per minute.

The volume of a sphere can be found using the equation V = 4/3 * pi * r^3, where V is the volume and r is the radius of the sphere.

The surface area of a sphere can be found using the equation A = 4 * pi * r^2, where A is the surface area.

To find the rate of change of the surface area, we can use the chain rule of calculus:

dA/dt = dA/dr * dr/dt

We know that dr/dt = 2409 cubic inches per minute (from the problem statement). To find dA/dr, we can take the derivative of the surface area equation with respect to r:

dA/dr = 8 * pi * r

Now we can substitute these values into the chain rule equation:

dA/dt = 8 * pi * r * dr/dt

When the radius of the sphere is 99 inches, we can substitute this value into the equation:

dA/dt = 8 * pi * 99 * 2409 cubic inches^2 per minute

So, the rate of change of the surface area of the sphere is 1903784*pi cubic inches^2 per minute.

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The inequality which represents the number and each type of clothing you can buy is 10.25x + 17y ≤ 50

This inequality represents the maximum amount of money you can spend at the store, given the cost of shirts and pants, and the number of each type of clothing you buy.

The x represents the number of shirts, and the y represents the number of pants. The inequality states that the total cost of the shirts (10.25x) plus the total cost of the pants (17y) must be less than or equal to $50.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality.

Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

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ok yx goes opposite side do cross multiplication

Answer:

The answer is Inconsistent.

Step-by-step explanation:

There is no solution.

Answer:

1. 10

2. 12

Step-by-step explanation:

1. 8² + 6² = y² (Taking the unknown side as y)

64 + 36 = 100

y² = 100

y = 10

2. 5² + x² = 13² (Taking the unknown side as x)

x² = 13² - 5²

= 169 - 25

= 144

x² = 144

x = 12

A collector offers to buy state quarters for 2000% of their face value. The face value of each quarter is 25 cents. At that rate 20 dollars Bryden will get for his four state quarters.

In the given question, a collector offers to buy state quarters for 2000% of their face value.

The face value of each quarter is 25 cents.

We have to find at that rate how many dollars Bryden will get for his four state quarters.

As given that,

Collector buy state quarters = 2000% of their face value

We can write 2000% as 20×100%.

It means that state quarters is 20 times of their face value.

As we know that, 4 quarter is equal to the one dollar. So,

Bryden get for his four state quarters = 20×1 dollars

Bryden get for his four state quarters = 20 dollars

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The equation P = -0.02n^2 + 3.4n - 16 represents the profit, P, in thousands of dollars for a small independent movie company as a function of the number of DVD copies produced, n, in thousands.

The equation is a quadratic equation, which means it is a polynomial equation of degree 2. The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b and c are constants and x is the variable. In this case, the equation can be written as P = -0.02n^2 + 3.4n - 16, where P is the variable, and -0.02, 3.4, and -16 are the constants.

The first term in the equation is -0.02n^2, which represents the cost of producing the DVD copies. As n increases, the cost of production also increases, and the coefficient -0.02 represents that the cost of production is directly proportional to n^2. The negative sign in front of the term indicates that as the number of copies increases, the cost of production also increases and thus the profit decreases.

The second term in the equation is 3.4n, which represents the revenue generated by the sale of the DVD copies. As n increases, the revenue generated also increases, and the coefficient 3.4 represents that the revenue is directly proportional to n. The positive sign in front of the term indicates that as the number of copies increases, the revenue generated also increases and thus the profit increases.

The last term in the equation, -16, represents the fixed costs associated with producing the DVD copies, such as overhead costs, marketing and distribution costs, etc. These costs are not directly related to the number of copies produced and are constant regardless of how many copies are produced.

In summary, the equation P = -0.02n^2 + 3.4n - 16 represents the profit for a small independent movie company as a function of the number of DVD copies produced. The profit is affected by the cost of production, revenue generated from sales, and fixed costs. As the number of copies increases, the cost of production increases, the revenue generated increases, and the fixed costs remain constant. The profit is the difference between the revenue generated and the costs incurred.

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Answer:

h = 32 cm

Step-by-step explanation:

the area (A) of a trapezium is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the distance between the parallel sides b₁ and b₂

given A = 1440 , b₁ = 54.6 , b₂ = 35.4 , then

[tex]\frac{1}{2}[/tex] h (54.6 + 35.4) = 1440 ( multiply both sides by 2 to clear the fraction )

h × 90 = 2880 ( divide both sides by 90 )

h = 32

the distance between the parallel sides is 32 cm

The two numbers are 4 and -4, and their product is 4 * -4 = -16, which is the minimum value.

Generally, To find two numbers whose difference is 8 and whose product is a minimum, we can use algebra. Let's call the two numbers x and y. We know that:

x - y = 8 (the difference between the two numbers is 8)

To find the product of the two numbers, we can multiply x and y:

xy = x(x - 8) = x^2 - 8x

To find the minimum value of the product, we can take the derivative of this expression with respect to x and set it equal to 0:

d(xy)/dx = 2x - 8 = 0

Solving for x, we find that x = 4.

Therefore, one of the numbers is 4. We can use the equation x - y = 8 to find the other number:

4 - y = 8

y = -4

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Therefore , the solution of the given problem of variable comes out to be where weights are the probability of that outcome.

A variable is a quality that may be measured and take on several values. A few examples of variables are height, age, salary, province of birth, school grades, and kind of dwelling.

Here,

Given :

A discrete random variable's anticipated value

So, in order to determine the expected value of a discrete random variable,

we may infer from the provided data that it is calculated as a weighting factor of the potential outcomes of that variable,

where weights are the probability of that outcome.

Therefore , the solution of the given problem of variable comes out to be where weights are the probability of that outcome.

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