Consider the simultaneous equations
3x² + 2xy = 4
x + y = a
where a is a real constant.
Find the complete set of values of a for which the equations have two distinct real solutions for x.
There are no values of a.
-2 < a < 2
-1 < a < 1
a = 0
a < -1 or a < 1
a < -2 or a < 2
All real values of a

The nth term of the quadratic sequence is aₙ = n² + 2n

What is a quadratic sequence?

Finding the nth term rule of a quadratic sequence: The nth term rule of a quadratic sequence can always be written in the form an² + bn + c.

To find this rule, we need to find a, b and c

Given data ,

Let the expression be represented as = A

Now , the value of A is

A = 3 , 8 , 15 , 24 , 35 ..

Now , taking the difference of the second term and first term , we get

d₁ = 8 - 3 = 5

d₂ = 15 - 8 = 7

d₃ = 24 - 15 = 9

So , the difference of the numbers in the sequence is odd multiples

Therefore , the sequence goes in the multiples of ( n + 2 )

Now , when n = 1

a₁ = 3

when n = 2

a₂ = 8

So , a₂ = n ( n + 2 )

substituting the value for n = 2 , we get

a₂ = 2 ( 2 + 2 )

a₂ = 2 x 4

a₂ = 8

when n = 3

a₃ = 15

So , a₃ = n ( n + 2 )

substituting the value for n = 3 , we get

a₃ = 3 ( 3 + 2 )

a₃ = 3 x 5

a₃ = 15

Therefore , the nth term of the quadratic sequence will be

aₙ = n ( n + 2 )

aₙ = n² + 2n

Therefore , the sequence is aₙ = n² + 2n

Hence , The nth term of the quadratic sequence is aₙ = n² + 2n

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The probability of rejecting the null when the alternative is true is d. 0.67

Given :

If α=.10 and β=.33, then the probability of rejecting the null when the alternative is true is .

Probability :

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

Null hypothesis :

A null hypothesis is a type of statistical hypothesis that proposes that no statistical significance exists in a set of given observations.

we know that ,

probability = 2 * 0.33 + 0.01

= 0.66 + 0.01

= 0.67

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Answer:

1/4

Step-by-step explanation:

The square root of 16 is 4, so its the same with fractions.

Answer:

(-4,5)

Step-by-step explanation:

The point (3, 9) is the point which satisfies both the equation.

What is an equation?

In arithmetic, an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =

Main body;

A)According to the given equation:

y = 3x  

y = 1 , x = 3

y = 2 , x = 6

y = 3 , x = 9

for the equation ,

y = x+6

y = 6 , x = 0

y = 5 , x = -1

y = 4 , x = -2

B) as y = 3x substitute it in other equation

3x = x+ 6

2x =6

x = 3

as y = 3x

y =3*3

y = 9

Hence ,point (3, 9) is the point which satisfies both the equation.

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The coordinate of point D and point E will be (x, y) and (-x, y), respectively.

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line in the m:n ratio, finding the mid-point of the line, etc.

Let the coordinate of the point D be (x, y).

Point E has a similar y-coordinate as point D. Then the ordinate of the points will be the same.

And the x-direction of point E is something contrary to the x-direction of point D. Then the coordinate of point E will be (-x, y).

The coordinate of point D and point E will be (x, y) and (-x, y), respectively.

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Answer:

16.7

Step-by-step explanation:

YX is similar to AX

XZ is similar to XB

so the triangle AXB is similar to YXZ thus AB is YC

The same goes for the rest of the triangles  (YAC and CBZ)

See image attached.

The number of arrangements when the order is considered is 12, Number of ways when the order is not considered is 6.

By choosing some items from a set and creating subsets, permutation and combination are two approaches to express a collection of things.

The act of placing every member of a set into a certain sequence or order is known as permutation.

The combination is a method of choosing things from a group in which (unlike permutations) the order of the choices is irrelevant.  

The formula for Permutations is given by

The formula for Combinations is given by

Here we have

4 letters A, B, C, and D  

We need to choose 2 letters from the given 4 letters  

When the order of the choices is taking consideration we use the formula of Permutations  

The number of ways of arrangements,  ⁴P₂ = (4!)/(4-2)!  

= [tex]\frac{4\times 3\times\ 2!}{2!}[/tex]  = [tex]4 \times 3[/tex]  = 12

When the order of the choices is not taking consideration we use the formula of Combinations

Number of ways of arrangements, ₄C₂ = (4!)/2!(4 - 2)!  

= [tex]\frac{4\times 3 \times \ 2!}{2! \times 2!}[/tex] = [tex]\frac{4\times 3 }{2 \times 1 }[/tex]  = [tex]2\times 3[/tex]  = 6  

Therefore,

The number of arrangements when the order is considered is 12, Number of ways when the order is not considered is 6.

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From the values provided and basic arithmetic operations on the fractions, The answer is 4.8 gallons.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

milk brought = x

used in one recipe = 2.4

1/4 th of remaining milk = (x-2.4)/4

remaining at end = 3/8 of x

final equation,

x-(2.4+(x-2.4)/4)=3x/8

5x/8=2.4+x/4-3/5

5x/8=1.8+x/4

3x/8=1.8

x=4.8 gallons

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Answer:

$153

Step-by-step explanation:

Multiply the 2 numbers

To determine which graph represents the function [tex]$f(x)=\frac{2 x-1}{x-1}$[/tex]make following steps:

What is  function?

A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x^2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.

Four main categories may be used to classify different sorts of functions. dependent upon element Function is defined as one to one, many to one, onto, one to one and into function.

1. The vertical asymptote is x=1.

2. Simplify the function[tex]f(x)=\frac{2 x-1}{x-1}=\frac{2 x-1-1+1}{x-1}=\frac{2(x-1)+1}{x-1}=2+\frac{1}{x-1}$[/tex].

Then the horizontal asymptote is y=2.

Only option C contains graph with such asymptotes.

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The missing length in the given figure is 14.

A ratio in mathematics depicts the product of two numbers. For instance, the proportion of oranges to lemons in a serving of fruit is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3). In a similar vein, the ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8. (or 3:4). (or 4:7).

Any number of numbers, including counts of people or things, weights, lengths, and times, among other values, can be a component of a ratio. In settings, both numbers are often restricted to positive values.

A ratio's two constituent numbers can be specified as "a" and "b," or they can both be omitted.

From the given figure,

AC/BC=EC/DC

28+x/18=x/6

28+x=3x

2x=28

x=14

Therefore, the missing length in the given figure is 14.

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While constructing a confidence interval for the mean, when the population standard deviation is unknown, then we use normal distribution .

The error bound EBM and confidence interval are calculated using a standard normal distribution when the population standard deviation is unknown. We must determine the value of z that places an area in the centre of the standard normal distribution Z N that is equal to the confidence level (in decimal form) (0, 1).

We rarely know the population standard deviation in practise. When the sample size was huge is the , statisticians were not hindered by this. As an estimate for, they used the sample standard deviations, and they then carried out the same steps as before to compute a confidence range that produced near enough findings.

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Answer: 2* (2w + w) = 60

Step-by-step explanation: I believe this is correct because to find the perimeter, we need to add both length and width, so this answer is the only one that expresses 2w + w being multiplied by 2 to get 60. I hope this helped.

Answer:

guy or girl

Step-by-step explanation:

The expression to model the amount of money will be 175 ^ 1.02^t.

An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

Since Iris’s checking account pays a simple interest at 2% per year. She has $175 in her account.

The function to model the amount of money in her checking account at any time will be:

= 175 ^ (1 + 2%)^t

= 175 ^ (1 + 0.02)^t

= 175 ^ 1.02^t

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The circle's radius is the same as the radius of the circle whose equation is x2 + y2 = 9.

A circle's standard equation is written as:

x² + y² + 2gx + 2fy + C = 0

The radius of the center is (-g, -f) and radius = √g² + √f² - C

Given a circle with the equation,

x² + y² - 2x - 8 = 0

Find the circle's center.

2gx = -2x

2g = -2

g = -1

Likewise, 2fy = 0.

f = 0

(-(-1), 0) = Centre (1, 0)

This demonstrates that the circle's center is on the x-axis.

r = radius

= √g² + √f² - C

By substituting,

radius = √1² + 0² - (-8)

          =√9  

          = 3 units radius

The circle's radius is three units.

The radius of the circle x² + y² = 9 is written as:

r² = 9

radius = 3 units

As a result, the radius of this circle equals the radius of the circle whose equation is x² + y² = 9.

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Decagon has a total of 5 reflection symmetries

A reflection symmetry of a shape is a line that divides the shape into two halves that are mirror images of each other. To find the number of reflection symmetries of the decagon, we can draw lines through the center of the decagon that pass through pairs of opposite vertices.

We can draw a total of 5 lines through the center of the decagon that pass through pairs of opposite vertices. Each of these lines is a reflection symmetry of the decagon. Therefore, the decagon has a total of 5 reflection symmetries.

A rotational symmetry of a shape is a rotation about a fixed point that leaves the shape unchanged.

To find the number of rotational symmetries of the decagon, we can count the number of times we can rotate the decagon about its center by 36 degrees (which is the central angle of the decagon) and obtain the same shape. In this case, we can rotate the decagon about its center by 36 degrees 10 times and obtain the same shape each time.

A decagon shaped like a five-pointed star has 10 sides and 5 vertices, and it looks like this:

unitsize (1.5 cm);

pair A, B, C, D, E, F, G, H, I, J;

A = dir(108);

B = dir(72);

C = dir(36);

D = dir(0);

E = dir(-36);

F = dir(-72);

G = dir(-108);

H = dir(-144);

I = dir(-180);

J = dir(-216);

draw(A--B--C--D--E--F--G--H--I--J--cycle);

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Answer: y=2

Step-by-step explanation:

6y-8=3y-2

3y=6

y=2

Answer:

ijsjsjdjdjjejjeks she e nsjksid the Earth travels in around the sun 6.2 Seasonal changes 6.3 Plants and animals are

Step-by-step explanation:

www2 and I 3333333 uth the sun is a bit better now and the Sun 6.2 is better off the moon

The value of the expression 2x+3 when x = 3 is 9.

What is linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given linear equation is

x + 2 - 6x = -13

Combine like terms:

(x - 6x) + 2 = -13

-5x + 2 = -13

The additive inverse of 2 is -2.

Add -2 on both sides:

-5x + 2 -2 = -13 -2

-5x = -15

Divide both sides by -5:

-5x/-5 = -15/-5

x = 3

Putting x = 3 in the expression 2x + 3

2x + 3 = (2×3) + 3

2x + 3 =6 + 3

2x + 3 = 9

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The 85th percentile of a normal distribution is the score that is greater than or equal to 85% of the scores in the distribution. This means that the score at the 85th percentile is the same as the score that would be earned by the top 15% of individuals in the distribution.

To find the score at the 85th percentile, we can use the standard normal distribution table or use a calculator to find the z-score corresponding to the 85th percentile. The z-score is the number of standard deviations that a score is above or below the mean of the distribution.

Using a calculator or table, we find that the z-score corresponding to the 85th percentile is 1.04. Since the mean of the distribution is 100 and the standard deviation is 15, this means that the score at the 85th percentile is 100 + (1.04 * 15) = 120.4.

Therefore, the score of an individual who is at the 85th percentile on the Weshcler IQ test is 120.4.

The lowest price that Mike should pay for 7 days' juice consumption is £6.16.

In order to calculate the cost of one item, divide the total cost of items by the total number of items. It is also called the unit rate of that item.

The per day requirement of Mike is 2/5 liters.

Then, for 7 days the requirement is 2/5 × 7 = 14/5 liters.

The rate of juice for 2 liter and 1 liter carton are given as £4.40 and  £2.60 respectively.

Then, the unit rate for both the carton is given by 4.40/2 = £2.20 and £2.60 respectively.

Since, the two liter carton has less unit rate, it can be used for 7 days consumption.

Now, the lowest price paid by mike is given as,

Unit rate of 2 liter carton × Total requirement of milk for 7 days

⇒ 2.20 × 14/5

⇒ 6.16

Hence, the lowest price paid by mike is £6.16.

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When the floor is 2.30 m in front of a vertical plane mirror and the bottom edge of the mirror is 38 cm above the floor, the horizontal distance from the mirror's base to the wall is 0.6935 m.

Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circle functions) that make up trigonometry.

Here,

Perpendicular Length,

=Vertical Distance of eyes - Vertical distance of the bottom edge of the mirror

=1.64-0.38

=1.26 m

Angle of Reflection,

= Perpendicular Distance / Distance between the person and mirror

tan θ=1.26/2.30

tan θ=0.548

θ=tan⁻¹(0.548)

θ=28.72°

Angle of Incidence = 90 degrees - angle of reflection

=90-28.72

γ=61.28°

Angle of incidence,

=Horizontal distance to floor / height of mirror

tan 61.28°=x/0.38

x=0.38*tan 61.28°

x=0.38*1.825

x=0.6935 m

The horizontal distance to the base of the wall is 0.6935 m when the floor stands 2.30 m in front of a vertical plane mirror whose bottom edge is 38 cm above the floor.

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Answer:

x² +y² -10x -8y +21 = 0

Step-by-step explanation:

try desmos graph

Increasing the area from 400 to 600 (50%) results in an increase in cost from 500 to 750 (50% increase), which shows that the cost is not proportional to the area.

In a situation where cost is proportional to area, the relationship between cost and area is said to be directly proportional. Direct proportionality means that if the value of one variable (in this case, area) is multiplied by a certain factor, then the other variable (in this case, cost) will also be multiplied by the same factor. The mathematical formula for direct proportionality is [tex]y = kx,[/tex] where y and x are the two variables, and k is the constant of proportionality. If the relationship between the variables is not proportional, then it is a non-proportional relationship.

The objects are proportional if increasing one quantity by a certain factor results in the other quantity increasing by the same factor. In this case, cost is proportional to area if doubling the area would double the cost. Based on the table, we can see that the cost is not proportional to the area since the cost does not increase by the same factor as the area. For example, increasing the area from 400 to 800 (double) results in an increase in cost from 500 to 1000 (also double). However, increasing the area from 400 to 600 (50%) results in an increase in cost from 500 to 750 (50% increase), which shows that the cost is not proportional to the area.

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A function assigns the values. The function is f(x) = (8x - 8)/(x² + 2x).

A function transfers each element's value from one set to a particular element in another set.

There is a denominator and a numerator in a rational function.

The x-values that the function approaches but never reaches are known as vertical asymptotes. We can get the vertical asymptotes by setting the denominator to zero.

Since x=-2 and x=0 are the vertical asymptotes, our function's denominator will be x(x+2) = x2+2x.

Y values that the function approaches but never reaches are known as horizontal asymptotes. The degree of the numerator must be less than the degree of the denominator since the horizontal asymptote is y=0. Our numerator will be x - 1 because the x-intercept is equal to 1.

At this time, One can assume that the function is f(x) = (x - 1)/(x2+2x).

Next, we must apply the f(2)=1 condition. If we enter x=2, f(x) ought to be equal to 1. However, we must multiply the function's right side by a constant called C.

Then, the constraint f(2)=1 must be used. F(x) should be equal to 1 if we substitute x=2. The right side of the function must be multiplied by a constant C, though.

1 = C(2 - 1)/(2²+2(2))

Solve for C.

1 = C / 8\s8 = C

Consequently, the equation will be f(x) = [8(x - 1)] / [(x2 + 2x)].

f(x) = (8x - 8) / (x² + 2x)

Thus, f(x) = (8x - 8)/(x2 + 2x) is the function.

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The partial fraction decomposition of the function is given as follows:

A/x + B/x² + C/(5x² + 9) + D/(5x² + 9)².

The function in this problem is defined as follows:

(x^4 + x² + 1)/(x²(5x² + 9)²)

Then the partial fraction decomposition is built considering the terms of denominator, as follows:

When a term is elevated to a power, the terms with the lower powers also have to be considered. For example, for the denominator x², x is also considered, hence the denominators are given as follows:

Then, considering the coefficients A, B, C and D, the partial fraction decomposition of the function is given as follows:

A/x + B/x² + C/(5x² + 9) + D/(5x² + 9)².

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The expression for the area that includes an exponent is 6² + (6 × 2) + 24

Area of the entire figure is 72 square inches

The dimension of the entire figure is 9 inches by 8 inches

From the question, we are to write an expression for the area of the entire figure

Area of the entire figure = Area of green shape + Area of white shape + Area of blue shape

Area of the entire figure = 6² + (6 × 2) + 24 square inches

The expression is 6² + (6 × 2) + 24

Thus,

Evaluating

Area of the entire figure = 6² + (6 × 2) + 24

Area of the entire figure = 36 + 12 + 24

Area of the entire figure = 72 square inches

b. The dimension of the entire figure

Width of the entire figure = Length of the green square + Width of the white rectangle

Width of the entire figure = 6 inches + 2 inches

Width of the entire figure = 8 inches

Then,

Length of the entire figure = Length of the white rectangle + Width of the blue rectangle

First, we will determine the width of the blue rectangle

Using the formula,

Area = l  × w

Where l is the length

and w is the width

24 = (2 + 6) × w

24 = 8 × w

w = 24/8

w = 3 inches

Therefore,

Length of the entire figure = 6 inches + 3 inches

Length of the entire figure = 9 inches

Hence, the dimension is 9 inches by 8 inches

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