Y = 1/4(4)^x ; x = 3/2

When deciding whether to use substitution or elimination to solve a system of linear equations, it is important to consider the size and complexity of the system.

Substitution is generally recommended for systems with two equations and two variables, as it can be a simpler and quicker approach. For larger systems with more equations and/or variables, elimination may be a better option as it can reduce the number of steps required to solve the system.

When using either method, it is important to keep track of all the steps you take and double check your work for accuracy. Additionally, both methods involve solving for one variable in terms of the others, so if you are dealing with an equation that already has only one unknown variable, then substitution could be the best approach. Ultimately, it is important to assess each situation individually and decide which method would be most effective.

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A falling object's height above the ground at time t is calculated using the formula s (t) = 5t2 + v0t + s0, where s is measured in metres, t is measured in seconds, v0 is the starting velocity in metres per second, and s0 is the starting location in meters. Thus, option D is correct.

((0 - 24t2) - 30t) + 4 = 0 Pull out like factors:  -16t2 - 30t + 4 =   -2 • (8t2 + 15t - 2)

Factoring 8t2 + 15t - 2

The last term, "the constant", is -2 Multiply the coefficient of the first term by the constant   8 • -2 = -16. Rewrite the polynomial splitting the middle term using the two factors found in step 2 above1 and 16

                  8t2 - 1t + 16t - 2

Add up the first 2 terms, pulling out like factors:

                 t • (8t-1)

                2 • (8t-1)

Add up the four terms of t • (8t-1)

              (t+2) •  (8t-1)

Therefore, 112 s the values of b.

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The equations kx – 2y = 3 and 3x + y = 5 will have a unique solution for k ∈ R - {-6}

Here we have equations  kx – 2y = 3 and 3x + y = 5

Here we need to find a value for k such that the following equations have a unique solution.

a system of 2 linear equations

a₁x + a₂y + a₃ = 0

b₁x + b₂y + b₃ = 0

does not have a unique solution only when

a₁/b₁ ≠ a₂/b₂

Here

k = a₁,          -2 = a₂

3 = b₁            1 = b₂

Hence,

k/3 ≠ -2

or, k ≠ -6

Hence the equations will have a unique solution for k ∈ R - {-6}

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Complete Question

For what value of k do the equations kx – 2y = 3 and 3x + y = 5 represent two lines intersecting at a unique point?

The inequality you provided is a linear inequality in one variable x. To find the solution to this inequality, we need to follow these steps:

First, we will simplify the inequality by combining like terms on the left side:

5 + 4x <= 6x + 4

4x <= x + 9

Next, we need to get x alone on one side of the inequality by subtracting x from both sides:

4x-x <= 9

3x <= 9

We will divide both sides of the inequality by 3:

x <= 3

The final step is to check our solution by plugging it back into the inequality and making sure that it satisfies the inequality: 5 + 4(3) <= 6(3) + 4

5 + 12 <= 18 + 4

17 <= 22  which is true

So the solution to the inequality 5 + 4x <= 6x + 4 is x <= 3. It's worth mentioning that this is the only solution that this inequality has since it's a linear inequality which has only one solution.

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1. The correct answer is 46 percent, 2. The correct answer is .07, 3. The correct answer is (34%,58%), 4. The correct answer is (32%,60%)

The term "standard error" is used to refer to the standard deviation of various sample statistics, such as the mean or median. For example, the "standard error of the mean" refers to the standard deviation of the distribution of sample means taken from a population. The smaller the standard error, the more representative the sample will be of the overall population.

The relationship between the standard error and the standard deviation is such that, for a given sample size, the standard error equals the standard deviation divided by the square root of the sample size. The standard error is also inversely proportional to the sample size; the larger the sample size, the smaller the standard error because the statistic will approach the actual value.

1. Let's calculate the percentage or proportion of patients that were dogs:

p = (7 + 4 + 5 + 5 + 2)/50 = 23/50 = 0.46

The correct answer is 46%

2. Let's estimate the standard error, using the given formula, this way:

S.e = √ (0.46 * 0.54)/50 = √0.049 = 0.07

The correct answer is .07

3. Let's calculate the confidence limits of the 90% confidence interval, this way:

Confidence limits = proportion +/- 1.645 * standard error

Confidence limits = 0.46 +/- 1.645 * 0.07

Confidence limits = 0.46 +/- 0.12

Confidence limits = 0.34, 0.58

The correct answer is (34%,58%)

4. Let's calculate the confidence limits of the 95% confidence interval, this way:

Confidence limits = proportion +/- 1.96 * standard error

Confidence limits = 0.46 +/- 1.96 * 0.07

Confidence limits = 0.46 +/- 0.14

Confidence limits = 0.32, 0.60

The correct answer is (32%,60%)

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Answer:

AC ≈ 4.28

Step-by-step explanation:

using the tangent ratio in the right triangle

tan35° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{3}{AC}[/tex] ( multiply both sides by AC )

AC × tan35° = 3 ( divide both sides by tan35° )

AC = [tex]\frac{3}{tan35}[/tex] ≈ 4.28 ( to the nearest hundredth )

The dimensions of the cylinder are -

{r} = √500/πh

{h} = (500/r²)

Given is the volume of the cylinder as -

V = 500 cm³

We can write -

V = 500

So, we can write -

πr²h = 500

So, we can write -

{r} = √500/πh

{h} = (500/r²)

Therefore, the dimensions of the cylinder are -

{r} = √500/πh

{h} = (500/r²)

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{Question in english -

What are the measurements of a cylinder (height, radius) if its volume is 500 cm3}

The value of Edubucks would be determined by a variety of factors, including:

Additionally, speculation and sentiment could also play a role in determining the value of Edubucks.

Edubucks is a virtual currency created by the educational platform Edmodo. It is used to reward students for completing tasks and participating in activities on the platform.

Also, Edubucks could also be described as the virtual currency created to motivate or compensate the effort made on certain task done by students which is meant to boost their morales and aid their eagerness to doing more.

Therefore, the correct answer is as given above

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In the realm of real numbers, there is no solution for square root of any negative number. Therefore, there is no negative range for the function f(x) = sqrt(x). The range extends from 0 to any number that is positive.

The range is [0,]=y: y≥0}. By looking at its defining equation, f(x)=x2, we can algebraically determine its domain. We are aware that the square root of a negative number cannot be taken. As a result, the expression that lies beneath the radical has to be positive or zero, not negative.

However, negative square roots are also possible. Consequently, the number -6 can be a principal square root of the number 36, but not a square root. As a result, the principal square root and the negative square root both have the same number.

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The bias that is taken care of here is that; Some of the population may not have access to other types of phones. Option A

When we talk about a bias in research we mean the kind of scenario that is able to cause the result of a research to become lobe sided. In other words, it is that which introduces inaccuracy to a research.

A lot of people if not everyone has access to a mobile phone and this would help more people to be able to participate in the interview. Some of these people may not have any of the other kinds of phone.

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Answer:

A

Step-by-step explanation:

took the test

The complex conjugate of 4 − 3i is;

4 - (-3i) = 4 + 3i .

Now, According to the question:

The complex number is basically the combination of a real number and an imaginary number. The complex number is in the form of a+ib, where a = real number and ib = imaginary number. Also, a,b belongs to real numbers and i = √-1.

Hence, a complex number is a simple representation of addition of two numbers, i.e., real number and an imaginary number. One part of it is purely real and the other part is purely imaginary.

The complex conjugate of a + bi is a - bi

So,  the complex conjugate of 4 − 3i is;

4 - (-3i) = 4 + 3i .

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Answer: p(2√2) = 17

Step-by-step explanation:

Given,

p(x) = x² + 2√2x + 1....(i)

To find p(2√2) , we need to substitute x=2√2 in the given equation

p(2√2) = (2√2)² + 2√2(2√2) + 1

            = 8 + 8 + 1

            = 17

So p(2√2) is 17

Answer: 17

Step-by-step explanation:

[tex]P(x) = x^{2} + 2\sqrt2x + 1[/tex]

[tex]P (2\sqrt{2}) = 2\sqrt{2})^2 + 2\sqrt{2}*2\sqrt{2} + 1[/tex]

[tex]P (2\sqrt{2}) = 8 + 8 + 1[/tex]

[tex]P (2\sqrt{2}) = 17[/tex]

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Answer:

When you solve a linear equation and get 2=2, this means that the equation is true and there is no solution. This is because both sides of the equation are equal, so there is no value that can satisfy both sides of the equation at the same time.

Answer: It means that the equation is balanced and both sides have the same value (they are equal)

The cost of the whole group would be: (24 * p) + 12 or 24p + 12.

The expression (24 * p) + 12 represents the total cost of the group. The "24 * p" part represents the cost of the individual tickets, with "p" representing the number of people in the group. The "12" represents the one-time group registration fee. The expression calculates the total cost by multiplying the number of people in the group by the cost of an individual ticket, and then adding the group registration fee to that total.

Specifically, the operation being used is arithmetic, specifically multiplication and addition. The expression provided is used to calculate the total cost for a group by multiplying the number of people in the group by the cost of an individual ticket and then adding the group registration fee to that total. This is a basic mathematical operation that is a part of arithmetic.

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Answer:

-f(x)

Step-by-step explanation:

Figure H is just Figure G reflected across the x-axis meaning that you just have to slap a negative symbol in front of whatever function gave you Figure H.

5n³ + 4n² -4n + 720 is the difference between these two given expressions.

Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.

Given a system of equation 3n³+ 4n²– 9 and -2n³+ 4n – 9³

We need to find the difference between These given Systems of equation

Difference = 3n³+ 4n²– 9 -( -2n³+ 4n – 9³)

Difference = 3n³+ 4n²– 9 + 2n³- 4n + 9³

Difference = 5n³ + 4n² -4n + 720

therefore, The difference between these two given equations is 5n³ + 4n² -4n + 720.

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If a polynomial function can be factored, you can factor it and set each component's value to zero to find its zeros.

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The sign of the discriminant [tex]b^{2}-4ac[/tex] of a quadratic equation determines how many real solutions there are to that quadratic equation.

The value of the expression is the discriminant of a quadratic equation in standard form : This quantity specifies how many different ways a quadratic problem can be solved.

Solutions to quadratic equations can be 0, 1, or 2. If the discriminant has a positive value, then there are two genuine solutions for x, and the graph of the solution has two different x-intercepts. There is only one actual solution for x if the discriminant's value is zero, which means that the solution's graph only has one x-intercept.

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Yes, 36 is a perfect square because 36 = 2² × 3², all numbers are in the power of two. This means that the square root of 36 is a positive integer. Therefore, 36 is a perfect square.

Perfect squares are special numbers in mathematics that have a pair of integer factors that are equal to each other. A number N is called a perfect square if it is equas to product of number, x with itself. Formula for perfect square,

N = x²

this implies that if N is equals to second power of a whole number then N is called perfect squares. We have, N = 36 and we have to check that it is perfect square or not. For this, firstly determine the prime factors of 36, that is 36 = 2× 2× 3 × 3 . Now, 36 = 2² × 3² = 6² ( since, 2 and 3 are prime numbers, a²×b² = (ab)² ). Therefore, 36 is equals to square of whole number 6. So, 36 is perfect square.

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Complete question:

Why is 36 a perfect square? or Is 36 a perfect squares?

The required Venn diagram for the given condition has been shown.

A Venn diagram is a graphical representation of the relationship between sets or groups of items. It consists of overlapping circles, each representing a different set, with the overlapping areas showing the items that belong to both sets.

Here,
U = 0 ≤ n ≤ 30
A = 2 ≤ n ≤ 30  [multiple of 2]
B = 3 ≤ n ≤ 30 multiple of 3
From above, the rectangle represents the universal set u, and the circle represents the two subsets A and B.

Thus, the required Venn diagram for the given condition has been shown.

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The binomial factor for the given expression is x = 4.

In mathematics, a binomial is an expression that is made up of two terms. The binomial factor of an expression is the part of the expression that is written in the form (x - a)^n, where a is a constant and n is a positive integer.

The binomial factor of x³ is x³. The equation x³ = 64 is not a binomial equation, as it does not have the form (x - a)^n = 0, where a is a constant and n is a positive integer. If you are trying to solve for x in the equation x³ = 64, one solution is x = 4. However, there are also three other solutions, which are the cube roots of 64 that are not real numbers (they are complex numbers).

Hence, The binomial factor for the given expression is x = 4.

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The product of  398×5 is equal to (400-2)×5

According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

Given here: The product of two numbers as 398×5

Now 398 can be rewritten as 400-2

Thus the expression 398×5 =(400-2)×5 ( Using distributive property)

                                1990   = 1990

Thus they are also equivalent.

Hence, The product of  398×5 is equal to (400-2)×5

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The angle measure of  m∠B = 24°.

Two angles are supplementary.

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Given:

Two angles are supplementary.

The m∠A is five times the sum of the m∠B plus 7.2°.

That means,

5(B + 7.2) + B = 180

6B = 180 - 36

B = 24.

Therefore, the angle measures of m∠B = 24°.

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Answer:

1449.28

Step-by-step explanation:

To find the principal amount that will amount to Rs. 2000 in 6 years 8 months at a 5% interest rate per annum, we can use the formula for compound interest:

A = P (1 + r/n)^(nt)

Where:

A = final amount

P = principal (the amount we are trying to find)

r = interest rate per annum (in decimal form)

n = number of times interest is compounded per year

t = time in years

So we can substitute these values into the formula and solve for P:

2000 = P (1 + 0.05)^(1 * 6.67)

2000 = P * 1.38

P = 2000/1.38

P = 1449.28

The principal amount that will amount to Rs. 2000 in 6 years 8 months at a rate of interest of 5% per annum is Rs. 1281.97.

The principal amount (P) that will amount to Rs. 2000 in 6 years 8 months at the rate of interest of 5% per annum can be calculated using the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = final amount

P = principal

r = rate of interest (5% per annum = 0.05)

n = number of times the interest is compounded per year (e.g. annually, semi-annually, quarterly)

t = time in years (6.67 years = 6 years 8 months)

Let's assume n = 12 (monthly compounding)

Substituting the values into the formula, we get:

2000 = P(1 + 0.05/12)^(12*6.67)

(To solve for P, we can divide both sides of the equation by the right side of the equation)

P = 2000 / (1 + 0.05/12)^(12*6.67)

P ≈ Rs. 1281.97

Therefore, the principal amount that will amount to Rs. 2000 in 6 years 8 months at a rate of interest of 5% per annum is Rs. 1281.97

It's important to note that this calculation is based on the assumption that the interest is compounded monthly, if the interest is compounded annually or semi-annually the amount will be different.

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The value of m∠DCQ is 31°.

What is a measure of an angle?

An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Here, we have

Given: mAD = 100, & m∠D = 99.

First, we find the measure of arc ABC

we know that

The inscribed angle is half that of the arc it comprises

so

m∠D = (1/2)[arc ABC]

we have

m∠D = 99°

substitute and solve for arc ABC

99° = (1/2)[arc ABC]

198° = [arc ABC]

Now, we find the measure of arc DC

we know that

arc ABC+arc AD+arc DC = 360° -----< by complete circle

substitute the given values

198°+100°+arc DC = 360°

arc DC = 360°-298°

arc DC = 62°

Now, we find the measure of angle DCQ

we know that

The inscribed angle is half that of the arc it comprises

so

m∠DCQ = (1/2)[arc DC]

we have

arc DC = 62°

substitute

m∠DCQ = (1/2)[62°] = 31°

Hence, the value of m∠DCQ is 31°.

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The angle with the largest measure is opposite the longest side. So the angle in triangle ABC has the largest measure is b) B.

A triangle is a geometric shape that has three vertices and three sides. The sides of a triangle are line segments of three different line segments. Meanwhile, the angles in a triangle are the intersections of two line segments that intersect at one point. Between the length and the size of the angle in a triangle has a proportional relationship, the greater the angle in the triangle, the longer the side opposite the angle.

Types of triangles include many different shapes but still have parts consisting of three sides and three angles. These types of triangles include equilateral triangles, isosceles triangles, arbitrary triangles, right triangles, obtuse triangles, and acute triangles.

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Partial sum rule is calculated by Sn=∑ni=1ai=n(a1+an)2.

A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit.

A partial sum is the total of a limited number of the series' terms. To see how the infinite sum behaves, we can examine a collection of these sums. The index of the final term in the sum is used to denote each of these partial sums.

When a group of numbers, known as addends or summands, are added together in mathematics, the outcome is their sum or total.

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[tex]\frac{2}{8}[/tex] fraction of the apple pie was served.

Two more pieces of the blueberry pie were served than the apple pieces.

Given that,

Both blueberry pie and apple pie were divided into 8 equal parts each.

To compute the fraction in eights of apple pie, we do a multiplication of the current fraction with 8 parts:

1 apple pie=8 pieces of apple pie

1/4 apple pie = [tex]\frac{1}{4}[/tex] * 8 pieces of apple pie = 2 pieces of apple pie.

1 blueberry pie=8 pieces of blueberry pie.

1/2 blueberry pie = [tex]\frac{1}{2}[/tex] * 8 pieces of blueberry pie = 4 pieces of apple pie.

Thus. 1/4 apple pie is 2 pieces out of 8 pieces of apple pie or written as [tex]\frac{2}{8}[/tex] a fraction of apple pie.

And they served blueberry pies are 4 pieces but served apple pies are 2 pieces, thus the count of pieces of blueberry pie is 2 more than the count of pieces of apple pie served.

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If the degree of the function is even then the end behaviour of the graph depends upon the leading coefficients of the function .

The End Behaviour of the graph of the polynomial is defined by the degree and the leading coefficient of the polynomial .

the end behaviour for the even degree polynomial is given as ;

(i) If the degree of the polynomial is even and the lead coefficient is also positive, then both the ends of graph of polynomial will point up.

(ii) If the degree is of polynomial is even and the lead coefficient is negative, then both ends of graph of polynomial  will point down.

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