Solve the simultaneous equations
y=2-5x
y = x² – 2x – 8

Answer: 7 and 1/2

Step-by-step explanation:

First convert both parts to improper fractions. 4 *2 + 1 =9 so we have 9/2 ÷ 3/5. Dividing by a fraction is the same as mtiplying by its reciprocal (swapping the top and bottom numbers) so we have 9/2 x 5/3. Multiplying fractions multiplies the top and bottom together so we get 45/6. 6 fits into 45 7 times with 3 left over so we get 7 3/6. 3 and 6 are both multiples of 3 so we can simplify by dividing both of them by 3 so we get our answer 7 and 1/2.

Answer:

The equation for the line which passes through the points given as (a, b) and (a, b+1), is x=a, which represents a vertical line.

Step-by-step explanation:

It is given that a line passes through the points whose coordinates are (a, b) and (a, b+1).

It is asked to find the linear equation which passes through the given points.

To do so, first determine the slope of the given line using the coordinates and the formula for the slope. Accordingly, proceed to find the equation of the given line.

Step 1 of 2

Determine the slope of the line.

The points through which the line passes are given as (a, b) and (a, b+1). Next, the formula for the slope is given as,

\($m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$\)

Substitute b+1&b for \($y_{2}$\) and \($y_{1}$\) respectively, and a&a for \($x_{2}$\) and \($x_{1}$\) respectively in the above formula. Then simplify to get the slope as follows,

\(m=\frac{b+1-b}{a-a}$\\ $m=\frac{1}{0}$\)

b+1. So the equation of the line cannot be found using the general point-slope form equation.

Step 2 of 2

Write the equation of the line.

So, by definition, the line that passes through the given points is a vertical line. Now, as its x- coordinate is a, so the equation of the line is given as x=a.

a) The proportion of odd numbers in the population is 2/3, or 0.667.

b) The probability distribution table is as follows:

Proportion of odd numbers Probability

0 1/9

0.5 4/9

1 4/9

c) The mean of the sampling distribution of the sample proportion of odd numbers is 0.833.

d) Based on the results, the sample proportion is an unbiased estimator of the population proportion.

a) The population consists of three numbers: 3, 4, and 11. The proportion of odd numbers in the population is 2/3, or 0.667.

b) To construct a probability distribution table for the sampling distribution of the proportion of odd numbers, we need to consider all possible samples of size 2 that can be taken with replacement from the population. There are 9 different samples, as listed in the problem statement. For each sample, we compute the proportion of odd numbers.

The probability distribution table is as follows:

Proportion of odd numbers Probability

0 1/9

0.5 4/9

1 4/9

c) To find the mean of the sampling distribution, we weight each possible proportion of odd numbers by its probability, and sum the results:

Mean = (0)(1/9) + (0.5)(4/9) + (1)(4/9) = 0.833

d) The sample proportion of odd numbers is an unbiased estimator of the population proportion if its expected value is equal to the population proportion. In this case, we have:

E(p) = 0(1/9) + 0.5(4/9) + 1(4/9) = 0.833

Since the expected value of the sample proportion is equal to the population proportion, we can conclude that the sample proportion is an unbiased estimator of the population proportion.

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Answer:

4.28 × 10^-5

Step-by-step explanation:

Answer:

answer is 312.00

Step-by-step explanation:

Trust me I just took the test

Answer:

1) AD = 9 in

2) DE = 9.25 in

3) ∠EDC = 36°

4) ∠AEB = 108°

5) 11.5 in

Step-by-step explanation:

1) AD = BC = 9in

2) AC = BD (diagonals are equal)

⇒ BD = 14.25

⇒ BE + DE = 14.25

⇒ 5 + DE = 14.25

DE = 9.25

3) Since AB ║CD,

∠ABE = ∠EDC = 36°

4) ∠ABE = ∠BAE = 36°

Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)

⇒ 36 + 36 + ∠AEB = 180

∠AEB = 108

5) midsegment = (AB + CD)/2

= (8 + 15)/2

11.5

We can see that the statement is not always true for any vectors u and v in V3.

The statement is not always true.

The cross product of vectors u and v in V3 is a vector that is orthogonal to both u and v. That is,

u x v ⊥ u and u x v ⊥ v

However, this does not necessarily mean that (u x v) * u = 0 for all u and v in V3.

For example, let u = <1, 0, 0> and v = <0, 1, 0>. Then,

u x v = <0, 0, 1>

(u x v) * u = <0, 0, 1> * <1, 0, 0> = 0

So in this case, the statement is true. However, consider the vectors u = <1, 1, 0> and v = <0, 1, 1>. Then,

u x v = <1, -1, 1>

(u x v) * u = <1, -1, 1> * <1, 1, 0> = 0

So in this case, the statement is also true. However, if we take the vector u = <1, 0, 0> and v = <0, 0, 1>, then

u x v = <0, 1, 0>

(u x v) * u = <0, 1, 0> * <1, 0, 0> = 0

So in this case, the statement is true as well.

However, if we take the vector u = <1, 1, 1> and v = <0, 1, 0>, then

u x v = <1, 0, 1>

(u x v) * u = <1, 0, 1> * <1, 1, 1> = 2

So in this case, the statement is not true.

Therefore, we can see that the statement is not always true for any vectors u and v in V3.

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Answer: x=45/3

Step-by-step explanation:

Answer:

x=2 , y=3

Step-by-step explanation:

Answer:

the answer for your question is 4832.46 cm3

The answer is 4) for some c, such that a < c < b, the derivative g'(c) =0. While it is possible.

Is g'(c)=0 necessary between a and b?

4) for some c, such that a < c < b, the derivative g'(c) is equal to zero.

The statement "g hasa minimum value on [a, b]" is true by the extreme value theorem, which states that a continuous function on a closed interval must have both a maximum and minimum value.

Similarly, the statement "g has a maximum value on [a,b]" is also true by the same theorem.

The statement "g(c) = 0 for some c, such that a < c < b" is also true by the intermediate value theorem for continuous functions, which states that if g(a) and g(b) have opposite signs, then there exists a value c between a and b such that g(c) = 0.

Therefore, the only statement that is not necessarily true is "for some c, such that a < c < b, g'(c) = 0." While it is possible for g'(c) to equal zero at some point between a and b, it is not a necessary condition for the given conditions in the question.

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Answer:

90

Step-by-step explanation:

Answer:

The measure of SRT is 90 degrees.

Step-by-step explanation:

The lines are perpendicular so they all will equal 90 degrees.

The association represented as a line connecting participating classes, and may optionally have a name, is known as a binary association. Thus, Option C is correct.

A binary association is the most common type of association in UML (Unified Modeling Language) and is used to represent a relationship between two classes. It consists of a line connecting two classes with optional arrowheads to indicate the direction of the relationship. The name of the association may be added near the line to describe the relationship between the two classes.

Binary associations can be further categorized as unidirectional or bidirectional, depending on whether the relationship flows in only one direction or both directions between the two classes. In addition, qualified associations can be used to specify additional details about the relationship, such as the role or attribute that links the two classes.

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The dividend of the given polynomial division is: x³ - 4x² + 2x + 5

We can write a polynomial dividend as the product of the divisor and the quotient added to the remainder. The terms of the polynomial division correspond to the digits (and place values) of the whole number division. This method allows us to divide two polynomials.

We are given:

Divisor = (x - 2)

Quotient = x² - 2x -2

Remainder = 1

Thus:

First term = x * x² = x³

Second term = -2x² - 2x² = -4x²

Third term = 2x

Fourth term = 5

Thus, the dividend = x³ - 4x² + 2x + 5

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The circumference of the circle is 26.38 inches and the area of the circle is 55.39 square inches, both rounded to the nearest hundredth.

The diameter of a circle is the distance across the circle passing through its center. In this problem, the diameter of the circle is given as 8.4 inches. We can use the formula for the circumference and the area of a circle in terms of its diameter to find the solutions.

First, we can find the radius of the circle by dividing the diameter by 2. So, the radius is 8.4/2 = 4.2 inches.

To find the circumference of the circle, we can use the formula:

C = πd

where d is the diameter. Substituting the value of d = 8.4 inches and π = 3.14, we get:

C = 3.14 x 8.4 = 26.376

Therefore, the circumference of the circle is 26.38 inches (rounded to the nearest hundredth).

To find the area of the circle, we can use the formula:

A = πr²

where r is the radius. Substituting the value of r = 4.2 inches and π = 3.14, we get:

A = 3.14 x (4.2)² = 55.3896

Therefore, the area of the circle is 55.39 square inches (rounded to the nearest hundredth).

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Answer:

c (the third option)

Step-by-step explanation:

Answer:

-2/3x+1

Step-by-step explanation:

The given problem can be solved using algebraic equations as shown below. The number of plain marbles can be represented by "x" while the number of colored marbles can be represented by "y". If there are 32 more plain marbles than colored marbles, then the number of plain marbles will be y + 32.

So, the equation representing the number of plain marbles will be x = y + 32.There are a total of 180 marbles, so x + y = 180.Substituting the value of x in this equation, we get (y + 32) + y = 180. Simplifying, we get:2y + 32 = 1802y = 180 - 32 = 148y = 148/2 = 74. Substituting the value of y in x = y + 32, we get: x = 74 + 32 = 106.So, Timmy has 106 plain marbles and 74 colored marbles.

The system of equations representing the number of marbles Timmy has is: x + y = 180x = y + 32. Substituting the value of y in the equation x = y + 32, we get x = 74 + 32 = 106, which means that Timmy has 106 plain marbles. The number of colored marbles is y = 74. Therefore, the system of equations representing the number of marbles Timmy has is: x + y = 180x = y + 32.

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Answer:

g+s=33

Step-by-step explanation:

I'm not sure if this is 100% correct, because you did not finish the question not provide me with answer choices. But I believe the answer should something along these lines.

The quotient of 405/27 fraction using division is 15.

It should be noted that the information is simply to divide the numbers.

In this case, the numerator is 405 and the denominator is 27

Therefore, the quotient based on the information illustrated will be:

= 405 / 27

= 15

Therefore, the quotient is 15.

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Answer:

3^5/3

log(1/2)

log2(16)

Step-by-step explanation:

u.

Number of ways the head coach, assistant coach and the team manager can be chosen from the group of 18 people is equal to 4896.

As given in the question,

Total number of people in a group is equal to 18

Number of people to be selected is equal to 3

Head coach , Assistant coach , and the team manager

Here order matters.

Number of ways to select three people from a group of 18 people is given by permutation ,

¹⁸P₃

= ( 18 ) ! / ( 18 - 3 )!

= 18! / !5!

= ( 18 × 17 × 16 × 15! ) / 15!

=  18 × 17 × 16

= 4896 ways

Therefore, number of ways the head coach, assistant coach and the team manager can be chosen from the group of 18 people is equal to 4896.

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Marissa's shape is classified as a scalene and obtuse triangle, considering it's concepts presented in this problem.

The triangle has three sides of unequal length, as the opposite angle measures are different, hence it is classified as an scalene triangle.

(it would be equilateral if all had the same length, and isosceles if two sides have the same length).

The triangle has one angle larger than 90º, hence it is classified as an obtuse triangle.

(acute with no angles of 90º or greater, right with one angle of exactly 90º).

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Answer:

Approximately 40,000 hours

Step-by-step explanation:

Time = distance/speed. T = 1,200,000,000/28,000, converted to: 1,200,000/28.

Rounding 28 to 30 for the estimate, divide by another ten: 120,000. Then divide by the remaining 3 from 30: 120,000/3 = 40,000.

It will take approximately 40,000 hours.

Step-by-step explanation:

π x r^2 + π x r^2 + 2 x π x r x h

4π + 4π + 16π = 24π

Answer:

110

Step-by-step explanation:

Z4=180-70:110‌ ‌ ‌ ‌ ‌ ‌

In the diagram, if ΔABC= ΔDEF, then angle A is congruent to angle D.

Option C.

Similar triangles are triangles that have the same shape, but not necessarily the same size. In other words, their corresponding angles are equal, and their corresponding sides are proportional in length.

Two triangles are considered similar if they satisfy one of the following conditions:

ABC ≅ DEF

∠A ≅ ∠ D

Thus, two triangles are similar if their corresponding angles are congruent, and their corresponding sides are in proportion, so angle A of triangle ABC is congruent to angle D of triangle DEF.

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The solutions to the given interval 0° ≤ θ < 2π, we have:

θ = 60° and θ = 300°

We can start by dividing both sides of the equation by 2 to get sin(θ) = √3/2.

Next, we recall the special values of sin(θ) for θ in the first quadrant (0° ≤ θ ≤ 90°), where sin(30°) = 1/2 and sin(60°) = √3/2. Since our current equation has a sine value of √3/2, we know that its solution lies between 30° and 60°.

To find the exact solutions, we need to use inverse trigonometric functions. Specifically, we can take the arcsine of both sides of the equation to get:

θ = arcsin(√3/2)

Using a calculator, we find that arcsin(√3/2) ≈ 60°. Therefore, the solutions on the interval 0° ≤ θ < 360° are:

θ = 60° + 360°k, where k is an integer.

Restricting the solutions to the given interval 0° ≤ θ < 2π, we have:

θ = 60° and θ = 300°

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The optimal dimensions for the garden to maximize the area are 30 feet by 18 feet, with fencing costing $2 per foot on three sides and $3 per foot on the fourth side.

To determine these dimensions, we start by setting up the equation based on the given information. The cost of fencing for three sides is equal to 2 times the sum of the length and width of the garden, while the cost of fencing for the fourth side is 3 times the length of the garden. Since the total cost of fencing should not exceed $120, we can set up the equation:

2(l + w) + 3l = 120

Simplifying this equation, we get:

5l + 2w = 120

Next, we aim to maximize the area of the garden, which is given by the formula A = lw. We can solve for one variable in terms of the other using the equation obtained above. Substituting the value of w in terms of l into the area equation, we have:

A = (120 - 2w)/5 * w

A = (120w - 2w^2)/5

To find the maximum area, we can take the derivative of the area equation with respect to w and set it equal to zero. Solving this equation, we find w = 30. Substituting the value back into the equation, we get l = 18.

Therefore, the optimal dimensions for the garden are 30 feet by 18 feet to maximize the area, with the given cost of fencing.

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Answer:

when X=1 y = -9/2

Step-by-step explanation:

\( - 4 < \frac{9}{8} > {}^{1} = - 4 < \frac{9}{8} > = - \frac{ 36}{8} = - \frac{9}{2} \)

The given equation can be solved for the value of x and y

i.e. x = (3y - 7)/4 & y = (4x + 7)/3.

What is the linear equation?

An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

We have,

The equation 4x=3y-7

So, here we can solve this equation for the x as well as y equals,

Firstly we will solve for x:

4x = 3y - 7

dividing the whole equation by 4 we get,

4x/4 = (3y - 7)/4

x = (3y - 7)/4

Similarly, we will solve for y:

4x = 3y - 7

3y = 4x + 7

dividing the whole equation by 3 we get,

3y/3 = (4x + 7)/3

y = (4x + 7)/3

Hence, the given equation can be solved for the value of x and y

i.e. x = (3y - 7)/4 & y = (4x + 7)/3

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