What is the x-coordinate of the point of intersection for the two lines below?
(2x + y = -9
(2x - 5y =-3

Answer:

To prove by contradiction that if a and b are both negative integers, then a+b is always negative, we assume the opposite, that is:

a and b are negative integers, but a+b is not negative.

Let's suppose that a and b are negative integers. This means that a and b are less than zero. Therefore, we can express a and b as:

a = -x (where x is a positive integer)

b = -y (where y is a positive integer)

Now, let's consider the sum of a and b:

a + b = (-x) + (-y) = -(x + y)

Since x and y are both positive integers, their sum (x + y) is also a positive integer. Therefore, we have:

a + b = -(x + y)

But since x + y is positive, the opposite of x + y (which is -(x + y)) is negative. Thus, we have proven that if a and b are both negative integers, then a+b is always negative.

Therefore, our assumption that a and b are negative integers, but a+b is not negative, is false. Hence, the statement "if a and b are both negative integers, then a+b is always negative" is true.

The volume of the cylinder having the same radius and height as that of the cone is found to be 300 cubic feet.

The volume of the cone is 100 cubic feet and the cone and cylinder has the same radius and height.

We know the volume of the cone is given by,

V = 1/3πr²h

1/3πr²h = 100 cubic feet

πr²h = 300 cubic feet

Where, r is the radius of the cone and h is height of the cone.

Now, the volume of the cylinder is given by,

V' = πr²h

V' = 300 cubic feet.

So, the volume of the cylinder is found to be 300 cubic feet.

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The production function Yt =A[αK tv v−1+(1−α)N tv v−1] v−1v does not exhibit constant returns to scale.

The concept of constant returns to scale is a property of production functions. It refers to a situation in which an increase in inputs such as labor, capital, or both results in a proportionate rise in output.

The production function Y = f(K, N) exhibits constant returns to scale if, for all values of K and N, there is a scalar λ such that Y(λK, λN) = λY(K, N)

If this condition holds, then we can say that the production function exhibits constant returns to scale.

Does the production function Yt =A[αK tv v−1+(1−α)N tv v−1] v−1v exhibit constant returns to scale?

Let us determine whether the production function

Yt =A[αK tv v−1+(1−α)N tv v−1] v−1v

exhibits constant returns to scale using the definition above.

Y(λK, λN) = A[α(λK) v (v−1) + (1−α)(λN) v (v−1)] v−1vY(λK, λN)

Y(λK, λN) = A[λvαK v (v−1) + λv(1−α)N v (v−1)] v−1vY(λK, λN)

Y(λK, λN) = A[λvαK v (v−1)v−1v + λv(1−α)N v (v−1)v−1v]Y(λK, λN)

Y(λK, λN) = λvA[αK v−1 + (1−α)N v−1] v

Since λ appears outside the bracket, the production function does not satisfy the condition of constant returns to scale because λ is not eliminated on both sides of the equation.

Therefore, we can conclude that the production function Yt =A[αK tv v−1+(1−α)N tv v−1] v−1v does not exhibit constant returns to scale.

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The solutions to the equation are: \theta = \frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}, \frac{9\pi}{4}, \frac{11\pi}{4}

Let us find all θ with 0 \leq \theta \leq 2\pi such that: (\sin \theta + \cos \theta)^2 = \frac{3}{2} Here is the explanation:Expand the square to obtain: \sin^2 \theta + 2\sin \theta \cos \theta + \cos^2 \theta = \frac{3}{2} Simplify: 2\sin \theta \cos \theta = \frac{1}{2} Divide through by 2: \sin \theta \cos \theta = \frac{1}{4} Notice that \sin \theta and \cos \theta have the same sign, either both positive or both negative. This is because they lie in the same quadrant. Let's consider the first quadrant 0 \leq \theta \leq \frac{\pi}{2}. Here both \sin \theta and \cos \theta are positive. Therefore: \sin \theta \cos \theta = \frac{1}{4} Taking square roots, we have: \sin \theta = \cos \theta = \pm \frac{1}{2 \sqrt{2}} Solving for \theta, we have: \theta = \frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4} These four angles are reflected in the second, third and fourth quadrants to give a total of $8$ solutions between 0 and 2\pi. Therefore, the solutions to the equation are: \theta = \frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}, \frac{9\pi}{4}, \frac{11\pi}{4}

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Among the following, the population mean u = (upper confidence limit) + (lower confidence limit) is not derived from the confidence interval.

A confidence interval is defined as the range of values that we observe in our samples and for which  we expect to find the value that accurately reflects the population.

In frequentist statistic, a confidence interval is a range of estimates for an unknown parameter.    

To find a confidence level for a data set by taking half of the size of the confidence interval, multiplying it by the square root of the sample size and then dividing by the sample standard deviation.

Confidence level refers to the percentage of probability,or certainty, that the confidence interval would contain the true population parameter when you draw a random sample many times. The most common confidence levels are 90%, 95% and 99%.

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Answer: 3

ur answer is 3

The value of angle S is 53°

Exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of two remote interior angles.

With this theorem we can say that

7x+2 = 4x+13+19

collecting like terms

7x -4x = 13+19-2

3x = 30

divide both sides by 3

x = 30/3

x = 10

Since x = 10

angle S = 4x+13

angle S = 4(10) +13

= 40+13

= 53°

Therefore the measure of angle S is 53°

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Answer:

=======================

Any rational number can be written in the form of p/q as per definition of a rational number.

In case with zero, it can be:

So, we'll have:

Answer:

1512 cm³

Step-by-step explanation:

Formula

Volume of right rectangular prism = Length × Breadth × Height

As given

Two blocks of wood are shaped as right rectangular prisms.

The smaller block has a length of 9 cm, a width of 3 cm, and a height of 7 cm.

As given

The dimensions of the larger block are double the dimensions of the smaller block.

Length of the larger block = 2 × Length of the smaller block

                                           = 2 × 9

                                           = 18 cm

Breadth of the larger block = 2 × Breadth of the smaller block

                                           = 2 × 3

                                           = 6 cm

Height of the larger block = 2 × Height of the smaller block

                                           = 2 × 7

                                           = 14 cm

Put in the formula

Volume of larger wooden block = 18 × 6 × 14

                                                    = 1512 cm³

Therefore the volume of the wooden block is 1512 cm³ .

Answer:

1,512 that’s the answer because u said double

e

d and 9 x 2 is 18,3 x 2 is 6, 7 x 2 is 14.Thani would muliply 18 x 6 x 14 that would get u https 1,512

Step-by-step explanation:

Answer:

f(10) means to input x = 10 into the function.

From inspection of the given function:

\(\sf f(10)=\dfrac{10}{2}=5\)

the "10" is the numerator of the fraction.

Therefore, swap the "10" for "x" to give the function in terms of x:

\(\sf f(x)=\dfrac{x}{2}\)

For a function

x is the input or domain

y is the output or range

Here

So

x=10

y=10/2

Hence the function is

Step-by-step explanation:

The two triangles are similar so

BC=BC

AB=AB

AC=AC

1.)5z=20 (÷b.s by 5)

z=4

2.)8=2x+2

8-2=2x

6=2x (÷b.s by 2)

x=3

3.)3y-3=15

3y=15+3

3y=18. (÷ b.s by 3)

y=6

The measures of the angles in the right triangle formed by the two regular pentagons are 18 degrees and 72 degrees.

The interior angles of a regular pentagon measure 108 degrees each. Therefore, if we have two regular pentagons, the right triangle formed by the two pentagons will have two angles that are equal to 108 degrees each.

These two angles are the complement of each other, meaning they add up to 90 degrees. Therefore, one of the angles in the right triangle formed by the two pentagons is 72 degrees, and the other is 18 degrees.

So, the measures of the angles in the right triangle formed by the two regular pentagons are 18 degrees and 72 degrees.

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Explanation

as we can see in the picture, after drawing the angles, we can observe the common angles is

I hope this helps you

The polynomial function in number 1 is incomplete and missing the degree of the polynomial.

The leading coefficient, degree, and end behavior. For number 2, the degree of the polynomial is 2, the leading coefficient is -3, and the end behavior is that as x approaches positive or negative infinity, the function approaches negative infinity. For number 3, the degree of the polynomial is 1, the leading coefficient is 3.9, and the end behavior is that as x approaches positive or negative infinity, the function approaches positive or negative infinity depending on the sign of the leading coefficient.

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Answer:

y = -2x - 3

Step-by-step explanation:

a) Sentences generated by grammar G consist of a sequence of terminal symbols that can be formed by applying the production rules. For example, a sentence consisting of 4 terminal symbols could be "num - num + num".

b) The regular expression representing the same sentences as grammar G would be: (num (+|-) num)* num

a) The grammar G consists of non-terminals E and S, terminals +, -, and num, and production rules that define how to generate sentences. To form a sentence, we start with the non-terminal E as the start symbol and apply the production rules recursively until we reach a sequence of terminal symbols.

The non-terminal S can be expanded to an empty string or to +S or -S, allowing for the generation of expressions with positive or negative signs. The non-terminal E can be expanded to S followed by E or to num, representing the recursive nature of the grammar.

b) The regular expression (num (+|-) num)* num represents the same set of sentences as grammar G. It allows for a sequence of one or more occurrences of num followed by either a plus or minus sign and another num. This pattern can repeat zero or more times, and finally, the sentence ends with a single num. This regular expression captures the structure and repetition of the production rules in grammar G.

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Answer:

There is no mode !

Step-by-step explanation:

Hello,

what is the mode of a set of data?

It is the value in the set that occurs most often.

To note that this is also possible to have a set of data with no mode.

in this example, let's order them

7, 8, 11, 12, 13, 14, 15, 20

There is no repetition, right? each value occurs only once.

So, there is no mode!

hope this helps

Answer:

Step-by-step explanation:

2 quarts = 8 cups.

$0.3 per cup

(0.3 x 8 = $2.40)

Answer:

Present age of son = 15 years

& Present age of father = 40 years

Step-by-step explanation:

Answer:

See below ~

Step-by-step explanation:

Let the father's age be x and son's age be y.

Equations formed :

Substitute value of x from Equation 1 in Equation 2.

Solution :

According to the question we have  approximately 99.74 percent of customers are willing to pay between $1.20 and $1.80 for a pint of frozen yogurt.

To answer this question, we will use the normal distribution formula and z-score.

First, we need to find the z-score for the lower limit of $1.20:

z = (1.20 - 1.50) / 0.10 = -3

Next, we need to find the z-score for the upper limit of $1.80:

z = (1.80 - 1.50) / 0.10 = 3

Now, we can use a z-table to find the area under the curve between these two z-scores.

The area to the left of z = -3 is 0.0013, and the area to the left of z = 3 is 0.9987.

To find the area between these two z-scores, we subtract the area to the left of z = -3 from the area to the left of z = 3:

0.9987 - 0.0013 = 0.9974

Therefore, approximately 99.74% of customers are willing to pay between $1.20 and $1.80 for a pint of frozen yogurt.

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Answer:

6

Step-by-step explanation:

Trust

Answer:

If this is the equation you meant to type (3x + 10 = 13x) then the answer is x = 1.

If this is the equation you meant to type (3x - 10 = 13x) then the answer is x = -1.

The equation of the parent square root function to represent the equation of the graphed function will be, y=√x-2

According to the statement

we have to show the square root function as a equation in the graphical representation.

So,

we know that the definition of a

Graph a diagram showing the relation between variable quantities, typically of two variables and it also show the relation between more than two variables.

Now, we know that the definition of Equation is a mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

And the equation obtained from the graph is a y=√x-2 by a some calculations in the graph.

So, The equation of the parent square root function to represent the equation of the graphed function will be, y=√x-2

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Answer:

Step-by-step explanation:

6). Equation of the line has been given as,

    4x + 9y = -9

    By converting this equation into y-intercept form,

    9y = -4x - 9

    \(y=-\frac{4}{9}x-\frac{9}{9}\)

    \(y=-\frac{4}{9}x-1\)

    By comparing this equation with y = mx + b

    Here, m = Slope of the line

    b = y-intercept

    Slope of the equation (m) = \(-\frac{4}{9}\)

    y-intercept (b) = -1

8). Equation of the line is,

    5x + 3y = 12

    3y = -5x + 12

    \(y=-\frac{5}{3}x+\frac{12}{3}\)

    \(y=-\frac{5}{3}x+4\)

    Slope of the line = \(-\frac{5}{3}\)

    y-intercept = 4

Answer:

C

Step-by-step explanation:

Because i took the test already

Step-by-step explanation:

The global extreme values of f(x, y) subject to the constraints:

f_min ≈ 0.426

f_max = 14/5 ≈ 2.8

Lagrange multipliers are a mathematical method used to find the extreme values (maximum or minimum) of a function subject to one or more constraints.

Given function is;

f(x, y) = 4x³ + 4x²y + 5y²;    where, x, y ≥ 0, x + y ≤ 1

First, we need to set up the Lagrangian function:

L(x, y, λ) = 4x³ + 4x²y + 5y² - λ(x + y - 1)

Taking partial derivatives with respect to x, y, and λ and setting them equal to zero, we get:

∂L/∂x = 12x² + 8xy - λ = 0

∂L/∂y = 4x² + 10y - λ = 0

∂L/∂λ = x + y - 1 = 0

Solving these equations simultaneously,

x = 2/5, y = 3/5, λ = 26/25

We also need to check the boundary of the feasible region, which is the line x + y = 1. We can set y = 1 - x and substitute into the function f(x, y):

g(x) = f(x, 1-x) = 4x³ + 4x²(1-x) + 5(1-x)² = 4x³ - x² + 6x - 5

Taking the derivative of g(x) with respect to x and setting it equal to zero,

g'(x) = 12x² - 2x + 6 = 0

Solving for x,

x = (1 ± √7)/6

Therefore, the global maximum of f(x, y) subject to the constraints is:

f_max = f(2/5, 3/5) = 4(2/5)³ + 4(2/5)²(3/5) + 5(3/5)² = 14/5

f_min = f((1 - √7)/6, (5 + √7)/6) = 4((1 - √7)/6)³ + 4((1 - √7)/6)²((5 + √7)/6) + 5((5 + √7)/6)² ≈ 0.426

Therefore, the global extreme values of f(x, y) subject to the constraints:

f_min ≈ 0.426

f_max = 14/5 ≈ 2.8

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The correct choice is within your skills and abilities.

Once you get to determine things you are capable of and things you are not capable of, you will be able to concentrate on your strengths more. This will in turn produce big results as compared to if you opted to concentrate on your weaknesses.

It will also result in no or less time wasted in doing what you are less capable of.

Its almost close to impossible to be able to do everything. Each person is gifted in a certain area or skill or capability. We are all different and that's okay.

Its so important to concentrate in the areas you are more comfortable with. This will help you much with improving your skills and abilities.

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Answer:

Step-by-step explanation:

a you just had to say a

See pics for answers

Answer:

Answer:

A. 2

Step-by-step explanation:

slope formula is :  or the difference in y-coordinates in 2 points divided by the difference in x-coordinates in 2 points.

in this question, they have given you both the difference in x and difference in y.

therefore this question is saying :  =

= 2

therefore, the correct slope value is A. 2

Step-by-step explanation:

Hi! The answer is going for be D (400)

Step-by-step explanation:

Out of 100 women, 8 were married 2 or more times which is 8% or 0.08

So out of 5000 women, the number of women married 2 or more times is: 0.08*5000 = 400

x/5000 = 8/100

x/50=8/1

x=400

Hope this helps! Have a good day!