Write an equation in slope-intercept form for the line that passes through (4, 7) and is perpendicular to the y-axis.

Answer:

length = 15

Width = 9

Step-by-step explanation:

In a rectangle opposite sides are equal.

5x - y- 8 =3x +5y + 4

5x - 3x  -y - 5y = 4 + 8

2x - 6y = 12

Divide the entire equation by 2

x  - 3y = 6  --------------(I)

3x + y - 4 = 2x - 6y - 3

3x - 2x + y + 6y = -3 + 4

x + 7y = 1 -------------(II)

Multiply equation (II) by (-1)

(I)            x - 3y = 6

(II)*(-1)    -x - 7y = -1   {Now add. 'x' will be eliminated}

                  -10y= 5

                      y = 5/(-10)

                     y = -0.5

Plugin y = -0.5 in equation (I)

x - 3*(-0.5) = 6

x  + 1.5 = 6

        x = 6 - 1.5

        x = 4.5

Length = 5x - y - 8

           = 5*4.5 - (-0.5) - 8

           = 22.5 + 0.5 - 8

            = 23 - 8

Length = 15

Width = 2x - 6y - 3

         = 2*4.5 - 6*(-0.5) - 3

         =  9 + 3 - 3

Width = 9

The linear system of equation y = -12x and 4x+2y= -8 has only one solution at 0.4,-4.8) .

The linear equation is  y = -12x and 4x+2y = -8

Now we solve the equations by substitution:

Using the value of y from the first equation and substituting in the second equation we get:

4x+2y = -8

or, 4x + 2(-12x)= -8

or, 4x -24x = -8

or, -20 x = -8

or, x = 0.4

At x=0.4 , y = -4.8

Hence solution is (0.4,-4.8) which represents the point of intersection of the two lines.

The collection of variable values in a linear equation that yields every feasible solution is referred to as the "solution of a linear equation." Unknown variables are used as one or more variables in linear equations to model real-world issues.

The solutions are the points at which the lines or planes used to describe the linear equations intersect or meet. The set of values for each variable in a system of linear equations is known as the solution set.

Disclaimer: the complete question is :

How many solutions does this linear system have y = -12x and 4x+2y= -8 have?

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The alternative hypothesis (H1) in this scenario puts forth a claim or belief about the treatment that is being administered to the individuals in the sample. It suggests that there is an effect or difference resulting from the treatment.

Specifically, the alternative hypothesis (H1) typically asserts that the treatment has a specific effect or outcome that is different from the null hypothesis (H0). It posits that the treatment has a significant impact on reducing or alleviating anxiety symptoms in the individuals compared to no treatment or a different treatment.

The alternative hypothesis is the researcher's assertion or hypothesis that they want to support or demonstrate through statistical analysis. It reflects the researcher's expectation that there is a meaningful relationship or effect resulting from the treatment being investigated.

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I hope that it helps you..

A premium is a payment Tom would make to the insurance company. This payment is usually once a month.

Keep in mind that this is not money that is paid out to Tom. The amount he would pay per month would depend on a number of risk factors. The higher the risk, the larger the premium. For instance, if Tom is buying health insurance and he lives a fairly unhealthy lifestyle (eg: smoker who doesn't exercise), then his premiums are likely to be higher compared to those who stay fit. This is because Tom will likely use health services more often compared to fit individuals, and thereby meaning that the insurance company is paying out more.

Let \(\(a\)\) and \(\(b\)\) be integers such that \(\(ab = 4\)\). We want to prove that \(\((a - b)^3 - 9(a - b) = 0\).\)

Starting with the left side of the equation, we have:

\(\((a - b)^3 - 9(a - b)\)\)

Using the identity \(\((x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3\)\), we can expand the cube of the binomial \((a - b)\):

\(\(a^3 - 3a^2b + 3ab^2 - b^3 - 9(a - b)\)\)

Rearranging the terms, we have:

\(\(a^3 - b^3 - 3a^2b + 3ab^2 - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\(a^3 - b^3 - 3a^2(4) + 3a(4^2) - 9a + 9b\)\)

Simplifying further, we get:

\(\(a^3 - b^3 - 12a^2 + 48a - 9a + 9b\)\)

Now, notice that \(\(a^3 - b^3\)\) can be factored as \(\((a - b)(a^2 + ab + b^2)\):\)

\(\((a - b)(a^2 + ab + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Simplifying further, we get:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\)

Now, we can observe that \(\(a^2 + 4 + b^2\)\) is always greater than or equal to \(\(0\)\) since it involves the sum of squares, which is non-negative.

Therefore, \(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\) will be equal to \(\(0\)\) if and only if \(\(a - b = 0\)\) since the expression \(\((a - b)(a^2 + 4 + b^2)\)\) will be equal to \(\(0\)\) only when \(\(a - b = 0\).\)

Hence, we have proved that if \(\(ab = 4\)\), then \(\((a - b)^3 - 9(a - b) = 0\).\)

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An isosceles trapezoid is a quadrilateral having the following properties: The median of an isosceles trapezoid is the line segment formed when we join the midpoint of one leg to the midpoint of the other leg of an isosceles trapezoid. The median forms a special theorem just for isosceles trapezoids.

Answer:

x ≈ 83.533

y = 9105.13

Step-by-step explanation:

Step 1: Substitution

109x = 79x + 2506

30x = 2506

x = 83.533

Step 2: Plug x in

y = 109(83.533)

y = 9105.13

Graphically:

Step-by-step explanation:

18(3x+1) = 54x+18

(6*9x) + (6*3) = 54x + 18

3(18x+2) = (6*9x)+(6*1)

(9*6x) - (9*2) = 18(3x-1)

54x+6 = (6*9x)+(6*1)

54x-18 = 18(3x-1)

Answer:

I believe it's the second one because it makes sense.

Step-by-step explanation:

I hope this helps you.

The distance between the stripes is 4040 feet (distance between curbs) minus 1515 feet (length of the curb between the stripes), which equals 2525 feet.

To find the distance between the two parallel stripes in the crosswalk, we can use the given information about the street. The distance between the parallel curbs of the street is 4040 feet. The length of the curb between the stripes is 1515 feet, and each stripe is 5050 feet long.

Since the crosswalk is bounded by two parallel stripes, the distance between the stripes can be calculated by subtracting the length of the curb between the stripes from the distance between the curbs of the street.

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Answer:

b and d

Step-by-step explanation:

Answer:

b and d

Step-by-step explanation:

True. Recursion is often necessary to solve certain types of problems that exhibit a recursive structure or require repeated subproblem solving.

Recursion is a programming technique where a function calls itself in its own definition. It allows for the decomposition of complex problems into smaller, more manageable subproblems that can be solved recursively. Recursion is particularly useful when problems exhibit a recursive structure, such as tree traversal, backtracking, or divide-and-conquer algorithms.

For example, problems like computing the factorial of a number, calculating Fibonacci numbers, or traversing a binary tree can be elegantly and efficiently solved using recursion. These problems can be broken down into smaller instances of the same problem until a base case is reached, and then the solutions are combined to solve the original problem.

However, it's worth noting that not all problems require recursion for their solution. There are alternative approaches, such as iterative loops or dynamic programming, which can be used depending on the problem's characteristics and requirements.

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Answer:

Prime. Prime numbers can only be divided by the whole number, or one.

The number of students in class were prime.

A number system is defined as a system of writing to express numbers.

Given,

Mr. Baker wants to divide his class into smaller, equal-sized groups of students. He can split them by using division method.

Class cannot be divided evenly into any size group except for individual groups of 1. We know that A division is a process of splitting a specific amount into equal parts.

He is unable to split the class students equally.

It means the number of students in class were prime numbers.

A prime number cannot be divided by any other number except itself.

If the number of students are composite then it can be splitted to equal groups.

Hence the number of students in class were prime.

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∂z/∂s = -sin()cos()t9 + cos()sin()9st2 and ∂z/∂t = sin()cos()s - cos()sin()81t.

To find ∂z/∂s and ∂z/∂t, we use the chain rule of partial differentiation. Let's begin by finding ∂z/∂s:

∂z/∂s = (∂z/∂)(∂/∂s)[(st9) cos(s9t)]

We know that ∂z/∂ is cos()cos() - sin()sin(), and

(∂/∂s)[(st9) cos(s9t)] = t9 cos(s9t) + (st9) (-sin(s9t))(9t)

Substituting these values, we get:

∂z/∂s = [cos()cos() - sin()sin()] [t9 cos(s9t) - 9st2 sin(s9t)]

Simplifying the expression, we get:

∂z/∂s = -sin()cos()t9 + cos()sin()9st2

Similarly, we can find ∂z/∂t as follows:

∂z/∂t = (∂z/∂)(∂/∂t)[(st9) cos(s9t)]

Using the same values as before, we get:

∂z/∂t = [cos()cos() - sin()sin()] [(s) (-sin(s9t)) + (st9) (-9cos(s9t))(9)]

Simplifying the expression, we get:

∂z/∂t = sin()cos()s - cos()sin()81t

Therefore, ∂z/∂s = -sin()cos()t9 + cos()sin()9st2 and ∂z/∂t = sin()cos()s - cos()sin()81t.

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The representation that is the most appropriate for showing how the price changed each year is given by:

The second graph.

There are two steps to identify the correct graph, as follows:

The input and the output variables are given as follows:

As the input variable is graphed on the horizontal axis, while the output variable is graphed on the vertical axis, the first and the fourth graphs are incorrect, as they have each variable on the wrong axis.

The price keeps changing throughout the years, that is, the price does not remain constant throughout the year, meaning that the domain is continuous, and thus the graph is composed by a solid line.

This means that the second graph is the correct graph in this problem. (the solid, approximately horizontal line).

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The length of a wave does not directly determine its depth. The depth of a wave is influenced by various factors, including the shape and size of the seafloor,

The temperature and salinity of the water, and the strength and direction of the current. Therefore, without additional information about these factors, it is impossible to accurately determine the depth of a wave based solely on its length. I suggest seeking the advice of an expert in oceanography or physics for a more comprehensive explanation.

The length of a wave is the distance between two successive points in the same phase, such as from crest to crest or trough to trough. In your case, the wave length is given as 30 feet. However, without additional information about the wave, we cannot determine its depth solely based on its length.

Depth refers to the vertical distance from the surface to the lowest point of a wave (trough), and it's not directly related to the wave length. Therefore, we cannot accurately choose an option (a, b, c, or d) for the depth based on the provided information.

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The length of the arc opposite a central angle that measures 46 degrees is 2.72 cm.

What is circle?

The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value.

in a circle of radius 3.4 cm

central angle that measures 46 degrees

length of arc = (46/360) * 2π*3.4

=2.72cm

Hence the length of the arc opposite a central angle that measures 46 degrees is 2.72 cm

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Answer:

y=35

Step-by-step explanation:

y in (-oo:+oo)

14 = (2*y)/5 // - (2*y)/5

14-((2*y)/5) = 0

(-2/5)*y+14 = 0

14-2/5*y = 0 // - 14

-2/5*y = -14 // : -2/5

y = -14/(-2/5)

y = 35

y = 35

Answer:

To expand (x + 4)², we can use the formula for squaring a binomial: (a + b)² = a² + 2ab + b². In this case, a = x and b = 4.

So,

(x + 4)² = x² + 2(x)(4) + 4²

= x² + 8x + 16

Thus, (x+4)² when expanded and simplified gives x² + 8x + 16.

Step-by-step explanation:

Answer:

x²n+ 8x + 16

Step-by-step explanation:

(x + 4)²

= (x + 4)(x + 4)

each term in the second factor is multiplied by each term in the first factor, that is

x(x + 4) + 4(x + 4) ← distribute parenthesis

= x² + 4x + 4x + 16 ← collect like terms

= x² + 8x + 16

The value of c so that cx-d=2x+4 has No Solution is c=2.

In the given question ,

we have

cx-d=2x+4       ....(i)

Given that d = 2 ,

We substitute the value of d=2 in equation (i)

On substituting we get

cx-2=2x+4

Simplifying further we get

cx=2x+4+2

cx=2x+6

cx-2x=6

x(c-2)=6

x=6/(c-2)

For x to have NO SOLUTION the denominator should be 0.

because when denominator becomes 0 the value becomes not defined , hence will have no solution.

Substituting the denominator = 0

we get c-2=0

c=2.

Therefore , the value of c so that cx-d=2x+4 has No Solution is c=2.

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The statement "The equation ax=0 gives an explicit description of its solution set" is true.

When the equation ax=0 is given, the solution set is explicitly described as x = 0.

In other words, the only solution to the equation is x being equal to zero. This can be verified by dividing both sides of the equation by a (assuming a is non-zero), which yields x = 0/a = 0.

Therefore, the solution set is explicitly described as x = 0.

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The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

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Answer: sqrt216

Step-by-step explanation:

First, find line segment AD

6^2 + b^2 = 12^2

36 + b^2 = 144

b^2 = 108

b = sqrt108

Now, to find x

sqrt108^2 = x^2 = 18^2

108 + x^2 = 324

x^2 = 216

x = sqrt216

not sure if I should simplify?

Steps Using Factoring By Grouping

\(4 {s}^{2} - 12s = - 9\)

\(4 {s}^{2} - 12s + 9 = 0\)

\((4 {s}^{2} - 6s) + ( - 6s + 9) = 0\)

\(2s(2s - 3) - 3(2s - 3) = 0\)

\((2s - 3)(2s - 3) = 0\)

\((2s - 3) {}^{2} = 0\)

 ‍ 

\(2 s - 3 = 0\)

\( \: \: \: \: \: \: \: 2s = 0 + 3\)

\( \: \: \: \: \: \: \: 2s = 3\)

\( \: \: \: \: \: \: \: \: \: s = \frac{3}{2} \)

\( \: \: \: \: \: \: \: \: \: s = 1 \frac{1}{2} \)

\( \: \: \: \: \: \: \: \: \: s = 1,5\)

\( \green {\boxed{s = \frac{3}{2} = 1 \frac{1}{2} =1,5}}\)

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Answer:

b= 64 m

Step-by-step explanation:

\(b^{2}\) + \(48^{2}\) = \(80^{2}\)

\(b^{2}\) = \(80^{2}\) - \(48^{2}\)

\(b\) = \(\sqrt{80^{2}-48^{2} }\)

 = \(64\) m

Answer:

is it math

Step-by-step explanation:

omg I really really really hate math

Answer: To find the discount, simply multiply the original selling price by the %discount:

ie:  39 x 33/100= $12.87

So, the discount is $12.87.

Step-by-step explanation: To find the sale price, simply minus the discount from the original selling price:

ie: 39- 12. 87=  26.13

So, the sale price is $26.13

Answer:

367

Step-by-step explanation:

l x w x h

=

6 x 4 x 15.3 = 367.2 ≈ 367

l = length

w = width

h = height