To solve this system of equations by elimination, what operation could be used to eliminate the y-variable and find the value of x? 2x − 4y = 6 −3x + 3y = 12 A) add 3 times the second equation to 4 times the first equation B) add 4 times the second equation to 3 times the first equation C) subtract 3 times the second equation from 4 times the first equation D) subtract 4 times the second equation from 3 times the first equation

The slope of a line perpendicular to a line with a slope of 3 is -1/3. This is because perpendicular lines have negative reciprocal slopes.

In mathematics, when two lines are perpendicular, their slopes are negative reciprocals of each other because the product of their slopes equals to -1. This means that if one line has a slope of 3, the slope of the other line would be the negative reciprocal of 3, which is -1/3. So, the slope of the other line is -1/3.

To understand this further, let's delve into the figure of Slope and the Algebra of Straight Lines. Here, 'm' represents the slope which is the rise over the run and 'b' is the y-intercept, which is the point at which the line crosses the y-axis. Considering the fact that the slope of the line is 3, there is an increase of 3 in the y-coordinate (or vertical axis) for every increase of 1 in the x-coordinate (or horizontal axis).

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Answer:

12 and 13 or

- 13 and - 12

A quadratic equation r² + r - 156 = 0

Step-by-step explanation:

Let the first number be r, it means that the second will be r + 1.Given that the product of two consecutive integers is 156. we may interpret that to mean that

r(r + 1) = 156

r² + r - 156 = 0

r² + 13r - 12r -156 = 0

(r + 13)(r - 12) = 0

r = -13 0r 12

if r = -13, r + 1 = -12

If r = 12, r + 1 = 13

Answer:

The answer is the option A

When it was purchased (year [tex]0[/tex]), the coin was worth [tex]\$3[/tex]

Step-by-step explanation:

we know that

The y-intercept of a function is the value of the function when the value of the independent variable  is equal to zero

In this problem we have

[tex]f(t)=3(2^{t})[/tex]

the independent variable is the variable t

so

Find the y-intercept

For [tex]t=0[/tex] ------> year zero

Find the value of the function

[tex]f(0)=3(2^{0})=\$3[/tex]

That means ----> When it was purchased (year [tex]0[/tex]), the coin was worth [tex]\$3[/tex]

Answer:

I think it's D

Step-by-step explanation:

Answer:  The correct option is (C) 28.2 oz.

Step-by-step explanation:  Given that a recipe calls for 0.800 kg of flour.

We are to find the number of ounces of flour that the recipe needs.

Given that

1 lb=16 oz  and  1 lb = 0.454 kg

We will be using the UNITARY method for solving the given problem.

We have

0.454 kg = 1 lb

So, 1 kg will be equal to [tex]\dfrac{1}{0.454}~\textup{lb}.[/tex]

Therefore, 0.8000 kg is equal to

[tex]\dfrac{1}{0.454}\times 0.800=1.762~\textup{lb}.[/tex]

Now, 1 lb = 16 oz.

So, 1.762 lb = 16 × 1.762 = 28.19 = 28.2 oz.

Thus, the recipe needs 28.2 oz of flour.

Option (C) is CORRECT.

Answer:

Sum of the sequence = 132.

Step-by-step explanation:

The given sequence is 153, 139, 125,.......n terms.

Sum of the arithmetic sequence will be

S = n/2[2a + (n -1)d]

where n = number of terms

a = first term of the sequence

d = common difference

for the given sequence

a = 153

n = 22

d = 139 - 153 = -14

Therefore sum of 22 terms of the sequence will be

S = (22/2)[2×153 - (22-1)14]

= 11×[306 - 21×14]

= 11×[306 - 294] = 11×12 = 132

Sum of 22 terms of this sequence is 132.

Answer:250

Step-by-step explanation:

To eliminate the parameter and find the cartesian equation of the curve x=3sin(t), y=4cos(t), we can use trigonometric identities. The cartesian equation of the curve is (x/3)^2 + (y/4)^2 = 1.

To eliminate the parameter and find the cartesian equation of the curve x=3sin(t), y=4cos(t), we can use trigonometric identities. Starting with the given equations:

x = 3sin(t)

y = 4cos(t)

We can rewrite the equation for x as:

x/3 = sin(t)

And the equation for y as:

y/4 = cos(t)

Using the identities sin2(t) + cos2(t) = 1, we can square both equations and add them together:

(x/3)2 + (y/4)2 = (sin2(t) + cos2(t)) = 1

This is the cartesian equation of the curve.

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Answer:

2x – 1 = x + 8

Step-by-step explanation:

We know that the central angle is an angle subtended at the center of the circle by any two points on the circle.

In the given figure of the circle, the center of the circle is C. Hence, the central angle must be subtended at the center C.

Since, angle FEB is not subtended at the center of the circle.

Hence, angle FEB is not a central angle.

Therefore, the given statement is FALSE.

Answer:

Amplitude : 4

Period: 2π

Mid-line: y=-1

A is correct

Step-by-step explanation:

We are given graph of periodic function.

We need to find amplitude, period and midline of the function.

From graph:

Maximum value  = 3

Minimum value = -5

[tex]\text{Mid-Line }=\dfrac{Max+Min}{2}[/tex]

[tex]\text{Mid-Line }=\dfrac{3-5}{2}=-1[/tex]

The mid-line equation, y=-1

Amplitude: Distance between mid-line and maximum value

Amplitude = 3-(-1) = 4

The amplitude of given graph is 4

Period: It is time when graph repeat their path.

In the given graph repeat their in 2π of interval.

The period of graph is 2π

This is a Physics problem involving Hooke's Law and Newton's second law of motion. The acceleration of a 25kg block when a spring it's resting on is extended by 0.4m is determined. The calculated acceleration is -3.2m/s², indicating the direction is opposite to the direction of displacement.

The subject matter of this question is physics, specifically the area of mechanics dealing with forces, mass, and acceleration (Newton's Laws). The stiffness of a spring is given as k=200N/m and it is unstretched when the 25 kg block is resting on it. We're tasked with finding the acceleration of the block when the spring is extended by s=0.4m.

Firstly, let's find the force on the block using Hooke's Law which states that the force exerted by a spring is equal to the spring constant times the displacement (F=-kx). So, F=-200N/m*(0.4m)=-80N. The negative sign just indicates that the force is in the opposite direction of the displacement.

Secondly, we apply Newton's second law of motion (F=ma), where m is the mass and a is the acceleration. Rearranging the equation to find acceleration gives us a=F/m. Substituting our values gives a=-80N/25kg = -3.2m/s². The negative sign here indicates the direction of the acceleration, opposite to the direction of displacement. So, the acceleration of the block when the spring is extended by 0.4m is -3.2m/s².

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To find out how much money Marcia has, a system of linear equations is set up and solved. Sue has $54, which means Marcia has $78 since she has $84 less than three times Sue's amount. They together have $132.

The question involves solving a system of linear equations to determine how much money Marcia has if she has $84 less than three times as much as Sue. Together they have $132. To solve this, let's name the amount Sue has as S, and consequently, Marcia has 3S - $84. Adding both amounts, we get the equation S + (3S - 84) = $132.

Combining like terms gives us 4S - 84 = $132. We solve for S by first adding 84 to both sides, which yields 4S = $216. Dividing both sides by 4 gives us S = $54. Knowing Sue's amount, we can compute Marcia’s by multiplying Sue’s amount by three and then subtracting 84, so 3 x $54 - $84 = $162 - $84 = $78. Therefore, Marcia has $78.

A log function is a way to find how much a number must be raised in order to get the desired number. The population of the city will be 1,200,000 in the year 2024.

A log function is a way to find how much a number must be raised in order to get the desired number.

[tex]a^c =b[/tex]

can be written as

[tex]\rm{log_ab=c[/tex]

where a is the base to which the power is to be raised,

b is the desired number that we want when power is to be raised,

c is the power that must be raised to a to get b.

For example, let's assume we need to raise the power for 10 to make it 1000 in this case log will help us to know that the power must be raised by 3.

The decrease in the population of the city can be written as,

[tex]\rm Final\ population=(Initial\ population)\times (1-r)^n[/tex]

[tex]1,200,000=1,405,233(1-0.011)^n\\\\0.8539=(0.989)^n\\\\\rm log(0.8539)=n\ log(0.989)\\\\n= \dfrac{log(0.8539)}{log(0.989)}\\\\n=14.279 \approx 14.3[/tex]

Since the initial population was 1,405,000 in the year 2010, then the population of the 1,200,000 will be 14 years later.

Thus, the population of the city will be 1,200,000 in the year 2024.

Learn more about Logarithm:

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Answer:

  B. Rectangle

Step-by-step explanation:

The cross section will be a rectangle, as illustrated in the attachment.

The correct answer is B. Rectangle.

 To determine the shape of the cross section, we need to understand the properties of a right triangular prism and the nature of the plane cut. A right triangular prism has two congruent right triangles as its bases, and the lateral faces are rectangles.

When a plane cut is made through points that are vertices of the base right triangle and is perpendicular to the opposite base, the cross section will intersect all the lateral edges of the prism. Since the lateral edges are perpendicular to the base, the cross section will have four right angles, making it a quadrilateral.

Furthermore, because the cut is perpendicular to the opposite base, the cross section will have two pairs of parallel sides. One pair of parallel sides comes from the intersection with the two lateral faces that are parallel to each other, and the other pair comes from the intersection with the base and the top face of the prism, which are also parallel.

 Given these properties, the most specific name for the shape of the cross section is a rectangle, as it is a quadrilateral with four right angles and opposite sides that are parallel and equal in length.

Therefore, the correct answer is B. Rectangle.