Name the property illustrated by each question.

5x · (4y + 3x) = 5x · (3x + 4y)

The slope of the given equation 12x = 7y - 10y is -4 (constant) thus it will be a linear equation.

A straight line on the coordinate plane is represented by a linear function.

A linear function is a function that varies linearly with respect to the changing variable.

Given the line,

12x = 7y - 10y

12x = -3y

-3y = 12x

Divide both sides by -3

y = -4x

The slope of any function is given as dy/dx or first differential

dydx = -4 so the slope is constant thus the line will be a linear equation.

The graph of the line also has been attached for refernce.

Hence "The slope of the given equation 12x = 7y - 10y is -4 (constant) thus it will be a linear equation".

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The equation 12x = 7y - 10y simplifies to 12x = -3y and is a linear equation because it can be rewritten in the form y = mx + b, where m is the slope (-4) and b is the y-intercept (0).

The equation 12x = 7y - 10y simplifies to 12x = -3y, which can then be written in the slope-intercept form as y = -4x. This is a linear equation because it can be expressed in the standard form y = mx + b, where m represents the slope and b is the y-intercept. In this equation, m equals -4 and b equals 0, indicating that the line crosses the y-axis at the origin (0,0).

Similar examples of linear equations include 7y = 6x + 8, 4y = 8, and y + 7 = 3x. These equations all have a constant rate of change, which is characteristic of linear relationships, where one variable is a constant multiple of the other plus a constant (y = a + bx). As a real-life example, the equation y = 55x + 75 represents the total labor charges to fix a car, with y being the dependent variable and x the independent variable, showcasing the linear relationship between hours worked and total charges.

The cost of one apple is 0.5, option C is correct.

Two or more expressions with an Equal sign is called as Equation.

Let A represents cost of one apple and B represents cost of one banana

Three apples and two bananas cost 2.00

3A+2B=2...(1)

Four apples and four bananas cost 3.00.

4A+4B=3..(2)

Let us multiply equation 1 with 2

6A+4B=4...(3)

Subtract equation 3 from 2

4A+4B-6A-4B=3-4

-2A=-1

A=1/2

A=0.5

Hence, the cost of one apple is 0.5, option C is correct.

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The amount of pizza she wants is:

                        [tex]\dfrac{1}{6}[/tex] of the pizza.

If there is 1/3 of a pizza left, and Becky only wants to eat 1/2 of it.

Then the amount of pizza she wants is:

          1/2 of the amount of the pizza left.

i.e. she wants:

[tex]\dfrac{1}{2}\times \dfrac{1}{3}=\dfrac{1}{6}[/tex]

This means that Becky wants 1/6 parts of the whole pizza.

This is an exponential growth problem. Let's write the equation for exponential growth.

[tex]P=P_{0} (1+r)^{n}[/tex]

Where,

From the problem, we know initial number of views, [tex]P_{0}[/tex], is 25. Rate of increase, r, is 0.18. Time, n, is 4 weeks. Plugging in these values in the equation and solving for P will give us the number of views expected in four weeks time.

[tex]P=(25)(1+0.18)^{4}\\=(25)(1.18)^{4}\\=48.47[/tex]

Rounding to nearest whole number, it is 48.

ANSWER: 48

Given that the preference for red and blue pens is equal and that there are 48 workers, Clark should order 24 blue pens for the office.

The student is interested in figuring out how many blue pens to order for 48 workers in an office knowing that the preferences for red and blue pens are equal. This means that for every 6 people who prefer red, the same number of people will prefer blue.

To determine the number of blue pens needed, we can use a simple proportion. Since 6 people prefer red and the same number prefer blue, we have a 1:1 ratio of red to blue preferences.

Therefore, the total number of blue pens needed would be half of the total number of workers:

Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = ax is x = ay.

The logarithmic function [tex]\bold{y=log_ax}[/tex] is defined to be equivalent to the exponential equation x = ay.

Real life example:

Some examples of this include sound (decibel measures), earthquakes (Richter scale), the brightness of stars, and chemistry (pH balance, a measure of acidity and alkalinity)

Three of the most common applications of exponential and logarithmic functions have to do with interest earned on an investment, population growth, and carbon dating.

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The correct answer is: The original price is = x = $500

Explanation:

Mathematically, we can write it as:

[tex] \frac{15}{100} * x = 75 [/tex]

x = Original Price

The above equation can be read as: "The 15% of the original price is $75."

Now we need to find the value of x:

[tex] x =\frac{75 * 100}{15} = 500 [/tex]

Hence,

The original price is = x = $500

The equation of the tangent line to the curve y = 2sinx at the point (pi/6,1) is y = sqrt(3)x + (1 - sqrt(3)(pi/6)).

To find the equation of the tangent line to the curve y = 2sinx at the point (pi/6, 1), we need to find the slope of the curve at that point. The slope of a curve at a point is equal to the derivative of the function at that point.

Taking the derivative of y = 2sinx, we have dy/dx = 2cosx. Evaluating this derivative at x = pi/6, we get dy/dx = 2cos(pi/6) = sqrt(3). Therefore, the slope of the tangent line is sqrt(3).

Now we have the slope and a point on the line, (pi/6, 1). We can use the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

Plugging in the values, we have y - 1 = sqrt(3)(x - pi/6).

Simplifying this equation, we get y = sqrt(3)x - sqrt(3)(pi/6) + 1. Finally, we can rewrite the equation in the form y = mx + b by simplifying the y-intercept, giving us y = sqrt(3)x + (1 - sqrt(3)(pi/6)).

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Answer:

Answer would be 15.

Step-by-step explanation:

We have to complete the expression given as

[tex]z^{2}+9z-90=(z-6)(z+?))[/tex]

We will try to factorize the expression given in the left side.

[tex]z^{2}+9z-90=z^{2}+15z-6z-90[/tex]

                      = z(z+15)-6(z-15)

                      =[tex](z-6)(z-15)[/tex]

Now we will compare this factorized form with the right side of the expression.

(z-6) (z-15) (= (z-6) (z+?)

We find question mark is 15.

Therefore, the answer is 15.

Answer:

JK = 6

Step-by-step explanation:

Given: We are given a parallelogram JKLM and ML = 6 units. and m∠K = 109°

We need to find length of JK.

Here we use the properties of parallelogram to find the length of Jk.

In a parallelogram, the opposite sides are parallel and equal in measures.

Therefore, ML = JK

Given: ML = 6

So, 6 = JK

Therefore, the length of JK = 6

Answer:

He bought 375 paper clips.

Step-by-step explanation:

Given,

The initial number of packs of paper clips = 7,

Also, the additional number of packs of paper clips = 8,

So, the total number of packs of paper clips = 7 + 8 = 15,

Now, the number of paper clips in each pack = 25,

Hence, the total number of paper clips = number of paper clips in each pack × total packs

= 25 × 15

= 375

Answer

23 and 24.

Explanation

let the first integer be x.

The next integer would be x + 1

Now form the equation

x + (x+1) = 46

x + x + 1 = 46

2x + 1 = 46

2x = 46 - 1

x = 45

x = 22.5        This is not an integer.

Since the question is asking for the least possible integer, unless we use 23 ≅22.5

The first integer been 23, the other one would be (23 + 1) = 24.

The least possible pair would be 23 and 24.

To reduce the fraction 28/98 to lowest terms, we prime factorize each number, cancel out the common factors, and simplify. The fraction 28/98 simplifies to 1/7.

The correct prime factorization of 28 is 2×2×7 (or 2²×7), and for 98 it's 2×7×7 (or 2×7²). To reduce the fraction 28/98 to lowest terms, we can remove the common factors in the numerator and the denominator.

Since both numerator and denominator have a 2 and a 7, we can replace them with '1'. After simplifying, the remaining factors in the numerator are 1 and the remaining factors in the denominator are 7. Therefore, 28/98 reduced to lowest terms is 1/7.

(x + f) + 2 = j    subtract 2 from both sides

x + f = j - 2       subtract f from both sides

x = j - f - 2

Final answer:

The length of the arc of a circle with a radius of 3 and a central angle of 340 degrees is 17π. This is calculated by converting the angle to radians and finding the proportion of this angle to the full circle's circumference (2πr).

Explanation:

To find the length of the arc of a circle with a radius of 3 and a central angle of 340 degrees, we first need to understand that arc length (Δs) is proportional to the central angle when measured in radians. The circumference (Δ4) of a circle is given by the formula Δ = 2πr. Since there are 360 degrees in a complete circle, which corresponds to 2π radians, we can set up a proportion to solve for the arc length of the 340-degree angle.

The proportion will look like this:

Convert the central angle from degrees to radians by multiplying it by π/180.

340 degrees * π/180 = 340π/180 radians.

Use the ratio of the angle in radians to the entire circle in radians (2π) to find the arc length: Δs = (Angle in radians/2π) * Circumference.

Δs = (340π/180) / (2π) * 2π * 3.

Simplify to find the arc length Δs.

The final step yields the arc length for the given central angle and radius:

Δs = (340/360) * 2π * 3 = (17/18) * 2π * 3.

Therefore, the length of the arc is Δs = 17π.

Answer:

It is a variable

Step-by-step explanation:

A variable is a characteristic, number, or quantity that increases or decreases over time or takes different values in different situations. Hope this helps.

Answer:

27

Step-by-step explanation:

Make a tree-diagram for all three-letter code words starting with A. Each path from the top to the bottom contains 3 letters, which is one of the code words beginning with A. There are 9 such code words. Clearly, there are 9 code words starting with B and 9 starting with C. In all, there are 27 code words.

Celeste is making fruit baskets for her service club, and she is not following the specific ratio but using a similar ratio of apples to oranges in her baskets.

Celeste is making fruit baskets for her service club, and the directions say to fill the boxes using 5 apples for every 6 oranges. However, Celeste is filling her baskets with 2 apples for every 3 oranges. To determine if Celeste is following the directions, we can compare the ratio of apples to oranges in her baskets with the ratio specified in the directions.

In the directions, the ratio of apples to oranges is 5 apples: 6 oranges, which can be simplified to 5/6. In Celeste's baskets, the ratio of apples to oranges is 2 apples : 3 oranges, or 2/3.

To compare these ratios, we can find the least common multiple (LCM) of the denominators (6 and 3), which is 6. Then, we can convert both ratios to have the same denominator using equivalent fractions:

5/6 * 1/1 = 5/6 and 2/3 * 2/2 = 4/6.

Since 4/6 is less than 5/6, Celeste is not following the directions exactly. However, she is still using a similar ratio of apples to oranges in her baskets.

Each equation matches with a surface as follows: A. Cone - ρ = 2cos(φ); B. Elliptic or Circular Paraboloid - z = r²; C. Plane - ρcos(φ) = 4; D. Half plane - θ = [(π)/3]; E. Circular Cylinder - r = 2cos(θ); and F. Sphere - r² + z² = 16 or r = 4.

In order to match each equation with the verbal description of the surface, it's important to recognize their respective characteristics.

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