Part A: If (72)x = 1, what is the value of x? Explain your answer.

Part B: If (70)x = 1, what are the possible values of x? Explain your answer.

The two linear equations represented in system A as :

3 x + 2 y =3   -------(1)

- 2 x - 8 y = -1  ------(2)

(1) × 2 + (2) × 3 gives

⇒ 6 x + 4 y - 6 x - 24 y = 6 -3

⇒ - 20 y = 3

⇒ y = [tex]\frac{-3}{20}[/tex]

Putting the value of y in equation (1), we get

[tex]3 x  - \frac{6}{20}=3\\\\ 3 x= \frac{66}{20} \\\\ x=\frac{11}{10}[/tex]

Two linear equation represented in system B is:

3.   -x - 14 y =1

4.   - 2 x - 8 y = -1

-2 ×Equation (3) + Equation (4)=

2 x +28 y- 2 x - 8 y= -2 -1

⇒ 20 y = -3

⇒y =[tex]\frac{-3}{20}[/tex]

Putting the value of y in equation (3),we get

[tex]-x + \frac{42}{20}=1 \\\\ x=\frac{22}{20}=\frac{11}{10}[/tex]

As Two system , that is system (A) and System (B) has same solution.

By looking at all the options , i found that Option (D) is correct. The two system will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 2 times the second equation of System A.

Answer:

(D)

Step-by-step explanation:

Two linear equations by system A is given as:

[tex]3x+2y=3[/tex]           (1)

[tex]-2x-8y=-1[/tex]          (2)

Multiply equation (1) with 2 and equation (2) with 3 and then adding, we get

[tex]6x+4 y-6x-24y=6-3[/tex]

[tex]-20y=3[/tex]

[tex]y=\frac{-3}{20}[/tex]

Putting the value of y in equation (1), we get

[tex]3x-\frac{6}{20}=3[/tex]

[tex]3x=\frac{66}{20}[/tex]

[tex]x=\frac{11}{10}[/tex]

Two linear equations by system B is given as:

[tex]-x-14y=1[/tex]       (3)

[tex]-2x-8y=-1[/tex]     (4)

Multiply equation (3) with -2 and adding equation (4), we get

[tex]2x+28y-2x-8y=-2-1[/tex]

[tex]20y=-3[/tex]

[tex]y=\frac{-3}{20}[/tex]

Putting the value of y in equation (3),we get

[tex]-x+\frac{42}{20}=1[/tex]

[tex]x=\frac{11}{10}[/tex]

As Two system , that is system (A) and System (B) has same solution.

Thus,  Option (D) is correct. The two system will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 2 times the second equation of System A.

Answer

b

Step-by-step explanation:

i got it on eduenity

Final answer:

The total selling expenses for February amount to $245,600, calculated by adding the sales commissions, sales manager's salary, advertising expenses, shipping expenses, and miscellaneous selling expenses together.

Explanation:

To calculate the total selling expenses for the month of February, each component of the selling expenses will be computed based on the provided sales revenue, and then all these components will be summed up.

Sales commissions: 5% of $900,000 = $45,000

Sales manager's salary: $96,000 (fixed cost)

Advertising expenses: $80,000 (fixed cost)

Shipping expenses: 2% of $900,000 = $18,000

Miscellaneous selling expenses: $2,100 + 0.5% of $900,000 = $2,100 + $4,500 = $6,600

Adding all these expenses together:

$45,000 + $96,000 + $80,000 + $18,000 + $6,600 = $245,600

Therefore, the total selling expenses for the month of February are $245,600.

Answer:

The Answer Is A. edge 2020

Step-by-step explanation:

The change in the amount of time that Alejandro studied on the first day to the amount of time he studied on the last day is given by -30 minutes, the correct option is A.

An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.

Alejandro studied for 6 consecutive days.

Let he studied for x minutes on the first day

Next day he studies (x + 5) minutes.

Each day the time is increasing by 5 minutes.

The equation for time he studied each day = x + 5 t

On last day he studied,

= x + 5 * 6

= x +30

The change in the amount of time that Alejandro studied on the first day to the amount of time he studied on the last day is given by

x - x -30

= -30 minutes

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Answer:

A

Step-by-step explanation:

The events "green eyes" and "brown hair" are not independent because the probability of a student having both green eyes and brown hair is not equal to the product of their individual probabilities.

To determine whether the events "green eyes" and "brown hair" are independent, we need to look at the probabilities of each event occurring separately and together.

The probability of having green eyes (P(Green Eyes)) is the total number of students with green eyes divided by the total number of students, which is 28/50.

The probability of having brown hair (P(Brown Hair)) is the total number of students with brown hair divided by the total number of students, which is 30/50.

The probability of having both green eyes and brown hair (P(Green Eyes AND Brown Hair)) is the number of students with both green eyes and brown hair divided by the total number of students, which is 16/50.

Events A and B are independent if P(A and B) = P(A) * P(B). Using this formula, we can determine if the events are independent:

P(Green Eyes AND Brown Hair) = P(Green Eyes) * P(Brown Hair)

16/50 ≠ (28/50) * (30/50)

Since the probability of having both green eyes and brown hair does not equal the product of the probabilities of having green eyes and having brown hair, these events are not independent.

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Running Speed = x
Cycling Speed = x + 9
19.5/x + 9 = 6/x
Cross multiply
19.5x = 6x + 54

19.5x - 6x = 54
13.5x = 54
x = 4
she runs 4 mph

Answer:

4 mph

Step-by-step explanation:

Final answer:

Sonya's annual take-home pay, after FICA taxes of 7.65% on her annual salary of $36,590, would be $33,790.86.

Explanation:

To calculate Sonya’s annual take-home pay after FICA taxes, we first need to understand that FICA consists of two separate taxes: Social Security and Medicare. The total rate for these combined is 7.65% of the gross income. Sonya’s annual salary is $36,590.

First, we calculate the total FICA tax Sonya has to pay:

Add these two amounts to get the total FICA tax:

$2,268.58 (Social Security) + $530.56 (Medicare) = $2,799.14

Finally, subtract this total FICA tax from the annual salary to find Sonya’s take-home pay:

$36,590 (annual salary) - $2,799.14 (FICA taxes) = $33,790.86

volume = PI x r^2 x h

using 3.14 for pi

volume = 3.14 x 2^2 x 3

volume = 37.7 cubic cm of wax needed

Round answer as needed

Answer:

12Pi cm3

Step-by-step explanation:

Final answer:

Using the two given points $(82, 4)$ and $(42, 9)$, the slope is calculated to be $-1/8$. Subsequently, by using the point-slope form of the line equation and simplifying, we find that the linear relationship between price and demand is described by $y = -1/8x + 57/4$, which corresponds to choice A.

Explanation:

To determine the linear equation that best models the price-demand relationship for the mini-recorders, we are given two points. At a price of $82, the demand is 400 recorders (4 hundred), and at a price of $42, the demand is 900 recorders (9 hundred). In the mathematical representation, these points are (82, 4) and (42, 9), where x is the price and y is the demand in hundreds.

To find the slope (m) of the line, we use the slope formula:

m = (y2 - y1) / (x2 - x1), which gives us m = (9 - 4) / (42 - 82) = 5 / (-40) = -1/8.

Now, we can use the point-slope form to find the equation of the line. Let's use the point (82, 4):

y - y1 = m(x - x1)

y - 4 = (-1/8)(x - 82)

Multiplying out the right-hand side of the equation, we have:

y - 4 = (-1/8)x + (82/8)

y - 4 = (-1/8)x + 10.25

Moving 4 to the other side to get 'y' by itself, the equation becomes: y = (-1/8)x + 10.25 + 4

This simplifies to:

y = (-1/8)x + 14.25

Converting 14.25 into quarters gives us 14.25 = 57/4. Hence the equation becomes:

y = (-1/8)x + 57/4 which matches choice A.

Final answer:

The correct equation that models the price-demand relationship is y = -1/8x + 57/4, where y is the demand in hundreds and x is the price per mini-recorder.

Explanation:

To find the equation that models the price-demand relationship, we need two points to determine the line: (x1, y1) = (82, 4) and (x2, y2) = (42, 9). The demand, y, is in hundreds of recorders and x represents the price per mini-recorder. The slope (m) of the line is given by the change in demand over the change in price: m = (y2 - y1) / (x2 - x1) = (9 - 4) / (42 - 82) = 5 / (-40) = -1/8. To find the y-intercept (b), we use one of the points and the slope in the linear equation formula y = mx + b. Using the point (82, 4), we have 4 = (-1/8)(82) + b. Solving this equation gives us b = 4 + (1/8)(82) = 4 + 10.25 = 14.25. Now the linear equation is y = -1/8x + 14.25. Since y needs to be in hundreds for the units to match the point given (400, 900), we must divide b by 100, resulting in b = 14.25 / 100 = 57/4. The final price-demand relationship is y = -1/8x + 57/4.

Answer: a. Circle

Step-by-step explanation:

Given equation: [tex](x-8)^2+(y-12)^2=25[/tex] which is equivalent to [tex](x-8)^2+(y-12)^2=5^2[/tex]

This equation is of the form [tex](x-h)^2+(y-k)^2=r^2[/tex] which is the standard equation of a circle centered at (h,k) with radius r.

On comparing given equation to the standard equation of  circle we have, h=8 and k=12 and r =2.

Therefore, given equation represent a circle centered at (8,12) and radius=5 units.

Final answer:

A straight line is determined by a minimum of two points. This is a fundamental concept in geometry and algebra, necessary for defining lines on any two-dimensional path or graph.

Explanation:

To determine the minimum number of points through which a straight line is drawn, we need to understand that a straight line is defined by only two points.

The minimum number of points through which a straight line is drawn is two. In geometry, a line extends infinitely in both directions but is determined by just two points. The concept of a line is fundamental in understanding various subjects such as algebra and geometry.

To convert a fraction to a decimal, divide the numerator by the denominator. For example, 1/2 converted to a decimal is 0.5.

To convert a fraction to a decimal, you use the method defined by option B: Numerator divided by Denominator (Numerator / Denominator). This will give you the decimal equivalent of the fraction. For example, if you have the fraction 1/2, you divide the numerator (1) by the denominator (2) to get 0.5, which is the decimal equivalent of the fraction 1/2.

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The tongue of a chameleon is 1.5 times its body length when expressed as a decimal.

If the tongue of a chameleon is one and a half times its body length, we express this as a decimal by multiplying the body length by 1.5. For example, if the body length is represented by 1 unit, then the tongue length would be 1  imes 1.5, which equals 1.5. Therefore, the length of the tongue as a decimal is 1.5 times the body length.

 2 x 2 = 4 x 3 = 12

2 x 3 = 6 x 3 = 18

2 x 2 = 4 x 2 = 8 x 3 = 24 x 3 = 72

2x2 = 4 x 3 = 12 x 3 = 36

 last one is the correct answer

Final answer:

To convert the equation y = -3/5x + 3 into standard form with integer coefficients, multiply both sides by 5 to get rid of the fraction, resulting in 5y = -3x + 15. Then, rearrange the terms to obtain the standard form, which is 3x + 5y = 15.

Explanation:

The equation y = -3/5x + 3 is given in slope-intercept form. To convert it into standard form using integer coefficients, we need to rearrange the terms so that all variables and constants are on one side of the equation and the constant is on the other side. The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

First, multiply both sides of the equation by 5 to clear the fraction:

5y = -3x + 15

Next, move the x-term to the left side of the equation:

3x + 5y = 15

Now, the equation is in standard form with integer coefficients.

Answer:

The LCM of given expressions is [tex]72a^3b^2[/tex].

Step-by-step explanation:

The given expressions are

[tex]24a^3b[/tex]

[tex]36ab^2[/tex]

Find factor form of each expression.

[tex]24a^3b=2\times 2\times 2\times 3\times a\times a\times a\times b[/tex]

[tex]36ab^2=2\times 2\times 3\times 3\times a\times b\times b[/tex]

LCM is the product of all factors where common factors are considered only once.

[tex]LCM(24a^3b,36ab^2)=2\times 2\times 2\times 3\times 3\times a\times a\times a\times b\times b[/tex]

[tex]LCM(24a^3b,36ab^2)=72a^3b^2[/tex]

Therefore the LCM of given expressions is [tex]72a^3b^2[/tex].