What is the length of the unknown leg in the right triangle?

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.

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

Answer

b

Step-by-step explanation:

i got it on eduenity

Answer:

Plus in s.

A=54(1/3)^2

First, apply exponents.

1/3 x 1/3= 1/9

A=54(1/9)

1/9 x 54= 6

Final answer: 6 square units

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:

The statement is false, it describes all parallelogram.

Step-by-step explanation:

The figure that has opposite sides with equal lengths and equal slopes and diagonals with slopes that are negative reciprocals must be a rhombus. This is a true statement

A rhombus is a quadrilateral with four equal-length sides in planar Euclidean geometry. The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths.

Given:

A figure that has opposite sides with equal lengths and equal slopes and diagonals with slopes that are negative reciprocals must be a rhombus,

Given that it possesses all the characteristics of a parallelogram, a rhombus is regarded as one of the exceptional parallelograms. The two lines of symmetry for a rhombus are its two diagonals. A line that splits an object into two equally sized halves is referred to as the axis of symmetry.

Thus, it is a Rhombus, As the opposite sides are parallel and equal and the diagonal of the rhombus is perpendicular.

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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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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.

Algebraic expression for 8 more than 5 times a number is 5x+8

In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations

Given,

8 more than 5 times a number

Consider the number is x

Then, 8 more than 5 times a number is

5x+8

Hence, Algebraic expression for 8 more than 5 times a number is 5x+8

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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.

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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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.

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 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.

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.

There are 4100625 possible passwords of 2 letters followed by 4 digits

The usable characters are:

Given that the characters can be repeated, and the password uses 2 letters and 4 digits.

The number of password is:

Password = 25* 25 * 9*9*9*9

Evaluate

Password = 4100625

Hence, there are 4100625 possible passwords

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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: