One of the legs of a right triangle measures 3 cm and its hypotenuse measures 6 cm. Find the measure of the other leg

The money invested by Phyllis with simple interest rate 3 1/2% and 3% per year is given by $7500 , and $3,000 respectively.

As given in the question,

Total amount with Phyllis is equal to $10,500

Let 'x' be the portion of Phyllis earning invested with 3 1/2% per year simple interest rate

Then $( 10,500 - x ) invested by Phyllis with simple interest rate 3% per year

Total interest earned by the investment = $352.50

0.035x + 0.03( 10,500 - x ) = $352.50

⇒0.035x + 315 - 0.03x = 352.50

⇒0.005x = 352.50 - 315

⇒0.005x = 37.5

⇒x = $7500

and $( 10,500 - x ) = $( 10,500 - 7500 )

                              = $ 3,000

Therefore, the amount of invested with simple interest rate 3 1/2% per year and 3% is equal to $7500 and $3,000 respectively.

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Answer: look at the picture

Step-by-step explanation: Hope this help :D

The derivative function for equations 1 and 2 will be

y' = -1/ [2√(1-x²)] and y' = 3/[2(1 + x²)] respectively

Here we need to find the derivative of

[tex]y = tan^{-1}\sqrt{\frac{1-x}{1+x} }[/tex]

Let x = cos2z

Hence we get

[tex]y = tan^{-1}\sqrt{\frac{1-cos2z}{1+cos2z} }[/tex]

[tex]or, y = tan^{-1}\sqrt{\frac{2sin^{2}z}{2cos^{2}z} }[/tex]

[tex]or, y = tan^{-1}(tanz)[/tex]

or, y = z

Hence dy/dx = dz/dx

We know that

x = cos2z

or, 2z = cos⁻¹x

or, 2 dz/dx = -1/√(1-x²)

Hence dy/dx = -1/ [2√(1-x²)]

The second equation is

[tex]y = 3tan^{-1}[x-\sqrt{1+x^{2}} ][/tex]

Let x = cotz

Hence we get

[tex]y = 3tan^{-1}[cotz-\sqrt{1+cot^{2}z} ][/tex]

[tex]y = 3tan^{-1}[cotz-\sqrt{cosec^{2}z} ][/tex]

or, y = 3tan⁻¹ [cotz - cosecz]

or, y = 3tan⁻¹ [cosz/sinx - 1/sinz]

or, y = 3tan⁻¹ [(cosz - 1)/sinz]

or, y = 3tan⁻¹ [-2sin²(z/2)/{2sin(z/2) cos(z/2)}]

or, y = 3tan⁻¹ [-sin(z/2)/cos(z/2)]

or, y = 3tan⁻¹ [-tan{z/2)]

or, y = 3tan⁻¹ [tan{-z/2)]

or, y = -3z/2

or, dy/dz = -3/2 dz/dx

We have

x = cotz

or, z = cot⁻¹z

or, dz/dx = -1/(1 + x²)

Hence we get

dy/dx = 3/[2(1 + x²)]

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The directions of XYZ in graph are left and right, top and bottom and outward from the screen respectively.

The term graph is known as a pictorial representation or a diagram that represents data or values in an organized manner.

Here we have to find the directions of XYZ on the graph.

Here we have know that X-Y-Z matrix is a three-dimensional structure whereby the x-axis and y-axis denote the first two dimensions and the z-axis is the third dimension.

And then in a graphic image, then the x denotes width, y denotes height and the z represents depth.

The directions of the x axis is in the plane of the screen and is positive toward the right and negative toward the left. Where as the directions of the y axis is in the plane of the screen and is positive toward the top and negative toward the bottom.

Finally the directions of the z axis is perpendicular to the screen or keyboard, and is positive extending outward from the screen.

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Yes, the order of the quantities in an inequality matters, and examples are given to show why.

The four inequality symbols, along with their meaning, are presented as follows:

It is known that the number 5 is greater than the number 3, hence the inequality that describes these numbers is given as follows:

5 > 3.

However, if we tried to apply the commutative property, that is, changing the order of the numbers, we would have that:

3 > 5.

Which is a false statement, as the number 3 is less than the number 5, and not more.

This shows that the order of the symbols in an inequality in fact does matter.

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The percent of fans that are between 18 and 27 years old is 16.80%.

From the information, the average age of a group of fans at a hockey game is 34 years with a standard deviation of 8 years and we want to calculate the percent of fans are between 18 and 27 years old.

It should be noted that this will be Illustrated through the normal curve.

The probability will be:

P(18 ≤ X ≤ 27)

= P(18 - 34/8) ≤ Z ≤ (27 - 34 / 8

= P(-2.0 ≤ Z ≤ -0.875)

= 0.1908 - 0.02275 (From the standard normal calculator)

= 16.80%

The percentage is 16.80%.

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Helen is not correct. The pressure decreases by 23.8% and not less than 20%.

The initial pressure is 70 N / 0.2 m^2 = 350 Pa (Pascals). If the force is increased by 10 N and the area is increased by 10 cm^2, the new pressure is 80 N / 0.3 m^2 = 266.67 Pa

To calculate the percentage change in pressure, we divide the change in pressure by the initial pressure and multiply by 100:

So Helen is not correct. The pressure decreases by 23.8% and not less than 20%.

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Answer: There are three 0s

240 x 25 = 6000 and there are three 0s in 6000

Answer:

Parallelogram formula- 1/2 x base xheight

Step-by-step explanation:

The domain of x=4 is (−∞,∞) and range is {y|y=4} .

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

(−∞,∞)

{x|x ∈ R}

y=4

is a straight line perpendicular to the y-axis, which means that the range is a set of one value  {y|y =4}

Set-Builder Notation:{y|y =4}.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

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Answer:

----------------------------------

According to the two-tangent theorem, two tangent segments drawn to one circle from the same external point are congruent.

That is:

We have EF = 10 units, it means EG is also 10 units.

The perimeter of triangle EHP is:

We can substitute:

Then the perimeter is:

EXPLANATION

2025 is a perfect square number hence we can determine its square root. 45 is the square root of 2025 as 45 multiplied by 45 gives the number 2025. Interestingly, – 45 × – 45 is also 2025. Hence It is represented as √2025 = 土45.

Answer:

Option b.  -2x + 3y - 6 = 0

Step-by-step explanation:

Let's look for a linear equation of the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).

Calculate the slope first.  Slope is the Rise/Run of any two points on a straight line.   Using the given points, (0,2) and (3,4) we find:

  Rise = 4 - 2 = 2

  Run = 3 - 0 = 3

Slope, m, Rise/Run = (2/3)

The equation becomes y = (2/3)x + b

To find b, enter either of the two given points.  

y = (2/3)x + b

2 = (2/3)(0) + b  :  for point (0,2)

b = 2

The equation becomes:  y = (2/3)x + 2

Reformat this to match the format of the answer options.  

y = (2/3)x + 2    

3y = 2x + 6      [Multiplied by 3]

3y - 2x - 6 = 0

-2x + 3y - 6 = 0     [rearrange]

This matches option b.

After 156.25 miles will the cost be the same to rent a car. This can be solved by the concept of cross-multiplication.

Fractions are multiplied by multiplying the numerator of the first fraction by the denominator of the second fraction, and the numerator of the second fraction by the denominator of the first fraction.

In order to get the second fraction's numerator, multiply the first fraction's denominator by it. Cross multiply is another name for the butterfly technique of multiplication. The cross-multiply technique is used to find one or more variables in a fraction.

Let, assume miles be m.

and, Let the total cost be x.

According to the question,

0.25m + 50 = x ........(i)

0.41m + 25 = x ........ (ii)

By solving equation (ii) by (i) we get -

0.16 m - 25 = 0

or, 0.16m = 25

or, m = 25 /0.16

or, m = 156.25

Thus, number of miles = 156.25 miles.

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Answer:

B. Yes, the constant of proportionality is 2.

Step-by-step explanation:

Given:

A linear relationship is shown in the table.

Time (hours) 2 4 6 8

Distance (miles) 4 8 12 16

Is the linear relationship also proportional? Explain.

A. No, the constant of proportionality is 2.

B. Yes, the constant of proportionality is 2.

C. No, there is no constant of proportionality.

D. Yes, there is no constant of proportionality.

Solve:

To know if a linear relationship is proportional, all we have to find out is if after we divide distance by time and if all equal the same. Ex: 4/4=1,3/3=1. As we can see all are equal to 1.

Let's see the table:

Time (hours)                    Distance (miles)

2                                                  4

4                                                  8

6                                                  12

8                                                  16

The formula for it is 'k=y/x'

where;

k: constant of proportionality  

y and x are two quantities that are directly proportional to each other.

Also means;

y = Distance

x = Time(Hours)

Time (hours)                    Distance (miles)

2                                                  4                                                4/2=2

4                                                  8                                                8/4=2

6                                                  12                                               12/6=2

8                                                  16                                                16/8=2

As you see all equal to 2. It a constant. Also means that;

Yes, the linear relationship is proportional and the constant of proportionality is 2.

Answer: B. Yes, the constant of proportionality is 2.

RevyBreeze

Answer:

c maybe

Step-by-step explanation:

Answer:

i cant see it very well but i wanna say its A but im not 100% sure

Step-by-step explanation:

Answer:

B. (1,4)

Step-by-step explanation:

you see the x and y coordinate by looking at the numbers (x,y) = (1,4)

15 + 25 = 40

10% of 40 = 4

Therefore, Caleb gave $4 to the church!

Hope this helps :D

Answer:

x+7+3y

Step-by-step explanation:

You just remove the parentheses in this case since you don't have to change any of the operations.  

Answer:

Step-by-step explanation:

x+7+3y simplifed

Answer:

After 2 years, there will be £ 2,121.80 in the account.

Step-by-step explanation:

Since £ 2000 was put into a bank account that pays 3% compound intrest per year, to determine how much will be in the account after 2 years the following calculation must be performed:

2000 x (1 + 0.03 / 1) ^ 1x2 = X

2000 x 1.03 ^ 2 = X

2,121.8 = X

Therefore, after 2 years, there will be £ 2,121.80 in the account.

Because the sine and cosine ratios involve dividing a leg (one of the shorter two sides) by the hypotenuse (the longest side), the ratio values will never be greater than one, because (some number) / (a larger number) is always less than one.

Sine & cosine are trigonometric functions of an angle in mathematics. In the context of a right triangle, the sine and cosine of an acute angle are defined as follows: for the specified angle, the sine is the ratio of the length of the side opposite that angle to the length of the triangle's longest side (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse.

The sine and cosine functions for an angle θ are simply denoted as sin θ and cos θ. In general, the definitions of sine and cosine can be extended to any real value expressed in terms of the lengths of specific line segments in a unit circle.

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The sample space of the experiment is 52.

The possibility that an event will occur among all potential events is known as probability. It ranges from 0 to 1. The probability is calculated by dividing the number of things by all of the items. Population includes the sample. When studying the entire population is challenging, it is studied.

52 cards in a deck

There are 12 face cards.

The experiment needs a sample space of 52 to find the face cards.

Given that a regular deck of cards is available.

The sample space required for the experiment to determine the probability of face cards must be found.

A face card may or may not be revealed when we pull a card from the deck. So, in order to rule out the possibility that a face card is present at the end of the deck, we must draw every card from a regular deck.

52 samples are therefore required for the experiment.

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Answer:

c = √52

Step-by-step explanation:

→ Write Pythagoras' theorem

a² + b² = c²

→ Substitute in the numbers

4² + 6² = c²

→ Simplify

52 = c²

→ Square root both sides

√52 = c

Answer: x = 3

Step-by-step explanation:

Simplifying

17x + -3 = 48

Reorder the terms:

-3 + 17x = 48

Solving

-3 + 17x = 48

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.

-3 + 3 + 17x = 48 + 3

Combine like terms: -3 + 3 = 0

0 + 17x = 48 + 3

17x = 48 + 3

Combine like terms: 48 + 3 = 51

17x = 51

Divide each side by '17'.

x = 3

Simplifying

x = 3

Answer:

0.75

Step-by-step explanation:

plato

The value of x for the equation is,

⇒ x = 3/4

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Expression is,

⇒ 1.5 (4)²ˣ = 12

Now, We can solve for x as;

⇒ 1.5 (4)²ˣ = 12

Divide by 1.5;

⇒ (4)²ˣ = 12/1.5

⇒ (4)²ˣ = 8

⇒ (2)⁴ˣ = 2³

By comparing we get;

⇒ 4x = 3

⇒ x = 3/4

Thus, The value of x for the equation is,

⇒ x = 3/4

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Answer:

Using substitution method

x= 2

y= 1

Answer:

Step-by-step explanation:

Equation of the smaller circle:

Equation of the greater circle:

The scale factor is the ratio of radiuses:

So the rule is:

Correct choice is A

Answer:

[tex]\sf A. \quad (x, y) \rightarrow \left(\dfrac{7}{2}x, \dfrac{7}{2}y \right)[/tex]

Step-by-step explanation:

The distance from the center of the circle to any point on the circumference is the radius.

From inspection of the given graph:

To find the scale factor of the dilation from the small circle C to the large circle C', divide the radius of the large circle by the radius of the small circle.

Therefore, the dilation is an enlargement of scale factor ⁷/₂ about the origin.

So the rule that represents the transformation is:

[tex]\sf (x, y) \rightarrow \left(\dfrac{7}{2}x, \dfrac{7}{2}y \right)[/tex]

Check (see attached):

Point (0, 2) is on circle C.

[tex]\implies \sf (0, 2) \rightarrow \left(\dfrac{7}{2}(0), \dfrac{7}{2}(2) \right)=(0,7)[/tex]

Point (1, √3) is on Circle C:

[tex]\implies \sf (1, \sqrt{3}) \rightarrow \left(\dfrac{7}{2}(1), \dfrac{7}{2}(\sqrt{3}) \right)=\left(3.5,6.06)[/tex]