A right triangle has a hypotenuse of 1 meter and a leg of 1/2 meter. What is the area of the triangle to the nearest hundredth of a square meter?​

By using tangent property of circle, it has been proved that [tex]\Delta[/tex] ABC is isosceles

What is tangent to a circle?

At first it is important to know about circle.

Circle is a two dimensional round figure in which every point of the circle maintains a fixed distance from a point known as the center. The fixed distance is called the radius of the circle.

The straight line which touches the circle at any point is known as the tangent to a circle.

Tangent property of circle is used here

[tex]\angle BAY = 72^{\circ}[/tex]

[tex]\angle ABC = 54^{\circ}[/tex]

[tex]\angle ACB = 72^{\circ}[/tex] [Angle in alternate segment are equal]

[tex]\angle BAC = 180 - (54 + 72)\\[/tex] [Sum of three angles of a triangle is 180°

          =   180 - 126

          =   54°

[tex]\Delta ABC[/tex] is isosceles

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Answer: $5.14

Step-by-step explanation:

divide $539.70 by 105 to get the answer

so 539.70 divide by 105 is 5.14

step1 get rid of the decimal but you will ad it later so

53970

/   105

=514

step2 move the decimal 2 places to the left.

Answer:

324 ft

Step-by-step explanation:

[tex]v=\sqrt{2gh}[/tex]

[tex]v^2=(\sqrt{2gh})^2[/tex]

[tex]v^2=2gh[/tex]

[tex]\frac{v^2}{2g}=\frac{2gh}{2g}[/tex]

[tex]\frac{v^2}{2g}=h[/tex]

[tex]\frac{144^2}{2(32)}=h[/tex]

[tex]\frac{20736}{64}=h[/tex]

[tex]324=h[/tex]

The simple interest on the loan of $600 at rate of 8% over a time period of 16 months is $664 and the interest generated is $64

The formula for simple interest helps you find the interest amount if the principal amount, rate of interest and time periods are given.

Simple interest formula is given as:

S.I = P(1 + rt)

Substituting the values into the formula

S.I = 600(1 + 0.08 * 16)

S.I = 664

The interest generated is $64

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Translation: What is the interest generated by $600, placed at 8% per year for 1 year 4 months?

Answer:

Let the width be x feet. As length is 3 feet longer, it is x+3 feet. As perimeter is twice of te sum of length and width, it is 2×(x+3+x)=2×(2x+3)=4x+6 feet.

Step-by-step explanation:

There are 39% of all the people on the trip are female students on a school trip.

One to fifteen teachers are assigned to every hundred students.

and there are 7:5 more female students than male students.

Let's say there are x teachers. Students multiply by 15 as a result.

Take the ratio of male to female as 7 years for the male and 5 years for the female.

The total student trip is made up of both male and female pupils.

Thus,

15x = 7y + 5y

15x = 12y

5x = 4y

x = 4/5y  ...eq 1

Then, the percentage of the female students.

5y/(x + 5x)×100

5y/16x ×100

Put the value of x from eq 1

625/ 16 = 39%

Thus, there are 39% of all the people on the trip are female students.

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Answer:  x = -2 through 1

Step-by-step explanation:

The domain are the x values that exist on the line. The line goes between -2 and 1. Therefore, that's the domain!

250 bicycles must be manufactured to minimize the cost.

The cost C in dollar of manufacturing x bicycles at a production plant is given by:

C(x) = 3x² - 1500x + 198,500

a. To find number of bicycle that can minimize the cost

differentiate C(x) with respect to x

C'(x) = 6x - 1500

equating C'(x) = 0

6x - 1500 = 0

x = 1500/6

x = 250 , is our stationary point

Differentiate C'(x) = 6x - 1500 again and put x = 250,

C''(x) = 6 (positive)

At x = 250 , cost is minimum

Therefore , 250 bicycles must be manufactured to minimize the cost.

b. C(x) = 3x² - 1500x + 198,500

putting x = 250,

C(x) = 3(250)² - 1500(250) + 198,500
= 187,500 - 375 ,000 + 198,500

= $11,000 is the minimum cost

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The height of utility poles is B. 12 meters.

The height of the utility pole will be calculated by the formula -

tan theta = perpendicular ÷ base, where theta is the angle of elevation, perpendicular is the height of utility pole and base is the distance from the base of pole to the wire.

Keep the values in formula to find the height of utility pole.

tan 59 = perpendicular ÷ 7

Perpendicular = tan 59 × 7

Perpendicular = 1.66 × 7

Performing multiplication on Right Hand Side of the equation

Perpendicular = 11.65 metres

On rounding off, we get 12 metres.

Thus, the height is B. 12 meters.

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The total amount of the money earned by Paige will be $1591.92.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Paige works at a department store and has a commission rate of 3 per cent. Her sales for the quarter were $4,596. If she earns $50 per day and she worked 30 days in the quarter.

The total amount of earnings will be,

TA = ( 50 x 30 ) + ( 0.02 x 4596)

TA = 1500 + 91.92

TA = $1591.92

Therefore, the total amount of the money earned by Paige will be $1591.92.

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Answer:

A = Ao * (1+ i)^n       amount Ao invested for n yrs at i/yr

14900 = 4500 (1.07)^n

3.311 = (1.07)^n

log 3.311 = n log 1.07 = n* .0294

n = log 3.311 / .0294 = .52 / .0294 = 17.6 yrs

Check:

Money will double about very 70 / 7 = 10 yrs

At 10 yrs around 9000 return

At 20 yrs 18,000 return - result appears reasonable

The length of the shorter leg is 16 units which was found using the given data.

A quadratic equation is a second-degree algebraic equation in x. In its usual form, the quadratic equation is ax² + bx + c = 0.

Given: The larger leg of a right triangle is twice more than three times the shorter leg, and the triangle's area is 400.

We know that,

Area of triangle = 1/2(larger leg)(shorter leg)

                  400=1/2(larger leg)(shorter leg)   Equation(1)

larger leg = 2 + 3(shorter leg)

We need to substitute this in Equation(1)

400 = 1/2[2+3(shorter leg)](shorter leg)

800 = 2(shorter leg) + 3(shorter leg)²

3(shorter leg)² + 2(shorter leg) - 800 = 0

Solving this quadratic equation,

we get, shorter leg = - 16 or +16

Thus, we found that the length of the shorter leg is 16 units as -16 cannot be the length because it is negative.

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The equation 22+(d-1)0.5 = 30 may be used to determine how many days it will take the plant to reach a height of 30 cm. The value of d is 17, and it stands for the number of days.

There are two definitions for an arithmetic sequence. It is a series where the differences between every two succeeding terms are identical or each term in an arithmetic sequence is formed by adding a fixed number (positive, negative, or zero) to its preceding term.

The following details are available to us:

A 22 cm tall basil plant that is gaining half a centimeter daily was purchased by Matteo.

We now have the arithmetic progression shown below with the common difference, indicated by the letter d:

22, 22.5, 23, 23.5, ...

The formula for calculating the nth term:

When an is the first term, a(n) = a+(n-1)d.

A) 22+(d-1)0.5 = 30

B) The plant still needs to develop 8 cm, as there is a difference of 8 cm between 30 and 22.

C) D's value:

22+(d-1)0.5 = 30

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Answer: positive

Step-by-step explanation:

123 1/23 + (-123 1/23)

123 1/23 - 123 1/23 = 0

0 is a positive number and not negative so the answer is negative

Answer:

$6.72

Step-by-step explanation:

1 us liquid pint =2 us cups

3.36*2 cups

Answer:

Step-by-step explanation:

28xy

Answer:

r ≤ -21.75

Step-by-step explanation:

Forming the equation,

→ r ÷ (-2.5) ≤ 8.7

Then the value of r will be,

→ r ÷ (-2.5) ≤ 8.7

→ r ≤ 8.7 × (-2.5)

→ r ≤ -21.75

Hence, value of r is -21.75.

A minimum of 3 weighings are required to identify the heavy marble out of 8 marbles.

As all the marbles weigh the same except one which is heavier, therefore firstly 8 marbles are divided into half. 4 marbles are placed in one pan while the other 4 are placed in another pan. In this two-pan balance, the pan which is lower than the other contains a heavier marble.

Now, the pan with heavier marble has 4 marbles which are again divided into half. 2 marbles are placed in each pan. Similarly, the pan with heavier marble goes down as compared to another pan with 2 marbles of the same weight. Now the final weighing is done by placing 1 marble in each pan out of 2 marbles taken from the pan which went down before as compared to another pan.

The pan with heavier marble will move down and thus with 3 weighings, a heavier marble is identified.

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Answer:

ii think that the figure will be determined by 13#

Step-by-step explanation:

you have to round up to the nearest meter

Answer:

Step-by-step explanation:

dees

Answer:

Step-by-step explanation:

Get the same denominator by multiplying 4/9 by 2/2 and 1/2 by 9/9 to get 8/18-9/18=-1/18

The two negative signs can become an addition to make -1/9+2/5 which can be rewritten as 2/5-1/9. We make them the same denominator and subtract to get 13/45.

Answer:

a. 87 b. 9 c. 4

Step-by-step explanation:

Answer:

XY = 12.4 cm

Step-by-step explanation:

a² + b² = c²

(4 cm)² + (XY)² = (13 cm)²

16 cm² + XY² = 169 cm²

XY² = 153 cm²

XY = √(153 cm²)

XY = 12.4 cm

Formula of parabola for given values is F(x) = 7.5(x^2-15.7x+61.32)

The general equation of a parabola in math is: y = a(x-h)^2 + k ,where (h,k) denotes the vertex. The standard equation of a the parabola is y^2 = 4ax.

We have, horizontal intercepts x=8.4 and x=7.3, passes through point(0, 8.2)

As we parabola is quadratic function,

f(x) = a(x-8.4)(x-7.3)

It is passing through the point (0, 8.2)

8.2 = a(-8.4)(-7.3)

a = 8.2/61.32 =7.5 (approx)

Now, equation of parabola is

F(x) = 7.5(x-8.4)(x-7.3)

f(x) = 7.5(x^2-7.3x-8.4x+61.32)

F(x) = 7.5(x^2-15.7x+61.32)

Thus, required equation of parabola is F(x) = 7.5(x^2-15.7x+61.32).

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The algebra properties associated to each case are listed below:

Case 1: Distributive property

Case 3: Associative property (multiplication)

Case 5: Existence of inverse (addition)

In this question we find three algebraic expressions, in which we need to determine what algebra property is used. The most important properties in real algebra are listed below:

Now we proceed to determine the property associated to corresponding operation:

Case 1

9 · (x + y) = 9 · x + 9 · y → Distributive property

Case 3

[8 · (3 / 2)] · 15 = 8 · [(3 / 2) · 15] → Associative property (multiplication)

Case 5

(6 · x + 1) + (- 6 · x + 1) = 0 → Existence of inverse (addition)

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An equation for revenue (r) as a function of (p) is R = 1380p - 10p²,

and R(25) = 28250.

Given that;

The cost of tickets for a specific series of concerts is set by a concert venue. The sales team discovers that 1,000 people on average attend concerts with tickets costing $38. The average attendance increases by 50 persons for every $5 decrease in price. Then,

Let 'T' be the number of times the price is decreased.

So, price;

     p = 38 – 5x

     x = (38 - p) / 5

And as per the given condition attendance;

a = 1000 + 50x

So, the Revenue is;

To develop an equation for revenue (r) as a function of p, the price of tickets;

R = p * a

R= p * (1000 + 50x)

But,  x = (38 - p) / 5

Then,

R = P * (1000 + 50(38 - p)/5)

  = p * (1000 + 380 - 10p)

  = p * (1380 – 10p)

  = 1380p - 10p²  → (I)

To get R(25) from (I);

R(25) = 1380(25) - 10(25)²

         = 34500 - 6250

         = 28250

Hence, an equation for revenue (r) as a function of (p) is R = 1380p - 10p²,

and R(25) = 28250.

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The area of the trapezoid is maximum when the fourth side be 20 inches.

Trapezoids are quadrilaterals with two parallel and two oblique sides. It is also known as a trapezium. A trapezoid is a four-sided closed shape or figure with a perimeter that covers some area.

By applying Pythagorean theorem,

[tex]c^2=a^2+b^2[/tex]

[tex]10^2=h^2+x^2[/tex]

[tex]100=h^2+x^2[/tex]

[tex]h^2=100-x^2[/tex]

[tex]h=\sqrt{100-x^2}[/tex]

Area of the trapezoid is,

[tex]A=\frac12 \times h\times (b_1+b_2)[/tex]

By substituting  the values of h, b1, and b2 in the above equation,

[tex]A=\frac12 \times \sqrt{100-x^2} \times (10+2\times x+10)[/tex]

[tex]A=\sqrt{100-x^2} \times (x+10)[/tex]

If we take the derivative of both sides of the equation in relation to x, we get

[tex]\frac{dA}{dx}=\frac{d}{dx}[\sqrt{100-x^2} \times (x+10)][/tex]

[tex]\frac{dA}{dx}=\sqrt{100-x^2} \ \frac{d}{dx} (x+10) + (x+10) \ \frac{d}{dx} \sqrt{100-x^2}[/tex]

[tex]\frac{dA}{dx}=\sqrt{100-x^2} - \frac{x^2+10 x}{\sqrt{100-x^2}}[/tex]

[tex]\frac {dA}{dx}=0[/tex]

[tex]0=\sqrt{100-x^2} - \frac{x^2+10 x}{\sqrt{100-x^2}}[/tex]

[tex]\sqrt{100-x^2} = \frac{x^2+10 x}{\sqrt{100-x^2}}[/tex]

100-x²=x²+10x

2x²+10x-100=0

x²+5x-50=0

(x-5)(x+10)=0

If, x+10=0

x=-10

The above value is not accepted because it is a negative value,

If, x-5=0

x= 5

The value is accepted because it is positive value

The length of the trapezium which should be fourth is,

b₂=2x+10

b₂= 2(5)+10

b₂=20

The area of the trapezoid is maximum when the fourth side be 20 inches

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The sum of the first 16 terms of the defined arithmetic sequence is given as follows:

-520/16.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant, being called common difference d.

The nth term of an arithmetic sequence is given by the equation presented as follows, called general equation:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term of the arithmetic sequence.

The sum of the first n terms is given by the equation presented as follows:

[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]

The sequence in this problem is defined as follows:

[tex]a_n = \frac{5}{8} - \frac{5}{16}n[/tex]

The first term is of:

[tex]a_1 = \frac{5}{8} - \frac{5}{16} = \frac{5}{16}[/tex]

Hence the 16th term of the sequence is of:

[tex]a_{16} = \frac{5}{8} - \frac{5}{16}(16) = \frac{5}{8} - 5 = -\frac{35}{8}[/tex]

Hence the sum of the first 16 terms of the arithmetic sequence is defined as follows:

[tex]S_{16} = 8\left(\frac{5}{16} - \frac{35}{8}\right) = 8 \times \left(-\frac{65}{16}\right) = -\frac{520}{16}[/tex]

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