Find tanθ + sinθ for the angle θ shown in the right triangle?

The point which satisfies equation is (-2,4)

What is circle?

A circle could be a form consisting of all purposes during a plane that are at a given distance from a given point, the centre.

Main body:

The center of circle formula is also known as the general equation of a circle. In a circle, if the coordinates of the center are (h,k), r is the radius, and (x,y) is any point on the circle, then the center of circle formula is given below:

Formula of circle =

(x - h)² + (y - k)² = r²

According to question:

center of circle = (2,1)

diameter of circle = 10 units

radius = 5 units

equation of circle ⇒

(x - 2)² + (y - 1)² = 25

for a point to lie on circle , it need to satisfy the equation of circle:

A) (1,-3)

⇒(1 - 2)² + (3 - 1)²

⇒(-1)² +2²

⇒5

so it does not lie on circle.

B) (-2,4)

⇒(-2 - 2)² + (4 - 1)²

⇒-4²+3²

⇒ 25

so, it satisfies the equation.

hence, the point which satisfies equation is (-2,4)

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Rate percent is 10%

A coefficient that is a quotient of two values, where the denominator is written in percentage points and has the same units as the numerator when it is multiplied by a unit of time.

According to the given information

Sum of money ( principal ) P = 5000 rupees

Interest obtained in money = 1500 rupees

Time duration T = 3 years

According to the given information

I = P × T × [tex]\frac{R}{100}[/tex]

1500 = 500 × 3 × R/100

Rate percent is 10%

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The type of the function for the given graph f(x) on the right is odd function.

An exact one of each element of Y is assigned to each element of X via a mathematical function from a set X to a set Y. The sets X and Y are denoted by the terms "domain" and "codomain," respectively.

The link between varying amounts and other variables was the foundational idea behind functions. The effect of time on a planet's position serves as an example of this. The infinitesimal calculus was used to develop the concept in the past, beginning at the end of the 17th century and continuing through the 19th century.

An odd function's graph possesses rotational symmetry with respect to the origin, which means that it doesn't change after being rotated by 180 degrees around the origin.

Therefore, The type of the function for the given graph f(x) on the right is odd function.

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Answer: b

Step-by-step explanation:

3^2 + x^2 = 9^2

9 + x^2 = 81

x^2 = 72

x = sqrt(72)

Hello,

I hope you and your family are doing well!

A) To find the annual growth rate between 1991 and 2008, we can use the compound interest formula:

S = P(1 + r)

Where S is the final value of the house, P is the initial value of the house, and r is the annual growth rate.

Plugging in the values from the problem, we get:

165,000 = 95,000(1 + r)

Dividing both sides of the equation by 95,000 gives:

1.737 = 1 + r

Subtracting 1 from both sides of the equation gives:

0.737 = r

The annual growth rate between 1991 and 2008 is 0.737.

B) To express the growth rate in percentage form, we can multiply it by 100%:

0.737 * 100% = 73.7%

So the annual growth rate between 1991 and 2008 was 73.7%.

C) To find the value of the house in the year 2011, we can use the compound interest formula again, with the initial value of the house set to the final value in 2008:

S = P(1 + r)

Plugging in the values from the problem, we get:

S = 165,000(1 + 0.737)

Solving for S gives:

S = 165,000 * 1.737 = 285,195

So the value of the house in the year 2011 will be approximately $285,195. Rounded to the nearest thousand dollars, this is $285,000

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Happy Holidays!

Applying the property of exponents, the remainder that the number 10^2023 leaves after division by 13 is 9.

The remainder is the amount left over after a division operation.

An exponent is a number that indicates how many times a base number is used as a factor in a multiplication expression.

From the property of exponent:

We can rewrite 10^2023 as (10^13)^155 * 10^8:

10^2023 = (10^13)^155 * 10^8

We can then use the property of exponents to simplify:

10^2023 = (10^(13*155)) * 10^8

Since 10^13 is congruent to 1 mod 13, 10^(13*155) is congruent to 1 mod 13 as well. Therefore, 10^2023 is congruent to 10^8 mod 13.

We can find the remainder by calculating 10^8 mod 13:

10^8 = 100000000

After dividing 100000000 by 13, we get a remainder of 9.

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Answer:

m∠A = 60

m∠D = 60

Step-by-step explanation:

∆ABC and ∆DEF are congruent triangles

So,

m∠A = m∠D

x + 30 = 2x

2x - x = 30

x = 30

So,

m∠A = x + 30 = 30 + 30 = 60

m∠D = 2x = 2(30) = 60

Thus, m∠A and m∠D are 60°

The interest over 18 months will be $105.00 if Margo borrows $1000, agreeing to pay it back with 7% annual interest.

It is defined as the interest on the based on the principal amount, it does not include the compounded amount. The interest calculate on the initial amount or borrowed amount.

It is given that:

Margo borrows $1000, agreeing to pay it back with 7% annual interest after 9 months

I = Prt

= 1.5 x 7%

= 1.5 x .07

= 0.105

= $1000 x .105

= $105.00

Thus, the interest over 18 months will be $105.00 if Margo borrows $1000, agreeing to pay it back with 7% annual interest.

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The ratio shows how many times one value is contained in another value.

The ratio of office buildings to hotels will be 9 : 4.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

The ratio of hotels to office buildings = 4 : 9

Now,

The ratio of office buildings to hotels will be 9 : 4.

Thus,

The ratio of office buildings to hotels will be 9 : 4.

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Answer:

the width of the rectangle is -5/3 inches.

Step-by-step explanation:

To find the perimeter of the rectangle, we add together the lengths of all four sides. Since the rectangle is 5 inches long and 2x inches wide, the perimeter is given by:

Perimeter = 5 + 2x + 5 + 2x = 10 + 4x

To find the area of the rectangle, we multiply the length by the width. The area is given by:

Area = 5 * 2x = 10x

Setting the perimeter equal to the area, we have:

10 + 4x = 10x

Subtracting 10 from both sides, we have:

4x = 10x - 10

Combining like terms, we have:

-6x = -10

Dividing both sides by -6, we have:

x = 10 / -6

Simplifying, we have:

x = -5/3

Answer:

c= 1.5t, c=t+0.5t and c=(1+0.5)t

Step-by-step explanation:

Given that, Clare scored 50% more points than Tyler, c is the number of points that Clare scored and t is the number of points that Tyler scored,According to question,c = 150% of tc = 1.5tHence, the correct options are c = 1.5t, c = t+0.5t and c = (1+0.5)t

Answer:

Step-by-step explanation:

1) x - 1 = 2x - 2

-x = -1

x = 1

2) 4x = x + 3

3x = 3

x = 1

3) x + 1 = x + 1

infinite solutions (parallel lines)

For graphing, just look at the y-intercept, in the equation y = mx + b.

b is the y-intercept, so, for you plot the y-intercpet on the y-axis. You look at m, which is the slope. For positive, you go up how many ever it says in the numerator and then to the right how many ever it says in the denominator. For a negative you do the same thing except you go down and then to the right, or up and to the left. For positive there is only up and then to the right. I hope this answers your question.

Answer:

6790 km

Step-by-step explanation:

move the decimal 3 places to the right.

The number of leaves on a tree which is 2 yards tall and receives 9 hours of sunlight is 324 leaves.

z = k × y × x

Where,

If y = 10 yards, x = 3 hours, z = 540 leaves

z = k × y × x

540 = k × 10 × 3

540 = 30k

k = 540/30

k = 18

Then, find z when y = 2 yards and x = 9 hours

z = k × y × x

= 18 × 2 × 9

z = 324 leaves.

In conclusion, given the constant of proportionality, the number of leaves on the tree is 324 leaves.

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The population of the state in 2000 was 23.1 million and the population will be 28.3 million after 13.4 years.

The definition of an exponential function is given by the equation

y = aeᵇˣ, where bx is an exponent.

The given equation is [tex]A = 23.1e^{0.0152t}[/tex].

To find the population of the state in 2000, substitute t = 0 in the given equation:

[tex]A =23.1e^{0.0152(0)}\\\\A = 23.1[/tex]

Now, Substitute A = 28.3 into the given equation and solve for t:
[tex]28.3=23.1e^{0.0152t}\\\\e^{0.0152t}=1.2251\\\\0.0152t=\ln(1.2251)\\\\0.0152t=0.2030\\\\t=13.4[/tex]

Hence, the population of the state in 2000 was 23.1 million and the population will be 28.3 million after 13.4 years.

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Answer:

35cm^2

Step-by-step explanation:

Things To Keep In Mind:

Height: 7 cm

Length: 10 cm

(L*H)/2=area of triangle

7*10=70

70/2=35

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4,034.06 ,5,965.94 are confidence interval for the population average wages at the factory.

What is confidence interval estimation?

Your estimate's mean plus and minus the range of that estimate's fluctuation is called a confidence interval.

                                              If you repeat your test, you can expect your estimate to fall between these numbers with a reasonable degree of certainty.  Another term for probability in statistics is confidence.

The formula for confidence interval estimation is:

μ = M ± Z(sM)

where:

M = sample mean

Z = Z statistic determined by confidence level

sM = standard error = √(s2/n)

M = 50000

Z = 2.58

sM = √(30002/64) = 375

μ = M ± Z(sM)

μ = 50000 ± 2.58*375

μ = 50000 ± 965.94

μ = 4,034.06 ,5,965.94

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The coordinates of the turning point on the curve with the quadratic equation y = 9 + 18x - 3x² is (3,36).

What is a quadratic equation?

Any equation of the form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

It is given that:

The quadratic equation is:

y = 9 + 18x - 3x²

To find the turning point:

Graph the above quadratic equation;

From the graph:

The maximum point from where the graph starts to decrease is (3,36)

Thus, the coordinates of the turning point on the curve with the Quadratic equation y = 9 + 18x - 3x² is (3,36).

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Profit is the money you have left after paying for business expenses.

The production of the products are given below with the profit as well:

a. Production of Product 1 = 50 units per week

b. Production of Product 2 = 0 units per week

c. Production of Product 3 = 145 units per week

d. Production of Product 4 = 10 units per week

e. Total Profit = $1250 per week

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Answer:

Step-by-step explanation:

A local manufacturing firm produces four different metal products, each of

which must be machined, polished and assembled. The specific time

requirements (in hours) for each product are as follows:

Machining,

hours

Polishing, hours Assembling,

hours

Product I 3 1 2

Product II 2 1 1

Product III 2 2 2

Product IV 4 3 1

There is sufficient evidence to support the claim.

What is sufficient evidence ?

Sufficient evidence is admitted evidence that has enough overall weight, in terms of relevance and credibility, to legally justify a particular conclusion.

This is left tailed test .

The null and alternative hypothesis is ,

H0 :  mu= 34

Ha :mu < 34

Test statistic(t) = (x)

n= root (29.5 - 34) / 1.70

root 35

Test statistic = -15.66

P-value = 0

Alpha = 0.05

P-value <Alpha

Reject the null hypothesis .

There is sufficient evidence to support the claim.

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Answer:

4x=4   or 4tims x =y

Step-by-step explanation:

1x4=4

3x4-=12

We can estimate the number of adult partons at 2187 by solving equations.

The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.

A function is an equation that has only one answer for y for every possible value of x.

When utilizing a function, each input of a specific type receives exactly one output.

A function is commonly referred to as f(x) or g instead of y. (x).

Because f(2) instructs us to do so, we should figure out the value of our function when x is equal to 2.

So, the total number of adults present was thus:

Let a be an adult, and b and c be kids.

Ticket totals:

a + c = 5200

c = (5200-a)

Total amount:

7.50a + 4.50c = 29961

In the first equation, swap out c with (5200-a).

7.5a + 4.5(5200-a) = 29961

7.5a + 23400 - 4.5a = 29961

7.5a - 4.5a = 29961 - 23400

3a = 6561

a = 6561/3

a = 2187

Therefore, we can estimate the number of adult partons at 2187 by solving equations.

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The expression that is equivalent to  ∛ 5 * [tex]\sqrt[5]{4}[/tex] is [tex]5^{1/3}*4^{2/5}[/tex]

A radical in mathematics is the opposite of an exponent, which is symbolized by the sign "n√" also known as root.

The number before the symbol or radical is regarded as an index number or degree, and it can either be a square root or a cube root and so on.

This equation represents exponents in fraction form and the basics for the calculation is from

x^(b/n)

[tex]\sqrt[n]{x}^{b}[/tex]

Rewriting the expression is done as below

∛ 5

= [tex]5^{1/3}[/tex]

and

[tex]\sqrt[5]{4}[/tex]

[tex]= 4^{2/5}[/tex]

combining both gives

∛ 5 * [tex]\sqrt[5]{4}[/tex]

[tex]5^{1/3}*4^{2/5}[/tex]

[tex]5^{1/3}*4^{2/5}[/tex] is the equivalent expression

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Answer: To find the value of m in the equation W = 1/2 * m * v^2, you need to know the values of W and v. The variable m represents the mass of the object, and W represents the kinetic energy of the object. The equation states that the kinetic energy of an object is equal to 1/2 of its mass multiplied by its velocity squared.

If you are given the values of W and v, you can solve for m by rearranging the equation as follows:

m = 2 * W / v^2

Plugging in the values of W and v will give you the value of m.

For example, if W = 100 joules and v = 10 meters per second, the equation would be:

m = 2 * 100 joules / 10 m/s^2 = 20 kilograms

This is the mass of the object.

[tex]m=\frac{2W}{v^{2} }[/tex].

[tex]W=\frac{1}{2} mv^{2}[/tex]

[tex]\frac{W}{\frac{1}{2} v^{2} }=m\\ \\[/tex]

[tex]m=\frac{W}{\frac{1}{2} v^{2} }\\ \\m=\frac{2W}{v^{2} }[/tex].

The solutions of the given system of Equations are (5/2, 41/2).

The set of values for each variable in a system of linear equations is referred to as the solution set.

The intersection or meeting points of the lines or planes used to illustrate the linear equations are also known as the solutions.

The elimination method is one way of resolving a system of linear equations. To obtain the equation in one variable using this technique, simply add or subtract the equations.

Here we have

y = 9x-2 --- (1)

y = 7x+3 --- (2)

From (1) and (2)

=>  9x - 2 = 7x + 3

=>  9x - 7x = 3 + 2

=> 2x = 5

=> x = 5/2

Substitute x = 5/2 in (1)  

=> y = 9(5/2) - 2  

=> y = (45/2) - 2

=> y = (45 - 4)/2

=> y = 41/2

Therefore,

The solutions of given system of Equations are (5/2, 41/2).

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The total weight of the water in a filled tank will be equal to 16,336 Pounds.

Every three-dimensional item takes up space in some way. The volume of this area is what is used to describe it. The area covered within an entity's three-dimensional bounds is referred to as its volume. The object's size is another name for it.

As per the given data in the question,

Radius, r = 10/2 = 5 ft.

Use the equation of the volume of a sphere,

V = 4/3πr³

We only require half of it then,

V =  2/3πr³

V = 261.8 ft³

So, the total weight will be,

W = 261.8 × 62.4

W = 16,336 Pounds.

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Answer:

There Are 40 Bicycles And 23 Tricycles

Step-by-step explanation:

Let, x be bicycles and y be tricycles

Condition 1;

: x + y= 63

: x =63-y

Condition 2;

Number Of Tires=149

:2x + 3y =149 [2x=Two Tires Of Bicycle And

3y=Three Tires Of Tricycle]

:x = 149-3y/2

Combination 1 & 2;

63-y = 149-3y/2

126-2y = 149-3y

y=23

x = 63-23

=40

Answer:

[tex]\huge\boxed{\sf 157.1 \ units^2}[/tex]

Step-by-step explanation:

Diameter = 20

Radius = Diameter/2 = 20/2 = 10

[tex]\displaystyle =\frac{\pi r^2}{2} \\\\r = 10\\\\= \frac{\pi (10)^2}{2} \\\\= \frac{100 \pi}{2} \\\\= \frac{314.2}{2} \\\\= 157.1 \ units^2\\\\\rule[225]{225}{2}[/tex]

Answer:

second

Step-by-step explanation:

2x+5>7

2x>2

x>1

therefore, second

The vertices of a rectangle are W(1, 2) X(4, 2) Y(4, 23) and Z(1, 23) Find the perimeter of the rectangle is 16.

We could use the distance formula to find the distance between the points in this problem, but when we look we see that the sides of the rectangle are parallel to the x and y-axis for each pair of sides. The first two points have a distance of 3 because 4-1=3. Since it is a rectangle, the opposite side will have the same length. For the sides perpendicular, we look at the points with the same x coordinate. Using (4,2) and (4,-3), we can calculate the length of the side by finding the distance by adding the absolute values of the y coordinate. 2+3=5. This means that the triangle has two sides with a length of 5 and two sides with a length of 3. Adding these together, 5+5+3+3 = 16.

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