angle bisector theorem

Answer:

Step-by-step explanation:

A circle with a diameter of 12 units and a center that lies on the y-axis would have an equation of the form:

(x - h)^2 + y^2 = r^2

where (h, 0) is the center of the circle, and r is the radius. We know that the diameter is 12 units, so the radius is half of that, which is 6 units.

Now we can check which of the given equations match this form:

x^2 + (y – 3)^2 = 36 : This is not in the required form, since the center is at (0, 3) and not on the y-axis.

x^2 + (y – 5)^2 = 6 : This is not in the required form, and also has a very small radius of sqrt(6), so it cannot have a diameter of 12 units.

(x – 4)² + y² = 36 : This is in the required form, with center at (4, 0), so it is a possible solution.

(x + 6)² + y² = 144 : This is in the required form, with center at (-6, 0), so it is also a possible solution.

x^2 + (y + 8)^2 = 36 : This is not in the required form, since the center is at (0, -8) and not on the y-axis.

Therefore, the two equations that represent circles with a diameter of 12 units and a center on the y-axis are:

(x – 4)² + y² = 36

(x + 6)² + y² = 144

Answer:

200

Step-by-step explanation:

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

[tex]a_{50}[/tex] = 4 + (50 -1)4

[tex]a_{50}[/tex] = 4 + 49(4)

[tex]a_{50}[/tex] = 4 + 196

[tex]a_{50}[/tex] = 200

a = the initial value.

n =  the term

d = the common difference

Helping in the name of Jesus.

The measure of the angles are 82. 7 degrees and 97. 3 degrees

Supplementary angles are simply described as those angles whose sum is equal or equivalent to 180 degrees.

Note that pair of angles on a straight line are supplementary to each other.

From the information given, we have that;

Let the angle of one be x

Then,

Angle 1 = x

Angle 2 = 14. 6 + x

Equate the angles

x + 14. 6 + x = 180

collect the like terms, we get;

2x = 180 - 14. 6

subtract the values

2x = 165. 4

x = 82. 7 degrees

Then, the second angle = 82. 7 + 14. 6 = 97. 3 degrees

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The area of triangle ABC is approximately 11.14 square inches.

To find the area of triangle ABC, we can use the formula:

Area = 1/2 * AC * BC * sin(C)

where the base is BC and the height is the perpendicular distance from A to BC.

To find the sine 63, we can use the sine of angle C:

sin C = sin(63)

Therefore, the area of triangle ABC is:

Area = 1/2 * 10 * 2.5 * sin(63)

When evaluated, we have

Area ≈ 11.14 square inches

So, the area of triangle ABC is approximately 11.14 square inches.

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we  should invest $479.17 each month to accumulate $81,000 in 12 years with an APR of 4 percent.

what is percent?

Percent is a way of expressing a number as a fraction of 100. The word "percent" comes from the Latin phrase "per centum," which means "by the hundred."

In the given question,

To calculate the monthly deposit needed to accumulate $81,000 in 12 years with an APR of 4%, we can use the formula for future value of an annuity:

FV = PMT x [(1 + r)ⁿ - 1] / r

Where:

FV = Future value of the investment (in this case, $81,000)

PMT = Monthly deposit

r = APR / 12 (monthly interest rate)

n = Number of months (12 years x 12 months per year = 144 months)

Substituting the given values, we get:

$81,000 = PMT x [(1 + 0.04/12)¹⁴⁴ - 1] / (0.04/12)

Simplifying this equation, we get:

PMT = $81,000 x (0.04/12) / [(1 + 0.04/12)¹⁴⁴ - 1]

PMT = $479.17

Therefore, you should invest $479.17 each month to accumulate $81,000 in 12 years with an APR of 4%.

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Answer:

the right answer is the third choice (-203)

A parallelogram would be formed by the coordinates [tex]A(1,-2), B(-8, -5), C(-2, 1), and D(2,16).[/tex]

In mathematics, a graph's points are frequently plotted on a coordinate surface. Each spot on the plane has an x- and y-coordinate that describes where it is. Knowing a point's coordinates is necessary in order to map it. (x, y).

Drawing the x-axis and y-axis, where x is the horizontal line and y is the vertical line, will allow us to display the points [tex]A(1, 2), B(-8, 5), and C(-2, 1)[/tex]  on the coordinate axes.

Then, beginning at the origin  [tex](0,0)[/tex] we can find point A by moving 2 units down on the y-axis and 1 unit to the right on the x-axis.

Starting at the beginning, move 8 units to the left on the x-axis and 5 units down on the y-axis to find Point B.  

Starting at the beginning, move 2 units left on the x-axis and 1 unit up on the y-axis to find Point C.

Point B would be moved by the vector (2,8) to point C, giving the coordinates of point D as  [tex](2,16).[/tex]

plot the coordinate axes below with the coordinates  [tex]A(1,-2), B(-8,-5)[/tex], and C(-2,1). in order for points A, B, C, and D to make a parallelogram, specify the coordinates of point D.

Therefore, a parallelogram would be formed by the coordinates A  [tex](3, -2), B (-3, 8), C (-5, -1),[/tex] and [tex]D (2, 16)[/tex]  .

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Answer:

Determine the lengths of sides and measures of angles in a right triangle by ... 9 = 12x. Cross Products Property. 9 = 3x. Subtract 9x from each side. 3 = x.

Answer (Please mark as brainliest):

STATEMENTS

∆ABD and ∆DCB; AB ≅ DC; AD ≅ BC

BD ≅ BD

∆ABD ≅ ∆DCB

REASONS

Given

Reflexive Property of Congruence

By SSS, since AB ≅ DC, AD ≅ BC, and BD ≅ BD.

Therefore, ∆ABD ≅ ∆DCB by SSS.

The customer can deposit up to $400 in their savings account as long as the total amount deposited between the two accounts does not exceed $600, since they deposited $200 in their checking account.

The problem tells us that the customer will deposit a maximum of $600 between their checking and savings accounts. This means that the total amount deposited in both accounts cannot be more than $600.

We also know that the customer deposited $200 in their checking account. Since they can deposit at most $600 in total, this means that they can deposit up to an additional $400 in their savings account. This is because $600 (maximum total deposit) - $200 (amount deposited in checking account) = $400 (maximum amount that can be deposited in savings account).

So, we can say that the amount the customer can deposit in their savings account is less than or equal to $400. In other words, they can deposit any amount from $0 to $400 in their savings account, as long as the total amount deposited between the two accounts does not exceed $600.

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In summary, equations A, C, and D are true for the number 9, while equation B is not.

In order to resolve this issue, we must substitute a number or expression that makes the equation true for the value 9 in the area denoted by the symbol "." Let's look at each equation individually:

A. 4 ÷ □ = 9/4

We can cross-multiply and simplify to find the answer to :

4(9/4) = □\s9 = □

Hence, for = 9, this equation is accurate.

B. 1/9 = □ ÷ 9

We may multiply both sides by 9 to find the answer to:

1 = □

This equation is valid for = 1, thus.

C. 7 ÷ □ = 7/9

We can cross-multiply and simplify to find the answer to :

7(9) = □\s63 = □

Hence, this equation is true for the value of = 63/7, which reduces to 9.

D. □ ÷ 1/9 = 81

We can multiply both sides by 1/9 to find the answer to:

□ = 81(1/9)\s□ = 9

So, this equation is true for □ = 9.

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Answer:

1966

Step-by-step explanation:

910x2=1820

23x2= 46

1820=46=1966

Step-by-step explanation:

2.5 km = 250000 cm

250000 cm /20000 = 12.5 cm on the map

12.5 cm ^2  x 20 0000 x 20 000   = 5 000 000 000 cm^2 = 500 000 m^2  

Answer: False

Step-by-step explanation:  A whale can't fly

Answer:

False

Step-by-step explanation:

Because a whale cannot fly

Answer:

Question 7 is correct.

205,000 (For Question 8)

Step-by-step explanation:

First, we need to find the value of x.

We need to subtract 1995 from 2010 to find out how many years would have passed.

This gives us 15, which is our x value.

Next, we need to solve for y.

We multiply 2000 by 15 to get 30,000.

Then, add 175,000 to 30,000 to get 205,000. That leaves us with the equation y = 205,000.

The Y value is equivalent to the population in 2010.

By answering the presented question, we may conclude that the balance  interest after 5 years is approximately $1,484.71.

In mathematics, interest is the amount of money gained or payable on an original investment or loan. You can use either simple or compound interest. Simple interest is calculated as a percentage of the initial amount, whereas compound interest is calculated on the principal amount plus any previously earned interest. If you invest $100 at a 5% annual simple interest rate, you will get $5 in interest per year for three years, for a total of $15.

for calculating the balance

[tex]A = Pe^(rt)\\[/tex]

this formula,

[tex]A = 1000e^(0.085*5)\\A = 1000e^(0.425)\\[/tex]

A ≈ $1,484.71

the balance after 5 years is approximately $1,484.71.

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Answer:1529.59

Step-by-step explanation:

1000e^(.085)5

The value of cos (90 - x ) = sin (x) = 7/11.

option B.

In trigonometry identity, we know that sin(x) = opposite / hypotenuse. Therefore, we can draw a right triangle with an angle x and opposite side 7 and hypotenuse 11.

Using the Pythagorean theorem, we can find the adjacent side of the triangle:

adjacent² = hypotenuse² - opposite²

adjacent² = 11² - 7²

adjacent² = 120

adjacent = √(120)

adjacent = 2 √(30)

Now, we can use the definition of cosine to find cos(90 - x):

cos(90 - x) = sin(x)

Therefore, cos(90 - x) = 7/11.

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[tex]f(x) = -5 * 2[/tex] is one conceivable exponential function (-x). The coordinates of this function are (0, -5) and (-2, -20).

Because the exponent's base falls between 0 and 1, this function depicts exponential decay. The output of the function decreases at an increasing rate as x rises because the value of 2(-x) shrinks. The function starts at a number larger than zero and lowers with time, as shown by the negative sign. The initial value of -5 denotes the function's beginning point. As a result, when x rises, the function's output gets closer to zero but never quite hits it.

Because to the diminishing nature of the exponent's base, the function [tex]f(x) = -5 * 2(-x)[/tex]  generally indicates exponential decay.

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Answer:

Area = 63.2 cm²

Step-by-step explanation:

To find the area of the given shape, we can split it into two shapes: a trapezium and a rectangle (as shown in the attached diagram).

Doing so gives us a rectangle with a length of 10 cm and a breadth of 2.8 cm at the bottom of the shape. Therefore its area:

Area = length × breadth

        = 10 cm × 2.8 cm

        = 28 cm²

We also get a trapezium, whose area can be found using the following formula:

[tex]\boxed{\mathrm{Area = \frac{1}{2} \times (a + b) \times h}}[/tex]

where:

• a, b ⇒ length of the parallel sides of trapezium

• h ⇒ distance between the parallel sides a and b

From the diagram attached below, we can see that the two parallel sides have lengths of 10 cm and 6 cm. Moreover, the distance between the parallel sides is 7.2 - 2.8 = 4.4 cm.

Therefore, using the above formula and information, we can calculate the area of the trapezium:

Area = [tex]\frac{1}{2}[/tex] × (6 + 10) cm × 4.4 cm

        = [tex]\frac{1}{2}[/tex] × 16 cm × 4.4 cm

        = 35.2 cm²

Now that we have the areas of the rectangle and trapezium, we can find the area of the whole shape simply by adding those two areas:

Area of shape = 28 cm² + 35.2 cm²

                        = 63.2 cm²

Therefore, the area of the given shape is 63.2 cm².

Answer:

To calculate the percent decrease in staff, we need to find the difference between the original number of employees and the new number of employees, and then divide that difference by the original number of employees. Finally, we can multiply the result by 100 to get the percent decrease.

The difference between the original number of employees (61) and the new number of employees (9) is:

61 - 9 = 52

Dividing 52 by the original number of employees (61) gives:

52/61 ≈ 0.8525

Multiplying 0.8525 by 100 gives:

0.8525 × 100 ≈ 85.25

Therefore, the percent decrease in staff is approximately 85.25%. Rounded to the nearest tenth, the answer is 85.3%.

Answer:

= 85.3%

Step-by-step explanation:

Find how many employees are left:

61 - 9 = 52

Divide 52 by 61

= 0.8524590...

Multiple it by 100 to find %

= 85.245

Round to nearest tenth

= 85.3%

Answer:

Step-by-step explanation:

there is no passage

1. The rate at which the faster child is working is 1/t.

2.The rate at which the slower child is working is 1/(2t)

3.The homework done by the faster child in 45 minutes is (1/t) * (3/4), since both children can complete the homework in 45 minutes.

4.The part of the homework done by the slower child in 45 minutes is (1/(2t)) * (3/4),

5.Thus, t=30 minutes, which is the time taken by the faster child to do the homework by herself.

6. Thus, 2t=90 minutes and t=45 minutes, which is the time taken by the slower child to do the homework by herself.

Time is a concept used to describe the progression of events from the past, through the present, and into the future. It is a measure of duration or an interval between two events, and it is often represented in units such as seconds, minutes, hours, days, weeks, months, and years.

1. Let t = the time needed for the faster child to complete the homework.

The faster child completes the homework twice as fast as the partner. Therefore, the rate at which the faster child is working is 1/t.

2.The rate at which the slower child is working is 1/(2t) since the slower child takes twice as long as the faster child to complete the homework.

3.The part of the homework done by the faster child in 45 minutes is (1/t) * (3/4), since both children can complete the homework in 45 minutes. In 45 minutes, the faster child completes 3/4 of the homework because she is working at a rate of 1/t, while the slower child is working at a rate of 1/(2t).

4.The part of the homework done by the slower child in 45 minutes is (1/(2t)) * (3/4), since both children can complete the homework in 45 minutes. In 45 minutes, the slower child completes 3/4 of the homework because she is working at a rate of 1/(2t), while the faster child is working at a rate of 1/t.

5.Let's use the equation P=rt, where P=1 (since the entire homework is done by one child alone) and r=1/t (since the faster child completes the homework in t time). Thus, t=30 minutes, which is the time taken by the faster child to do the homework by herself.

6.Similarly, we can use the equation P=rt, where P=1 (since the entire homework is done by one child alone) and r=1/(2t) (since the slower child takes twice as long as the faster child to complete the homework). Thus, 2t=90 minutes and t=45 minutes, which is the time taken by the slower child to do the homework by herself.

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The formula to find the length of an arc of a circle is given by L = rθ, where L is the length of the arc, r is the radius of the circle, and θ is the angle measured in radians and the radius of the circle is 2.

To find the length of the arc, we use the formula L = rθ. Substituting the given values, we get:

L = rθ

L = r( [tex]\frac{\pi}{2}[/tex]) or ( [tex]\frac{\pi}{2}[/tex])r

We are also given that the length of the arc is 1π, so we can write:

( [tex]\frac{\pi}{2}[/tex])r = 1π

Simplifying this equation, we get:

r = (1π) ÷ ( [tex]\frac{\pi}{2}[/tex])

r = 2

We can say that the length of an arc that is intercepted by an angle of  [tex]\frac{\pi}{2}[/tex] radians is equal to half the circumference of the circle. Since the length of the arc is given as 1π, we can find the radius of the circle by dividing 1π by [tex]\frac{\pi}{2}[/tex], which gives us 2.

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The complete question is:

In a circle, an angle measuring  [tex]\frac{\pi}{2}[/tex] radians intercepts an arc of length 1π. Find the radius of the circle in simplest form.

The shape of the cross - section can be described as being a rectangle.

The perimeter of the cross section can be found to be  28.98 inches.

The area of the cross - section is therefore 50.94 square inches.

Since the plane intersects the cube through four of its vertices and opposite edges, the shape of the cross-section is a rectangle.

To find the length of the diagonal of the cube's face, we can use the Pythagorean theorem for a right triangle with sides of 6 inches:

d^2 = 6^2 + 6^2

d^2 = 36 + 36

d^2 = 72

d = √72 = 8.49 inches

To find the perimeter of the cross-section, we use the formula for the perimeter of a rectangle:

P = 2(length + width) = 2(6 + 8.49) = 2(14.49) = 28.98 inches

To find the area of the cross-section, we use the formula for the area of a rectangle:

A = length × width = 6 × 8.49 = 50.94 square inches

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The sample variance and standard deviation of the data set {21, 12, 6, 9, 11} are approximately 31.2 and 5.6, respectively, rounded to one decimal place.

Standard deviation is another measure of how spread out the data points are from the sample mean. It is simply the square root of the variance. In other words, it measures the average amount of deviation of the data points from the sample mean.

To find the sample variance and standard deviation, we can use the following formulas:

The sample variance is 30.3 and the standard deviation is approximately 5.5.

To find the sample variance, we first find the sample mean:

(21 + 12 + 6 + 9 + 11) / 5 = 11.8

Then we use the formula for the sample variance:

where n is the sample size, x is the sample mean, xi is each data point, and is the total. When we enter the values, we obtain:

[tex]s^2[/tex] = [tex]((21 - 11.8)^2 + (12 - 11.8)^2 + (6 - 11.8)^2 + (9 - 11.8)^2 + (11 - 11.8)^2) / (5 - 1)[/tex]

[tex]s^2[/tex] ≈ 30.3

To find the standard deviation, we take the square root of the variance:

s ≈ √30.3 ≈ 5.5

Therefore, the answer is:

OA. 02:

OB. 11

OA. S = 5.5

OB. σ = 5.5

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Answer:

-5, 0, 5

Step-by-step explanation:

Option B : The volume of the sphere with a diameter of 10 inches is approximately 523.6 cubic inches, and the closest answer choice is (B) 1150 cubic inches.

In the given diagram, we can see that the diameter of the sphere is 10 inches.

The volume of a sphere is given by the formula:

V = (4/3) * π * [tex]r^3[/tex]

where r is the radius of the sphere.

We know that the diameter of the sphere is 10 inches, so the radius is half of that, which is 5 inches.

Substituting the given values, we get:

V = (4/3) * π * [tex]5^3[/tex]

V = (4/3) * π * 125

V = 523.6 [tex]in^3[/tex] (rounded to one decimal place)

So, the closest answer choice to the volume of the sphere is (B) 1150 [tex]in^3[/tex].

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Answer:

Step-by-step explanation:

B. Now, look at the list of verbs in part A. Select the correct subject pronoun for each verb.

11) ___ escribimos

A. ustedes

B. nosotros

With the given values of circle, the value of x=3 and VS = 5.

What is circle?

A circle is a geometrical shape consisting of all the points in a plane that are equidistant from a given point called the center of the circle.

Since VZ = UZ, then Z is on the perpendicular bisector of QR and ST. This means that Z divides QR and ST into two equal parts.

Using the midpoint formula, we can find the midpoint of QR and ST:

Midpoint of QR = ( (1/2)*(4x-2) , 0 ) = (2x-1, 0)

Midpoint of ST = ( (1/2)*10 , 8 ) = (5, 8)

Since Z is the midpoint of QR and ST, we can set up two equations:

2x-1 = 5

0 = 8

The second equation is not possible, so we ignore it. Solving the first equation gives us:

2x-1 = 5

2x = 6

x = 3

Now that we know x, we can find the length of VS:

VS = ST - TV = ST- (ST/2) = 10 - (5) = 5

Therefore, x = 3 and VS = 5.

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Answer:

Let L be the length of the rectangular garden. We know that the perimeter of a rectangle is given by: P = 2L + 2W where P is the perimeter, L is the length, and W is the width. In this case, we are given that the perimeter is 372 m and the width is 88 m. Substituting these values into the equation, we get: 372 = 2L + 2(88) Simplifying and solving for L, we get: 372 = 2L + 176 2L = 196 L = 98 Therefore, the length of the rectangular garden is 98 m.

Answer: L = 98 m

Step-by-step explanation:

The perimeter of a rectangle can be found with this formula:

      P = 2W + 2L

➜ P is Perimeter

➜ W is Width

➜ L is Length

We will input known values and solve for the length. To solve, we will use multiplication and inverse operations.

      372 m = 2(88 m) + 2L

      372 m = 176 m + 2L

      196 m = 2L

      L = 98 m

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