4-6 study guide and intervention isosceles and equilateral triangles

Part A. When we have two chords that intercept at one of the exterme points of a circle, like this:

Then the relationship between the minor arc and the interior angle of the chords is:

therefore, if we substitute according to the given circle we have:

Therefore, angle a is 85°.

Part B. The angle formed by a tangent and a chord of a circle is half the the arc that is formed:

We have that:

Now, we substitute:

Therefore, "b" is 105°.

Part C. Given the following configuration:

The following relationship holds:

Now, we substitute the values according to the given circle:

Now, we divide both sides by "c":

Therefore, the value of "c" is 13.5

Part D. In the following configuration:

The following relationship holds:

Now, we substitute the values:

Solving the operations:

therefore, the angle "d" is 80 degrees.

The given length measurements are converted and given below.

Unit conversion is a process with multiple steps that involve multiplication or division by a numerical factor or, particularly a conversion factor.

Given is to convert the given measurements as -

a) 192 km

b) 15500 dam

c) 85000 m

d) 3360 hm

e) 860000 dm

We can write the measurements as -

a) 192 km            

192 Km = 192000 meters

b) 15500 dam

15500 dam = 15500 x 10 = 155000 meters

c) 85000 m

85000 m = (85000/1000) Km = 85 Kilometers

d) 3360 hm

3360 hm = 3360 x 100 = 336000 meters

e) 860000 dm

860000 dm = 860000 x 0.1 = 860000 x 1/10 = 86000 meter

Therefore, the given length measurements are converted and given above.

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Answer:

8/12, 11/16, 3/4, 4/8

Step-by-step explanation:

hope this helps

Exponential functions do not have a vertex.

"Exponential function, as its name suggests, involves exponents. An exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).

In mathematics, an exponential function is a function of form \(f(x) = a^{x}\), where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0."

"The standard form of a quadratic equation is y = ax² + bx + c and the vertex form of the same is y = a (x - h)² + k. Here, the vertex form has a square in it. So to convert the standard to vertex form we need to complete the square."

We know that, the graph of an exponential function consists of a horizontal asymptote. However, there is no quadratic function available that consists of a horizontal asymptote.

Hence, exponential functions do not have a vertex.

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Answer:

78.5 ft3

Step-by-step explanation:

First we need to find the volume of both containers.

The volume of a cylinder is given by the equation:

Volume = pi * diameter^2 * height / 4

If cylinder A has a diameter of 6 feet and height of 15 feet, we have:

Volume_A = pi * 6^2 * 15 / 4 = 424.115 ft3

If cylinder B has a diameter of 8 feet and height of 10 feet, we have:

Volume_A = pi * 8^2 * 10 / 4 = 502.6548 ft3

After pumping the water from A to B, the volume of the empty portion of B will be the difference of their volumes:

Volume_B - Volume_A = 502.6548 - 424.115 = 78.5398 ft3

Rounding to the nearest 10th of a cubic foot, we have a difference of 78.5 ft3

The number of solutions of the equation tan(x) + sec(x) = 2cos(x) in the interval [0,2π] is 4.

To find the number of solutions, we need to analyze the given equation in the interval [0,2π]. Let's simplify the equation step by step:

Start with the given equation: tan(x) + sec(x) = 2cos(x).

Convert sec(x) to its reciprocal form: tan(x) + 1/cos(x) = 2cos(x).

Multiply both sides by cos(x) to eliminate the denominators: cos(x)tan(x) + 1 = 2cos^2(x).

Use the identity cos^2(x) = 1 - sin^2(x) to rewrite the equation: cos(x)tan(x) + 1 = 2(1 - sin^2(x)).

Distribute 2 on the right side: cos(x)tan(x) + 1 = 2 - 2sin^2(x).

Move all terms to one side to form a quadratic equation: 2sin^2(x) + cos(x)tan(x) - 2 = 0.

Apply the identity tan(x) = sin(x)/cos(x) to the equation: 2sin^2(x) + sin(x) - 2cos(x) = 0.

Factor the quadratic equation: (2sin(x) - 1)(sin(x) + 2cos(x)) = 0.

Now, we have two separate equations:

i) 2sin(x) - 1 = 0.

ii) sin(x) + 2cos(x) = 0.

Solve equation i) for sin(x): sin(x) = 1/2.

The solutions for equation i) in the interval [0,2π] are x = π/6 and x = 5π/6.

Solve equation ii) for sin(x)/cos(x): sin(x)/cos(x) = -2.

Rearrange the equation: tan(x) = -2.

The solutions for equation ii) in the interval [0,2π] are x = 7π/4 and x = 3π/4.

Combining the solutions from both equations, we have a total of 4 solutions in the interval [0,2π]: x = π/6, 5π/6, 7π/4, and 3π/4.

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Step-by-step explanation:

that's look so complicated lol

The amount of rain the city received in July is r = 2.5 inches

Given data ,

City received 3/4 inch of rain on July 31

Now , it represents 3/10 of the total amount of rain this to received in July

So , the equation is represented as A

Now , the value of A is

( 3/10 )r = 3/4

Multiply by 10 on both sides , we get

3r = 30/4

Divide by 3 on both sides , we get

r = 30/12

r = 2.5 inches

Hence , the city received 2.5 inches of rain

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Answer:

18.6 months

Step-by-step explanation:

Given that :

Best fit line from scatterplot :

y=-12.05x +224.26

x = Number of month

y = charge on battery

Number of months a typical battery uses before being dead completely :

When battery is dead completely ; charge =0, y = 0

y = -12.05x + 224.26

0 = - 12.05x + 224.26

12.05x = 224.26

x = 224.26 / 12.05

x = 18.610788

Hence, 18.6 months before battery is completely dead.

In summary, to find the null spaces of the matrices given in exercises 9 and 10, use the Gauss-Jordan elimination method and refer to the Remarks that follow example 3 in section 4.2 of the text. This will give the dimension of the null space and the number of free variables.
In exercises 9 and 10, the null space of the given matrices can be found by solving the homogeneous linear system of equations. In order to do this, use the Gauss-Jordan elimination method. Refer to example 3 in section 4.2 of the text for a detailed explanation. Afterwards, use the Remarks that follow the example to determine the dimension of the null space and the number of free variables.

The null space of a matrix is the set of all vectors that produce a zero vector when the matrix is multiplied by the vector. Therefore, to find the null space of a matrix, the homogeneous linear system of equations needs to be solved. The Gauss-Jordan elimination method involves adding multiples of one row to another to get a row with all zeroes. After this is done for all the rows, the equations can be solved for the free variables. The number of free variables will determine the dimension of the null space. Refer to example 3 in section 4.2 of the text for more details.

The Remarks that follow the example are important when determining the dimension of the null space and the number of free variables. In the Remarks, it is mentioned that the number of free variables is equal to the number of columns with a zero row. Therefore, after using the Gauss-Jordan elimination method to get the row with all zeroes, the number of columns with a zero row can be counted. This will give the dimension of the null space and the number of free variables.

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True

A triangle with all the three sides equal equilateral

Hope this helped you- have a good day bro cya)

Answer:

9 servings

There should be an answer to that. Answer: There are 9 servings. step- by- step Explanation: We would first divide 22.5/2.5. This will give us the amount of time 2.5 will go into 22.5, providing us with the amount of servings

Step-by-step explanation:

The vector y can be expressed as the sum of two orthogonal vectors, ₁ in Span {u} and 2 orthogonal to u, and 1₂- x2 = [-17/8, 73/8] - [1, -1] = [-25/8, 81/8].

Orthogonal vectors are vectors that are perpendicular to each other in an n-dimensional space. Geometrically, orthogonal vectors form a right angle (90 degrees) between them.

Let us begin by defining the concepts of orthogonal vectors and span of a vector space.

Orthogonal vectors: Two vectors are said to be orthogonal if their dot product is zero.

Span of a vector space: A vector space's span is defined as the collection of all linear combinations of its vectors.  

It is possible to express y as a linear combination of u and another vector that is orthogonal to u.

There are a few steps involved in this procedure that must be followed.

Let us begin with the first step, which is to obtain a unit vector for u.

1. u = [2,2] / √8, which gives us the unit vector of u.

2. Now, we need to find a vector ₁ in Span{u} so that the dot product of ₁ and u is the same as the dot product of y and u.₁ = y * u / u * u

= [18 - |[5]|] * [2,2] / 8

= [11/2, 11/2]

3. Now we need to find a vector ₂ that is orthogonal to u.

The cross product of any vector in R² and u gives us a vector orthogonal to u.₂ = [x1, x2], u × ₂ = 0

where u = [2,2] and

u × ₂ = (2 * x2 - 2 * x1) = 0

solving which we get x2 = x1.4.

So, ₂ can be [x1, x2] = [1, -1].5. y can be expressed as a linear combination of ₁ and ₂:y = a₁ * ₁ + a₂ * ₂,

where a₁ = y * ₁ / ₁ * ₁ = [18 - |[5]|] * [11/2, 11/2] / ([11/2]²)

= 33/8 and

a₂ = y * ₂ / ₂ * ₂

= [18 - |[5]|] * [1, -1] / ([1]² + [-1]²)

= -5. y = a₁ * ₁ + a₂ * ₂

= [33/8, 33/8] + [-5, 5]

= [-17/8, 73/8].

Therefore, the vector y can be expressed as the sum of two orthogonal vectors, ₁ in Span {u} and 2 orthogonal to u, and 1₂- x2 = [-17/8, 73/8] - [1, -1] = [-25/8, 81/8].

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Answer:

A

Step-by-step explanation:

Concept :-

On converting :-

\(\bf\implies y + 5 =\dfrac{1}{3}(x-9)\\\\\bf\implies y + 5 =\dfrac{1}{3}x - 3 \\\\\bf\implies y = \dfrac{1}{3}x - 3 - 5 \\\\\bf\implies\boxed{\red{y = \dfrac{1}{3}x -8 }}\)

Answer:

hello i misss u hello love u

Answer:

Buffalo

Step-by-step explanation:

jfvjuvf

Answer:

90

Step-by-step explanation:

its a right angle

b. The statement "the probability that x falls between 10 and 20" is false.

A continuous random variable X has a uniform distribution between 5 and 15 (inclusive), meaning it can take any value between 5 and 15 with equal probability.

We need to find the probability that X falls between 10 and 20. Since the range of X is only between 5 and 15, we can only consider the range of 10 to 15 within this interval.

For a uniform distribution, the probability density function (pdf) is:

f(x) = 1 / (b - a)

where 'a' and 'b' are the lower and upper limits of the distribution, respectively. In this case, a = 5 and b = 15, so:

f(x) = 1 / (15 - 5) = 1 / 10

Now, to find the probability that X falls between 10 and 15, we can integrate the pdf over this interval:

P(10 ≤ X ≤ 15) = ∫[1/10]dx from 10 to 15

P(10 ≤ X ≤ 15) = [x/10] from 10 to 15

P(10 ≤ X ≤ 15) = (15/10) - (10/10) = 1/2

So, the probability that X falls between 10 and 20 is 1/2, not 1.0. Therefore, the statement is the probability that x falls between 10 and 20 is false.

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Answer:

C= 3g

Step-by-step explanation:

Answer:

22.05 mi.²

Step-by-step explanation:

A = bh

A = (4.5 mi)(4.9 mi)

A = 22.05 mi.²

When the sample size is increased, the LCL comes closer to the process mean and the UCL moves farther from the process mean.Hence, (c) When a Type I error is made, the process will be declared out of control and adjusted when the process is actually in control.

(d) When a Type II error is made, the process will be declared in control and allowed to continue when the process is actually out of control. The probability of a Type I error for a sample of size 10 is 0.0027, for a sample of size 20 is 0.0014, and for a sample of size 30 is 0.0010. Increasing the sample size provides a more accurate estimate of the process mean and reduces the probability of making a Type I error.

The advantage of increasing the sample size for control chart purposes is that the error probability is reduced as the

When the sample size is increased, the LCL comes closer to the process mean and the UCL moves farther from the process mean.The process will be declared out of control and adjusted when the process is actually in control.When a Type II error is made, the process will be declared in control and allowed to continue when the process is actually out of control.

The probability of a Type I error for a sample of size 10 is 0.0027, for a sample of size 20 is 0.0014, and for a sample of size 30 is 0.0010.The advantage of increasing the sample size for control chart purposes is that the error probability is reduced as the sample size is increased.

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Answer:

t > 0.5

Step-by-step explanation:

It is t > 0.5 because this specifies that the time needed to bake a cake is more than 0.5 hrs, or 30 minutes.

Answer:

16

Step-by-step explanation:

12+4=16

Answer:8

Step-by-step explanation:

You are wanting a negative 1

So you start by getting to zero would take 7 “jumps”

Then u need to get into the negative by one

So when you go back one you get 8 jumps total

Answer:

153.94 cm

Step-by-step explanation:

d=2r (need radius (r) to solve for the area)

14=2r

r=7

A=πr²

A=π(7)²

A=π49

A=153.94

When there is a multiplication between a term with parenthesis and another term we apply the distributive property:

It says that the parenthesis indicates that the term outside will multiply each of the terms inside it.

For the first parethesis:

- 3(2x + 4) = (-3) · 2x + (-3) · 4

since

(-3) · 2x = -6x

(-3) · 4 = -12

then

- 3(2x + 4) = (-3) · 2x + (-3) · 4

- 3(2x + 4) = -6 x - 12

For the second

– (2x + 4) ​= – 1 (2x + 4)

= ​(-1) · 2x + (-1) · 4

=-2x -4

We can see in this case that both parenthesis are the same, then it is the common factor of - 3(2x + 4) and – (2x + 4) ​,

We can factor it by separating it of each term and letting the remaining terms inside a parenthesis

- 3(2x + 4) – (2x + 4) ​= (2x + 4) ( -3 -1)

= (2x + 4) ( -4)

= -4 (2x + 4)

Answer: One newton-meter is equal to 8.8507457676 inch pounds.

Step-by-step explanation:

As a simple example, if you wish to convert 5 newton-meters into inch pounds, you should multiply 5 by 8.8507457676 to give you a total of 44.253728838 inch pounds (or 44.254 rounded to 3 decimal places).

One newton-meter is equal to 8.8507457676 inch pounds.

What is nanometer ?

A nanometer (NM) is a unit of size this is equal to at least one billionth of a meter. it's miles extensively used as a scale for building tiny, complex, and atomic scale computing and digital additives - mainly in nanotechnology

As a simple example, if you wish to convert 5 newton-meters into inch pounds,

you should multiply 5 by 8.8507457676 to give you a total of 44.253728838 inch pounds (or 44.254 rounded to 3 decimal places).

Therefore, One newton-meter is equal to 8.8507457676 inch pounds.

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Answer:

Step-by-step explanation:

C because it is given that from 0 to (a,0) only need steps and similarly with b only need b amount of steps to reach (0, b). Therefore to reach point P, you just need (a, b).

Answer:

Step-by-step explanation:

We know that the perimeter is the sum of side lengths.

Substitute the values and solve for x:

Answer:

\(perimeter = h + l + b \\ = x + 2x - 2 + 3x + 1.5 = 11.5 \\ x \: terms \: togather \\ x + 2x + 3 x- 2 + 1.5 = 11.5 \\ 6x - .5 = 11.5 \\ 6x = 11.5 + .5 \\ 6x = 12 \\ x = \frac{12}{6} \\ x = 2 \\ thank \: you\)

Answer:

the answer is 15 as that is a 90 degree angle

Step-by-step explanation: