XB is the angle bisector of ZAXC. MZAXB= 23°BVC сFind the following:mZBXC =MZAXC =

The increase in height (rise) of the balloon is \(35.53 feet\)

What is Pythagorean Theorem?

Pythagoras' theorem states that "the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides."

The angle of elevation is generated by the intersection of the horizontal line and the line of sight. If the line of sight is directed upward from the horizontal line, the resulting angle is an angle of elevation.

According to the given information:

Given that,

Initial angle of elevation = \(19.3^{0}\).

Final angle of elevation = \(32.3^{0}\).

Distance = \(126 feet\).

How to calculate the height (rise).

In order to determine the increase in height (rise) of the balloon, we would apply Pythagorean Theorem. Mathematically, this is given by this formula:

tan∅ = \(\frac{height}{adj}\)

height = adjacent \(*\) tan∅

At an initial angle of elevation:

height \(=126* tan 19.3^{0} \\= 126 * 0.3501\\= 44.11 feet\)

At a final angle of elevation:

height \(=126* tan 32.3^{0} \\= 126* 0.6321\\= 79.64 feet\)

For the change in height:

Δh \(= 79.64-44.11\\=35.53 feet\)

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The probability that a mouse leaves first and then a bat is given as follows:

14/55.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

As the animal is not replaced, the probabilities for this problem are given as follows:

Hence the probability is given as follows:

4/11 x 7/10 = 2/11 x 7/5 = 14/55.

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Answer:

yes-

Step-by-step explanation:

im not to sure if its right but

7+7=14

12+12=24

The coordinates of the triangle P'Q'R' is P'(x, y) = (- 4, - 1), Q'(x, y) = (- 2, - 2) and R'(x, y) = (1, 1), respectively.

In this problem we know the three vertices of a triangle on a Cartesian plane and we must determine the coordinates of its image by applying rigid transformations. According to the statement, the vertices of the image are obtained by applying a translation formula:

P'(x, y) = P(x, y) + T(x, y)        (1)

Where:

If we know that P(x, y) = (2, - 4), Q(x, y) = (4, - 5), R(x, y) = (7, - 2) and T(x, y) = (- 6, 3), then the coordinates of the vertices of the image are:

P'(x, y) = (2, - 4) + (- 6, 3)

P'(x, y) = (- 4, - 1)

Q'(x, y) = (4, - 5) + (- 6, 3)

Q'(x, y) = (- 2, - 2)

R'(x, y) = (7, - 2) + (- 6, 3)

R'(x, y) = (1, 1)

The coordinates of the triangle P'Q'R' is P'(x, y) = (- 4, - 1), Q'(x, y) = (- 2, - 2) and R'(x, y) = (1, 1), respectively.

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Answer:

A' (7,7)

B' (10,4)

C' (6,5)

Step-by-step explanation:

Add 9 to every x value and 3 to every y value.

Answer:

A'(7,7)

B'(10,4)

C'(6,5)

Step-by-step explanation:

⭐What is a translation?

⭐What is the translation notation?

The problem tells us to translate ΔABC 9 units to the right, and 3 units up because it is inside the <>, and the numbers are positive.

To translate the vertices of ΔABC, we have to add the respective x and y coordinates of the translation rule to each vertecie of ΔABC.

A(-2,4):

B(1,1):

C(-3,2):

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Answer:

\(P(Not\ 3) = \frac{5}{6}\)

Step-by-step explanation:

Given

\(S = \{1,2,3,4,5,6\}\) --- sample space

Required

P(not 3)

First, we list out all outcomes that are not 3.

We have:

\(Not\ 3 = \{1,2,4,5,6\}\) --- 5 possible outcomes

\(S = \{1,2,3,4,5,6\}\) ---- 6 total outcomes

So, P(Not 3) is calculated as:

\(P(Not\ 3) = \frac{n(Not\ 3)}{n(S)}\)

\(P(Not\ 3) = \frac{5}{6}\)

Answer: 5/6

Step-by-step explanation: khan academy

The answer is D: conjecture

The key words in the description are "look for a pattern and then form an educated guess." This suggests making a hypothesis or assumption based on the observed pattern, which is the definition of a conjecture.

The other answer choices are defined as follows:

A. conjugation - the act of changing a verb to agree with its subject

B. conjunction - a connecting word

C. congruence - the state of agreeing, matching, or coinciding

D. conjecture - an opinion or conclusion formed on the basis of incomplete information

So option D, conjecture, is the best match for forming an educated guess based on an observed pattern in induction.

Answer:

0

Step-by-step explanation:

x² + 3x - 2

(5)² + 3 × 5- 2

25 + 15 - 2

40 - 2

38...

Answer:

\(y = 2x + 9\)

Step-by-step explanation:

This is so because the slope of a line is the same as the gradient, hence m=2

And y-intercept is the same as c in the formula y=mx+c

Answer: 45.5 miles

Step-by-step explanation: divide182 by 4

Answer:

182/4=45.5

the bus travels 45.5 miles in 1 hour

I hope this helps!!

Step-by-step explanation:

Answer:

working on a answer one second

Step-by-step explanation:

Answer:

The dividend is 3935.

Step-by-step explanation:

Division:

Suppose we have a division of a by b.

a is the dividend, b is the divisor. The result is the quotient, that i will call q, and the rest is given by r.

They are related the following way:

a = q*b + r

That is, the divident is the multiplication of the divisor and the quotient, added by the rest.

The partial quotients are 20 and 4.

This means that the quotient is q = 20*4 = 80.

A division problem has 49 as its divisor. The remainder is 15. What is the dividend?

So b = 49, r = 15. Then

a = q*b + r = 49*80 + 15 = 3935

The dividend is 3935.

Answer:

The transformation is " a horizontal translation 4 units to the right " ⇒ (d)

Step-by-step explanation:

Let us revise the translation of a function

Let us look at the graph and choose some points on the f(x) and find their images on y

∵ Point  (1, 2) lies on f(x)

∵ Point (5, 2) lies on y

∵ Point  (3, 8) lies on f(x)

∵ Point (7, 8) lies on y

→ There is no change in the y-coordinates of the points, the change

  only in the x-coordinates

∴ The translation is horizontally

∵  5 - 1 = 4 units ⇒ positive value means to right

∴ f(x) is translated 4 units to the right

∴ The answer is " a horizontal translation 4 units to the right " (d)

The system of equation that describes the relation between the total cost (Y) and the number of tickets purchased (X) in a single visit to the park is Y = 3X + 20 i.e, option (C)

Define System of Equation

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given,

Cost of theme park is = $20

Tickets for each ride and attraction are = $3 a piece

Number of tickets purchased = X

So, total cost of tickets is = 3 * X

Total cost of visit to the theme park is = Y

So, the equation we get

Y = 3X + 20

Hence, the system of equation that describes the relation between the total cost (Y) and the number of tickets purchased (X) in a single visit to the park is Y = 3X + 20 i.e, option (C).

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When w = 10 and z = 2, the value of expression 2w⁻²z⁰ is equal to 1/50. So, correct option is A.

The expression 2w⁻²z⁰ can be simplified as follows:

2w⁻²z⁰ = 2/w² * z⁰

Since z⁰ = 1 for any non-zero value of z, we can simplify further:

2w⁻²z⁰ = 2/w² * 1

Now we can substitute w = 10 into the expression:

2(10)⁻² * 1 = 2/100 = 1/50

In general, when we have a negative exponent in an expression, we can rewrite it as a positive exponent in the denominator. In this case, w⁻² can be rewritten as 1/w². Additionally, any number raised to the power of 0 is always 1, so z⁰ = 1. By simplifying the expression, we can easily substitute the given values of w and z to evaluate the expression.

So, correct option is A.

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Answer:

11

Step-by-step explanation:

equation:

9-(-2)

the term "difference" means there's subtraction.

and when you have to subtract a negative number from a posotive number you are going to add.

hope this helps :) good luck!

Answer:

140°

Step-by-step explanation:

ArcDB is a curved piece of a circle. If you know the measures of the "central angles" (angles with their vertex at the center of the circle) then you can find the measure of the arc.

AngleAPB = 40°

AngleBPC = 90°

So AngleCPD must be equal to 50° see image.

ArcDB is equal to AngleBPD (90° + 50°)

ArcDB = 140°

see images.

Answer:

The slope is 0.

Step-by-step explanation:

Suppose we have two points in a data set, the slope is given by the change in the output divided by the change in the input.

In this question:

Two points: (0,-20) and (1,-20)

Change in the output: -20 - (-20) = -20 + 20 = 0

Change in the input: 1 - 0 = 1

Slope: 0/1 = 0

The slope is 0.

The simplest form of the expression is -3x³ + 2x² + 13x -10

An algebraic expression in mathematics is an expression that is made up of letters and numbers, along with algebraic operations (addition, subtraction, multiplication, etc).

-(x − 2)(3x² + 4x − 5) can be expressed in simplest form as follows:

-(x − 2)(3x² + 4x − 5) = (-x +2)(3x² + 4x − 5)

                                 = -x(3x² + 4x − 5) + 2(3x² + 4x − 5)      

                                 = -3x³-4x²+5x + 6x²+8x-10

                                 = -3x³ + 2x² + 13x -10

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Answer:

the answer is 87.5.

Step-by-step explanation:

If you divide 700 by 2 it equals 350. Then when you multiply 350*0.25, 87.5 or 87 1/2 is your answer

Answer:

A

Step-by-step explanation:

f(x) = x

x = 3

->

f(3) = 3

A

Answer:

undefined

Step-by-step explanation:

because

the figure does not appear

Step-by-step explanation:

6b x>=1

6c y>7

7a x>3

7b -2<=2x<6

-1<=x<3

answer:-1,0,1,2,3

Answer:

Step-by-step explanation:

This equation represents the relationship between the exponential functions y = e^x and y = (10^(x-1)). These two functions are equal to each other for all values of x. This can be shown by taking the natural logarithm of both sides of the equation, which gives us:

ln(e^x) = x-1

In this equation, ln(e^x) is equal to x, since the natural logarithm of an exponential expression with a base of e is the exponent. Therefore, we can simplify the equation by taking the natural logarithm of both sides:

ln(10^(x-1)) = x-1

e^(x-1) = 10^x

The two functions e^x and 10^(x-1) are the same function with different bases, so they follow the same pattern. The fact that these two functions are equal to each other for all values of x can also be shown by graphing the two functions and seeing that they overlap perfectly.

The angle that the ramp makes with the ground is approximately 28.07 degrees.

If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.

Here,
The sin of the angle θ is the ratio of the opposite side (height of the ramp) to the adjacent side (length of the inclined portion of the ramp):

Sin(θ) = 8/17

We can use a calculator to find the inverse sin of this ratio to get the angle θ:

θ = sin⁻¹(8/17)

θ ≈ 28.07 degrees

Therefore, the angle that the ramp makes with the ground is approximately 28.07 degrees.

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When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.

The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.

Replacing x with 1, we have:

ƒ(1) = -4(1) - 5

Simplifying further:

ƒ(1) = -4 - 5

ƒ(1) = -9

Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.

Let's break down the steps taken to arrive at the solution:

1. Start with the function f(x) = -4x - 5.

2. Replace x with 1 in the function.

3. Evaluate the expression by performing the necessary operations.

4. Simplify the expression to obtain the final result.

In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.

It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.

Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.

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Answer: Perimeter = 42.2 m

              Area = 81.1125 m²

Step-by-step explanation:

                                                      Lower     Upper

Length is given as 15.8    -->         15.75 ≤ L < 15.85

width is given as 5.2       -->           5.15 ≤ w < 5.25

Perimeter = 2L + 2w     (Upper bound)

                = 2(15.85) + 2(5.25)

                =   31.7      +   10.5

                =   42.2

Area = Length x width     (Lower bound)

        = 15.75 x 5.15

        = 81.1125

The equation 2 log₅ x = log₅ 4 + log₅ 9 has two solutions: x = 6.

To solve the equation 2 log₅ x = log₅ 4 + log₅ 9, we can use logarithmic properties to simplify and find the value of x.

Using the properties of logarithms, we can rewrite the equation as follows:

2 log₅ x = log₅ (4 * 9)

Next, we simplify the right side:

2 log₅ x = log₅ (36)

Now, we can use the property of logarithms that states logₐ b = c is equivalent to aᶜ = b. Applying this property, we have:

x² = 36

Taking the square root of both sides, we get:

x =  √36

Since the square root of 36 can be either positive or negative, we have two possible solutions:

x = 6

It's important to note that when working with logarithmic equations, we must always check if the obtained solutions satisfy the domain restrictions of the original equation. In this case, since the logarithm has a base of 5, the solution x = 6.

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