Joel and Melinda provide the following proofs for vertical angles to be equal:

Joel's proof: angle 2 + angle 3=180° (t is a straight line)
angle 1 + angle 2 = 180° (PQ is a straight line)
Therefore, angle 1 + angle 2 = angle 2 + angle 3 (Transitive Property of Equality)
Hence, angle 1 = angle 3 (Subtraction Property of Equality)

Melinda's proof: angle 1 + angle 2 + angle 3 + angle 4 = 360°
Therefore, angle 1 + angle 4 = 180° (t is a straight line)
Hence, angle 4 = angle 2 (Transitive Property of Equality)

Which statement is correct?
A Joels is correct
B Melindas is correct
C Both Melinda and joels is correct
D Neither is correct

The logarithmic equation is solved to find x to be equal to 9

How to solve the equation

To solve the equation, we can use logarithmic properties to simplify and solve for x

[tex]\(\log_6(4x^2) - \log_6(x) = 2\)[/tex]

[tex]log_6\left(\frac{4x^2}{x}\right) = 2[/tex]

[tex]log_6(4x) = 2[/tex]

6²= 4x

36 = 4x

x = 9

The solution to the equation [tex]\(\log_6(4x^2) - \log_6(x) = 2\) is \(x = 9\).[/tex]

To solve the equation [tex]\(\log_6(4x^2) - \log_6(x) = 2\)[/tex], you can use the properties of logarithms.

First, apply the quotient rule of logarithms to combine the two logarithms:

[tex]\[ \log_6\left(\frac{4x^2}{x}\right) = 2 \][/tex]

Simplify the expression inside the logarithm:

[tex]\[ \log_6(4x) = 2 \][/tex]

Now, rewrite this equation in exponential form:

[tex]\[ 6^2 = 4x \]\[ 36 = 4x \][/tex]

Now, solve for x:

[tex]\[ x = \frac{36}{4} \]\[ x = 9 \][/tex]

So, the solution to the equation [tex]\(\log_6(4x^2) - \log_6(x) = 2\) is \(x = 9\).[/tex]

The time would be 2.71 seconds after the ball is thrown does it hit the ground.

Velocity is defined as the displacement of the object in a given amount of time and is referred to as velocity.

A ball is thrown from a height of 140 feet with an initial downward velocity of 8 ft/s.

The ball's height h (in feet) after t seconds is given by the following.

⇒ h = 140-8t - 16t²

h = 0 at the ground.

We divide both sides of the equation by (-8) to yield:

⇒ 0 = 2t² + t - 17.5

where a = 2, b= 1, c = -17

[tex]t = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\t = \dfrac{-1\pm\sqrt{2^2-4\times2\times-17.5}}{2\times2}[/tex]

t = [-1 ± √141] / (4)

t = 2.71 and -3.21

For this problem, time can only be positive, so ignore the negative solution.

Therefore, the time would be 2.71 seconds after the ball is thrown does it hit the ground.

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The distance and speed are illustrations of linear equations

The given parameters are:

[tex]\mathbf{Rate = 6}[/tex]

[tex]\mathbf{Initial = 9}[/tex]

(a) The standard equation

Because the distance reduces with time, the equation is:

[tex]\mathbf{y = Initial-Rate \times x}[/tex]

This gives

[tex]\mathbf{y = 9 - 6\times x}[/tex]

[tex]\mathbf{y = 9 - 6x}[/tex]

Add 6x to both sides

[tex]\mathbf{6x + y = 9}[/tex]

(b) The y-intercept

This is the initial distance away from home.

So, the y-intercept is 9

(c) The x-intercept

Set y to 0, to calculate the x-intercept

[tex]\mathbf{6x + y = 9}[/tex]

[tex]\mathbf{6x + 0 = 9}[/tex]

[tex]\mathbf{6x = 9}[/tex]

Divide both sides by 6

[tex]\mathbf{x = 1.5}[/tex]

This is the initial time away from home.

So, the x-intercept is 1.5

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Answer:

I think it is Angle B prime C prime D prime

Step-by-step explanation:

A'B'C'D' is a translation so they are congruent.So the figure B'C'D' is congruent or equal to BCD. Please let me know if i'm right

If the inflation rate increases faster than their income, people will most likely use a higher proportion of their incomes on basic needs

Inflation is the rate of increase in prices over a given period of time. Inflation is typically a broad measure, such as the overall increase in prices or the increase in the cost of living in a country.

According to the question

If the inflation rate increases faster than their income, people will most likely:

As

inflation rate increases  means increase in prices of goods and services  over a given period of time.

i.e

People will use a higher proportion of their incomes on basic needs .

Hence, If the inflation rate increases faster than their income, people will most likely use a higher proportion of their incomes on basic needs.

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when numbers are in parenthesis the first number is x the second is y

(x,y)

sine they give you (2, blank)

2 = x so replace x in the equation with 2

 so y=2x+5 becomes y=2(2)+5

 so y = 2*2+5 = 9

 y=9

 so it should be (2,9)

Answer:

f(x), h(x), g(x)

1940 ~~~~~~~~~~~~ APEX

If an ice cream store sells 2 drinks, in 3 ​sizes, and 8 flavors, the number of ways can a customer order a​ drink will be 48.

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

It given that, An ice cream store sells 2 ​drinks, in 3 sizes, and 8 flavors.

We have to find the number of ways can a customer order a​ drink,

It is obtained by multiplying all the possible cases for that event, Multiplication is one type of arithmetic operation. There are basically four types of arithmetic operations.

=2×3×8

=48

Thus, if an ice cream store sells 2 drinks, in 3 ​sizes, and 8 flavors, the number of ways can a customer order a​ drink will be 48.

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The appropriate model of the function is:

                        Linear model

We are given a table of values as:

           x               f(x)

           1                15

           2               12

           3                9

           4                6

           5                 3

Clearly we could observe that with each increasing value of x the value of function decreases by 3.

This means that the range of change is constant.

Hence, the relation is linear ( as the rate of change is constant )

Also, the equation that models this data set is given by:

                       [tex]y=f(x)=18-3x[/tex]

Answer with explanation:

Total number of different candidates who are playing the game=7

Suppose, Seven candidates are represented  by ={A,B,C,D,E,F,G}

Total Possible Outcome =7

→Probability that , "A" gets his scrap of paper , means the paper on which he or she has written his or her name

                             [tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{7}[/tex]

→Now, 6 candidates are left.

Probability that , "B" gets his scrap of paper , means the paper on which he  or she has written his or her name

                             [tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{6}[/tex]  

→Now, 5, candidates are left.

Probability that , "C" gets his scrap of paper , means the paper on which he or she has written his or her name

                             [tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{5}[/tex]  

→Now, 4 candidates are left.

Probability that , "D" gets his scrap of paper , means the paper on which he or she has written his or her name

                             [tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{4}[/tex]  

→Now, 3 candidates are left.

Probability that , "E" gets his scrap of paper , means the paper on which he or she has written his or her name

                             [tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{3}[/tex]  

→Now, 2 candidates are left.

Probability that , "F" gets his scrap of paper , means the paper on which he or she has written his or her name

                             [tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{2}[/tex]  

→Now, a single candidates is left.

Probability that , "G" gets his scrap of paper , means the paper on which he or she has written his or her name

                             [tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{1}=1[/tex]  

Required Probability

                 [tex]=\frac{1}{7} \times\frac{1}{6} \times\frac{1}{5} \times\frac{1}{4} \times\frac{1}{3} \times\frac{1}{2} \times 1\\\\=\frac{1}{5040}[/tex]    

The required exact value of the given trigonometric function is sin(17π/12) = (√6 + √2)/4

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

The trigonometric function is given in the question, as follows:

sin(17π/12)

To find the value of sin(17π/12), we can use the following trigonometric identity:

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

In this case, we can write:

sin(17π/12) = sin(π/3 + π/4)

We know that sin(π/3) = √3/2 and cos(π/3) = 1/2, and sin(π/4) = cos(π/4) = √2/2.

Therefore, we can use the above identity to get:

sin(17π/12) = sin(π/3)cos(π/4) + cos(π/3)sin(π/4)

         = (√3/2)(√2/2) + (1/2)(√2/2)

         = (√6/4) + (√2/4)

         = (√6 + √2)/4

So the answer is option (c): √6 + √2 / 4.

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The given problem supplies as with the surface area of the beach ball and we are to look for the required radius. Assuming that the beach ball is perfectly shaped in the form of a sphere, then the formula for calculating the surface area of a sphere is given as:

SA = 4 π r^2

where r is the radius of the sphere and SA is the surface area which is given to be 7238 in^2

Rewriting the formula in terms of r:

r^2 = SA / 4 π

r = sqrt (SA / 4 π)

Solving for r:

r = sqrt (7238 in^2 / 4 π)

r = 24 in

Answer:

24 inches

Answer:

Selling price of an item is $256.50 (A).

Step-by-step explanation:

Given : WE have  given an item listed at $400 subject to a discounted series of $25%, 10%, and 5% .

To find : Find the selling price of an item.

Formula used : Selling price = marked price - discount.

Solution : We have an item listed at = $400.

Discount percentage = $25% , $10% , $5.

Discount 1  = $400 ×[tex]\frac{25}{100}[/tex] = $100.

Selling price = $400-100 = $300.

Discount 2 = $300 ×[tex]\frac{10}{100}[/tex] = $30.

Selling price = $300-30 = $270.

Discount 3  = $270 ×[tex]\frac{5}{100}[/tex] = $13.50.

Final selling price = $270-13.50 = $256.50.

Therefore, Selling price of an item is $256.50 (A).

if they were rounded to the tens place

18 would round to 20

16 would round to 20

17 would round to 20

 14 would round to 10

 so April would be different.

Final answer:

To find the distance from Larry's house to his friend's house, we use the relationship between distance, speed, and time for his trip to and from his friend's house, taking into account the different speeds and total travel time of 5 hours.

Explanation:

The student's question asks to find the distance from Larry's house to his friend's house given his speed and total travel time in both directions. To solve this problem, we use the formula distance = speed × time. Let's call the distance one way d, the time to travel to the friend's house t1, and the time to travel back t2. Larry's speed going to the friend's house is 60 miles per hour and coming back is 50 miles per hour. The total travel time is 5 hours.

So for the trip to the friend's house we have:

d = 60 × t1

And for the trip back:

d = 50 × t2

Since the total travel time is 5 hours:

t1 + t2 = 5

Substituting the expressions for d from the first two equations into the third, we get:

60t1 + 50t2 = 60(5)

Using the fact that t1 + t2 = 5, we solve for either variable, say t1, which gives us t2 as well. After finding t1 and t2, we plug either of those back into the original distance equations to find d, which will be the distance from Larry's house to his friend's house. The answer should be rounded to the nearest mile.