Find the distance between the two points rounding to the nearest tenth (if necessary). (-6,5) and (3,-7)​

The distance between points (-6,5) and (3,-7)​ is 15 units.

In the coordinate plane, the points are denoted by coordinate and the distance means the physical distance between them.

Let's consider we have two points (x₁, y₁) and (x₂, y₂) the distance between these two points is given by the formula;

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

Given the points  (-6,5) and (3,-7)​

Here x₁ = -6 , x₂ = 3

y₁ = 5 and y₂ = -7

So,

[tex]d = \sqrt {\left( {-6 - 3 } \right)^2 + \left( {5 +7 } \right)^2 }[/tex]

d = √225

d = 15 units.

Hence "The distance between points (-6,5) and (3,-7)​ is 15 units".

To learn more about the distance between two points,

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Please help!
Simplify the expression using order of operations:25 - 5 + 36/9 - 6(7)

Match the pronoun type to the example.

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Patricia and Emma work together. They both have the same amount of money invested in their portfolios. Their investments are listed in the table. Two months ago, the company Patricia and Emma work for started incurring losses, and now its share price has started falling. Which statement is correct given the scenario?

Patricia’s Investmentscompany stocks, bonds, mutual funds, domestic stocks, and international stocksEmma’s Investmentscompany stocks

A. 

Patricia’s portfolio will be affected the most because she has too many assets in her portfolio.

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Daredevil Danny takes a practice jump as shown on the graph below. Complete the steps to determine the equation for the parabolic trajectory of his practice jump.

a) What are the key aspects of any parabola? What do the key aspects tell you about the graph?

(5 points)


It goes all the way up to its max point and comes down. Its max point is 32 and how far it went was from 15 to 35


b) What are the key aspects of Daredevil Danny’s practice jump shown in the graph provided? Describe each value and how it is determined. (10 points)


It is a standard form graph and he needs to figure out the speed he is going to go and the angle


Step 2: Solve for coefficient a.

a) What equation is used to find the vertex form of a parabola with the vertex (h, k)? (5 points)


F(x)=ax2+bx+c

b) Solve for the coefficient a in the vertex form for the parabola in Daredevil Danny’s practice jump using key aspects from step 1. As you solve for the coefficient, explain each step of the process in detail. (15 points)



The picture of the question in the attached figure we know that The equation of a vertical parabola in vertex form is given by where a is the leading coefficient (h,k) is the vertex Looking at the graph we have a vertical parabola open downward (coefficient a is negative)The vertex is a maximum The vertex is the point (25.32) substitute in the equation













c) What is the vertex form of the parabola from Daredevil Danny’s practice jump? (5 points)


f(x)=-12/25(x-25)^2+32

Step 3: Change from vertex form to standard form.

To get Daredevil Danny through the Flaming Hoop Jump of Awesome, you will need to know the values of a, b, and c, which are the coefficients of the quadratic equation in standard form.

a) What is the equation for a parabola in standard form? (5 points)

y = ax^2 + bx + ct




b) Convert the vertex form of the equation you wrote above to standard form. (10 points)







c) What are the values for coefficients a, b, and c in the quadratic equation for Daredevil Danny’s practice jump? (5 points)






Step 4: Calculate the equation for the flaming hoop jump.

Using the same method for the practice jump, write the standard form of the equation that will get Daredevil Danny safely through the Flaming Hoop Jump of Awesome!

a) Write the vertex form by substituting in values for x, y, h, and k, and then solve for a. Show your work. (10 points)










b) Determine the values of a, b, and c. Show your work. (10 points)



c) Using your values of a, b, and c, did Daredevil Danny successfully pass through the Flaming Hoop Jump of Awesome? If not, describe what happened. Then, go back to critique your work and revise it. Write about your revision. (5 points)



d) Once you have determined the correct values of a, b, and c, verify algebraically that Daredevil Danny will successfully pass through the Flaming Hoop Jump of Awesome. (5 points)


Please help I only need help with steps 2 and 3!

Write an equation of the line that passes through (2, 7) and (0, −5).

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