Explain how you can use base ten block to find 2.16÷3

Answers

Answer 1

Answer: You can use base ten blocks to find 2.16/ 3 by using 7 base ten blocks and 2 base one blocks.

Answer 2

Answer: you can take two hundreds blocks and then 16 tenths then just divide.

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The formula for the volume of a cylinder is V = πr2h. The volume of a cylinder is three times the volume of a cone with the same radius and height. If the volume of a cone with the same height as a cylinder equals the volume of the cylinder, the equation for the radius of cone R in terms of the radius of cylinder r is

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Since the cone volume formula is V=1/3πr2h , and the volume of a cylinder is V=πr2h , the ratio of cone to cylinder 3/1 or 3 : 1

The graph of the quadratic parent function is reflected across the x-axis, then shifted 5 units down and 4 units right. Write the equation of the new function in vertex form.

Answers

Answer:

y = -(x -4)² -5

Step-by-step explanation:

-f(x) is a reflection of f(x) across the x-axis.

f(x) -5 is a translation down by 5 units.

f(x -4) is a translation right by 4 units.

Applying these transformations to y = x² gives, successively, ...

y = -x²

y = -x² -5

y = -(x -4)² -5 . . . . . . the new equation in vertex form

This is about reflection of graphs.

y = -(x - 4)² + 5

We are told the graph is that of the quadratic parent function. Now, in transformations of quadratic functions, the parent function of the quadratic group is usually expressed as;

y = x²

Now, we are told that this quadratic parent function is reflected across the x-axis. This means the value of the y-coordinate will become negative and we have;

-y = x²

It is now shifted 5 units down. This means we will now have;

-y = x² - 5

It is now shifted 4 units down. This means we now have;

-y = (x - 4)² - 5

Dividing through by -1 to get;

y = -(x - 4)² + 5

Read more at; brainly.com/question/19333139

Use the distributive property to multiply

-7 (2x - 4)

I think it's -14x + 28

Answers

-14x+28 is correct. Good job!

It is-14x + 28 way to go!

Match the sequence (term) with the correct type of sequence (definition).Match Term Definition
128, 32, 8, 2, ... A) Arithmetic, common difference is 5
1, 3, 9, 27, ... B) Arithmetic, common difference is -3
5, 10, 15, 20, ... C) Geometric, common ratio is 0.25
20, 17, 14, 11, ... D) Geometric, common ratio is 3

Answers

The correct answer among all the other choices is 20, 17, 14, 11, ... D) Geometric, common ratio is 3. This is the sequence (term) with the correct type of sequence (definition) among the examples given. Thank you for posting your question. I hope this answer helped you. Let me know if you need more help.

The function y = -0.03(x - 14)^2 + 6 models the mump of a red kangaroo where x is the horizontal distance in meters and y is the vertical distance in meters for the height of the jump. What is the kangaroo's maximum height? How long is the kangaroo's jump?

Answers

From the vertex of the quadratic equation, we find that: The kangaroos maximum height is of 6 meters.

From the roots of the equation, we find that: The kangaroo's jump is 28.14 meters long.

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Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

$f(x) = ax^(2) + bx + c$

It's vertex is the point $(x_(v), y_(v))$

In which

$x_(v) = -(b)/(2a)$

$y_(v) = -(\Delta)/(4a)$

Where

$\Delta = b^2-4ac$

If a<0, the vertex is a maximum point, that is, the maximum value happens at $x_(v)$ , and it's value is $y_(v)$ .

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Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^(2) + bx + c, a\neq0$ .

This polynomial has roots $x_(1), x_(2)$ such that $ax^(2) + bx + c = a(x - x_(1))*(x - x_(2))$ , given by the following formulas:

$x_(1) = (-b + √(\Delta))/(2*a)$

$x_(2) = (-b - √(\Delta))/(2*a)$

$\Delta = b^(2) - 4ac$

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The quadratic equation is:

$y = -0.03(x - 14)^2 + 6$

Placing in standard form:

$y = -0.03(x^2 - 28x + 196) + 6$

$y = -0.03x^2 + 0.84x + 0.12$

Thus, it has coefficients $a = -0.03, b = 0.84, c = 0.12$

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The kangaroo's maximum height is the y-value of the vertex, thus:

$\Delta = b^2 - 4ac = (0.84)^2 - 4(-0.03)(0.12) = 0.72$

$y_(v) = -(\Delta)/(4a) = -(0.72)/(4(-0.03)) = 6$

The kangaroos maximum height is of 6 meters.

----------------------------

The length of the kangaroo's jump is the positive root. The roots are found at the values of x for which y = 0, thus, the solutions of the quadratic equation.

$x_(1) = (-0.84 + √(0.72))/(2(-0.03)) = -0.14$

$x_(2) = (-0.84 - √(0.72))/(2(-0.03)) = 28.14$

The kangaroo's jump is 28.14 meters long.

A similar question is given at brainly.com/question/16858635

Answer:

Kangaroo's maximum height is 6 m and the kangaroo's jump is 28 m long

Step-by-step explanation:

Given : $y = -0.03(x - 14)^2 + 6$

To Find : What is the kangaroo's maximum height? How long is the kangaroo's jump?

Solution:

$y = -0.03(x - 14)^2 + 6$

x is the horizontal distance in meters

y is the vertical distance in meters for the height of the jump.

Substitute y = 0

$0 = -0.03(x - 14)^2 + 6$

$0.03(x - 14)^2 = 6$

$(x - 14)^2 = (6)/(0.03)$

$(x - 14)^2 =200$

$(x - 14) =√(200)$

$(x - 14) =14.142$

$x =14.142+14$

$x =28.142$

x≈ 28 m

Now the maximum height will be attained at mid point i.e. $(28)/(2) =14$

Now substitute x= 14

$y = -0.03(14 - 14)^2 + 6$

$y = 6$

So, kangaroo's maximum height is 6 m and the kangaroo's jump is 28 m long

Which method would be the most efficient method to solve x^2-6=0

Answers

adding 6 to both sides and taking the square root, remember that x can be the poitivie and negative root
x^2-6=0
add 6
x^2=6
squaer root both sides
x=√6

x=+√6 and -√6

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