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Cerrena [4.2K]
3 years ago
11

Suppose a rectangle will undergo a rotation about the origin of a coordinate plane and a translation of 6 units down. Which of t

hese is a true statement?
The resulting rectangle will be congruent to the original rectangle regardless of the order of the rotation and the translation.
The resulting rectangle will be congruent to the original rectangle only if the rotation occurs before the translation.
The resulting rectangle will be congruent to the original rectangle only if the translation occurs before the rotation.
The resulting rectangle will not be congruent to the original rectangle regardless of the order of the rotation and the translation.
Mathematics
1 answer:
nikdorinn [45]3 years ago
6 0

Answer: The resulting rectangle will be congruent to the original rectangle regardless of the order of the rotation and the translation.

Step-by-step explanation: Since a dilation is not performed, the shape and size stay the same no matter how it is moved throughout the coordinate plane.

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I have these factoring questions I need help with.
snow_lady [41]

f(x)=4x^2+4x-3

1. Determine y-intercept.

<em>The y-intercept is (0,-3). Substitute x = 0 in the equation as we get f(x) = -3 as the y-intercept.</em>

2. Determine the zeros.

<em>Factor the polynomials first. </em>(2x-1)(2x+3) <em>This is the factored form. The zeros are the roots of equation. Therefore, the zeros are 1/2 and -3/2</em>

3. Determine the Axis of Symmetry

<em>We can solve this by using the formula of </em>x=-\frac{b}{2a}  <em>However, I'll be solving the Axis of Symmetry with Calculus instead.</em>

<em />f'(x)=2(4x^{2-1})+1(4x^{1-1})-0\\f'(x)=8x+4<em />

<em>Then let f'(x) = 0 to find the Axis of Symmetry.</em>

<em />8x+4=0\\8x=-4\\x=-\frac{4}{8}\\x=-\frac{1}{2}<em />

<em>Therefore, the Axis of Symmetry is -1/2</em>

4. Determine the vertex.

<em>Substitute the value of Axis of Symmetry in f(x).</em>

<em />f(x)=4(-\frac{1}{2})^2+4(-\frac{1}{2})-3\\f(x)=4(\frac{1}{4})-2-3\\f(x)=1-2-3\\f(x)=-4<em />

<em>Therefore the vertex is at (-1/2, -4)</em>

5. Does the vertex representing max-pont or min-point?

<em>The vertex represents the minimum point. The graph is upward, meaning the minimum point is the point that gives the LOWEST Y-VALUE. </em>

7. Graph f(x)

<em>Unfortunately I won't be able to graph. But I can tell you to graph a parabola that has the most curve at the vertex and intercepts y-axis at (0,-3).</em>

<em>--------------------------- </em>End of Part 1 --------------------------------

2. Write the general form of Quadratic Function in standard form.

y=ax^2+bx+c

<em>The graph can be easily determined about the y-intercept and being an upward or downward parabola along with how narrow or wide the parabola is. </em>

<em>For example, c value is the y-intercept as defined. When a > 0, the parabola is upward and when a < 0, the parabola is downward. The more value of | a | is, the more narrow it will be and the less value of | a | it is, the wider it will be.</em>

3. Write in Factored Form

y=(x+a)(x+b)\\y=(x-a)(x-b)\\y=(x+a)(x-b)\\y=(x-a)(x+b)

<em>These are factored forms with different types of operators.</em>

<em>The equation can be easily determined about the roots of equation. For example, if the function is in f(x) = (x+2)(x-1) Then the roots would be x = -2 and 1 as the graph will intercept x-axis at (-2,0) and (1,0)</em>

4. Write in Vertex Form.

y=a(x-h)^2+k

<em>The equation can be easily determined for the vertex, axis of symmetry and the same narrow/wide/upward/downward parabola again.</em>

<em>The vertex is at (h,k) and the axis of symmetry is at x = h.</em>

<em>For example, </em>y=(x-2)^2+3<em />

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3 0
3 years ago
Plz help ASAP I will mark u branliest
-BARSIC- [3]

Answer:

Brainliest?

Step-by-step explanation:

1.

subtract 1 from both sides

divide by 2

2.

add 5 to each side

divide by 4

6 0
3 years ago
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In the given diagram, find the values of x, y, and z.
anyanavicka [17]

Answer:

B) x=64, y=21, z=64

Step-by-step explanation:

X=180-116=64

Y cannot equal 115, and one angle is already 95, and that would put it over 180.  The only remaining choice for y=21

z=180-95-21=64

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3 years ago
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Answer:

1188 grams of water

Step-by-step explanation:

x is the grams of water

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sugar/total is 12/12+x

and 1% ratio is 12/12+x=1/100

so x would be 1188 grams of water.

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2 years ago
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kap26 [50]

Answer:

f ^-1 (x) =7X/5 - 2/5

Step-by-step explanation:

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