Answer:
The 1st Graph (A)
Step-by-step explanation:
Test by substituting values for "x":
<em>By substituting the numbers of 0</em> (0 < -3), <em>-1 </em>(-1 < -3), <em>and -2</em> (-2 < -3), <em>does that make the statement true</em>?
The answer is FALSE. None of those values are satisfactory.
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<em>Therefore, by substituting</em> <em>-4</em> (-4 < -3), <em>-5</em> (-5 < -3), <em>and -6</em> (-6 < -3), <em>these values are satisfactory and makes the statement true</em>.
Answer:
One triangle can be constructed
Step-by-step explanation:
I took the test hope this helps
The population is increasing at the rate of 220
Explanation:
Given that the population of Hannah's town is increased from 1500 to 2600 in five years.
This can be written in expression as
and
We need to determine the rate of change of population.
The rate of change can be determined using the formula,
where and
Substituting the values in the formula, we have,
Simplifying, we have,
Dividing, we get,
220
Thus, the population is increasing at the rate of 220
Answer:
see explanation
Step-by-step explanation:
Given a quadratic equation in standard form
ax² + bx + c = 0 ( a ≠ 0 )
Then for the equation to have 2 real roots , the discriminant must be greater than zero , that is
b² - 4ac > 0
x² + x + c = 0 ← is in standard form
with a = 1, b = 1, c = c , then
b² - 4ac > 0
1² - (4 × 1 × c) > 0
1 - 4c > 0 ( subtract 1 from both sides )
- 4c > - 1
Divide both sides by - 4, reversing the inequality as a result of dividing by a negative quantity.
c <
Answer:
see below for drawings and description
Step-by-step explanation:
For geometry problems involving translation, rotation, and reflection—transformations that change location, but not size ("rigid" transformations)—it might be helpful for you to trace the image onto tracing paper or clear plastic so that you can manipulate it in the desired way. Eventually, you'll be able to do this mentally, without the aid of a physical object to play with.
For the images attached here, I copied the triangle onto a piece of clear plastic so I could move it to the desired positions. The result was photographed for your pleasure.
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a. Translation means the image is moved without changing its orientation or dimensions. You are asked to copy the triangle so that the upper left vertex is moved to what is now point E. See the first attachment.
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b. Reflection means the points are copied to the same distance on the other side of the point or line of reflection. Just as an object held to a mirror has its reflection also at the mirror, any points on the line of reflection do not move. Reflection flips the image over. See the second attachment.
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c. Rotation about point D means point D stays where it is. The angle of rotation is the same as the angle at D, so the line DE gets rotated until it aligns with the line DF. The rest of the triangle maintains its shape. See the third attachment.