Which statements accurately describe the function f(x) = 3√18^x? Check all that apply. A. The domain is all real numbers.
B. The range is y > 3.
C. The initial value is 3.
D. The initial value is 9.
E. The simplified base is √2.
F. The simplified base is 3√2.
Answers
Option B is incorrect: the range is not y > 3, because, for negative values of x, f(x) < 3, e.g. for x = -1, f(x) = 3 * sqrt(18^(-1)) = 3*sqrt(1/18) = 3*0.2357 = 0.7071 < 3.
Option C is correct: f(0) = 3*sqrt(18^0) = 3*sqrt(1) = 3 * 1 = 3
Option D is incorrest: (see working for option C)
A) The domain is all real numbers;
C) The initial value is 3; and
F) The simplified base is 3√2.
Explanation:
A) The domain is the set of numbers that can be use for x. In this function, there are no domain restrictions; this means there are no values for x that will not give you a value for y. This means that all numbers work, which we say is "the set of all real numbers."
C) To find the initial value (starting point), substitute 0 for x:
f(x) = 3(√18)ˣ
f(0) = 3(√18)⁰
f(0) = 3(1) = 3
Thus the initial value is 3.
F) The base of the current function is √18; this is because that is what is raised to a power. If we simplify this, we find the prime factorization of 18, looking for pairs of factors to take out.
The prime factorization of 18:
18 = 2*9
9 = 3*3
This means 18 = 2*3*3; it gives us √18 = √(2*3*3). We have a pair of 3's under the radical, so we take a 3 out; this leaves a 2 under the radical:
√18 = √(2*3*3) = 3√2.
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Answer:
x = 109 degrees.
Step-by-step explanation:
The angle opposite the 45 degrees = 45 degrees (vertical angles)
Also the angle opposite to the 75 degree angle = 75 degrees for the same reason.
Now if we take the triangle on the left. the bottom right angle
180 - 75 - 45 = 60 degrees ( because the angles in a triangle sum to 189 degrees.
Next we find the left bottom angle of the triangle on the right.
This is 180 - 60 - 79 = 41 degrees (because these 3 angles are on the same straight line).
Finally x = 41 + 68 = 109 degrees ( external angle of a triangle theorem).
Answers
so putting the values of x and y in the equation, we get 10y -3x should be -11
so, 10* (-5) - 3 *2 = -50-6 = -56
case B , value of equation = 10*4 - 3*1 = 37
case C, value of equation = 10*6 -3*16.3 = -11.1
Case D, value of equation = 10*8-3*23 = 11
Ans will be C
Answers
30-pound dog ... 1 milligram of the medicine
w pound dog ... d milligram of the medicine
30 * d = 1 * w
30 * d = w
The correct result would be 30 * d = w.
Answer:
a
Step-by-step explanation:
right on edge
Answers
The correct option is (A). and
are connected at point Y.
is reflected across XY and then is reflected another time across YZ to form
.
Given, and
are connected at point Y.
is reflected about XY will shift the marked angle from left to right while the right side angle will remain at the same location and the triangle will remain upright to give
Reflection about the YZ will give the marked angle and the right angle in the same location and the vertex X will then be changed to P.
Thus , can be mapped to
with two reflections.
In the second option, we have is reflected 3 times which is more than 2 times as said in question. so this statement is false.
In next option is reflected across side XY and then is shifted downwards to form
.since here we have only one reflection, so this statement is also false.
4) In option 4 is reflected and then rotated thus option 4 is also not a correct option.
Hence the correct statement is and
are connected at point Y.
is reflected across XY and then is reflected another time across YZ to form
.
For more detail follow the link:
Answer:
The correct option is the first option;
Triangle XYZ and PYT are connected at point Y. Triangle XYZ is reflected across XY and then is reflected another time across YZ to form triangle PYT
Step-by-step explanation:
To answer the question we look at each option as follows;
1) The parameters given are triangle XYZ and PYT are connected at point Y
Triangle XY is reflected about XY will shift the marked angle from left to right while the right angle will remain at the same location and the triangle will remain upright to give triangle X'Y'Z'
Reflection about the YZ will give; the marked angle and the right angle in the same location and the vertex X will then be changed to P
Therefore, triangle XYZ can be mapped to triangle PYT with two reflections
2) In the second option, we have triangle XYZ is reflected 3 times which is more than 2 times as in the question, therefore, option two is less suited as an answer to the question
3) Triangle XYZ is reflected across side XY and then is shifted down to form triangle AYT
Therefore, since we have only one reflection, option 3 is also not appropriate as an answer
4) In option 4 triangle XYZ is reflected and then rotated therefore option 4 is also not a correct option.
Answers
Every rational number can be written as a fraction with whole numbers
on top and bottom. Irrational numbers can't.
Working method of recognizing them:
Any number that you can write down completely, on paper, using number digits without any symbols, is a rational number, whether you write it as a fraction or as a decimal.
Popular misconception:
A rational number doesn't necessarily produce a decimal that ends, and a decimal that never ends is not necessarily an irrational number.
Examples: 1/3, 1/7, 1/9, 1/11 are never-ending in decimal form.
Whole numbers are the positive integers and zero.
Counting numbers are the whole numbers without zero.
Integers are the whole numbers plus their negatives.
Answers
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Since Solise want to plant both trees and bushes in the same number of rows, you need to find the common factor.
Since the question is asking what the greatest number of rows she can plant, you have to find the greatest common factor.
The greatest common factor of 24 and 16 is 8.
You can plant 24 bushes in 8 rows (meaning you can divide it by 8), and 16 trees in 8 rows (meaning you can divide it by 8). Since the greatest number you can divide them both by is 8, the GCF of 24 and 16 is 8.
So the greatest number of rows Solise can plant is 8 rows.
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