The values are in the solution set of the compound inequality are (-6, -3), (3, 8).
<h3>What is inequality?</h3>
Inequality is the phenomenon of unequal distribution of resources and opportunities among the given function.
To find the number that are solutions to the compound inequalities, the value of x is
First inequality:
4(x +3) ≤0
4x +12 ≤0
4x ≤-12
x ≤-3
The value of x lies in the interval = (-∞ , -3]
Second inequality:
x +1 >3
x>2
The value of x lies in the interval = (2 , ∞)
So, the interval solution is (-∞ , -3] U (2 , ∞)
Thus, the values are in the solution set of the compound inequality are (-6, -3), (3, 8).
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Answer:
Right or positively skewed
Step-by-step explanation:
From the median and the interquartile range we can find the first and third quartile values Q3=40.15+(4.98/2)=42.64 and Q1=37.66.
Now we have enough evidence to conclude that is Right or positively skewed
1. The mean is above the median
2. The mean is 43.70, which is above the third quartile (42.64), meaning that after the mean there's less than 30% of the data.
The evidence suggests that most of the data is concentrated at the bottom of the distribution making it right or positively skewed.
The reflection transformation in the question is a rigid transformation,
therefore, the image and the preimage are congruent.
The statements that are true are;
Reasons:
The given parameter are;
Triangle ΔABC is reflected across the line 2·X, to map onto triangle ΔRST
Required:
To select the true statements
Solution:
A reflection is a rigid transformation, therefore, the distance between corresponding points on the image and the preimage are equal.
Therefore;
AB = RS
BC = ST
AC = RT
Given that the image formed by a reflection is congruent to the preimage, we have;
ΔABC ≅ ΔRST
∠ABC ≅ ∠RST
m∠ABC = m∠RST by the definition of congruency
∠BCA ≅ ∠STR
m∠BCA = m∠STR by the definition of congruency
∠BAC ≅ ∠SRT
m∠BAC = m∠SRT by the definition of congruency
Therefore, the true statements are;
- <u>AB = RS</u>; Image formed by rigid transformation
- <u>∠ABC ~ ∠RST</u>; Definition of similarity
- <u>ΔABC = ΔRST</u>; By definition of congruency
- <u>m∠BAC = m∠SRT</u>; by the definition of congruency
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