Solve the inequality. Graph your solution. $$ - 5.3 x > 21 |
1 answer:
The solution to the inequality - 5.3 + x > 21 is x > 26.3
In mathematics, inequality refers to a relation which makes a non-equal comparison between two numbers or other mathematical expressions. In other words, it is a relationship between two expressions or values that are not equal to each other. It is used generally used to compare two numbers on the number line by their size.
In order to solve the given inequality - 5.3 + x > 21, add 5.3 both sides.
- 5.3 + x + 5.3 > 21 + 5.3
x > 26.3
The solution means that the value of x is greater than 26.3. The solution is graphed on a number line.
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Answer:
: Use the Pythagorean Theorem
Answer:
x = 67.50 ft
Step-by-step explanation:
Consider, ΔMAB and ΔMNP,
∠M = ∠M (Common)
Given AB║NP and let MN as transversal,
∠MAB = ∠MNP (alternate angle)
Also, Given AB║NP and let MP as transversal,
∠MBA = ∠MPN (alternate angle)
Therefore, ΔMAB ≅ ΔMNP (By AAA similarity )
Thus, by CPCT,
consider first two ratios,
Substitute the values, MA = MN - AN = 49.5 ft
On solving for x , we get, x = 67.50 ft
Thus, value of x is 67.50 ft
Answer:
Problem 1)
Problem 2)
Problem 3)
Step-by-step explanation:
Problem 1: ∠DEG
From the diagram, we know that ∠DFG intercepts Arc DG.
Inscribed angles have half the measure of its intercepted arc. Therefore:
We know that m∠DFG = 38°. So:
∠DEG also intercepts Arc DG. Hence:
We know that Arc DG measures 76°. Hence:
Alternate Explanation:
Since ∠DEG and ∠DFG intercept the same arc, ∠DEG ≅ DFG. So, m∠DEG = m∠DFG = 38°.
Problem 2: Circle with Centre O
(Let the bottom left corner be A, upper be B, and right be C.)
∠ACB intercepts Arc AC.
Inscribed angles have half the measure of its intercepted arc. Therefore:
Since m∠ACB = 70°:
∠<em>x</em> is a central angle and also intercepts Arc AC.
The measure of a central angle is equal to its intercepted arc. Thus:
The sum of the interior angles of a polygon is given by the formula:
Where <em>n</em> is the number of sides.
Since the inscribed figure is a four-sided polygon, its interior angles must total:
Therefore:
Substitute and solve for <em>y:</em>
Problem 3: ∠EDG
∠EFG intercepts Arc EDG.
Inscribed angles have half the measure of its intercepted arc. Therefore:
Since m∠EFG = 115°:
A full circle measures 360°. Hence:
Since we know that Arc EDG measures 230°:
Solve for Arc EFG:
∠EDG intercepts Arc EFG.
Inscribed angles have half the measure of its intercepted arc. Therefore:
Since we know that Arc EFG measures 130°: