Jill and Erika made 4 gallons of lemonade for their lemonade stand. How many quarts did they make?
2 answers:
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Answer:
Recursive:
Explicit:
And the 20th term is 225.
Step-by-step explanation:
We have the sequence:
35, 45, 55, 65.
Notice that each subsequent term is 10 more than the previous term.
Therefore, our common difference is (+)10.
Recursive Rule:
The standard format for the recursive rule is:
Where a is the initial term and d is the common difference.
From our sequence, we know that a the initial term is 35.
And as determined, our common difference d is 10.
Substitute. Hence, our recursive rule is:
Explicit Rule:
The standard format for the explicit rule is:
Where a is the initial term and d is the common difference. So, let’s substitute 35 for a and 10 for d. Hence, our explicit formula is:
Now, let’s find the 20th term. We will utilize the explicit rule since the recursive rule can get tedious. Substitute 20 for n because we would like to 20th term. Thus:
Evaluate:
Hence, the 20th term is 225.
In the congruent triangles both triangle are same . In this triangle 2.3.3 congruent triangle image given below to understand better.
According to the question, given that
2.3.3 congruent triangle under congruence triangle are explain:
Both triangles are said to be congruent if the three angles and three sides of one triangle match the corresponding angles and sides of the other triangle. We can see from the examples PQR and XYZ that PQ = XY, PR = XZ, and QR = YZ, and thus P = X, Q = Y, and R = Z. Then, we can state that XYZ and PQR.
To be congruent, the two triangles must be the same size and shape. It is necessary for both triangles to be superimposed on one another. A triangle appears to be in a different place or have a different look as we rotate, reflect, and/or translate it.
Two triangles must meet five requirements in order to be congruent. The congruence properties are SSS, SAS, ASA, AAS, and RHS.
SSS Congruence Criteria
Side-Side-Side criterion is referred to as the SSS criterion. According to this standard, two triangles are congruent if their respective triangles' three sides are equal to one another.
The three angles of BAC must be identical to the corresponding angles of XYZ if, according to the SSS condition, BAC XYZ.
SAS Congruence Criteria
Side-Angle-Side criterion is referred to as the SAS criterion. According to this standard, two triangles are said to be congruent if their matching sides and included angles are the same on each side of each other.
The third side (AB) and the other two angles of ABC must be identical to the equivalent side (XY) and the angles of XYZ if ABC XYZ under the SAS condition.
ASA Congruence Criteria
Angle-Side-Angle criterion is also known as ASA criterion. According to the ASA criterion, two triangles are congruent if any two of their included sides and related angles are equivalent in size to those of the other triangle.
AAS Congruence Criteria
Angle-Angle-Side criterion is also known as the AAS criterion. Two triangles are said to be congruent according to the AAS criterion if any two angles and the non-included side of one triangle match the corresponding angles and side of the second triangle.
RHS Congruence Criteria
Right angle-hypotenuse-side congruence is referred to as the RHS criterion. If the hypotenuse and side of one right-angled triangle are equal to the hypotenuse and the corresponding side of another right-angled triangle, then two triangles are said to be congruent according to this criterion.
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