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3 years ago

7

What is the converse of the given conditional statement?

1 answer:

Paha777 [63]3 years ago

7 0

The converse of an if statement is a statement in which the hypothesis and conclusion are switched.

<span>You will get into college if you work hard.

The "if" part is the hypothesis.
The "then" part is the conclusion.

Rewrite the original if statement in the if-then form:

If you work hard, then you will get into college.

The hypothesis is the if part: "you work hard"
The conclusion is the then part: "you will get into college"

To write the converse, switch the hypothesis and the conclusion.

If you get into college, then you worked hard.

This happens to be choice A.
</span>

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3 years ago

A linear sequence starts a+3b a+7b a+11b the 2nd term has value 19 the 5th term has value 67 work out the values of a and b

alekssr [168]

Answer:

$a = -9$

$b = 4$

Step-by-step explanation:

Given

Sequence: a+3b, a+7b, a+11b

2nd term = 19

5th term = 67

Required

Find a and b

First, the 5th term needs to be calculated;

Using formula for Arithmetic Progression (AP), the formula goes thus

$T_n = T_1 + (n - 1)d$

Where n = 5

T_1 = a + 3b ------------ FIrst term

$d = T_2 - T_1 or T_3 - T_2$ --- Difference between two successive terms

$d = a + 7b - (a + 3b)$

$d = a + 7b -a - 3b$

$d = a - a + 7b - 3b$

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So, $T_n = T_1 + (n - 1)d$ becomes

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Now that we have values for 2nd and 5th term;

From the second, T2 = 19 and T5 = 67

This gives

$a + 7b = 19$ --- Equation 1

$a + 19b = 67$ ---- Equation 2

Make a the subject of formula in (1)

$a = 19 - 7b$

Substitute these values in equation 1

$a + 19b = 67$ becomes

$19 - 7b + 19b = 67$

$19 + 12b = 67$

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$12b= 67 - 19$

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Divide both sides by 12

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Hence, the values of a and b are -9 and 4 respectively.

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