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Ad libitum [116K]
1 year ago
15

If a conditional statement is “If the sun shines, people will be in good moods”, what is the statement “If the sun does not shin

e, people will not be in good moods.” A. converse B.conditional C. inverse D. contrapositive
Mathematics
1 answer:
77julia77 [94]1 year ago
7 0

Answer:

C. Inverse

Step-by-step explanation:

The second statement is the inverse, because in an inverse, the hypothesis and the conclusion are both negated. In this case, the sun doesnt shine and the people wont be in a good mood, as opposed to the sun will shine, and the people will  be in a good mood.

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Milton spilled some ink on his homework paper. He can't read the coefficient of $x$, but he knows that the equation has two dist
Lera25 [3.4K]

Answer:

Sum = -81

Step-by-step explanation:

See the comment for complete question.

Given

c = 36 ----- Constant

No coefficient of x^2

Required:

Determine the sum of all distinct positive integers of the coefficient of x

Reading through the complete question, we can see that the question has 3 terms which are:

x^2 ---- with no coefficient

x ---- with an unknown coefficient

36 ---- constant

So, the equation can be represented as:

x^2 + ax + 36 = 0

Where a is the unknown coefficient

From the question, we understand that the equation has two negative integer solution. This can be represented as:

x = -\alpha and x = -\beta

Using the above roots, the equation can be represented as:

(x + \alpha)(x + \beta) = 0

Open brackets

x^2 + (\alpha + \beta)x + \alpha \beta = 0

To compare the above equation to x^2 + ax + 36 = 0, we have:

a = \alpha + \beta

\alpha \beta = 36

Where: \alpha, \beta and \alpha \ne \beta

The values of \alpha and \beta that satisfy \alpha \beta = 36 are:

\alpha = -1 and \beta = -36

\alpha = -2 and \beta = -18

\alpha = -3 and \beta = -12

\alpha = -4 and \beta = -9

So, the possible values of a are:

a = \alpha + \beta

When \alpha = -1 and \beta = -36

a = -1 - 36 = -37

When \alpha = -2 and \beta = -18

a = -2 - 18 = -20

When \alpha = -3 and \beta = -12

a = -3 - 12 = -15

When \alpha = -4 and \beta = -9

a = -4 - 9 = -13

At this point, we have established that the possible values of a are: -37, -20, -15 and -9.

The required sum is:

Sum = -37 -20 -15 - 9

Sum = -81

7 0
1 year ago
The sum of Orion and Sagan’s age is 24, and the difference between their ages is 6. Find their ages given that Orion is older th
Katarina [22]

Let's say that Sagan's age is x and Orion is x + 6 (since Sagan is younger by 6 years).


We know that Orion's age + Sagan's age is 24, so x + x + 6 is 24


2x = 18

x = 9


That means that Sagan is 9, and Orion is 9+6 or 15.

6 0
1 year ago
Cara has $25 to buy dry pet food and treats for the animal shelter. A pound of dog food cost $2 and treats are $1 apiece. If she
nordsb [41]
<span>If dog food costs $2 a pound and Cara buys 9 pounds, her expenditure on dog food is 9 x 2. This makes $18. If she has a total budget of $25 and spends $18 on dog food, she has $7 left over for treats (25 - 18 = 7). At $1 each, she can buy up to 7 treats.</span>
5 0
1 year ago
Plane A has just 1 ton of fuel left and has requested plane B to refuel it. Plane B has 21 tons of fuel. Fuel transfer happens a
garri49 [273]

Answer:

y = x + 1 y = -x + 21

(0, 1) (0, 21)

(1, 2) (1, 20)

(2, 3) (2, 19)

(3, 4) (3, 18)

Step-by-step explanation:

6 0
1 year ago
Read 2 more answers
Emma is 10 years old. she asked her father how old he is. her father answered, "when you are my age I will be 70." how old is Em
umka2103 [35]

Answer:

40

Step-by-step explanation:

Emma age: yE = 10 + x   (x is timeline)

Father age: yF = A + x (x is timeline, A is Father age today)

in time x1: Emma will be A years old, and Father will be 70 years old.

yE (x1) = 10 + x1 = A

yF (x1) = A + x1 = 70

System of equations with unknown values: x1 and A.

substract equation 1 - equation 2:

10 - A = A - 70 ⇒ 80 = 2A ⇒ A = 40

So, father is 40 years old now

8 0
1 year ago
Read 2 more answers
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