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natka813 [3]
3 years ago
13

Find a and b given f(x) = ax + b, f(1) = 7, and f(3) = -5.

Mathematics
1 answer:
sergejj [24]3 years ago
3 0

Answer:

a = - 6, b = 13

Step-by-step explanation:

Given f(1) = 7 , that is f(x) = 7 when x = 1

f(3) = - 5 , that is f(x) = - 5 when x = 3

Substitute these values into f(x) = ax + b

a + b = 7 → (1)

3a + b = - 5 → (2)

Subtract (1) from (2) term by term to eliminate b

(3a - a) + (b - b) = - 5 - 7

2a = - 12 ( divide both sides by 2 )

a = - 6

Substitute a = - 6 into either of the 2 equations and solve for b

Substituting into (1)

- 6 + b = 7 ( add 6 to both sides )

b = 13

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There are 15 candidates for 4 job positions.
Veronika [31]

Answer:

32760 ways

Step-by-step explanation:

Given

Number of Candidates = 15

Job Positions = 4

Required:

Number of outcomes

This question represent selection; i.e. selecting candidates for job positions;

This question can be solved in any of the following two ways

Method 1.

The first candidate can be chosen from any of the 15 candidates

The second candidate can be chosen from any of the remaining 14 candidates

The third candidate can be chosen from any of the remaining 13 candidates

The fourth candidate can be chosen from any of the remaining 12 candidates

Total Possible Selection = 15 * 14 * 13 * 12

<em>Total Possible Selection = 32760 ways</em>

<em></em>

Method 2:

This can be solved using permutation method which goes thus;

nPr = \frac{n!}{(n-r)!}

Where n = 15 and r = 4

So;

nPr = \frac{n!}{(n-r)!} becomes

15P4 = \frac{15!}{(15-4)!}

15P4 = \frac{15!}{11!}

15P4 = \frac{15*14*13*12*11!}{11!}

15P4 = 15*14*13*12

15C4 = 32760

<em>Hence, there are 32760 ways</em>

8 0
3 years ago
A professora Luísa observou que o numero de meninas de turma dividido pelo numero de meninos dessa turma e 0,48. Qual e o menor
saw5 [17]

Respuesta:

37 estudiantes

Explicación paso a paso:

El número de niños dividido por el número de niñas = 0,48

Dejar :

x = número de niños; y = número de niñas

Tenemos ;

x / y = 0,48

Conversión a decimal;

0.48 es equivalente a 48/100

Reduciendo a la forma más simple:

48/100 = 12/25

Comparando:

x / y = 12/25

x = 12; y = 25

El menor número posible de estudiantes:

x + y = 12 + 25 = 37 estudiantes

5 0
2 years ago
Employees at a clothing store recieve 20% discounts on what they purchase at that store. How much will an employer save on a $45
mamaluj [8]
Easiest way to work it out is to divide by ten, that gives 10% of your original number. Multiply that by two to get 20% and minus that from the original number to get the discount.
450/10 = 45 which is 10% of 450.
20% of 450= 10% x 2 or 45 x 2
therefor 20% of 450 is 90.
450-90 = the discount the shoppers recieve.

4 0
3 years ago
Every positive number has two square roots , a principal square root and its _____?
lukranit [14]
Definition: <span>The square root of a number is another number, which on multiplying with itself, will give the original number.
</span>
Every positive number has two square roots. One square root is positive, while the other is exactly same, but negative. The positive square root of a number is called its principle square root. For example, 10 and -10 are the two square roots of 100, but 10 is called the principle square root. 

Hence e<span>very positive number has two square roots , a principal square root and its opposite negative.</span>
<span />


3 0
3 years ago
Read 2 more answers
Brianna bought snacks for her team's practice. She bought a bag of oranges for $2.72 and a 20-pack of juice bottles. The total c
posledela

Answer:

each bottle was $2.12 :P

Step-by-step explanation:

➼start by making an equation to find the price of the juice pack, in this case x would be the price of the juice pack because its unknown, the juice pack price(x) added to the price of the oranges(2.72) and equal the total(45.12), the before tax part is not needed info

2.72 + x = 45.12

➼now our aim to get x alone to find out its worth so we will have to do the opposite and subtract 2.72 from everything, since its positive

2.72-2.72=0 crosses out

45.12-2.72=42.4

➼which gets us x = 42.4 so one 20 pack is 42.40 dollars but we arent done yet, to find out the price of EACH bottle we must divide 42.4 by 20!

42.4/20=2.12

➼so to sum it up, each bottle is $2.12 :)

4 0
3 years ago
Read 2 more answers
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