All categories

2 years ago

If (3+√5)(4-√5)=a+b√5, where a and b are integers, then what is the value of a + b?

Mathematics

1 answer:

defon2 years ago

4 0

54 = 2 x 3³
So, if a and b are integers, a=2 and b=3

You might be interested in

For what value(s) of k will the relation not be a function

skelet666 [1.2K]

We are given two relations

(a)

Relation (R)

$R=[((k-8.3+2.4k),-5),(-\frac{3}{4}k,4)]$

We know that

any relation can not be function when their inputs are same

so, we can set both x-values equal

and then we can solve for k

$k-8.3+2.4k=-\frac{3}{4} k$

$3.4k-8.3=-\frac{3}{4}k$

$3.4k\cdot \:10-8.3\cdot \:10=-\frac{3}{4}k\cdot \:10$

$4k-83=-\frac{15}{2}k$

$34k=-\frac{15}{2}k+83$

$\frac{83}{2}k=83$

$83k=166$

$k=2$ ............Answer

(b)

S = {(2−|k+1| , 4), (−6, 7)}

We know that

any relation can not be function when their inputs are same

so, we can set both x-values equal

and then we can solve for k

$2-|k+1|=-6$

$2-\left|k+1\right|-2=-6-2$

$-\left|k+1\right|=-8$

$\left|k+1\right|=8$

Since, this is absolute function

so, we can break it into two parts

$|f\left(k\right)|=a\quad \Rightarrow \:f\left(k\right)=-a\quad \mathrm{or}\quad \:f\left(k\right)=a$

$k+1=-8\quad \quad \mathrm{or}\quad \:\quad \:k+1=8$

we get

$k+1=-8\quad$

$k=-9$

$k+1=8\quad$

$k=7$

so,

$k=-9\quad \mathrm{or}\quad \:k=7$ ...............Answer

5 0

3 years ago

A motor is 85.4 % efficient: that is, the output is 85.4 % of the input. What is the input if the motor delivers 10.75 hp. ( Rou

Ludmilka [50]

Answer:

12.6 hp

Step-by-step explanation:

Represent the input by n. 10.75 hp

Then 0.85n = 10.75 hp, and n (the input) is --------------- = 12.6 hp

0.85

5 0

3 years ago

F(x) = -x² – 10x + 16<br> Find f(-7)

Gala2k [10]

Answer:

-5

Step-by-step explanation:

or, f(x) = -x^2+10x+16

or, f(7) = (-7)^2+10*-7+16 (-7*-7=49)

=49-70+16

=65-70

=-5

5 0

3 years ago

Please help me with 10-12 +BONUS

dedylja [7]

Hi!

10.

This question is basically asking you, 10 is 40% of what number?

10 × 100 / 40 = 25

Fred must do 25 math problems.

12.

Bed & Bath = 40%

Clothing = 0.625 = 62.5%

Appliances = 20%

Electronics = 0.25 = 25%

Least to Greatest: Appliances (20%), Electronics (25%), Bed & Bath (40%), Clothing (62.5%).

4 0

3 years ago

Which is smaller,two-thirds of 27 or two-fifths of 20?

shtirl [24]

" of " means multiply

2/3(27) = 54/3 = 18
2/5(20) = 40/5 = 8

so 2/5 of 20 is smaller

7 0

3 years ago