MATHEMATICS HIGH SCHOOL

If x and y are integers, and 3x + 2y = 13, which of the following could be the value of y ?A. 0
B. 1
C. 2
D. 3
E. 4

Answers

Answer 1
Answer: They are all integers so...
first lets substitute
A.3x=13
X=13/3
b.3x+2=13
3x=11
x=11/3
c.3x+4=13
3x=9
x=3
d.3x+6=13
3x=7
x=7/3

E.3x+8=13
3x=5
x=5/3

therefore the possible is letter c because it must be an integer and the definition of integer states that it is not a decimal nor a fraction
Answer 2
Answer: C. 2
Because
3x+2(2)=13
3x+4=13
3x=9
x=3

None of the other solutions work out so that both x and y are integers.

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Find the slope and equation of the tangent line to the graph of the function at the given value of x.f(x)=x^4-20x^2+64;x=-1

Answers

The slope is the differential of the function.

Recall, if y = x^n,  (dy/dx) =  nx^(n-1).

y=x^4-20x^2+64;  x = -1.  To differentiate this, we do it for each term.

(dy/dx) = (4)(x^(4 -1))  - (2)(20x^(2-1) + 0*64x^(0-1)        (Note 64 = 64x^0, x^0 =1)
           =  (4)x^(3) - 40x^(1)  + 0
            =    4x^3  -  40x^1. 

(dy/dx)  =    4x^3  -  40x.   Note at x = -1.


(dy/dx), x = -1,   =     4(-1)^3  -  40(-1)                         
                         =    -4 +  40  = 40 - 4 = 36.

Slope at x = -1 is 36.
Cheers.

Paulo uses an instrument called a densitometer to check that he has the correct ink colour.For this print job the acceptable range for the reading on the densitometer is 1.8 ± 10%.

What is the acceptable range for the densitometer reading?


exactly 1.8

from 0 to 3.6

from 1.0 to 2.6

from 1.62 to 1.98

from 1.8 to 1.98

Answers

If it is said that the range of the answer should be +/- 10% of the particular value, we have to find out the percentage of that particular value. Therefore 10% of 1.8 is,

1.8 * 10/100 = 0.18

If we add this value to the original value,
1.8+0.18 = 1.98

If we subtract this value from the original value,
1.8-0.18 = 1.62

therefore the range will be,
from 1.62 to 1.98

Solve each equation by finding all roots x^4-16=0

Answers

{ x }^( 4 )-16=0\n \n { x }^( 4 )=16\n \n x=\pm \sqrt [ 4 ]{ 16 } \n \n \therefore \quad x=\pm 2
add both sides by 16
so you'll have x^4 =16
take the 4th root of both sides and you'll get x=  2

Pizzas come in 4 different sizes, each with or without a choice of 4 toppings. How many ways are there to order a pizza?the answer is not 20 or 48

Answers

16 different ways you multiply 4 by 4

A customer buys five cans of baked beans, four packets of brown sugar and two packets of biscuits from a supermarket.He gives the cashier R150.00 and gets R26.00 in change. A can of baked beans costs half as much as a packet of biscuits whilst a packet of sugar is R3.00 cheaper than a packet of biscuits.1.How much did all the items cost?
2.Calculate the cost of a can of baked beans, a packet of sugar and a packet of biscuits.
3.How much will 8 cans of baked beans,1 packet of sugar and 6 packets of biscuits cost?

Answers

can of baked beans = x 
packet of brown sugar = y
packet of biscuit = z

5x + 4y + 2z = 150 - 26 ⇒ 5x + 4y + 2z = 124 is the total cost of all items.

can of baked beans = x = 1/2 of z
packet of sugar = y = z - 3

5(z/2) + 4(z-3) + 2z = 124
5z/2 + 4z - 12 + 2z = 124
5z/2 + 6z = 124 + 12
2(5z/2 + 6z) = 2(136)
5z + 12z = 272
17z = 272
z = 16 cost of a packet of biscuit.

x = 1/2 of z = 16/2 = 8 cost of a can of baked beans
y = z - 3 = 16 - 3 = 13 cost of a packet of sugar

5x + 4y + 2z = 124
5(8) + 4(13) + 2(16) = 124
40 + 52 + 32 = 124
124 = 124

8(8) + 1(13) + 6(16) = 64 + 13 + 96 = 173 total cost on question 3.

Shanna attends school for 1 week longer than 3/4 of the year. How many weeks in a year dies Shanna attend school ?

Answers

Answer:

40 weeks

Step-by-step explanation:

We must find the relationship between weeks and years. Given that 52 weeks make a year, it means that 3/4 of the year would be equivalent to

= 3/4 * 52 weeks

= 39 weeks

Since we know that Shanna attends school for 1 week longer than 3/4 of the year, it means she added school for 1 week more than 39 weeks. The number of weeks she attended school is thus

= 39 +1

= 40 weeks
3/4 of a year consist of three months per quarter

so 3/4 of a year is 9 months

each month have 4 weeks

multiply 9x4 to get 36, which is the number of weks there is in 3/4 of a year 
now add one week since Shanna attended one week longer 

and now you get 37 weeks Shanna attended school
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