Mathematics, 15.10.2019 07:30 dinaukiq

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1) 7/8 + 2/5 = ? (simplest form)
2) 2 1/3 * 1/4 = ? (simplest form)
3) divide £72 in the ratio 2: 3: 1
4) 39/65 people in a book club have blonde hair what percentage does not have blond hair?
5) 20% of 90 = ?
6) factorise: 2x^2 + 18x^3
7) expand: (y - 8)(y - 6)
8) factorise: x^2 + 4x + 3
9) evaluate: y^0
10) 0.0342 in standard form
11) if x = -4 and y = 3 find z, when z = 4x - y^3
12) 'x' the subject of: y + 2x = x - 2
13) solve: 8 - 7x = 22
14) find nth term of the following: 5, 10, 15,
15) estimate (63128) / 32.9
16) 938 21 = ?

Answers: 3

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Answers

Answer from: whocares1234

1) $\frac{7}{8}+\frac{2}{5}=\frac{7\times5+2\times8}{40}=\frac{35+16}{40}=\frac{51}{40}$ .

2) $2\frac{1}{3}\times \frac{1}{4}=\frac{7}{3}\times\frac{1}{4}=\frac{7}{12}$

hence, answer is 7/12.

3) We have to divide £72 in the ratio 2:3:1

the total of the ratio is=2+3+1=6

so on dividing 72 into 6 parts we have 72/6=12

First '2' parts=2×12=24

second '3' part=3×12=36

last '1' part=1×12=12

so dividing £72 in the ratio 2:3:1 is: £24,£36 and £12

4) 39 people out of 65 have blonde hair.

Number of people who do not have blonde hair=65-39=26

percentage people who do not have blonde hair is given by:

$=\frac{26}{65}\times100\\ \\=40%$

Hence, percentage people who do not have blonde hair is 40%

5) 20% of 90= (20/100)×90

=18

Hence, 20% of 90 is 18.

6) Factorise

$2x^2+18x^3=2x^2(1+9x)\\\\2x^2+18x^3=18x^2(x+\frac{1}{9})$

7) Expand

$(y-8)(y-6)=y(y-8)-6(y-8)=y^2-8y-6y+48\\\\(y-8)(y-6)=y^2-14y+48$

x^2+4x+3=x^2+x+3x+3=x(x+1)+3(x+1)=(x+3)(x+1) .

$y^{0}=1$

10)

$0.0342=3.42\times10^{-2}$

11) x= -4 y=3

and z=4 x-y^3

z=4×(-4)-3^3

z= -43

12) $y+2x=x-2\\\\2x-x=-y-2\\\\x=-y-2$

13) $8-7x=22\\\\7x=8-22\\\\7x=-14\\\\x=-2$

Hence x= -2

14) 5,10,15,20,.... $a_{1}=5=5\times1 , a_{2}=10=5\times2 , a_{3}=15=5\times3,........,a_{n}=5n=5\timesn$

Hence, nth term is 5n.

15) (63×128)/32.9=245.106.

16) 938×21=19698.

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is