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Answer:

x = [tex]\frac{3}{20}[/tex]

Step-by-step explanation:

Given

x + [tex]\frac{3}{2}[/tex] + (x - 1) = [tex]\frac{4}{5}[/tex]

Multiply through by 10 ( the LCM of 2 and 5 ) to clear the fractions

10x + 15 + 10(x - 1) = 8

10x + 15 + 10x - 10 = 8

20x + 5 = 8 ( subtract 5 from both sides )

20x = 3 ( divide both sides by 20 )

x = [tex]\frac{3}{20}[/tex]

x + 3/2 + x - 1 = 4/5

Collect the same terms

x + x + 3/2 - 1 = 4/5

2x + 3/2 - 2/2 = 4/5

2x + (3 - 2)/2 = 4/5

2x + 1/2 = 4/5

2x + 0.5 = 0.8

Subtract both sides 0.5

2x + 0.5 - 0.5 = 0.8 - 0.5

2x + 0 = 0.3

2x = 3/10

Divide both sides by 2

2x ÷ 2 = ( 3/10 ) ÷ 2

x = 3/10 × 1/2

x = 3/20

_________________________________

3/20 + 3/2 + ( 3/20 - 1 ) = 4/5

3/20 + 30/20 + ( 3/20 - 20/20 ) = 4/5

(3 + 30)/20 + (3 - 20)/20 = 4/5

33/20 - 17/20 = 4/5

(33 - 17)/20 = 4/5

16/20 = 4/5

4 × 4 / 4 × 5 = 4/5

4/5 = 4/5

Thus we found the correct value of x .

And we're done...

Answer:

A

Step-by-step explanation:

Parallel lines have the same gradient

For line y=-4x-1, the gradient is -4 and so that of this new line will also be -4

Now,

y-y1=m(x-x1)

y-2=-4(x-2)

y-2=-4x+8

y=-4x+8+2

y=-4x+10

Answer:

x ≈ 28.8°

Step-by-step explanation:

Using the sine ratio in the right triangle

sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{3.9}{8.1}[/tex] , then

x = [tex]sin^{-1}[/tex] ([tex]\frac{3.9}{8.1}[/tex] ) ≈ 28.8° ( to the nearest tenth )

Answer:

x = -4

Step-by-step explanation:

Plug in -4 into the function and solve for x:

f(x) = 6x + 20

-4 = 6x + 20

-24 = 6x

-4 = x

So, the answer is x = -4

Answer:

The one of (L,b)= (5m, 10m) is the only correct answer.

Step-by-step explanation:

P= 2(L+b)

A= L×b

make b subject of formula in area we have;

b= A/L

in perimeter; p= 2(L +(A/L))

p= (L²+A)/L

pL= L²+A

L²-pL+A= 0

L²-30L+50=0

L²-25L-5L+50=0

L(L-25)-5(L-25)=0

(L-5)(L-25)= 0

L= 5 or 25m

substitute in A

50= 5b or 50= 25b

b= 10 or 2m

Answer:

$2,400

Step-by-step explanation:

Note: The correct years is 4 not 44

The Principal  = $10,000

Time period = 4 years

Rate = 6 % p.a.

Simple Interest = Principal * Rate * Time

Simple Interest = $10,000 * 6% * 44

Simple Interest = $2,400

So, the amount of interest Diego earned after four years is $2,400

Answer:

[tex]given\Longrightarrow AB=AC[/tex]

[tex]\angle \;C=\angle \:B=60\ [isosceles ~triangle][/tex]

[tex]\angle~A+\angle~B+\angle~C=180[/tex]

[tex]x+60+60=180[/tex]

[tex]x+120=180[/tex]

[tex]x=180-120[/tex]

[tex]x=60[/tex]

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HOPE IT HELPS

HAVE A GREAT DAY!!

Answer:

32

Step-by-step explanation:

I'm very confirm with my answer mark me as brainliest plsssss

[tex]\bold{\frac{5}{13} or 0.38}[/tex]

Answer:

Solution given:

here

by using Pythagoras law

hypotenuse =

[tex]\displaystyle\sqrt{adjacent ²+opposite ²}\\=\sqrt{15²+36²}=39[/tex]

Cos C=[tex]\frac{adjacent} {hypotenuse}=\frac{15}{39}=\frac{5}{13} or{0.38}[/tex]

Answer:

D = 51, other = 30

Step-by-step explanation:

d = | 5  1 |

     |-1  10|

D = (5 x 10) - ( 1 x -1) = 50 + 1 = 51

| 2   4|

|-3   9|

(2 x 9) - (4 x -3) = 18 + 12 = 30

Answer two 20p coins make 40p

Step-by-step explanation:

Answer:

20 number of 20p makes £4.

Step-by-step explanation:

Let the number of 20p be x

Therefore,

                [tex]x \times 0.20 = 4\\\\x = \frac{4}{0.20} = \frac{4 \times 100}{ 20} = 4 \times 5 = 20[/tex]

Answer:

Answer: The b-value is the middle number, the number next to the X

Answer:

x^4+4x^3+6x^2+7x+2

Answer:

[tex]f^{-1}[/tex] (x) = [tex]\frac{5x}{x-2}[/tex]

Step-by-step explanation:

let y = f(x) and rearrange making x the subject

y = [tex]\frac{2x}{x-5}[/tex] ( multiply both sides by x - 5 )

y(x - 5) = 2x ← distribute left side

xy - 5y = 2x ( subtract 2x from both sides )

xy - 2x - 5y = 0 ( add 5y to both sides )

xy - 2x = 5y ← factor out x from each term on the left side )

x(y - 2) - 5y ← divide both sides by y - 2

x = [tex]\frac{5y}{y-2}[/tex]

Change y back into terms of x with x = [tex]f^{-1}[/tex] (x) , then

[tex]f^{-1}[/tex] (x) = [tex]\frac{5x}{x-2}[/tex]

Look into the image. I hope it helps❤

Answer:

1.3 meters

Step-by-step explanation:

The question is: What is the position of Michael's hands relative to the surface of the water?

It seems like it is asking for the amount of space between Michael's hands, and the surface of the water.

His hands are 1.8 meters below his feet, and his feet are 0.5 meters above the water.

To solve: subtract

1.8-0.5

1.3

I hope this helps!

Hello,

Answer D

[tex]\begin{array}{|c|c|}x&y\\--&-------------\\-1&-3*\sqrt{-1+1} =-3*0=0\\0&-3*\sqrt{0+1} =-3*1=-3\\3&-3*\sqrt{3+1} =-3*2=-6\\8&-3*\sqrt{8+1} =-3*3=-9\\15&-3*\sqrt{15+1} =-3*4=-12\\--&-------------\\\end{array}[/tex]

Answer:

4.8 miles per hour.

Step-by-step explanation:

Average speed=Total distance/Time taken

=26.2miles/5.5hour

=4.8 miles per hour

ᴀɴsᴡᴇʀ:

1.Example, x²-25 can be factored as (x+5)(x-5).

2.This method is based on the pattern (a+b)(a-b)=a²-b², which can be verified by expanding the parentheses in (a+b)(a-b).

3.When an expression can be viewed as the difference of two perfect squares, i.e. a²-b², then we can factor it as (a+b)(a-b). For example, x²-25 can be factored as (x+5)(x-5).

ʜᴏᴘᴇ ɪᴛ ʜᴇʟᴘs!

☞︎︎︎ᴄᴀʀʀʏ ᴏɴ ʟᴇᴀʀɴɪɴɢ☜︎︎︎

Answer:

60

Step-by-step explanation:

180-100 = 80

80-20 = 60

Answer:

14

Step-by-step explanation:

[tex]f(x) = {x}^{2} + 10 \\ \therefore \: f(2) = {2}^{2} + 10 \\ \therefore \: f(2) = 4 + 10 \\ \therefore \: f(2) = 14 \\ \\ g(x) = |x| \\ \therefore \:g(2) = |2| \\ \therefore \:g(2) = 2 \\ \\ f(2) + g(2) = 14 + 2 \\ \red{ \bold{(f + g)(2) = 14}}[/tex]

Step by step Explanation:

[tex]f(x) = x2 + 10g(x) = 1[/tex]

[tex](f + g)(2).[/tex]

Step 1

The equation is in standard form.

Step 2

Divide both sides by x.

Step 3

Dividing by x undoes the multiplication by x.

Step 4

Divide x 2 + 10 g x by x.

My Answer is.

Answer:

a) 120°

Step-by-step explanation:

i think this is the right answer

Answer:

3 by 2

Step-by-step explanation:

3+2+3+2=10

3*2=6

Hope this Helps!!!

Answer:

A.

Step-by-step explanation:

C and D do not create any x² terms when doing the multiplications. so, they are out.

B stands for (a+b)×(a-b) = a² - b².

so, that would give us a "-4" at the end and is not fitting to the "+4" term at the end of the original expression.

that leaves us with A.

let's verify :

(4x+2i)(4x-2i)

it follows the same rule as B :

(a+b)(a-b) = a² - b²

a = 4x

b = 2i

you remember, i = sqrt(-1).

so, we get

(4x)² - (2i)² = 16x² - 4×(sqrt(-1))² = 16x² - 4×(-1) = 16x²+4

bingo !

Answer:

Step-by-step explanation:

the answer is A

Given:

For two events X and Y,

[tex]P(X)=\dfrac{2}{3}[/tex]

[tex]P(Y)=\dfrac{2}{5}[/tex]

[tex]P(X|Y)=\dfrac{1}{5}[/tex]

To find:

The probabilities [tex]P(Y\cap X), P(Y)\cdot P(X)[/tex].

Solution:

Using the conditional probability:

[tex]P(X|Y)=\dfrac{P(Y\cap X)}{P(Y)}[/tex]

[tex]P(X|Y)\times P(Y)=P(Y\cap X)[/tex]

Substituting the given values, we get

[tex]\dfrac{1}{5}\times \dfrac{2}{5}=P(Y\cap X)[/tex]

[tex]\dfrac{2}{25}=P(Y\cap X)[/tex]

And,

[tex]P(Y)\times P(X)=\dfrac{2}{5}\times \dfrac{2}{3}[/tex]

[tex]P(Y)\times P(X)=\dfrac{4}{15}[/tex]

Therefore, the required probabilities are [tex]P(Y\cap X)=\dfrac{2}{25}[/tex] and [tex]P(Y)\times P(X)=\dfrac{4}{15}[/tex].

Answer:

Cost of 1 pound tea is $ 9.2.

Cost of 1 pound coffee is $ 10.3.

Step-by-step explanation:

Let the cost of tea is $ per pound and cost of coffee is $ q per pound.

4 p + 5 q = 88.30 .... (1)

9 p + 6 q = 144.60 ....(2)

Solving (1) and (2) we get

p = $ 9.2

q = $ 10.3

Answer:

18 seconds

Step-by-step explanation:

5x9=45 so 2x9=18