Which expression is equivalent to 10i/2-i

Answer:

-320000

Step-by-step explanation:

Given

Lost Land = 80,000 acres yearly

Duration 4 years

Required

The total change

Represent the total change with y;

y is calculated as thus;

[tex]y = Lost\ Land * Duration[/tex]

[tex]y = -80,000 acres * 4[/tex]

[tex]y = -320000\ acres[/tex]

Hence, a total of 320000 acres were lost during the period

Answer:

53°, 127°, 127°

Step-by-step explanation:

Two intersecting lines form two pairs of angles:

So if one of the angles is measured 53°, then the other angles are:

Answer:

z = -5

y = 1

x = 4

Step-by-step explanation:

2z = -10 ➡ z = -5

4y -(-5) = 9 ➡ 4y = 4 and y = 1

2x + 3 + (-5) = 6 ➡ 2x = 8 and x = 4

Answer:

X = 6

Step-by-step explanation:

Subtract 1 x from both sides so the equation will be 3x = 18.  Then divide 3x by 3 and 18 by 3 to get 6

Answer: [tex]x=6[/tex]

Subtract x from both sides

[tex]4x-x=x+18-x\\3x=18[/tex]

Divide both sides by 3

[tex]3x=3=18/3\\x=6[/tex]

Answer: The digit in the thousand place is '9'.

Step-by-step explanation: The given number is 5_278.

The difference between the values of the digits in the thousandth place and the tenth place is 8930.

The digits in the tenth place is already given, which is 7

Let's assume the digits in the thousandth place is x,

Answer:

[tex]=\left(\frac{15}{2},\:\frac{5}{2}\right)[/tex]

Step-by-step explanation:

[tex]\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)\\\\\left(x_1,\:y_1\right)=\left(6,\:4\right),\:\left(x_2,\:y_2\right)=\left(9,\:1\right)\\\\=\left(\frac{9+6}{2},\:\frac{1+4}{2}\right)\\\\=(\frac{15}{2} , \frac{5}{2} )\\\\[/tex]

Answer:

Step-by-step explanation:

Given the vectors based on the number line as RS = 7y +3, ST = 5y +8, and RT = 83, the equation RS+ST = RT will be used to get the unknown.

Substituting the given equation into the expression we will have;

7y +3+5y +8 = 83

collect like terms'

7y+5y+3+8 = 83

12y + 11 = 83

12y = 83-11

12y = 72

y = 72/12

y = 6

b) Substitute y = 6 into RS and ST

Given RS = 7y+3

RS = 7(6)+3

RS = 42+3

RS = 45

For ST;

ST = 5y+8

ST = 5(6)+8

ST = 30+8

ST = 38

Answer:

0 Is Integer ,

rational and a

whole number.

Hope it helps.

Answer:

x=23, y=14

Step-by-step explanation:

The triangles are indeed simular

1. Find the cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of ₹ 3 per m².

a = 51 m, b = 37 m, c = 20 m

semiperimeter:  p = (51+37+20):2 = 54 m

Area of triangle:

[tex]A=\sqrt{p(p-a)(p-b)(p-c)}\\\\A=\sqrt{54(54-51)(54-37)(54-20)}\\\\A=\sqrt{54\cdot3\cdot17\cdot34}\\\\A=\sqrt{9\cdot2\cdot3\cdot3\cdot17\cdot17\cdot2}\\\\A=3\cdot2\cdot3\cdot17\\\\A=306\,m^2[/tex]

Rate:  ₹ 3 per m².

Cost:  ₹ 3•306 = ₹ 918

2. Find the area of the isosceles triangle whose perimeter is 11 cm and the base is 5 cm.

a = 5 cm

a+2b = 11 cm  ⇒  2b = 6 cm   ⇒  b = 3 cm

p = 11:2 = 5.5

[tex]A=\sqrt{5.5(5.5-3)^2(5.5-5)}\\\\ A=\sqrt{5.5\cdot(2.5)^2\cdot0.5}\\\\ A=\sqrt{11\cdot0.5\cdot(2.5)^2\cdot0.5}\\\\A=0.5\cdot2.5\cdot\sqrt{11}\\\\A=1.25\sqrt{11}\,cm^2\approx4.146\,cm^2[/tex]

3. Find the area of the equilateral triangle whose each side is 8 cm.

a = b = c = 8 cm

p = (8•3):2 = 12 cm

[tex]A=\sqrt{12(12-8)^3}\\\\ A=\sqrt{12\cdot4^3}\\\\ A=\sqrt{3\cdot4\cdot4\cdot4^2}\\\\A=4\cdot4\cdot\sqrt{3}\\\\A=16\sqrt3\ cm^2\approx27.713\ cm^2[/tex]

4. The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.

a = 2x

b = 3x

2x + 2•3x = 32 cm  ⇒ 8x = 32 cm   ⇒  x = 4 cm  ⇒ a = 8 cm, b = 12 cm

p = 32:2 = 16 cm

[tex]A=\sqrt{16(16-8)(16-12)^2}\\\\ A=\sqrt{16\cdot8\cdot4^2}\\\\ A=\sqrt{2\cdot8\cdot8\cdot4^2}\\\\ A=8\cdot4\cdot\sqrt2\\\\ A=32\sqrt2\ cm^2\approx45.2548\ cm^2[/tex]

Answer:

9x - 24 ÷ 6

Step-by-step explanation:

Quotient means that one number will be divided by another, so the division sign will be involved in the expression.

9 times x minus 24 translates to 9x - 24.

Now, put it all together.

9x - 24 ÷ 6 will be the expression.

Hope that helps.

==============================================

Work Shown:

F = future value

P = present value = 280

r = rate of inflation in decimal form = 0.08

t = elapsed time in years = 2

---------

F = P*(1+r)^t

F = 280*(1+0.08)^2

F = 326.592

F = 326.59

Answer:

The eight in the first number is ten times larger than the eight in the second number.

Answer:

The equation that represents the perimeter of the rectangle is:

[tex]\text{Perimeter} = \frac{2}{3} \times [4l-27][/tex]

Step-by-step explanation:

The perimeter of a rectangle is given by the formula:

Perimeter = 2 × [l + w]

It is provided that the width of a rectangle is 9 less than one-third it's length.

That is:

[tex]w = \frac{1}{3}l-9[/tex]

The perimeter is given as 45.

The equation that represents the perimeter of the rectangle is:

[tex]\text{Perimeter} = 2 \times [l + \frac{1}{3}l-9]\\\\\text{Perimeter} = 2 \times [\frac{3l+l-27}{3}]\\\\\text{Perimeter} = 2 \times [\frac{4l-27}{3}]\\\\\text{Perimeter} = \frac{2}{3} \times [4l-27][/tex]

Thus, the equation that represents the perimeter of the rectangle is:

[tex]\text{Perimeter} = \frac{2}{3} \times [4l-27][/tex]

Answer:

AB = 38.6metres

Step-by-step explanation:

Given the right angled triangle ABC with hypotenuse AB and ∠CAB to be 75°, the opposite side of the triangle will be the side facing the angle ∠CAB directly and this is side BC. The adjacent side of the triangle will be side CA.

To get the length of the hypotenuse AB, we will use the trigonometry identity SOH, CAH, TOA.

According to CAH;

Cos∠CAB = adjacent/hypotenuse = CA/AB

Substituting CA = 10 metres and ∠CAB = 75° into the equation;

Cos75° = 10/AB

AB = 10/cos75°

AB = 10/0.2588

AB = 38.6metres

Hence the length of the hypotenuse AB is 38.6metres.

Answer:

38.6 m

Step-by-step explanation:

Answer:

m = slope= 5/3

Step-by-step explanation:

[tex](-6, -2) = (x_1,y_1) \\ (-1.5, 5.5) (x_2 ,y_2) \\ \frac{y - y_1}{x - x_1} = \frac{y_2 - y_1}{x_2 -x _1} [/tex]

[tex] \frac{y - ( - 2)}{x - ( - 6)} = \frac{5.5 - ( -2 )}{ - 1.5 - ( - 6)} \\ \frac{y + 2}{x + 6} = \frac{5.5 + 2}{ - 1.5 + 6} [/tex]

[tex] \frac{y + 2}{x + 6} = \frac{7.5}{4.5} \\ 4.5(y + 2) = 7.5(x + 6)[/tex]

[tex]4.5y + 9 = 7.5x + 45 \\ 4.5y = 7.5x + 45 - 9 \\ 4.5y = 7.5x + 36[/tex]

Divide through by 4.5

[tex] \frac{4.5y}{4.5} = \frac{7.5x}{4.5} + \frac{36}{4.5} \\ y = \frac{5}{3} x + 8 \\ [/tex]

Answer:

The inequality is

88<x<93

Step-by-step explanation:

The average of Shondra's test scores in physics is between 88 and 93.

Let me give out the meaning of some inequality symbols

<= Less than or equal to

>= Greater than or equal to

< Less than

> Greater than

Let the average score be x

In this case , the average score is between 88 and 93

The inequality is

88<x<93

Answer:

x = 0

y = 3

Step-by-step explanation:

Step 1: Write systems of equations

9x - 2y = -6

5x + 4y = 12

Step 2: Rewrite 1st equation

9x = 2y - 6

x = 2/9y - 2/3

Step 3: Substitute

5(2/9y - 2/3) + 4y = 12

Step 4: Solve for y

10/9y - 10/3 + 4y = 12

46/9y - 10/3 = 12

46/9y = 46/3

y = 3

Step 5: Plug in y to find x

5x + 4(3) = 12

5x + 12 = 12

5x = 0

x = 0

Answer:

what's the question though ?

Answer:

Linear

Step-by-step explanation:

Answer:

the answer is Linear

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

We can create a ratio of the amount of students who picked green over the total amount of students.

9 students picked the green pattern, and a total of 50 students were surveyed. This means the ratio is [tex]\frac{9}{50}[/tex].

To turn [tex]\frac{9}{50}[/tex] into a percentage, we must divide it's numerator by it's denominator and multiply by 100.

[tex]8\div50=0.18\\\\0.18\cdot100=18[/tex]

So the green bar's height will be 18.

Hope this helped!

Answer:

don't give up try and you will find the answers

Answer:

Lulu's money = £81

Ruby's money= £108

Emma's money= £72

Step-by-step explanation:

Let

Lulu's money = x

Ruby's money= y

Emma's money= z

x+y+z= 261

Lulu spent 2/3 of her money Ruby spent 1/2 of her money and Emma spent 3/4 of her money.

2/3x = 1/2y= 3/4z

2/3x= 1/2y

4/3x= y

2/3x= 3/4z

8/9x= z

x+y+z= 261

x+4/3x+8/9x= 261

9x+12x+8x= 2349

29x= 2349

X= 81

4/3x= y

4/3(81) =y

108= y

8/9x= z

8/9(81)= z

72= z

Answer:

Step-by-step explanation:

Each of them had different amount of money. Lulu spent 2/3 of her money Ruby spent 1/2 of her money and Emma spent 3/4 of her money.

1 answer

·

Top answer:

Answer:Lulu= £81Ruby=£108Emma=£ 72

Answer:

$1.50 per card

Step-by-step explanation:

Knowns:

$10 to spends, Wants to buy $7 book and two equal priced cards.

10 = 7 + 2x

Subtract 7 from both sides to find out how much money Dave has after he buys his book.

3 = 2x

Divide each side by 2 to find out how much he cana spend on each card

x = 1.50

i hope this helps!

-TheBusinessMan

Answer:

6:1

Step-by-step explanation:

48:( 4+4 )

= 48:8

= 6:1

Answer:

(−∞,−7/2)∪(−7/2,3)∪(3,∞)

Step-by-step explanation:

(x-3)

----------------

2x^2 +x -21

First factor the denominator

(x-3)

----------------

( 2x +7) (x-3)

The domain is restricted when the denominator goes to zero

2x+7 =0    x-3 =0

2x = -7     x-3=0

x = -7/2    x =3

This two points are not in the domain

(−∞,−7/2)∪(−7/2,3)∪(3,∞)

Answer:

the answer is 28

Step-by-step explanation:

This is simple

if 5 people need 2 gallons we can use that to figure out how many gallons 75 people need.

75 divided by 5 is 15. so if 5 fits into 75 15 times that means that 75 people need 15 times 2 gallons or 30 gallons of fruit punch.

But the problem ask how much "additional" fruit punch so we subtract 2 from 30 to get 28 additional gallons of fruit punch

Answer:If an N-gon (polygon with N sides) has perimeter P, then each of the  

N sides has length P/N.  If we connect two adjacent vertices to the  

center, the angle between these two lines is 360/N degrees, or 2*pi/N  

radians.  (Do you understand radian measure well enough to follow me  

this far?)

The two lines I just drew, plus the side of the polygon between them,  

form an isosceles triangle.  Adding the altitude of the isosceles  

triangle makes two right triangles, and we can use one of them to  

derive the equation

 sin(theta/2) =  s/(2R)

where theta is the apex angle (which I said is 2*pi/N radians), R is  

the length of the lines to the center (the radius of the circumscribed  

circle), and s is the length of the side (which I said is P/N).

Putting those values into the equation, we have

 sin(pi/N) = P/(2NR)

so that

 P = 2NR sin(pi/N)

gives the perimeter of the N-gon with circumradius R.

Can we see a connection between this formula and the perimeter of a  

circle?  The perimeter of the circumcircle is 2*pi*R.  As we increase  

N, the perimeter of the polygon should get closer and closer to this  

value.  Comparing the two, we see

 2NR*sin(pi/N) approaches 2*pi*R

 N*sin(pi/N)   approaches pi

You can check this out with a calculator, using big numbers for N such  

as your teacher's N=1000.  If you calculate the sine of an angle in  

degrees rather than radians, the formula will look like

 N*sin(180/N) --> pi

Step-by-step explanation:

Answer:

Midpoint is (-6,-34)

Step-by-step explanation:

(6+(-18))/2. (-41+(-27))/2

-12/2. (-68)/2

-6. , - 34

Distance =(6--18)^2 +(-14--27)^2

23^2. +13^2

529 +169

= 698

So u will find the square root of 698

The ans u get is the distance