Solve this linear equation
a+b=8
a-b=4

The 2 unknown numbers are 4 and 5 .

Let the numbers be x and x + 1.

From the given information,

[tex]\dashrightarrow\sf \ \ \ x^2 + (x + 1)^2 = 41 \\ \\ \\ [/tex]

[tex]\dashrightarrow\sf \ \ \ 2 {x}^{2} + 2x + 1 = 41 \\ \\ \\ [/tex]

[tex]\dashrightarrow\sf \ \ \ 2 {x}^{2} + 2x + 1 - 41=0 \\ \\ \\ [/tex]

[tex]\dashrightarrow\sf \ \ \ {x}^{2} + x - 20 = 0 \\ \\ \\ [/tex]

[tex]\dashrightarrow\sf \ \ \ (x + 5)(x - 4)=0 \\ \\ \\ [/tex]

[tex]\dashrightarrow\sf \ \ \ { \underline{ \boxed{ \bf{ \red{x = - 5,4}}}}} \ \bigstar \\ \\ [/tex]

But, as we know -5 is not a natural number,

Hence, x = 4 .

So the 2 unknown numbers are :

★ Solution :

Let the number be x and x + 1.

[tex]\rule{130}1[/tex]

[tex]\underline{ \large \purple{ \mathscr{\dag\:A \bf{ccording} \: to \: \mathscr {Q} \bf{uestion} ....}}}[/tex]

[tex]:\implies\sf x^2 + (x + 1)^2 = 41 \\\\\\:\implies\sf 2x^2 + 2x + 1 - 41 = 0\\\\\\:\implies\sf 2x^2 + 2x + 40 = 0\\\\\\:\implies\sf x^2 + x - 20 = 0\\\\\\:\implies\sf x^2 + x - 20 = 0\\\\\\:\implies\sf x^2 + x - 20 = 0\\\\\\:\implies\sf x^2 + 5x - 4x - 20 = 0\\\\\\:\implies\sf x(x + 5) - 4(x + 5) = 0\\\\\\:\implies\sf (x + 5)(x - 4) = 0\\\\\\:\implies\underline{\boxed{\sf x = -5, 4}}[/tex]

⠀

We know that -5 is not a natural number. Hence, x = 4.

[tex]\therefore\:\underline{\textsf{The two consecutive natural number is \textbf{4 and 5}}}.[/tex]

Answer:

[tex] \boxed{ \bold{ \boxed{ \sf{2}}}}[/tex]

Step-by-step explanation:

[tex] \sf{4x + 8 = 16}[/tex]

Move 8 to right hand side and change its sign

⇒[tex] \sf{4x = 16 - 8}[/tex]

Subtract 8 from 16

⇒[tex] \sf{4x = 8}[/tex]

Divide both sides of the equation by 4

⇒[tex] \sf{ \frac{4x}{4} = \frac{8}{4} }[/tex]

Calculate

⇒[tex] \sf{x = 2}[/tex]

Hope I helped!

Best regards!!

Answer:

see explanation

Step-by-step explanation:

A rational number can be expressed in the form

[tex]\frac{a}{b}[/tex] where a and b are integers

Given

- 27 = [tex]\frac{-27}{1}[/tex] ← in rational form

Thus - 27 is a rational number

Answer:

a) 820

b)450

c)  -540

d) -294

e) 1440

f) 1425

Step-by-step explanation:

a) it is an arithmetic progression with ratio=4

   a1=3,

     a2=3+r=3+4=7.....

    a20=a1+19r

so a20=3+19*4=3+76=79

S=(a1+an)*n/2 where n=20

so S=(3+79)*20/2=820

b) a15=a1+14*r=2+14*4=2+56=58

S=(a1+a15)*15/2=(2+58)*15/2=60*15/2=30*15=450

It is the same formula for all  the exercises

S=(a1+an)*n/2 ,     where n is the number of terms

c) a40=30+39*(-3)=30-87=-57

So S=(30-57)*40/2=-540

d) a14=5+13*(-4)=5-52=-47

S=(5-47)*14/2=-42*14/2=-42*7=-294

e) it is 5+7+9+......+75

nr of  terms  = (an-a1) :r+1=(75-5):2+1=36

S=(5+75)*36/2=36*40=1440

f) ratio=7-4=3

the  same formula for n= (91-4):3+1=87:3+1=29+1=30

S=(4+91)*30/2=95*30/2=2850/2=1425

Answer:

-16% change

Step-by-step explanation:

The formula for a percent decrease is [tex]\frac{original-new}{original}\cdot100[/tex]. The original value was 986, and the new value is 828.24, so we can substitute inside the equation.

[tex]\frac{986-828.24}{986} \cdot100\\\\\frac{157.76}{986} \cdot100\\\\0.16\cdot100\\\\16[/tex]

So the percent change is -16%.

Hope this helped!

Step-by-step explanation:

1 / (sin 10°) − √3 / (cos 10°)

Multiply top and bottom of the first fraction by ½ cos 10°.

½ cos 10° / (½ cos 10° sin 10°) − √3 / (cos 10°)

Multiply top and bottom of the second fraction by ½ sin 10°.

½ cos 10° / (½ cos 10° sin 10°) − ½√3 sin 10° / (½ sin 10° cos 10°)

Combine fractions.

(½ cos 10° − ½√3 sin 10°) / (½ sin 10° cos 10°)

Change ½ to sin 30°, and change ½√3 to cos 30°.

(sin 30° cos 10° − cos 30° sin 10°) / (½ sin 10° cos 10°)

Use angle sum formula.

sin(30° − 10°) / (½ sin 10° cos 10°)

sin 20° / (½ sin 10° cos 10°)

Multiply top and bottom by 4.

4 sin 20° / (2 sin 10° cos 10°)

Use double angle formula.

4 sin 20° / sin 20°

4

We are given the equation 1 / sin(10°) - √3 / cos(10°) = 4, and want to prove that 1 / sin(10°) - √3 / cos(10°) equals 4.

Let's start by combining the expressions '1 / sin(10°)' and '√3 / cos(10°)' in the expression '1 / sin(10°) - √3 / cos(10°).'

1 / sin(10°) - √3 / cos(10°)

= cos(10°) - √3sin(10°) / sin(10°) [tex]*[/tex] cos(10°)

Now let's multiply the numerator and denominator by a common value. In this case it's most suitable to multiply both by 2. We will receive the expression 2(cos(10°) - √3sin(10°)) / 2(sin(10°) [tex]*[/tex] cos(10°)). We can further simplify this expression knowing that 2(sin(10°) [tex]*[/tex] cos(10°)) = 2sin(20°).

2(cos(10°) - √3sin(10°)) / 2sin(20°)

We can now bring the two on the bottom to the numerator, becoming 1 / 2.  Remember that the ' 1 / 2 ' will be distributed now. After the distribution we receive the expression 4( 1 / 2(cos(10°) - √3 / 2sin(10°)) /  2sin(20°). We can now use the trivial functions 1 / 2 = sin(30°), and √3 / 2 = cos(30°).

4(sin(30°)(cos(10°) - cos(30°)(sin(10°) ) / sin(20°))

= 4((sin(30 - 10°)) / sin(20°) = 4

Answer:

(x-10)(5x+2)

Step-by-step explanation:

this is the answer of the question.you can clearly see in the pic of the solution

Answer:

[tex]\boxed{12}[/tex]

Step-by-step explanation:

[tex]6/\frac{1}{2} =6*2=12[/tex]

Answer:

[tex]3a \times x - y - x - y \\ 3a \times x - x - y - y \\ 3a \times - 2y - \\ - 6ay[/tex]

Answer:

8,3

Step-by-step explanation:

Answer: 40%

Step-by-step explanation:

Answer: 2/5 or 40%

Step-by-step explanation: 15 + 10 = 25 and 10/25 simplifies to 2/5.

Answer:-8, -6,-3, 4 is the correct answer

Step-by-step explanation:

Answer:

Answer A

Step-by-step explanation:

Answer:

a number squared plus twice a number minus one equals zero

Step-by-step explanation:

Answer:

π − 12

Step-by-step explanation:

lim(x→2) (sin(πx) + 8 − x³) / (x − 2)

If we substitute x = u + 2:

lim(u→0) (sin(π(u + 2)) + 8 − (u + 2)³) / ((u + 2) − 2)

lim(u→0) (sin(πu + 2π) + 8 − (u + 2)³) / u

Distribute the cube:

lim(u→0) (sin(πu + 2π) + 8 − (u³ + 6u² + 12u + 8)) / u

lim(u→0) (sin(πu + 2π) + 8 − u³ − 6u² − 12u − 8) / u

lim(u→0) (sin(πu + 2π) − u³ − 6u² − 12u) / u

Using angle sum formula:

lim(u→0) (sin(πu) cos(2π) + sin(2π) cos(πu) − u³ − 6u² − 12u) / u

lim(u→0) (sin(πu) − u³ − 6u² − 12u) / u

Divide:

lim(u→0) [ (sin(πu) / u) − u² − 6u − 12 ]

lim(u→0) (sin(πu) / u) + lim(u→0) (-u² − 6u − 12)

lim(u→0) (sin(πu) / u) − 12

Multiply and divide by π.

lim(u→0) (π sin(πu) / (πu)) − 12

π lim(u→0) (sin(πu) / (πu)) − 12

Use special identity, lim(x→0) ((sin x) / x ) = 1.

π (1) − 12

π − 12

Answer:

Line PQ. Not enough Info for the Plano tho.

Step-by-step explanation:

Look at the 2 points, and thats the name of the line.

Answer:

(- 1, 8 )

Step-by-step explanation:

Under a reflection in the line y = x

a point (x, y ) → (y, x ) , thus

(8, - 1 ) → (- 1, 8 )

The image of (8, -1) after a reflection over the line y = x is, (- 1, 8).

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

We have to given that;

A point (8, - 1) is reflected over the line y = x.

Now, We know that;

The image of point (x, y) after reflection over the line y = x is,

⇒ (x, y) → (y, x)

Thus, The image of (8, -1) after a reflection over the line y = x is,

⇒ (8, - 1) → (- 1, 8)

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Answer:

3n + 2

Step-by-step explanation:

[tex]−n+(−4)−(−4n)+6[/tex]

Open the parentheses

[tex] - n - 4 + 4n + 6 \\ [/tex]

Add similar elements

[tex] - n + 4n - 4 + 6 \\ 3n + 2 \\ [/tex]

Answer:

[tex] - n + 6[/tex]

Step-by-step explanation:

[tex] - n + ( - 4) - ( - 4n) + 6 = - n - 4n + 4n + 6 = - 5n + 4n + 6 = - n + 6[/tex]

Answer:

Step-by-step explanation:

((b+2)(b+12)/(b+2)(b+3))*(b+3)

= (b+12)

Answer:

The possible midpoints of AB are [tex]\frac{19}{2}[/tex] and [tex]\frac{13}{2}[/tex].

Step-by-step explanation:

Let suppose that A and B have one-dimensional coordinates. GIven that [tex]A = 8[/tex] and [tex]AB = 3[/tex], there are two possible locations for B:

[tex]B_{1} = A+AB[/tex]

[tex]B_{1} =8+3[/tex]

[tex]B_{1} = 11[/tex]

[tex]B_{2} = A-AB[/tex]

[tex]B_{2} = 8-3[/tex]

[tex]B_{2} = 5[/tex]

The midpoint equations for each case are, respectively:

[tex]m_{1} = \frac{A+B_{1}}{2}[/tex]

[tex]m_{1}=\frac{8+11}{2}[/tex]

[tex]m_{1} = \frac{19}{2}[/tex]

[tex]m_{2} = \frac{A+B_{2}}{2}[/tex]

[tex]m_{2} = \frac{5+8}{2}[/tex]

[tex]m_{2} = \frac{13}{2}[/tex]

The possible midpoints of AB are [tex]\frac{19}{2}[/tex] and [tex]\frac{13}{2}[/tex].

Answer:

Step-by-step explanation:

[tex]8 + 9x + 4(11 - 2x) \\ = 8 + 9x + 44 - 8x \\ = 8 + 44 + 9x - 8x \\ = 52 + x[/tex]

Answer:

0.06 cubic meters per year...

Step-by-step explanation:

The rate of water flows through a pipe is 0.06 cubic meters per year.

It is the volume of fluid flows out from the container per unit time.

Given that,

Water flows through a pipe at a rate of 6 fluid ounces per day. It can be written as:

Water flows per day ⇔ 6 fluid ounces

∴ Water flows per year ⇔  365 x (6 fluid ounces)

Volume of water in milliliter,

Water flows per year ⇔  365 x (6 x 29.574 ml )

Volume of water in cubic meter,

Water flows per year ⇔  365 x ([tex]\frac{6 x 29.574}{1000000}[/tex] [tex]m^{3}[/tex]) = 0.06477   [tex]m^{3}[/tex]

Hence Water flows per year round value to the nearest hundredth is 0.06  [tex]m^{3}[/tex].

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Answer:

x=6

Step-by-step explanation:

127-83=9x-10

44=9x-10

+10.0 +10.0

54=9x

divide by 9 on both sides

x = 6

Answer: m=6

Step-by-step explanation:

[tex]9+12m=6+15\left(m-1\right)[/tex]

[tex]6+15\left(m-1\right)=15m-9[/tex]

[tex]9+12m=15m-9[/tex]

subtract 9 on both sides

[tex]9+12m-9=15m-9-9[/tex]

[tex]12m=15m-18[/tex]

subtract 15m on both sides

[tex]12m-15m=15m-18-15m[/tex]

[tex]-3m=-18[/tex]

divide by -3 on both sides

[tex]\frac{-3m}{-3}=\frac{-18}{-3}[/tex]

since [tex]\frac{-a}{-b}=\frac{a}{b}[/tex]

[tex]\frac{-18}{-3}=6[/tex]

[tex]m=6[/tex]

Answer:

430 cm² is right answer ✔️

Step-by-step explanation:

A=2(wl+hl+hw)

=2(5×15+7×15+7×5)

=430cm²

hope it helped you:)

Answer:

80

Step-by-step explanation:

82-12+10

82+10-12

92-12

80

The number of people in the restaurant will be 80

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that there are 82 people in a restaurant. Four groups of 3 leave and then five groups of 2 enter.

The expression will be solved as below:-

E = 82-12+10

E = 82+10-12

E = 92-12

E = 80

Therefore, the number of people in the restaurant will be 80

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Answer:A)Gives hints to reader about a future event.

Step-by-step explanation:

Answer:

A) Gives hints to reader about a future event.

Step-by-step explanation:

Foreshadowing is one of the storytelling device that gives hints to readers about the future events.

Hope this helps ;) ❤❤❤

Answer:

Step-by-step explanation:

taking A(3, 3), B(6, 6), C(9,3) and D(6,0)

we have:  [tex]y_A=y_C\quad and\quad x_B=x_D[/tex] so the AC and BD are diagonals, that means:

AB = BC = CD = DA = s

[tex]s=\sqrt{(6-3)^2+(6-3)^2}=\sqrt{3^2+3^2}=\sqrt{18}\\\\\\A=s^2=(\sqrt{18})^2=18[/tex]

Answer:

513.95

Step-by-step explanation:

First you have to divide 7776 by 343. Then you raise the answer to the second power

Answer:

(- 3, 5 )

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 90°

a point (x, y ) → (- y, x ) , thus

(5, 3 ) → (- 3, 5 )

Answer:

$605

Step-by-step explanation:

The correct question is

Taho Earns His Regular Pay Of $11 Per Hour For Up To 40 Hours Of Work Per Week. For each hour over 40 hours of work per week. Taho earns 1½ times his regular pay. How much does Taho earn in a week in which he works 50 hours?

a. $550

b. $605

c. $625

d. $750

e. $825

For the first $40 that Taho works, he earns $11 x 40 = $440

For the extra $10 (since he worked 50 hrs that week)

1½ of $11 per hr = 1.5 x $11 = $16.5

for the 10 days extra = $16.5 x 10 = $165

total pay = $440 + $165 = $605