The price of a ring was increased by 9% to £1800. What was the price before the increase? Give your answer to the nearest penny.

The magnitude and the direction of the vector formed by (4, 6) and (-2, 1) are [tex]\sqrt{85}[/tex] (approx. 9.2 units) and 49.4° north of west. (Correct choice: C)

First, we need to determine the expression of [tex]\overrightarrow {RS}[/tex] by vector sum:

[tex]\overrightarrow{RS} = S(x,y) - R(x,y)[/tex]

[tex]\overrightarrow{RS} = (-2, 1) - (4, -6)[/tex]

[tex]\overrightarrow {RS} = (-6, 7)[/tex]

The magnitude and the direction of the vector are determined by Pythagorean theorem and inverse trigonometric functions, respectively:

[tex]\|\overrightarrow{RS}\| = \sqrt{(-6)^{2}+7^{2}}[/tex]

[tex]\|\overrightarrow{RS} \| = \sqrt{85}[/tex]

θ = tan⁻¹ (7/-6)

θ ≈ 130.601°

The magnitude and the direction of the vector formed by (4, 6) and (-2, 1) are [tex]\sqrt{85}[/tex] (approx. 9.2 units) and 49.4° north of west. (Correct choice: C) [tex]\blacksquare[/tex]

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Answer:

E) 36 ft²

Step-by-step explanation:

Formulae

The shape is made up of 2 congruent triangles and 3 different rectangles.

Area of triangle = 1/2 x 3 x 4 = 6 ft²

Area of rectangle 1 = 2 x 4 = 8 ft²

Area of rectangle 2 = 2 x 3 = 6 ft²

To calculate the area of the 3rd triangle, we need to use Pythagoras' Theorem to determine the length of the hypotenuse of the right triangle.

   a² + b² = c²

⇒ 3² + 4² = c²

⇒ 25 = c²

⇒ c = √(25)

⇒ c = 5 ft

Therefore, area of rectangle 3 = 2 x 5 = 10 ft²

Total Surface Area

Total SA = 2 triangles + rectangle 1 + rectangle 2 + rectangle 3

               = (2 x 6) + 8 + 6 + 10

               = 36 ft²

Answer:

i am pretty sure it's A or B

Step-by-step explanation:

hope this helps

→(·°ω°·)←

Cities are pretty far from each other so you would have to use miles

Answer: the answer is d which is Miles .

Step-by-step explanation: it is Miles because there is a far distance bbetween Cities .HOPE IT HELPS YOU .PLEASE GIVE BRAINLIEST . THANKS .

That part is total cookies as per algebraic formula x^2-(a+b)x+ab=0

Hence

The inequality is

[tex]\\ \rm\rightarrowtail x^2-30x+224>=0[/tex]

[tex]\\ \rm\rightarrowtail (x-14)(x-16)>=0[/tex]

[tex]\\ \rm\rightarrowtail 14\leqslant x\leqslant 16[/tex]

Solution range

Atleast means the range

Atleast 2 more than Martha

A rectangle with area of 12 square units would have sides of length 4 units and 3 units. Area would therefore be 4 x 5.

A rectangle must be such that one side is longer than the other side.

The area of a rectangle is found as:

= Length x Width

As the area is 12, the length and width have to be numbers that when multiplied, will give you 12.

The factors of 12 which allow this to happen are:

= 1, 2, 3, 4, 6, 12

From here you can use 3 and 4.

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[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's solve ~

The given equations are :

[tex]\qquad \sf  \dashrightarrow \:x + y = 32[/tex]

and

[tex]\qquad \sf  \dashrightarrow \:y = 7x[/tex]

Now, plug in the value of y from equation 2 into equation 1 to find out the value of x ~

[tex]\qquad \sf  \dashrightarrow \:x + y = 32[/tex]

[tex]\qquad \sf  \dashrightarrow \:x + 7x = 32[/tex]

[tex]\qquad \sf  \dashrightarrow \:8x = 32[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 32 \div 8[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 4[/tex]

Now, plug the value of x in equation 2 to find y

[tex]\qquad \sf  \dashrightarrow \:y = 7x[/tex]

[tex]\qquad \sf  \dashrightarrow \:y = 7 \times 4[/tex]

[tex]\qquad \sf  \dashrightarrow \:y = 28[/tex]

➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖

Answer: acute angle

Step-by-step explanation: acute angle is the smallest starting from 0 to 90 DDegrees .

Answer:

2. |-4| < |-8|

3. |-5| > 1

5. |-2| = |2|

Answer:

2,3,5 are correct

Step-by-step explanation:

i took the test

The quadratic equation that can be used to represent the thickness of the border is 4x²+18x-3258=0.

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers.

It is written in the form of ax²+bx+c.

As it is given that the length and the width of the centre area are 72 inches and 36 inches, respectively. When the dimensions of the centre area are converted into the feets, it will be,

[tex]\rm Length = \dfrac{72\ inches}{12} = 6\ feet[/tex]

[tex]\rm Width= \dfrac{36\ inches}{12} = 3\ feet[/tex]

If we take the borders of the table into account, the length and the breadth  of the table will become,

Length = (6+x+x) = (6+2x)

Width = (3+x+x) = (3+2x)

We know that the area of a rectangle is given as the product of the length and width, and also it is mentioned that the area of the entire table is 3,276 square feet. Therefore, the area of the table can be written as,

[tex]{\rm Area=Length \times Width}\\\\3276 = (6+2x)(3+2x)\\\\3276= 18+ 12x+ 6x + 4x^2\\\\4x^2+18x+18-3276=0\\\\4x^2+18x-3258=0\\[/tex]

Thus, the quadratic equation that can be used to represent the thickness of the border is 4x²+18x-3258=0.

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The new price of the picture frame is  £1853

Given the following parameters

Percentage increase =  9%

Increment = £153

Determine the original value if the frame

9% of x = £153

0.09x = £153

x = £153/0.09
x = £1700

New price = £1700  + £153
New price = £1853

Hence the new price of the picture frame is  £1853

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a. answer:_77

2_ (7 * 9) _ 16

2_ (63) _16

_61_16

_77

Answer:

1.05 x 10^0.

Step-by-step explanation:

1.05 x 10^3 / 1 x 10^3

= 1.05/1  x 10^(3-3)

= 1.05 x 10^0

Answer:

$391.00

Step-by-step explanation:

Typically, regular work hours are paid at the rate given ($8.50), and overtime is "time and a half", or 1.5 times the regular pay.

We will get paid 40 hours at $8.50, and 4 four hours at 1.5x$8.50:

[tex]40(8.5)+4(1.5)(8.5)\\340+51\\391[/tex]

You will get paid $391.00 in gross pay, before taxes :)

Question 1

Focus on the triangle on the left.

sine is the ratio of opposite over hypotenuse

sin(angle) = opposite/hypotenuse

sin(44) = w/30

w = 30*sin(44)

w = 20.839751 approximately

Now move onto the triangle on the right. We'll use cosine this time.

cos(angle) = adjacent/hypotenuse

cos(x) = w/45

cos(x) = 20.839751/45

cos(x) = 0.463106

x = arccos(0.463106) ... arccosine is the same as [tex]\cos^{-1}[/tex]

x = 62.412286

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

Question 2

Focus on the triangle on the left.

sin(angle) = opposite/hypotenuse

sin(32) = w/5

w = 5*sin(32)

w = 2.649596

Now move to the triangle on the right.

sin(angle) = opposite/hypotenuse

sin(x) = w/5

sin(x) = 2.649596/5

sin(x) = 0.5299192

x = arcsin(0.5299192) .... arcsine is the same as [tex]\sin^{-1}[/tex]

x = 31.999996

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

Question 3

This time we use the tangent ratio.

Focus on the triangle that has legs of w and 16.

tan(angle) = opposite/adjacent

tan(70) = 16/w

w*tan(70) = 16

w = 16/tan(70)

w = 5.823524

Now let y = x+w and focus on the largest triangle this time.

tan(angle) = opposite/adjacent

tan(41) = 16/y

y = 16/tan(41)

y = 18.405895

This leads to:

y = x+w

x = y-w

x = 18.405895 - 5.823524

x = 12.582371

use a calculator and the correct answer is 0.019134405

and then round off the that answer into 2 significant number

sin^-1(√3-1/2√2)

please give me answer

The fraction of the game that Daniel's team scores 2 or more runs is 1/4 of the game.

A box plot is used to study the distribution and level of a set of scores. Scores are distributed into 4 groups. Each group has a value of 25%

The first quartile, is the first line on the box. The first quartile represents 1/4 of the score.

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1 glass..........1/4 liter

n glass.......... 5 liters

n = 1 x 5 : 1/4

n = 5 x 4

so there are 20 glasses

Answer:

2.5

Step-by-step explanation:

BASED ON GIVEN DATA:

⇒ 2 STUDENTS SPENT 2.5 (2 1/2) MINUTES

⇒ 1 STUDENT SPENT 3 MINUTES
⇒ 1 STUDENT SPENT 4.5 MINUTES

THE MOST COMMON AMOUNT OF TIME TAKEN IS 2.5 MINUTES BECAUSE OF THE 2 STUDENTS.

Answer:  0.5  minutes

Step-by-step explanation:  

Answer: answer C.

Step-by-step explanation: you have to add and divide

Answer:

a. House hold laundry

b. Beverages

c. Snacks

Step-by-step explanation:

Do mark brainliest.

#a

For branch A

For branch B

#b

For branch A

For branch B

#c

Branch A

Branch B

Branch B performed better

Answer:

12 days

Explanation:

480 >/= 36.39x + 20.25

The  inequality to determine x, the maximum number of days Miguel

can afford to rent while staying within his budget is

202.5 + 36.39x ≤ 480

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Charges per day = $36.39

Charges per mile = $0.90

Total miles = 225

Total charges for 225 miles.

= 225 x 0.90

= $202.5

The maximum amount to spend = $480

The inequality for the maximum number of x days.

202.5 + 36.39x ≤ 480

Thus,

The  inequality to determine x, the maximum number of days is

202.5 + 36.39x ≤ 480

Learn more about inequalities here:

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#SPJ2

Answer:

6

Step-by-step explanation:

sqrt(3) x sqrt(12) = sqrt(3) x sqrt(4x3) = sqrt(3) x 2sqrt(3)

= 2 ( sqrt(3)² ) = 2 x 3 = 6

Let's see

[tex]\\ \rm\rightarrowtail \sqrt{3}\times \sqrt{12}[/tex]

[tex]\\ \rm\rightarrowtail \sqrt{3}\times \sqrt{2(2)(3)}[/tex]

[tex]\\ \rm\rightarrowtail \sqrt{3}\times 2\sqrt{3}[/tex]

[tex]\\ \rm\rightarrowtail 2(3)[/tex]

[tex]\\ \rm\rightarrowtail 6[/tex]

Answer:

[tex]1,000,000 \: {m}^{3} [/tex]

Step-by-step explanation:

[tex]0.001 \: {km}^{3} \\ \\ = 0.001 \times {(1000)}^{3} \\ \\ = 0.001 \times 1,000,000,000 \\ \\ = 1,000,000 \: {m}^{3} [/tex]

Answer:

x = 3, y = 1

Step-by-step explanation:

Given:

[tex]\begin{bmatrix}x+4y=7\\ 4x-3y=9\end{bmatrix}[/tex]

Solve:

[tex]\mathrm{Substitute\:}x=7-4y[/tex]

[tex]\begin{bmatrix}4\left(7-4y\right)-3y=9\end{bmatrix}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]\begin{bmatrix}28-19y=9\end{bmatrix}[/tex]

[tex]\mathrm{For\:}x=7-4y[/tex]

[tex]\mathrm{Substitute\:}y=1[/tex]

[tex]x=7-4\cdot \:1[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]x=3[/tex]

[tex]\mathrm{The\:Answer\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]x=3,y=1[/tex]

Check Answer:

3 + 4(1)

7 (1) = 7

True

4(3) - 3(1)

12 - 3 = 9

True

Hence, x = 3 , y =1

~lenvy~

Step-by-step answer:

If there are 40% students that are girls , and the rest are 250 boys. Then that must mean there are 60% boys. Because that is the compliment.

i)

Because we know that 60% of the people in the group are boys, and that the amount of boys amounts to 250, we can model an equation like this.

[tex]Total * 0.6 = 250[/tex].

[tex]Total = 250/0.6[/tex]

[tex]Total = 417[/tex]

There are 417 students

ii)

Because we know that the total amount is 417, we can find the amount of girls there are by multiplying the total by the percentage.

[tex]417 * 0.4 = 167[/tex]

There are 167 students that are girls.

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

Plug in the values of the variables & simplify:-

[tex]\longrightarrow\pmb{4x^2y^2}[/tex]

The values of the variables are:-

[tex]\bigstar{\boxed{x=2~and~y=-2}[/tex]

Simplify:-

[tex]\longrightarrow\pmb{4(2)^2(-2)^2}[/tex]

[tex]\longrightarrow\pmb{4*4-4}[/tex]

[tex]\longrightarrow\pmb{16-4}[/tex]

[tex]\longrightarrow\pmb{12}[/tex]

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

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)

Answer:

the answer for this is 4.

Answer:

The value of x = -21/5

Step-by-step explanation:

=> -5x-21 =0

=> -21 = 5x

=> -21/5 = x

Answer:

Step-by-step explanation:

you want to set the equation equal to 0

-5x - 21 = 0

add 21 to both sides to get the variable by itself

-5x = 21

divide both sides by -5

x = - 21/5

Answer:

x=23/10

Step-by-step explanation:

the dash is a fraction