Find the value of x in each case. Give reasons to justify your solutions!

BRAINLY SHALL BE GIVEN

L, M ∈

KN


1. m ∠KLP+m∠PLM = __180___

2. _3x____+m∠PLM = _180_____ Substitution

3. m∠PLM = _______ Algebra

4. m∠PMN=m∠P+m∠______ _______________

5. ____2x+72__ = _____x_+180°−3x Substitution

6. x= ___27___ Algebra

The unit rate of 9 inches of rain in 72 hours is calculated by dividing the depth of the rainfall by the duration, resulting in a unit rate of 0.125 inches of rain per hour.

To express 9 inches of rain in 72 hours as a unit rate, you divide the total amount of rain by the total number of hours to find the rainfall intensity per hour. The calculation would go as follows:

Write down the total rainfall depth: 9 inches.

Write down the duration over which the rain occurred: 72 hours.

Divide the total rainfall depth by the duration to calculate the unit rate: 9 inches / 72 hours = 0.125 inches per hour.

So, the unit rate is 0.125 inches of rain per hour.

Answer:

Ummmmm none I guess

Step-by-step explanation:

rawr

Answer: 27

Step-by-step explanation: bc thats what some random persons teacher said.

Answer:

Don't know

Step-by-step explanation:

Which way? Clockwise or Counterclockwise?

The two numbers that fulfill these properties are 12 and 30. They both have a highest common factor of 6 and a lowest common multiple of 60.

The two numbers that fit the description provided both need to be greater than 6, have a highest common factor (HCF) of 6, and a lowest common multiple (LCM) of 60.

For two numbers to have an HCF of 6, they must be multiples of 6. Looking at multiples of 6 that are greater than 6, we have 12, 18, 24, 30 etc. Since the LCM must be 60, we aim to find two numbers that when multiplied would produce 60. This leads us to the pair 12 and 30.

12 and 30 have an HCF of 6 (because 12=2*2*3 and 30=2*3*5, so the HCF is 2*3=6), and 12 and 30 both have an LCM of 60. Therefore, the two numbers are 12 and 30.

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The two numbers that meet these criteria, are greater than 6 and the ones that have the highest common factor as 6 and lowest common multiple as 60, are 6 and 60.

In this problem, we are asked to find two numbers that have the following properties: they are both greater than 6, their highest common factor(HCF) is 6 and their lowest common multiple(LCM) is 60. Since HCF is 6, it's logical to assume that the two numbers can be multiples of 6. As per hints given the highest common factor of two numbers is 6 and the lowest common multiple is 60, the numbers should be 6 and 60 as these are the only two numbers that satisfy all conditions.

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Answer:

- 1,5 liters

Step-by-step explanation:

Answer:

The water must be added to 1 liter of a 5% saline solution to get a 2% saline solution is 1.5 litres

Explanation:

We assume that the quantity of water added to be x litres. The quantity of saline in the existing solution is 5% of 1litre = 0.05 litres, with the addition of water, the quantity of new solution becomes (1 + x) litres. As per the problem, the percentage of saline in new solution should be equal to 2%. Therefore,

[tex]\frac{0.05}{1+x} \times 100=2[/tex]

So, 5 = 2(1+x)

2x = 5 - 2

[tex]x=\frac{3}{2}=1.5[/tex]

So, 1.5 litres water should be added to make the 1litre 5% saline solution a 2% saline solution.

Answer:

jaqueline, because 3.6/18 =0.2 and 5.4/30=1.8

Step-by-step explanation:

Final answer:

Terrance is traveling at a faster speed of 12 mph compared to Jaqueline's 10.8 mph, after converting their biking times to hours and calculating the speed for each.

Explanation:

To determine who is traveling at a faster speed, we calculate the speed (rate) at which each student is biking. Speed is computed using the formula: speed = distance / time. For Terrance, who bikes 3.6 miles in 18 minutes, we must first convert minutes to hours, so 18 minutes is 0.3 hours (since 1 hour = 60 minutes). Thus, Terrance's speed is 3.6 miles / 0.3 hours = 12 miles per hour (mph).

For Jaqueline, who bikes 5.4 miles in 30 minutes, we also convert the minutes to hours to get 0.5 hours. Jaqueline's speed is 5.4 miles / 0.5 hours = 10.8 mph.

Comparing the two speeds, Terrance has a faster speed at 12 mph compared to Jaqueline's 10.8 mph.

There are two numbers whose sum is 64. The larger number subtracted from 4 times the smaller number gives 31. Then the numbers are 45 and 19

Given that, There are two numbers whose sum is 64.  

Let the number be a and b in which a is bigger.

Then, a + b = 64 ------ eqn (1)

The larger number subtracted from 4 times the smaller number gives 31.  

4 x b – a = 31  

4b – a = 31 ----- eqn (2)

We have to find the numbers.

So, from eqn (2)

a = 4b – 31

Subatitute a in (1)

4b – 31 + b = 64

On solving we get

5b  = 64 + 31  

5b = 95

b = 19

So, b = 19, then eqn 1

a + 19 = 64

On simplification,

a = 64 – 19

a = 45  

Hence, the two numbers are 45 and 19

Answer:

$810

Step-by-step explanation:

you have to turn your commission into a decimal and then multiply it by the total amount and then you will get your answer

The saleswoman earned $810 in commission last month.

To find the commission earned by the saleswoman, we need to calculate 9% of the total merchandise sold.

9% of $9000 = $9000 * 0.09 = $810.

Therefore, the saleswoman earned $810 in commission last month.

Answer:

8 times

Step-by-step explanation:

57/7=8.1428571428... round down to the nearest whole number.

Answer:

$40,$60

Step-by-step explanation:

Let the money in the first month be x.

2x+20=100

x=40

Option A. x 7 8 9 10 y -49 -56 -63 -70 is the right answer.

Step-by-step explanation:

The inverse of a function means that the input becomes the output of the function and the output becomes input. When the function is given in the form of ordered pairs, the fiirst element of each ordered pair represents input and second element represents the output.

So, for given function: {(-49,7), (-56,8), (-63,9), (-70,10)}

The inverse will be:

{(7, -49), (8,-56), (9,-63), (10, -70)}

Hence,

Option A. x 7 8 9 10 y -49 -56 -63 -70 is the right answer.

Keywords: Function, Inverse

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Correct Answer:

X= 7, 8, 9, 10

Y= -49, -56, -63, -70

Answer:

i would like to say the answer is FALSE

Step-by-step explanation:

Answer:

"Calculation" is a mathematical determination of finding the size or number of something while "pattern" is a sequence of elements that is being repeated in a predictable manner.

Step-by-step explanation:

Calculation- This process allows you to put elements together or transform them into a new result. It produces an obvious change.

For example: 7 x 6 = 42

The numbers 7 and 6 when multiplied produces 42.

Pattern- This process allows you to put the elements in an intelligible way. The elements are organized or repeated regularly.

For example: A, B, C, A, B, C, A, B, C

It is noticeable that the letters A, B and C are being repeated in the same way.

The displacement [tex](\( \Delta x \))[/tex] of the compression spring when a 60-kilogram person stands on it, with a spring constant of 2500 N/m, is approximately -0.2352 meters. The negative sign indicates the direction of the displacement. Therefore, the correct answer is D.

To find the displacement [tex](\( \Delta x \))[/tex] of the spring, you can use Hooke's Law:

[tex]\[ F = -k \cdot \Delta x \][/tex]

Where:

- F is the force applied (weight in this case),

- k is the spring constant, and

- [tex]\( \Delta x \)[/tex] is the displacement of the spring.

Rearrange the formula to solve for [tex]\( \Delta x \)[/tex]:

[tex]\[ \Delta x = -\frac{F}{k} \][/tex]

Substitute the given values:

[tex]\[ \Delta x = -\frac{mg}{k} \]\[ \Delta x = -\frac{(60 \, \text{kg})(9.8 \, \text{m/s}^2)}{2500 \, \text{N/m}} \][/tex]

Calculate the result:

[tex]\[ \Delta x \approx -0.2352 \, \text{m} \][/tex]

The negative sign indicates that the displacement is in the opposite direction to the applied force. Therefore, the correct answer is:

D) [tex]\( -0.2352 \, \text{m} \)[/tex]

Answer:

20% x 5 = 100%

6.8 x = 34

so there was 34 oz of water in the full bottle

Step-by-step explanation:

Answer:

230

Step-by-step explanation:

12 sections total

5 red, 4 green, the rest black

12-5-4 = 3 sections are black

3/12 = 1/4 of the sections are black

1/4 represents the probability of landing on black for one spin

(1/4)*921 = 230.25 which rounds to 230

We expect to land on a black section about 230 times out of 921 times total.

Answer:

[tex]x^{2}[/tex]-5x+6

Step-by-step explanation:

(x-2)(x-3)

= [tex]x^{2}[/tex] -5x + 6

Answer:

this is the answer. hope it helps you

Here this is the answer, i hope this helps u have a great day ik this is late sorry...

NEVERMIND sorry this was the answer for another question, this is incorrect for this one.

The solution is y=(7a+9b)÷8

Step-by-step explanation:

Given equation is;

[tex]\frac{2y-a}{3}=\frac{a+3b}{4}[/tex]

Multiplying both sides by 12;

[tex]12*\frac{2y-a}{3}=\frac{a+3b}{4}*12\\4(2y-a)=3(a+3b)\\8y-4a=3a+9b\\8y=3a+4a+9b\\8y=7a+9b[/tex]

Dividing both sides by 8;

[tex]\frac{8y}{8}=\frac{7a+9b}{8}\\y=\frac{7a+9b}{8}[/tex]

The solution is y=(7a+9b)÷8

Keywords: linear equations, variable

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Answer:

x= 3s -8

3 times Sarah's age is 3s hence the expression is as shown

Emily's age in terms of Sarah's age can be expressed by the algebraic expression '3s - 8', where 's' is Sarah's age.

The student's question asks to express Emily's age in terms of Sarah's age, s. In the problem, it is stated that Emily is 8 years less than 3 times Sarah's age. This relationship can be expressed as an algebraic expression, where Emily's age, e, is equal to '3s - 8'. In this expression, 's' represents Sarah's age(12 years old in this case), '3s' means '3 times Sarah's age', and '- 8' represents '8 less than' the amount.

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Answer:

In 15 days

Step-by-step explanation:

Eva Volunteers Every 3 Days:

So, Eva volunteers on:

3rd, 6th, 9th, 12th, 15th, 18th, 21st...and so on DAYS

Jin Volunteers Every 5 Days:

So, Jin volunteers on:

5th, 10th, 15th, 20th, 25th...and so on DAYS

So, we see NEXT which day they vounteer together. Looking at the list, we see that it is on 15th day. This is also the LCM (Least Common Multiple) of 3 and 5.

So, in 15 days, they volunteer on the same day again.

Answer:

(500r + 1500) sheets per day.

Step-by-step explanation:

The school office uses r reams of white paper and 3 reams of blue paper every day.

Now, the total number of reams of paper that the school office uses every day will be (r + 3) reams.

Now, we know that 1 ream of paper is equivalent to 500 sheets of paper.

So, the school office uses a total 500(r + 3) sheets of paper every day.

Now, using the distributive property the total number of sheets will be = (500r + 1500) (Answer)

Answer:(500+1500)

Step-by-step explanation:

Answer:

64x⁶

Step-by-step explanation:

(4x²)³

= 4³(x²)³   <=the third power applies to both of the terms in the bracket

= 64x⁶      <=simplify

(x²)³ = x⁶ because when powers are raised to a power, they multiply.

(x²)³ = x²⁽³⁾ = x⁶

Answer:

1 1/13

Step-by-step explanation:

2/1 6/7

2/ 13/7

2/1*7/13

14/13

1 1/13

The division of '2' by '1 6/7' involves the conversion of the mixed number to an improper fraction, after which it becomes '2 * 7/13'. This simplifies down to '14/13' or '1 1/13'.

To calculate the division of '2' by '1 6/7', we first have to convert '1 6/7' to an improper fraction. '1 6/7' equals '13/7' when simplified. So, now the task is to divide '2' by '13/7'. In the division of fractions, we multiply the first fraction by the reciprocal of the second fraction. Thus, this becomes '2 * 7/13' (i.e. '2' over '1' times '7' over '13'). Multiplying the numerators together gives us '14', and multiplying the denominators together gives us '13'. Therefore, '2 divided by 1 6/7', in simplest form, is '14/13' or '1 1/13' when converted to a mixed number.

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Answer:

The general equation of a circle is x² + y² - 6x - 16y + 48 = 0

Alice should buy 1.36 kilograms of veal.

Step-by-step explanation:

Given,

According to store's scale;

2.20 pounds = 1 kilogram

1 pound = [tex]\frac{1}{2.20}\ kg[/tex]

As Alice wants to buy 3 pounds, therefore,

3 pounds = [tex]\frac{1}{2.20}*3\\[/tex]

[tex]3\ pounds = \frac{3}{2.20}\\3\ pounds = 1.36\ kg[/tex]

Alice should buy 1.36 kilograms of veal.

Keywords: unit rate, fractions

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Answer:

1.36

Step-by-step explanation:

she wants to buy 3 pounds of veal

we multiply 3 pounds by 1 kg/2.20 lbs

we get 1.36 pounds

Answer:

Step-by-step explanation:

[tex]\bold{METHOD\ 1:}[/tex]

[tex]\triangle ABC\sim\triangle DE F\qquad(\text{similar tringles)}\\\\\text{Therefore corresponding sides are in proportion:}\\\\\dfrac{BA}{AC}=\dfrac{ED}{DF}\\\\\text{Substitute}\ BA=360,\ AC=600,\ ED=30\\\\\dfrac{360}{600}=\dfrac{30}{DF}\qquad\text{cross multiply}\\\\360DF=(600)(30)\\\\360DF=18000\qquad\text{divide both sides by 360}\\\\DF=50[/tex]

[tex]\bold{METHOD\ 2:}[/tex]

[tex]\text{Use the Pythagorean theorem:}\\\\leg^2+leg^2=hypotenuse^2\\\\\text{We have}\ leg=40,\ leg=30,\ hypotenuse=DF.\\\\\text{Substitute:}\\\\40^2+30^2=DF^2\\\\1600+900=DF^2\\\\2500=DF^2\to DF=\sqrt{2500}\\\\DF=50[/tex]

The measure of DF cannot be determined without additional context or a specific function. DF could imply distance in a physics scenario or represent an infinitesimal change in a function in calculus.

The measurement of DF seems to be a question related to calculus and physics, specifically pertaining to infinitesimal changes and dynamics. In calculus, df represents an infinitesimally small change in a function, often a result of changing variables x and y. In a physics context, DF can be interpreted as the distance fallen in a typical free fall scenario under gravity, with an initial velocity. Unfortunately, without additional context or a specific function provided, the measure of DF cannot be accurately determined.

For example, in the context of electromagnetism, dF could represent the infinitesimal force on a wire carrying current in a magnetic field, according to the formula dF = i (dl) x B, where i represents current, dl represents an infinitesimal length of wire, and B represents the magnetic field.

Answer:

1:250

Step-by-step explanation:

[tex]\sqrt{15625/0.25}[/tex]

=[tex]\sqrt{62500}[/tex]

=250

Answer:

The first one

Step-by-step explanation:

0.35÷5=0.07

0.75÷10=0.075

1.00÷12=0.08

1.35÷15=0.09

Answer:

The total cost of  to re-decorate the community hall is £2172.

Step-by-step explanation:

We have been given that a community hall is in the shape of a cuboid. The hall is 40m long 15m wide and 3m high.

The paint will be required for 4 walls and ceiling.

Let us find area of walls and ceiling.

Are of Walls and Ceiling = [tex]2(l+b)h+lb=2(40+15)3+(40\times15)= 6\times55+600= 330+600 =930m^2[/tex]

Therefore, the area of walls and ceiling is 930 square meters.

Given: Cost for 10 litre of paint is £10 and 10 litre paint covers 25 square meter. Therefore,  

Total Painting cost = [tex]10 \times \frac{930}{25} = \£372[/tex]

Therefore, the total painting cost of wall is £372.  

Tiles will be required for floor. Let us find the area of floor.

Area of floor = [tex]l \times b = 40\times15 =600m^2[/tex]

Given: 1m squared floor tiles costs £3. So,

Total Cost for tiles = [tex]3\times600= \£1800[/tex]

Therefore, the total cost for tiles is £1800.

Now let us find total cost of  to re-decorate the community hall;

Total Cost =  the total painting cost of wall + the total cost for tiles = [tex]\£1800+\£372= \£2172[/tex]

Hence, the total cost of  to re-decorate the community hall £2172.

To redecorate the community hall, the cost for tiling the floor will be £4500, and the cost for painting will depend on the price per tin, with a total of 93 tins needed to cover 930m².

To calculate the total cost of re-decorating the community hall, we need to find the areas that need painting and tiling. Since the hall is a cuboid, the paintable area includes the four walls and the ceiling. The floor requires tiling.

The combined area of the four walls can be found by calculating the perimeter of the base, which is the sum of all sides ((2 × length) + (2 × width)), and then multiplying by the height. The ceiling is simply the length multiplied by the width.

Here is how to calculate the areas and costs:

Therefore, the cost for tiling the floor will be £4500, and the cost for painting will be 93 tins (if each tin is assumed to cost a certain amount, which is not specified in the question).