Your Assignment
Is x = 6 a solution to the equation 5(x – 3) = x + 13?
Follow the steps to find out.
1. Rewrite the equation 5(x – 3) = x + 13 with 6 substituted for x. Write a question mark over the equal sign to show that you're testing to see if the equation is true. (2 points)

2. Simplify both sides. Show your work.

3. Is x = 6 a solution to the equation? Why or why not? (3 points

4. Find a value of x that is a solution to 5(x – 3) = x + 13. Describe how you found the solution. (3 points)
please help me!

Given:-

By using formula:-

Solution:-

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hope it helps! :)

Answer:

Step-by-step explanation:

According to question

    [tex]4ax^{2} +9x+c < 0[/tex]

This means that the coefficient of the highest degree term

([tex]4ax^{2}[/tex]) must be positive

And the constant term (c) must be negative

So, the according to condition

   4a must be positive,

    which means a must be positive

And, c must be negative

          [tex]a > 0\\c < 0[/tex]

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It should be noted that the relationship between the balance and the number of withdrawals is linear, because there is a constant amount of $10 per withdrawal.

To confirm this, we can calculate the differences in balance for each pair of withdrawals:

Between withdrawals 3 and 2: 170 - 140 = 30

Based on the information, the starting amount is $200.

The equation to illustrate the withdrawal will be:

= 200 - 10w

where w = withdrawal.

These differences are constant, which means the rate of change of the balance is constant too.

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Answer:  1/2of 2/3 = 1/2 of 2 Third(s)= 1 third

Answer:

perimeter = 8a³b + 4ab

area = 4a^4b²

Step-by-step explanation:

perimeter = 2a³b + 6a³b + 4ab

perimeter = 8a³b + 4ab

area = bh/2

area = 4ab × 2a³b / 2

area = 4a^4b²

Answer:

The area of a circle can be found using the formula A = πr^2, where r is the radius of the circle. If the diameter of each circular light is 7 inches, the radius would be half of that, or 3.5 inches.

Therefore, the area of one circular light would be:

A = π * 3.5^2 = 3.5^2 * π = 12.25 * π square inches.

Since there are three circular lights, the total area of all three would be:

3 * 12.25 * π = 36.75 * π square inches.

Step-by-step explanation:

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Final Answer:

There are 0.036 decimeters in 3.6 millimeters.

Explanation:
To convert from millimeters to decimeters, we can use the following measurement conversion:

1 millimeter = 0.01 decimeters

So, to find out how many decimeters are in 3.6 millimeters, we can multiply 3.6 by 0.01:

3.6 * 0.01 = 0.036

Therefore, there are 0.036 decimeters in 3.6 millimeters.

The slope of the line, 9.75, is the amount of money she makes per hour of work. The y-intercept of the line, -25, is the amount of money she starts with, since she owes her sister $25 and has worked 0 hours.

Extent, volume, and supply are all nouns. the sum of two or more amounts; the complete worth, impact, or importance of anything.

A number is a mass or accumulation, especially of something impossible to count: amount of The appropriate quantity of sand wasn't delivered. Animals were kept on a small amount of land. He donated money on a regular basis to a charity.

We know that slope =

[tex]$m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Here, slope m is

[tex]$m=\frac{53 -14}{8 -4 }[/tex]

[tex]$m=\frac{39}{4 }[/tex]

m = 9.75

And putting the value in y-intercept form we have

y = 9.75x – 25

Therefore, The slope of the line, 9.75, is the amount of money she makes per hour of work. The y-intercept of the line, -25, is the amount of money she starts with, since she owes her sister $25 and has worked 0 hours.

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The money needs to be in the account for 5 years on simple interest at the rate 5% to earn R500.

The interest on a loan or principal amount can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more. When you pay back a loan, the monthly interest is deducted first, and any remaining funds are applied to the principle.

Let us suppose the time period as x.

The simple interest is given as:

SI = PRT/100

Where,

SI = Simple Interest = 500

P = Principal = 2000

R = Rate = 5%

T = x

Substituting the values:

500 = (2000)(5)(x) / 100

500 = 100x

x = 5 years

Hence, the money needs to be in the account for 5 years on simple interest at the rate 5% to earn R500.

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By using unitary methods, the amount of rope is needed for both sites is 350 meters.

Unitary method is a mathematical problem-solving technique that involves finding the value of one unit and using it to calculate the value of other units.

Let's start by looking at Site A, which is a rectangular area with a length of 60 meters and a width of 40 meters. To surround this area with rope, we need to measure the perimeter, which is the distance around the site.

=> Perimeter = 2 (length + width)

=>  2(60 + 40)

=> 2 x 100

=> 200 meters

Therefore, we need 200 meters of rope to surround Site A.

Now let's move on to Site B, which is also rectangular but has a length of 45 meters. To find the width of Site B, we can use the fact that it is similar in shape to Site A. Similar shapes have the same angles and proportional sides, so we can use a unitary method to find the missing dimension.

The length ratio of Site B to Site A is

=> 45/60 = 3/4

Since the shapes are similar, the width of Site B must also be 3/4 of the width of Site A.

Width of Site B = 3/4 x 40 = 30 meters

Now we can use the same formula as before to find the perimeter of Site B:

Perimeter = 2 (length + width)

=> 2(45 + 30)

=> 2 x 75

=> 150 meters

Therefore, we need 150 meters of rope to surround Site B.

To find the total amount of rope needed for both sites, we simply add the two perimeters:

Total rope needed = 200 + 150 = 350 meters

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The mystery number is 8. It is the number that is greater than 4 and less than 15 which when paired with 32 has an LCM of 32.

The mystery number is 8. To find this number, we first need to determine the Least Common Multiple (LCM) of two numbers. The two given numbers are 4 and 32. To find the LCM, we can list out the multiples of each number until we find a common multiple. The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, and so on. The multiples of 32 are 32, 64, 96, 128, and so on. We can see that 32 is the first common multiple of 4 and 32. Therefore, the LCM of 4 and 32 is 32. We are then told that the mystery number is greater than 4 and less than 15. This means the mystery number must be 8, since it is the only number between 4 and 15 that when paired with 32, has an LCM of 32.

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There are a total of 8 + 7 = 15 digits of the form x15y that are divisible by 15.

A number is divisible by 15 if and only if it is divisible by both 3 and 5.For a number of the form x15y to be divisible by 5, y must be either 0 or 5.

For a number of the form x15y to be divisible by 3, the sum of its digits must be divisible by 3. Since the sum of the digits is x + 1 + 5 + y = x + y + 6, x + y must be either 0, 3, 6, 9, 12, or 15.

So, we need to find all possible values of x and y such that x + y is one of these six values, and y is either 0 or 5.

If y = 0, then x must be one of the numbers 0, 3, 6, 9, 12, 15, 18, or 21, for a total of 8 possibilities.

If y = 5, then x must be one of the numbers 2, 5, 8, 11, 14, 17, or 20, for a total of 7 possibilities.

Therefore, there are a total of 8 + 7 = 15 digits of the form x15y that are divisible by 15.

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Answer:

Gavin made a Profit of $66.69 that is 93% Profit

Step-by-step explanation:

First, we calculate the Selling Price of Jeans after converting from GBP to USD on the given rate:

Rate: £1 = $1.34

Quantity: 3

Price in USD = Selling Price per pair * Rate in USD

£34.50 * 1.34 = $46.23 per pair of jeans.

Total Selling Price = Price Per Pair * Quantity
= 46.23 * 3
= $138.69

Total Profit = Total Selling Price - Total Cost Price
= $138.69-$72
= $66.69

Percentage of Profit = Total Profit / Total Cost Price
=66.69 / 72
=92.65

Therefore, the Profit Percentage is 92.65 % the nearest whole number would be 93%

To calculate Gavin's percentage profit, find the difference between the selling price and the buying price, and calculate the percentage of the buying price that the profit represents.

To calculate Gavin's percentage profit, we need to find the difference between the selling price and the buying price, and then calculate the percentage of the buying price that the profit represents.

Gavin's percentage profit is approximately 92.6%.

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For the given sets A = { 3, 5, 9 } and set B = { 2, 4, 5, 6, 9, 12 } then the value of AU B is equal to { 2, 3, 4, 5, 6, 9, 12 }.

Two different sets A and set B are equal to :

Set A =  { 3, 5, 9 }

Set B =  { 2, 4, 5, 6, 9, 12 }

Union of two different set A and B is defined as set having all the elements of set A and set B .

Union of two sets A and B is represented by AU B .

AU B

=  { 3, 5, 9 } ∪  { 2, 4, 5, 6, 9, 12 }

= { 2, 3, 4, 5, 6, 9, 12 }

Therefore, the union of two given sets A and set B is given by :

AU B =  { 2, 3, 4, 5, 6, 9, 12 }.

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Answer:

Howard's pencil is 750 millimeters

Step-by-step explanation:

[tex]\begin{array}{|l}\underline{km~}\\~~~~~\underline{|hm~}\\~~~~~~~~~~~\underline{|dam}~~~~~~~~\nwarrow~\div10\\~~~~~~~~~~~~~~~~~\underline{|m~~}\\~~~~~~~~~~\searrow~~~~~~~\underline{|dm~}\\~~~\times10~~~~~~~~~~~~~~~~~~\underline{|cm~}\\\underline{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~|mm~}\end{array}\\~~~~~~~~~~~\rm Converting ~Length ~ Unit[/tex][tex]~[/tex]

Step-by-step:

75 cm = 75 × 10 mm

75 cm = 750 mm

The fraction of the group are boys with brown eyes with total group of students who attend the math club is equals to the 2/9.

Let us assume that total number of students who attend the math club be 'x'. Now, according to problem, half of students who attend the math are boys. So, boys students out of total students who attend the math club, B = ( 1/2)x --(1)

Also, 4/9 of them boys have brown eyes. That is the boys students have brown eyes out of boys students who attend the math club, E = 4/9 of B

=> (4/9)B --(2)

We have to determine the relationship between boys with brown eyes (E) and the group of students (x). so, let's replace B in second equation with the expression present in eqution (1).

=> E = (4/9)(x/2)

For simplification, multiply the two fractions, that denominator with denominator and numerator with numerator.

=> E = 4x/18

For further simplification, simply dividing both the numerator and denominator by their common factor, ( 4, 18 ) = 2,

=> E = 2x/9

so, the required relationship between E and x is 2/9. Hence, required value is 2/9.

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Complete question :

a group of students attend a math club half the students are boys and 4/9 of the boys have brown eyes what fraction of the group are boys with brown eyes.

Answer:

The first item that fits into an envelope 20 L, 10°H and 4"W and weighs 10oz is a "Flat size mail." According to the rate chart, the first ounce of Flat size mail costs $0.88 and each additional ounce costs $0.17. The cost for the 10 ounces of this item will be $0.88 + 9 x $0.17 = $1.83.

The second item that fits into an envelope 8 L, 5" H and 0.20 W and weighs 2.5oz is a "Letter size mail." According to the rate chart, the first ounce of Letter size mail costs $0.44 and each additional ounce costs $0.17. The cost for the 2.5 ounces of this item will be $0.44 + 1.5 x $0.17 = $0.75.

So, the total cost for both items will be $1.83 + $0.75 = $2.58.

The triangles that do not follow the similarity statement and therefore are not similar triangle are ACT and CAR

Similar triangles are triangles that have the same shape, but may have different sizes. Their corresponding angles are congruent, and the corresponding sides are proportional. In other words, if you were to enlarge or shrink one triangle uniformly, it would overlap exactly with the other triangle.

In this problem, we can find two triangles that are similar and that implies that they must be equal to one another.

In this case, we have

1. ART ≈ CAT

2. CAR ≈ CTA

Only ACT ≠ CAR

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Miss Carol's bank account is losing money at a daily rate of $15, After giving money to her friend, Miss Carol's account balance fell by $65 leaving her with $435.

We must calculate Miss Carol's account balance's daily decline in order to ascertain the rate of change in her bank account.

Since Miss Carol lent her friend $65 this month, her account balance is reduced by $65, leaving her with $500 - $65 = $435.

The information that her account is losing $15 every day can then be put to use. We can write this as:

Rate of change = -$15 per day

The negative symbol signifies a declining amount on her account.

Therefore, Miss Carol's bank account is losing money at a daily rate of

$15, After giving money to her friend, Miss Carol's account balance fell by $65 leaving her with $435.

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The rate of change of Jakes earning is, 0 or no change.

Rate is a ratio of change in one quantity w.r.t. change in another quantity. The net change in one quantity is written as, Δy and the net change in another quantity is written as, Δx.

So formula for the rate is,

m = change in one quantity/change in another quantity = Δy/Δx

On Monday, Jake earned $90 by washing 18 cars.

Therefore, his earning rate was:

= $90 / 18 cars

= $5 per car

On Tuesday, Jake washed 9 cars and earned $45.

Therefore, his earning rate was:

= $45 / 9 cars

= $5 per car

On Wednesday, Jake washed 12 cars and earned $60.

Therefore, his earning rate was:

= $60 / 12 cars

= $5 per car

We can see that Jake's earning rate remained constant over the three days at $5 per car.

Therefore, the rate of change of Jake's earnings is 0, or no change.

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Answer:

a) 8:32 am

b) 5 occasions

The image of (2, 3) under a dilation with center at the origin and a scale factor of −3 will be (-6, -9).

What is Image of a point ?

Dilation is the process of resizing or altering an object. With the aid of the specified scale factor, it is a transformation that reduces or enlarges the objects. The initial figure is referred to as the pre-image, while the new figure acquired after dilatation is known as the image.

Given point : (2,3)

the scale factor is -3 which means the point should be enlarged by -3 times to get the desired image.

So, we can write as : (a, b) where,

     a = 2 × -3 =  -6

and, b = 3 × -3 = -9

Hence, the coordinates of the image will be (-6, -9).

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The average rate of change of the function over the interval [2,3] will be around 3.

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

For example to draw the equation y = 3x +2 this will draw a straight line in the coordinate geometry.

The rate of change is given by dy/dx

The average rate of change can be given as:

= (difference in y coordinate)/(difference in x coordinate)

= Δy/Δx

Average rate of change = ( 11 - 8 )/(3 - 2 )

                                        = 3

Hence, the average rate of change is 3

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Answer: A.

Step-by-step explanation:

Answer:

Reflect ABC over the y axis.  Translate ABC 1 unit to the right.  C is the center, dilate ABC with a scale factor of 2.

Step-by-step explanation:

Klaus wil be behind where he started with a distance of 8miles

Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.

Distance can also be defined as the space or gap between two points.

Velocity = distance/time

distance = velocity × time

time = 60minutes = 1hr

therefore the distance made by Klaus in 60 minutes =

= 8 ×1

= 8miles

therefore within 60 minutes Klaus will cover a distance of 8miles from where he started.

Klaus and Rachel will be at same position with the same speed

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2.25 km on the ground is represented by 9cm on the map.

What is the actual distance?

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or to an estimate based on other factors in common usage.

Here, we have

Given: The scale on the map is 1:25000

We have to find the actual distance of 9 cm on the map.

First, we have to find the actual distance of 1 cm on the map:

1cm = 25000cm

1cm = 250m

1cm = 0.25km

Now Find the actual distance of 9 cm on the map:

1cm = 0.25km

9cm = 9(0.25) = 2.25km

Hence, 2.25 km on the ground is represented by 9cm on the map.

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The value of the probability P(2) is 0.11

From the question, we have the following parameters that can be used in our computation:

The table of values

As a general rule:

The sum of probabilities must equal to 1

Using the above as a guide, we have the following:

0.1 + P(2) + 0.35 + 0.1 + 0.3 + 0.04 = 1

Evaluate the like terms

This gives

P(2) + 0.89 = 1

So, we have

P(2) = 0.11

Hence, the solution is 0.11

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Answer:

3

Step-by-step explanation:

You multiply the pre-image by 3 to get the image numbers.

Answer:

B.3

Step-by-step explanation:

The scale factor is 3 because all of the images are dilated 3 times larger than the preimage.

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Answer:

120 general admission

280 with student with a student ID

Step-by-step explanation:

x is tickets for general admission

y is tickets with a student ID

5x+3.5y=1580

x+y=400

y=400-x

5x+3.5(400-x)=1580

5x+1400-3.5x=1580

1.5x=180

x=120

120+y=400

y=280