make x the subject: y=4x+3

The title is explains what the graph is about. Scale: The scale is the numbers that show the units used on the bar graph. Labels: Both the side and the bottom of the bar graph have a label that tells what kind of data is shown.

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Answer:

The length of the short side was 12 and the length of the long side was 32

Step-by-step explanation:

We will say that the length is the shorter side, and be using l as the variable, and that width is the longer side, and be using w as the variable. The first two equations we have are:

w = l + 20

And

2(2l + 3w) = 240

We will start with the second equation, then substitute in the first equation for w. We have:

4l + 6w = 240

Divide both sides by 2:

2l + 3w = 120

Then, we substitute in l + 20 for w, giving us:

2l + 3l + 60 = 120

Subtract 60 from both sides and combine like terms:

5l = 60

l = 12

So, the original length was 12, now substituting this into our first equation gives us:

w = 12 + 20 = 32

So the original width was 32. So, the length of the short side was 12 and the length of the long side was 32.

Hope this helped!

you can choose my starting team in equation of 7 x 6 x 5 x 4 x 3 x 2 x 1 = 7 x 5 x 4 x 3 x 2 = 2520 ways.

7 x 6 (choose 7 players from 15) x 5 x 4 x 3 x 2 x 1 (7 players in any order) = 7 x 5 x 4 x 3 x 2 (7 players in any order, ignoring the goalie)

= 2520 ways.

In order to figure out how many ways I can choose my starting team, I can use a combination equation. Start by taking the number of players (15) and subtracting the number of players I need for the starting team (7). This gives me 8 players who will not be chosen. Now, I can calculate the number of ways I can choose the 7 players from the 15 available players. This is equal to 15 x 14 x 13 x 12 x 11 x 10 x 9. This is the same as 7 x 6. Now, I need to account for the order in which I choose the players. Since the 6 players other than the goalie can be interchangeable, I can use the equation 7 x 6 x 5 x 4 x 3 x 2 x 1. This gives me 2520 ways to choose my starting team. To simplify this, I can factor out the 7 and the 1, leaving me with 7 x 5 x 4 x 3 x 2, which is still equal to 2520. Therefore, I can choose my starting team in 2520 ways.

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The cost in dollars if a cab ride 49 miles long is $ 110.

The question is not complete, a table of travel costs and distance data should be provided. A table that is similar to the table that should be provided is in the attachment. From the table, it can be seen that if the mileage increases by 5 miles, the cost will increase by $ 12.5. The data graph will be in the form of a straight line.

The equation of the line if two points are known

(y - y₁)/(y₂ - y₁) = (x - x₁)/(x₂ - x₁)

(c - c₁)/(c₂ - c₁) = (d - d₁)/(d₂ - d₁)

(c - 12.5)/(25 - 12.5) = (d - 5)/(10 - 5)

(c - 12.5)/12.5 = (d - 5)/5

5 × (c - 12.5) = 12.5 × (d - 5)

5c - 62.5 = 12.5d - 125

5c = 12.5d - 125 + 62.5

5c = 12.5d - 62.5

c = 2.5d - 12.5

If a cab ride is 49 miles long,

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The volume of the composite solid 28.26 cm³

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The volume is the space occupied for a solid figure.

For the composite:

Volume of composite = volume of cylinder + volume of cone

For cylinder:

height is 2.5, radius : 3 inches

Volume of cylinder = π * radius² * height = π * (3)² * 2.5 = 70.65 cm³

For cone:

height is 3, radius : 3 inches

Volume of cone = (1/3) * π * radius² * height = (1/3) * π * (3)² * 3 = 28.26 cm³

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The image of the point (-8, 0) after a rotation of 270 degrees counterclockwise is (0,8).

What is rotation?

The term "rotation" refers to an object moving in a circle around its center. Different forms can be rotated at an angle around the centre. A rotation is a map in mathematics. The term "rotation group of a unique space" refers to all rotations that revolve around a fixed point and form a group beneath a structure. With respect to three-dimensional shapes, we can turn or rotate the elements about an endless number of fictitious axes.

Here When rotating a point 270 degrees counterclockwise about the origin our point A( x , y) becomes A'(y,-x). Then

=> (x , y) = (-8,0)

Now 270 degrees counter clockwise rotation then,

=> (y,-x) = (0,-(-8))

=> (y,-x)=(0,8)

Hence the image of the point (-8, 0) after a rotation of 270 degrees counterclockwise is (0,8).

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The match from the simplified answer are;

1. 3x³ + 2x + 10

2. 2x² - 4x + 7

3. 3x³ -6x² - 2x + 7

4. 7x³ + 6x² -4x + 7

Algebraic expressions are described as expression that is composed of factors, constants, variables, terms and coefficients.

These algebraic expressions are also composed of mathematical operations, such as;

From the information given, we have that;

(3x³ + 10x² + 2x) - (10x² + 7x - 10)

expand the bracket

3x³ + 2x + 10

(7x² -12x + 4) - (5x² - 8x -3)

expand the bracket

2x² - 4x + 7

(5x³ - 3x + 7) - (2x³ + 6x² -x )

expand the bracket

3x³ -6x² - 2x + 7

(5x³ -3x + 7) +(2x³ +6x² - x)

expand the bracket

7x³ + 6x² -4x + 7

Hence, the expressions are 3x³ + 2x + 10, 2x² - 4x + 7, 3x³ -6x² - 2x + 7 and 7x³ + 6x² -4x + 7

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The measurement of side AC in the given right triangle is 10.12 units.

A triangle having at least one angle measuring 90° is called a right triangle.

Given that, a triangle ABC, right-angled at A,

AB = 15 and BC = 18.1, we need to find AC,

Please refer to the figure attached,

Using Pythagoras theorem,

BC² = AB² + AC²

AC² = BC² - AB²

AC² = (18.1)² - 15²

AC² = 327.61 - 225

AC² = 102.61

AC = 10.12

Hence, the value of AC = 10.12

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1000 is the amount of garbage that was initially dumped in the landfill before any additional garbage was added. i.e: It is the quantity of garbage on Day 0.

The initial function given in the problem is n = 2000x + 1000.

The definition of a function's initial value is its starting value, which is unaffected by any variables used in the function.

The given function is:

n = 2000x + 1000

where the amount of trash is n, and the number of days is x. We'll set the variable (x) equal to zero to obtain the starting value.

Therefore, initially:

n = 2000(0) + 1000 = 1000

This indicates that the trash had a value of 1000 at day zero.

Therefore 1000 represents the amount of trash that was originally present in the landfill before dumping any extra trash.

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Answer:

(- 4, - 2 ) and (- 1, 2 )

Step-by-step explanation:

to determine which ordered pairs make the equation true

substitute the x and y coordinates of each point into the left side of the equation and if  equal to the right side then it is a solution.

(3, - 1 )

4(3) - 3(- 1) = 12 + 3 = 15 ≠ - 10 ← not true

(- 4, - 2 )

4(- 4) - 3(- 2) = - 16 + 6 = - 10 ← true

(1, 4 )

4(1) - 3(4) = 4 - 12 = - 8 ≠ - 10 ← not true

(- 1, 2 )

4(- 1) - 3(2) = - 4 - 6 = - 10 ← true

The polynomial with roots 4, 2i, and −2i is f(x)= x^3-4x^2+4x-16, which can be found by using the factor theorem.

c. f(x)= x^3-4x^2+4x-16

The polynomial with the given roots is a cubic polynomial. To get the coefficients of the polynomial, we can use the factor theorem. The factor theorem states that if a polynomial has a factor (x - a), then a is a root of the polynomial.

Therefore, the polynomial with roots 4, 2i, and -2i is f(x) = (x - 4)(x - 2i)(x +2i)

Expanding this polynomial, we get f(x) = x^3-4x^2+4x-16

The polynomial with roots 4, 2i, and −2i is f(x)= x^3-4x^2+4x-16, which can be found by using the factor theorem.

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The oldest type of currency still in use today, according to the claim, is metal.

Money is a good that is frequently used as a basis of economic exchange. It is used to communicate values and prices and is the primary determinant of value. By effortlessly traveling from one person to another and from one country to another, money fosters commerce.

Money is derived from the Latin term moneta, which means "coin," through the French term monnaie. It is thought that the Latin phrase came from a temple dedicated to Juno on Capitoline, being one Poland's seven hills. Juno was frequently linked to riches in ancient times.

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Answer: Hello how are you doing today?

Step-by-step explanation: How may I help you?

On solving the provided question, we can say that by using N= 2X + 1 or  N = 2X-1  will do the job for composite numbers.

By multiplying two small positive integers, you can create a composite number, which is a positive integer. Likewise, any positive integer that has at least one divisor besides itself and 1. Positive whole numbers make up composite numbers. It lacks prime (that is, it has divisors other than 1 and itself). The first several composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, and are frequently referred to simply as "composites." In other words, composite odd numbers encompass all non-prime odd numbers. for illustration: 9, 15, 21, etc. No. As a result, 2 only possesses the divisors 1 and 2. To put it another way, since 2 only has two divisors, it is not a composite number.

by using N= 2X + 1

or

N = 2X-1

will do the job for composite numbers.

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∠3 is congruent to ∠1. Hence, proved.

Two angles are said to be complementary angles if they add up to 90 degrees. In other words, when complementary angles are put together, they form a right angle (90 degrees).

Given that, ∠3 and ∠2 are complementary; m∠2 + m∠3 = 90°---------(I)

From the given figure,

m∠1 + m∠2 = 90°---------(II)

From the given equation (I) and (II), we get

m∠1 + m∠2=m∠2 + m∠3

m∠1 ≅ m∠3

Hence, proved.

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Answer: 1 moles KI = 166.00277 gram using the molecular weight calculator and the molar mass of KI.

Step-by-step explanation

Answer was found by using the molecular weight calculator and the molar mass of KI.

Hope this helps :)

Answer:

no

Step-by-step explanation:

.63 is different from .603

Answer:

600,000

Step-by-step explanation:

The mathematical concept demonstrated in this question is the process of exponential growth. Exponential growth demonstrates an increase in quantity by a percentage or factor over time. It is represented by the general formula [tex]f(x) = a(1+r)^{x}[/tex] where a is the initial amount, r is the growth rate, and x is the time interval expressed as an integer.

For this problem, we can see that the initial population of the town is 345,000, and it increases by a rate of 20% each year. We can determine that the growth rate is 20% because 1 + r = 1.2, so r must be equal to .20 (or 20%). We are given that t = 3, so we can plug that value in to the function given.

We calculate the population in 3 years to be 596,160. This can be approximated to 600,000.

Using Euclid's theorem for the right triangle AD  is ≈ 2.67

DB = 4 and DC = 6 , We need to find AD

Using Euclid's theorem for the right triangle

∴ DB² = AD * DC

∴ 4² = AD * 6

∴ 6 AD = 16

∴ AD = 16/6 = 8/3 ≈ 2.67

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Answer:

Step-by-step explanation:

Distance between top of the tower and point of observation = 100 meters
Angle of Elevation = 45 degrees

Let's draw a right angle triangle with the following specifications.

tan(45 degrees) = x/100

tan(45 degrees) = 1

100(1) = x

x =  100 meters

The height of the tower is 100 meters.

Yes , we can construct a triangle which has the side lengths as 11 cm 12 cm and 15 cm , because the given sides satisfies the criteria to form a triangle .

The Condition for the sides to form a triangle is that the Sum of the any two sides of the triangle must be greater than the third side of the triangle .

The sides of the triangle are given as ⇒ 11cm ,12cm and 15cm ;

On adding the two sides ,

we get ;

⇒ 11 + 12 = 23 > 15 ; True

⇒ 12 + 15 = 27 > 11 ; True

⇒ 11 + 15 = 26 > 12 ; True

So , we can see that all the three conditions are satisfied .

Therefore , the triangle can be constructed with the sides 11cm ,12cm and 15cm .

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In a sequence, each term after the first is four more than three times the previous term. The fifth term is 403.then First term is 3.

Let a1 be the first term....then the successive terms are

3a1 + 4,  9a1 + 16,  27a1 + 52,  81a1 + 160    

So  81a1 + 160 = 403     subtract 160 from each side

81a1 = 243    divide both sides by 81

a1 = 3

in other word

403 - 4 = 399/3 = 133

133 - 4 = 129/3 = 43

43 - 4 = 39/3 = 13

13 - 4 = 9/3 = 3

So, first term = 3

In a sequence, each term after the first is four more than three times the previous term. The fifth term is 403.then First term is 3.

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Answer: Hello sorry i read the question wrong at first. but the answer id relation 1, 2 and 3.

Step-by-step explanation: all inputs (x) have to have different outputs (y) :)

Answer:

We can start solving this problem by finding the two numbers that bound the range of integers we're looking for.

First, we can approximate $\sqrt{5}$ to the nearest integer by finding the square root of 5. We know that 2^2 = 4 and 3^2 = 9, so 2 < $\sqrt{5}$ < 3. Therefore, $\sqrt{5}$ is a little bit more than 2 and a little bit less than 3.

Therefore, there are 6 integers that fall between $\sqrt{5}$ and $\sqrt{50}$ on a number line.

Step-by-step explanation:

Similarly, we can approximate $\sqrt{50}$ to the nearest integer by finding the square root of 50. We know that 7^2 = 49 and 8^2 = 64, so 7 < $\sqrt{50}$ < 8. Therefore, $\sqrt{50}$ is a little bit more than 7 and a little bit less than 8.

Now we know that the range of integers we are looking for is between 2 and 7, inclusive. There are 7-2+1 = 6 integers between 2 and 7: 2, 3, 4, 5, 6, 7.

Therefore, there are 6 integers that fall between $\sqrt{5}$ and $\sqrt{50}$ on a number line.

So, the variance of the number of tornadoes in a year given that at least one tornado occurs is 3.

The Poisson distribution is a discrete probability distribution that describes the number of events that occur in a fixed interval of time or space, given the average number of events per interval.

For a Poisson distribution with mean λ, the variance is equal to λ.

Given that at least one tornado occurs in a year, the mean number of tornadoes is 3. Therefore, the variance is also equal to 3.

So, the variance of the number of tornadoes in a year given that at least one tornado occurs is 3.

It's worth noting that this result is based on the assumption that the number of tornadoes follows a Poisson distribution with mean 3, which may not always be the case in real-world scenarios. The actual number of tornadoes in a given year can be influenced by various factors such as climate, weather patterns, and geography.

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The gradient vector field ∇f of f(x, y) = 7 x2 + y2 is ∇f(x, y) = <14x, 2y>.

The gradient vector field ∇f of a scalar function f(x, y) is given by the vector function

∇f(x, y) = <∂f/∂x, ∂f/∂y>.

In this case, the function f(x, y) = 7x^2 + y^2 and we can find the gradient vector field as follows:

∇f(x, y) = <∂f/∂x, ∂f/∂y> = <14x, 2y>

This vector field points in the direction of steepest ascent at each point in the xy-plane, and its magnitude at each point is equal to the rate of change of f in that direction.

To sketch the gradient vector field, we can plot the vector <14x, 2y> at various points in the xy-plane. The direction of the vector at each point will be the direction of steepest ascent of the function f, and the length of the vector will indicate the rate of change of f in that direction.

We can notice that for the function f(x,y) = 7x^2+y^2, the function is always increasing as we move along the direction of the vector <14x,2y> and the vectors are always pointing away from the origin, which means that the origin is a local minimum of the function.

It's important to note that this is a paraboloid. The direction of steepest ascent is the direction of the tangent of the paraboloid at any point, which is pointing upwards from the vertex of the paraboloid.

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Answer:

The total boxes would be 625,000

Step-by-step explanation:

5,000,000÷8=625,00

If you have 5,000,000 toys and each box holds 8 toys, you need to divide the number of toys that will fit into a box from the total number of toys

Answer:

Step-by-step explanation:

Unfortunately, without more information, it is not possible to accurately predict the number of pounds someone would be overweight if they spent 8 hours per day using a computer. The graph provided does not provide enough data to make an accurate prediction. It is possible, however, to make an educated guess based on the graph. Looking at the graph, it appears that someone who spends 8 hours per day on the computer would likely be somewhere between 20 and 40 pounds overweight.

Answer:

x > 11/-8

Step-by-step explanation:

1/5(x + 2) -1/4(2-x)> 1/3(x + 4) -1/4(5-x)

=60×1/5(x +2)-60×1/4(2-x)>60×1/3 (x+4)-60×1/4(5-x)

=12(x +2)-15(2- x)> 20(x+4)-15(5-x)

=12x + 24 - 30 + 15x > 20x + 80 - 75 + 15x

=12x + 15x - 20x -15x > 80 -75 -24 +30

=27x -35x > 80 - 99 + 30

=-8x > 11

=-8x/-8 > 11/-8

=x > 11/-8.

Hence the truth set of the inequality is said that (x : x > 11/-8).

On solving the provided question, we can say that by unitary method 14 more hours must she work to earn an additional 154 dollars

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

here,

jessie worked = 22 hours last week at the auto shop

shop and earned = 242 dollars

1 hour = 242/22

154 dollars = 22/242*154 = 0.0909090909 * 154 = 13.9999999986 = 14 hours

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