Can the sides of a triangle have lengths 5, 15, and 20?

solved, 3x+2/x+7 = 3x²+21x+2/x+7

solution:

3x+2/x+7

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x times x+7/x+7

we get,

3x(x+7)/x+7 + 2/x+7

since 3x(x+7)/x+7 and 2/x+7  have the same denominator, add them by adding their numerators.

we get,

3x (x+7) +2/x+7

Do the multiplications in 3x(x+7)+2.

we get, 3x²+21x+2/x+7

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The adult tickets sold were 409.

11a + 3c = 3520

Where "a" is the number of adult tickets sold and "c" is the number of child tickets sold.

We also know that the theater sold a total of 464 tickets, so we can add the following equation:

a + c = 464

We can now use the first equation to solve for one of the variables, and then substitute it into the second equation:

11a + 3c = 3520

3c = 3520 - 11a

c = (3520 - 11a)/3

We know that:

a + c = 464

We can substitute the value of c into this equation:

a + (3520 - 11a)/3 = 464

a + (3520 - 11a) = 464*3

a + 3520 - 11a = 1392

12a = 4912

a = 4912/12

a = 409

So, the theater sold 409 adult tickets last night

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The distance between points (2, 3) and (-4, 5) is 6.3 units.

As we know according to the distance formula the distance between points (x₁, y₁) and (x₂, y₂) is given by,

[tex]d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}[/tex]

Here we have been given points (2,3) and (-4,5)

Let us assume that  (x₁, y₁) = (2, 3)

and (x₂, y₂) = (-4, 5)

Let d represents the distance between points (2,3) and (−4,5)

Using above distance formula the distance d between given points would be,

[tex]\Rightarrow d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}\\\\\Rightarrow d = \sqrt{[(-4 - 2)^2 + (5 - 3)^2]}\\\\\Rightarrow d = \sqrt{[(-6)^2 + (2)^2]}\\\\\Rightarrow d = \sqrt{36+4}\\\\\Rightarrow d = \sqrt{40}\\\\\Rightarrow d = 6.3~units[/tex]

Therefore, the distance is 6.3 units.

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The complete question is:

What is the distance between points (2,3) and (−4,5)  ?

The percentage of data within 2 standard deviations of the mean is given as follows:

100%.

Using a calculator, the measures for this problem are given as follows:

The bounds within two standard deviations of the mean are given as follows:

All the measures in this problem are within these bounds, hence the percentage is of 100%.

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The product of 64 are 1, 2, 4, 8, 16, 32, 64 and its factors in pairs are (1, 64), (2, 32), (4, 16), and (8, 8).

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

The set of integers that can be divided evenly by 64 is called the factorization of 64. Overall, there are 7 components that make up 64: 1, 2, 4, 8, 16, 32, and 64, with 64 being the largest. The prime factors for the number 64 are 1, 2, 4, 8, 16, 32, and 64. Its factors in pairs are 1, 64, 2, 32, 4, and 16. (8, 8).

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No, 0 is neither an infinite solution nor no solution.

The solution x = 0 implies that the value 0 satisfies the equation, so there is a solution. “No solution” implies that there is no value, not even 0, which would satisfy the given equation.

Let us take an example for a more reasonable interpretation,

An example is the equations

² + 1 = 0 and

− 3 = 2 − 3

Suppose that is real.

The first equation has no solution, while the second equation has a solution = 0.

Hence, 0 can be a solution to a system of equations.

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Answer:

21

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

28 - 25%=21

The value of y in the expression x + 7y = 18 when x = - 3 is 3.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

We know Substitution in mathematics is when we replace some specific numerical values with variables according to our wants or given in the problem.

Given, x = - 3 and x + 7y = 18.

Replacing x with - 3 in x + 7y = 18.

- 3 + 7y = 18.

7y = 18 + 3.

7y = 21.

y = 21/7.

y = 3

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The type of the function y = -2x + 3 is a linear function.

Function in math is known as a rule that gives value of a dependent variable that corresponds to specified values of one or more independent variables.

Here we have given that the function y = -2x +3 and here we need to identify the type of the function.

As we all know that the type of function called linear function is defined as a function that has either one or two variables without exponents.

While we consider the definition we have identified that the given function is is the linear function because in the given function there is no exponents in it so it can fall under the category of the function called exponents.

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Here are some suggestions to assist you make sure you are consuming enough liquids to keep your hydration levels at good levels.

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There are an infinite number of combinations of water that Andrew and Michael could have each drank as long as the sum is 500.

Since Andrew and Michael drank a total of 500 fluid ounces of water, any combination of water that they drank must add up to 500 fluid ounces.

Let's call the amount of water Andrew drank as "a" and the amount of water Michael drank as "m". Then, we can write the equation: a + m = 500.

There are an infinite number of combinations of water that Andrew and Michael could have each drank as long as the sum is 500. Here are a few examples:

Andrew drank 250 fluid ounces and Michael drank 250 fluid ounces.

Andrew drank 200 fluid ounces and Michael drank 300 fluid ounces.

Andrew drank 100 fluid ounces and Michael drank 400 fluid ounces.

and so on.

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The multiplicative inverse of 'a' is indicated by a-1 or 1/a. In other words, the multiplicative inverse of a number is explained as 1 divided by the number.

The multiplication inverse of 3 is 1/3.

The multiplication inverse of 8 is. 1/8.

The multiplicative inverse is defined as the reciprocal of a given number. It is used to clarify mathematical expressions.

The word 'inverse' infers something opposite/contrary in effect, position, order, or direction. A number when multiplied by its multiplicative inverse results in 1.

The multiplicative inverse formula is called that the product of a number and its reciprocal is 1.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{14x + 14x}\\\\\mathsf{= 14(\dfrac{1}{2}) + 14(\dfrac{1}{2})}\\\\\mathsf{= \dfrac{14}{1}\times \dfrac{1}{2} + \dfrac{14}{1} \times \dfrac{1}{2}}\\\\\mathsf{= \dfrac{14\times1}{1\times2} + \dfrac{14\times1}{1\times2}}\\\\\mathsf{= \dfrac{14}{2} + \dfrac{14}{2}}\\\\\mathsf{= 7 + 7}\\\\\mathsf{= 14}\\\\\\\huge\text{Therefore, your answer should be:}\\\huge\boxed{\mathsf{14}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

14x + 14x = 14

Step-by-step explanation:

Given expression,

→ 14x + 14x

Now we have to use,

→ x = 1/2

Let's simplify the expression,

→ 14x + 14x

→ 14(1/2) + 14(1/2)

→ (14/2) + (14/2)

→ 7 + 7

→ 14 => {final value}

Hence, required answer is 14.

The axis of symmetry is the y-axis and the vertex for the function

f(x) = 3(x - 2)²+ 4 is (2,4).

Given f(x) = 3(x - 2)² + 4

The graph will be symmetrical to the y-axis and since a> 0, the parabola opens up.

The axis of symmetry is the line that divides a parabola into two symmetrical parts. The vertex is the point where the axis of symmetry intersects the parabola.

The axis of the symmetry is x=2

The vertex form of a parabola is y = a (x - h)²+ k

The vertex is given by (h,k) coordinates.

In order to find the vertex, we need to compare the given equation to the vertex form of the parabola.

f(x) = 3(x - 2)²+ 4=0

a = 3, h = 2 and k = 4

Thus the vertex of the function is (2,4).

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The total cost of the fence will be £841. The solution is obtained using the concept of perimeter of triangle.

What is perimeter of triangle?

Any two-dimensional figure's perimeter is determined by the space surrounding it. By summing the lengths of the sides, we can determine the perimeter of any closed shape.

We are given a right-angled triangle with one angle 59° and the adjacent side as 145 meters.

We know that tan θ = Opposite side/Adjacent side

⇒ tan 59° = Opposite side/145

⇒ 1.66 = Opposite side/145

⇒ 241 meters(approx) = Opposite side

Now, using pythagoras theorem,

⇒Hypotenuse^2 = Base^2 + Perpendicular^2

⇒Hypotenuse^2 = 241^2 + 145^2

⇒Hypotenuse^2 = 58,081 + 21,025

⇒Hypotenuse^2 = 79,106

⇒Hypotenuse = 281 meters(approx)

Perimeter of triangle = Sum of three sides

⇒ Perimeter = 145 + 241 + 281

⇒ Perimeter = 667 meters

The fence costs £ 1.26 per meter

Total cost of fence = 1.26 * 667 = £840.42 = £841

Hence, the total cost of the fence will be £841.

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The required number of actual meters represented by 18 centimeters on the blueprint is 3.6 meters.

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
A scale on a blueprint drawing of a house shows that 10 centimeters represent 2 meters.

Scale factor,
10 centimeter: 2 meters = 1 centimeters : 0.2 meters

So,
18 centimeters = 18 × 0.2 meters = 3.6 meters.

Thus, the required number of actual meters represented by 18 centimeters on the blueprint is 3.6 meters.

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the product of the given expressions will be x([tex]x^{5/12}[/tex])

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

[tex]x^{2/3}[/tex] * [tex]x^{3/4}[/tex]

= [tex]x^{2/3+3/4}[/tex]

=[tex]x^{17/12}[/tex]

=x([tex]x^{5/12}[/tex])

Hence the product of the given expressions will be x([tex]x^{5/12}[/tex])

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The point (7, 10.5) is on the graph of both equations and satisfies the system of equations.

To find the solution to a system of equations, we need to find the values of x and y that satisfy both equations simultaneously.

The system of equations is:

y = 2x - 3.5

x - 2y = -14

We can begin by solving one of the equations for one of the variables, for example, we can solve the first equation for y:

y = 2x - 3.5

Next, we can substitute this expression for y into the second equation:

x - 2(2x - 3.5) = -14

This gives us:

x - 4x + 7 = -14

-3x = -21

x=7

Now we can substitute this value of x back into the first equation to find the corresponding value of y:

y = 2(7) - 3.5

y = 10.5

So the solution to the system of equations is x = 7, y = 10.5.

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a) About 99.7​% of organs will be between 205 grams and 415 grams.

b) The percentage of organs weighing between 240 grams and 380 grams is of 95%.

c) The percentage of organs less than 240 grams or more than 380 grams is of 5%.

d) The percentage between 240 grams and 415 grams is of: 97.35%.

These approximate percentages are defined by the Empirical Rule, for a normally distributed variable:

The first three questions are quite straight forward, while for the fourth we consider the symmetry of the normal distribution, as follows:

Hence the total percentage is of:

0.95 x 50 + 0.997 x 50 = 97.35%.

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The subsequent three words in the list. 3 14, 32, 60, 98, ... is 276 . In this case, the order is 3, 14, 32, 60, 98, and 276.

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The next three terms in the sequence are 79, 90, and 101.

a) To find a formula for the sequence, we can use a difference table.

First, let's write out the first few terms of the sequence:

3, 14, 32, 60, 98, ...

Next, we'll create a difference table:

n | Term | Difference

1 | 3 |

2 | 14 | 11

3 | 32 | 18

4 | 60 | 28

5 | 98 | 38

We see that the difference is increasing by 10 each time, so our formula can be written as:

Term = 11n + 3

To check the formula, we can plug in a few values of n and see if it matches the terms in the sequence:

n = 1, Term = 11(1) + 3 = 14

n = 2, Term = 11(2) + 3 = 32

n = 3, Term = 11(3) + 3 = 60

The formula matches the terms in the sequence, so it is correct.

b) To find the next three terms in the sequence, we can use our formula:

n = 6, Term = 11(6) + 3 = 79

n = 7, Term = 11(7) + 3 = 90

n = 8, Term = 11(8) + 3 = 101

So the next three terms in the sequence are 79, 90, and 101.

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Answer:

32.9 cm^2

Step-by-step explanation:

In the absence of a diagram, lets use the one shown in the attached worksheet.  The assumption is that the "blue areas" are the four sections of the circle that extend beyond the square boundaries.  The approach is to calculate areas for both the circle and the square.

Square = (11 cm)^2              =  121 cm^2

Circle = (3.14)*(14/2 cm)^2  =   153,9 cm^2

Subtract the square from the circle.  That removes all the circle area, except for the four sections outside the square.  The result is 32.9 cm^2

The required probability has been shown on the number as illustrated in the figure.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
There are two veggies (carrots, and celery) and three types of meat (ham, turkey, and bologna),

This results in 3*2 = 6 distinct combinations of meat and a vegetable. Here, we are limited to choosing just one of each kind. List 2 shows the 6 different combinations. List 1 is inaccurate because you can only take one vegetable at a time and not both.

List 2 alternatives that state "ham, carrots" and "turkey, carrots" should be circled. Two things have been circled. This is one of a total of six.

Probability is given as,
= 2/ 6
= 1/3

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Answer:

40%

Step-by-step explanation:

There are 5 options to roll: 1, 2, 3, 4, and 5.

This means you have a 1 out of 5 chance of rolling each number.

This question is asking for 1 AND 2, not just one number. So, we have a 2 out of 5 chance of rolling that, because 2 options are acceptable instead of just one number.

I'm not sure which form you are looking for, but 2 out of 5 is the same as saying 2/5. Most probability solutions are wanted as a percentage. To find that just solve 2/5, which is 0.4. Move the decimal to the right twice, and that is a 40% chance.

It will take 8 days for 50 children to catch the flu

The given equation states as follows:

P = 110/(1+7e⁻⁰²²ⁿ     (Where n stands for t)

P = 110/(1+7e⁻⁰²²ⁿ = 2.2

7.e⁻⁰²²ⁿ = 2.2 - 1

7.e⁻⁰²²ⁿ = 1.2/7

0.22n = In (12/7)

n= 8.02

Recall that n=t

Therefore t = .02

Therefore time = 8 days

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Draw a circle over the number to begin plotting an inequality, such as x>9, on a number line (e.g., 9). If the sign also says equal to (or), then complete the circle.

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For the value of k is equal to 6, the system of equations,

kx + 3y - (k – 3) = 0 and 12x + ky - k = 0 have infinitely many solutions

Here we have equations

kx + 3y - (k – 3) = 0

12x + ky - k = 0

For a system of 2 linear equations,

a₁x + a₂y + a₃ = 0

b₁x + b₂y + b₃ = 0

They will have infinitely many solutions if

a₁/b₁ = a₂/b₂ = a₃/b₃

here,

k = a₁,          3 = a₂          - (k – 3) = a₃

12 = b₁         k = b₂           - k = b₃

Hence

k/12 = 3/k = (3 - k)/(-k)

Taking up

3/k = (3 - k)/(-k)

we get

3 = k - 3

or, k = 6

hence for k = 6, the equations will have infinite solutions.

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Complete Question

What is the value of k such that the following pair of equations has infinitely many solutions?

kx + 3y - (k – 3) = 0

12x + ky - k = 0

Answer:Kids grow at their own pace. Big, small, tall, short — there is a wide range of healthy shapes and sizes among children. Genetics, gender, nutrition, physical activity, health problems, environment, and hormones all play a role in a child's height and weight. And many of these things can vary widely from family to family.

Step-by-step explanation:

The formula for the sum rule is: P(A or B) = P(A) + P(B) - P(A and B)

The sum rule, also known as the addition rule of probability, states that the probability of any two events occurring together is the sum of the probability of each event occurring individually, minus the probability of them both occurring at the same time. The formula for the sum rule is:

P(A or B) = P(A) + P(B) - P(A and B)

where A and B are two events and P(A) and P(B) are the probabilities of each event occurring individually, and P(A and B) is the probability of both events occurring at the same time.

The sum rule is used when the two events are mutually exclusive, meaning that they cannot happen at the same time. In this case, P(A and B) = 0, so the formula becomes:

P(A or B) = P(A) + P(B)

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Answer:

135°

Step-by-step explanation:

Angles 1 and 6 have the same measure and sum to a 90 degree angle

   so they are each 45°

Angles 1 and 4 are equal as well   45°

then angle 5 = 90 + 45 = 135 °

Angles 5  2  9 and 7 are all equal     angle 9 = 135 °

Answer:

The second one :( y> 4x - 7) and y<1