I need help pls, I don't understand

Answer:

21,  22, 23   or

-23, -22 , -21

Step-by-step explanation:

The 3 consecutive integers are x, x + 1, and x + 2

Sum of the squares of the 3 consecutive integers:

x² + (x+1)² + (x+2)² = 1454     Expand this equation

x² + x² + 2x + 1 + x² + 4x + 4 = 1454   Combine like terms

3x² + 6x + 5 = 1454

3x² + 6x + 5 - 1454= 0

3x² + 6x - 1449 = 0

Use quadratic equation to solve for the roots of x:  (a = 3, b = 6,

c= -1449)

x = 21, -23

The consecutive numbers are: x, (x + 1), (x + 2)

21,  22, 23

-23, -22 , -21

The range of this relation include the following: D. {-2, 3, 5}.

In Mathematics and Geometry, a range can be defined as the set of all real numbers that connects with the elements of a domain. This ultimately implies that, a range simply refers to the set of all possible output numerical values (real numbers), which are shown on the y-coordinate (y-axis) of a graph.

Based on the information provided in this scenario, the domain and range of this relation in interval notation are as follows:

Domain = {3, 6, 8}

Range = {-2, 3, 5}.

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Based on the information, the product of the first equation is 9p-75, and the product of the second equation is -47.

We can use the formula:

Where a and b can be any expressions. Substituting the first expression into the formula:

Substituting the second equation into the formula:

Therefore, the product of the first equation is 9p-75 and the product of the second equation is -47.

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The amount in the bank after 7 years increases as the compounding frequency increases, and it is highest when interest is compounded continuously.

Using the formula A = P(1 + r/n)^(nt), where:

A = the amount in the account after t years

P = the principal (initial amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

a) If interest is compounded annually:

A = 2000(1 + 0.05/1)^(1*7) = $2,835.08

b) If interest is compounded quarterly:

A = 2000(1 + 0.05/4)^(4*7) = $2,888.95

c) If interest is compounded monthly:

A = 2000(1 + 0.05/12)^(12*7) = $2,905.03

d) If interest is compounded continuously:

A = Pe^(rt) = 2000e^(0.05*7) = $2,938.36

Therefore, the amount in the bank after 7 years increases as the compounding frequency increases, and it is highest when interest is compounded continuously.

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Answer:

68/25

Step-by-step explanation:

Answer:

Step-by-step explanation:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,144,233,377,610,987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, ... Can you figure out the next few numbers?

We see that f(-1) = g(1) = 5. Therefore, the solution to the system of equations is x = -1.

A system of equations is a set of two or more equations that are to be solved simultaneously. Each equation in the system represents a relationship between variables, and the solution to the system is the set of values for the variables that satisfy all of the equations in the system.

One way to solve a system of equations is by substitution. We can solve one of the equations for one of the variables in terms of the other variable, and then substitute that expression into the other equation to get an equation in one variable. We can then solve that equation for the variable, and use that value to find the value of the other variable.

Another way to solve a system of equations is by elimination. We can add or subtract the equations in the system to eliminate one of the variables, and then solve for the other variable. We can then use that value to find the value of the eliminated variable.

To find a solution to the system of equations that includes the quadratic function f(x) and the linear function g(x), we need to find the value of f(x) for each value of x and compare it to the corresponding value of g(x). If f(x) and g(x) are equal for any value of x, then that value is a solution to the system.

Substituting each value of x into the quadratic function f(x), we get:

f(-2) = 2(-2)² + (-2) + 4 = 10

f(-1) = 2(-1)² + (-1) + 4 = 5

f(0) = 2(0)² + 0 + 4 = 4

f(1) = 2(1)² + 1 + 4 = 7

f(2) = 2(2)² + 2 + 4 = 14

Comparing these values to the corresponding values of g(x), we see that f(-1) = g(1) = 5. Therefore, the solution to the system of equations is x = -1.

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Answer:

18 5-dollar bills

10 20-dollar bills

(h+3)² simplified is:(h+3)² = h² + 6h + 9

What is binomial?

Binomial refers to a type of probability distribution that describes the number of successes in a fixed number of independent trials.

The expression (h+3)² is a binomial squared. When we square a binomial, we use the formula:

(a+b)² = a² + 2ab + b²

where a and b are any numbers or variables. In this case, our binomial is (h+3), so we can use the formula with a=h and b=3:

(h+3)² = h² + 2h3 + 3²

The first term, h², comes from squaring the h in the binomial. The second term, 2h3, comes from multiplying the two terms in the binomial together and then doubling the result. Finally, the third term, 3^2, comes from squaring the 3 in the binomial.

Simplifying the expression, we can combine like terms. We have h² as the first term, 23h as the second term, and 3^2 as the third term. 23h is equal to 6h, so we can rewrite it as:

(h+3)² = h² + 6h + 9

And that is the simplified form of the expression (h+3)².

Therefore,  (h+3)² simplified is:(h+3)² = h² + 6h + 9

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Answer:

$140.70

Step-by-step explanation:

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The x-axis is where the circle centre is located. Three units make up the circle's radius. This circle's radius coincides with the radius of the circle whose equation is x² + y² = 9.

The y coordinate of a circle's centre will be 0 if the circle's centre is on the x-axis. The circle's equation will therefore have the generic form x2 + y2 + 2gx + c = 0, where g and c are constants.

Circle's standard equation is written as:

x²+y²+2gx+2fy+C=0

Centre is (-g, -f)

radius = √g²+f²-C

Given a circle whose equation is : x²+y²-2x-8=0

Get the centre of the circle

2gx = -2x

2g = -2

g = -1

Similarly, 2fy = 0

f = 0

Centre = (-(-1), 0) = (1, 0)

This demonstrates circle's centre is on the x-axis.

r = radius = √g²+f²-C

radius = √1²+0²-(-8)

radius =√9 = 3 units

The circle has a radius of three units.

For the circle x²+y²=9, radius is expressed as:

r² = 9

r = 3 units

As a result, this circle's radius matches that of the circle whose equation is x² + y² = 9.

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the the coordinates of the resulting point are (18, -8). of the resulting point are (18, -8).

What is center of dilation?

The center of dilation is a fixed point in the plane.

Starting with point B(5, -2), if we move it 4 units to the right and 2 units down, we get:

B'(9, -4)

Next, we need to dilate the point by a factor of 2, using the origin as the center of dilation. This means we need to multiply both the x-coordinate and y-coordinate of B' by 2.

So, doubling the x-coordinate of B' gives:

2 × 9 = 18

And doubling the y-coordinate of B' gives:

2 × (-4) = -8

Therefore, the coordinates of the resulting point are (18, -8).

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Answer: 3/2 or 1 1/2 or 1.5

Step-by-step explanation:

9/8 times 2 is 2.25 or 9/4

9/4-6/8= 3/2 or 1 1/2 or 1.5

Using the half angle formula, cos(-π/12) =  ±√[2 + √3]/4]

The half angle formula for cosine is cosФ/2 = ±√[(1 + cosФ)/2]

Since we want to find the value of cos(-pi/12) using the half angle formula, we have that cosФ/2 = cos(-π/12)

⇒ Ф/2 = -π/12

⇒  Ф = -π/12 × 2

⇒ Ф = -π/6

So, substituting this into the equation, we have

cosФ/2 = ±√[(1 + cosФ)/2]

cos(-π/6)/2 = ±√[(1 + cos(-π/6))/2]

= ±√[(1 + cos(π/6))/2]

Now, we know that cos(π/6) = √3/2

So, substituting this into the equation, we have that

cos(-π/6)/2 = ±√[(1 + cos(π/6))/2]

cos(-π/12 = ±√[(1 + cos(π/6))/2]

= ±√[(1 + √3/2)/2]

= ±√[[2 + √3]/2)/2]

= ±√[[2 + √3]/2 × 2]

= ±√[2 + √3]/4]

So,  cos(-π/12) =  ±√[2 + √3]/4]

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By answering the presented question, we may conclude that As a result, adding the isosceles triangle categorization is superfluous and redundant in this circumstance.

A triangle is a polygon since it has three sides and three vertices. It is a basic geometric shape. Triangle ABC refers to a triangle with the vertices A, B, and C. In Euclidean geometry, a single plane and triangle are obtained when the three points are not collinear. If a triangle has three sides and three corners, it is a polygon. The triangle's corners are the spots where the three sides meet. The sum of three triangle angles equals 180 degrees.

An isosceles triangle has two sides of equal length, but a right triangle has one angle that measures 90 degrees. As a result, an isosceles right triangle is one with two equal-length sides and one 90-degree angle.

The Pythagorean theorem states that in any right triangle, the two legs (the sides next to the right angle) are always of equal length. Hence, if we know that a triangle has one 90-degree angle and two equal-length sides, we already know that it is a right triangle and that the two legs are equal. As a result, adding the isosceles triangle categorization is superfluous and redundant in this circumstance.

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Therefore, the perimeter of the rectangle is 42 centimeters.

The concept of area is used in many areas of mathematics, science, and everyday life. It is used in geometry to calculate the area of various shapes, such as triangles, circles, and polygons. It is also used in physics to calculate the amount of surface area of an object that is exposed to air or water, and in architecture and engineering to determine the amount of material needed to construct a building or structure.

Here,

To find the perimeter of a rectangle, we need to know its length and width. We are given that the width of the rectangle is 9 centimeters, and the area of the rectangle is 108 square centimeters.

We can use the formula for the area of a rectangle:

Area of rectangle = length x width

Plugging in the values we have:

108cm² = length x 9cm

Solving for the length, we can divide both sides by 9cm:

length = 108cm² / 9cm

length = 12cm

So, the length of the rectangle is 12 centimeters.

To find the perimeter of the rectangle, we can use the formula:

Perimeter of rectangle = 2 x (length + width)

Plugging in the values we have:

Perimeter of rectangle = 2 x (12cm + 9cm)

Perimeter of rectangle = 2 x 21cm

Perimeter of rectangle = 42cm

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Answer:11.4999...

Step-by-step explanation:

Any number when rounding that starts with 1, 2, 3 4 will be rounded down. All numbers above will be rounded up. Therefore, you find the largest number that will still round down.

I think it might be:

Between 1754 and 1885 European imperialism was global. Nations like Britain, France, and Spain grew their Empires in the Americas, on the continent of Africa, and in parts of Asia. Their colonies created power and wealth for European businesses and governments. Eventually, many European countries held a meeting to decide how to divide up the world to avoid wars and conflict between themselves. This meeting was called the Conference.

Is the function above continuous: B. not continuous at x = 0.

In Mathematics and Geometry, a continuous function can be defined as a type of function in which there is no discontinuities or breaks between the intervals for the points plotted on a graph.

In Mathematics and Geometry, a discrete function can be defined as a type of function in which the ordered pair of values on the x-axis and y-axis are separate from each other and unconnected.

By critically observing the graph shown above, we can reasonably infer and logically conclude that it represents a discrete function because it is not continuous at x is equal to 0 i.e x = 0.

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Total percentage of adults who preferred soccer or baseball: is 25%

what is percentage ?

Percentage is a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%". For example, 50% means 50 out of 100, or 50/100 as a fraction.

In the given question,

The circle graph shows the percentage of adults who preferred each sport. To find the percentage of adults who preferred soccer or baseball, we need to add the percentages for soccer and baseball.

Soccer: 11%

Baseball: 14%

Total percentage of adults who preferred soccer or baseball: 11% + 14% = 25%

Therefore, 25% of adults preferred soccer or baseball.

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Answe: The distance of light bulb can be calculated using equation of parabola. The parabola is a plane curve which is U-shaped.

Step-by-step explanation:

Answer:

To check whether 40, -40, 16, or -16 is the solution of the equation 28 = d - 12, we can substitute each value into the equation and see if it results in a true statement.

When we substitute 40 into the equation, we get:

28 = 40 - 12

Simplifying, we get:

28 = 28

This is a true statement, so 40 is a solution of the equation.

When we substitute -40 into the equation, we get:

28 = -40 - 12

Simplifying, we get:

28 = -52

This is not a true statement, so -40 is not a solution of the equation.

When we substitute 16 into the equation, we get:

28 = 16 - 12

Simplifying, we get:

28 = 4

This is not a true statement, so 16 is not a solution of the equation.

When we substitute -16 into the equation, we get:

28 = -16 - 12

Simplifying, we get:

28 = -28

This is not a true statement, so -16 is not a solution of the equation.

Therefore, the only solution of the equation 28 = d - 12 is d = 40.

Step-by-step explanation:

1. w=4 v=-3

2. y=6 x=-2

4. m=6 p=3

5. b=-2 a=4

7. c=8 d=-7

8. g=-3 f=5

10. j=2.5 k=4

11. x=4 y=1.5

13. x=2 y=1

14. y=6 x=5

[tex]\textit{height of an equilateral triangle}\\\\ h=\cfrac{s\sqrt{3}}{2}~~ \begin{cases} s=\stackrel{length~of}{a~side}\\[-0.5em] \hrulefill\\ h=4\sqrt{3} \end{cases}\implies 4\sqrt{3}=\cfrac{s\sqrt{3}}{2} \\\\\\ 8\sqrt{3}=s\sqrt{3}\implies \cfrac{8\sqrt{3}}{\sqrt{3}}=s\implies 8=s[/tex]

the dimensions of the table runner are  [tex]20[/tex] inches in length and [tex]4[/tex] inches in width.

Let's denote the width of the table runner as "w" inches. Since the length is 5 times greater than the width, the length would be 5w inches.

The area of a rectangle is calculated by multiplying its length by its width. Given that the area of the table runner is 80 square inches, we can set up the following equation:

Length × Width = Area

[tex](5w) \imes w = 80[/tex]

Simplifying further:

[tex]5w^2 = 80[/tex]

Dividing both sides by 5:

[tex]w^2 = 16[/tex]

Taking the square root of both sides:

w = ±4

Since the width cannot be negative in this context, we discard the negative value. Therefore, the width (w) of the table runner is [tex]4[/tex] inches.

Substituting this value back into the equation for length:

Length   [tex]= 5w = 5 \times 4 = 20[/tex] inches

So, the dimensions of the table runner are  [tex]20[/tex] inches in length and 4 inches in width.

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Answer:

1/6 of flowers were blue

In this expression, the GCF is 5. Therefore, we can factor out a 5 to get 5(x² - y²).

The difference of squares formula states that the difference of two squares can be factored into the product of two terms, one of which is the sum of the terms and the other is the difference of the terms.

When factoring polynomials, it is important to factor out the greatest common factor (GCF).

In this expression, the GCF is 5.

Therefore, we can factor out a 5 to get 5(x² - y²).

Now, we can expand the parentheses and factor out the remaining terms. Since both terms are perfect squares, we can factor them using the difference of squares formula:

5(x² - y²) = 5(x + y)(x - y)

In this case, the terms are x and y, resulting in the factorization of  5(x² - y²) into 5(x + y)(x - y).

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Answer:

3/6, 4/8, 5/10, 6/12, 7/14, 8/16, 9/18, 10/20, etc...

Step-by-step explanation:

The left digit it always half of the one on the right, increasing by one every time.

1/2 ===> 2/4 ===> 3/6 ===> 4/8...

The function g(x) is a cubic function, which is a transformation of the cube root parent function, f(x) = 3√x. The equation for g(x) is g(x) = 3x3, where a = 3, b = 0, c = 0, and d = 0.

Function is a set of instructions or commands that can be used to perform a specific task. It is a reusable code that can be used over and over again to perform a similar task. Functions are used to structure programs, making them easier to read, understand, and debug. Functions are also used to divide a large program into smaller, more manageable parts.

The function g(x) is a cubic function, which is a transformation of the cube root parent function, f(x) = 3√x. A cubic function is a polynomial of degree 3, where the highest exponent of the variable is 3. The general equation for a cubic function is y = ax3 + bx2 + cx + d, where a, b, c, and d are constants. This equation can be rearranged to express the function in terms of x, as follows:

g(x) = ax3 + bx2 + cx + d

By plugging in the values for f(x), we can determine the values of a, b, c, and d. We can start by setting f(x) equal to g(x).

3√x = ax3 + bx2 + cx + d

By taking the cube root of both sides, we can determine the value of a:

a = 3

Next, we can substitute this value into the equation for g(x):

g(x) = 3x3 + bx2 + cx + d

From this, we can see that b = 0, c = 0, and d = 0. Therefore, the function g(x) is a cubic function with equation g(x) = 3x3.

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We need to collect 46 newspapers to be certain that at least two newspapers have the same number of pages.

According to the Pigeonhole Principle, if we have n+1 pigeons and n holes, then there must be at least one hole with two or more pigeons. Similarly, if we have n+1 newspapers with n possible page counts, then there must be at least one page count that appears in two or more newspapers.

In this case, we have a range of 38 possible page counts (46 - 9 + 1), so we need at least 39 newspapers to guarantee that each possible page count appears in at least one newspaper.

However, to guarantee that at least two newspapers have the same number of pages, we need one more newspaper than the number of possible page counts, so we need a total of 46 newspapers. Therefore, if we collect 46 newspapers, we can be certain that at least two of them have the same number of pages.

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