Solve the quadratic equation by completing the square
X^2+14x+35=0
First choose the appropriate form and fill in the blanks with the correct numbers
Then solve the equation if there is more than one solutionseparate them with commas

Answer: 7 1/2 minutes

Answer:

7.5 mins.

Step-by-step explanation:

We know the unit rate is 1.5 mins for 1 km. So we can just multiply both numbers by 5.

1.5/1 = 7.5/5

It takes a shark 7.5 (7 1/2) minutes to swim 5 km.

Answer:

p = 6 , q = 43

Step-by-step explanation:

x² + 12x - 7

using the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² + 12x

=x² + 2(6)x + 36 - 36 - 7

= (x + 6)² - 43 ← in the form (x + p)² - q

with p = 6 and q = 43

The graph of f(x) is the second one, so the correct option is B.

Here we have f(x), a piecewise function, and we want to see which one of the four graphs is the correct one.

You can see that the first domain of the function is:

x ≤ -4

So we must have a closed circle at x = -4, when the parabola ends.

The second domain is:

-4 < x < 1

So x here is not equal to -4 nor 1, so this part starts and ends with open circles.

finally, the linear part starts with a closed circle.

Also, notice that the line has a negative slope, so it goes down, then we can discard the first option.

Then we can see that the correct option is the second graph.

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Answer:

No

Step-by-step explanation:

The surface area of a cylinder is 284m² and it's volume is 366.9m³

To find the surface area and volume of a cylinder, we need to know the radius (r) and height (h) of the cylinder. The formulas for the surface area (A) and volume (V) of a cylinder are as follows:

From the given question, the data are;

a. The surface area of the cylinder is;

SA = 2π(4)² + 2π(4)(7.3)

SA = 283.999≈284m²

b. The volume of the cylinder is

v = πr²h

v = π(4)²(7.3)

v = 366.9m³

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The figure verifies triangle inequality theorem: B. by showing that the sides with lengths of 7 and 4 will only meet when they lie on the third side.

In Euclidean geometry, the triangle inequality theorem states that the sum of any two (2) sides of a triangle must be greater than or equal (≥) to the third side of the triangle.

Mathematically, the triangle inequality theorem is given by this expression (a + b ≥ c).

In this context, we can logically deduce that the figure would verify triangle inequality theorem by showing that the sides with lengths of 7 and 4 would only meet when they lie on the third side of the triangle.

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Step-by-step explanation:

the center of the circle is the midpoint of the diameter.

and the radius is the distance of the midpoint to either endpoint (or simply half of the distance between the diameter endpoints).

the midpoint between points A and B

(xm, ym) = ((xa + xb)/2, (ya + yb)/2)

in our case the midpoint (center of the circle) is

((-6 + 2)/2, (10 + 3)/2) = (-4/2, 13/2) = (-2, 6.5)

about the radius

diameter² = (-6 - 2)² + (10 - 3)² = (-8)² + 7² = 64 + 49 =

= 113

diameter = sqrt(113) = 10.63014581...

radius = diameter / 2 = 5.315072906... ≈ 5.315

After answering the presented question, we can conclude that expressions Therefore, the population of the rural city in 2030 is approximately 11,014.18.

In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the expression 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.

To approximate the population in 2030, we need to find the value of P(t) when t = 44, since 2030 is 44 years after 1986.

Using the given exponential growth model, we have:

\(P(t) = 3400^(0.0371t)\\P(44) = 3400^(0.0371*44)\\P(44) = 3400^1.6334\\P(44) = 11014.18\\\)

Therefore, the population of the rural city in 2030 is approximately 11,014.18.

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1) Sum = x + (x+5) = 2x + 5 years

2) Difference = 2x + 5 - (x + 25) = 2x + 5 - x - 25 = x -20

The neighborhood can help children build new relationships by holding a winter festival with activities for children and families.

In today's world, where everyone is quite busy in their own world, children have academic pressure and many more.

They tend to detach themselves from people, and hence many relationships ruin.

Building relationship helps the children grow and makes them more sociable. It boots their intelligence and makes them aware of the importance of having a relationship and building bonds with people.

The neighborhood holds a winter festival with activities for children and families is a great way to build new relationships.

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complete question:

Which of the following describes a way that neighborhoods help children build new relationships?

OA neighborhood holds a winter festival with activities for children and families.

O Families of the neighborhood walk around the block on differing weeknights.

O Lawn crews ensure that the neighborhood is properly maintained each week.

O Members of the community form a Neighborhood Watch team.

To solve the equation 7(x + 3) = 7(x + 5), we can start by simplifying both sides of the equation:

7x + 21 = 7x + 35

Subtracting 7x from both sides, we get:

21 = 35

This is a contradiction, as 21 is not equal to 35. Therefore, the equation has no solution.

However, the problem states that the equation has an infinite number of solutions. This can only happen if the missing number is a factor that appears on both sides of the equation, and therefore cancels out when we simplify the equation.

Looking at the equation, we can see that both sides have a factor of 7, which cancels out when we simplify the equation. Therefore, the missing number must be the factor that was torn off, which is 7 multiplied by the difference between the two numbers inside the parentheses:

7(5 - 3) = 14

Therefore, the missing number is 14, which corresponds to answer option B.

The tangent point of the line, given the center of the circle can be found to be  ( 5.39, -10.07).

We have the equation of the tangent line as 4x + 5y = -29 and the center of the circle as (-2, 4).

Equation of the line containing the radius as:

y - 4 = (5/4)(x - (-2))

y - 4 = (5/4)(x + 2)

Solving the system of equations:

y = (-4/5)x - 29/5

y - 4 = (5/4)(x + 2)

Eliminate y by substituting the first equation into the second:

(-4/5)x - 29/5 - 4 = (5/4)(x + 2)

Now, solve for x:

(-4/5)x - 29/5 - 20/5 = (5/4)x + 10/4

(-4/5)x - (5/4)x = 10/4 + 49/5

(-16/20)x - (25/20)x = 25/4 + 196/20

(-41/20)x = 221/20

x = 221/41

Now, find the y-coordinate by plugging the value of x into one of the equations. Let's use the first equation:

y = (-4/5)(221/41) - 29/5

y = (-884/205) - 1181/205

y = -2065/205

The tangent point is (221/41, -2,065/205) or ( 5.39, -10.07).

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The required numbers should be changed only by a unit, as proceeding from ten to 1 hundred.

Given that,
To determine how much each number needs to change for a ten for 1 hundred.

A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing the numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.

Here,
According to the question,
The number from ten to 1 hundred,
10, 11, ......,99, 100.
From the above series, it can be concluded that each number is greater than by unity from the previous number.

Thus, hte required numbers should be changed only by a unit, as proceeding from ten to 1 hundred.

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The class width used for the frequency distribution is 6.

The class midpoint for the class 23-29 is 26.

The class midpoint for the class 30-36 is 33.

The class midpoint for the class 37-43 is 40.

To find the class width of the frequency distribution, we need to determine the range of each age class. The range is the difference between the upper and lower boundaries of each class. Looking at the table, we can see that the class boundaries are as follows:

23-29

30-36

37-43

For the class 23-29, the lower boundary is 23 and the upper boundary is 29. To find the class width, we subtract the lower boundary from the upper boundary:

Class width = 29 - 23 = 6

So, the class width for the frequency distribution is 6.

To find the class midpoint for each class, we take the average of the lower and upper boundaries of each class.

For the class 23-29:

Class midpoint = (23 + 29) / 2 = 52 / 2 = 26

For the class 30-36:

Class midpoint = (30 + 36) / 2 = 66 / 2 = 33

For the class 37-43:

Class midpoint = (37 + 43) / 2 = 80 / 2 = 40

So, the class midpoint for the class 23-29 is 26, for the class 30-36 is 33, and for the class 37-43 is 40.

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Mary owes $13564 income tax.

Governments apply income taxes as a sort of tax on the income produced by people and businesses under their control. Government duties, public services, and citizen goods are all paid for through income tax revenue.

Given that the taxable income is $68,562.

Income tax is the tax charged on an individual's or entity's income

Using the table as a guide, $68,562 falls within the income range $31,850 - $77,100

So, the tax is $4386 added to 25% of the excess over $31850

This is calculated as:

tax = $4386 + 25%(income - 31,850)

In our case,

income = $68562

Substitute $68,562 for income

Tax = $4386 + 25%(68,562 - 31,850)

Solve the expression in the bracket

tax = 4386 + 9178

Add the terms of the expression

tax = 13,564

therefore, Mary owes $13564 in income tax.

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The value of n can be determined by finding the number of visible arcs in the pattern, which is 30 in this case.

To determine the value of n, we need to find the relationship between the total length of visible areas and the number of circles (n).

In the given pattern, each circle contributes to the visible area twice: once as its circumference and once as the overlapping part with the adjacent circles. Since the circumference of each circle is 1 unit, the visible area contributed by each circle is 2 units.

Therefore, the total length of visible areas can be expressed as 2n. Given that the total length is 60 units, we can set up the equation:

2n = 60

Solving this equation, we find:

n = 60/2 = 30

Thus, the value of n is 30.

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Answer:

c

Step-by-step explanation:

how you gonna give me 20 if you listed it as 10

Answer:

D

Step-by-step explanation:

4(2000)=8000; 4(300)=1200; 4(20)=80; 4(6)=24

Answer:20

Step-by-step explanation:

Answer:

6 rows have 5 desks.

6 + 2 = 8 rows have 4 or 5 desks.

The ratio is 6:8 = 3:4.

Lee's TV costs $4.05 to operate for a month of 30 days.

To calculate the cost of operating Lee's TV for a month, we need to find out the total number of kilowatt-hours (kWh) of electricity consumed by the TV during that time.

First, let's find out how many watts Lee's TV consumes in a day:

250 watts/hour x 3 hours/day = 750 watts/day

To convert this to kilowatts, we divide by 1000:

750 watts/day ÷ 1000 = 0.75 kilowatts/day

Now, we can calculate the total number of kilowatt-hours consumed by the TV in a month:

0.75 kilowatts/day x 30 days = 22.5 kilowatt-hours

Finally, we can calculate the cost of operating the TV for a month:

22.5 kilowatt-hours x 18 cents/kilowatt-hour = $4.05

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Answer:

W = 54.7*e^0.038t

11.6 years

Step-by-step explanation:

Given that :

Initial value = 54.7 trillion dollars

Continuous Growth rate (r) = 3.8% = 0.038

Using the exponential growth model formula :

W = P0*e^kt

Where ;

y = final amount ; P0 = initial value ; t = time ; k = growth rate constant

W = 54.7*e^0.038t

Value of t when W = 85 trillion

W = 85

85 = 54.7*e^0.038t

85 / 54.7 = e^0.038t

1.5539305 = e^0.038t

Take In of both sides

0.4407875 = 0.038t

Divide both sides by 0.038

t = 11.599672

t = 11.6 years

Answer:

2/3 (x-12)

Step-by-step explanation:

2/3x-8

2/3(x-3x4)

2/3(x-12)

The given question is incomplete as the graph is missing.

But, considering a line graph, the following parameters can be represented on the x-axis and y-axis:

X-Axis                                                     Y-Axis

Year                                                         Population

Time                                                         Number of employees hired

Identical items purchased                      Total cost in dollars    

What does the blank observed line represent in each graph?  

The blank observed line represents the time. A line graph is basically used to connect the quantitative values over the different time intervals. The change in values over time is easier to estimate, by the help of the line graph. For example: in a graph showing the year on the x-axis and the population on the y-axis, the blank line represents the change in population over the years, the increase or decrease or the rate of change.  

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Answer:

the answer is D. F(x) = 1/x(x-3)

Step-by-step explanation:

Answer:

x = 2 and x = 4

Step-by-step explanation:

The solution of the given equation is shown on the graph

There are two intercepts with coordinates of

The x-coordinates are

Correct option is 3 or C.

Answer:

C

Step-by-step explanation:

On the graph, you can see that we are given two points; (2, 2) and (4, -22)

Since we are looking for the value of "x", we need the x value of the given points.

The x values in both points are 2 and 4. Thus are the solutions.

Best of Luck!

Answer:

  (d)  (1, 2)

Step-by-step explanation:

You want to know which of the given points satisfies the inequality.

We find it easiest to plot the given points on a graph of the solution. This shows us that (1, 2) is a solution to the inequality. (It lies in the solution area.)

__

Additional comment

Another way to choose the answer is to try each of the points in the inequality.

If you can visualize the boundary line (without plotting it) as a line with positive slope and a y-intercept of 2, you can more readily reject the first choice and accept the last choice. (0, 3) is above the y-intercept, and (1, 2) is to the right of it (in the solution space).

You may also recognize the x-intercept will be -3, so the second choice lies above the boundary line.

The graph in the attached picture shows

The number of calories per minutes

We can see the line passes through points (0, 0) and (10, 200)

Then to find the number of calories per minute, divide the y-coordinate by the x-coordinate in the second point

(a) To find the number of minutes, reverse the answer above

Minutes per calorie = 1/20

(b) The slope of the line is the value of calories per min

Then the slope is 20 calories per min

The slope of the graph is 20

Answer:

i think the answer is B, good luck

Answer:

c i do believe good luck with the answer

A statement that correctly compares the graph of function g with the graph of function f include the following: C. The graph of function g is a vertical compression of the graph of function f.

In Mathematics and Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.

Therefore, the dimension or side lengths of the dilated geometric object would be stretched or compressed (shrunk) depending on the scale factor that is applied.

When the parent function \(f(x) = e^x -4\) is vertically compressed by a scale factor of 1/2, the transformed function g(x) is given by the following equation;

g(x) = kf(x)

g(x) = 1/2f(x)

\(g(x) = \frac{1}{2} e^x -4\)

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