Which of the following is equivalent to the quadratic equation below after completing the square?
x² +6x-3=12
A. (x+6)² = 12
B. (x+3)² = 24
C. (x+6)² =9
D. (x+3)² = 9​

Using the table your total monthly fixed expenses is 977.43.

Rent payment $953. 20/month

Auto payment $165. 87/month

Telephone $56. 98/month

Auto insurance $714. 36/six months

Once-a-week outing $35. 00/week

= 953.20 + 165.87 + 56.98 + 714.36/6 + (35*4)

= 1435.11

= 2412.54 - 1435.11

=977.43.

An expense is something that calls for the transfer of funds, or fortune in general, from one person or organization to another as payment for a good, service, or other type of cost. Rent is a cost to a tenant. Tuition is a cost to parents or students. Purchasing anything like food, clothing, furniture, or a car is frequently referred to as a cost.

A cost that is "paid" or "remitted" usually in exchange for anything of value is referred to as an expense. "Expensive" refers to something that appears to be very expensive. "Inexpensive" refers to something that appears to be inexpensive. "Expenses of the table" include costs associated with eating, drinking, a feast, etc.

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The polynomial whose real zeros and degree are given will be x(x + 1)(x - 6). And the remaining zeroes of f(x) will be - 7i.

Let a, b, c, and d are the zeroes of the polynomial.

Then the polynomial is given as,

⇒ (x - a)(x - b)(x - c)(x - d)

The degree of the polynomial will be greater than or equal to the number of zeroes.

Form a polynomial whose real zeros and degree are given.

Zeros: -1, 0, 6 and Degree: 3

Then the polynomial is given as,

⇒ (x + 1)(x + 0)(x - 6)

⇒ x(x + 1)(x - 6)

Information is given about a polynomial​ f(x) whose coefficients are real numbers.

Degree​ 4; ​ zeros: 7i, 2, -2

The last root will be opposite to the 7i and will be - 7i.

The polynomial whose real zeros and degree are given will be x(x + 1)(x - 6). And the remaining zeroes of f(x) will be - 7i.

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The total cost of the bridge will be (200/2) × 8 × 1000 + 50 × 10 + 500 = $90,000.

The formula for calculating the cost of a bridge is Cost = (Area of Bridge/2) × Unit Weight of Steel × Unit Price of Steel + Cost of Labor + Cost of Other Materials. By using this formula, we can determine the total cost of the bridge by considering the area of the bridge, the weight of the steel used, the price per unit of steel, the cost of labor, and the cost of other materials. For example, if the area of the bridge is 200m^2, the unit weight of steel is 8 tonnes/m^3, the unit price of steel is $1000/tonne, the cost of labor is $50 per hour, and the cost of other materials is $500, then the total cost of the bridge will be (200/2) × 8 × 1000 + 50 × 10 + 500 = $90,000. Thus, by using this formula, we can easily calculate the cost of the bridge and understand why local politicians are dragging their feet in building a new bridge.

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Answer: Editorial is data is the correct answer.

Step-by-step explanation: I took test and it is confirmed correct.

The height of the helium tank is; Option D: 36 inches

The formula for the volume of a cylinder is;

V = πr²h

Where;

V is volume

r is radius

h is height

We are given;

Radius(r) = diameter/2 = 12/2

r = 6 inches

Volume; V = 1296π in³

1296π = π * 6² * h

h = 1296/36

h = 36 inches

We conclude that is the height if the helium tank

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Answer:

its height is 36 inches

Step-by-step explanation:

The algebraic expression that corresponds to the sentence "I think of a number, subtract 4, then divide by three" is given as follows:

(n - 4)/3.

The sentence for this problem is given as follows:

"I think of a number, subtract 4, then divide by three".

The number is unknown, hence the variable used to represent the number is given by n.

Then the subtraction of the number n by 4 is represented by the expression presented as follows:

n - 4.

The division of the entire expression by 3 means that the parenthesis has to be applied to (n - 4), due to the precedence of operators, hence:

(n - 4)/3.

The problem asks for the algebraic expression that represents the sentence.

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Answer (vertex form): y=4(x+2)^2 - 11

Answer (standard form): y=4x^2 + 16x + 5

A 1-factor graph is a graph that can be decomposed into one or more 1-factors. In other words, a 1-factor graph is a graph that can be partitioned into disjoint perfect matchings.

In graph theory, a 1-factor is a subgraph of a graph that forms a perfect matching, or 1-factorization. A perfect matching is a set of edges in a graph such that each vertex is incident to exactly one edge in the set. A 1-factorization of a graph is a collection of perfect matchings such that every vertex is included in exactly one perfect matching.

The study of 1-factors and 1-factorizations is an important area of graph theory because of its connections to other areas of mathematics such as algebra, combinatorics, and statistical physics. It has various applications including coding theory, scheduling, and transportation networks.

1-factor graph theory is the study of graphs that can be decomposed into 1-factors and the properties of such graphs. This field of study helps to understand the conditions under which a graph can be decomposed into 1-factors and the properties of such graphs.

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The largest number that divides two or more numbers evenly is greatest common divisor (GCD).

The biggest positive number that divides any non-zero integer by two or more is known as the greatest common divisor.

The greatest common divisor is the biggest number that divides two or more numbers proportionally (GCD).

Using the LCM method, the steps to calculate the GCD of (a, b) are as follows:

Find the result of a and b in step 1.

Find a and b's least common multiple (LCM) in step two.

Step 3: Dividing the results of Steps 1 and 2.

Step 4: The value that results from division is the most significant common divisor of (a, b).

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The percentage of the 90 students on the Springfield High School varsity soccer team who are seniors is 31%.

The percentage is a portion of a whole number or value.

Using percentages is a way of expressing values compared to others in relative terms.

The percentage refers to the ratio, which is obtained as the quotient of a numerator and a denominator, which is then multiplied by 100.

The total number of students on the Springfield High School varsity soccer team = 90

The makeup of the soccer team = freshmen, sophomores, juniors, and seniors

The number of seniors on the soccer team = 28

The percentage of seniors on the soccer team = 31.11% (28/90 x 100)

Thus, we can conclude that about 31 percent of the soccer team consists of seniors.

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We may use the ratio of length to width and the new length of the image to determine the width of the enlarged image.

Step 1: The original image's length to width ratio is 5:2, which may be expressed as 5/2.

Step 2: We are aware that the enlarged image is 15 inches long.

Step 3: We may apply the formula length/width = new length/new width to determine the width of the enlarged image. The known values of the original ratio and the new length can be substituted in: 5/2 = 15 inches / new width.

Step 4: To find the new width, we must cross multiply and divide, so multiply the new width by 5/2 to get 15 inches, and divide both sides by this number to get 6 inches.

  Therefore, The expanded image has a 6 inch width.

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The value of Double integral will be [tex]\mathrm{I}=4 \int_0^4 \ln |1+\mathrm{x}| \mathrm{dx}[/tex]

A two-dimensional region can be integrated using double integrals. They enable us to, among other things, calculate the volume beneath a surface.

The integrals of a function in two variables over a region in R2, or the real number plane, are referred to as double integrals in mathematics. It is possible to write the double integral of a function of two variables, such as f(x, y), over a rectangular region as: R f (x, y) d A = R f (x, y) d x d y.

We know that by the property of integral [tex]$\int u \mathrm{udv}=u v-v \int d u$[/tex]

[tex]$$\begin{aligned}& \mathrm{I}=4 \int_0^4 \ln |1+\mathrm{x}| \mathrm{dx}=\left[\mathrm{x} \ln (1+\mathrm{x})-\int \mathrm{x} \frac{.1}{1+\mathrm{x}} \mathrm{dx}\right]_0^4 \\& \mathrm{I}=4\left[\mathrm{x} \ln (1+\mathrm{x})-\int\left(1-\frac{1}{1+\mathrm{x}}\right) \mathrm{dx}\right]_0^4 \\& \mathrm{I}=4[\mathrm{x} \ln (1+\mathrm{x})-\mathrm{x}+\ln |1+\mathrm{x}|]_0^4 \\& \mathrm{I}=[4 \ln (5)-4+\ln (5)]-[0-0+0] \\& \mathrm{I}=4[5 \ln 5-4] \\& \mathrm{I}=20 \ln 5-16\end{aligned}$$[/tex]

We have to evaluate the given double integral

[tex]$$\iint_{\mathrm{R}} \frac{4 \mathrm{x}}{1+\mathrm{xy}} \mathrm{dA} \text { where } \mathrm{R}=[0,4] \times[0,1]$$[/tex]

[tex]$$\begin{aligned}& \mathrm{I}=\int_0^4 \int_0^1 \frac{4 \mathrm{x}}{1+\mathrm{xy}} \mathrm{dydx}=\int_0^4 4 \mathrm{x}\left[\frac{|1+\mathrm{xy}|}{\mathrm{x}}\right]_0^1 \mathrm{dx} \\& \mathrm{I}=\int_0^{44}[\ln |1+\mathrm{x}|-0] \mathrm{dx}=4 \int_0^4 \ln |1+\mathrm{x}| \mathrm{dx}\end{aligned}$$[/tex]

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Answer: 33 - g = 56

less than means -

is means =

This depends on the size of the room. If the room is an average sized bedroom, it will likely take him around 4 to 6 hours to paint the entire room.

1. The first step is to identify the size of the room.

2. Once the size is identified, it is necessary to calculate the total amount of time it would take to paint the entire room.

3. The time it takes to paint a room is dependent on the size of the room, the type of paint used, and the quality of the painter.

4. If the room is an average size bedroom and Marcus is an experienced painter, it should take him between 4 to 6 hours to paint the entire room.

This depends on the size of the room. If the room is an average sized bedroom, it will likely take him around 4 to 6 hours to paint the entire room.

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The given statement is untrue about Pat. Therefore, it is invalid.

If each of the premises must be true in order for the conclusion to be true, the argument can only be validated if it does so. The term "valid" refers to a statement that is true, whereas the term "invalid" refers to a statement that is untrue.

The given situation is an invalid one. Because it's still feasible for Pat to be a woman, even if the premise is accurate. She could be a single woman. Because of this, the premise cannot be used to prove that she is a woman.

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The exact value of cos I in simplest radical form is 5 /√29

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

The exact value of cos I in simplest radical form can be found by using trigonometric ratios.

cos I = adjacent / hypotenuse

The opposite is where the angle I is facing. That is opposite = 2

The hypotenuse is where the right angle is facing. That is hypotenuse = √29

The adjacent is the side left after picking opposite and hypotenuse. That is adjacent = 5

cos I = 5 /√29

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Answer: 60in²

Step-by-step explanation:

Answer: 60

Step-by-step explanation:

So to solve this, you need to know how to find the area of a trapezoid.

In case you don't know this equation, I'll explain it briefly.

The area of a trapezoid = (a+b)*h/2, where a and b are the base lengths and h is the height of the trapezoid.

We can solve this problem using this equation, which would look like:

Area = (9+11)*6/2

= 20*6/2

= 60

Answer: 4xy²(5-y)

Step-by-step explanation:

To factorize, we must take out common multiples in both parts of the equation. Think of 20xy² and -4xy³ as two completely separate parts. Now, we need to see which parts of the equation are found in both. For instance, 4 can go into both, an x can go into both, and y² can go into both. Now, we simply factor.

Bring the similarities out to the front: 4xy²()

Now, use division to find what would be inside the parenthesis: 5 - y

Now, combine these two parts: 4xy²(5-y)

To check your work, you can simply multiply the outside of the parenthesis by the inside, and you should get the same as what you started with. Hope this helps!

The rate of change of the radius is -9/(2π*99) inches/second.

The volume of a cylinder can be found with the equation V = πr^2h, where V is the volume, r is the radius, h is the height and π is a constant. We know that the volume is constant at 1318 cubic inches and we know that the height of the cylinder is increasing at a constant rate of 9 inches per second.

V = πr^2h

1318 = π * 99^2 * h

Now we can differentiate this equation with respect to time.

dV/dt = 2πr*dr/dt * h + πr^2 * dh/dt

where dV/dt is the rate of change of the volume, dr/dt is the rate of change of the radius and dh/dt is the rate of change of the height.

Now we know that dV/dt = 0, dh/dt = 9 and we know the value of r, we can substitute these values in the above equation and solve for dr/dt

0 = 2π * 99 * dr/dt * h + π * 99^2 * 9

dr/dt = -9/(2π*99) inches/second

The rate of change of the radius is -9/(2π*99) inches/second at the instant when the radius of the cylinder is 99 inches.

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Answer: 5

Step-by-step explanation:

We are looking for the number of years below the 25th percentile, which is given by the first quartile.

Since the first quartile is 5, we know that about 25% of Carlson High School teachers have fewer than 5 years of experience.

The measurements of all the angles, if one angle is a right angle (90 degrees), and the second angle's measurement is six times smaller than the third angle's measurement of 180 degrees.

As per the data given in the above question are as bellow,

The data provided are as bellow.

The known angle (90) a pronumeral of r.

give the second angle (the one with all the subtraction) a pronumeral or x.

The third angle the pronumeral of y

x = 7y - 6

90 + x + y = 180

90 + 7y - 6 + y = 180

90 + 8y - 6 = 180

90 + 8y =186

8y = 96

y = 12.  

the third angle is 12

so 12 + 90 = 102

the second angle must equal 88 to make it to 180

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Note the correct question is as bellow,

Given a right triangle, find the measures of all of the angles, if one angle is a right angle (90 degrees) and the measure of the second angle is six less than seven times the measure of the third angle. This is represented by the equation x=7y - 6

The information shows that f(4)=f(30) tells us that the weight of a particular female panda at 4 years old is the same as her weight at 30 years old.

It is a mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable).

In this case, Dr. Coleman is a zoologist who studies giant pandas. Giant pandas are very tiny when they are born but grow to be quite large. The function f(x) gives the weight, in pounds, of a particular female panda when she was x years old.

The function illustrated shows that the weights are the same.

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All three parts of the given problem regarding trails, paths and walks have been solved below.

A path is defined as a way in which we can traverse the graph such that neither vertices nor the edges are repeated. In the given graph we can see that for going from a to c there are 4 ways that satisfy the condition of a path. A Trail is an open walk in which no edge is repeated but the vertex can be repeated. So, in the given graph we can see that there are 3!(4) ways in which we can go from a to b and then c and 4 paths in which we can go directly from a to c.

The walk is a sequence of vertices and edges of a graph that can be closed if we come to the same point after traversing the graph or open if we go from one point to another. In the given graph since we go from a point to c point the walk is open but the length of edges of the walk is not defined so if we take the no. of edge length to be 4

there can be 44 ways

so,

number of paths from a to c = 4

number of trails from a to c = 4+3!(4)= 28

number of paths from a to c = 4+3!(4)+2!(6)+1!(4)= 44

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The interpretation of the value, 29,864, in the quadratic regression equation is the initial loss incurred by the company. The correct option is therefore;

A quadratic regression equation is the equation of the parabola that corresponds of best fits the points of the dataset on the coordinate plane.

The points on the graph of the question, obtained from a similar question, posted online are;

Number of units [tex]{}[/tex]           Profits ($)

500 [tex]{}[/tex]                         -10000

1200  [tex]{}[/tex]                   3000

2500  [tex]{}[/tex]                   27000

3200  [tex]{}[/tex]                   40000

3600  [tex]{}[/tex]                   45000

4300  [tex]{}[/tex]                   47000

5000  [tex]{}[/tex]                   45000

6750  [tex]{}[/tex]                   20000

The polynomial regression equation that corresponds to the points in the above table, obtained with MS Excel is presented as follows;

y = -0.004·x² + 34.637·x - 29864

Where;

y = The profit made

x = Number of units

When the company produces 0 units, x = 0, we get;

The 29864 is therefore the loss of $29864, of the company when the company produces zero units.

The correct option is therefore;

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The inequality that satisfies the number of hours of volunteer work that saul could complete each month to meet his goal is 21 hours.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

Different types of inequalities are represented by a variety of notations, including:

The symbol a <  b indicates that a is smaller than b.

When a > b is used, it indicates that an is bigger than b.

Given,

Hours Saul plans to volunteer in the 9-month period = 225 hours

Also,

Hours of volunteering he has already completed = 36 hours

=> Number of hours left = 225 - 36 =189 hours

Number of months= 9

=> Minimum number of hours he has to volunteer per month

=> [tex]\frac{Number of hours left}{Number of months}[/tex]

=>[tex]\frac{189}{9}\\ 21 hours[/tex]

=>Minimum number of hours saul has to volunteer per month ≥ 21 hours

Therefore, The number of hours of volunteer work that saul could complete each month to meet his goal is 21 hours.

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Therefore , the solution of the given problem of interest rate comes out to be $271.94 you will be depositing every month.

The original capital is multiplied by the interest rate, the loan term, and other factors to calculate simple interest. A simple return is equal to the principal plus interest hrs. This method of calculating interest is the simplest. The most typical method is to calculate it as a fraction of the principal amount. For instance, he was only liable for paying his portion of the interest if he acquired $100 from a buddy and agreed to repay the money on 5% interest. $x (0.05) = $5. When you make loans or lend money, you both have to pay interest. Interest is frequently determined as a percentage of a loan.

Here,

Given  :  interest = 9%

time  =35 years

amount = 800000

Using formula :

=> FV.( r / [tex](1+r) ^{n}[/tex] -1)

=>  800000 (0.09/12 / [tex](1 + 0.09/12 )^{12*35}[/tex] - 1 )

=> 271.94

Therefore,

the total amount you deposit will only be

=> 35*12 times $271.94, or

roughly total amount => 35*12*271.94= 114214.8 dollars, out of the estimated $800,000.

The balance will be what the account earns or accumulates over the next 35 years.

Therefore , the solution of the given problem of interest rate comes out to be $271.94 you will be depositing every month.

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Big boxes have 1/4 of 20 gigabytes of ram will be 5 gigabytes.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Big boxes have 1/4 of 20 gigabytes of ram.

Then the multiplication of the numbers 1/4 and 20 will be given by putting a cross sign between them. Then we have

⇒ (1/4) x 20

⇒ 20 / 4

⇒ 5 gigabytes

Big boxes have 1/4 of 20 gigabytes of ram will be 5 gigabytes.

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No , it is not possible to draw a triangle with the given side length of 4cm , 3cm , and 7cm as sum of two sides ( 4cm + 3cm ) is not greater than the third side ( 7cm).

As given in the question,

Measure of the required triangle are given as follow:

Measure of Side length 1 = 4cm

Measure of Side length 2= 3cm

Measure of Side length 3 = 7cm

To draw a triangle following condition need to be satisfied:

Sum of the measure of two side length is always greater than the measure of the third side length.

Here for a given triangle ,

4cm + 3cm

= 7cm

= measure of the side length 3

It does not satisfied the required property to draw a triangle.

Therefore, it is not possible to draw a triangle with given measurements as ( 4cm + 3cm ) is not greater than the third side.

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Answer:

Step-by-step explanation:

Since the line segment RST is perpendicular to OM, the length of RT can be determined by using the Pythagorean Theorem.

Let RT = x

We know that:

OS = OM - OS = 7 cm

Using the Pythagorean Theorem, we can solve for x:

x^2 = OS^2 + RT^2

x^2 = (7 cm)^2 + x^2

2x^2 = 49 cm^2

x^2 = 24.5 cm^2

x = √24.5 cm = 4.94 cm

Therefore, the length of RT = 4.94 cm

Answer:

Step-by-step explanation:

120 degrees per angle - It says that it's a *regular* hexagon

The conditions for constructing a t-confidence interval are met.

In order to construct a t-confidence interval for the mean amount of time the students spend completing the homework assignment, the following conditions must be met:

The data must be a random sample from the population of interest
The sample size must be sufficiently large (typically, n > 30)
The data should be approximately normally distributed
The population standard deviation or variance must be unknown
From the information provided it can be inferred that the data is a random sample (30 students out of 75 students) and that the population standard deviation or variance is unknown. If the sample size is greater than 30, and the data is approximately normal or the sample size is large, then the conditions for constructing a t-confidence interval are met.

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