find the degree of the term. 7x^2

ANSWER

x = 4; 5x + 1 = 21

EXPLANATION

First, we have to find the value of x using the given equation,

To do so, divide both sides by 2,

Now, with x = 4, replace it into the expression given to find its value,

Hence, the value of the expression is 21.

By solving a quadratic equation we can see that the width of the path measures 20 meters.

We know that the pool measures 18 meters by 20 meters, then the area of the pool alone is:

A = 18m*20m = 360 m^2

Now, if the path has a width x, then the rectangle that includes the path and the pool has dimensions:

(18m + 2x) and (20m + 2x)

And its area is given by:

(18m + 2x)*(20m + 2x)

And we know it is equal to 1520 m^2, then (i'm not writting the units in the computation):

(18 + 2x)*(20 + 2x) = 1520

360 + 4x^2 + 76x = 1520

Now we just need to solve that quadratic equation:

4x^2 + 76x - 1520 + 360 = 0

4x^2 + 76x - 1160 = 0

The solutions are:

x = (-76 ± √(76^2 - 4*4*(-1160))/(2*4)

x = (-76 ± 156)/4

We only care for the positive solution, which gives:

x = (-76 + 156)/4 = 20

We conclude that the width of the path measures 20 meters.

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Joanne, as the store manager at Glitter, is exercising her legitimate power that she obtains from her position of authority.

Legitimate power refers to the authority that comes with a specific role or position within an organization. In this case, Joanne's role as store manager grants her the power to make decisions and direct her sales staff. She uses this power to require her team to stay after normal work hours to complete tasks such as pricing and displaying new merchandise before each holiday season. This demonstrates that her power is derived from her position within the company rather than her personal attributes or expertise.

It is important to differentiate legitimate power from other forms of power, such as expert power, coercive power, and soft power. Expert power is based on one's knowledge and skills in a specific area, while coercive power involves using threats or force to get others to comply. Soft power, on the other hand, refers to influencing others through persuasion, diplomacy, and personal appeal.

In the context of this scenario, Joanne's power is primarily legitimate, as it stems from her position as store manager, rather than her expertise or personal influence.

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Answer:

x = 6

Step-by-step explanation:

3x-4=2x+2

x-4=2

x=6

Answer:

x = 6

Step-by-step explanation:

∠ 12 and ∠ 10 are corresponding angles and are congruent, thus

3x - 4 = 2x + 2 ( subtract 2x from both sides )

x - 4 = 2 ( add 4 to both sides )

x = 6

To evaluate the line integral over the closed curve C using Green's theorem, we need to calculate the double integral of the curl of the vector field over the region enclosed by the curve.

Green's theorem relates a line integral around a closed curve to a double integral over the region enclosed by the curve. It states that for a vector field F = ⟨P, Q⟩ and a closed curve C defined by the parameterization r(t) = ⟨x(t), y(t)⟩, the line integral of F around C is equal to the double integral of the curl of F over the region D enclosed by C:

∮C F · dr = ∬D curl(F) · dA

In this case, we want to evaluate the line integral over the closed curve C. The curve C is formed by traveling in straight lines between the points (-4, 1), (-4, -4), (1, -3), (1, 4), and back to (-4, 1), in that order.

To apply Green's theorem, we first need to calculate the curl of the vector field F = ⟨P, Q⟩. Let's assume the vector field is given by F = ⟨P, Q⟩ = ⟨P(x, y), Q(x, y)⟩.

Next, we need to find the region D enclosed by the curve C. The region D is the interior of the polygon formed by the given points (-4, 1), (-4, -4), (1, -3), (1, 4), and (-4, 1).

Once we have the curl of the vector field and the region D, we can evaluate the double integral of the curl over D to obtain the desired result.

The application of Green's theorem allows us to relate the line integral of a vector field around a closed curve to a double integral over the region enclosed by the curve. It provides a powerful tool for calculating line integrals by converting them into double integrals, which are often easier to evaluate.

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Answer:

AE = 30

GD = 5

GF = 10

Step-by-step explanation:

Centroid of medians divide median in the ratio 2 : 1

Therefore,

AG : GE : 2 : 1

Let AG = 2x & GE = x

Since, AG = 20....(given)

Therefore, 2x = 20

x = 20/2

x = 10

GE = x = 10

AE = AG + GE = 20 + 10 = 30

CG : GD : 2 : 1

Let CG = 2x & GD = x

Since, CG = 10....(given)

Therefore, 2x = 10

x = 10/2

x = 5

Since, GD = x

Therefore, GD = 5

BF = 30

2x + x = 30

3x = 30

x = 30/3

x = 10

GF = 10

Answer: X = 16

Step-by-step explanation:

so 6^(X-4) = 6^12

X = ?

we can rewrite it as X - 4 = 12 since the bases are the same

now solve for X

X = 12 + 4

X = 16

Answer:

The first one is 20, second is 5 3/5, the third one should be 22.8, fourth is 1, fifth is 15.9

Step-by-step explanation: Add all the numbers up (for each shape). For the parallelogram multiply the top and right sides by two.

Answer:

c/sin(60°) = 14/sin(25°)

c = 14sin(60°)/sin(25°) = 28.7

The answer to the given question is Yes, we can. We can conclude that there are two distinct subsets of the 14 3-digit numbers in the list which have the same sum.

There are \(2^{14}\) = 16384 subsets. Since each number goes in the range from 0 through 999 and there are at most 14 3-digit numbers in a subset, the sum of any subset of the numbers will be in the range from 0 through 14 x 1000.

So, there are at most 14001 possible values for the sum of a subset of the 3-digit numbers. Since 16384 > 14001, if each subset is plotted to the value of its sum, then there need to be at least two different subsets which are plotted on to the same value.

For that reason, there are at least two different subsets whose numbers sum to the same value.

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Answer:

\( M = \frac{e}{C^2 } \)

Step-by-step explanation:

\(e=MC^2 \\ \frac{e}{C^2 } = M \\ \huge \red{ \boxed{M = \frac{e}{C^2 } }}\)

To solve the initial value problem y'' - 2y' - 3y = 0, with y(0) = 1 and y'(0) = 2, we can use the method of Laplace transforms.

First, we take the Laplace transform of the given differential equation to obtain an algebraic equation in terms of the Laplace transform of the unknown function y(t). Then, we solve the algebraic equation for the Laplace transform of y(t) using standard algebraic techniques. Finally, we take the inverse Laplace transform to obtain the solution y(t) in the time domain.

Applying the Laplace transform to the given differential equation, we have s²Y(s) - sy(0) - y'(0) - 2(sY(s) - y(0)) - 3Y(s) = 0, where Y(s) represents the Laplace transform of y(t). Simplifying this equation, we get (s² - 2s - 3)Y(s) - (s - 2) = s²Y(s) - 3s - 4. Rearranging the equation, we have Y(s) = (s - 2) / (s² - 2s - 3).

To solve this equation for Y(s), we can decompose the expression into partial fractions, which yields Y(s) = 1 / (s - 3) - 1 / (s + 1). Taking the inverse Laplace transform of Y(s), we obtain y(t) = e^(3t) - e^(-t), which is the solution to the initial value problem.

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Where k is a constant

When y = 36 , x = 3 , z=3

The value of y is 40

Answer:

90

hope this helps!:)

Step-by-step explanation:

Answer:

$1 or $1.25

Step-by-step explanation:

Not sure. Maybe

It is also the foundation of many important algorithms, such as Euclidean Algorithm, which is used to find the greatest common divisor of two integers.

The Quotient-Remainder Theorem is a basic and important theorem in the domain of number theory. It is also known as the division algorithm.

To prove the Quotient-Remainder Theorem, we can use the well-ordering principle, which states that every non-empty set of positive integers has a least element.

Suppose that there exists another pair of integers q' and r' such that

\(n = q'd + r',\)

where r' is greater than or equal to zero and less than d.

Then, we have: \(dq + r = q'd + r' = > d(q - q') = r' - r.\)

Since d is greater than zero, we have |d| is greater than or equal to one. Thus, we can write: |d| is less than or equal to \(|r' - r|\) is less than or equal to \((d - 1) + (d - 1) = 2d - 2\).

This implies that |d| is less than or equal to 2d - 2,

which is a contradiction.  q and r are unique. The Quotient-Remainder Theorem is a powerful tool that has numerous applications in number theory and other fields of mathematics.

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Step-by-step explanation:

Para hacer las porciones para 32 personas, multiplique cada cantidad de ingrediente por 4 ya que la receta proporciona 8 porciones y 8 * 4 = 32

Papa seca = \(\frac{1}{2} *4\)

                     = 2 papas secas

Cerdo = \(\frac{1}{2} *4\)

       = 2 kg de carne de cerdo

Cebollas = 1 * 4

            = 4 cebollas grandes

Aji panca = 3 * 4

               = 12 cucharadas de aji panca

Ajo molido = \(1\frac{1}{2} *4\)

                       = \(\frac{3}{2} *4\)

                       = 6 cucharadas de ajo molido

Sal = 1 * 4

      = 4 cucharadas de sal

Answer:

y + 2.4 ≤ 35

Step-by-step explanation:

Less than or equal to sign is ≤

The sentence can be represented by the inequality:

y + 2.4 ≤ 35

Subtract 2.4 from both sides

y + 2.4 - 2.4 ≤ 35 -2.4

y ≤ 35 - 2.4

y ≤ 32.6

Therefore, y is less than or equal to 32.6

Answer:

No 1/3 is not greater than 5/9.

Step-by-step explanation:

The height of the trapezoid is 7 meters.

The area of the trapezoid in square meters is 129.5

An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.

A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases.

The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.

Area of a trapezoid is calculated by the formula

= 0.5 * (sum of bases) * height

form the figure the given dimensions are

bases = 25 m and 12 m

height = 7 m

area of trapezoid

= 0.5 ( 25 + 12) * 7

= 0.5 (37) * 7

= 129.5 m^2

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a0 is the regression term that describes the constant or intercept in the linear regression equation.

In a simple linear regression model, the equation takes the form of y = a0 + a1x + e1, where y is the dependent variable (or response variable), x is the independent variable (or predictor variable), a0 is the intercept or constant term, a1 is the coefficient of the independent variable, and e1 is the error term.

The intercept term, a0, represents the value of the dependent variable when the independent variable is zero. For example, in a linear regression model that predicts salary based on years of experience, the intercept would represent the starting salary for someone with zero years of experience. The intercept is an important component of the regression equation because it allows us to make predictions for values of x that are outside the range of our observed data.

The coefficient, a1, represents the change in the dependent variable for each one-unit increase in the independent variable. In the salary example, the coefficient would represent the average increase in salary for each additional year of experience.

Both the intercept and coefficient are estimated from the data using methods such as least squares regression. Once these values are estimated, we can use them to make predictions for new values of x.

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We sum up these line integral values to get the total line integral over the closed rectangle curve.

To evaluate the line integral using Green's Theorem, we first calculate the curl of the given vector field.

The given vector field is F = (x cos y) dx - (x sin y) dy.

Taking the partial derivatives of the components with respect to their corresponding variables, we find that ∂(x cos y)/∂y = -x sin y and ∂(-x sin y)/∂x = -sin y. The curl of F is then given by ∇ × F = -sin y - (-x sin y) = -sin y + x sin y = (1 - sin y) x sin y.

Next, we evaluate the line integral over the closed counter-clockwise oriented rectangle. Applying Green's Theorem, the line integral is equal to the double integral of the curl of F over the region enclosed by the curve.

Since the curve is a rectangle, we can parameterize each side separately and evaluate the integrals. Integrating over the sides (1,0) to (2,0), (2,0) to (2,7), (2,7) to (1,7), and (1,7) to (1,0), we obtain the respective values for each line integral.

Finally, we sum up these line integral values to get the total line integral over the closed rectangle curve.

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Answer:

23%

Step-by-step explanation:

Answer:

23 %

Step-by-step explanation:

The total money earned:

124+ 30+ 46 =200

Percent earned babysitting

money earned babysitting / total * 100%

46/200 * 100 = 23 %

Answer:

x = 33

Step-by-step explanation:

4x-25+3x+25+2x-3+4x+3x+15 = 540

16x + 12 = 540

16x = 540 - 12

x = 528/16

x = 33

Answer:

Step-by-step explanation:

Given,

\( {( \frac{5}{2} )}^{x} + {( \frac{5}{2} )}^{x + 3} \)

\( = {( \frac{5}{2}) }^{x} + {( \frac{5}{2}) }^{x} \times {( \frac{5}{2} )}^{3} \)

\( = ( \frac{5}{2} ) ^{x} (1 + {( \frac{5}{2} )}^{3} \)

\( = {( \frac{5}{2} )}^{x} (1 + \frac{125}{8} )\)

\( = {( \frac{5}{2} )}^{x} ( \frac{1 \times 8 + 125}{8} )\)

\( = {( \frac{5}{2}) }^{x} ( \frac{8 + 125}{8} )\)

\( {( \frac{5}{2} )}^{x} ( \frac{133}{8} )\)

Comparing with A • \( {( \frac{5}{2}) }^{x} \)

A = \( \frac{133}{8} \)

Hope this helps...

Good luck on your assignment...

Answer: D) square root 49

Step-by-step explanation: a rational number is a number that eventually ends. Square root 49 is the answer, because it terminates.

Step-by-step explanation:

this creates 2 similar triangles.

that means all angles are the same. and all the side lengths of one triangle correlate to the side lengths of the other triangle by the same multiplication factor.

2 × f = 5

f = 5/2 = 2.5

now the same factor applies to the relation of the heights :

5'4" × 5/2

to help us, let's convert her height into a fraction too.

1 ft = 12 in

4 in = 1/3 ft

5'4" = 5 1/3 ft = 16/3 ft

16/3 × 5/2 = 80/6 = 40/3 = 13 1/3 ft = 13'4"

so, the tree is 13 ft and 4 inches tall.

Answer:

Step-by-step explanation:

x+x+(2x+7)+(2x+5)=360

6x+12=360

6x=344

x=\(\frac{172}{3}\)

m∠R=m∠T=x=\(\frac{172}{3}\)

m∠S=2x+7=\(\frac{172*2+21}{3} =\frac{365}{3}\)

m∠Q=2x+5=\(\frac{172*2+15}{3}=\frac{359}{3}\)

Answer:

Step-by-step explanation:

x+x+(2x+7)+(2x+5)=360

6x+12=360

6x=344

x=

m∠R=m∠T=x=

m∠S=2x+7=

m∠Q=2x+5=

Answer:

-6

Step-by-step explanation:

Use pemdas. You go left to right

(-1)(-2)(-3)

2(-3)

-6