Find the equation of the line. Use exact numbers. y=y=y, equals x+x+x, plus

Equation which is equivalent to the formula solved for r in term of A is   [tex]Or = \sqrt{\frac{A}{r}-2 }[/tex].

What is circle?

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.

A circle is also termed as the locus of the points drawn at an equidistant from the centre.

What is radius?
Radius of a circle is the distance from the center of the circle to any point on it's circumference. It is usually denoted by 'R' or 'r'.

What is circumference?

Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of circle defines the region occupied by it.

Given that;

[tex]A = \pi{({r+2})^{2}}[/tex]

[tex](r+2)^{2} =\frac{A}{\pi}[/tex]  (equivalent transformation)

[tex]r + 2 = \sqrt{\frac{A}{\pi} }[/tex]

[tex]r = \sqrt{\frac{A}{\pi} -2}[/tex]

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Answer:

a = 6 , b = - 44

Step-by-step explanation:

x² + 12x - 8

using the method of completing the square

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

x² + 2(6)x + 36 - 36 - 8

= (x + 6)² - 44 ← in the form (x + a)² + b

with a = 6 and b = - 44

The length of each factory worker on average is 25.57 lengths

From the question, we have the following parameters that can be used in our computation:

Total length of the pool = 179 lengths

Number of workers = 7

The length of each on average is calculated as

Average length = Total length of the pool/Number of workers

Substitute the known values in the above equation

So, we have the following equation

Average length = 179/7

Evaluate the quotient

Average length = 25.57

Hence, the average length is 25.57 lengths

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Answer:1.4<x

math math math

Answer:daddy

Step-by-step explanation:gay

The missing values are:

m∠1 = 36°

m∠2 = 122°

m∠3 = 122°

m∠4 = 38°

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

The figure has two triangles.

58° and m∠3 is a straight angle.

58 + m∠3 = 180

m∠3 = 180 - 58

m∠3 = 122

Now,

m∠3 + m∠4 + 20 = 180

122 + m∠4 + 20 = 180

m∠4 = 180 - 122 - 20

m∠4 = 180 - 142

m∠4 = 38

m∠3 and m2 are opposite angles.

Opposite angles are equal.

m∠3 = m∠2 = 122

Now,

m∠1 + m∠2 + 22 = 180

m∠1 + 122 + 22 = 180

m∠1 = 180 - 144

m∠1 = 36

Thus,

The missing values are:

m∠1 = 36°

m∠2 = 122°

m∠3 = 122°

m∠4 = 38°

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The equation for the representation of the given situation will be

y = x - 0.54x, and the graph of the equation should only be in the first quadrant because x and y is representing a price which can't be negative.

An equation is a statement that says that the value of two mathematical expressions is equal.

Given that, a cinema sends out a coupon for ​54% off the price of a ticket.

The equation for this situation will be y = x - 0.54x,

And the line of this equation will always lie in the first quadrant because values of x and y in the first quadrant are always positive, and here x and y are prices which can't be negative.

Hence,  the graph of the equation should only be in the first quadrant because x and y is representing a price which can't be negative and The equation for the representation of the given situation will be

y = x - 0.54x

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a) The confidence interval is given as follows: (71.43, 77.17).

b) The manufacturer's claim is not correct, as 78 is not a part of the interval.

c) A sample of 55 employees is needed to achieve the desired margin of error.

The bounds of the t-distribution confidence interval, used when only the standard deviation for the sample is known, are given by the equation presented as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

The variables of the equation are presented as follows:

The critical value, considering the 95% confidence level and 12 - 1 = 11 df, is of:

t = 2.201.

The remaining parameters, namely sample mean, sample standard deviation and sample size are given as follows:

[tex]\overline{x} = 74.3, s = 4.52, n = 12[/tex]

(obtained using a calculator from the sample given in this problem).

The bounds of the interval are given as follows:

The interval does not contain the number 78, hence it is not a good estimate for the mean amount.

For item c, the z-distribution is used, as the population standard deviation is used, hence the minimum sample size is obtained as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]1.04 = 1.96\frac{3.91}{\sqrt{n}}[/tex]

[tex]1.04\sqrt{n} = 1.96 \times 3.91[/tex]

[tex]\sqrt{n} = \frac{1.96 \times 3.91}{1.04}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96 \times 3.91}{1.04}\right)^2[/tex]

n = 55. (rounded up, as a sample size of 54 would mean that the margin of error would be slightly above 1.04).

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The slope of the line is - 2 with the equation as 2 x + y - 2 = 0

We are given that:

y intercept of the line = 2

Point is (0, 2)

It is parallel to the line 2 x + y = - 5

Slope of line 2 x + y = - 5:

y' = - 2

m = - 2

Slope of parallel lines are equal

m = m'

m' = - 2

Equation of the line:

y - y₁ = m( x - x₁)

y - 2 = - 2( x - 0)

y - 2 = - 2 x

2 x + y - 2 = 0

a) standard form of the equation = 2 x + y - 2 = 0

b) slope of the line = m' = - 2

c) point-slope form = (y - 2) / (x - 0) = - 2

d) Properties of algebra used = cross multiplication and simplification.

Therefore, we get that, the slope of the line is - 2 with the equation as 2 x + y - 2 = 0

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A.The length of each path is 130 meters.

Given:

The park resembles an isosceles trapezoid.

Figure shows a trapezium . AC and BD are diagonals. The length of BD is 14x plus 4, and AC is 11x plus 31.

we know that:

Diagonals are equal in isosceles trapezoid.

14x + 4 = 11x + 31

14x - 11x = 31 - 4

3x = 27

divide by 3 on both sides

3x/3 = 27/3

x = 9

Diagonal length = 14x + 4.

= 14*9 + 4

= 126 + 4

= 130 meters.

Therefore The length of each path is 130 meters.

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The compound interest is obtained as $91.81, rounded off to the nearest hundredth.

In order to compute compound interest, multiply the principle of the original loan by the annual interest rate multiplied by the number of compound periods minus one. You will then be left with the principal amount of the loan plus compound interest. The entire compound interest is then obtained by deducting the initial principal.

The equation that results will look like this:

Compound Interest = [tex]P(\left(1+r\right)^{ t}-1)[/tex]

Amount, rate of interest and time is given as $1500, 2% and 3 years respectively.

First, change r as a percent to r as a decimal.

r = R/100

r = 2/100

r = 0.02 rate per year,

Then solve the equation for compound interest.

[tex]\text{Compound Interest}=1500(\left(1+0.02\right)^{3}-1)\\=1500(1.061208-1)\\=15000\cdot 0.061208\\\\=91.81[/tex]

So, the compound interest is obtained as $91.81, rounded off to the nearest hundredth.

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Answer: its 1591.81

Step-by-step explanation:

I took the test and tried with the answer on top and got it wrong.

The height of a person is 5.2ft in centimeter: 158.49cm

So, the conversion of measurement from the unit feet to centimeters is provided by the feet-to-centimeter calculator.

Approximately 30.48 cm makes up one foot.

1 ft = 30.48 cm

Therefore, 5.2 feet equals 5.2 x 30.48 centimeters.

5.2 feet is therefore equal to 158.49 cm in centimeters.

Hence, the height of a person who is 5.2 feet tall to centimeters is 158.49cm.

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Rearranging the equation, making h the subject of the formula, h =  v² / 2g

we rearrange equations and formulas by using inverse operations to make one variable the subject of the formula.

In order to change the subject of, or rearrange, a formula items in the formula need to be arranged so a different variable is the subject.

In our case the the formula needs to be rearrange to make h the subject of the formula.

Therefore,

v = √2gh

square both sides of the equation

v² = (√2gh)²

v² = 2gh

divide both sides by 2g

v² / 2g = 2gh / 2g

h = v² / 2g

Therefore,

h = v² / 2g

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The equation for the value of x will be 11/C.

According to the question,

We have the following equation:

Cx — 4 = 7

Now, we can easily find the value of x from this equation by following the given steps.

We will first add 4 on both sides of the equation:

Cx = 7+4

Adding the two numbers on the right hand side:

Cx = 11

Dividing by C on both sides of the equation:

x = 11/C

(More to know: we can now find the value of x if the value of C is given.)

Hence, the equation for the value of x will be 11/C.

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0.065=x/5800

x=$377; that is the dollar value of the decrease

The account is now worth $5423.

Answer:

Step-by-step explanation:

Answer:

168

Step-by-step explanation:

Let the area of the square be [tex]x[/tex].

[tex]\frac{4}{7}x-\frac{5}{6}\left(\frac{3}{7}x \right)=36 \\ \\ \frac{4}{7}x-\frac{5}{14}x=36 \\ \\ \frac{8}{14}x-\frac{5}{14}x=36 \\ \\ \frac{3}{14}x=36 \\ \\ \frac{1}{14}x=12 \\ \\ x=168[/tex]

It is a function because the mapping .

(A) Due to the fact that there are no two values in Set B that have only one value in Set A mapped to them, the mapping diagram above represents a function.

(B) A function's very special property is that it associates one output with each input.

(C) Set A represents the domain, whereas Set B represents the range. Therefore, there would be exactly one value in the range that was unique for each value in the domain and would be present for each value in the domain.

In mathematics, a function from a set X to a set Y assigns each element of X exactly one element of Y. The subsets X and Y are referenced to as the function's domain and codomain, correspondingly. A function is described as a relationship between a group of inputs with one output each. A function is, to describe it simply, a connection between inputs in which each input is associated to exactly one output. Every function has a domain and a codomain, or range. A function is a type of rule that produces one output from one input. Y=X2 is a good illustration of this. Any input for x yields a single output for y.

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Answer:

y = - 17

Step-by-step explanation:

6y + x = - 59 → (1)

x = - 2y + 9 → (2)

substitute x = - 2y + 9 into (1)

6y - 2y + 9 = - 59

4y + 9 = - 59 ( subtract 9 from both sides )

4y = - 68 ( divide both sides by 4 )

y = - 17

The given statement "In a geometric sequence, the difference between each pair of consecutive terms must be the same" is false.

Number sequence is a progression or an ordered list of numbers governed by a pattern or rule. For example -

3, 6, 9, 12, 15

x, x + 2, x + 4, x + 6

Given is the following statement -

"In a geometric sequence, the difference between each pair of consecutive terms must be the same"

The given statement is false as the statement mentioned above is the definition of a arithmetic sequence. In geometric sequence, the ratio of each pair of consecutive terms must be the same. Mathematically -

a[n + 1]/a[n] = r {constant}

Therefore, the given statement "In a geometric sequence, the difference between each pair of consecutive terms must be the same" is false.

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The quadratic equation y = - 4 · x² - 8 · x + 60 contains the points (3, 0), (- 5, 0) and (- 6, - 36).

In this question we find the coordinates of three points set on Cartesian plane and we are asked to find the quadratic equation that contains the these points. The standard form of the quadratic equation is shown below:

y = a · x² + b · x + c

Where:

We can determine the values of the three coefficients because the number of known points is equal to the number of coefficients. Then, we have the following system of linear equations by replacing x and y on each of the three points:

9 · a + 3 · b + c = 0

25 · a - 5 · b + c = 0

36 · a - 6 · b + c = - 36

Then, the solution to the system is found by numerical methods:

(a, b, c) = (- 4, - 8, 60)

The equation that contains the three points is y = - 4 · x² - 8 · x + 60.

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Given that Max wanted to test a new dishwasher detergent to see if it was less likely to leave residue on his dishes, the suitable null hypothesis in Max’s experiment will be "the new detergent will leave more residue than the old one".

In statistics, a null hypothesis means a typical theory which suggests that no statistical relationship and significance exists in a set of given single observed variable between the two sets of observed data and measured phenomena.

Therefore, the Option B is correct.

Missing options' The new detergent will leave less residue than the old one. The new detergent will leave more residue than the old one. O The new detergent is equally likely to leave residue compared to the old detergent. The old detergent will leave more residue than the new detergent."

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The correct way to replace equation 1 into equation 2 using the substitution method is 2x+(-5x+10) = 7.

According to the question,

We have the following two equations:

Equation 1: y = -5x+10

Equation 2: 2x+y = 7

Now, we will substitute the value of y from equation 1 in equation 2.

So, we have the following expression:

2x+(-5x+10) = 7

(More to know: we can also solve this equation to find the value of x and then the obtained value of x can be put in equation 1 to find the value of y.)

Hence, the correct option is B.

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2y(xy+4)

Hope this answers your question!

Answer:

2y(xy+4)

Step-by-step explanation:

First, Distribute

you get 2y(xy+4) because you have to isolate the like terms than find a gcf of the terms

The shape has a surface area of: Surface Area = 282.6 in²

The given parameter is represented on the figure

In this case, the figure is a cone with the following parameters

Radius, r = 5 inches

Height, h = 12 inches

The surface area of the cone is then calculated as

A = πr * (r + √(h² + r²))

Substitute the known values in the above equation, so, we have the following representation

A = 3.14 * 5 * (5 + √(12² + 5²))

Evaluate the expression

A = 282.6

Hence, the surface area is 282.6 square inches

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Answer:

x = -5

y = -2

Step-by-step explanation:

-3x + 4y = 7 ⇒ ( 1 )

7x - 12y = -11 ⇒  ( 2 )

Multiply the equation ( 1 ) by 3.

( 1 ) × 3

3( -3x + 4y = 7 )

-9x + 12y = 21  ⇒ ( 3 )

Let us find the value of x.

Add equations ( 2 ) & ( 3 ).

( 2 ) + ( 3 )

7x - 12y - 9x + 12y = - 11 + 21

Combine like terms.

-2x = 10

Divide both sides by -2.

x = -5

Let us find the value of y.

For that, let us use equation ( 1 ) and replace x with -5 and make y the subject.

- 3x + 4y = 7

-3 × -5 + 4y = 7

15 + 4y = 7

Subtract 15 from both sides.

4y = 7 - 15

4y = -8

Divide both sides by 4.

y  = -2

The solution to the inequality given as 2x+5y<1 has the coordinates of (-10, 4)

From the question, we have the following inequality that can be used in our computation:

2x+5y<1

Solving further, we need to collect the like terms

Since there are no like terms in the expression, it remains unchanged

So, the inequality becomes

2x + 5y < 1

Subtract 5y from both sides of the inequality

This gives

2x < 1 - 5y

Divide both sides by 2

The expression becomes

x < 1/2 - 5/2y

Evaluate

x < 0.5 - 2.5y

At this point, we assume any value for y and then solve for x

Assume that the value of y is 4

So, we have the following representation

x < 0.5 - 2.5 * 4

Evaluate the products

x < -9.5

This means that x is less than -9.5 when y is 4

-10 is less than -9.5

So, we have

x = -10 and y = 4

Express as ordered pairs (i.e. coordinates)

(x, y) = (-10, 4)

Hence, the coordinates of the solution is (-10, 4)

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Answer: 49

Step-by-step explanation:

by using triangle ABC and the known values of triangle XYZ, we can divide side XY/AB, 28/4=7. By doing the same with YZ/BC, 56/8=7, we find that the scale factor is 7. With this information, we multiply side CA by the scale factor, 7x7=49.