A Japanese garden has a circular koi pond in the middle that has a radius of 3 feet.
What is the area of the Japanese garden around the koi pond? Use 3.14 for pi
195.74 ft2
224.00 ft2
252.26 ft2
337.04 ft2

ANSWER

[tex]x = \sqrt{5} [/tex] units

EXPLANATION

Let the other leg be x units.

According to the Pythagoras Theorem, the sum of the squares of the two shorter legs should add up to the square of the hypotenuse.

This implies that,

[tex] {x}^{2} + {2}^{2} = {3}^{2} [/tex]

[tex]{x}^{2} + 4=9[/tex]

Group the constant terms,

[tex]{x}^{2}=9 - 4[/tex]

[tex]{x}^{2}=5[/tex]

Take square root.

[tex]x = \sqrt{5} [/tex]

Answer:

0.00329

This is rounded to three significant figures.

The zeros before 32876 will not count as significant since they are before the non-zero numbers.

Answer:

0.00329

Step-by-step explanation:

The leading zero's are not significant, only there for place value.

The significant digits are 32876 ← 5 significant figures

which rounds to 329 ← 3 significant figures

0.0032876 ≈ 0.00329

If you are looking for the expanded version, this is it. It is also possible to group either an a from (a^2 + 2b) or a b from (2ab + b^2). Hope this helps!

Answer:

[tex](a+b-c)(a+b+c)=a^2+2ab+b^2-c^2[/tex].

Step-by-step explanation:

We want to expand: [tex](a+b-c)(a+b+c)[/tex].

We use the distributive property to obtain:

[tex](a+b-c)(a+b+c)=a(a+b+c)+b(a+b+c)-c(a+b+c)[/tex].

We now expand to get:

[tex](a+b-c)(a+b+c)=a^2+ab+ac+ab+b^2+bc-ac-bc-c^2[/tex].

This finally simplifies to

[tex](a+b-c)(a+b+c)=a^2+2ab+b^2-c^2[/tex].

Exact Form:

d

=

−

7

−

√

47

2

,

−

7

+

√

47

2

d

=

-

7

-

47

2

,

-

7

+

47

2

Decimal Form:

d

=

−

0.07217269

…

,

−

6.92782730

…

Answer: 20

Step-by-step explanation:

d=-2

Plug in to get 4(-2+7)

Do what's in () -2+7=5

Then multiply 4(5)=20

Answer:

The probability is  0.0015

Step-by-step explanation:

We know that the average [tex]\mu[/tex] is:

[tex]\mu=500[/tex]

The standard deviation [tex]\sigma[/tex] is:

[tex]\sigma=100[/tex]

The Z-score is:

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

We seek to find

[tex]P(x>800)[/tex]

The Z-score is:

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

[tex]Z=\frac{800-500}{100}[/tex]

[tex]Z=3[/tex]

The score of Z = 3 means that 800 is 3 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the conficion of 3 deviations from the mean has percentage of 0.15%

So

[tex]P(x>800)=0.0015[/tex]

Answer:

2

Step-by-step explanation:

Total Marbles = 16

Fractional amount blue marbles = 1/8

Number of blue marbles = fractional amount * Total marbles

Number of blue marbles = 1/8 * 16

Number of blue marbles = 2

Answer: 2

Step-by-step explanation:

16 divided by 1/8 = 2

Answer:

[tex]P=338\ in[/tex]

Step-by-step explanation:

we know that

The perimeter of the red figure is equal to

[tex]P=2[22+27+22+98][/tex] ----> because the sides of the figure are tangent to the circle

[tex]P=2[169][/tex]

[tex]P=338\ in[/tex]

Answer:

Step-by-step explanation

Perimeter is sum of the measurement of all sides of a polygon . The polygon we have in this question is formed by using the tangents from a given circle .

The concept we are going to use here is that if we draw two tangents from the same point outside on a given circle, the length of both tangents are always equal .

There are 8 sides of this polygon , That means there are four pairs because length of them are equal .

So perimeter is equal to two times the sum of four sides given to us .

Perimeter = 2( 22+27+22+98)

Perimeter = 2(169)

Perimeter = 338 in

Answer: Triangle

Step-by-step explanation: If you cut it vertically, the base is changed into a triangle.

Hope this helps!

It's actually very simple. Semicircle is a half of a circle. So the area and perimeter is also divided by 2. Also the radius is a half of diameter so 130.

[tex]Area=\frac{\pi130^2}{2}\approx\frac{53092.92}{2}=\boxed{26546.46ft^2}[/tex]

Hope this helps.

r3t40

Answer:

26 units

Step-by-step explanation:

As the sales for the same month in past four years is given, they will be used to determine the sales for next month.

We have to find the average of previous 4 years' sale for the same month

So,

n = 4

The formula for average is:

[tex]Avg = \frac{Sum of values}{number of values}[/tex]

[tex]=\frac{ 24+30+23+27}{4}[/tex]

[tex]= \frac{104}{4}[/tex]

[tex]= 26[/tex]

26 is the average number of units that can be expected to be sold the next month ..

based on the previous average sales, one can expect to sell an average of 26 units next month.

To calculate the average number of units one can expect to sell next month based on past sales, we need to find the mean of the provided sales data. The actual sales data for the last four years are 24 units, 30 units, 23 units, and 27 units. To find the average (mean), we add up these amounts and then divide by the number of data points.

The sum of the units sold is 24 + 30 + 23 + 27 = 104 units. Since there are four years of data, we divide 104 units by 4 to get the average.

Average units sold = 104 units / 4 = 26 units.

Therefore, based on the previous average sales, one can expect to sell an average of 26 units next month.

Answer:

y=15x+100

Step-by-step explanation:

increases by 15, 100 is starting free

Answer:

Step-by-step explanation:

Say that your equation is 2x+4=8, x=2

you would plug in the 2 where your x is so, 2(2) +4=8

then you'd solve regularly.

Hope my answer has helped you!

Answer:  

The slope of a line that is perpendicular to the given line is [tex]-\frac{3}{2}[/tex]

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

Solve for "y" from the equation of the line [tex]2x - 3y - 5 = 0[/tex]:

[tex]2x - 3y - 5 = 0\\\\-3y=-2x+5\\\\y=\frac{-2}{-3}x+\frac{5}{-3}\\\\y=\frac{2}{3}x-\frac{5}{3}[/tex]

You can observe that the slope of this line is:

[tex]m=\frac{2}{3}[/tex]

By definition, the slopes of perpendicular lines are negative reciprocal, then, the slope of a line that is perpendicular to the give line, is

[tex]m=-\frac{3}{2}[/tex]

Answer:

D. 70​

Step-by-step explanation:

If VX is the bisector of V, then UX=WX.

This implies that:

[tex]3z-4=z+6[/tex]

Group similar terms:

[tex]3z-z=4+6[/tex]

[tex]2z=10[/tex]

z=5

WU=2(z+6)

WU=2(5+6)

WU=2(11)=22 units

VW=VU=5z-1

Put z=5 to get;

VW=VU=5(5)-1

VW=VU=25-1

VW=VU=24

The perimeter of VWU=24+24+22=70 units

Answer:

Perimeter of triangle VUW = 70.

Step-by-step explanation:

Since VX is angle bisector and VX is perpendicular to UW then triangle UVX is congruent to triangle WVX using ASA property.

then UV=WV...(i) {corresponding sides of congruent triangle are equal.}

and UX=WX ...(ii)  {corresponding sides of congruent triangle are equal.}

then 3z-4=z+6

3z-z=6+4

2z=10

z=5

then UW=(3z-4)+(z+6)=3(5)-4+(5)+6=22

WV=5z-1=5(5)-1=24

UV=WV=24

Then perimeter of triangle VUW is

UV+WV+UW=24+24+22=70

Hence final answer is:

Perimeter of triangle VUW = 70.

Answer:

Option A.

Step-by-step explanation:

The given expression is

[tex]-25[/tex]

According to the reflexive property of equality, all values are equal to itself.

a = a

where, a be any real number.

Using the reflexive property we can say that

[tex]-25=-25[/tex]

It means -25 is equal or equivalent to -25.

Therefore, the correct option is A.

Note: If the given expression is [tex]\sqrt{-25}[/tex], then

[tex]\sqrt{-25}=\sqrt{25}\sqrt{-1}[/tex]        [tex][\because \sqrt{ab}=\sqrt{a}\sqrt {b}][/tex]

[tex]\sqrt{-25}=5i[/tex]             [tex][\because \sqrt{-1}=i][/tex]

Then the correct option is B.

Answer:5i

Step-by-step explanation:

Answer: x=10

Step-by-step explanation: hope it helped:)

Final answer:

The solution to the equation involves applying the quadratic formula to a rearranged version of the equation, solving for the value(s) of x. This can only be done accurately if the initial equation is correctly presented without typos.

Explanation:

The original equation presented by the student has a typo. However, using information provided, we can approach similar equations to demonstrate the solving process. For instance, the equation (2x)² = 4.0 (1 - x)² involves taking the square root of both sides to find the value of x. This involves rearranging and solving the quadratic equation that is created when you expand and combine like terms.

When solving a quadratic equation, such as ax² + bx + c = 0, we may use the quadratic formula: x = (-b ± √(b²-4ac)) / (2a), which will provide the two potential values of x. This process is crucial when the value of x is not a small enough percentage of a coefficient in the equation to use approximation methods.

If we were solving an equation like x² + 0.00088x - 0.000484 = 0, we would apply the quadratic formula to find the exact values of x.

The tan of angle C in triangle XYZ is 0.8.

To find the tan of angle C, we first need to determine the values of angle C, side XC, and side ZC. In triangle XYZ, angle Y is a right angle, so angle C must be angle Z. Since side YZ is opposite angle X, side YZ is equal to side XC.

Using the Pythagorean theorem, we can find side XC:

XC = sqrt(XY^2 + YZ^2)

= sqrt(3^2 + 4^2)

= sqrt(9 + 16) = sqrt(25) = 5.

Now, we can calculate the tan of angle C using the formula tan(C) = opposite side (YZ) / adjacent side (XC).

Therefore, tan(C) = 4 / 5 = 0.8.

#18 answer is 52

#19 answer is 152,100

and I cant make out the rest can you please write them in the comments of this answer?

Answer:

r = 2.5

Step-by-step explanation:

The equation given says y = r * x

So, the y value would be an unknown times the given x value.

To solve for r, all you have to do is divide.

25 ÷ 10 = 2.5

12.5 ÷ 5 = 2.5

10 ÷ 4 = 2.5

2.5 is the constant of proportionality.

Answer:

The answer is C: y = 2x + 3

Step-by-step explanation:

I took the test

Linear function is, y = 2 x + 3.

According to the question:

From the points we can see the y-intercept of the line is 3 as it passes through point (0, 3).

y = 2 x - 4

y-intercept is -4 ≠ 3, incorrect.

y = 2 x - 3

y- intercept is -3 ≠ 3, incorrect.

y = 2 x + 3

y- intercept is 3 = 3, correct.

Learn more about y -intercept  here:

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Answer:

Amplitude = -4; period = π; phase shift: x = π/2

Step-by-step explanation:

* Lets revise the trigonometry translation  

- If the equation is y = A sin (B(x + C)) + D  

* A is the amplitude  

- The amplitude is the height from highest to lowest points and  

  divide the answer by 2  

* The period is 2π/B  

- The period is the distance from one peak to the next peak

* C is the horizontal shift  (phase shift)

- The horizontal shift is how far the function is shifted to left  

  (C is positive) or to right (C is negative) from the original position.  

* D is the vertical shift  

- The vertical shift is how far the function is shifted vertically up

  (D is positive) or down (D is negative) from the original position.  

* Now lets solve the problem

∵ f(x) = A sin (B(x + C)) + D  

∵ f(x) = -4 sin (2x + π) - 5 ⇒ take 2 from the bract (2x + π) common factor

∴ f(x) = -4 sin 2(x + π/2) - 5

∴ A = 4 , B = 2 , C = π/2 , D = -5

∵ A is the amplitude

∴ The amplitude is -4

∵ The period is 2π/B  

∴ The period = 2π/2 = π

∵ C is the horizontal shift  (phase shift)

∴ The phase shift π/2 (to the left)

* Amplitude = -4; period = π; phase shift: x = π/2

The amplitude of the function f(x) = −4 sin(2x + π) − 5 is 4, its period is π, and it has a phase shift of x = -π/2.

The amplitude of a trigonometric function like f(x) = −4 sin(2x + π) − 5 is the coefficient in front of the sine function which determines the maximum and minimum value of the function's graph. In this case, the amplitude is the absolute value of -4, which is 4.

The period of the function is found by taking 2π divided by the coefficient of x inside the sine function, which is 2 in this case, yielding a period of π.

The phase shift of the function is determined by solving the equation 2x + π = 0 for x, which gives us a phase shift of x = -π/2. Therefore, the correct description is amplitude of 4, a period of π, and a phase shift of x = -π/2.

First of all, we compute the points of interest, i.e. the points where the curve cuts the x axis: since the expression is already factored, we have

[tex]x(x-1)(x+2) = 0 \iff x=0\ \lor\ x-1=0\ \lor\ x+2=0[/tex]

Which means that the roots are

[tex]x=0\ \lor\ x=1\ \lor\ x=-2[/tex]

Next, we can expand the function definition:

[tex]y = x(x-1)(x+2) = x^3 + x^2 - 2x[/tex]

In this form, it is much easier to compute the derivative:

[tex]y' = 3x^2+2x-2[/tex]

If we evaluate the derivative in the points of interest, we have

[tex]y'(-2) = 6,\quad y'(0)=-2,\quad y'(1)=3[/tex]

This means that we are looking for the equations of three lines, of which we know a point and the slope. The equation

[tex]y-y_0=m(x-x_0)[/tex]

is what we need. The three lines are:

[tex]y-0=6(x+2) \iff y = 6x+12[/tex]  This is the tangent at x = -2

[tex]y-0=-2(x-0) \iff y = -2x[/tex]  This is the tangent at x = 0

[tex]y-0=3(x-1) \iff y = 3x-3[/tex]  This is the tangent at x = 1

The total points could be 50.

It has 20 questions, so each question is worth: 50/20 = 2.5 points each.

She got 16 correct, so her score was: 16 x 2.5 = 40

Answer: A) given

B) definition of congruent

C) definition of bisect

Step-by-step explanation:

8 Doubled Is 16

16 Increased By 1 Is 17

Answer:

Step-by-step explanation:

if 2.5, sqrt(18), and 5 make up the sides of a right triangle, then they must satisfy A^2+B^2=C^2, where C is the longer side (hypotenuse).

In this case, 5 is the greater of the 3, so let's see if it satisfies our equation:

2.5^2+sqrt(18)^2=5^2

-> 6.25+18 = 24.25 =/= 25

-> Therefore the answer is a resounding no.

The numbers 2.5, the square root of 18, and 5 cannot form a right triangle. This is determined via the Pythagorean Theorem, which these numbers do not satisfy when squared and added together.

In the context of mathematics, specifically geometry, a set of numbers can form a right triangle if they adhere to the Pythagorean Theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as a² + b² = c².

Here, let's test the three numbers you've given: 2.5, √18, and 5. First, square each of the values: 2.5² = 6.25, (√18)² = 18, and 5² = 25.

If we consider 2.5 and √18 as sides a and b, and 5 as side c (the hypotenuse), the Pythagorean theorem would look like this: 6.25 + 18 = 24.25 ≠ 25. Thus, these numbers cannot form a right triangle because they do not satisfy the Pythagorean Theorem.

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Answer:

(2, 3)

Step-by-step explanation:

There is an easy way to solve this.

Set it up like this, where one end point is on top of the midpoint.

To get from 6 to 4, you subtract 2. So subtract 2 from 4 (that's where the x coordinate comes from). To get from 1 to 2, you add 1. So add 1 to 2 (that's where the y coordinate comes from)

If this sounds confusing, please comment and I'll help ASAP.

Answer:

2.4103

Step-by-step explanation:

The first step in evaluating the sample standard deviation of a data set involves the determination of the sample mean.

The sample mean is simply the average value of the data set;

sample mean = [tex]\frac{7+3+4+2+5+6+9}{7}=5.1429[/tex]

The next step is to evaluate the sum of the squares of deviations from the mean;

sum of squares of deviation = [tex](7-5.1429)^{2}+(3-5.1429)^{2}+(4-5.1429)^{2}+(2-5.1429)^{2}+(5-5.1429)^{2}+(6-5.1429)^{2}+(9-5.1429)^{2}=34.8571[/tex]

We then divide the sum of squares of deviation by (n-1) where n is the sample size to obtain the sample variance;

variance = [tex]\frac{34.8571}{7-1}=5.8095[/tex]

The standard deviation is simply the square-root of variance;

[tex]\sqrt{5.8095}=2.4103[/tex]

Answer:

∠4 = a + b

Step-by-step explanation:

Given ∠2 = a and ∠3 = b

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the 2 given angles from 180 for ∠1

∠1 = 180 - (a + b) = 180 - a - b

Now

∠1 and ∠4 form a straight angle and are supplementary, hence

∠4 = 180 - (180 - a - b) = 180 - 180 + a + b = a + b

Answer:

y = 4x - 6.

Step-by-step explanation:

Slope-intercept form is y = mx + c where m = the slope and c = the y-intercept.

4x = y +6

Subtract 6  from both sides:

4x - 6 = y

we would write it as y = 4x - 6.

Answer:

Slope intercept form

y = 4x - 6

Step-by-step explanation:

Slope intercept form y = mx + b

In this case 4x = y +6

Re-write

y + 6 = 4x

Subtract 6 from both sides

y = 4x - 6  <-------Slope intercept form