The radius of a circular park is 120 m to the nearest meter what is the circumference of the park?

Step-by-step explanation:

You use PEMDAS parenthesis, exponents, multiplication, addition, subtraction.

First you will change the -(-3) into positive

-55+-7x6+3x4

Now change the +-7 into negative 7

-55-7x6+3x4

Now multiply 7 times 6...

-55-42+3x4

Now multiply 3 times 4...

-55-42+12

Now add the two negatives, 55 and 42

-97+12

Now add those...

-85

Answer:

1. a. 3xy²(7x²y³ + 5x - 4y)

2. a. (3x + 2)(5x + y)

3. d. (2a + b)(5x - 4)

Step-by-step explanation:

For #1, your answer was missing an exponent, which I boldfaced. Every term has a y² in common. Then, in numbers 2 and 3, just factor each group one at a time.

Ex: [10ax + 5bx] - [8ay - 4by]

Considering that there is no real question content here, we can't be for sure, so I am just going to say 100% probability since it seems like that is the only card he can pick from ; ~ ;

Use the formula V= πr²h

π = [tex]\frac{22}{7}[/tex]

r = 3 ft

h = 10 ft

^^^^Plug these numbers into their corresponding spot into the formula given above

V = [tex]\frac{22}{7}[/tex]×[tex]3^{2}[/tex]×10

To evaluate apply the rules of PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction)

Parentheses

There are none so go on to the next step

Exponent

[tex]3^{2}[/tex] = 9

so...

V = [tex]\frac{22}{7}[/tex]×9×10

Multiplication (multiply from left to right)

V = [tex]\frac{198}{7}[/tex]×10

V = [tex]\frac{1980}{7}[/tex]

V ≈ 282.857 ft³

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

The correct answer option is [tex]\frac{25}{9}[/tex].

Step-by-step explanation:

We are given the following expression and we are to evaluate it when [tex]a = 5[/tex] and [tex]k = -2[/tex]:

[tex][\frac{3^2a^{-2}}{3a^{-1}} ]^k[/tex]

Substituting the given values of  [tex] a [/tex] and [tex] k [/tex] to get:

[tex][\frac{3^2(5)^{-2}}{3(5)^{-1}} ]^{-2}[/tex]

[tex]\frac{3^{(2\times -2)}.5^{(1\times-2)}}{3^{(-1\times-2)}.5^{(2\times-2)}}[/tex]

[tex]\frac{3^{-4}.5^{-2}}{3^{-2}.5^{-4}}[/tex]

[tex]3^{-2}.5^2[/tex]

[tex] \frac { 1 } { 3 ^ 2 } . 2 [/tex]

[tex] \frac { 1 } { 9 } . 2 5 [/tex]

[tex] \frac { 2 5 } { 9 } [/tex]

ANSWER

Point if discontinuity:

[tex]{x}= \pm3[/tex]

Zero of the function is

[tex]x = 0[/tex]

EXPLANATION

The given rational function is:

[tex]f(x) = \frac{3x}{ {x}^{2} - 9} [/tex]

This function is not continous when

[tex] {x}^{2} - 9 = 0[/tex]

[tex] {x}= \pm \sqrt{9} [/tex]

[tex]{x}= \pm3[/tex]

The function is zero when,

[tex]3x = 0[/tex]

[tex]x = 0[/tex]

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]y\geq (x-4)^{2}[/tex]

The solution is the shaded area above the vertical parabola

using a graphing tool

see the attached figure

Answer:

[tex]x=2- 3\sqrt{2}[/tex] or [tex]x=2+3\sqrt{2}[/tex]

Step-by-step explanation:

We want to solve for x in the equation;

[tex](x-2)^2-18=0[/tex]

Add 18 to both sides

[tex](x-2)^2=18[/tex]

We solve by the square root method.

[tex]x-2=\pm \sqrt{18}[/tex]

[tex]x-2=\pm 3\sqrt{2}[/tex]

Add 2 to both sides

[tex]x=2\pm 3\sqrt{2}[/tex]

Split the plus or minus sign.

[tex]x=2- 3\sqrt{2}[/tex] or [tex]x=2+3\sqrt{2}[/tex]

Therefore the exact solution is [tex]x=2- 3\sqrt{2}[/tex] or [tex]x=2+3\sqrt{2}[/tex]

Answer:

There are 720 ways to award the medals

Step-by-step explanation:

* Lets explain the difference between permutations and combinations

- Both permutations and combinations are collections of objects

- Permutations are for lists (order matters)  

- Combinations are for groups (order doesn't matter)  

- A permutation is an ordered combination.  

- Permutation is nPr, where n is the total number and r is the number  

 of choices

# Example: chose the first three students from the group of 10

  students, n = 10 and r = 3,then 10P3 is 720

- Combinations is nCr, where n is the total number and r is the number  

  of the choices

# Example: chose a group of three students from the group of 10

  students n = 10 and r = 3,then 10C3 is 120

* Lets solve the problem

- There are six runner

- There are 6 medals awarded for first place through sixth place

- Each medal is different

- The order is important because they arranged from 1st position to

  the 6th position

∴ We will use the permutation

∵ There are 6 medals for 6 runners

∵ 6P6 = 6 × 5 × 4 × 3 × 2 × 1 = 720

∴ There are 720 ways to award the medals

Answer: option b.

Step-by-step explanation:

You need to remember that:

[tex]b^\frac{m}{n}=\sqrt[n]{b^m}\\\\\sqrt[n]{a^n}=a[/tex]

Then, you can rewrite [tex](-32)^\frac{3}{5}[/tex] as:

[tex]=\sqrt[5]{(-32)^3}[/tex]

Now you need to descompose 32 into its prime factors:

[tex]32=2*2*2*2*2=2^5[/tex]

Rewriting:

 [tex]=\sqrt[5]{(-2^5)^3}[/tex]

The power of a power property states that:

[tex](a^b)^c=a^{(bc)}[/tex]

Then:

[tex]=\sqrt[5]{(-2)^{15}}=(-2)^3=-8[/tex]

Answer: Option C

[tex]y=5[/tex], [tex]x=10[/tex]

Step-by-step explanation:

If the lines m and n are parallel then the large triangle and the small triangle are similar triangles, because they have equal angles.

By definition for similar triangles it is satisfied that if they have sides of length a, b, c and a ', b' and c 'then:

[tex]\frac{a}{a'}=\frac{b}{b'} =\frac{c}{c'}[/tex]

In this case

[tex]a = 12\\a' = 4\\c = 15\\c' = y[/tex]

So:

[tex]\frac{12}{4}=\frac{15}{y}[/tex]

[tex]3=\frac{15}{y}[/tex]

[tex]y=\frac{15}{3}[/tex]

[tex]y=5[/tex]

Therefore

if [tex]x+y=15[/tex] and [tex]y=5[/tex] then [tex]x =10[/tex]

Finally

[tex]y=5[/tex], [tex]x=10[/tex]

Answer:

A = (3,-2)  

reflect along the y -axis ; set x=-x  

(-3,-2)  

reflect along the x-axis ; set y=-y  

A' = (-3,2)  

Same for B,C and D  

ABCD is reflected across the y-axis and then the x-axis.

Step-by-step explanation:

Answer:

A )rotate 90 degrees counterclockwise,then shift 2 units up.

Step-by-step explanation:

Given  : graph .

To find : what transformation were applied to ABC to obtain A’B’C.

Solution : We have given graph

Parent ABC triangle with coordinates A(2 ,2) ; B (5 ,6) ; C ( 8 , 2).

Transformed triangle with coordinates  A' (-2 ,4) ; B' (-6 ,7) ; C' ( -2 ,15).

By the rotational of 90° counter clockwise : (x ,y) →→ ( -y , x ).

And it is shifted by 2 unit up

(x ,y) →→ ( -y , x + 2 ).

A(2 ,2) →→ A' (-2 ,4)

B (5 ,6) →→ B' (-6 ,7)

C ( 8 , 2) →→ C' ( -2 ,15).

Therefore, A )rotate 90 degrees counterclockwise,then shift 2 units up.

Answer:

[tex]D=13.8\ ft[/tex]

Step-by-step explanation:

we know that

If the tank half-filled with water is at 20 feet, then the height of the tank is 40 feet

The volume of the cylindrical tank is equal to

[tex]V=\pi r^{2}h[/tex]

we have

[tex]h=40\ ft[/tex]

[tex]V=6,000\ ft^{3}[/tex]

assume

[tex]\pi =3.14[/tex]

substitute and solve for r

[tex]6,000=(3.14)r^{2}(40)[/tex]

[tex]r^{2}=6,000/[(3.14)(40)][/tex]

[tex]r=6.9\ ft[/tex]

Find the diameter

Remember that the diameter is two times the radius

[tex]D=6.9*2=13.8\ ft[/tex]

Answer:

[tex]330,\frac{5\pi }{3},\frac{7\pi }{6}, \frac{2\pi }{3} ,\frac{\pi }{2}[/tex]

Step-by-step explanation:

We have to find the alternate angles regarding π

So,

[tex]\frac{\pi }{2} = 90 \\330\\\frac{5\pi }{3} = 300\\\frac{7\pi }{6} = 210\\\frac{2\pi }{3} = 120[/tex]

As we have all the angles in number form, we can sort them in descending order to get the answer

330, 300, 210, 120, 90

Writing using pi form

[tex]330,\frac{5\pi }{3},\frac{7\pi }{6}, \frac{2\pi }{3} ,\frac{\pi }{2}[/tex]

Hence, Option D is correct ..

Answer:

D) 330, [tex]\frac{5\pi }{3}[/tex], [tex]\frac{7\pi }{6}[/tex], [tex]\frac{2\pi }{3}[/tex], [tex]\frac{\pi }{2}[/tex]

Step-by-step explanation:

To find the order from greatest to least, we need to convert all [tex]\pi[/tex] terms to degrees.

We know that π = 180°

[tex]\frac{\pi }{2} = \frac{180}{2} = 90[/tex]

[tex]\frac{5\pi }{3} = \frac{5*180}{3} = \frac{900}{3} = 300[/tex]

[tex]\frac{7\pi }{6} = \frac{7*180}{6} = \frac{1260}{6} = 210[/tex]

[tex]\frac{2\pi }{3} = \frac{2*180}{3} = \frac{360}{3} = 120[/tex]

Now we have converted all in degrees. Let's arrange them from greatest to least.

330, 300, 210, 120, 90

Let's write them using [tex]\pi[/tex] term.

330, [tex]\frac{5\pi }{3}[/tex], [tex]\frac{7\pi }{6}[/tex], [tex]\frac{2\pi }{3}[/tex], [tex]\frac{\pi }{2}[/tex]

Therefore, the answer is D) 330, [tex]\frac{5\pi }{3}[/tex], [tex]\frac{7\pi }{6}[/tex], [tex]\frac{2\pi }{3}[/tex], [tex]\frac{\pi }{2}[/tex]

Answer:

Shanna's family

Step-by-step explanation:

d/t = r (distance/time = rate)

Harlin: 363/6 = 60.5 mph

Kevin: 435/7 = 62.14 mph

Shanna: 500/8 = 62.5 mph

Hector: 215/5 = 43 mph

In the given equation, x is the amount of merchandise she sold.

Replace x with 1900 and solve.

0.24(1900) + 300 = 456 + 300 = 756

Her salary would be $756

Answer:

Step-by-step explanation:

https://brainly.com/question/2264840 Link to this question, but the answer is:

Carissa receives 17$ for each 100$ of merchandise she sells.This is on top of the traditional rate of 300 dollars a month.She will make 623$ for 1900$ worth of merchandise.

Answer:

The measurement of the required angle = 116°

Step-by-step explanation:

Let the measure of its supplement = x

The measurement of the required angle = 2x - 12

x + 2x -12 = 180

3x - 12 = 180

3x = 180 + 12

3x = 192

x = 192/3

x = 64°

The measurement of the required angle = 2 * 64 - 12 = 128 - 12 = 116°

Answer:

6a^4-2a

Step-by-step explanation:

First step: Distributive Property -2a^4-2a+8a^4

Second step: Combine like terms 6a^4-2a

Answer:

28°

Step-by-step explanation:

Hello!

The measurement (not mesrement) of k is 28°, because the shown 28° angle and angle k are "vertical angles" and thus are equal.

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

let [tex]log_{125}[/tex] 5 = n, then

5 = [tex]125^{n}[/tex]

note that 125 = 5³ ⇒ [tex](5^3) ^{n}[/tex] = [tex]5^{3n}[/tex]

Since bases are equal ( both 5) equate the exponents

3n = 1 ( divide both sides by 3 )

n = [tex]\frac{1}{3}[/tex]

The value of the expression log₁₂₅5 is 1/3.

The correct option is A.

The inverse of exponentiation is the logarithm. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.

Given:

A logarithmic expression,

let log₁₂₅5 = x

Then simplifying,

5 = (125)ˣ

That means,

x = 1/3

Therefore, x = 1/3.

To learn more about the logarithms;

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Answer:

y+7 = 4/3(x-9)

Step-by-step explanation:

Point slope form of an equation of a line is

y-y1 = m(x-x1) where (x1,y1) is the point and m is the slope

y--7 = 4/3(x-9)

y+7 = 4/3(x-9)

Answer:

SLOPE INTERCEPT FORM: y = 4/3x - 19

POINT SLOPE FORM: y - (-7) = 4/3(x - 9)

Step-by-step explanation:

Point slope formula is y - y1= m(x - x1)

Insert the information:

➡️y - (-7) = 4/3(x - 9)

(this is point slope form)^

distribute.

➡️y + 7 = 4/3x - 12

move constants on the left side to the right, to get y = mx + b.

➡️y = 4/3x - 19

I didn't know if you just wanted point slope form or to make it slope intercept form, so here's both.

let's notice that this triangular pyramid has a triangular base, that triangle has a base of 14 and an altitude of 8.485, whilst the pyramid also has a height of 12.

[tex]\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=&area~of\\ &its~base\\ h=&height\\ \cline{1-2} h=&12\\ B=&\frac{1}{2}(14)(8.485) \end{cases}\implies V=\cfrac{1}{3}\left[ \cfrac{1}{2}(14)(8.485) \right](12) \\\\\\ V=4\cdot (7\cdot 8.485)\implies V=237.58[/tex]

Answer:

x² + x + 8 = 0

Step-by-step explanation:

Given

(x - 2)² + 5(x + 2) - 6 = 0 ← expand (x - 2)² and distribute parenthesis by 5

x² - 4x + 4 + 5x + 10 - 6 = 0 ← collect like terms on left side

x² + x + 8 = 0 ← equivalent quadratic equation

Answer:

x² + x + 8 = 0

Step-by-step explanation:

(x-2)^2 + 5(x+2) - 6=0                     { (a-b)² = a² -2ab + b²; here a = x & b = 2}

x²- 2*x*2 + 2² + 5 x + 10 -6 = 0

x² - 4x + 4 + 5x + 10 - 6 = 0

x² + x + 4 + 10 - 6 = 0

x² + x + 8 = 0

Answer:

(2, -7).

Step-by-step explanation:

The center is the midpoint of the diameter.

This is  (5 + -1) / 2 ,  (-6+(-8)/2)

= (4/2, -14/2)

= (2, -7).

Answer: The center is (2,-7)

Step-by-step explanation:

In this case the center of this circle is the midpoint of its diameter. Then you need to use this formula:

[tex]Midpoint=Center=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

Knowing that this circle has a diameter whose endpoints are (5, -6) and (-1, -8), you can identify that:

[tex]x_1=5\\x_2=-1\\y_1=-6\\y_2=-8[/tex]

Then you can substitute these coordinates into [tex]Center=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex], getting:

[tex]Center=(\frac{5+(-1)}{2},\frac{-6+(-8)}{2})[/tex]

[tex]Center=(\frac{5-1}{2},\frac{-6-8}{2})[/tex]

[tex]Center=(2,-7)[/tex]

Answer:

The solution is:

Step-by-step explanation:

We have the following equation

[tex]-4(2x+3)=2x+6-(8x+2)[/tex]

To solve the equation apply the distributive property

[tex]-4(2x+3)=2x+6-(8x+2)[/tex]

[tex]-4*2x+3(-4)=2x+6-(1)*8x+2*(-1)[/tex]

Now simplify the expression

[tex]-8x-12=2x+6-8x-2[/tex]

[tex]-8x-12=-6x+4[/tex]

Add 6x +12 on both sides of the equation

[tex]-8x-12+6x+12=-6x+4+6x+12[/tex]

[tex]-2x=4+12[/tex]

[tex]-2x=16[/tex]

Divide both sides of the equality between -2

[tex]\frac{-2}{2}x=\frac{16}{-2}[/tex]

Answer:

C. x = 5, y = 2

Step-by-step explanation:

Simply plug in each given term in the answer choices, evaluate, then find out which two will make the system of equations authentic, or genuine.

Using the properties of exponents the expression rewritten as

3 • b^5 • c^5

You can group the repeated factors (b and c) and use exponents to represent their multiplication.

The expression 3•b•b•b•b•b•c•c•c•c•c can be written as:

(3)•(b•b•b•b•b)•(c•c•c•c•c)

This can be further simplified by raising b and c to their respective exponents:

(3)•(b^5)•(c^5)

Therefore, the rewritten expression is 3•b^5•c^5.

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The question is asking about how long it will take 3 people to trim a hedge if we know that 4 people can do it in an hour. This is an example of an inverse proportion problem. It would take the three people 45 minutes to trim the hedge.

The question asked is about the concept of rate and inverse proportion in mathematics. The problem states that four people can trim a hedge in one hour. If three people were to do the task, they would collectively be less productive per hour, consequently, it would take them longer to trim the hedge. We can calculate the new time by setting up a proportion of 4 people / 1 hour = 3 people / x hours

Cross-multiplying gives: 4x = 3 which simplifies to x = 3/4 hours. Since there are 60 minutes in an hour, multiply the fraction by 60 to convert to minutes. Thus, it would take the three people 45 minutes to trim the hedge.

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Answer:

D

Step-by-step explanation:

Since the triangle is right using the cosine ratio to solve for BC

noting that the exact value of cos45° = [tex]\frac{1}{\sqrt{2} }[/tex], so

cos45° = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{BC}{n}[/tex]

Multiply both sides by n

n × cos45° = BC

n × [tex]\frac{1}{\sqrt{2} }[/tex] = BC

[tex]\frac{n}{\sqrt{2} }[/tex] × [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex] = BC

Hence BC = [tex]\frac{n\sqrt{2} }{2}[/tex] → D

The right-angle triangle is given with one angle of 45 degrees. The length of segment BC is n√2/2.

A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse.

The angle of a right angle is always 90 degrees.

Since the triangle is right angle

by using the cosine ratio to solve for BC

The value of cos45° = 1/√2 ,

So,

cos45° = BC / AC = BC / n

Multiply both sides by n

n × cos45° = BC

n × 1/√2 = BC

n/√2 × √2 /√2 = BC

Hence, BC = n√2/2

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Answer:

A. supplementary

Step-by-step explanation:

Note the angle measurements of BOC. m∠BOC = 90°

Now note that line FC is a straight line, which makes it's measurement = 180°

Subtract 90 from 180: 180 - 90 = 90°

Both are 90°, which, when combined makes a supplementary angle.