The city council is planning to construct a park on North Street that has a triangular perimeter. They want to place a fountain at a point equidistant from all three sides of the park. Where should the council place the fountain?
A.
at the point of intersection of the angle bisectors and perpendicular bisectors of the park
B.
at the center of the inscribed circle of the park
C.
at the center of the circumscribed circle of the park
D.
at the point of intersection of the lines perpendicular to two sides of the park
E.
at the point of intersection of the medians of the park

Answer:

[tex]8\sqrt{3}\ units[/tex]

Step-by-step explanation:

Let

x----> the side opposite the 60 angle

Applying the law of sines

[tex]\frac{8}{sin(30)}=\frac{x}{sin(60)}\\ \\x=8*sin(60)/sin(30)\\ \\x=8\sqrt{3}\ units[/tex]

Ken earned $128 from his part-time job and spent 25% of it, leaving him with $96. He then donated 1/6 of the remaining money to charity, which equals $16.

This problem is about percentages and fractions. Ken earned $128 from his part-time job and spent 25% of it on games, which equals <$128 * 25/100 = $32>. So after buying games, Ken is left with <$128 - $32 = $96>. Ken then decides to donate a fraction, 1/6 of the remaining money to charity. To figure out how much he donates, we multiply $96 by 1/6, which is <$96 * 1/6 = $16>. So, Ken donates $16 to charity from his summer job earnings.

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Answer:

The graph is as attached.

Step-by-step explanation:

Simply draw a line of x = 2 on your graph paper.

That line should be a complete line not dotted line.

Since x is greater than 2, shade the left side of the line because we are interested in the right side (where x is greater and equal to 2)

Answer:

Here, the given inequality,

[tex]x\geq 2[/tex]

Related equation is,

x = 2

Which is the equation parallel to y-axis and passes through (2,0),

Also, 0 ≥ 2 ( False )

The shaded region of the inequality will not contain the origin,

Now, '≥' shows the solid line.

Thus, by the above explanation,

We can graph the given inequality ( shown below )

The answer to this is:

B. 190

The sum of the first 10 terms of the sequence an=4n-3 is 190.

The question is asking for the sum of the first 10 terms of the sequence defined by an=4n-3. To find the sum, we first list the first 10 terms by substituting values of n from 1 to 10 into the formula. Thus, for n=1, a1=1(4)-3=4-3=1; for n=2, a2=2(4)-3=8-3=5; and so on until n=10, a10=10(4)-3=40-3=37.

The first ten terms of the sequence are: 1, 5, 9, 13, 17, 21, 25, 29, 33, and 37. The sum of these terms can be calculated as 1+5+9+13+17+21+25+29+33+37 = 190.

Answer:

12cm.

Step-by-step explanation:

The radius is half of a circe.

6 * 2 = 12.

Answer:

37.68 cm

Step-by-step explanation:

the circumference of a circle  is :   P = 2π r

P= 2×3.14×6 =37.68 cm

They were able to make 40 burgers with it

Answer: 40 hamburgers

Step-by-step explanation:

15 pounds x 16 ounces=240 ounces of hamburger meat

Each burger is 6 ounces 240 divided by 6= 40 hamburgers

Answer: [tex]68ft^2[/tex]

Step-by-step explanation:

The formula for calculate the surface area of a rectangular prism is:

[tex]SA=2lw+2lh+ 2wh[/tex]

Where "l" is the lenght, "w" is the width and "h" is the height.

In this case, you know that the top of the flower box is opened, then, the formula changes to:

[tex]SA=lw+2lh+2wh[/tex]

You can identify that the dimensions of the box are:

[tex]l=10ft\\w=2ft\\h=2ft[/tex]

Then you must substitute these values into the formula [tex]SA=lw+2lh+2wh[/tex].

 Finally, you get that the surface area of the open-top flower box is:

[tex]SA=lw+2lh+ 2wh\\SA=(10ft)(2ft)+(2)(10ft)(2ft)+(2)(2ft)(2ft)]\\SA=68ft^2[/tex]

Answer:

The surface area of box =  64 ft²

Step-by-step explanation:

From the figure we can see that a cuboid with length = 10 ft, width = 2 ft and height = 2 ft

To find the surface area of cuboid

Surface area = 2(lb + bh +  lh) - lh

  = [2(10 * 2) + (2 * 2) + (10 * 2)] - (10 * 2)

  = [2( 20 + 4 + 20)] - 20

  = 2 * 44 - 20 = 84 - 20 = 64 ft²

The correct answer is surface area of box =  64 ft²

156

Explanation:

3 x -4 =-12

-12 x -12 = 144

2 x 6 = 12

12 + 144 =156

Answer:

60

E

Step-by-step explanation:

Givens

a = - 4

b = 6

Formula

3a^2 + 2b

Solution

3(-4)^2 + 2*6

3(16) + 12

48 + 12

Answer: 60

Answer:

The chef would need 5 bags

Step-by-step explanation:

Because 3 times 5 equals 15

To determine the number of bags of flour the chef should buy, divide the total weight required (15 lb) by the weight of one bag (3 lb), resulting in the need to purchase 5 bags.

To find out how many bags of flour the chef should buy, we need to divide the total weight of flour needed by the weight of one bag. If a bag weighs 3 lb, and the chef needs 15 lb, we calculate it as follows:

Determine the total weight needed: 15 lb.

Determine the weight of one bag: 3 lb.

Divide the total weight by the weight of one bag: 15 lb \/ 3 lb = 5 bags.

Therefore, the chef should buy 5 bags of flour to have a total of 15 lb.

Answer: [tex]10x^2+3xy+6x-y^2+3y[/tex]

Step-by-step explanation:

You need to remember the Product of powers property:

[tex](a^m)(a^n)=a^{(m+n)}[/tex]

Then, knowing this property, now you have to apply the Distributive property. So:

[tex](2x+y)(5x-y+3)=\\\\=(2x)(5x)-(2x)(y)+(2x)(3)+(y)(5x)-(y)(y)+(y)(3)\\\\=10x^2-2xy+6x+5xy-y^2+3y[/tex]

Finally, to simplify this expression, you need to add the like terms.

Therefore, you get that the product is:

[tex]=10x^2+3xy+6x-y^2+3y[/tex]

Answer:

10 3 6 -1 3

Step-by-step explanation:

Check the picture below.

make sure your calculator is in Degree mode.

ANSWER

[tex] \frac{1}{2} [/tex]

EXPLANATION

The frequency of a wave function refers to the number of times the graph repeats its cycle within the interval [0,2π]

We can observe explicitly from the graph that the frequency is half.

The period of the given function is 4π

[tex] \frac{2\pi}{b} = 4\pi[/tex]

[tex]b = \frac{2\pi}{4\pi} = \frac{1}{2} [/tex]

Hence the frequency is half.

Answer:

15

Step-by-step explanation:

3 options x 5 options = 15 total options

Answer:

thats just things u needto remember.

Step-by-step explanation:

The expression is not factorable with rational numbers.

5

x

−

9521

The solution of the inequality {5x < 9521} is given by the inequality → x < 1904.2.

An inequality is used to compare two or more expressions or numbers.

For example -

2x > 4y + 3

x + y > 3

x - y < 6

Given is to find the solution set of the inequality →

5x < 9521

The given inequality is -

5x < 9521

Dividing by {5} on both sides, we get -

(5x/5) < (9521/5)

x < 1904.2

Therefore, the solution of the inequality {5x < 9521} is given by the inequality → x < 1904.2.

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In order to find out the total number of crayons, you multiply the number of cases by the number of boxes per case, and then by the number of crayons per box. Assuming the store donated 5 cases, the daycare center received a total of 960 crayons.

To determine how many crayons the daycare center received from the store, we need to multiply the number of cases the store donated by the number of boxes in each case, and then multiply that by the number of crayons in each box. Let's break it down step by step:

Assuming the store donated 5 cases (the number of cases was not specified in the question, so we need to assume a number for this example), here's how you would calculate it:

Therefore, the daycare center received a total of 960 crayons.

Answer:

a) yes

b) yes

c)  days

d) equation: 18 - 0.8x =1.2

solution: 21

e)inequality: equation: 18 - 0.8x [tex]\geq[/tex]1.2

solution: x < 21. This means that if he drives for less than 21 days the warning sign won't turn on.

Step-by-step explanation:

a) 18 - 15*0.8 = 6 so yes

b) 18 - 20*0.8 = 18 - 16 = 2

d) 18 - 0.8x =1.2

0.8x = 16.8

x = 16.8/0.8 = 21

Final answer:

a. No, the car cannot go 15 days without the warning light turning on. b. No, the car cannot drive 20 days without the light coming on. c. 'T' in the expression 18 - 0.8t stands for the number of days of fuel usage. d. Diego's car can go 21 days before the warning light turns on. e. The inequality 18 - 0.8t > 1.2 represents the situation.

Explanation:

a. To determine if Diego's car can go 15 days without the warning light turning on, we need to find out how much fuel will be left after 15 days of usage. Each day the car uses 0.8 gallons of fuel, so after 15 days, the car will have used 15 * 0.8 = 12 gallons of fuel. Starting from a full tank of 18 gallons, the remaining fuel after 15 days will be 18 - 12 = 6 gallons. Since the warning light comes on if the remaining fuel is 1.2 gallons or less, Diego's car will not be able to go 15 days without the warning light turning on.

b. To determine if Diego's car can drive 20 days without the light coming on, we follow the same steps as in part a. After 20 days, the car will have used 20 * 0.8 = 16 gallons of fuel. Starting from a full tank of 18 gallons, the remaining fuel after 20 days will be 18 - 16 = 2 gallons. Since the remaining fuel is less than 1.2 gallons, the warning light will turn on before 20 days.

c. In the expression 18 - 0.8t, 't' represents the number of days of fuel usage.

d. To determine the number of days Diego's car can go before the warning light turns on, we need to solve the equation 18 - 0.8t = 1.2. Rearranging the equation, we have 0.8t = 18 - 1.2, which simplifies to 0.8t = 16.8. Dividing both sides by 0.8, we get t = 21. So Diego's car can go 21 days before the warning light turns on.

e. To write an inequality that represents this situation, we can say that the remaining fuel after t days should be greater than 1.2 gallons. This can be expressed as 18 - 0.8t > 1.2. Solving this inequality, we get t < 21. This means that Diego's car can go up to 20 days before the warning light turns on, but on the 21st day, the warning light will turn on.

Answer:

[tex]y=10x-32 \\ \\ x=\frac{y}{10}+3.2[/tex]

Step-by-step explanation:

[tex]y=10x-32[/tex]

Because that's the equation given.

To solve for x, isolate the variable and then divide by the coefficient.

[tex]y=10x-32 \\ \\ 10x=y+32 \\ \\ x=\frac{y}{10}+\frac{32}{10} \\ \\ x=\frac{y}{10}+3.2[/tex]

Answer:

Step-by-step explanation:

In elementary algebra, the quadratic formula is the solution of the quadratic equation. There are other ways to solve the quadratic equation instead of using the quadratic formula, such as factoring, completing the square, or graphing.

My bro is right good job

Answer:

6 & 2

21 & 9

8 & 12

18 & 6

Step-by-step explanation:

Answer:

81y^4 - 16x^2, difference of squares.

Step-by-step explanation:

So we need to expand the following product:

(9y2-4x)(9y2+4x) = 9y2*9y2 + 4x*9y2 - 4x*9y2 -4x*4x = 81y^4 - 16x^2

And this type of product is the difference of squares.

Answer:

Step-by-step explanation:

The given expression is ( 9y² - 4x) (9y² + 4x)

We will simplify the given expression

(9y² - 4x) (9y² + 4x) = 9y² (9y² + 4x) - 4x (9y² + 4x)  [Distributive property]

= 81y⁴ + 36xy² - 36xy² - 16x²

= (81y⁴ - 16x²)

This simplified form is the difference of squares of terms (9y²) and (4x)

Answer:

Step-by-step explanation:

Use the order of operations.

First multiplication next addition and subtraction (from left to right).

4 + (-3) - 2 × (-6)

= 4 - 3 + 12

= 1 + 12

= 13

(-)(-) = (+)

(+)(-) = (-)(+) = (-)

(+)(+) = (+)

Answer:

13

Step-by-step explanation:

12x+1 = 13

Answer:

Part 1) The domain is

[tex]x\leq 4[/tex]

All real numbers less than or equal to 4

Part 2) The range is

[tex]y\geq 0[/tex]

All real numbers greater than or equal to 0

Step-by-step explanation:

Part 1) Find the domain

Observing the graph

we know that

The domain is the interval for x ------> (-∞,4]

so

[tex]x\leq 4[/tex]

All real numbers less than or equal to 4

Part 2) Find the range

Observing the graph

we know that

The range is the interval for y ------> [0,∞)

[tex]y\geq 0[/tex]

All real numbers greater than or equal to 0

Answer:f

1/4y +-7/4 is your answer hope this help if it did mark me brainliest

Step-by-step explanation:

Answer:

the answer is d

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:  x7

 x7

Step by step solution :

Step  1  :

           x14

Simplify   ———

           x7  

Dividing exponential expressions :

1.1    x14 divided by x7 = x(14 - 7) = x7

Answer:

x7

Step-by-step explanation:

It would B. 9.

Reason to this is because the radius is outlined by line GL. GL is half of the diameter which is GJ.

The answer is B. 9 because GJ is the circumference of the circle and they’re basically asking you to find the radius and the radius is half the circumference and half of 18 is 9 so the answer would be B.

Answer:

A. AB and EF

B. AC, CB, and EF

D. AD, DB, and EF

Step-by-step explanation:

The lengths would help  you to calculate the volume of the oblique pyramid are:

An oblique pyramid is known to be a type of shape that is often known as 'right pyramid'.

Note that its shape is one that has the ap.ex "is shaped" to one side and as such the options that can best explain the volume of the oblique pyramid is the ones written above.

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ANSWER

[tex]d = 3 \sqrt{13} [/tex]

EXPLANATION

We use the distance formula to find distance between two points.

[tex]d = \sqrt{(x_2-x_1)^2 +(y_2-y_1)^2} [/tex]

The two points are R(-1, 0) and S(8, 6).

We substitute the points into the formula to get:

[tex]d = \sqrt{(8 - - 1)^2 +(6-0)^2} [/tex]

[tex]d = \sqrt{(9)^2 +(6)^2} [/tex]

[tex]d = \sqrt{81+36} [/tex]

[tex]d = \sqrt{117} [/tex]

[tex]d = 3 \sqrt{13} [/tex]

Therefore the distance between the two points is [tex]3 \sqrt{13} [/tex] units.

Answer:

The distance between these points = 3√13

Step-by-step explanation:

Points to remember

Distance formula

Length of a line segment with end points (x1, y1) and (x2, y2) is given by,

Distance = √[(x2 - x1)² + (y2 - y1)²]

It is given two points R(-1, 0) and  S(8, 6)

To find the distance

Here, (x1, y1)  = (-1, 0) and (x2, y2) = (8, 6)

Distance = √[(x2 - x1)² + (y2 - y1)²]

= √[(8 - -1)² + (6 - 0)²]

= √[(8+1)² + (6)²]

 =√[(9)² + (6)²]

 = √[(81 + 36)]

 =√117 = √(3 * 3 * 13)

 = 3√13

The distance between these points = 3√13

Answer:

Step-by-step explanation:

X+2x-5= 40

3x-5=40

+5=+5

3x=45

3x/3=45/3

X=15

Answer:

Step-by-step explanation:

The sum of two number is 40 would be:

[tex]x+y=40[/tex]

The second number is 5 less than twice the first number would be:

[tex]y=2x-5[/tex]

Now, we can find the value by solving this system of equations, we will isolate x in the first equation, then we replace it in the second equation:

[tex]x=40-y[/tex]

[tex]y=2(40-y)-5\\y=80-2y-5\\y+2y=75\\3y=75\\y=\frac{75}{3}=25[/tex]

Then, we replace this value in one equation of find the other variable:

[tex]x+25=40\\x=40-25\\x=15[/tex]

Therefore, the value of the first number is 15 and the second number is 25.

Answer:

3/11

Step-by-step explanation:

First, determine how many dogs are at the boarding service:

2+8+22+12 = 44

Then:

# of Dobermans          12

--------------------------  =  ------- = 6/22 or 3/ 11

     total # of dogs         44

The desired ratio is 3/11.