In 2000 the number of students enrolled at Arlington County day school was 823 students in 2010 the population was approximately 705 students find the percent of change in the enroll students at Arlington County day school from 2000 to 2010 in identify it as an increase or decrease

Answer:

658.24 m

Step-by-step explanation:

Let A be the point from where Elton started. Connect points A and C, you get triangle ABC with AB=500 m, BC=350 m and m∠B=100°. Use the cosine rule to determine the length of the segment AC:

[tex]AC^2=AB^2+BC^2-2\cdot AB\cdot BC\cdot \cos \angle B,\\ \\AC^2=500^2+350^2-2\cdot 500\cdot 350\cdot \cos 100^{\circ},\\ \\AC^2=250000+122500-350000\cdot (-0.174),\\ \\AC^2\approx 433276.8622,\\ \\ AC\approx 658.24\ m.[/tex]

Answer:

658.24 m

Step-by-step explanation:

The figure makes a triangle with vertices abc.

Where ab = 500 m

           bc = 350 m

The angle abc = 100°

Using the cosine rule we can find the distance ac.

ac² = 500²+350² - 2×500×350×cos100°

      = 372,500 - -60,776.86

      = 433,276.86

ac = √433,276.86

    = 658.24 m

Answer:

Step-by-step explanation:

2 equal 90° angles, we can use an equation

x + 15 = 90

x = 90 - 75

x = 15°

-------------------------

check

90 = 15 + 75

90 = 90

the answer is good

Answer:

The value is  of given expression is -5+6i.

Step-by-step explanation:

The given expression is

[tex](-3+3i)+(-2+3i)[/tex]

It can be written as

[tex]-3+3i-2+3i[/tex]

Now combine like terms.

[tex](-3-2)+(3i+3i)[/tex]

[tex](-3-2)+(3+3)i[/tex]

Simplify each parenthesis.

[tex](-5)+(6i)[/tex]

[tex]-5+6i[/tex]

Therefore the value is  of given expression is -5+6i.

Answer:

A parallelogram is a quadrilateral whose opposite sides are parallel.

It's properties include:

- The opposite sides of a parallelogram are parallel.

- A diagonal of a parallelogram divides it into two congruent triangles.

- The opposite sides of a parallelogram are congruent.

- The opposite angles of a parallelogram are congruent.

- The consecutive angles of a parallelogram are supplementary.

- The diagonals of a parallelogram bisect each other.

a quadrilateral whose both pair of opposite side are equal and parallel to each other is called a parallelogram

[tex]AREA OF PARALLELOGRAM => BASE X HEIGHT = BXH [/tex]

any side of parallelogram can be chosen as the base of parallelogram the perpendicular dropped on that side from opposite vertex is known as height attitude

Answer:

355 senior citizen tickets were sold.

Step-by-step explanation:

Assuming a to the the ticket of adults and s to be the ticket of senior citizens, we can write two equations as:

[tex]a +s=465[/tex] --- (1)

[tex]23a+13s=7145[/tex] --- (2)

From equation 1, [tex]a=465-s[/tex].

Substitute [tex]a[/tex] in equation 2 to get:

[tex]23 (465-s) + 13s = 7145[/tex]

[tex]10695 - 23s +13s =7145[/tex]

[tex]-10s = -3550[/tex]

[tex]s = 355[/tex]

Therefore, there were 355 senior citizen tickets sold.

The point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

We have the slope m = 4 and the point (2, 1). Substitute:

[tex]y-1=4(x-2)[/tex]      use distributive property

[tex]y-1=(4)(x)+(4)(-2)[/tex]

[tex]y-1=4x-8[/tex]        add 1 to both sides

[tex]\boxed{y=4x-7}[/tex]

2) 5x>x+4

5x-x>x-x+4

4x>4

4x/4>4/4

x>1

3) 3x+4<10

3x+4-4<10-4

3x< 6

3x/3<6/3

x<2

4) -10x+5-4>7x-10

-10x+1>7x-10

-7x     -7x

-17x+1>-10

-1          -1

-17x>-11

/-17    /-17

+1(-x< 0.6470588)

x>0.6470588 (I'm kinda iffy about this one, so tell me if its right or not)

5)6x+3< 7x-10

6x+3-6x<7x-10-6x

3<x-10

3+10<x-10+10

13<x

6) 2x-4<8x+2

2x-4-2x<8x+2-2x

-4<6x+2

-4-2<6x+2-2

-6<6x

-6/-6<6x/-6

1>x (remember when you divide by a negative number you have to flip the sign)

(I'm sure you kinda get the idea of how you do it so I'll just put the answers for the rest of the questions)

7) x<0

8) s>1

9) t<2

10) x<11

11) x>12

12) x<20

13) r<5

14) s>36

15) x<8

Tell me if any of them were incorrect, I hope this helped a little!

Answer:

1.-4x + 2 >0

Is x < 1/2

Step-by-step explanation: This is the number 1 question of this assignment.

Answer: 2

You can use a calculator to compute the square root of 4 to get 2.

Or you can think of a geometric square with side lengths of some number that multiply to an area of 4. The only possible square is a 2 by 2 square since 2*2 = 4. This is where the term "square root" comes from for the most part.

Answer:

[tex]f^{-1}=+-\sqrt{x+1}[/tex]

Step-by-step explanation:

f(x) = x^2 -1

We need to find f^-1(x)

WE find inverse of f(x)

Replace f(x) with y

[tex]y= x^2 -1[/tex]

Replace x  with y  and y with x

[tex]x= y^2 -1[/tex]

Solve for y

add 1 on both sides , [tex]x+1= y^2[/tex]

To remove square , take square root on both sides

[tex]\sqrt{x+1} =\sqrt{y^2}[/tex]

[tex]\sqrt{x+1} =y[/tex]

[tex]y=+-\sqrt{x+1}[/tex]

Replace y with f^-1

[tex]f^{-1}=+-\sqrt{x+1}[/tex]

Answer:

Inverse function is

[tex]f^{-1}(x)=\pm \sqrt{x+1}[/tex]

Step-by-step explanation:

Given that [tex]f(x)=x^2-1[/tex]

Now using that equation of f(x), we need to find equation of the inverse function

[tex]f(x)=x^2-1[/tex]

[tex]f^{-1}(x)[/tex]

Step 1: Replace [tex]f^{-1}(x)[/tex] with y

[tex]y=x^2-1[/tex]

Step 2: Switchx and  y

[tex]x=y^2-1[/tex]

Step 3: Solve for y

[tex]x=y^2-1[/tex]

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

[tex]x+1=y^2[/tex]

[tex]y^2=x+1[/tex]

take square root of both sides

[tex]y=\pm \sqrt{x+1}[/tex]

Hence inverse function is

[tex]f^{-1}(x)=\pm \sqrt{x+1}[/tex]

The solution to the system of equations is (12, 30).

Option B is the correct answer.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We also find the solution in a system of equations using the substitution or elimination method.

Example:

2x + 4 = 8

The solution is x = 2.

We have,

To solve the system of equations using the substitution method,

We solve one equation for one of the variables and substitute the expression into the other equation.

Let's solve the first equation for y:

y = 2x + 6

Now, substitute y = 2x + 6 into the second equation and solve for x:

3x - y = 6

3x - (2x + 6) = 6

3x - 2x - 6 = 6

x = 12

Now that we have found x, we can substitute it back into either of the original equations to find y.

Let's use the first equation:

y = 2x + 6

y = 2(12) + 6

y = 30

Therefore,

The solution to the system of equations is (12, 30).

Learn more about solutions of equations here:

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Answer:

the answer is false.

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

2x+y=3

⇒ This equation can be written in the form of y = mx + c where m is the slope, c is the y-intercept and x and y are x and y coordinates respectively of the point where the the line passes.

2x+y=3

y = -2x + 3.

If the line passes through the origin (0,0), then c = 0. This is not the case in our eqation.

Again if the question passes through the origin, by substituting the point (0,0) in the question it would satify it.

2x+y=3  ⇒ 2(0) + 0 = 3

                     0 + 0 ≠ 3

                      0 ≠ 3

The statement is false.

Answer:

Step-by-step explanation:

you dont have enough information to solve the problem, you need to know the length of the ladder in order to find the closet length of the building.

Answer: 1.60x + 1.75y is less than or equal to 10

Step-by-step explanation:

Since the strawberries cost $1.60 per pound, it would be x pounds times $1.60 for the total cost of strawberries. Since the raspberries cost $1.75 per pound, it would be y pounds times $1.75 for the total cost of the raspberries. The total cost of both, or 1.60x + 1.75y, must be equal to or less than 10 because she cannot spend over 10 dollars.

The situation can be represented by the equation 1.60x + 1.75y = 10, where x represents the pounds of strawberries and y represents the pounds of raspberries. To find out how many pounds of strawberries and raspberries Joy can buy, we can rearrange the equation and solve for x and y.

The situation can be represented by the equation 1.60x + 1.75y = 10, where x represents the pounds of strawberries and y represents the pounds of raspberries. To find out how many pounds of strawberries Joy can buy, we can rearrange the equation to solve for x: x = (10 - 1.75y) / 1.60. Similarly, to find out how many pounds of raspberries Joy can buy, we can rearrange the equation to solve for y: y = (10 - 1.60x) / 1.75.

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Answer:

8.4 * 10^6

Step-by-step explanation:

8.4 * 10^6

1 million = 1 * 10^6

8 million 4 hundred thousand is 8.4 * 10^4 because this number is 8.4 times bigger than a million.

Answer: No

Step-by-step explanation:

23,453 is not a perfect square, this is because no rational number times itself equals 23,453, which can be proven if you go into a calculator and find the square root of 23,453, which is about 153.1437 (but it continues going, making it an irrational number.)

Hope this helps!

Answer:

6) 24+4x

7) -24x+32

8) -21+42x

9)-24x-12

10) 72- 18x

Step-by-step explanation:

for each problem, you need to distribute the single variable to the parenthesis  for the final answer. For example, 3 (4x-25) > 3 x 4x = 12x > 3x-25 = -75 now you put both answers together making it 12x-75

Answer:

Step-by-step explanation:

The installation cost is $300 and the cost per square foot is $4 . So the total price is y= 4x + 300 (where x is square foot).

slope is 4 and y intercept is 300

for 375 sqft. the cost is y= 4(375) +300 = 1800

the cost is $1800

Answer: Marcus can make 6 sandwiches.

Step-by-step explanation:

If you have 12 slices of bread and use 2 for each sandwich you would do 12/2, which equals 6.

Final answer:

To find out how far Sarah can drive on a full tank of gas, the correct proportion is '77/3.6 = x/15'. This compares the known miles driven to gallons used, scaled up to a full tank of 15 gallons, representing the distance with 'x'. So the correct option is d.

Explanation:

The student is working on solving a proportion problem related to fuel consumption and driving distances. To find out how far Sarah can drive her car on a full tank of gas, we need to set up a proportion that compares miles driven to gallons used, and then scale it up to a full tank of gas.

Since Sarah drove 77 miles on 3.6 gallons of gas, we can compare this to a full tank of 15 gallons to find the total distance she can drive, represented by 'x'. The correct proportion is 77 miles to 3.6 gallons as 'x miles' is to 15 gallons.

The correct proportion is d. 77/3.6 = x/15, as it reflects the direct relationship between miles driven and gallons of fuel. When the gallons are increased from 3.6 to 15, we expect the miles that can be driven to increase proportionally.

[tex]x\Delta y=x-5y\\\\3\Delta(-4)\qquad\text{put the values x = 3 and y = -4 to the expression x - 5y}:\\\\3\Delta(-4)=3-5(-4)=3+20=23[/tex]

Answer: y = 17x

Step-by-step explanation:

Note that the equation that will be used is: y = mx + b,in which m = slope and b = y-intercept.

Solve for b:

0 = 17(0) + b

Simplify:

0 = 0 + b

b = 0

Equation: y = 17(x)

~

ABOUT POINT SLOPE FORM:

ABOUT PROBLEM:

y - Y1 = m (x - X1)

y - 0 = 17 (x - 0) --- IN POINT SLOPE FORM

Hope this helps you!!! :)

Answer:

Number of marbles are 200000

Step-by-step explanation:

Rectangular box:

length = 5 feet

width =4 feet

height =3 feet

now, we can find volume of box

[tex]V=L\times W\times H[/tex]

[tex]V=5\times 4\times 3[/tex]

[tex]V=60ft^3[/tex]

Volume of marbles:

We know that shape of marbles will be in sphere

we are given

diameter =1 inch

radius =0.5 inch

[tex]r=\frac{0.5}{12} ft[/tex]

now, we can find volume

[tex]V=\frac{4}{3}\pi r^3[/tex]

we can plug value

[tex]V=\frac{4}{3}\pi (\frac{0.5}{12})^3[/tex]

[tex]V=0.00030[/tex]

now, we can find number of marbles

Number of marbles = ( volume of box)/( volume of marbles)

So, number of marbles are

[tex]=\frac{60}{0.00030}[/tex]

[tex]=200000[/tex]

Answer:

What points do I check?

Step-by-step explanation:

Answer:

x= -1/4

x= 3

Step-by-step explanation:

Any irrational number never ends. So, you can take square roots. 4 is the square root of 16, and 6 is the square root of 36. So, take the square root of any number between 16 and 36 except for 25. For example, 17 is between 16 and 36. So, sqrt(17) is therefore irrational. You can't take the square root of 25 because that would result in a rational number, 5.

Answer:

The difference is 145.7

Step-by-step explanation:

89+56.7= 145.7

Answer:

-32.3

Step-by-step explanation:

I got -32.3 because when I subtracted -89 from 56.7 I got -32.3. If you don't know how to subtract integers it's simple, you just subtract 89 from 56.7 then choose the sign that has the greater absolute value. In this case -89 has the greater absolute value, so you take the negative sign.

Answer:

C and D

Step-by-step explanation:

The Middles were the same length and the side of the alligator are slightly longer.

The correct options are:

C.  Center-- The crocodiles have a greater median length than the alligators.

D.   Spreads--  The lengths of the alligators are more spread out.

Median of the data--

The median is the central tendency of the data and it always exist in the middle of the data.

By looking at the data.

We observe that the Median of the data :

Crocodile lie at : 17

and that of the alligator lie at : 9

Hence, the median for the crocodile is more than for the alligators.

Spread--

The spread in the data means how far the data points are from the center of the data i.e. mean or median.

By looking at the data crocodile we observe that all the data points are close to the median.

whereas in the data alligator one of the data point is far from the median.

Hence, the spread in case of alligator is more as compared to that of crocodiles.

Answer:

Yes, one of a rhombus's properties is that the diagonals bisect vertex angles.

The diagonals of a rhombus bisect the vertex angles.

Yes, the diagonals of a rhombus bisect the vertex angles.

To understand this, we can consider that in a rhombus, the diagonals are perpendicular to each other, and when a diagonal bisects an angle, it creates two congruent triangles.

Therefore, the diagonals of a rhombus do indeed bisect the vertex angles.

Answer:

area of a triangle is 1/2bh

1/2 X 15 x 9 = 67.5 square feet

Step-by-step explanation:

For this case we must find the area of a flower bed with a triangle shape.

The area of a triangle is given by:

[tex]A = \frac {b * h} {2}[/tex]

Where:

b: It's the base

h: It's the height

Substituting the given values:

[tex]A = \frac {15 * 9} {2}\\A = 67.5\ ft ^ 2[/tex]

Answer:

[tex]A = 67.5\ ft ^ 2[/tex]

Final answer:

The question compares two breathing rates: 15 breaths every 36 seconds and 90 breaths every 3 minutes. When converted to breaths per minute, the rates are 25 breaths/minute and 30 breaths/minute respectively, indicating that they are not equivalent.

Explanation:

The question asks whether 15 breaths every 36 seconds and 90 breaths every 3 minutes represent an equivalent rate of breathing. To solve this, we need to determine if the two rates are the same when converted to a common time unit.

First, let's convert 36 seconds to minutes: 36 seconds is 0.6 minutes (since 1 minute is 60 seconds). Next, we calculate the breathing rate per minute for the first scenario by dividing the number of breaths by the number of minutes: 15 breaths / 0.6 minutes = 25 breaths/minute.

Now let's look at the second rate of 90 breaths every 3 minutes. This can be simplified by dividing the number of breaths by the number of minutes: 90 breaths / 3 minutes = 30 breaths/minute. Clearly, 25 breaths/minute is not equivalent to 30 breaths/minute. Therefore, 15 breaths every 36 seconds and 90 breaths every 3 minutes are not equivalent rates of breathing.