A falcon flying at a height of 200 yards spots a sparrow flying at a height of 150 yards. The location of the sparrow makes an angle of 40° from the horizontal line through the falcon's location. What is the distance x between the falcon and the sparrow? Assume that the ground beneath the birds is level.

Answer:

28.26

Step-by-step explanation:

π r² = A

A = (3.14) (3²)

A = 3.14 · 9 = 28.26

Hello There!

WHAT WE KNOW

Pi = 3.14

R = 3

HOW TO SOLVE

A = 3.14*9

Answer 28.26

Answer:

x=5, Now you just have to insert x into the equation for DG

Step-by-step explanation:

2x+4=4x-6

-2x     -2x

 4=2x-6

+6     +6

 10=2x

÷2   ÷2

5=x

Answer:

W = 7.5 in

Step-by-step explanation:

We'll use the formula for the perimeter of a rectangle:  P = 2W + 2L.

Here, L = W + 5, so P = 2W + 2L becomes:

P = 2W + 2(W + 5), and this equals 40 in.

Thus we have the equation in W (the desired variable) as follows:

2W + 2(W + 5) = 40 in, or 4W + 10 = 40.

Then 4W = 30, and W = 7.5 in.

Based on the perimeter of this rectangle, the width is 7.5 inches.

The perimeter of a rectangle is calculated by:

= Length + Width + Length + Width

Assuming the width is denoted by x, the length would be:

Length = 5 + Width

Length = 5 + x

The perimeter is given so we can solve for the width:

Length + Width + Length + Width  = Perimeter

5 + x + x + 5 + x + x = 40

10 + 4x = 40

4x = 40 - 10

x = 30/4

x = 7.5 inches

In conclusion, the width is 7.5 inches.

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Answer:

Step-by-step explanation:

If you're given a line, determine its slope.

Any parallel line you construct must have the same slope as does the given line.

Any perpendicular line you construct must have a slope which is the negative reciprocal of the slope of the given line.

Parallel lines have the same slope.

And perpendicular lines have negative reciprocal slopes. Ex. 2/3 x and -3/2x

±1/2. The equation [tex]4x^{2} =1[/tex] has two possible solutions +1/2 and -1/2.

The problem is a quadratic equations and it can be solved using the equation [tex]x=-b±\frac{\sqrt{b^{2} -4ac} }{2a}[/tex].

Ordering the quadratic equation given in the problem, we obtain [tex]4x^{2} -1=0[/tex] where a = 4, b = 0, and c = -1

Substituting the values

[tex]x=±\frac{\sqrt{-4(4)(-1)} }{2(4)}=±\frac{\sqrt{16}}{8} =±\frac{4}{8} \\x=±\frac{1}{2}[/tex]

The answer is:

The correct option is the second option,

[tex]4x^{2}=+-\frac{1}{2}[/tex]

We are given the expression:

[tex]4x^{2}[/tex]

Now, solving we have:

Applying square root to both sides of the equation in order to isolate x:

[tex]4x^{2}=1\\\\\sqrt{4x^{2} } =+-\sqrt{1}\\\\2x=+-1\\\\x=+-\frac{1}{2}[/tex]

Hence, the correct option is the second option,

[tex]4x^{2}=+-\frac{1}{2}[/tex]

Have a nice day!

Answer:

the answer is a. y=2x+4

Answer: A y = 2x + 4

for USATestprep

Answer:

C

Because of the markings showing equal length lines 7x + 4 is double 4x or 48 is three times the length of 4x

Either solve 7x + 4 = 8x

4 = x

Or solve 48 = 12x

4 = x

Substitute back in to 7x + 4 ......MN = 7 x 4 + 4 = 32

Answer:

w/5 ≥ 25

Step-by-step explanation:

Quotient means division

w/5

is at least means great than or equal to

w/5 ≥ 25

Answer:

answer is B...2 1/2

Step-by-step explanation:

4(t+1)=6t-1

4t+4=6t -1

4t-6t+4=6t-6t-1

-2t+4=-1

-2t+4-4=-1-4

-2t=-5

Divide by -2 for -2t and -5

-2t/-2=-5/-2

t=5/2= 2 1/2

Answer is b) 2 1/2

Answer:

1st pic: Answer is 3

2nd pic: Answer is 5

3rd pic: Answer 4

Step-by-step explanation:

Answer:

f(1/3) = 1

Step-by-step explanation:

Given

f(n)=3n

We have to find f(1/3).

In order to find the value of the given function at a point, we put the value in the function where the variable is used.  

i.e. to find f(2) for f(x); x will be replaced by 2 in the function. Similarly to find f(1/3), we will replace n by 1/3 in the function.

So to find  

f(1/3)=3*  1/3

=1

So, the value of f(1/3) is 1 ..

Answer:

f(x) = x + 4

Step-by-step explanation:

Given

y - x - 4 = 0 ( add x to both sides )

y - 4 = x ( add 4 to both sides )

y = x + 4 ( let y = f(x) )

f(x) = x + 4

The correct option is C.

Carlos can make 4 different burgers by choosing between beef or turkey and wheat or white roll.

To calculate the number of different burgers Carlos can make, we'll use the fundamental principle of counting.

Step 1: Determine the number of options for the type of burger. Carlos can choose either beef or turkey, so there are 2 options.

Step 2: Determine the number of options for the type of roll. Carlos can choose either wheat or white, so there are 2 options.

Step 3: Multiply the number of options for each step together to find the total number of combinations.

Number of burger options × Number of roll options = Total combinations

2 options for type of burger × 2 options for type of roll = 4 total combinations

So, Carlos can make 4 different burgers.

Answer: C. 4

The complete question is here:

Carlos can choose from a beef or turkey burger and from a wheat or a white roll. How many different burgers can he make?

A. 8

B. 3

C. 4

D. 2

Answer:

5.5360

Step-by-step explanation:

I added

5+0.5= 5.5

5.5+0.03=5.53

5.53+0.006=

5.5360

the correct answer is b.33

Answer:

b

Step-by-step explanation:

Answer:

Craig earns $1,200 each month

Explanation:

We are given that Craig pays a total of $720 each year for his telephone service

We also know that a year has 12 months

This means that:

Craig pays [tex]\frac{720}{12}= 60[/tex] dollars each month for his telephone services

We are given that the monthly phone bill is [tex]\frac{1}{20}[/tex] of his monthly earnings

Assume that his monthly payment is x

We have:

[tex]\frac{1}{20}x = PhoneBill\\ \\ \frac{1}{20}x = 60\\ \\   x=60*20 = 1200[/tex] dollars

Hope this helps :)

Craig earns about $1200 each month and pays a total of $720 each year for his telephone service.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the amount earned each month

Hence:

(1/20)x * 12 months = 720

x = 1200

Craig earns about $1200 each month and pays a total of $720 each year for his telephone service.

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The answers are:

- The quantity that represents the initial number of bacteria is 64.

- The quantity that represents the rate at which the number of bacteria is increasing is (1+0.12) or 1.12 which means the growth rate percentage for the bacteria is 0.12 or (0.12*100), it will be 12%.

To solve the problem, and complete the statements, we need to remember the form of the exponential growth.

The exponential growth formula is given by the following formula:

[tex]P(t)=StartAmount(1+PercentageRate)^{t}[/tex]

Where,

Start Amount, is the starting population or amount.

(1+Percentage Rate), is the increasing rate

Percentage Rate, is the growth rate percentage.

t, is the time elapsed.

Now, we are given the following expression:

[tex]P(3)=64(1.12)^{3}[/tex]

Which can be rewrited as:

[tex]P(3)=64(1+0.12)^{3}[/tex]

So, we have that:

- The quantity that represents the initial number of bacteria is 64.

- The quantity that represents the rate at which the number of bacteria is increasing is (1+0.12) or 1.12 which means the growth rate percentage for the bacteria is 0.12 or (0.12*100), it will be 12%.

Have a nice day!

Answer:

b

Step-by-step explanation:

Answer:

171 sq units.

Step-by-step explanation:

Since you don't specify you want a the side surface area only, we'll calculate both.

First, the base...

We have a square with a side of 9 units.

Area of the base is then 9 x 9 = 81 sq units.

For the sides, we have 4 triangles with a base of 9 and a height of 5 units.

The area of a triangle is calculated with A = (b * h)/2

So, each of the sides of the pyramid has an area of:

A = (9 * 5) / 2 = 22.5 sq units

There are four sides, so total lateral area: 4 * 22.5 = 90 sq units.

Total area: 81 + 90 = 171 sq units.

ANSWER

C)

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

EXPLANATION

A linear function is a function whose graph is a straight line.

The graph of y=x is a straight line.

The graph of y=3x -7 is also a straight line.

The graph of y=x² is a parabola.

This graph is not a straight line .

It is a non-linear function.

y=3 and y=13 are also straight lines.

The correct choice is C.

Final result :

 (x + 5) • (x + 4)

 ———————

         2        

Step by step solution :

Step  1  :

           x2 - 16

Simplify   ———————

           2x + 6

Step  2  :

Pulling out like terms :

2.1     Pull out like factors :

  2x + 6  =   2 • (x + 3)

Trying to factor as a Difference of Squares :

2.2      Factoring:  x2 - 16

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 16 is the square of 4

Check :  x2  is the square of  x1

Factorization is :       (x + 4)  •  (x - 4)

Polynomial Long Division :

2.3    Polynomial Long Division

Dividing :  x + 4

                             ("Dividend")

By         :    x + 3    ("Divisor")

dividend     x  +  4

- divisor  * x0     x  +  3

remainder         1

Quotient :  1  

Remainder :  1  

Equation at the end of step  2  :

 (((x2)+8x)+15) (x+4)•(x-4)

 ——————————————•———————————

     (x-4)        2•(x+3)  

Step  3  :

           x2 + 8x + 15

Simplify   ————————————

              x - 4    

Trying to factor by splitting the middle term

3.1     Factoring  x2 + 8x + 15

The first term is,  x2  its coefficient is  1 .

The middle term is,  +8x  its coefficient is  8 .

The last term, "the constant", is  +15

Step-1 : Multiply the coefficient of the first term by the constant   1 • 15 = 15

Step-2 : Find two factors of  15  whose sum equals the coefficient of the middle term, which is   8 .

     -15    +    -1    =    -16

     -5    +    -3    =    -8

     -3    +    -5    =    -8

     -1    +    -15    =    -16

     1    +    15    =    16

     3    +    5    =    8    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  3  and  5

                    x2 + 3x + 5x + 15

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x+3)

             Add up the last 2 terms, pulling out common factors :

                   5 • (x+3)

Step-5 : Add up the four terms of step 4 :

                   (x+5)  •  (x+3)

            Which is the desired factorization

Equation at the end of step  3  :

 (x + 5) • (x + 3)   (x + 4) • (x - 4)

 ————————————————— • —————————————————

       x - 4            2 • (x + 3)  

Step  4  :

Canceling Out :

4.1    Cancel out  (x+3)  which appears on both sides of the fraction line.

Canceling Out :

4.2    Cancel out  (x-4)  which appears on both sides of the fraction line.

Final result :

 (x + 5) • (x + 4)

 ——————---

         2        

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=x^2-4&(1)\\y=-2x-5&(2)\end{array}\right\\\\\text{Put (1) to (2):}\\\\x^2-4=-2x-5\qquad\text{add}\ 2x\ \text{and 5 to both sides}\\\\x^2+2x+1=0\\\\x^2+x+x+1=0\\\\x(x+1)+1(x+1)=0\\\\(x+1)(x+1)=0\\\\(x+1)^2=0\iff x+1=0\qquad\text{subtract 1 from both sides}\\\\x=-1\\\\\text{put the value of}\ x\ \text{to}\ (2):\\\\y=-2(-1)-5\\\\y=2-5\\\\y=-3[/tex]

Answer: Hello there!

The system of equation given is:

y = x^2-4

y = -2x-5

And we want to solve this system:

the first step we can do is replace y in the first equation by the given in the second equation:

y = x^2-4 = -2x - 5

now we can solve it for x:

x^2-4 +2x + 5 = 0

x^2 +2x + 1 = 0

and now we can use the cuadratic equation forumla:

this is, if we have a function of the form:

ax^2 + bx + c = 0

the solutions are:

[tex]x = \frac{-b +/- \sqrt{b^2 -4ac} }{2a}[/tex]

in our equation we have a=1, b = 2 and c= 1

we replace it in the formula given, and we obtain:

[tex]x = \frac{-2 +/- \sqrt{2^2 -4*(1)} }{2} = \frac{-2 +/- \sqrt{4 - 4} }{2} = -2/2 = -1[/tex]

Now we got the value of x, and we could replace it in one of the equations and get the value of y:

y = -2x-5

y = -2*(-1) - 5 = 2 -5 = -3

then the pair is (-1, -3)

and the correct option is D.

Answer:

{-2, -14, -26, -50}

Step-by-step explanation:

The range of the function is the function evaluated at each point of the given domain. So to find the range of the function we need to find the value of the function for each point in the domain:

- For x = -8

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

[tex]f(-8)=-2(-8)-18[/tex]

[tex]f(-8)=16-18[/tex]

[tex]f(-8)=-2[/tex]

The first value of the range of the function is -2

- For x = -2

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

[tex]f(-2)=-2(-2)-18[/tex]

[tex]f(-2)=4-18[/tex]

[tex]f(-2)=-14[/tex]

The second value of the range is -14

- For x = 4

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

[tex]f(4)=-2(4)-18[/tex]

[tex]f(4)=-8-18[/tex]

[tex]f(4)=-26[/tex]

Th third values of the range is -26

- For x = 16

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

[tex]f(16)=-2(16)-18[/tex]

[tex]f(16)=-32-18[/tex]

[tex]f(16)=-50[/tex]

The fourth and last value of the range is -50

Now we can put all the values of the range together

The range of the function is {-2, -14, -26, -50}

Answer:

The three friends took 6p + 5 peaches home

Explanation:

We are given that the three friends picked 2p, 4p+3 and 3p+2 peaches

This means that:

Total picked = 2p + 4p + 3 + 3p + 2 = 9p+5 peaches

Now, we know that the owner will take p peaches from each of the three friends

This means that:

Amount taken by owner = 3p peaches

Finally, to get the amount that the three friends will take home, we subtract the amount that the owner will take from the total amount they picked

This means that:

Number of peaches they took home = total picked - amount taken by owner

Number of peaches they took home = 9p + 5 - 3p

Number of peaches they took home = 6p + 5 peaches

Hope this helps :)

Answer:

[tex]a.\ 54ft^3\\b.\ 5yd^3\\c.\ 11,943,936in^3\\d.\ 162ft^3[/tex]

Step-by-step explanation:

a. Remember that:

[tex]1yd^3=27ft^3[/tex]

Then, 2  cubic yards to cubic feet is:

[tex](2yd^3)(\frac{27ft^3}{1yd^3})=54ft^3[/tex]

b. 135 cubic feet to cubic yards is:

[tex](135ft^3)(\frac{1yd^3}{27ft^3})=5yd^3[/tex]

c. Remember that:

[tex]1ft^3=1,728in^3[/tex]

Then, 6,912 cubic feet to cubic inches:

[tex](6,912ft^3)(\frac{1,728in^3}{1ft^3})=11,943,936in^3[/tex]

d. 279,936 cubic inches to cubic feet is:

 [tex](279,936in^3)(\frac{ft^3}{1,728in^3})=162ft^3[/tex]

Answer:

A 54ft3

B 5yd3

C 11,943,936in3

D 162ft3

Step-by-step explanation:

Answer:

i think its A if it isnt im sorry

Step-by-step explanation:

Answer:

The second option :: V = [tex](25-2x)(20-2x)x[/tex] is correct.

Step-by-step explanation:

The vertical side was 25 inches before cutting out the corners.  

The horizontal side was 20 inches before cutting out the corners.

So now, if you fold all of the corner up, you get a box that has a height of "x".  

The sides are now missing a length of x from each end.  

So the longer edges of the box are now [tex](25-2x)[/tex] inches

The shorter edges of the box are now [tex](20-2x)[/tex] inches

The volume of a box is given by V = length x width x height

So, here the volume becomes:

V = [tex](25-2x)(20-2x)x[/tex] cubic inches.

Final answer:

To find the number of sliders and chicken wings in the combination meal, set up a system of equations and solve. There are 2 sliders and 10 chicken wings in the combination meal.

Explanation:

In order to find the number of sliders and chicken wings in the combination meal, we can set up a system of equations. Let's assume that the number of sliders is 's' and the number of chicken wings is 'c'. We know that each slider has 250 calories and each chicken wing has 60 calories. The total number of sliders and chicken wings in the combination meal is 12, so we have the equation s + c = 12.

We also know that the total number of calories in the combination meal is 1100. Since each slider has 250 calories and each chicken wing has 60 calories, we can write the equation 250s + 60c = 1100.

Now we can solve this system of equations to find the values of 's' and 'c'.

Multiplying the first equation by 60, we get 60s + 60c = 720. Subtracting this equation from the second equation, we get 250s - 60s = 1100 - 720, which simplifies to 190s = 380. Dividing both sides by 190, we find that s = 2.

Substituting this value back into the first equation, we have 2 + c = 12. Solving for 'c', we find that c = 10.

Therefore, there are 2 sliders and 10 chicken wings in the combination meal.

Here, the given equation is,

x^2+y^2+px+6y-3=0

By copairing it with x^2+y^2+2gx+2fy+c=0, we get,

2g=p or, g=p/2

2f=6 or, f=3

c=-3

now the radius is,

r^2=g^2+f^2-c

or, 4^2=(p/2)^2 +3^2 -(-3)

or, 16= p^2/4 +9+3

or, 16-9-3=p^2/4

or p^2/4=4

or, p^2=4×4

or p^2=4^2

or p=4

therefore the rewuired value of p is 4.

Answer:

Possible values are 4 and -4.

Step-by-step explanation:

First complete the square on the x and y terms:

x^2 + y^2 + px + 6y - 3 = 0

(x + 0.5p)^2 - 0.25p^2 + (y + 3)^2 - 9 - 3 = 0

(x + 0.5p)^2 + (y + 3)^2 = 12 + 0.25p^2

This is the standard form of the equation of the circle where the right side = radius^2 so we can write:

12 + 0.25p^2 = 4^2

0.25p^2 = 16 - 12 = 4

Taking square roots:-

0.5p = +/- 2

p = 2 / 0.5 , -2 / 0.5

p = 4, -4.

the sum of all interior angles in a polygon is

180(n - 2)

n = number of sides in the polygon

this polygon has 5 sides, so is a PENTAgon, so the sum of all its sides is

180(5 - 2) => 180(3) =>  540

so then

[tex]\bf 90+148+(3x+10)+(x)+112=540\implies 360+4x=540 \\\\\\ 4x=180\implies x=\cfrac{180}{4}\implies x=45[/tex]