Two birds sit at the top of two different trees. The distance between the first bird and a birdwatcher on the ground is 29. 7 feet. The distance between the birdwatcher and the second bird is 42. 1 feet. What is the angle measure, or angle of depression, between this bird and the birdwatcher? Two trees that are 29 point 7 feet tall with a bird on top of each. Distance between birdwatcher and first bird is 42 point 1 feet. Angle of depression between birdwatcher and first bird is unknown. © 2011 Jupiter Images Corporation 45. 1° 44. 9° 54. 8° 35. 2°.

The system of equations that can be used to determine whether the road intersects the boundary of the tower’s signal is

 [tex]y = 2x^2 - 16x + 34\\11y = -5x + 62[/tex]

If a quadratic equation is written in the form

[tex]y=a(x-h)^2 + k[/tex]

then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)

For the given situation, the quadratic equation has vertex (h,k) = (4,2) and it passes through (5,4).

If we consider the equation to be of the form [tex]y=a(x-h)^2 + k[/tex],

then, as h = 4, k = 2, it becomes [tex]y = a(x-4)^2 + 2[/tex]

Now since it passes through (5,4), thus at x = 5, and y = 4, the equation must be true, or:

[tex]y = a(x-4)^2 + 2|_{(x,y) = (5,4)}\\\\4 = a(5-4)^2 + 2\\4 = a + 2\\a = 2[/tex]

Thus, the quadratic equation in consideration is: [tex]y = 2(x-4)^2 + 2 = 2x^2 + 32 -16x + 2\\y = 2x^2 - 16x + 34[/tex]

The straight line in consideration connects points (–3, 7) and (8, 2).

Equation of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]  is

[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]

Since we've got [tex](x_1, y_1) = (-3,7) \: \rm and \: \: (x_2, y_2) = (8,2)[/tex]

We get the equation of the straight line in consideration as:

[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)\\\\(y-7) = \dfrac{2-7}{8 - (-3) } (x-(-3))\\\\y - 7 = -\dfrac{5}{11}(x+3)\\\\11y = -5x + 62[/tex]

Therefore, the system of equations that can be used to determine whether the road intersects the boundary of the tower’s signal is

[tex]y = 2x^2 - 16x + 34\\11y = -5x + 62[/tex]

These equations' graphs' intersection is the solution to this system

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Answer:

y-2(x-4)^2=2

5x+11y=62

Step-by-step explanation:

a on edge 22

Answer:

There are [tex]3p^2[/tex] animals on the farm

Step-by-step explanation:

2p^2-p+4 . p^2+p+1

[tex](2p^2-p+4)+(p^2+p+1)\\2p^2+p^2+p-p+4+1\\3p^2+5[/tex]

Answer:

3p² + 5

Step-by-step explanation:

since no equations are given I will simply add on the number of cows and buffaloes.

total number of animal= number of cows + number of buffaloes

= 2p²- p + 4 + p² + p + 1

= 3p² +5

Answer:

Your answer is 580

Step-by-step explanation:

The equation that show the relationship is given by 8x + 6y = C + D

An equation is an expression used to show the relationship between two or more numbers and variables.

Let x represent the number of Crows and y represent the number of doves, Let C represent the number of trigs needed for Crow and D the amount of twigs needed for dove, hence:

x + y = 1500    (1)

also:

8x + 6y = C + D  (2)

The equation that show the relationship is given by 8x + 6y = C + D

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Answer:

16:9

Step-by-step explanation:

Product of two polynomials can be done by distribution of multiplication over addition. The product of [tex](x+5)^2[/tex] is [tex]x^2 + 10x + 25[/tex]

Suppose a, b and c are three numbers. Then we have:

[tex]a(b + c) = a\times b + a\times c[/tex]

(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)

They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.

Example:

[tex]x^3 + 4x + 3[/tex]

is a polynomial.

Using both above facts, as the given expression is [tex](x+5)^2[/tex]

Its product result is obtained as

[tex](x+5)^2 = (x+5)(x+5) = x(x+5) + 5(x+5) = x^{1+1} + 5x + 5x + 25\\\\(x+5)^2 = x^2 + (5+5)x + 25 \text{\:(Addition of coefficients of like terms)}\\\\(x+5)^2 = x^2 + 10x + 25[/tex]

It is a fact that result of a polynomial product is polynomial. Thus, the obtained product is a polynomial since x + 5 was a polynomial.

Thus,

The product of [tex](x+5)^2[/tex] is [tex]x^2 + 10x + 25[/tex]

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It should be d

Sorry if this is not correct

Answer:

Step-by-step explanation:

You have more than 1/2 the solution just by knowing the slope.

General equation

y = mx + b         where m is the slope and b is the y intercept.

m = 3/4

Solution

y = 3/4 x + b      Now you need the point to solve for b

x = 2

y = 2                  Substitute these values into the line

2 = 3/4 * 2 + b   Simplify the right

2 = 1 1/2 + b

2 = 3/2 + b        Subtract 3/2 from both sides

2 - 3/2 = b         Combine

1/2 = b

So the y intercept is 1/2

Answer

y = 3/4 x + 1/2

or

y = 0.75 x + 0.5        

The mean number of calls for Sami is 2.25 calls per day and for Marta it is 2.5 calls per day

The person who made more calls per day is Marta.

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

Sami = 27 / 12 = 2.25 calls per day

Marta = 45 / 18 = 2.5 calls per day

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1 = sin²0 + cos²0

sin²0 = 1 - cos²0

sin²0 = 1 - 11/36

sin²0 = 25/36

sin 0 = 5/6 or -5/6

In the first quadrant, the values for sin, cos and tan are positive.

sin0 = 5/6

Answer:

13.3 miles

Step-by-step explanation:

So you're driving <----- for 3 miles

Then you start driving up for 13 miles

This makes a right triangle with sides of 3 and 13

using pathagoreas, a^2+b^2=c^2

3^2+13^2=c^2

9+169=c^2

178=c^2

Square root both sides

c= 13.3416640641

Rounding, it's 13.3 miles

Answer:

B- n = 1

Step-by-step explanation:

"For all the positive integers n" is a qualifying statement. The number used has to be positive and also must be an integer. Integers are whole numbers and their opposites, so basically no fractions and no decimals. Answer A is a fraction and C is a decimal and D is negative and a decimal. So they don't work for this problem.

The value is n to show that the first step in a proof by mathematical induction of for all the positive integers is 1.

Thus, option B is correct.

The conditions can be checked through the options.

The option C and D will be eliminated because the condition is for all the positive integers n but n is decimal here.

For n = 1/4, the solution will be in fractions.

So, it does not hold true for n= 1/4.

For n = 1

[tex]\dfrac{n(n + 1)(2n + 1)}{6}[/tex]

 =[tex]\dfrac{1(1 + 1)(2 \times 1 + 1)}{6}[/tex]

= 1

Thus, the value is n  to show that the first step in a proof by mathematical induction of for all the positive integers n is 1.

So, option B is correct.

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Answer:

11/2

Step-by-step explanation:

Given Mixed fraction is 51/2

Step 1: Multiply 5 by 2: 5 × 2 = 10

Step 2: Add 10 with 1: 10+1 = 11 (New numerator value).

Hence, the improper fraction is 11/2.

11/2 is 5 1/2 as a fraction.

Mixed fraction is a number contain whole number and a proper fraction.

Given:

Mixed fraction is 5 1/2

To convert mixed fraction into proper fraction:

To get the fraction from mixed number you just need to take the number standing alone, multiply with the denominator and add with the numerator and keep it on top with the denominator in place to turn it into a fraction.

Step 1: Multiply 5 by 2: 5 × 2 = 10

Step 2: Add 10 with 1: 10+1 = 11 (New numerator value).

Proper fraction is 11/2.

Therefore, 11/2 is 5 1/2 as a fractions.

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Answer:

I believe the answer is the 3rd one

Step-by-step explanation:

Answer:

18 yards

Step-by-step explanation:

Rectangle area = Length (L) x Width (W)

63 yd^2 = L*W

63 yd^2 = L*(3.5 yd)

L = 18 yards

Answer:

/ = 18 yd

Step-by-step explanation:

I took the quiz and this was the correct answer.

Answer:

316.168

Step-by-step explanation:

you get 316.168 Liters or 316168 mL

please mark brainliest i need one more!

Answer:

316.168

Step-by-step explanation:

that is the answer when i tried this equation

Answer: no solutions

Step-by-step explanation:

6x+4x-1=2(5x+4)

10x-1=10x+8

+1 +1

10x=10x+9

The equation is not true. It has no solutions.

Answer:

156°

Step-by-step explanation:

the total internal angle of a triangle in 180°
so,

180 - (85 + 71)
= 24°

this is the internal angle, to find the external angle subtract this value from 180
so,

180 - 24
= 156° (answer)

Answer:

(-4,0)

Step-by-step explanation:

if you substitute the number 0 then it is (-4,0). and there is your answer!

Answer:

A) 63.576

Step-by-step explanation:

1/10 can also be 10/100 which is 10%

10% of 0.06 = 0.006

Answer:

Step-by-step explanation:

m∠A = arctan [tex]\frac{9.6}{7.2}[/tex] ≈ 53°  

Answer: Cos(33/65) or 0.99996

Step-by-step explanation:

Cos of an angle is described as

Cosine = adjacent / hypotenuse

where adjacent is the closest side to the angle so in this case adjacent is IH

Hypotenuse is the longest side of a right triangle ALWAYS

sooooo Cosine of angle h is cos(33/65) or decimal form 0.99996

Answer:

x = 15

Step-by-step explanation:

Supplementary = 180 °

Add the numbers

[tex](2x + 20) + 130 = 180[/tex]

[tex]2x + 150 = 180[/tex]

Subtract 150 from both sides of the equation

[tex]2x+150- 150 =180 - 150[/tex]

Simplify

[tex]2x = 30[/tex]

Divide both sides of the equation by the same term

[tex]\frac{2x}{2} =\frac{30}{2}[/tex]

Simplify/Solution =

[tex]x=15[/tex]

Hence, x = 15.

[RevyBreeze]

Answer:

42,640

Step-by-step explanation:

[tex]205 \times 208 = (200 + 5)(200 + 8) \\ formula \: to \: be \: used \: \\ \red{ \boxed{ \bold{(x + a)(x + b) = {x}^{2} + (a + b)x + ab}}} \\ \\ \implies \: 205 \times 208 \\ \\ = (200 + 5)(200 + 8) \\ \\ = {(200)}^{2} + (5 + 8)(200) + (5)(8) \\ \\ = 40000 + (13)(200) + 40 \\ \\ = 40000 + 2600 + 40 \\ \\ = 42,640[/tex]

Answer:

V = c/q - 1

Step-by-step explanation:

hope this helps if u need anymore help let me know

Answer: The answer is 25

Step-by-step explanation: because it said he spend $5 on ice cream then he had $20 left so that mean he had 25 - 5 = 20

[tex] \dashrightarrow \tt8(2.5 – 0.5)[/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \tt8(3)[/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \tt8 \times 3[/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \tt24[/tex]

Answer:

16

Step-by-step explanation:

I think the question is either incorrect or a number is being omitted in the options.

But, lets make do with what we have here so you have an idea of how its been solved.

USING THE ORDER OF OPERATIONS IS BEING FOLLOWED SO THAT EVERYONE CAN ARRIVE AT THE SAME ANSWER.

8(2.5 - 0.5)  = 8 (2)    = 16

Answer:

y = 4x hope this Helps!

Step-by-step explanation:

y = kx

k = y/x = 60/15 = 4

y = 4x

Probability of an event is its chance of . The probability that a student not liking mountains doesn't like beach is: Option b: 40.4%

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}}[/tex]

Where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

For the given case, from the table (image attached below), we can see that, there are total 94 students who do not like mountains. Now, out of those 94, there are 38 students not liking beach.

Thus, if A = a student not liking beach

B = not liking mountains,

Then ,

P(A|B) = P(A ∩ B)/P(B) = [tex]\dfrac{38/158}{94/158} = \dfrac{38}{94} \approx 0.404 = 40.4\%[/tex]

Thus, probability of a student not liking beach given that that student doesn't like mountains is 40.4% approx.

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Answer:

40.4%

Step-by-step explanation: