A lifeguard spots a swimmer in the lake at an angle of depression
of 32°. He spots a sailboat, further out, at an angle of depression of 13°. If the lifeguard is 36.5 dm away from the swimmer and 84.7 dm away from the sailboat, how far is the swimmer from the sailboat? Round your answer to the nearest tenth of a dm
Help me please! thank you

Slope of AB = 2; Slope of DC = 2

Slope of AD = -1/2; Slope of BC = -1/2

Both pairs of opposite sides are parallel because they have the same slope, therefore, quadrilateral ABCD is a parallelogram.

A parallelogram is a quadrilateral that has two pairs of opposite sides that have the same lengths and are parallel to each other.

Since the opposite sides of a parallelogram are parallel, therefore, they have the same slope value.

Slope = change in y / change in x.

Find the slope of AB and DC. then AD and BC:

Slope of AB = (-2 - 2)/(-3 -(-1)) = -4/-2

Slope of AB = 2

Slope of DC = (-3 - 1)/(-1 - 1) = -4/-2

Slope of DC = 2

Slope of AD = (-3 -(-2))/(-1 -(-3)) = -1/2

Slope of AD = -1/2

Slope of BC = (2 - 1)/(-1 - 1) = 1/-2

Slope of BC = -1/2

Therefore, since AB and DC have the same slope, they are parallel, so also is AD and BC parallel because they have the same slope, therefore, quadrilateral ABCD is a parallelogram.

Learn more about parallelogram on:

https://brainly.com/question/3050890

#SPJ1

Hello! So...

We are given the following to solve:

[tex]-9+8=?[/tex]

In order to solve this, we simply need to add.

[tex]-9+8=-1[/tex]

Hence, our solution is -1, and would be marked -1 on a number line. Graph is displayed below.

____________________________________

Hope this helps! If so, lmk! Thanks and good luck!

Answer:

[tex]\textsf{D)} \quad P(n)=0.024n^2-0.3n+4.3[/tex]

Step-by-step explanation:

From inspection of the graph, when the number of coils is 10, the length of the spring is between 0 cm and 20 cm.

Substitute n = 10 into the equation of each given answer option:

[tex]\begin{aligned}\textsf{Option A}: \quad P(10)&=10^2+4.3\\ & =100+4.3\\&=104.3\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Option B}: \quad P(10)&=10^2-0.3(10)+4.3\\ & = 100-3+4.3\\&=97+4.3\\&=101.3\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Option C}: \quad P(10)&=0.24(10^2)+4.3\\&=0.24(100)+4.3\\&=24+4.3\\&=28.3\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Option D}: \quad P(10)&=0.024(10^2)-0.3(10)+4.3\\ & = 0.024(100)-3+4.3\\&=2.4-3+4.3\\&=-0.6+4.3\\&=3.7\end{aligned}[/tex]

Therefore, as 0 < P(10) < 20, the only suitable equation is Option D:

[tex]\boxed{P(n)=0.024n^2-0.3n+4.3}[/tex]

Answer:

x = 5

Step-by-step explanation:

Comment

The three sides need to add up to 23 (the perimeter is given as 23)

Givens

The sides are

Solution

x + x + 3 + 2x = 23                   Combine

4x + 3 = 23                               Subtract 3 from both sides

4x + 3-3 = 23-3                         Combine

4x = 20                                      Divide  by 4

4x/4 = 20/4

x = 5

The three sides of a triangle is x, x+3 and 2x. If the perimeter is 23 feet. Find the value of x.

In this question we are given

We are asked to calculate the value of x.

To solve this problem first we have to form an equation.

Let us solve this question.

We know that the perimeter of a triangle is the sum of all three sides.

According To Question

x + x + 3 + 2x = 23

→ 2x + 3 + 2x = 23

→ 4x + 3 = 23

→ 4x = 23 - 3

→ 4x = 20

→ x = 20/4 = 5

x = 5

The value of x is 5.

[tex] \rule{70mm}{2pt}[/tex]

The simplified solution for B in the equation -4 ( - 6 - b) = 1/3 (B + 16) is B = 56 + 12b

Given,

The equation: - 4 (- 6 - b) = 1/3 (B + 16)

We have to simplify the equation and find B.

Lets simplify:

-4 ( - 6 - b) = 1/3 (B + 16)

Here,

(- 4 × - 6) - 4 × - b = 1/3 × B + 1/3 × 16

24 + 4b = B/3 + 16/3

24 + 4b = (16 + B) / 3

Multiply 3 to both sides:

(24 + 4b) × 3 = (16 + B) × 3 / 3

72 + 12b = 16 + B

Add -16 to both sides:

72 + 12b - 16 = 16 + B - 16

Then,

B = 72 + 12b - 16

B = 56 + 12b

That is, the simplified solution for B in the equation -4 ( - 6 - b) = 1/3 (B + 16) is B = 56 + 12b

Learn more about simplification here:

https://brainly.com/question/6592817

#SPJ1

The system of inequalities that models the situation is given as follows:

Before we build the inequalities, we have to consider that the variables of the system are given as follows:

Jeremy and his dad worked at least 85 combined hours last week, hence the first inequality is:

x + y ≥ 85.

They collected a total of more than $1000 by charging $20 per hour, hence the second inequality is:

20x + 20y ≥ 1000.

20(x + y) ≥ 1000.

The minimum number of hours that each can work is of 0, that is, they cannot work a negative number of hours, hence the constraints are:

The problem is incomplete, and it asks for the system of inequalities that models the situation.

More can be learned about a system of inequalities at https://brainly.com/question/11994104

#SPJ1

Interpolation is the process of foretelling the value of a function f at a location inside the observed range of values for and. Predicting the value of y when it is outside the range indicated by the points and areas where the values and have been observed is known as extrapolation.

The values for two different numerical variables are represented by dots in a scatter plot (also known as a scatter chart or scatter graph). Each dot's location on the horizontal and vertical axes represents a data point's values. To view relationships between variables, utilize scatter plots.

Interpolation is the process of foretelling the value of a function f at a location inside the observed range of values for and. Predicting the value of y when it is outside the range indicated by the points and areas where the values and have been observed is known as extrapolation.

For an independent variable that lies outside the range of our data, we use function to forecast the value of the dependent variable. We extrapolate in this situation.

To learn more about scatter plots refer to:

https://brainly.com/question/6592115

#SPJ13

Answer:

Sample Answer: An interpolation has a result which lies within the scatterplot’s cluster of data points. An extrapolation lies outside the cluster. An interpolation is more reliable than an extrapolation.

Step-by-step explanation:

The algebraic equation and the original price is:

original price - discount = sales price

x - 27 = 89

x = 116

An algebraic equation is made up of two expressions that are made up of variables or numbers that are connected by an arithmetic operation.  

A discount reduces the price of a good or service. In order to determine the price of a good after the discount has been applied, subtract the amount of the discount from the original price of the item.

original price - discount = sales price

x - 27 = 89

Combine similar terms: x = 89 + 27

Add similar terms together: x = 116

To learn more about how to calculate discounts, please check: https://brainly.com/question/26061308

#SPJ1

Answer: i is just a variable I believe so _ + 7 = 9

So i (<- the variable) would = 2

Answer:   0.483

Step-by-step explanation: add a zero and a point to the right f it

Answer:

B

Step-by-step explanation:

Answer:

x = 37 , ∠ P = 17° , ∠ Q = 126° , ∠ R = 37°

Step-by-step explanation:

the sum of the 3 angles in Δ PQR = 180°

sum the 3 angles and equate to 180

x + x - 20 + 3x + 15 = 180

5x - 5 = 180 ( add 5 to both sides )

5x = 185 ( divide both sides by 5 )

x = 37

Then

∠ P = x - 20 = 37 - 20 = 17°

∠ Q = 3x + 15 = 3(37) + 15 = 111 + 15 = 126°

∠ R = x = 37°

Answer:

1. you can ask directly or indirectly

[tex]32^{\frac{1}{25}}\cdot 2^x ~~ = ~~8^{\frac{1}{4}}\implies (2^5)^{\frac{1}{25}}\cdot 2^x~~ = ~~(2^3)^{\frac{1}{4}}\implies 2^{\frac{5}{25}}\cdot 2^x~~ = ~~2^{\frac{3}{4}} \\\\\\ \stackrel{same~exponent}{\underset{same~base}{2^{\frac{5}{25}+x}~~ = ~~2^{\frac{3}{4}}}}\implies \cfrac{5}{25}+x~~ = ~~\cfrac{3}{4}\implies \cfrac{1}{5}+x~~ = ~~\cfrac{3}{4}[/tex]

[tex]\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{20}}{20\left( \cfrac{1}{5}+x \right)~~ = ~~20\left( \cfrac{3}{4} \right)}\implies 4+20x~~ = ~~15 \\\\\\ 20x=11\implies {\Large \begin{array}{llll} x=\cfrac{11}{20} \end{array}}[/tex]

The counterexample for the conjecture If the perimeter of a rectangle is 40 units, the area must be at least 1 square unit is: A rectangle with length 19.99 units and width 0.01 unit has a perimeter of 40 units and an area of 0.1999 square unit.

The term counterexample refers to an instance or example that makes the statement false. This is used in logic to check if a statement is true or not. Counter example tend to counter the statement being discussed with valid points.

The question wants to show the relationship that may exist between perimeter and area of a rectangle.

The counterexample provided the dimensions that gave the perimeter which is 40 but failed to give area of 1 square unit

Read more on  counterexample here: https://brainly.com/question/24881803

#SPJ1

Answer:

Step-by-step explanation:

The one in blue

Based on the information illustrated, it should be noted that 6 × ✓3 .will be 36.

It should be noted that the information that's illustrated has to do with the square root of numbers. It should be noted that a square root simply means a number that when multiplied by itself will be able to give the original number that's given in the question.

Based on the information, the numbers will be illustrated thus:

6 × ✓36

It should be noted that ✓36 = 6

Therefore, 6 × ✓36

= 6 × 6

= 36

Therefore, the correct option is 36.

Note that the options aren't well written.

Learn more about numbers on:

brainly.com/question/148825

#SPJ1

The coordinates of the point of intersection is equal to (3, 5).

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect, meet, or cross each other, which is typically represented as an ordered pair containing the point, x-axis and y-axis.

Next, we would solve the given equations simultaneously to determine the coordinates of the point of intersection as follows:

y = 1 - 2x

y = x - 5

Re-arranging the equation, we have:

y + 2x = 1

y - x = -5

Subtracting, we have:

3x = 6

x = 6/2

x = 3.

For y-coordinate, we have:

y + 2x = 1

y + 2(3) = 1

y + 6 = 1

y = 1 - 6

y = -5.

Read more on point of intersection here: https://brainly.com/question/13513373

#SPJ1

[tex]3 \sqrt{5} - 2 \sqrt{7} + \sqrt{9 \times 5} - \sqrt{4 \times 7} \\ = 3 \sqrt{5} - 2 \sqrt{7} + ( \sqrt{9} \times \sqrt{5} ) - ( \sqrt{4} \times \sqrt{7} ) \\ = 3 \sqrt{5} - 2 \sqrt{7} + 3 \sqrt{5} - 2 \sqrt{7} \\ = 3 \sqrt{5} + 3 \sqrt{5} - 2 \sqrt{7} - 2 \sqrt{7} \\ = 6 \sqrt{5} - 4 \sqrt{7} [/tex]

OPTION C IS THE ANSWER.

Answer:

6√5 - 4√7

Step-by-step explanation:

hope it helps!!

Balance of Kevin after 1 quarter will be 1.0055(x)

Compound interest is interest that is calculated using both the starting amount and the interest that has accrued over time.

Interest is considered to be compounded quarterly if it is compounded four times each year.

If interest is compounded four times or quarterly each year, the formula for the amount at time t is as follows.

A = P( ( 1 + (r/4))⁴ⁿ

A = Accumulated amount

P= Principal amount

r = interest rate

n = time

Given that Kevin has x dollars in an account that pays 2.2% interest, compounds quarterly

∴ P = x

r = 2.2% = 2.2/100

To find balance after one quarter , i.e. time n = 1/4 year

⇒ Balance = accumulated amount  =$  x(1 + 2.2/400)¹  = $ 1.0055(x)

Therefore, Balance of Kevin after 1 quarter will be 1.0055(x)

To know more about compound interest, visit:

https://brainly.com/question/14295570

#SPJ13

Answer: 34.50

Step-by-step explanation: Since 3 bags cost 17.25 and Marco would buy 6, 3 times 2 is 6 so 17.25 times 2 is 34.50

Answer:

its 3 because 4^-n=1/256

We move all terms to the left:

4^-n-(1/256)=0

We add all the numbers together, and all the variables

-n+4^-(+1/256)=0

We add all the numbers together, and all the variables

-1n-(+1/256)=0

We get rid of parentheses

-1n-1/256=0

We multiply all the terms by the denominator

-1n*256-1=0

We multiply elements

-256n-1=0

We move all terms containing n to the left, all other terms to the right

-256n=1

n=1/-256

n=-1/256

Answer:

Well, if we consider [tex]r[/tex] as y and [tex]q[/tex] as x.

Step-by-step explanation:

So, typically, a linear function is either represented using function notation

[tex]f(x)=mx+b[/tex]

Or in slope-intercept form

[tex]y=mx+b[/tex]

This question is oddly using the variables r and q in place of y and x. If we replace them to be y and x, it will be a linear equation (because the slope is constantly changing).

But, if you aren't allowed to replace r and q to be y and x, then it isn't a linear function.

A number line and expression show how to find the distance from 4 to 1 is: B. A number line from -5 to 5 and two points on 1 and 4.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.

This ultimately implies that, a number line can be used to determine the difference between two numbers such as 4 and 1. Also, a number line typically increases in numerical value towards the right and decreases in numerical value towards the left.

In this context, we can reasonably infer and logically deduce that number line C shows the distance from 4 to 1.

Read more on number line here: brainly.com/question/17325155

#SPJ1

it x/383

i myself i dont even knkw hownto do this brk i just want points so please dont listen to this try you hardest dont give up and keep looking for others but i just want sum piote bro i gotta finish my ezam too man so good luck tho.

Answer: 3x^12

Step-by-step explanation:

66 / 22 = 3

We can add exponents when multiplying them.

-3 + 12 = 9

I don't know what the dropdown menus are, but Mike is half-correct. The opposite of a number is the number with the opposite sign, so the opposite of 5 is -5. But the absolute value of a number is its distance from zero on a number line, and distances can't be negative, so the absolute value of 5 is 5, not -5.

Answer:

You need at least 101 cans of food in order to meet or surpass the goal.

Step-by-step explanation:

a.

135+89=224

224+c>=325

b.

224-224+x>=325-224

x>=101

You need at least 101 cans of food in order to meet or surpass the goal.

Answer: 3.3%

Step-by-step explanation:

Principal not given.

SI = PRT/100

CI = P(1+R/100)^T -

SI + CI = 85470

[P×7×2]//100 + P [1+ (7/100)]^2 = 85470

on solving: P = 3,00,000

P = 300000 SI for 2 years = 42000

CI = Rs 43470

The difference= Rs 1470

as percentage to CI = [1470/ 43470] ×100

= 3.38%