Kayla parks her car at the corner of Ogilvie and Montreal Rd. She walks 80m East and then turns 30° to the left towards her office building and continues walking for another 100m until she reaches her building. She then takes the elevator to her office 60m above ground level and looks out the window. She can see her car from here. How far is it from where she is to her car in a direct line?

Answers

Answer 1

9514 1404 393

Answer:

  184 m

Step-by-step explanation:

The direct distance from Kayla's car (C) to the door of her office building (B) can be found using the Law of Cosines. The interior angle of the triangle at the turning point is 180° -30° = 150°, so the distance is ...

  t² = b² +c² -2bc·cos(T)

  t² = 80² +100² -2·80·100·cos(150°) = 30256.406

The direct distance from her window to the car can be found from the Pythagorean theorem. The legs of the right triangle are the distance from the car to the building (CB) and the height from the building entrance to the window (BW).

  CW = √(t² +60²) ≈ 184.001

The direct line distance from Kayla to her car is 184 meters.

_____

For the first computation, we used the usual notation for a triangle, where capital letters (CTB) are the vertices and angles, and corresponding lower-case letters are their opposite sides.

Kayla Parks Her Car At The Corner Of Ogilvie And Montreal Rd. She Walks 80m East And Then Turns 30 To

Related Questions

What is the area of the shaded part of the figure?

Answers

Answer:

14cm²

Step-by-step explanation:

3x2=6,

3x2=6,

2x1=2,

6+6+2=14 cm^2

What is the domain of the relation described by the set of ordered pairs (-2,8), (-1,1) (0,0) (3,5), (4,-2)?

Answers

Step-by-step explanation:

(-2,-1,0,3,4) are the domain

(x,y)=(domain,range)

simply x components are the domain whereas y components are the range

Which key feature depends on the leading coefficient and the degree of the
function?
A.Axis of symmetry
B.End behavior
C.Intercepts
D.Rate of change

Answers

Answer:

B.End behavior

Step-by-step explanation:

Limit as x goes to infinity:

To find the limit as x goes to infinity of a function, we consider only the leading coefficient and the term with the highest degree of the polynomial, and this limits determines the end behavior of a function, and thus, the correct answer is given by option b.

What is the area of a triangle with a base of 9 units and a height of 7 units? O A. 15.75 sq. units O B. 126 sq. units O c. 63 sq. units O D. 31.5 sq. units SUBMIT வன் PREVIOUS​

Answers

Answer:

D. 31.5 sq. units

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh

A = 1/2 ( 9)(7)

A = 63/2

A = 31.5 units^2

Step-by-step explanation:

For this, we'll use a formula for the area of a triangle.

Area (A) = ( Base (B) * Height (H) ) / 2

[tex]A = (B * H )/2[/tex]

Plug in given values.

[tex]A = (9*7)/2[/tex]

Multiply within parentheses.

[tex]A = (63)/2[/tex]

Divide by 2.

[tex]A = 31.5[/tex]

Answer:

D. 31.5 sq. units

ms.+sanchez+bought+3+pounds+of+turkey+to+make+sandwiches+for+her+family+.+She+uses+.25+of+a+pound+for+each+sandwich+.+How+many+sandwiches+can+she+make+?

Answers

Answer:

she can make 12 sandwiches

Step-by-step explanation:

3/.25 is the solution

You need to solve a system of equations. You decide to use the elimination method. Which of these is not allowed? 2x - 3y = 12
-x + 2y = 13
O A. Multiply the left side of equation 2 by 2. Then subtract the result from equation 1.
O B. Multiply equation 1 by 2 and equation 2 by 3. Then add the new equations.
C. Multiply equation 2 by-2. Then add the result to equation 1. ​

Answers

Answer:

A.

Step-by-step explanation:

The Elimination Method is the method for solving a pair of linear equations which reduces one equation to one that has only a single variable.

If the coefficients of one variable are opposites, you add the equations to eliminate a variable, and then solve.

If the coefficients are not opposites, then we multiply one or both equations by a number to create opposite coefficients, and then add the equations to eliminate a variable and solve.

When multiplying the equation by a coefficient, we multiply both sides of the equation (multiplying both sides of the equation by some nonzero number does not change the solution).

So, option B is not allowed (it is not allowed to multiply only one part of the equation)

Your friend offers to place a bet with you. He will pay you $1 if your favorite sports team wins the game on Tuesday night. But you will pay him $3 if his team wins. Your team has an 80% chance of winning, whereas his only has a 20% chance. This bet is in your favor. True or False.

Answers

False because $1 =$1 not $3

True. The expected value of the bet is positive ($0.2),

What is probability?

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Let's calculate the expected value of the bet for both outcomes:

If your team wins: You get paid $1, so the expected value is 0.8 × $1 = $0.8

If your friend's team wins: You pay $3, so the expected value is 0.2 × -$3 = -$0.6

The overall expected value of the bet is the sum of these two outcomes: $0.8 + (-$0.6) = $0.2

Since the expected value of the bet is positive ($0.2), this means that on average, you can expect to win money if you take this bet. Therefore, the bet is in your favor.

Learn more about probability here:

brainly.com/question/11234923

#SPJ2

The longest leg is Select one:

a. 5√3

b. 10√3

c. 5

d. 20

Answers

Answer:

D:20

sqrt(3) is less than 2 thus 10*sqrt(3) is less than 20

Step-by-step explanation:

El largo de un terreno es el doble de la medida de su ancho, como se muestra en la imagen. Si el perímetro es de 96 hectómetros, ¿cuáles son las dimensiones del terreno?

Answers

Answer:

Step-by-step explanation:

The following configured particulars are states, in accordance by the interrogate:

Perimeter = 96 hectometers.

Assuming the figure is a square, we can assume that,

S = A side length where,

4s = 96, where all side lengths are equivalent.

If so, then s = 24

Thus, that means that w, denoted as width, must be less than or equal to 24.

In addition, likewise, l, denoted as length, must be less than or equal to 24.

Furthermore, the length is acknowledged or stated to be twice that of the width:

Length = 2w

The listed above may be equated to the following:

2w + 2L = 96

2(24) + 2L = 96

2L + 48 = 96

2L = 48

L = 24

Thus, the width of the figure is equivalent to 24. (Length divided by two).

Thus, the length of the figure is equivalent to 24 (twice the width).

*I hope this helps.

An investor puts $800 into an account that pays 7.5% interest compounded annually. The total amount A in the account after t years is given by which function below?
A = 800(1.75) ^t
A = 800(1.075) t
A = 800(1.075)^ t
A = 800 + (1.075)^ t

Answers

Answer:

A = 800( 1.075)^(t)

Step-by-step explanation:

The equation for interest is

A = p (1+r/n) ^ nt   where p is the principle, r is the interest rate, n is the number of times per year  and t is the years

A = 800( 1+ .075/1)^(1*t)

A = 800( 1.075)^(t)

Let's see

[tex]\\ \tt\leadsto A=P(1+r/n)^{nt}[/tex]

n is 1

[tex]\\ \tt\leadsto A=P(1+r)^t[/tex]

[tex]\\ \tt\leadsto A=800(1+0.075)^t[/tex]

[tex]\\ \tt\leadsto A=800(1.075)^t[/tex]

Option C

The diameter of a circle is inches what is the area?

Answers

Answer:

Pie( r ^2)

Step-by-step explanation:

Here value of r is in inches

Answer quick please.

Answers

Answer

The Answer is A C D

Step-by-step explanation:

Round 61,565 to the
nearest hundred.

Answers

Answer:

61600

Step-by-step explanation:

the 3rd digit is the hundreds. because the digit in the 10s is greater 5, we round it up

Answer:

61,600 is your answer please

The length of the base of a triangle is twice it’s height. If the area of the triangle is 441 square kilometers, find the height

Answers

Answer:

21 kilometers

Step-by-step explanation:

Let the height be [tex]x[/tex]. Then, the length of the base is [tex]2x[/tex]. The formula for the area is of the triangle is given by base*height/2. Therefore, the area of the triangle is equal to [tex]\frac{x \cdot 2x}{2} = x^2[/tex], which is in turn equal to 441. Since [tex]x[/tex] must be positive, then [tex]21^2=441[/tex], meaning that the height is [tex]21[/tex] kilometers.

Which of the following relations represents a function?

Question 4 options:

{(–1, –1), (0, 0), (2, 2), (5, 5)}


{(0, 3), (0, –3), (–3, 0), (3, 0)}


{(–2, 4), (–1, 0), (–2, 0), (2, 6)}


None of these

Answers

Answer:

The first option

Step-by-step explanation:

A function is where one input only has one output, in the other options we can see inputs having different outputs, 0,3 and 0-3 in the second and in the third -2,4 and -2,0.

Which of the following choices shows the complete factorization of 50?
52 • 5
2 • 25
52 • 2
None of these choices are correct.

Answers

Answer: None of these choices are correct

Explanation

The factorization of 50 is 2*5^2

None is correct

How do you know if a radical can be simplified? Explain.

Answers

Answer:

An expression is considered simplified only if there is no radical sign in the denominator. If we do have a radical sign, we have to rationalize the denominator . This is achieved by multiplying both the numerator and denominator by the radical in the denominator.

Question 13 plz show ALL STEPS so I can learn thnx

Answers

9514 1404 393

Answer:

  a) (x³ -x² +x +2) +2/(x+1)

  b) (x² +2x -5) +6/(x+3)

Step-by-step explanation:

Polynomial long division is virtually identical to numerical long division, except that the quotient term does not require any guessing. It is simply the ratio of the leading terms of the dividend and divisor. As with numerical long division, the product of the quotient term and the divisor is subtracted from the dividend to form the new dividend for the next step.

The process stops when the dividend is of lower degree than the divisor.

In part (a), you need to make sure the dividend expression has all of the powers of x present. This means terms 0x³ and 0x² must be added as placeholders in the given dividend. They will become important as the work progresses.

If a student (represented by initials) was chosen at random, find P(HHU C).

Answers

Answer:

[tex]P(HH\ u\ C) = \frac{13}{16}[/tex]

Step-by-step explanation:

Given

The Venn diagram

Required

[tex]P(HH\ u\ C)[/tex]

This is calculated as:

[tex]P(HH\ u\ C) = \frac{n(HH\ u\ C)}{n(U)}[/tex]

Where:

[tex]n(U) = 16[/tex] --- count of students

[tex]n(HH\ u\ C) =13[/tex]

So, we have:

[tex]P(HH\ u\ C) = \frac{n(HH\ u\ C)}{n(U)}[/tex]

[tex]P(HH\ u\ C) = \frac{13}{16}[/tex]

Hii guys plz help me

Answers

Answer:

B is the answer

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

you would have to multiply 2000 and the 25 and then divide

An account manager for a local software firm believes there is a relationship between the number of contacts and the amount of the sales. To verify this belief, the following data was collected: Salesperson Number of Contacts Sales (in millions) 1 14 24 2 12 14 3 20 28 What is the dependent variable

Answers

Answer:

Amount of sales

Step-by-step explanation:

The dependent variable also called the measured or predicted variable is simply the variable obtained due to inputs in of the independent variable. It is the variable which is being measured in an experiment. Here, the test is that the number of sales depends on the number of contact. Here, the number of contacts will has an influence or determines the amount of sales, hence, the number of contacts is the independent variable while the amount of sales is the dependent variable.

What are the coordinates of A’ after a 90° counterclockwise rotation about the origin.

Answers

Answer:

A' (- 1, - 5 )

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 90°

a point (x, y ) → (- y, x ), then

A (- 5, 1 ) → A' (- 1, - 5 )

Use the substitution method to solve the system of equations. Choose the
correct ordered pair.
y = 12x-8
y = 8x
A. (4, 12)
B. (5, 11)
C. (2,16)
O D. (3, 15)

Answers

Answer:

C. (2,16)

Step-by-step explanation:

[tex]y=12x-8\\y=8x\\\\\\8x=12x-8\\-4x=-8\\x=2\\\\y=8(2)=16[/tex]

Answer:

It might be B

Step-by-step explanation:

12(5)-8

8(11)

52

88

Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x=tcost, y=tsint, t=π

Answers

Step-by-step explanation:

the answer is in the image above

The product of a negative integer and a positive integer is?
PLEASE ANSWER A, B, C

Answers

Answer:

a. negative

b. negative

c. positive

Step-by-step explanation:

a. When a negative and positive integer are being multiplied the product will always be negative. For example, -3*2=-6.

b. Before answering this question it is helpful to realize that it is the exact same as part a. This is because the commutative property states that order does not matter in multiplication. So the answer is also negative, 2*-3=-6.

c. If two negative integers are multiplied then the product will be positive. Whenever two integers of the same sign are multiplied the product is positive. The opposite is true when they have different signs; the product will always be negative. An example of two negative integers would be -3*-2=6.

find the exact value of tan -75​

Answers

the exact value of tan -75 can be found by finding the coterminal angle (285) and taking the tangent of that

Internet providers: In a survey of 780 homeowners with high-speed Internet, the average monthly cost of a high-speed Internet plan was $64.22 with standard deviation S10.75. Assume the plan costs to be approximately bell-shaped. Estimate the number of plans that cost between $42.72 and $85.72. pprosimately bell-shaped. The number of plans that cost between $42.72 and $85.72 is:_________

Answers

Answer:

Hence the number of plans that cost between $42.72 and $ 85.72 is

95.44 %.

Step-by-step explanation:

Now the given are

μ = $64.22.

σ = $10.75.

Here,

[tex]P\left ( 42.72 < x< 85.72 \right )=P\left ( \frac{42..72-64.22}{10.75}< \frac{x-\mu }{\sigma } < \frac{85.72-64.22}{10.75}\right )\\P\left ( 42.72 < x< 85.72 \right )= P\left ( -2.00< Z <2.00 \right )\\P\left ( 42.72 < x< 85.72 \right )= P\left (Z<2.00\right )-P\left ( Z<-2.00 \right )\\P\left ( 42.72 < x< 85.72 \right )= P\left (0.9772\right )-P\left (0.0228\right )\\Probability = 0.9544[/tex]

Probability = 95.44%.

X^2 + bx + 49 is a perfect squad trinomial what is one possible value of b? & I need help with the others also due soon!

Answers

20. (2) 14

A perfect square trinomial will factor into two expressions that are the same, for example: x^2 + 6x + 9 = (x + 3)(x + 3). Since this problem has a C value of 49, it will factor into (x + 7)(x + 7). 7 doubled is 14, therefore one possible value of B is 7.

21. (4) 2, -12

x^2 + 10x + 25 = 24 + 25

(x + 5)^2 = 49

x + 5 = +/- 7

x = 2, -12

22. (3) 3 + sqrt(17)

x^2 - 6x = 8

Complete the Square

x^2 - 6x + 9 = 8 + 9

(x - 3)^2 = 17

x - 3 = +/- sqrt(17)

x = 3 + sqrt(17), 3 - sqrt(17)

23. (1) 1, -5

x^2 + 4x - 5 = 0

x^2 + 4x = 5

x^2 + 4x + 4 = 5 + 4

(x + 2)^2 = 9

x + 2 = +/- 3

x = 1, -5

Hope this helps!

Use differentials to approximate the change in cost corresponding to an increase in sales (or production) of one unit. Then compare this with the actual change in cost.

Function x-Value
C=0.025x^2 + 3x + 4 x=10

dC= ___________
ΔC= __________

Answers

Answer:

dC=3.5

DC is between 3.475 and 3.525

Step-by-step explanation:

So let dx=1 since the change there is a change in 1 unit.

Find dC/dx by differentiating the expression named C.

dC/dx=0.05x+3

So dC=(0.05x+3) dx

Plug in x=10 and dx=1:

dC=(0.05×10+3)(1)

dC=(0.5+3)

dC=3.5

Let D be the change in cost-the triangle thing.

Since dx=1 we only want the change in unit to be within 1 in difference.

So this means we want it to be from x=9 to x=1] ot from x=10 to x=11.

Let's do from x=9 to x=10 first:

DC=C(10)-C(9)

DC=[0.025×10^2+3×10+4]-[0.025×9^2+3×9+4]

DC=[2.5+30+4]-[0.025×81+27+4]

DC=[36.5]-[2.025+31]

DC=[36.5]-[33.025]

DC=3.475

Now let's do from x=10 to x=11

DC=[0.025×11^2+3×11+4]-[0.025×10^2+3×10+4]

DC=[0.025×121+33+4]-[36.5]

DC=[3.025+37]-[36.5]

DC=[40.025]-[36.5]

DC=3.525

So DC, the change in cost where the change in unit is 1, is between 3.475 and 3.525.

Chris is reading a book that has nine-hundred seventy-eight pages in it. Every night
Chris reads a number of pages that can be rounded to the nearest hundred. The rst
night Chris reads one-hundred two pages. The second night Chris reads ninety-eight
pages. The third night Chris read one-hundred fty-four pages. The fourth night Chris
reads fty-six pages. The fth night Chris reads two-hundred thirty-four pages. The
sixth night Chris reads forty-eight pages. The seventh night Chris reads one-hundred
seventy pages. On what nights does Chris read a number of pages that can be rounded
to the nearest hundred? Show all your mathematical thinking.

Answers

9514 1404 393

Answer:

  Every night

Step-by-step explanation:

The problem statement tells you ...

  "Every night Chris reads a number of pages that can be rounded to the nearest hundred."

Then it asks you ...

  "On what nights does Chris read a number of pages that can be rounded to the nearest hundred?"

If we take the problem statement at face value, the answer must be ...

  "Every night."

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