Luke's house is due west of Toronto and due south of Barrie. Toronto is 16 kilometres from Luke's house and 20 kilometres from Barrie. How far is Barrie from Luke's house, measured in a straight line?

Answers

Answer 1

Using the Pythagorean Theorem, it is found that Barrie is 12 miles from Luke's house, in a straight line.

What is the Pythagorean Theorem?

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

This problem can be modeled by a right triangle, with [tex]l_1 = 16, l_2 = d, h = 20[/tex], hence:

[tex]h^2 = l_1^2 + l_2^2[/tex]

[tex]16^2 + d^2 = 20^2[/tex]

[tex]d^2 = 144[/tex]

[tex]d = 12[/tex]

Barrie is 12 miles from Luke's house, in a straight line.

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Related Questions

BRAINLIEST AND 100 POINTS!

The equation yˆ=−5.131x2+31.821x−3.333 approximates the number of people standing in line to catch a commuter train x hour after 5 a.m.

What is the best estimate for the number of people in line at 7 a.m.?

23

27

32

40

Answers

Answer:

The answer is 40. I'm 100% sure.

Answer:

D.40

Step-by-step explanation:

solve plssss before i dieee i give points

Answers

Answer:

should be 66% of children and 1650 children in the town

Step-by-step explanation:

A silo of a barn consists of a cylinder capped by a hemisphere. The
height of a cylinder is 60 feet and its diameter is 30 feet. What is the approximate volume of the entire silo

Answers

The approximate volume of the entire silo which consists of a cylinder capped by a hemisphere is 42,390 cubic feet

Volume of the silo

Volume of a cylinder = πr²h

where,

π = 3.14

Radius, r = diameter / 2

= 30 ft / 2

= 15 ft

Height, h = 60 ft

Volume of a cylinder = πr²h

= 3.14 × 15 × 15 × 60

= 42,390 cubic feet

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#SPJ1

what is the area of this object? ​

Answers

Answer: no idea

Step-by-step explanation:

14. You deposit $500 in a savings account that
carns 7% interest compouncted anually.
A.) write a function that represents the balance
after t years
B.) What is the balance after 2 years?

Answers

A) Balance = 500(1.07)^t
B) Balance after 2 years = 500(1.07)^2 = $572.45

Answer:

A)    A(t) = 500e^(0.07)(t)

B)    575.137

Step-by-step explanation:

PLEASE HELP ME MATH IS HARD
Use the rectangle shown in the coordinate plane to answer each question.
1. Rotate rectangle KLMN 90º counter-clockwise about the origin. List the ordered pairs for each vertex of K'L'M'N'.
2. What do you notice about the ordered pairs of the original figure and the ordered pairs of the rotation about the origin?

Answers

Answer:

See below ↓

Step-by-step explanation:

1)

On rotating KLMN by 90° counterclockwise,the new coordinates are :K' = (-3, -6)L' = (-5, -4)M' = (-2, -1)N' = (0, -3)

2)

What do we notice here?We notice that on rotating from Quadrant II to Quadrant III, we find that all the x and y values become negative (other than N' which changes intercepts from x to y)

Answer:

Step-by-step explanation:

Rotate counter-clockwise = from right towards left  

Rotate 90° about the origin = We can think that our rectangle is a flag and that we added a pole to it. The pole is rotated counter-clockwise about the origin until we have the 90°. Where is the flag now positioned?

(Draw a line from origin to one of the rectangle's points; draw another line from origin that is ⊥ to the previous one. You rotate that point 90° from right to left and will lend on the new line.)

1. K (-6, 3) L (-4, 5) M (-1, 2) N (-3, 0) → K' (-3,-6) L'(-5, -4) M'(-2, -1) N'(0, -3)

2. We notice that the rule for rotating 90° about the origin is (x, y)→(-y, x)

which fraction is larger: 3/10 or 2/7
Plot on a number line

Answers

Answer:

3/10 is bigger

Step-by-step explanation:

covert into a decimal so 0.3 is bigger than 0.2857

What common donminator of 1/3 and 3/4

Answers

Answer:

12

Step-by-step explanation:

The least common denominator (LCD) of 1/3 and 3/4 is 12, because if you multiply the denominators of both fractions, 3 * 4 = 12.

This would change the fractions to-

1/3 * 4/4 = 4/12

3/4 * 3/3 = 9/12

I hope this was helpful! Have a lovely day!! :)

In a parallelogram ABCD, angle a=70, find 2angle d​

Answers

Answer:

D = 110

Step-by-step explanation:

Given,

In a parallelogram ABCD,

∠A =70∘

∠A + ∠B = 180∘.. (supplementary angles)

∠B = 180∘ – 70∘ = 110∘

∠A = ∠C and ∠B = ∠D.. (Opposite angles of parallelogram)

∠A = 70∘, ∠B = 110∘, ∠C = 70∘, ∠D = 110

the answer is gon b 110

If tomorrow i said, "the day before yesterday was saturday",then what is today?​

Answers

Answer:

Monday

Step-by-step explanation:

If day before yesterday was Saturday, so today is Monday.

At Garland School,
3/5 of the 490 students are boys.
At Bowood School, 5/7
of the 945 students are girls.
Which school has the greater number of girls and by how many?
You must show your working.

Answers

490 x 2/5 = 980/5 = 196 girls at Garland


945 x 5/7 = 4725/7 = 675 girls at Bowood


Bowood has more girls:

675-196 = 479 more

When spinning a penny, Claire believes the proportion of times the penny lands on heads is higher than 0.5. She spins a penny 50 times and it lands on heads 32 times. The P-value for the test of the hypotheses, H 0: p = 0.5, and H alpha: p greater-than 0.5, is 0.02, What is the correct interpretation of this value?

Answers

It depends on what the level of significance (alpha) is.

Since alpha is not stated, I'll assume that alpha = 0.05 by default.

Because the p-value is smaller than alpha, we reject the null hypothesis.

Therefore, we conclude that the alternative hypothesis is correct and the proportion of heads is greater than 0.5

3. You want to have $4000 in your savings account after 2 years. Find the amount you should deposit for each of the situations described below. a. The account pays 3% annual interest compounded monthly. b. The account pays 4% annual interest compounded continuously.​

Answers

Answer:

Part A)

About $3767.34.

Part B)

About $3692.47.

Step-by-step explanation:

Part A)

Recall that compound interest is given by the formula:
[tex]\displaystyle A = P\left(1+\frac{r}{n}\right)^{nt}[/tex]

Where A is the final amount, P is the initial amount, r is the interest rate, n is the number of times compounded per year, and t is the number of years.

To obtain $4000 after two years, let A = 4000 and t = 2.

Because the account pays 3% interest compounded monthly, r = 0.03 and n = 12.

Substitute and solve for P:

[tex]\displaystyle \begin{aligned} (4000) & = P\left(1+\frac{(0.03)}{(12)}\right)^{(12)(2)} \\ \\ P & = \frac{4000}{\left(1+\dfrac{(0.03)}{(12)}\right)^{(12)(2)}} \\ \\ & \approx \$3767.34\end{aligned}[/tex]

In concluion, about $3767.34 should be deposited.

Part B)

Recall the formula for continuous compound:

[tex]\displaystyle A = Pe^{rt}[/tex]

Where e is Euler's number.

Hence, let A = 4000, r = 0.04 and t = 2. Substitute and solve for P:

[tex]\displaystyle \begin{aligned}(4000) & = Pe^{(0.04)(2)} \\ \\ P & = \frac{4000}{e^{(0.02)(4)}} \\ \\ & \approx \$3692.47 \end{aligned}[/tex]

In conclusion, about $3692.47 should be deposited.

oshua wants to buy a flat-screen TV that costs $625. He saves $62.50 each week to buy the TV. In how many weeks will he have enough money to make his purchase?

Answers

Answer:

ten weeks

Step-by-step explanation:

62.50 multiped by 10 moves the decimal over 1 to the right which makes it 625 :)

Eli planted 14 out of his 20 tomato plants so far in his garden. What percentage of his tomato plants has he planted?

Answers

Answer:

70%

Step-by-step explanation:

First we express this as a fraction:

14/20

Then we express it as a decimal: (by doing 14÷20)

0.7

Now we express it as a percentage by multiplying the decimal by 100:

0.7×100%

70%

Answer:

70%

Step-by-step explanation:

GIven:

Eli planted 14 out of his 20 tomato plants so far in his garden. What percentage of his tomato plants has he planted?

Solve:

14/20 x 100

0.7 x 100

70%

Hence, 70% of his tomato plants he planted.

~Lenvy~

Leon and Omar went to grab ice cream after track practice. They each chose a container shaped like a cone or a cylinder. The dimensions of each container are shown in the drawing.

Answers

The volume of the cone and cylinder with a radius of 7 cm and height of 10 cm is 513.33 cm³ and 1540 cm³ respectively.

What is volume?

Volume is the amount of space occupied by a three dimensional shape or object.

Let us assume the cone and cylinder has a radius of 7 cm and height of 10 cm, hence:

Volume of the cone = (1/3) * π * radius² * height = (1/3) * π * 7² * 10 = 513.33 cm³

Volume of the cylinder = π * radius² * height = π * 7² * 10 = 1540 cm³

The volume of the cone and cylinder with a radius of 7 cm and height of 10 cm is 513.33 cm³ and 1540 cm³ respectively.

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can someone please help me

Answers

Like the given triangle is an isosceles triangle, the value of ∠ABC is 72°.

Types of Triangles

There are 3 main classifications for triangles refer to its sides.

Equilateral triangle - This triangle presents all sides with the same dimensions and the all angles equal to 60°.Isosceles triangle - This triangle presents two sides with the same dimensions and it has two angles with equal size.Scalene triangle  - This triangle presents all sides with different dimensions and it has all angles no equal size.

The figure shows that the given triangle is an isosceles triangle because it has two equal sides (AB=AC). If it is an isosceles triangle, this triangle presents two sides with the same dimensions (AB=AC). and it has two angles with equal size(∠ACB=∠ABC).

Knowing the sum internal angles of triangle is 180°. You can write:

3x+6x+6x=180

15x=180

x=12

Like ∠ABC=6x, then ∠ABC=6*12=72°.

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Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points)

Part B: Solve for k in each type of transformation. (4 points)

Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)

Answers

A) The transformations can be a vertical translation and an horizontal translation.

B) K = 8 and K' = 16

C) g(x) = f(x + 8)

    g(x) = f(x) + 16.

Which type of transformation could be used?

A ) By looking at the graph, we see that g(x) can be a translation to the left by K units or up by K' units.

B) In the case the translation is to the left, we can see that it the graph is moved 8 units, so K = 8.

In the case that the translation is up, we can see that it is for 16 units, so we have k' = 16.

C) How to write the equations?

An horizontal translation is written as:

g(x) = f(x + K).

Because the translation is to the left, we have that K is positive, then in our case we have:

g(x) = f(x + 8).

For the vertical translation the formula is:

g(x) = f(x) + K'

In our case, we have:

g(x) = f(x) + 16

If you want to learn more about transformations, you can read:

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Answer:The transformations can be a vertical translation and an horizontal translation.B) K = 8 and K' = 16C) g(x) = f(x + 8)    g(x) = f(x) + 16.Which type of transformation could be used?A ) By looking at the graph, we see that g(x) can be a translation to the left by K units or up by K' units.B) In the case the translation is to the left, we can see that it the graph is moved 8 units, so K = 8.In the case that the translation is up, we can see that it is for 16 units, so we have k' = 16.C) How to write the equations?An horizontal translation is written as:g(x) = f(x + K).Because the translation is to the left, we have that K is positive, then in our case we have:g(x) = f(x + 8).For the vertical translation the formula is:g(x) = f(x) + K'In our case, we have:g(x) = f(x) + 16

Step-by-step explanation:


7. The area of the parallelogram is 450 m2. What is
the height?
A. 25 m
B. 36 m
C. 50 m
D. 72m

Answers

The answer is 36 sq. ft. Find the area of the following parallelograms. Example 3. Base = 7 meters, Height = 3.5 meters. First, write

h = height of the parallelogram. a = side of the parallelogram (AD) x = any angle between the sides of the parallelogram (∠DAB or ∠ADC) d1 = diagonal of the parallelogram (p)
...
Area = ½ × d1 × d2 sin (y)

how do i solve (2[tex](\frac{2}{3} r^{2} s^{7} )^{2} * (\frac{1}{6} r^{3}s)[/tex]

Answers

Answer:

5x+1=7

Step-by-step explanation:

Whats 5-5-5-5-5-5x5757575

Answers

Answer:

-28787890

Step-by-step explanation:

Olivia borrowed $5,000 for 5 years at 5% simple interest.

Answers

Answer:

The answer is $1250

Step-by-step explanation:

Solution,

Principle (P) = $ 5,000

Time (T) = 5 years

Rate(R) = 5 %

Simple Interest (I) = ?

Now,

We have,

Simple Interest (I) = P×T×R/ 100

= 5,000×5×5/100

= $1250

The length of the base of an isosceles triangle is x. The length of a leg is 3x−6. The perimeter of the triangle is 65. Find x.

Answers

Answer:

x = 11

Step-by-step explanation:

Hello!

In an isosceles triangle, the two legs are congruent by the property Base angle Theorem. It is isosceles when both angles on the base are congruent.

So, since the base is x, and the measure of one leg is 3x - 6, we know that the other leg is also 3x - 6 in length.

The equation for perimeter is :  leg + leg + base = Perimeter

We can plug in 65 for the perimeter because it's given

Solve for x:

x + 3x - 6 + 3x - 6 = 657x - 12 = 657x = 77x = 11

The value of x is 11.

Find the measure of ∠ABC.

Answers

Answer:

170°

Step-by-step explanation:

There is a total of 180° and the angle is 10° less...

So, 180°-10° = 170°

Please 5 stars if correct!!!

I hope this helps!!!

An arrow is shot vertically upward at a rate of 190 feet per second from ground level. Use the projectile formula
h
=

16
t
2
+
v
0
t
+
h
0
h
=
-
16
t
2
+
v
0
t
+
h
0
to determine when the height of the arrow will be 471 feet.

Answers

The height of the arrow will be 471 feet at 8.35s and 3.53s

What is an equation?

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

h represent the height of the arrow after t seconds.

h(t) = -16t² + v₀t + h₀

v₀ is the initial velocity = 190 ft/s, h₀ is the initial height = 0m, hence:

h(t) = -16t² + 190t

At 471 feet:

471 = -16t² + 190t

0 = -16t² + 190t - 471

t = 8.35 or 3.53

The height of the arrow will be 471 feet at 8.35s and 3.53s

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X + 2x + 8 = X = 10 + 6

Answers

Answer:

x = 8/3

Decimal form: 2.66666666667

Step-by-step explanation:

Given:

[tex]x+2x+8=10+6[/tex]

Solution:

[tex]\mathrm{Add\:similar\:terms:}\:x+2x=3[/tex]

[tex]3x+8=10+6[/tex]

[tex]\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}[/tex]

[tex]3x+8-8=16-8[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]3x=8[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}3[/tex]

[tex]\frac{3x}{3}=\frac{8}{3}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]x=\frac{8}{3}[/tex]

[tex]x=2.66666666667[/tex]

~lenvy~

Answer/Step-by-step explanation:

Base on the given we are..

Solving for x:

Solve:

X + 2x + 8 = X = 10 + 6          {x+2x= 3x}

3x + 8 = 10 + 6                        {10+6=16}

3x + 8-8=16-8                           {16-8=8}

3x = 8                                  {divide both sides by same term}

3x/3 = 8/3

Therefore,

x = 8/3

Decimal form = 2.66666666667

[RevyBreeze]

100 points! need done asap

An unfair spinner has sections labeled 1 2 or 3 that are all twice as large as each of the sections labeled 4 5 or 6 Develop a probability model to describe all possible outcomes of one spin of the spinner

Answers

Answer:

look at the pic and stay safe!! hope it helps


The total cost f(x), in dollars, for renting a bowling lane for x hours is shown:
f(x) = 2x + 12
What does f(14) represent?
A. The number of dollars it costs to rent the bowling lane for 14 hours
B. The number of games you can bowl for a cost of $14
ting
C. The number of games you can bowl in 14 hours
D. The number of hours the bowling lane can be rented for a cost of $14

Answers

A. the number of dollars it costs to rent the bowling lane for 14 hours.

please help me I will mark BRAINLIEST ​

Answers

Answer:

See attached diagram

a) Points shown in blue

b) correlation is negative since the y-values decrease as the x-values increase.

c) Line of best fit needs to have the same number of points above as below.

Answer:the largest angle has a measure of ____degrees.

Answers

el angulo mayor tiene una medida de 360° grados


Angle 1=x
Angle 2= 3x
Angle3= x+40
5x+40= 180
180-40=140 140/5=28 =x
Angle 1= 28
Angle2=84
Angle 3=68
Largest =angle2: 84degrees
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