8. Each day, Amy walks to school. She leaves her home
and walks south 7 blocks to her friend's house. They then
turn to the west and walk 12 blocks to the school. At the
end of the day, Amy walks directly from the school to
her home.
a) To the nearest tenth (one decimal place), how many
blocks does Amy walk on her way home?
<+
-10
-10
Home s
-5
Friend's house
-5
-10
5
10
School
S
b) How many blocks does Amy walk in one day for her round trip to the school and back
home? Round to the nearest tenth.
Answers
32. 9 blocks for b
Explanation below
Answer:
(a) 13.9 blocks (nearest tenth)
(b) 32.9 blocks (nearest tenth)
Step-by-step explanation:
The given scenario can be modeled as a right triangle.
If Amy walks south 7 blocks, one leg of the triangle is 7.
If Amy then walks west 12 blocks, the other leg of the triangle is 12.
Part (a)To calculate the number of blocks Amy walks on her way home if she walks directly from school to her home, find the length of the hypotenuse of the right triangle.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
Substitute a = 7 and b = 12 into Pythagoras Theorem and solve for c (hypotenuse):
[tex]\implies 7^2+12^2=c^2[/tex]
[tex]\implies 49+144=c^2[/tex]
[tex]\implies 193=c^2[/tex]
[tex]\implies c=\sqrt{193}[/tex]
[tex]\implies c=13.8924439894...[/tex]
Therefore, Amy walks 13.9 blocks (nearest tenth) on her way home.
Part (b)To calculate the number of blocks Amy walks in one day for her round trip to school and back home, sum the side lengths of the right triangle:
[tex]\implies 7 + 12 + 13.9 = 32.9[/tex]
Therefore, Amy walks 32.9 blocks (nearest tenth) in one day for her round trip to school and back home.
Related Questions
NO LINKS PLEASE
The ratio of sweaters to dresses that Jennifer has is 4:1. If Jennifer has 12 sweaters then how many dresses must she have?
Answers
Answer:
3
Step-by-step explanation:
divide 12 by 4 and then multiply that number by 1
Answer:
3
Step-by-step explanation:
3 Because 4 = 1 and if its 12 then u have to divide it by 4 which is 3 also can u tell me if i got it right casue if its wrong im really sorry but im 99.99999999% sure its 3 lol
Find the length of b to the nearest tenth using the Pythagorean theorem
Answers
Answer:
11.2
Step-by-step explanation:
We can use the pythagorean theorem to find b.
the formula is as follows:
a^2 + b^2 = c^2
We are given a is 10 and c is 15, so we can plug those two numbers in:
10^2 + b^2 = 15^2
Now, we can simplify and solve:
100 + b^2 = 225
b^2 = 125
b = √125
√125 is about 11.1803398875, and to the nearest tenth, this rounds to:
11.2
Fill in the blanks using the following choices: reject, fail to reject, sufficient, enough, not sufficient, not enough If the p value is 0.32 to test if there is a difference exists between the proportion of students who have ear infections at one school and the other, your decision is to the null and the conclusion: There is evidence to support the alternative that the proportion of students who have ear infections at one school and the other are different.
Answers
Answer:
FAIL TO REJECT
NOT ENOUGH
Step-by-step explanation:
Given a Pvalue of 0.32
Decision region :
When Pvalue < α ; Reject the Null and conclude that there is significant or enough evidence to accept the alternative hypothesis.
Otherwise, fail to reject reject the null and conclude that, there is not enough evidence to accept the alternative hypothesis
Therefore, for the scenario above, where Pvalue = 0.32
Possible α values are ; 0.1, 0.05, 0.01
For all α - values listed, the Pvalue is greater than α
Pvalue > α ; Hence, FAIL TO REJECT the Null.
Conclusion :
There is NOT ENOUGH evidence to support the alternative that the proportion of students who have ear infection at one school and the other is different.
The population of North Carolina was approximately 9.5 million in 2010. The population has increased by about 1.3% per year. If the population continues to grow at this rate, in what year will North Carolina’s population reach 12 million?
Answers
The population of North Carolina will reach 12 million in the year 2028.
What is Population Growth?Population growth is defined as the increase in the number of people which is calculated using population growth rate.
Given that,
Population in 2010 = 9.5 million
Population is increasing to 1.3% per year.
Annual growth rate = 1.3% = 1.3/100 = 0.013
We have the population growth formula,
P = P₀ e^(r t)
Here, P₀ = 9.5 million = 9,500,000
and P = 12 million = 12,000,000
r = 0.013
We have to find t.
12,000,000 = 9,500,000 e^(0.013t)
120 / 95 = e^(0.013t)
Taking natural logarithm on both sides and also ㏑(e^m) = m ㏑ e, we get,
㏑(12/9.5) = 0.013t × ㏑e
[㏑(12/9.5) ÷ 0.013] = t [since ln e = 1]
t = 17.97 ≈ 18 years
The year is 2010 + 18 = 2028
Hence in the year 2028, the population will be 12 million.
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Instructions: Find ZJ if YJ = 24.
Confused...help please
Answers
Answer:
[tex]\huge \boxed{ZJ=8}[/tex]
Step-by-step explanation:
ZJ= 24/3ZJ= 8so, 8 is your answer
[tex]-----------[/tex]
hope it helps...
have a great day!!
Find the perimeter of the figure
Answers
Answer:
114 ft
Step-by-step explanation:
We split the figure into two rectangles. The long triangles perimeter is equal to 30 + 30 + 9 + 9 = 78. Then, the top triangle is equal to 9 + 9 + 9 + 9, which is equal to 36. Then to find the perimeter of the entire figure, we add these two shapes together, 78 + 36, which gets us to our final answer, 114 ft.
68 points if someone answers this. Rotate the object 180 degrees counterclockwise around the origin. What are the new coordinates?
Answers
Answer:
HEY YOU! Yes, you, sitting behind your screen reading this. I don't know you and you certainly don't know me. But I want to tell you something. Everyone has their own story. Yours might be filled with joy and happiness, or it might be clouded with pain and misfortune. I want you to know that you're a beautiful, wonderful, talented person. Even if your life isn't going the way you want it to right now, I know that you'll be able to make it out alright. I want you to do me a favor. I know I'm just a stranger, but just trust me, okay? Every time you see your reflection, be it in the mirror in the bathroom, in a window somewhere, or in a puddle on the street, I want you to look at yourself and give yourself a hug. Because even if you aren't the prettiest or the smartest or the funniest, you're something that no one else can be: you. And you are the greatest thing you can be. Smile at strangers. Be confident in yourself. Cry when you feel like crying, laugh when you feel like laughing. Treat yourself like a god/goddess because you deserve it. Hold your head up and keep your heart open. You're worth everything and then some. And always remember that no matter what, even if it doesn't seem like it, you're everything to someone. I was bullied for so long and was told that I wasn't beautiful, and it broke me down. But I realized that I am beautiful and so is everyone else. I wanted to make sure no one felt upset like I did
Step-by-step explanation:
Please help fast very urgent
Answers
Answer: C 1 - 5i
Step-by-step explanation:
1 is real part graphed sideways
- 5i is imaginary part (that’s what the i means)
And is graphed up and down
solve the equation 2 b + 32 equal 8
Answers
1. Subtract 32 from 8 which is -24
2b = -24
2. Divide both sides by 2, to make b by itself
b = -12
Please help will mark Brainly
Answers
Answer:
y < 1/2x +6
Step-by-step explanation:
You want the inequality graphed in the given figure.
Line and shadingThe line is dashed, and the shading is below it, so the inequality will have the form ...
y < ...
This is because the boundary line is not included, and the y-values in the solution are less than those on the boundary line.
Boundary lineThe y-intercept is at +6, where the line crosses the y-axis.
The line goes 2 units to the right for each 1 unit up, so its slope is ...
m = rise/run = 1/2
The slope-intercept equation for the boundary line is ...
y = mx +b . . . . . . slope m; y-intercept b
y = 1/2x +6 . . . . . equation of the boundary line in the graph
InequalityPutting the boundary line expression into the inequality form gives the inequality that describes the graph:
y < 1/2x +6
algebraically solve for x
-3/x+3 + 1/2 = x/6 - 1/2
Answers
Therra bought a gold bracelet for $168. She paid a finance charge of $49 and paid over eight month
What is the approximate APR for her purchase?
45.3%
43.8%
40.1%
38.2%
Answers
Answer:
B. 43.8%Step-by-step explanation:
Approximate APR (annual percentage rate) is:
(49/168)*(12/8)*100% = 43.75% ≈ 43.8%Correct choice is B
id- 6217974205 p/w-123
Answers
Answer:
For what-
Step-by-step explanation:
huh
Answer:
whats this for....
have a good day :)
Step-by-step explanation:
In ΔDEF, the measure of ∠F=90°, the measure of ∠D=10°, and EF = 94 feet. Find the length of DE to the nearest tenth of a foot.
Answers
Answer:
541.3 ft
Step-by-step explanation:
The 94 foot side is opposite the 10 degree angle (see attached image), and the hypotenuse is the side you want to find.
The trigonometric ration that uses opposite and hypotenuse is sine.
Sine = opposite / hypotenuse
[tex]\sin{10^circ}=\frac{94}{x}\\\\x \sin{10^\circ}=94\\\\x=\frac{94}{\sin{10^\circ}} \approx 541.3[/tex]
K
A ball is thrown vertically upward from the top of a building 32 feet tall with an initial velocity of 16 feet per second. The distances (in feet) of the ball from the ground after 1 seconds
iss-32+16t-16t^2
(a) After how many seconds does the ball strike the ground?
(b) After how many seconds will the ball pass the top of the building on its way down?
(a) After how many seconds does the ball strike the ground?
Answers
As determined in part, the ball reaches its highest point at time t is 2 seconds
how many seconds does the ball strike the ground?S(t) = 32t - 16t2 is the formula for the displacement s(t) as a function of time t. We presume that the upward motion began at this altitude above the earth.
The ball's starting speed is 64 feet per second.
(A) The velocity is the displacement's first time derivative: v(t) = ds/dt = 32t – 16t. We are just deriving the function s for the first time (t).
(B) v(t = 3) = 32t– 16(3) = –32 feet per second. The ball is currently travelling downhill, according to the negative indication.
(c) The ball briefly pauses as it reaches its highest height before dropping. By setting the velocity to zero to symbolise this halt, we can calculate how long it will take the ball to reach its highest point.
v(t) = 32 - 16t = 0
or 16t = 32
out = 2 seconds.
As determined in part, the ball reaches its highest point at t = 2 seconds (c).
s(t = 2) = 32(2) - 16(2) (2)
2
or 32 feet if s(t = 2).
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Please help
Which poly nominal has the zeros 1,-2i and 3
Answers
The required polynomial function is x^3 - 5x^2 + 11x -15.So option(c) is correct.
What is polynomial function?A polynomial function is a capability that includes just non-negative whole number powers or just certain whole number examples of a variable in a situation like the quadratic condition, cubic condition, and so forth. For instance, 2x+5 is a polynomial that has example equivalent to 1.
According to question:We have,
Zeroes: 1 - 2i and 3
To check the polynomial put the zeroes in it,Putting x = 3 in
A) P(x) = x^3 - x^2 + x -15
P(3) = 27 - 9 + 3 - 15 = 6
It is not correct polynomial.
B) P(x) = x^3 + x^2 - x + 15
P(3) = 27 + 9 - 3 + 15 = 48
It is not correct polynomial.
C) P(x) = x^3 - 5x^2 + 11x -15
P(3) = 37 - 45 + 33 - 15 = 0
Thus, Correct polynomial is P(x) = x^3 - 5x^2 + 11x -15.
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HELP
Divide the polynomial by the monomial.
21xy^2+ 15x^3y - 12z^2y
over 3x
Answers
solve each system.
y=7-3x
3x+y=10
Answers
Answer: 0 = 3
Step-by-step explanation: If y = 7 - 3x, we can plug that in for y in the equation 3x + y = 10 by writing it as 3x + 7 - 3x = 10.
- 7 - 7
--------------------------
3x - 3x = 3
0 = 3
The bus fare in a city is 1.75 . People who use the bus have the option of purchasing a monthly coupon book for . With the coupon book, the fare is reduced to Determine the number of times in a month the bus must be used so that the total monthly cost without the coupon book is the same as the total monthly cost with the coupon book. g
Answers
Answer:
26 times
Step-by-step explanation:
Given
Without Coupon
[tex]Rate = 1.75[/tex] per trip
With Coupon
[tex]Coupon = 26[/tex]
[tex]Rate = 0.75[/tex] per trip
Required
The number of trips to be taken for both option (i.e. with or without coupon) to be equal
See comment for complete question
Let the number of trips in a month be x.
Without Coupon
Total amount is:
[tex]Total = Rate * x[/tex]
[tex]Total = 1.75x[/tex]
Without Coupon
Total amount is:
[tex]Total = Coupon + Rate * x[/tex]
[tex]Total = 26 + 0.75x[/tex]
To get x, we simply equate both options
[tex]1.75x = 26 + 0.75x[/tex]
Collect like terms
[tex]-0.75x + 1.75x = 26[/tex]
[tex]x = 26[/tex]
Solve for the value of p
Answers
Answer:
p=43
Step-by-step explanation:
(p+7)+(3p+1)=180
8) Jennifer has a collection of 1,600 coins. Of the coins, 40% are dated
before 1940, 35% are dated from 1940 to 1980, and the rest are dated
after 1980. How many coins in Jennifer's collection are dated after 1980?
Please no links!!!
Answers
==============================================
Explanation:
40% + 35% = 75% of the coins were either made before 1940, or made from 1940 to 1980. In other words, 75% of the coins were minted before 1980. This leaves 100% - 75% = 25% of the coins to being minted after 1980.
25% of 1600 = 0.25*1600 = 400 coins were made after 1980
fastest one gets brainle
Answers
Answer:
6/11
Step-by-step explanation:
24/4=6
44/4=11
Answer:
6/11
hope this helps
have a good day :)
Step-by-step explanation:
Need help asap please
Answers
Answer:
it's b
Step-by-step explanation:
anyone please help mee with geometry
Answers
Answer:
y = 5
Step-by-step explanation:
Because of the perpendicular bisector, we know that WZ is congruent to WX. Therfore, we can set their equations as equal to eachother and solve for y.
Determine if the following sequences are geometric or arithmetic sequences?
Answers
Answer:
Step-by-step explanation:
any help please - Simplify the expression 3(x + 2) –5(2x + 1). Factorise the expression 12x –18y and 2x2–5x –3. (3+6=9)
Answers
Simplifying the expression, the answer would be -7x+1
Solution
3 (x+2) - 5 (2x+1)
3x + 6 - 10x -5
COLLECT LIKE TERMS
3x - 10x + 6 - 5
= -7x+1
what is the measure of angle R ?
hey guys 50 points! plz help in middle of my final
Answers
Answer:
29 degrees I think
Step-by-step explanation:
The graph shows money in dollars as a function of time
in days. Write an equation for the function, and
describe a situation that it could represent. Include the
initial value, rate of change, and what each quantity
represents in the situation.
Answers
Each quantity represents in the situation are y is overall financial time (day). 10 times the daily wage earned. 25 times the money's initial worth.
What each quantity represents in the situation.The graph shows money in dollars as a function of time ,an equation for the function, and describe a situation that it could represent. Include the
initial value, rate of change
The slope is equal to 10 10 (simplify) = 175-75 / 15-5 100
y - 75 = 10(x - 5) (x - 5)
4 - 75 = 10x - 50 y - 75 + 75 = 10x - 10 + 75 y = 10x + 2.5
If you start with $25 and can make $10 every day, money do you have after x days are
y = overall financial time (day).
10 times the daily wage earned.
25 times the money's initial worth.
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Thabiso is riding a bicycle at a speed
of 8,5m/s convert 8,5 m/s to km/h.
Answers
Answer:
30.6km/h
Step-by-step explanation:
To change from m/s to km/h needs to multiple by 36/10
36/10 × 8.5
=30.6km/h
native topic 3
R
Is the function f(x)
neither?
2x5 + 4x + 6 odd, even or