Lucy starts from home and travels 3 miles south to the post office. From the post office, she travels 4 miles east to the gas station. As it is known south and east directions form right angle. Since the entire trip forms a triangle, this triangle is right with right angle at post office.
Call the vertices of this triangle P - post office, G - gas station, H - home. Then HP and PG are legs of this triangle and GH is hypotenuse.
From the given data:
HP=3;PG=4;GH=5;∠P=90°.The smallest angle is opposite to the smallest side. The smallest side is leg HP, so the smallest angle is G that is the angle at gas station.
Answer: correct choice is A.
In this exercise we have to mark the correct alternative corresponding to the location, so we have:
Letter A
The following information was then given by the statement:
Lucy starts from home and travels 3 miles south to the post officeFrom the post office, she travels 4 miles east to the gas station.Imagining the paths made by lucy as a triangle, we know that the longest path that corresponds to the hypotenuse will be from the gas station to her house, so:
HP=3;PG=4;GH=5;P=90°.We have:
[tex]180-90=90\\90/2=45\\45-15=30[/tex]
The smallest angle is at the gas station.
See more about triangles at brainly.com/question/25813512
f(x) = 7x − 13. Find f−1(x).
Is 7040 yards more than or less then 4 miles
The perimeter of the following rectangle is 40 inches. What is the length of w?
Bottom: 14 in.
Side: Unknown
2.9 in.
6 in.
12 in.
26 in.
6 inches is the answer
P= 2( L+W)
Answer: 6 inches
Step-by-step explanation:
Given: The perimeter of the rectangle = 40 inches
Let the unknown side be w.
And the bottom side l=14 in.
We know that the perimeter of rectangle is given by :-
[tex]\text{Perimeter}=2(l+w)\\\Rightarrow40=2(14+w)\\\Rightarrow\frac{40}{2}=14+w\\\\Rightarrow20=14+w\\\Rightarrow\ w=20-14)\\\Rightarrow w=6\ in.[/tex]
Hence, the the length of w = 6 inches.
Find an explicit formula for the arithmetic sequence -11,-3,5,13,...
The sum of the components of anything equals the whole thing. Which property/postulate does this statement represent?
Answer this question, me and my partner have no idea what to do I'm very confused
Using Pythagorean inequalities, determine which set of the given three sides produces an obtuse triangle. A. 4, 5, 6 B. 5, 13, 19 C. 12, 14, 25 D. 21, 72, 75
Answer:
Obtuse triangle sets
B. 5, 13, 19
C. 12, 14, 25
Step-by-step explanation:
The Pythagorean inequality for the sides of the triangle to be an obtuse:
[tex]a^2 + b^2 < c^2[/tex], where a, b and c are the sides of the triangle.
The other Pythagorean inequalities are:
[tex]a^2 + b^2 > c^2[/tex], for Acute triangle
[tex]a^2 + b^2 = c^2[/tex], for Right triangle
Now let's check which set of the given sets satisfy the above inequality.
Option A
4, 5, 6
Here a = 4, b = 5 and c = 6
[tex]4^2 + 5^2 < 6^2\\16 + 25 < 36\\41 < 36\\[/tex]
Which is not true.
Here [tex]a^2 + b^2 > c^2[/tex], So this is Acute triangle
Option B
5, 13, 19
Here a = 5, b = 13 and c = 19
[tex]5^2 + 13^2 < 19^2\\25 + 169 < 361\\194 < 361\\[/tex]
Which is true. This is Obtuse triangle
Option C
Here a = 12, b = 14 and c = 25
[tex]12^2 + 14^2 < 25^2\\144 + 196 < 625\\340 < 625\\[/tex]
Which is true. This is obtuse triangle.
Option D
Here a = 21, b = 72 and c = 75
[tex]21^2 + 72^2 < 75^2\\441 + 5184 < 5625\\5625 < 5625\\[/tex]
Which is not true for obtuse.
Here [tex]a^2 + b^2 = c^2[/tex], for Right triangle
So this is Right triangle.
Answer:
c
Step-by-step explanation:
just did it
help What is the length of the unknown leg in the right triangle?
A baker uses 5.5 lb of flour daily how many ounces of flour will he use in two weeks
1 pound = 16 ounces
16 * 5.5 = 88 ounces per day
88*7 = 616 ounces per week
616 * 2 = 1232 ounces in 2 weeks
What is the probability of receiving a 6 or a 9 from a deck of 52 cards and an ace or a king?
Final answer:
The probability of selecting a heart or a face card from a standard deck of cards is approximately 42.31%, which is significantly higher than the probability of selecting just a heart suit face card, which is about 5.77%.
Explanation:
To calculate the probability of selecting a heart or a face card, we first need to count the number of favorable outcomes. There are 13 hearts in a deck of cards and 12 face cards (Jacks, Queens, and Kings, with 3 in each suit). However, there are overlap cards that are both hearts and face cards (Jack, Queen, King of Hearts), which amount to 3 cards. We must subtract these to avoid double counting. So, the formula to find the total number of favorable outcomes is:
Favorable outcomes = Total hearts + Total face cards - Overlap of hearts and face cards
Favorable outcomes = 13 (hearts) + 12 (face cards) - 3 (heart face cards) = 22
Next, we calculate the probability:
P(A) = Favorable outcomes / Total number of cards
P(A) = 22 / 52 ≈ 0.4231 or 42.31%
This is the probability of selecting a heart or a face card from a standard deck. Comparing this to the probability of selecting a heart suit face card (which is 3/52 or about 5.77%), it is clear that selecting a heart or a face card is much more likely.
Therefore, the probability of selecting either a heart or a face card is less than the probability of drawing only heart-suit face cards, since the number of favorable outcomes for the latter is smaller.
What are the next letters? BE GJ LO QT
alicia bough 3.8 pounds of cashews for 15.74 about how much was cost per pound
find the mean absolute deviation
Answer:
(MAD) Mean Absolute Deviation: 3.28
Step-by-step explanation:
Mean: 4 + 5 + 8 + 10 + 15 = 42/5 = 8.4
8.4 - 4 = 4.4
8.4 - 5 = 3.4
8.4 - 8 = 0.4
8.4 - 10 = 1.6
8.4 - 15 = 6.6
Mean Absolute Deviation: 4.4 + 3.4 + 0.4 + 1.6 + 6.6 = 16.4/5 = 3.28
Robert buys 3 pounds of bananas at $0.50 per pound and 3 pounds of apples at $1.00 per pound. Which of the following expressions represents the total cost of the fruit he bought (in dollars
Answer:
The answer is $3(0.50+1.00)
Step-by-step explanation:
Robert bought 3 pounds of bananas at $0.50 per pound which can be expressed as:
[tex]3*0.50[/tex]
And 3 pounds of apples at $1.00 per pound which can be expressed as:
[tex]3*1.00[/tex]
As Robert bought the apples and bananas, you can add both expressions:
[tex]3*0.50 + 3*1.00[/tex]
This expression can be factorized as:
[tex]3(0.50+1.00)[/tex]
or
[tex]3(1.50)[/tex]
Both expressions will give you the same result, which is $4.50.
Evaluate for C=3 and d=-5
(3c^2-3d)^2-1000
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Solve the following quadratic equation. 3(x + 5)2 = 60
Solve the equation
-3x+1+10x=x+4
Describe how to model -3x + 7=28 with algebra tiles
Halle has 36 feathers, 48 acorns, and 60 agates. She wants to put all of these items into bowls with the same number of feathers, acorns, and agates in each bowl and none left out. What is the maximum number of bowls she can put the items into?
48-36 =12
60-48=12
36/12 =3
48/12=4
60/12=5
the maximum number of bowls is 12
Answer:
12
Step-by-step explanation:
A cable is 7.1m long. How long is the cable in decimeters?
I REALY NEED HELP!
A number line contains points Q, R, S, and T. Point Q is on the coordinate 24, R is on the coordinate 28, S is on the coordinate 29, T is on the coordinate 42. Find the probability that a point chosen at random on QT is on ST. Express your answer as a percent.
25%
42.2%
50%
72.2%
Answer:
The correct option is 4.
Step-by-step explanation:
It is given that Point Q is on the coordinate 24, R is on the coordinate 28, S is on the coordinate 29, T is on the coordinate 42.
Total numbers lie on line QT is
[tex]42-24=18[/tex]
The numbers lie on line ST is
[tex]42-29=13[/tex]
The probability that a point chosen at random on QT is on ST is
[tex]P=\frac{\text{The numbers lie on line ST}}{\text{Total numbers lie on line QT}}\times 100[/tex]
[tex]P=\frac{13}{18}}\times 100[/tex]
[tex]P=72.222\approx 72.2\%[/tex]
The probability that a point chosen at random on QT is on ST is 72.2%. Therefore option 4 is correct.
Stumped on how to solve this one! The numbers just aren't making sense to me
30 = 3/5
so 1/5 = 10 miles
there are 20/5 in 4 inches
10*20 = 200
they are 200 miles apart
A cabinet maker buys 3.5 liters of oak varnish. The varnish cost $4.95 per liter. What is the total cost of 3.5 L of varnish ?
sum of 6 divided by a number and that number divided by 6
what is 9 hours from now
Rolf spent 15 hours last week practicing his saxophone if 3/10 of the time was spent practicing warm up routines, how much time did he spend practicing warm up routines ?
Which expression is equivalent to 17x − 8x + 2 and why?
2 − 9x, because (17x − 8x) + 2 = −9x + 2 = 2 − 9x
2 + 9x, because (17x − 8x) + 2 = 9x + 2 = 2 + 9x
11x, because 17x − 8x + 2 = 9x + 2 = 11x
7x, because 17x − 8x + 2 = 17x − 10x = 7x
Answer:
2 + 9x, beacuse (17x - 8x) + 2 = 9x+2
Step-by-step explanation:
Combine like Terms: 17x - 8x + 2=
9x+2
PLEASE HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1) A dealer sold 112 cars during the month of May and 96 during the month of June. What was the percentage of the decrease?
2) At an evening performance, 85% of the seats in a movie house was occupied. If 34 people attended this performance, what was the seating capacity of the movie house?
3) A merchant sold articles of clothing at 140% of what he paid for them. What did he pay for an article that he sold for $84?
4) A family spent 486 a week for food. This was 20% of its weekly income. What was its weekly income?
5) An agent sold 250 boxes of apples at $6.50 each. He charged a commission of 5%. What was his commission?
6) At the rate of $0.80 per $100, how much does it cost to insure a car against fire and theft for $1,650?
A rope stretches directly depending on the load it must carry. If a load of 8 pounds stretches the rope 9.6 inches, the constant of proportionality is equal to:
8(9.6)
8/9.6
9.6/8
"Our proportionality constant would be how much the rope stretches versus the weight being hung. This is set up by simply dividing the two numbers.
9.6 inches / 8 pounds
or for every pound hung, it will stretch 1.2 inches so we know if it stretches 6 inches, we can set up an equation 6 inches = 1.2 [inches/pound] * pounds solve for weight to get 5 pounds being hung from the rope."
Answer: 9.6 inches / 8 pounds
Step-by-step explanation: I got it right
A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?