A boat travels 21 miles due north and then 28 miles due east.Then the boat travels in a straight line back to its starting point.Solve to find the straight line distance of the boat to its starting point.
A.28 miles
B.33 miles
C.35 miles
D.49 miles
When the boat headed 21 miles north then 28 miles to the east then back to its starting point, it formed a right angle triangle. And that straight line the question is talking about is the hypotenuse.
Use the Pythagorean Theorem to solve for hypotenuse.
The Pythagorean Theorem states that for any right triangle the following is true: when you take the sum of both of the legs squared it will equal to the hypotenuse squared.
In equation form: a^2+b^2=b^2
Where the variables a and b are the legs. And the variable c is the hypotenuse.
Plug in the values.
21^2 + 28^2 = c^2
441 + 784 = c^2
1225 = c^2
35 = c
So, the straight line is 35 miles long.
Estimate a 15% tip for each bill shown.
a. $57.80
_______
b. $122.46
_______
Answer:
a. $57.80
$66.47
b. $122.46
$140.829
Step-by-step explanation:
Find the maximum walking speed of giraffe with leges 6.03 feet long
Answer:
13.89 ft/s
Step-by-step explanation:
We know that the cheetah is the fastest land animal on Earth, but what if it were not allowed to run? Biologists model maximum walking speed by the equation = √, where g is the acceleration due to gravity (9.8 m/s2 or 32 ft/s2) and L is the length of the leg (in metric or standard units). In the situations below, use this information to answer the questions.
(Hint: It will be useful to know 1 m = 3.23 ft for conversions)
1. Find the maximum walking speed of a giraffe with legs 6.03 feet long.
Solution:
Speed is the ratio of the total distance travelled to the time taken to reach this distance. Speed is given by the formula:
Speed = distance / time
Given that the maximum walking speed (s) is given by the equation:
= √, where g is the acceleration due to gravity (9.8 m/s² or 32 ft/s²) and L is the length of the leg (in metric or standard units).
The giraffe has a length of leg (L) of 6.03 feet, hence:
s = √(32 ft/s² * 6.03 ft)
s = √192.96
s = 13.89 ft/s
which equation represents the graph below
y= x/35
y=35x
y=x-35
y=x+35
Answer:
B: y=35x
Step-by-step explanation:
You can verify this by plugging 1 to be x (35*1=35) and 2 (35*2=70)
math for 3rd grade plz help
Answer:
18 r2
Step-by-step explanation:
Answer:
59
Step-by-step explanation:
for the first answere
Juana went shopping with $ 50 and spent $ 45. What percentage of her money did she spend?
Answer: 90%
Step-by-step explanation:
Answer:
90%
Step-by-step explanation:
In order to find the percentage of the money Juana spent while shopping, you must take the amount of money spent and divide it by the total amount of money.
$45 dollars spent divided by $50 dollars total will give you your fraction, in decimals:
45 / 50 = 0.90
Multiply by 100% to find your percentage
0.90 * 100% = 90.0%
Edmond goes to the doctor for a check-up. When he gets home, he tells his mother that he weighs 1,360 ounces and is 62 inches tall. What is Edmond's height and weight in feet and pounds, respectively?
Answer:
113.3 pounds
5.17 ft
Step-by-step explanation:
Step one:
given data
weighs 1,360 ounces and is
Height = 62 inches tall.
Required:
We are expected to perform unit conversion
from ounces to pounds
and from inches to feet
Step two:
1 pound is 16 ounces
x pound is 1360 ounces
cross multiply
16x= 1360
x= 1360/16
x= 113.3 pounds
Step three
1 inches is 0.0833333ft
62 inches is x ft
cross multiply
x= 5.17 ft
A grain silo is in the shape of a cylinder with a hemisphere top. They cylinder is 20 feet tall. The volume of the silo is 2106 cubic feet. Find the radius of the silo.
Answer:
The radius of the silo is 5.788 feet.
Step-by-step explanation:
Since the silo has the shape of a cylinder, then;
Volume of the silo = Volume of a cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h
Where: r is the radius of the silo, and h is the height.
Given that: volume = 2106 cubic feet, and height = 20 feet.
Then,
2106 = [tex]\frac{22}{7}[/tex] x [tex]r^{2}[/tex] x 20
2106 = [tex]\frac{440}{7}[/tex][tex]r^{2}[/tex]
2106 x 7 = 440[tex]r^{2}[/tex]
14742 = 440[tex]r^{2}[/tex]
[tex]r^{2}[/tex] = [tex]\frac{14742}{440}[/tex]
[tex]r^{2}[/tex] = 33.5045
⇒ r = [tex]\sqrt{33.5045}[/tex]
= 5.78831
r = 5.788 feet
The radius of the silo is 5.788 feet.
3
Question 5 (1 point)
Saved
Line AB has a slope of
value of k.
3
4.
and the endpoints A(11,3) and B(3, k). Determine the value of k
3
-41
9
-9
dont click this one it is not the right answer
WILL GIVE BRAINLIEST IF YOU GIVE AN EXPLANATION. In the packaging part of a warehouse, boxes of blue cups must be moved from the staging area located at an origination point along a conveyor belt described by a vector with components ⟨6, 30⟩. If boxes of red cups are moved 2.5 times the distance along the same belt, which describes the vector that shows the path of the boxes of red cups? Round the magnitude to the nearest whole number if necessary.
Answer:
components: ⟨15, 75⟩, magnitude: about 76
I got this right edge 2020
Component: (15, 75), magnitude about 76 is our correct answer.
Boxes of blue cups moving along a conveyor belt are described by a vector with components (6, 30).
Boxes of red cups are moving along the same conveyor belt but 2.5 times the distance blue cups moved.
We need to find the vector that describes the boxes of red cups and the magnitude of this vector.
What is a vector?A vector is a quantity that has magnitude and direction denoted by:
[tex]V = (V_x, V_y)\\\\Where~~V_x = Vcos\theta~~and~~V_y = Vsin\thetaV_x ~and~V_y~are~ its~ components.[/tex]
Its magnitude is given by:
[tex]|V| = \sqrt{V_x+V_y}[/tex]
Since boxes of red cups move 2.5 times the distance along the same belt as blue cups moved.
We can describe the vector that shows the path of the boxes of red cups as:
= 2.5 x (6, 30)
= ( 2.5x6, 2.5x30 )
= ( 15, 75 )
The magnitude of the vector ( 15, 75 ) is:
[tex]|V| = \sqrt{15^2+75^2}\\\\|V| = \sqrt{225+5625}\\\\|V| = \sqrt{5850}\\\\|V| = 76.48\\\\|V| = 76[/tex]
Rounding 76.48 to its nearest whole number we get,76.
Thus, we have the required vector along with its component as (15, 75) and the magnitude about 76.
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In this diagram, mZACD = [ ? 1°
answer this please !!
Answer and work in the picture above
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4
Use the graph that shows the solution to f(x) = g(x).
f(x) = - *x² + 3x + 1
g(x) = x - 1
f(x)
ox)
What is the solution to f (x) = g(x)?
4
-3-2
x = 0
x = 2
f(x)
3
2
g(x)
2
Answer:
x = 4
Step-by-step explanation:
Both A and B are similar
We have no problems with f(x) as it is similar on both plots
A graph of g(x) however shows that it is the second plot that is correct
Thus,
To get the solution , we need the point at which both graphs crosses each other
we can see this at the point x = 4 and thus that is our solution
Today a 9 friends went out for lunch. Their total bill was 55.09, including tax and gratuity. One of them ordered only soda and needed to pay only $1.25. The other 8 friends ordered the same daily special. How much did each of the other friends need to pay
Answer:
6.73
Step-by-step explanation:
55.09-1.25= 53.84
53.84/8=6.73
Sara can complete 3/4 of a puzzle in 7/8 of an hour. How much a puzzle can she complete in an
hour?
Answer:
x = 6/7 of a puzzle
Step-by-step explanation:
Number of puzzle : time taken
= 3/4 : 7/8
How much a puzzle can she complete in an hour?
Let
x = number of puzzle to complete
Number of puzzle : time taken
= x : 1
Equate both ratios to solve for x
3/4 : 7/8 = x : 1
3/4 ÷ 7/8 = x / 1
3/4 × 8/7 = x / 1
24/28 = x / 1
Cross product
24 * 1 = 28 * x
24 = 28x
x = 24/28
= 6/7
x = 6/7 of a puzzle
Simplify the expression (22+19b) +7
Answer:
there is no multiplication, so just 29+ 19b
Answer: i solved it for you, but all you have to do is add this 19b + 29
Step-by-step explanation:
I really hope this helps!! Have an amazing day!! :)
Can someone help me pls
Answer:
D
Step-by-step explanation:
Answer:
That’s prolly D
Step-by-step explanation:
Other stuff don’t make sense
Tyler is riding his bike from his house to the store, which is 4 MI away. Tyler gets to the store it 18 minutes after he leaves his house.Find Tyler speed in miles per minute. Use dimensional Analysis to check the reasonableness of your answer
Answer:
0.22 miles/minute
Step-by-step explanation:
Tyler is riding his bike from his house to the store, which is 4 MI away. Tyler gets to the store it 18 minutes after he leaves his house.Find Tyler speed in miles per minute.
The formula for speed is given as:
Distance/Time
Hence:
Tyler's distance = 4 miles
Time = 18 minutes
Speed(Miles/ minute) = 4 miles/18 minutes
= 0.2222222222 miles per minutes
= 0.22 miles/minute
Evan is going to invest in an account paying an interest rate of 5.4% compounded continuously. How much would Evan need to invest, to the nearest dollar, for the value of the account to reach $1,360 in 12 years?
answer: 711
711.403641819=P
On solving the provided question, we can say that - the value of the simple interest will be $ 881.28.
What is interest ?Multiplying the principal by the interest rate, time, and other factors yields simple interest. Simple return equals principle times interest times hours is the marketed formula. It is easiest to compute interest using this formula. A percentage of the principle balance is how interest is most commonly computed. The interest rate on the loan is known as this percentage.
here,
we have
P = 1360;
R = 5.4 ;
T = 12
so, we get,
SI = 1360 X 5.4 X 12 /100
SI =88128/100
= 881.28
Hence, On solving the provided question, we can say that - the value of the simple interest will be $ 881.28.
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4a⁴b(2b³)‐²
------------------
6a³
Answer:
A
Step-by-step explanation:
i cant figure out how to do this question plz help!
Answer:
[tex] slope (m) = \frac{1 - (-5)}{2 - (-1)} [/tex]
[tex] = \frac{1 + 5}{2 + 1} [/tex]
[tex] = \frac{6}{3} = 2 [/tex]
Step-by-step explanation:
Find the slope (m) using the two points given, (-1, -5) and (2, 1):
[tex] slope (m) = \frac{rise}{run} = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Let,
[tex] (-1, -5) = (x_1, y_1) [/tex]
[tex] (2, 1) = (x_2, y_2) [/tex]
Plug in the values into the equation:
[tex] slope (m) = \frac{1 - (-5)}{2 - (-1)} [/tex]
[tex] = \frac{1 + 5}{2 + 1} [/tex]
[tex] = \frac{6}{3} = 2 [/tex]
PLEASE OF YOU CAN SHOW THE WORK:
The accompanying diagram shows a flagpole that stands on level ground. Two cables, r and s, are attached to a pole at a point 20 feet above the ground. The combine length of the two cables is 70 feet. If cable r is attached to the ground 8 feet from the base of the pole, what is the measure of the angle, x, to the nearest degree, that cable s makes with the ground? N = 20 ft S 8 t
Answer:
[tex]x\approx24^\circ[/tex]
Step-by-step explanation:
We know that r and s have a combined length of 70. Therefore:
[tex]r+s=70[/tex]
Notice that we can determine r by using the Pythagorean Theorem. In this case, r is the hypotenuse, and 20 and 8 are the legs. Therefore:
[tex]a^2+b^2=c^2[/tex]
Substituting 20 and 8 for a and b and r for c yields:
[tex]20^2+8^2=r^2[/tex]
Compute:
[tex]464=r^2[/tex]
Therefore:
[tex]r=\sqrt{464}=\sqrt{16\cdot 29}=4\sqrt{29}[/tex]
Now, we can determine s. We know that:
[tex]s+r=70[/tex]
So, by substitution:
[tex]s+4\sqrt{29}=70[/tex]
Therefore:
[tex]s=70-4\sqrt{29}[/tex]
Now, notice that, with respect to x, 20 is the opposite side and s is the hypotenuse.
Therefore, we can use the sine ratio. The sine ratio is the ratio between a right triangles opposite side to its hypotenuse.
In this case, the opposite to x is 20, and the hypotenuse is s, or 70-4√29. Therefore:
[tex]\displaystyle \sin(x^\circ)=\frac{20}{s}[/tex]
By substitution:
[tex]\displaystyle \sin(x^\circ)=\frac{20}{70-4\sqrt{29}}[/tex]
Take the inverse sine of both sides:
[tex]\displaystyle x^\circ=\sin^{-1}\Big(\frac{20}{70-4 \sqrt{29}} \Big)[/tex]
Use a calculator. Therefore:
[tex]x\approx24.37^\circ\approx24^\circ[/tex]
what 3x(a-12)=???????
3ax-36x is the correct answer.
Hope it helps!
12. Your family attends a comic convention. Each autograph costs
$20 and each photograph costs $50. Your family buys a total of
5 autographs and photographs for $160. How many photographs
does your family buy?
Answer:
2 photographs
Step-by-step explanation:
Mark as Brainliest.
Because I am Indian and solving your question from India.
Your family buys two photographs at a comic convention.
What is the equation?The equations are defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let x be the number of autographs and y be the number of photographs. We know that:
x + y = 5 (the total number of autographs and photographs)
20x + 50y = 160 (the total cost of the autographs and photographs)
We are looking for the number of photographs (y) that your family buys.
We can use the first equation to solve for x in terms of y:
x = 5 - y
Then we can substitute this expression for x into the second equation:
20(5 - y) + 50y = 160
100 - 20y + 50y = 160
50y = 60
y = 12/5
y = 2.4
Since the number of photographs has to be a whole number, we can see that your family buys 2 photographs.
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Can you help me out with both of these pls
How many 3-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if repetition of digits is allowed?
I WILL MARK BRAINLIEST
w=2, p=3 ........ 5p-2w
Answer:
11
Step-by-step explanation:
5 times 3 {subracted by} 2 times 2
15 - 4 = 11
Ms. Mosher recorded the math test scores of six
students in the table below.
Student
Student
Score
72
Andrew
John
80
85
George
Amber
93
78
Betty
Roberto
80
Determine the mean of the student scores, to the
nearest tenth. Determine the median of the student
scores. Describe the effect on the mean and the
median if Ms. Mosher adds 5 bonus points to each
of the six students' scores.
¿Con qué número se debe empezar a enseñar?
Answer:
numero 0
Step-by-step explanation:
Porque es cero
Answer:
With what number to start teaching?
Step-by-step explanation:
I like 3, 5, and 7
HURRY PLS
Which graph represents the solution set for the compound inequality below?
-x+ 10 27
x-10 2 7
+
789 10 11 12 13 4 s 6
789 10 11 12 13 14 15 16 17
0
6 8 10 12 14 16 18 20
0 24 68 10 12 14 16 18 20
Answer:
hi
Step-by-step explanation:
i think it is C and sure