Given :
A mountain climber started his climb at 50 feet above see level .
He then raised 3 feet to rest in his cot to make his final 10 feet climb down.
To Find :
An expression to find his position relative to his final position.
Solution :
Let , final position is h .
h is given by :
[tex]h=\text{(Initial position)-(initial descended)+(height raised to rest)-(final descended)}\\\\h=50 -28 +3-10\ feet\\\\h=15\ feet[/tex]
So , his final position is 15 feet .
Hence , this is the required solution .
if a=120 degrees find the measures of b,c, and d
Answer:
<b=120°,<c=60° & <d=60°
Step-by-step explanation:
Here,
given that <a=120°
<a is vertically opposite to <b
We know,vertically oppposite angles are equal
So,<a=<b=120°
<a & <c lies on a straight angle.
So,<c=180°-120° (Sum of two angles on a straight angle is 180°)
<c=60°
Again,<c is vertically opposite to <d.
So,<d=60°.
If this trapezoid is moved through the
translation (x+3, y-2), what will the
coordinates of D' be?
After a translation (x+3, y-2) the coordinates of D' be (4, 0).
What is a trapezoid?An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.
A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.
The altitude is the measurement of the angle perpendicular to the parallel sides.
The area of a trapezoid is (1/2)×(sum of the two parallel sides)×height.
From the given figure of this trapezoid in a coordinate plane, the points of D is (1, 2).
Now, If this trapezoid is moved through the translation (x + 3, y - 2) the coordinates of D' will be (1 + 3, 2 - 0) ⇒ (4, 0).
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Find the area of a circle with a radius of 7 meters.
Step-by-step explanation:
Area of a circle = πr^2 = π(7)^2 = 49πm^2.
Answer:
153.94 meters
Step-by-step explanation:
A= [tex]\\\pi[/tex][tex]r^2[/tex]
[tex]A=\pi \\[/tex][tex]7^2\\[/tex]
[tex]7^2 = 49[/tex]
[tex]\pi[/tex] x [tex]49 = 153.94[/tex]
Find the missing angles with reasons. plz quick it is due today
Answer:
d = 64, e = 64, g = 55, f = 55
Step-by-step explanation:
Answer:
[tex] \boxed{ \bold{ \sf{see \:below}}}[/tex]
Step-by-step explanation:
d = 64° ( Being vertically opposite angles )
e = 64 ° ( Being alternate angles )
2. g + 125 ° = 180 ° ( sum of supplementary angle)
Move 125 to right hand side and change it's sign
g = 180° - 125°
Subtract 125 ° from 180 °
g = 55 °
f = g ( being alternate angles )
f = 55 °
Hope I helped!
Best regards! :D
Convert 4,700,000,000 from standard form to scientific notation. 470 × 107 47 × 108 4.7 × 109 478
Answer:
4.7 * 10 ^9
Step-by-step explanation:
4,700,000,000
Scientific notation is of the form
a * 10 ^b where a is a number between 1 and less than 10
Move the decimal so that it is a number between 1 and less than 10
4,700,000,000 becomes 4.700000000 and we moved the decimal 9 places to the left b is +9 ( positive because we moved to the left) We can drop the extraneous zeros
4.7 * 10 ^9
Diego needs to put down sod on a yard that measures 30 feet by 45 feet. Company A says it can do the job for $3.90 per roll of sod, where one roll of sod is a rectangle with dimensions of 2 feet by 5 feet Company B says it can do the job for $150.00 per pallet that covers 450 square feet plus a $45 one-time dellvery charge. Which company is a better deal ? How much will Diego save?
Answer:
Company B is the better deal. Diego will save $31.5.
Step-by-step explanation:
First, find the area of the rectangle: 45*30=1350 sq.ft.
Next, find out how much it will cost for Company A: $3.9 for 2 x 5 ft (10 sq.ft)
Divide 1350 by 10 to see how many of their sod rolls will fit into his yard=135.
Multiply $3.9 by 135=526.5$
Do the same with Company B: $150 for 450 sq.ft plus $45 delivery.
Dived 1350 by 450 to see how many rolls= 3
Multiply $150 by 3= $450, then add $45= $495
Subtract Company B's $495 from Company A's $526.5= $31.5 <-how much Diego saved.
Diego will save $31.50 by choosing Company B instead of Company A.
What is Algebra?For business A:
The yard's entire square footage is calculated as,
⇒ 30 x 45
⇒ 1,350 square feet
The total area covered by each roll of sod must then be determined in square feet is calculated as,
⇒ 2 x 5
⇒ 10 square feet per roll
The total quantity of sod rolls required is calculated as,
⇒ 1,350 / 10
⇒ 135
The price of each roll of sod is $3.90, making the total price of the sod calculated as,
⇒ 135 x $3.90
⇒ $526.5
For business B:
The garden is still 1350 square feet in size overall. Pallets have a surface area of 450 square feet each, thus a total of:
⇒ 1,350 / 450
⇒ 3
The price of the sod is $150.00 per pallet, making the total price calculated as,
⇒ 3 x $150
⇒ $450
In addition, there is a $45.00 one-time shipping fee. Therefore, Company B's overall cost is calculated as,
⇒ $450.00 + $45.00
⇒ $495.00
We can see by comparing the two options that Company B is the better value because it is less expensive than Company A. Diego will save:
⇒ $526.50 - $495.00
⇒ $31.50.
Diego will save $31.50 by choosing Company B instead of Company A.
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chris is investing how long it takes his dog to react to different sounds. What is the independent variable?
if you see this I really need help on this question asap ty so much... "The flagpole in the diagram below has a height of 10ft. The shadow is 12 feet long. What is the distance from the top of the flagpole to the far end of its shadow? (round your answer to the nearest hundredths)"
Answer:
15.62 feet
Step-by-step explanation:
If the flagpole is 10ft tall and the shadow is 12ft long, and you need to find the distance from the top of the flagpole to the far end of the shadow, to get your answer, you must use the pythagorean theorum.
[tex]a^{2} + b^{2} = c^{2}[/tex]
let height of flagpole = a
let length of shadow = b
let distance between the two = c
[tex]10^{2} + 12^{2} = c^{2} \\100 + 144 = c^{2}\\244 = c^{2}\\\sqrt{244} = \sqrt{c^{2}} \\\sqrt{244} = c\\15.62 = c[/tex]
George was building a staircase for his dog to get up on his bed. The first step is made from 2 boards, the second out of 4 boards, and the third out of 6 boards. There are 8 steps in the staircase. How many boards did George use to create the last step? A 10 B 12 C 16 D 24
Answer: C
Step-by-step explanation: I am a big brain pro.
the product of a and eleven
Answer:
11a
Step-by-step explanation:
you can't find the exact answer unless we know what a is equal to
Is 7.525225222....... rational or irrational ?
Answer:
It is irrational
Step-by-step explanation:
7.525225222....... is non terminating non reoccurring
Therefore it is irrational
help please urgent!!!! 10 points
Answer:
[See Below]
Step-by-step explanation:
✦ First you need to know the area of a triangle:
✧ ½ x b x h
✦ Now write you formula out:
✧ ½ x 5 x 4
✦ Now just solve:
✧ 5 x 4 = 20
✧ 20 / ½ = 10
So it'd be 10 m²
~Hope this helps Mate. If you need anything feel free to message me.
Help me I need this fast!!
Simplify [tex]\frac{9x^2 - 3x}{6x - 45x^2}[/tex]
There are multiple ways of going about this, but what I find easiest for a problem like this is to find the GCF of all the terms.
The GCF of [tex]9x^2,-3x,6x,-45x^2[/tex] is [tex]3x[/tex].
Meaning that we can take out 3x out of all the terms and still be left with the simplest, yet equivalent for of the expression.
[tex]\frac{2x-1}{2-15x}[/tex]
the prism has a volume up to 150.find the length of the prism
Step-by-step explanation:
We have to know that in order to solve for the volume of a rectangular prism, we have to use this formula: l * w * h. This stands for length multiplied by width multiplied by height.
Step 1
Let's look at the numbers we already have. The height of the prism is 4 feet and the width is 5 feet. When we multiply them together, we got 20 feet.
Step 2
The volume of this prism adds up to 150 square feet. To find the length of this prism, we have to divide 150 by 20.
[tex]150 / 20=7.5[/tex]
Our final answer: l = 7.5 feet
We can check our answer by multiplying all the numbers together.
4 * 5* 7.5 = 150
BC has one endpoint
B(3,2) and a midpoint
T(6,-2). Find the
coordinates of the
other endpoint, C.
Thank you in advance!!
Answer:
Step-by-step explanation:
(3 + x)/2 = 6
3 + x = 12
x = 9
(2 + y)/2 = -2
2 + y = -4
y = -6
(9, -6) the other endpoint C
Kareem says that the ratio 4:1 is equivalent to the ratio 12:9 because
4 + 8 = 12 and 1 + 8 = 9. Is Kareem correct? Explain how you know.
Answer:
because the way she asked it and the way she put in in form
Kareem is incorrect the ratio of 4:1 can never be equal to the ratio of 12:9.
What is a ratio?In mathematics, ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number. The fraction is defined as the division of the whole part into an equal number of parts.
It is given that Kareem says that the ratio 4:1 is equivalent to the ratio 12:9 because 4 + 8 = 12 and 1 + 8 = 9. Calculate the ratio now.
The above statement is wrong the ratio will be calculated as:-
12 / 9 = ( 3 x 4 ) / ( 3 x 3 )
Take 3 commons from the numerator and the denominator of the ratio.
= 4 / 3
Therefore, Kareem is incorrect the ratio of 4:1 can never be equal to the ratio of 12:9.
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A real estate agent's base salary is 22,000 per year. The agent earns a 4% comission on total sales. How much must the agent sell to earn 60,000 in one year
Answer: 950,000
Step-by-step explanation:
base salary is 22,000
Target 60,000
60,000-22,000 =38,000 which is 4%
So 38,000/4 = 9,500 which is 1%
So 9,500 * 100 = 950,000 which is 100% total sale
So commission of 4% on 950,000 is 38,000
Therefore 38,000 + 22,000 = 60,000
NEED ANSWER ASAP!!! PLEASE
Answer:
8
Step-by-step explanation:
find the value of x.
x+7+9=3x-6
x+16=3x-6
10=2x
x=5
plug into the equation for ST.
x+3
5+3 = 8
Lauren answered 150 questions correctly on her multiple choice history final that had
a total of 200 problems. What percentage of questions did Lauren answer correctly
on the final exam?
14. Sixteen is the same as the quotient of a number and 12.
Answer:
16 = n/12
Step-by-step explanation:
16 = n/12
Please help ASAP this is due tomorrow
Answer:
c= hy−w /6y
Step-by-step explanation:This is what i got.
Can anybody help me? I do not understand this
Answer:
f(0) = 3x : 0
f(1) = 3x : 3
f(2) = 3x : 6
f(3) = 3x : 9
Step-by-step explanation:
NEED BOTH ANSWERED!!!
Is the relation a function?
○ True
○ False
Answer:
The first picture without the diagram is true, and the other one is false.
Step-by-step explanation:
A relation can be a function if the domain has exactly one range. IT CANT HAVE TWO Y-VALUES.
Z= pi^3h, solve for h
Answer:
Z/ pi^3 = h
Step-by-step explanation:
Z= pi^3h
Divide each side by pi ^3
Z/ pi ^3= pi^3h/pi ^3
Z/ pi^3 = h
Solve the right triangle. Side AB is 2.9, but I don't know how to find two missing angles with three sides and a 90-degree angle. Please explain your answer.
Angle A = 68 degrees
Angle B = 22 degrees
Side AB = 2.9 cm
The three values are approximate
=========================================================
Explanation:
a = BC = 2.7 and b = AC = 1.1 are the two legs of the right triangle.
Use the pythagorean theorem to find the length of the hypotenuse
a^2 + b^2 = c^2
2.7^2 + 1.1^2 = c^2
8.5 = c^2
c^2 = 8.5
c = sqrt(8.5)
c = 2.91547594742266
c = 2.9
The hypotenuse is c = AB = 2.9
--------------------
We then use trig ratios to find the two missing angles.
Let's say we ignore the hypotenuse and focus on the two legs of the triangle.
With respect to reference angle A, side BC is opposite and AC is adjacent
Use the tangent ratio to get
tan(angle) = opposite/adjacent
tan(A) = BC/AC
tan(A) = 2.7/1.1
tan(A) = 2.45454545454546
A = arctan(2.45454545454546)
A = 67.8336541779176
A = 68
Note: arctan is the same as inverse tangent or [tex]\tan^{-1}[/tex]. Make sure your calculator is in degree mode.
-------------------
Similarly,
tan(angle) = opposite/adjacent
tan(B) = AC/BC
tan(B) = 1.1/2.7
tan(B) = 0.4074074074074
B = arctan(0.4074074074074)
B = 22.166345822082
B = 22
Or you could use the value of A to get B = 90-A = 90-68 = 22. This works because A+B = 90 as we're working with a right triangle. In other words, A and B are complementary angles.
-------------------
In summary we found
A = 68
B = 22
AB = 2.9
what is 2/5 + 7/8?
a - 9/40
b - 9/13
c - 50/40
d - 51/40
Answer:
51/40
Step-by-step explanation:
2/5+7/8
(2*8/5*8)+(7*5/5*8)
16/40+35/40
=>51/40
Identify the domain and range of the relation {(-5, 4, (-4, -1), (-2, 1), (0, 4), (1, 3)
Answer:
Domain: -5. -4, -2, 0, 1
Range: 4, -1, 1, 3
The noontime temperature was 29F. This was 4F lower than predicted. Write and solve an equation to determine the predicted noontime temperature. Show that your answer is reasonable
Answer:
x=33
Step-by-step explanation:
First you haft to find what x is to find the answer
x - 4 = 29
First add 4 to -4 so the cancel out and then you add 4 to 29.
x - 4 = 29
+4 +4
-----------------
x = 33
Help me with this. Am just bad with this
Answer:
0.36
or
Step-by-step explanation: