========================================================
Explanation:
Consider a square on paper that is 3 inches by 3 inches. It's area would be 3*3 = 9 square inches.
The ratio 1 to 38 means that 1 inch on paper corresponds to 38 inches in real life (assuming the "1 to 38" doesn't have any verbal units attached to it; if so, then refer to the note below). So a 3 by 3 square corresponds to a 114 by 114 square because 3*38 = 114.
The area of the second larger square is 114*114 = 12,996 square inches.
Now divide the two areas: (12,996)/(9) = 1444
It's probably not entirely obvious, but through a bit of playing around with various numbers, you should find that 38^2 = 1444. It's not a coincidence that this happens. The linear scale factor is 38 which means the area scale factor is 38^2 = 1444.
In short, the larger square in real life has area that is 1444 times that of its scaled down counterpart.
Or put another way:
large area = 1444*(small area)
------------------
Side note: This all assumes that the numbers in "1 to 38" are both the same unit. If we had a mixed ratio of units like "1 inch to 38 feet", then the answer would be different. You would need to convert from feet to inches, and then follow the steps above to get a different answer.
10 Jenny has 12 marbles.
1
of these 12 marbles are large.
4
The rest of these 12 marbles are small.
Each large marble has a weight of 70 grams.
Each small marble has a weight of 50 grams.
Work out the total weight of the 12 marbles.
Answer:
620
Step-by-step explanation:
12-1=11
11x50
1x70
add the two totals and you should get 620
Hope this helps!
In Exercises 6 and 7, find sin J, sin K, cos J, cos K, tan J and tan K. Write each answer as a fraction and as a decimal rounded to four places.
Answer: Refer to the diagram below for the answers
========================================================
Explanation:
The rules I'm using are
sin(angle) = opposite/hypotenusecos(angle) = adjacent/hypotenusetan(angle) = opposite/adjacentThe opposite side is the leg furthest from the reference angle. For example, if J is the reference angle, then leg LK is the opposite side. The adjacent side would be JL for reference angle J. The opposite and adjacent swap when you swap the reference angle.
The hypotenuse is always the longest side and always opposite the largest angle (always opposite the 90 degree angle).
------------
An example calculation would be:
sin(angle) = opposite/hypotenuse
sin(J) = LK/JL
sin(J) = 30/34
sin(J) = 0.8824
I'm referring to the triangle with sides 16,30,34. The other trig ratios are handled in pretty much the same way (use the rules mentioned above).
Which ordered pairis a solution to the system of inequalities graphed here
Answer:
B. (1,4)
Step-by-step explanation:
If you go over to the right by 1 and up by 4 the point will land inside the blue, hence it is the answer since the rest do not land inside the blue.
How do I do this trigonometry problem? or where do I even start.
Answer:
∅=6
Step-by-step explanation:
let ∅=x
[tex]\csc(3x+15)=\frac{1}{\sin(3x+15)}\\\sin(5x+3)*(\frac{1}{\sin(3x+15)})\\\frac{\sin(5x+3)}{\sin(3x+15)}=1\\\sin(5x+3)=\sin(3x+15)\\5x+3=3x+15\\2x=12\\x=6[/tex]
Sam took a flight from Malaysia to UK. He left Malaysia at 12 pm local time. The flight time was 12 hours. If Malaysia is 7 hours ahead of UK, what was the local time in UK when he arrived?
Given:
Sam left Malaysia at 12 pm local time.
The flight time was 12 hours.
Malaysia is 7 hours ahead of UK.
To find:
The local time in UK when he arrived.
Solution:
It is given that Sam left Malaysia at 12 pm local time and the flight time was 12 hours.
12 hours after 12 pm is 12 am. It means local time in Malaysia when he reached UK is 12 am.
Malaysia is 7 hours ahead of UK. So, we need to subtract 7 hours from 12 am to get the local time in UK when he arrived.
12 am is midnight. So, 7 hours before 12 am is 5 pm.
12 am - 7 hours = 5 pm
Therefore, the local time in UK when he arrived is 5 pm.
Which of the following is the equation of the line with a slope 3 and y-intercept of 4?
A.3x+y+4=0
B.3x-y-4=0
C.3x-y+4=0
D.3x+y-4=0
Answer:
B.
Step-by-step explanation:
-y = -3x + 4
y = 3x - 4
slope 3 y-intercept 4
Help me please and no links
Answer:
x = -2
x=-12
Step-by-step explanation:
5 | x+7| +14 = 39
Subtract 14 from each side
5 | x+7| +14-14 = 39-14
5 | x+7| = 25
Divide each side by 5
5 | x+7| /5 = 25/5
| x+7| = 5
Make two equations, one positive and one negative
x+7 =5 x+7 = -5
Subtract 7 from each side
x+7-7 = 5-7 x+7-7 = -5-7
x = -2 x=-12
help, with this math question please :)
answer choices are shown in the photo
Answer:
A. 3 * 10^4
Step-by-step explanation:
9 * 10^7
3 * 10^3
9 is 3 times 3, so there is 3
10^7 is 10^4 times 10^3, so there is 10^4
So it is 3 * 10^4
{x+y=-4
{y=2x-1
Help please. Thanks in advance.
The value of a Van Gogh painting increases by 7.3% each year. If it was valued at $94,000 in 1952, what will be its estimated worth in 2020?
Answer:
$11,321,630
Step-by-step explanation:
We solve using Exponential growth formula
A(t) = Ao (1 + r)^t
Ao = Initial worth = $94,000
r = Growth rate = 7.3% = 0.073
t = Time in years = 2020 - 1952
= 68 years
A(t) = Current worth in 2020 = After 68 years
A(t) = 94000 × ( 1 + 0.073)^68
A(t) = 94000 × 120.44286946
A(t) = 11,321,629.729
Therefore, the estimated worth of the Van Gogh painting in 2020 approximately = $11,321,630
Use the following function rule to find f(8). f(x) = (-4 + x)2
f(8) =
Answer:
16
Step-by-step explanation:
f(x) = (-4 + x)^2
Let x=8
f(8) = (-4 + 8)^2
Parentheses first
= 4^2
Then powers
= 16
Peter flips a standard coin twice What is the probability that the coin lands on tails both times?
А. 1/4
B. 2
C. 1
D. 1/2
PLEASE ANSWER FASTTT
answer:
the answer is going to be ½
Solve the equation by quadratic formula. Round to the nearest Tenth, if necessary
x^2 - 49 = 0
Answer:
[tex]x = 7 \: or \: x = - 7.[/tex]
Step-by-step explanation:
[tex] {x}^{2} - 49 = 0[/tex]
Then
[tex] {x}^{2} = 49 [/tex]
So
[tex]x = 7 \: or \: x = - 7.[/tex]
Answer:
x = -7 , 7
Step-by-step explanation:
a² - b² = (a + b)(a - b)
x² - 49 = 0
x² - 7² = 0
(x + 7)(x -7) = 0
x + 7 = 0 ; x - 7 = 0
x = -7 ; x = 7
What's the relationship between y and x
Answer:
Step-by-step explanation:
The relationship between x and y is called a linear relationship because the points so plotted all lie on a single straight line. The number 95 in the equation y=95x+32 is the slope of the line, and measures its steepness.
ILL GIVE YOU 5 STARS
Answer:
if the formela right
so this is the answer
4. At a convenience store, juice costs $3.25 and magazines cost $8.50. What is an algebraic expression for
the total income received by the convenience store for the sale of juice and magazines?
b) 3.25W + 8.57 c) 3.25j + 8.5m d) none of the above
Answer:
the answer is c
Step-by-step explanation:
juice would be 1 variable and magazines would be another. u would put each variable next the things that they represent, so j for juice would be put with 3.25 because that's how much 1 bottle costs. The variable m would be with 8.5 because that's how much the magazines cost.
Find the interest rate if $6600 has
a final value of $8847 in 4 years.
Give your answer to 1 d.p.
Answer:
Interest = $ 2247.00
Step-by-step explanation:
principal=$6600
Amount=$8847
time=4 years
Interest=Amount - principal
=$8847 - $ 6600
=$2247 =
=$2247.00
A pole that is 3.4 m tall casts a shadow that is 1.61 m long. At the same time, a nearby building casts a shadow that is 36.75 m long. How tall is the building?
Round your answer to the nearest meter.
Answer:
Step-by-step explanation:
Set this up as a proportion with pole/building height on the top and shadow length on the bottom, using x for the unknown, which is the height of the building:
[tex]\frac{pole/building}{shadow}:\frac{3.4}{1.61}=\frac{x}{36.75}[/tex] and cross multiply to solve:
1.61x = 124.95 so
x = 78 m
A town has a population of 17000 and grows at 4% every year. What will be the population after 12 years. To the nearest whole number
Answer:
17000+3400 =
Step-by-step explanation:
Answer:
25,160
Step-by-step explanation:
ok if it grows 4% every year, 12 years later it will have grown 48%. so 48% of 17,000 is 8,160, so 17,000+8,160=25,160, so that is the population after 12 years.
what is the correct answer
Answer:
D. 2√2
Step-by-step explanation:
In a 45° 45° 90° triangle, the hypotenuse is the leg length multiplied by √2. So divide by √2 to find x.
x = 4/√2 = 2√2
Solve the system by graphing y=-2x + 2
y=-2x - 2
Answer:
hope it helps...
have a great day!!
ANSWER PLEASEEEE!!!!!!!!!!!
Answer:
2^-6 is the correct answer
Step-by-step explanation:
Answer:
Step-by-step explanation:
[tex]\frac{1}{64}[/tex]
=[tex]\frac{1}{2^6}[/tex]
according to the indices rule if u take denominator to the numerator the it exponent must be negative if it is positive and vice versa.So.
=[tex]2^{-6}[/tex]
how to find Rational numbers on numberline
Answer:
expand the distance between the nearest two integers on your numberline. so, you can find many rational numbers such as fractions between them.
Answer: In representation of rational numbers on the number line are discussed here. We know how to represent integers on the number line.To represent the integers on the number line, we need to draw a line and take a point O on it. Call it 0 (zero).
Set of equal distances on the right as well as on the left of O. Such a distance is known as a unit length. Let A, B, C, D, etc. be the points of division on the right of 'O' and A',B', C', D', etc. be the points of division on the left of 'O'. If we take OA = 1 unit, then clearly, the point A, B, C, D, etc. represent the integers 1, 2, 3, 4, etc. respectively and the point A', B', C', D', etc. represent the integers -1, -2, -3, -4, etc. respectively.
(23 points)I need help really fast my last question
• exponential and linear growth
•Trolls Will be reported aww lol
Please I just need this answer right
Answer:
It's Option A. the more detailed answer is in you other, exact same, question.
note that others only get half of the points you pay. the are split between two answers
Task 21 The north pole is in the middle of the ocean. A person at sea level at the north pole would be 3,949 miles from the center of Earth. The sea floor below the north pole is at an elevation of approximately -2.7 miles. The elevation of the south pole is about 1.7 miles. How far is a person standing on the south pole from a submarine at the sea floor below the north pole?
For the figure shown, find m<1.
Answer:
Step-by-step explanation:
Sum of angles of a triangle = 180
So, 56 + 58 + x = 180
114 + x = 180
x = 116
Now ∠ 1 + ∠x = 180 [ straight line angles]
∠ 1 + 66 = 180
∠1 = 180 - 66 = 114°
OR
You can use the rule : Exterior angle = sum of 2 interior opposite angles.
56 + 58 = ∠1
114 = ∠1
i need help with this!
Answer:
surface area of the square pyramid
=(10×10)+(2×10×8)
=100+160
=260 yd²
answer is first option
Please do not put any files and links. pick 1 answer. help please this is so hard for me tbh
Answer:
let's convert the 25 yards into feets -> 75 feet of wire.
now let's subtract the alrdy used 15 ½ feet from we that
we got 59 ½ feet left
now let's just take ⅓ of this, just by dividing by 3.
since this seems to be a mess in calculation, let's put in the effort to convert in into inches first.
59 ½ feet = 59½*12 inches = 714 feet
now we should be able to take ⅓ of it cleanly (since we just multiplied by 12)
⅓ of 714 is just as dividing 714 by 3
= 238
the time machine needs 238 inches of wire
this isn't just picking an answer tough, on the bottom of the exercises are the unit conversations
These are some more questions
A jewelry box has a volume of 240 in cubic in. Its height is 12 inches, its width x in inches and its length ( x + 8) inches.
Answer:
Width of the box = 2 inches
Step-by-step explanation:
Volume of a box = length × width × height
Volume of the box = 240 cubic inches
Length of the box = (x + 8) inches
Width of the box = x inches
Height of the box = 12 inches
Volume of a box = length × width × height
240 = (x + 8) * x * 12
240 = (x² + 8x) * 12
240 = 12x² + 96x
12x² + 96x - 240 = 0
x² + 8x - 20 = 0
Solve quadratic equation using factorization method
x² + 10x - 2x - 20 = 0
x(x + 10) -2(x + 10) = 0
(x + 10) (x - 2) = 0
x + 10 = 0 OR x - 2 = 0
x = -10 OR x = 2
Width of the box can not be a negative value
Therefore,
Width of the box = 2 inches