9514 1404 393
Answer:
(b) 1 foot = 3/8 inch
Step-by-step explanation:
The given ratio is ...
actual : scale = 4" : 1/8"
You know that 1 foot = 12 in = 3×4 in, so you can multiply the above ratio by 3 to see what it is for 1 foot.
actual : scale = 3×4" : 3×1/8"
= 12" : 3/8"
= 1 foot : 3/8 in
______
Alternate approach
Essentially, we're saying that the ratios between actual measures and those on a scaled drawing or model form a proportion.
scale / actual = (1/8")/(4 in) = ??/(12 in)
Multiplying by 12 in, we get ...
?? = (12 in)(1/8")/(4 in) = 3×1/8"
?? = 3/8"
__
More detail
Notice that this only works when the units in the ratio (12 in)/(4 in) cancel to give a pure number 12/4 = 3.
If we had put 1 foot in the proportion, then we would end up with ?? being expressed in feet, not inches:
(1/8")/(4") = ??/(1 ft)
?? = (1 ft)(1/8")/(4") = (1 ft)(1/32) = 1/32 ft
Then, to find the answer to the question, we would have to find out how many inches is 1/32 ft.
1/32 ft = (1/32)(12 in) = 12/32 in = 3/8 in
__
End comment
For best results, the units in corresponding parts of a proportion should be the same.
16/x = 2/7 cross multiplication
Answer:
x=56
Step-by-step explanation:
16 x 7= x * 2
[tex]x=\frac{16 x7}{2}[/tex]
x=56
Hope this helps :)
A 29-meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at 7 meters per minute. At a certain instant, the bottom of the ladder is 21 meters from the wall.
Complete question
A 29-meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at 7 meters per minute. At a certain instant, the bottom of the ladder is 21 meters from the wall.
What is the rate of change of the distance between the bottom of the ladder and the wall at that instant(in meters per minute)
Answer:
[tex]\frac{dx}{dt}=11.94m/min[/tex]
Step-by-step explanation:
From the question we are told that
Slant height [tex]z=29m[/tex]
Change in Vertical height [tex]\triangle y=7m/s[/tex]
Horizontal length [tex]x=21[/tex]
Generally in finding the distance form the top to the bottom of the wall it is mathematically given by
[tex]x^2+y^2=z^2[/tex]
[tex]21^2+y^2=29^2[/tex]
[tex]y^2=29^2+21^2[/tex]
[tex]y=35.81[/tex]
Generally solving for the differential equation is mathematically represented as
[tex]x^2+y^2=29^2[/tex]
[tex]2x*\frac{dx}{dt} +2y*\frac{dy}{dt} =0[/tex]
[tex]x*\frac{dx}{dt} +y*\frac{dy}{dt} =0[/tex]
[tex](21)*\frac{dx}{dt} +(35.81)*(-7) =0[/tex]
[tex](21)*\frac{dx}{dt} -250.64 =0[/tex]
[tex]\frac{dx}{dt}=\frac{250.64}{21}[/tex]
[tex]\frac{dx}{dt}=11.94m/min[/tex]
The rate of change of the distance between the bottom of the ladder and the wall at that instant is 6.67 meter per minute.
Let us consider that distance between the top of the ladder and the ground is x meter and distance between the bottom of the ladder and the wall is y meter.
So, A right angle triangle is formed.
Since, the bottom of the ladder is 21 meters from the wall.
So, [tex]y=21[/tex]
Applying Pythagoras theorem,
[tex]x^{2} +y^{2}=(29)^{2} \\\\x^{2} +(21)^{2}=(29)^{2} \\\\\\x^{2} =841-441=400\\\\x=\sqrt{400} =20[/tex]
Given that, the distance between the top of the ladder and the ground is decreasing at 7 meters per minute.
[tex]\frac{dx}{dt}=-7meter/min[/tex]
Differentiate below equation with respect to time.
[tex]x^{2} +y^{2}=(29)^{2} \\\\2x\frac{dx}{dt}+2y\frac{dy}{dt}=0 \\\\2(20)(-7)+2(21)\frac{dy}{dt}=0\\\\\frac{dy}{dt}=\frac{280}{42}=6.67meter/min.[/tex]
Thus, the rate of change of the distance between the bottom of the ladder and the wall at that instant is 6.67 meter per minute.
Learn more about Differentiation here:
https://brainly.com/question/14023950
Simplified to create an equivalent expression
(2+2w)•4+9(w+3)=
Answer:
17 w + 35
Step-by-step explanation:
You get this answer by using PEMDAS.
Help please!!!!!!!!!
Answer:
440 square inches
Step-by-step explanation:
5 x 8 x 11 = 440
Example:
Brigette is putting a border around a scrapbook cover.
The cover is 12 inches tall and 14.5 inches wide. How
much border does Brigette need?
Answer:
53
Step-by-step explanation:
You need the perimeter, which is all sides added together
Answer:
53
Step-by-step explanation:
Perimeter= w+w+h+h
w=width
h=height
w=14.5
h=12
12+12=24
14.5+14.5=29
29+24=53
Help please :( !
Compare . Who picked fruit at a faster pace ?
Answer:
Shawn.
Step-by-step explanation:
We can solve for apples per hour and pears per hour. For Shawn, to get the apples per hour, we do 4/2 which is 2 bushels of apples per hour. For pears, we do 5/2 which is 2.5 bushels of pears per hour.
When Carla is picking, we can do:4/3 which is 1 and 1/3, which is her apple bushel picking per hour. For her pears, she picks them at 2 bushels of pears per hour.
Since Shawn picks her apples quicker per hour, and her pears quicker per hour, Shawn picks at a faster fruit pace.
which of the following is geometric sequence?
Answer:
Choice C
Step-by-step explanation:
A geometric sequence is usually one that multiply or divide to get to the next number in the sequence. So let's go through them to see which one gets multiplied since all of the choices are increasing.
Choice A:
[tex]1^{+3},4^{+1},5^{+4},9^{+5},14[/tex]
Nope that's not what we're looking for.
Choice B:
[tex]3^{+3},6^{+3},9^{+3},12^{+3},15[/tex]
This would be a perfect arithmetic sequence but not the type of sequence we are looking for.
Choice C:
[tex]6^{*3},18^{*3},54^{*3},162[/tex]
Yes! See how this one is multiplying by 3 and not adding or subtracting.
Choice D:
[tex]3^{+2},5^{+3},8^{+5},13^{+7},21[/tex]
Nope this is not it either.
The price of a ski pass decreased by $3 per month over a 6-month period. What is the
total change during this period for the price of the pass?
Answer:
18 (a)
Step-by-step explanation:
but I hope it works
5m+3m
simplify expression
Answer:
=8m
Step-by-step explanation:
=5m+3m
=m+m+m+m+m+m+m+m
=8m
Answer:
8m
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
5m + 3m
Step 2: Simplify
Combine like terms: 8mCan someone solve the joke please?
Why did the new boy steal a chair from the classroom?
Answer:
Because the teacher told him to take a seat.
Answer:
Lol. Because the teacher told him to take a seat.
find each missing measure find GF and m
i think its 50 im not completley for sure though
categorize the graph as linear increasing linearly decreasing exponential growth or exponential...
Answer:
Choice C
Step-by-step explanation:
The line is a linear line because it's straight exponential lines are more like an arch.
Next the line is increasing because it's going up not down if it was down it would be decreasing.
C) Linear increasing is the category of the graph.
The line is a linear line because its straight exponential lines are more like an arch. Next, the line is increasing because it's going up not down if it was down it would be decreasing.
What is a linear increase in a graph?If a linear graph is growing then its gradient is superb, for the reason that while x will increase by using 1, y adjustments through an advantageous quantity. If a linear graph is lowering, the gradient is a terrible range.
The key difference between linear and exponential increases is the slope of the curves (this is, the rate of an exchange over the years). A linear boom function has an advantageous constant slope, while an exponential increase feature has a high-quality slope that is continually growing.
Despite the fact that you're probably really familiar with growth, any increase that reasons the output Y to be larger than the enter X is known as a non-linear boom. In standard, the outputs of human interest grow in a non-linear style.
Learn more about Linear increasing here: https://brainly.com/question/4025726
#SPJ2
Find the slope and the y intercept please help what do I do
Answer:
Slope: -7
y-intercept: (0,12)
Answer:
here give my friend the brainliest ^^;
Step-by-step explanation:
Can someone please help me with these quadratic formula word problems. I'll give the best answer the brainiest and 25 points.
Answer:
6.C10.BMARK ME AS BRAINLY#Carry On LearningA pool has a circumference of about 150.82 meters. Find the radius.
Answer:
96.0 or 96.01499407
Step-by-step explanation:
r = C / (pi x 2)
Use a quadratic equation to find two real numbers with a sum of -43 and a product of 306.
Answer:
Real numbers = 39 and 9
Step-by-step explanation:
The standard form of a quadratic equation is ax² + bx + c = 0
Given the following data;
a = 1
b = -43
c = 306
Quadratic equation formula is;
[tex] x = \frac {-b \; \pm \sqrt {b^{2} - 4ac}}{2a} [/tex]
Substituting into the equation, we have;
[tex] x = \frac {-(-43) \; \pm \sqrt {43^{2} - 4*1*306}}{2*1} [/tex]
[tex] x = \frac {43 \pm \sqrt {1849 - 1224}}{2} [/tex]
[tex] x = \frac {43 \pm \sqrt {625}}{2} [/tex]
[tex] x = \frac {43 \pm 25}{2} [/tex]
[tex] x_{1} = \frac {43 + 25}{2} [/tex]
[tex] x_{1} = \frac {68}{2} [/tex]
[tex] x_{1} = 39 [/tex]
[tex] x_{2} = \frac {43 - 25}{2} [/tex]
[tex] x_{2} = \frac {18}{2} [/tex]
[tex] x_{2} = 9 [/tex]
Therefore, the two real numbers are 39 and 9.
The quadratic equation now becomes;
x² - 43x + 306 = (x - 39)(x - 9) = 0
A company that makes hair care products at 9000 people try a new shampoo. Of the 9000 people, 18 had a mid allergic reaction. What percent of the people had a mid allergic reaction
Answer:
0.2% of the people had mid allergic reaction.
Step-by-step explanation:
Given that:
Number of people tested for a new shampoo = 9000
Number of people who had allergic reaction = 18
Percent of people = [tex]\frac{People\ who\ have\ reaction}{Total\ number}*100[/tex]
Percent of people = [tex]\frac{18}{9000}*100[/tex]
Percent of people = 0.002 * 100
Percent of people = 0.2%
Hence,
0.2% of the people had mid allergic reaction.
solve the inequality 9-12>-13
A. q>1
B. q>-1
C. q>25
D. q>-25
Answer:
C
Step-by-step explanation:
Please help me I need the answer now!!
Answer:
an ordered pair
the point where all the lines intersect (which is located by the ordered pair above)
No solutions (in case for example you have parallel lines, so no point there they intersect)
Infinitely Many Solutions (this is when for example you have one single equation, each point of the line is a solution and there are infinite points)
Step-by-step explanation:
basically a "system" means finding a solution that is valid for each equation, like a logical AND
so in this case it means finding a point that lies on each line, and that point can only exists (the intersection of those lines) or not exist (they are parallel)
if the system is made of one single linear equation then you have infinite solutions
4g2 (-g)3 = -4g5
True
False
Answer:
true for sure it \s pretty easy to do but hard to explain
Answer:
the answer is false I think
What is x/ 2 - 8 > 22!
Answer:
x>60
Step-by-step explanation:
when solving for X that is
Answer:
x>60
Step-by-step explanation:
x/2-8>22
+8 +8
-------------------
x/2>30
x>60
Aimee noticed her plant grew Two-thirds of an inch every week since it sprouted. She created this graph to show its growth.
On a coordinate plane, a graph titled Plant Growth has Weeks Since Sprouting on the x-axis and Height (inches) on the y-axis. Points (3, 2) and (6, 4) are plotted.
Which statement about Aimee’s graph is true?
Aimee’s graph is correct because the ratio Two-thirds is to 1 is equal to 2:3, which her graph shows in each point.
Aimee’s graph is incorrect because the ratio Two-thirds is to 1 is equal to 3:2, so she should have switched her points.
Aimee’s graph is correct because it shows 3 inches of plant growth every two weeks.
Aimee’s graph is incorrect because it shows 2 inches of plant growth with each point instead of Two-thirds of an inch.
Answer:
It's C
Step-by-step explanation:
I got a 100% on edge, have a delightful day Chicos y chicas!
Answer: A
Step-by-step explanation:
PLEASE HELP ASAP I need major help, please. Helps me will get 44 points please I am willing to give this many away because I really need this help please don't just put something random for points.
You are a high school senior with a part-time job at a retail store. Your employer pays you $9.75 per hour. Last week, you worked a total of 30 hours.
The following payroll deductions were taken from your gross pay:
Federal income tax (withholding) at 10%
Social Security tax at 6.2%
Medicare tax at 1.45%
Use the check stub below to help you think through the problem.
check stub
The amount for GROSS EARNINGS for this pay period was $
Hey there!
The answer to your question is $240.87
First we need to find how much he earned:
9.75 x 30
292.50
Now, we find the amount of all the deductions:
292.50(0.1 + 0.062 + 0.0145)
51.63
Now, we take this off the total pay:
292.50 - 51.63
240.87
The amount of pay after deductions was 240.87
Hope it helps and have an amazing day!
Answer:
$243.34425 round it up to the nearest 100th place
Step-by-step explanation:
9.75*30
=$295.5
=$295.5*10/100
for Federal income tax is $29.55
$295.5*6.2/100
Social Security tax $18.321 round it up $18/32
$295.5*1.45/100
Medicare tax is $4.28475 round it up to the nearest 100ths place $4.28
add all of them
$29.55+$18.321+4.28475= $52.15575 round it up = $52.16
sutract the amount you got paid
$295.5-$52.16=$243.34425
or you could have done
add all the %
10+6.2+1.45=17.65*295.5/100
=52.15575
hope it helped
The soil in Sean's backyard is made up of 45% sand. If he has 1000 lbs of soil in his yard, how many pounds of sand are there?
Answer: 450 lbs
Step-by-step explanation:
45/100 is 45%
Since there are 1000 lbs we multiply 45/100 by 10, giving us 450/1000
Therefore 45% of 1,000 is 450
450 pounds of sand is present in the soil.
What is percentage?
'A percentage is a number or ratio expressed as a fraction of 100. A percentage is a dimensionless number, that is, it has no unit of measurement.'
Total weight of soil in Sean's backyard = 1000 pounds
Percentage of sand in the soil = [tex]\frac{45}{100}[/tex]
Total amount of sand in the soil = ( [tex]\frac{45}{100}[/tex] × 1000 ) lbs
= 450 lbs
Hence, we can conclude, 450 pounds of sand is present in the soil in Sean's backyard.
Learn more about percentage here: https://brainly.com/question/92258
#SPJ2
HELP ASAP
1.Which number or symbol is a variable in the following algebraic expression?
5 + 4y x 32
a 5
b 4
c y
d 2
2.Convert the following word phrase to an algebraic expression:
9 less than a number.
a x - 9
b 9 -x
c 9 ÷ x
d x ÷ 9
Answer: 1.C 2.B
Step-by-step explanation:
answer for brainlist due in 30 mins
Answer: y=-4x+9
Step-by-step explanation:
m= -4
b=9
Answer:
the slope is 4
y-intercept is -2
and the equation is
y=4x -2
I need this ASAP please!
8x^3 − 125y^3/(2x + 5y)3 ÷ 4x^2 + 10xy + 25y^2/4x^2 + 20xy + 25y^2
To divide by a fraction, multiply by its reciprocal.
8x^3 − 125y^3/(2x + 5y)^3 ⋅ 4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y^2
Simplify the numerator.
Rewrite 8x^3 as (2x)^3.
(2x)^3 − 125y^3/(2x + 5y)^3 ⋅ 4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y^2
Rewrite 125y^3 as (5y)^3.
(2x)^3 − (5y)^3/(2x + 5y)^3 ⋅ 4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y^2
Since both terms are perfect cubes, factor using the difference of cubes formula,
a^3 − b^3 = (a − b) (a^2 + ab + b^2) where a = 2x and b = 5y.
(2x − (5y)) ((2x)^2 + 2x (5y) + (5y)^2)/(2x + 5y)^3 ⋅ 4x + 20xy + 25y^2/ 4x^2 + 10xy + 25y^2
Multiply 5 by −1.
(2x − 5y) ((2x)^2 + 2x (5y) + (5y)^2)/(2x + 5y)^3 ⋅ 4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y^2
Apply the product rule to 2x.
(2x − 5y) (22x^2 + 2x (5y) + (5y)^2)/(2x + 5y)3 ⋅ 4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y2
Raise 2 to the power of 2.
(2x − 5y) (4x^2 + 2x (5y) + (5y)^2)/(2x + 5y)^3 ⋅ 4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y^2
Rewrite using the commutative property of multiplication.
(2x − 5y) (4x^2 + 2 ⋅ 5xy + (5y)^2)/(2x + 5y)^3 ⋅ 4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y^2
Multiply 2 by 5.
(2x − 5y) (4x^2 + 10xy + (5y)^2)/(2x + 5y)^3 ⋅ 4x^2 + 20xy + 25y^2/ 4x^2 + 10xy + 25y^2
Apply the product rule to 5y.
(2x − 5y) (4x^2 + 10xy + 52y^2)/(2x + 5y)^3 ⋅ 4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y^2
Raise 5 to the power of 2.
(2x − 5y) (4x^2 + 10xy + 25y^2)/(2x + 5y)^3 ⋅ 4x^2 + 20xy + 25y^2/4x^2 + 10xy + 25y^2
Cancel the common factor of 4x^2 + 10xy + 25y^2.
((2x − 5y)/(2x + 5y)^3) (4x^2 + 20xy + 25y^2)
Multiply
(2x − 5y) (4x^2 + 20xy + 25y^2)/ (2x + 5y)^3
Factor using the perfect square rule.
Rewrite 4x^2 as (2x)^2.
(2x − 5y) ((2x)^2 + 20xy + 25y^2)/ (2x + 5y)^3
Rewrite 25y^2 as (5y)^2.
(2x − 5y) ((2x)^2 + 20xy + (5y)^2)/ (2x + 5y)^3
Check that the middle term is two times the product of the numbers being squared in the first
term and third term.
20xy = 2 ⋅ (2x) ⋅ (5y)
Rewrite the polynomial.
(2x − 5y) ((2x)2 + 2 ⋅ (2x) ⋅ (5y) + (5y)2)/(2x + 5y)^3
Factor using the perfect square trinomial rule a^2 + 2ab + b^2 = (a + b)^2, where a = 2x and b = 5y.
(2x − 5y) (2x + 5y)^2/ (2x + 5y)^3
Cancel the common factor of (2x + 5y)^2 and (2x + 5y)^3.
Factor (2x + 5y)^2 out of (2x − 5y) (2x + 5y)^2.
(2x + 5y)^2 (2x − 5y) / (2x + 5y)^3
Cancel the common factors.
2x − 5y / 2x + 5y
Answer:
This may be wrong but: (2x - 5y) ((2x)^2 + 10xy + (5y)^2) over (2x + 5y) (4x^2 + 10xy + 25y^2)
Step-by-step explanation:
Write the slope in slop intercept form of the line that has a slope of m=2 and goes through thr point. (-3,-5)
answers:
A. y=2x+5
B: y=2x+1
C: =y=2x-1
D: y=3x-2
Answer:
B. y = 2x + 1
Step-by-step explanation:
Substitute the information into the point-slope form equation.
y - y₁ = m(x - x₁)
y - (-5) = 2(x - (-3)
y + 5 = 2(x + 3)
y + 5 = 2x + 6
y = 2x + 1
Answer:
c!
Step-by-step explanation:
PLEASE answer as soon as you can! First correct answer will get BRAINLIEST!!! :)
Answer:
(x-3)(x-5)
Step-by-step explanation:
Answer:
x = 3 or x= 5
Step-by-step explanation:
Δ = (-8)² - 4×15
= 64- 60
=4
and 4≥0
so x = (8 - √4 )÷2 = 3
or x= (8 + √4 )÷2 = 5
so P(x) = (x-3) (x-5)
A bag contains 49 coins consisting of quarters and dimes. There are 2.5 times as many quarters as there are dimes in the bag. Write a system of equations that models this situation. How many dimes are in the bag?
pls write step by step so that I can understand :)
Answer:
Dimes = 35
Quarters = 14
Step-by-step explanation:
Let
quarters = q
Dimes = d
Total coins = 49
There are 2.5 times as many quarters as there are dimes in the bag
Dimes = 2.5q
Quarters + Dimes = Total
q + 2.5q = 49
3.5q = 49
q = 49/3.5
q = 14
d = 2.5q
= 2.5 * 14
= 35
d = 35
Therefore,
Dimes = 35
Quarters = 14
Answer:
The system of equations that models this equation area:
d + q = 49
q = 2.5d