Answer:
x = 7
y = -7/2
Step-by-step explanation:
(x+6i)=(3-i)+(4-2yi)
First look at the real parts
x = 3 +4
x = 7
Then look at the imaginary part
6i= -i -2yi
6 = -1-2y
Add 1 to each side
6+1 = -2y
7 = -2y
Divide by -2
7/-2 = y
A nurse mixes 50 cc of a 60% saline solution with a 10% saline solution to produce a 20% saline solution. How much of the 10% solution should he use?
Answer:
The nurse should use 200cc of the 10% saline solution in order to produce a 20% saline solution.
Step-by-step explanation:
to the given mix we add a quantity of a lower mix to generate another.
50cc at 60% + Xcc at 10% = (50 + X)cc at 20%
50 x 60% + X x 10% = (50 + X) x 20%
30 + 0.1X = 10 + 0.2X
30 - 10 = 0.2X - 0.1X
20 = 0.1X
20/0.1 = X
X = 200
An object is moving at a speed of 4 meters per month. Express this speed in inches
per hour. Round your answer to the nearest hundredth.
*Note: you must use these exact conversion factors to get this question right.
Distance / length
Time
1 foot (ft) = 12 inches (in)
1 minute (min) = 60 seconds (sec)
1 yard (yd) = 3 feet (ft)
1 hour (hr) = 60 minutes (min)
1 mile (mi) = 5280 feet (ft)
1 day (day) = 24 hours (hr)
1 meter (m) = 100 centimeters (cm)
1 week (week) = 7 days (days)
1 kilometer (km) = 1000 meters (m)
1 month (month) = 30 days (days)
1 inch (in) = 2.54 centimeters (cm)
1 year (year) = 365 days (days)
1 foot (ft) = 0.305 meters (m)
1 mile (mi) = 1.609 kilometers (km)
Answer:
0.22inches/hourStep-by-step explanation:
Given the speed of an object to be 4metres/month, we are to express the speed in inches/hour.
First we will need to convert 4meters to inches
From the conversion factors given,
1 foot (ft) = 0.305 meters (m)
x ft = 4metres
cross multiply
x * 0.305 = 4*1
x = 4/0.305
x = 13.115ft
4 metres = 13.115ft
Then we will convert 13.115ft to inches
From the conversion factors,
1 foot (ft) = 12 inches (in)
13.115ft = y
cross multiply
y = 13.115*12
y = 157.377 inches
Hence 4 metres = 157.77inches.
For 1 month to hour
First we need to convert month to days and from the conversion factor
1 month = 30 days
Next is to convert 30days to hours
Since 1 day = 24hours
30days = z
z = 30* 24
z = 720hours
Hence 1 month = 720hours
On converting 4metres/month to inches/hour
4metres/month = 157.77inches/720hours
4metres/month = 0.219inches/hour
Hence the speed of the object in inches per hour to the nearest hundredth is 0.22inches/hour
16. Rahul cycles at a speed of 6km/hr to reach school in 20 minutes. What should his
speed be if he wants to reach school in 15 minutes?
Step-by-step explanation:
Distance to school = (6km/h)(1/3h) = 2km
2km in 15 minutes = 8km in 60 minutes.
Hence his speed should be 8km/h.
What is 2x=4????????????
Answer:
x = 2
Step-by-step explanation:
2× = 4
x = 2
2x = 4
4/2 = 2
so...
2(2) = 4
x = 2
If I fall for 18 s what would my final velocity be, if I started from rest.
Answer:
176.58 m/s
Step-by-step explanation:
assume that the acceleration due to gravity, g = 9.81 m/s²
I also assume we neglect air resistance (hence we assume no terminal velocity)
recall that one of the equations of motions can be expressed as
v = u + at, where
u = initial velocity = 0 (because it says you started from rest)
v = final velocity (we are asked to find this)
a = acceleration due to gravity = 9.81 m/s²
t = time = given as 18s
simply substitute the above into the equation.
v = 0 + (9.81)(18)
v = 176.58 m/s
When the movie is half over, popcorn sells for half price. Which expression can be used to determine the new cost for 3 orders of popcorn and 3 drinks? 3 Left-bracket one-half (3.50) + 1.35 Right-bracket One-half (3.50) + 3 (1.35) One-half left-bracket 3 (3.50) + 3 (1.35) right-bracket (3.50) (3) divided by one-half + 1.35
Answer:
3[1/2(3.50)+1.35]Step-by-step explanation:
The expression for new cost is 3(3.50/2 + 1.35)
What is equations?A mathematical statement that consists of two expressions connected by an equal sign is called an equation.
Given the cost of popcorn is half when movie is half over,
according to question
original cost of popcorn = 3.50
cost at interval = 3.50/2
cost of drink = 1.35
cost of 3 drink = 3 x 1.35
cost of 3 popcorn = 3 x 3.50/2
expression for new cost for 3 orders of popcorn and 3 drinks
3 x 3.50/2 + 3 x 1.35
= 3(3.50/2 + 1.35)
Hence the expression is 3(3.50/2 + 1.35)
Learn more about equations;
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The function f(x) is shown on the graph.
What is f(0)
Answer:
-6 only
Step-by-step explanation:
i just did the test
Solve for x.
144=12(x+7-2) Steps please
Answer:
x=7
Steps:
12=x+7-2
12= x + 7 - 2
12 = x + 5
-x = 5 - 12
-x = -7
x = 7
Convert the given amount to the given unit.
6.5 lb; ounces
6.5 lb =
ounces
Answer:
the answer is 104
Step-by-step explanation:
1= 16
6= 96
0,5=8
What is the sum of 9+10=???
Answer:
19 but if its is the joke version then 21
Step-by-step explanation:
Answer:
19
Step-by-step explanation:
8. Joe walked 5 miles north, 9 miles east, then 9 miles north, and 7 miles east. If Joe decides to
walk straight back to where he started, how far must he walk?
Answer:
tim has an after school delivery service that he provides for several small retailers in town. he uses his bicycle and charges $1.25 for a delivery made within 1 1/2 miles, $1.70 for a delivery of at least 1 1/2 miles but less than 1 3/4 miles. $2.15 for a delivery of at least 1 3/4 miles but less than 2 miles, and so on. if tim raised his rates by 10%, what would he be paid to deliver a package 3 1/8 miles?
since the rate was 45 cents i multiplied 0.45 by 1.1 and got 0.495 and then i kept adding to the cost and 1/4 to the amount of miles until i got 3 1/8 miles. my answer was 4.715 so i rounded to 4.72, is that correct?Step-by-step explanation:
What type of move takes Figure A to Figure B?*
Answer: Rotation
Step-by-step explanation:
From the figure , we can observe that both figure A and b are absolutely congruent.
To translate a figure to make congruent images , we use rigid motions (Translation, Reflection, Rotation)
It is Rotation because of we move Figure A 180 degrees clockwise about the fixed point O, we will get Figure B .
It cannot be reflection because both figures are not mirror images.
It cannot be translation because all points on Figure A is not moving , as point O remained at same position throughout this which is not possible in translation.
how many pennies fit in a 22-inch circle?
Answer :
663 Pennies can fit into a 22-inch circle
The required number of pennies fit in the circle is 13.
Area of the Circle:The formula of the area of the circle is [tex]A=\pi r^2[/tex]
As we know that the standard radius of a penny is 0.75 inch
So, the area of the one penny is,
[tex]A=\pi r^2\\A=3.14\times (0.75)^2\\A=1.77[/tex]
So, the total number of pennies fit in the 22-inch circle is,
[tex]n=\frac{22}{1.77} \\n=12.49\\n\approx 13[/tex]
Learn more about the topic of the area of the circle:
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Solve the equation below for y.
8x+4y=20
Convert 32,190 inches /year to yards
Answer:
2.4 yards a day
Step-by-step explanation:
32,190 inches = 894.167 yards
894.167 / 365 = 2.4 yds/day
The conversion of 32,190 inches /year to yards/day yields: 2.4 yards/day
To convert 32190 inches/year to yards per day;
We must first find the conversion factor of inches to yards andWe must also find the conversion factor of years to days.In essence, since 1 inch = 0.0278 yards.
Therefore, we have;
32190 inches/year = 32190 × 0.0278 yards/year.= 894.88yards/year.However, 365 days make one year;
Therefore,
894.88 yards/year = (894.88/365) yards/day.= 2.4 yards/day.
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How do I solve an absolute value question?
Answer:
absolute value is how many units it is away from 0. meaning that -6 and 6 both have an abosolute value of 6.
Step-by-step explanation:
3x−5−2(−x+9)=2 plz help
Answer:
X = 5
Step-by-step explanation:
multiply what is in the ( )
-2 ( -2)
-2 ( 9)
3x -5 +2x -18 = 2
combine like terms
5x -23 = 2
add 23 to both sides
5x = 25
divide 25 by 5
X = 5
A graph titled Population of Old Town has Time (years after 2000) on the x-axis, and number of people on the y-axis. A line goes through points (4, 7,000) and (6, 6,500).What is the slope for this scenario?
-500
-250
-1/4
200
Answer:
-250
Step-by-step explanation:
It was right on edge
Answer:
The answer is -250
Step-by-step explanation:
it was on edge and i got it right
Students are planning the backdrop for the school play. The backdrop is 15 feet wide and 10 feet high. Every 16 inches on the scale drawing represents 5 feet on the backdrop What is the area of the scale drawing?
Answer:6
Step-by-step explanation:
An average African elephant weighs about 9,072 pounds. How is this number written in scientific notation?
Answer:9.072×10³
Step-by-step explanation:
A number is said to be written in a scientific notation or standard form if it is expressed in the form a×10n where 1 is less than or equal to a and a is less than 10 and n is an integer
9072 is more than 10
So 9072÷10=907.2
Still 907.2 is more than 10
So 907.2÷10=90.72
Still 90.72 is more than 10
So 90.72÷10=9.072
9.072 is less than 10
We divided 9072 by 1000 and 1000 as a power of ten is 10³
So the answer is 9.072×10³
Answer:
9.07210
math it's so fun right? :)
2x+3y=12 complete the missing value in the solution to the equation
Answer:
(-6,8) is your answer.
Step-by-step explanation:
1. 2x + 3y = 12
2. 2x +3 * 8 = 12
3. 2x + 24 = 12
4. 2x = -12
5. x = -6
So, our final answer is (-6,8)
78.84 meters= Centimeter
Answer:
7884 Centemeters
Step-by-step explanation:
Proving the Congruent Supplements Theorem
Try
Statements Reasons
Given: 21 and 22 are supplements, 23
and 24 are supplements, and
2124
Prove. 22 23
m2 1 + m 2 = 180
m23+ m24 = 180
21 and 22 are supp.
23 and 24 are supp
21 24
m2 1 + m 2 = m 3 + m24
Statements
Reasons
3
2
Assemble the proof by dragging tiles to
the Statements and Reasons columns
Answer:
From
m∠1 = m∠4
m∠1 + m∠2 = m∠3 + m∠4
m∠2 = m∠3 [tex]{}[/tex] Identity property
∠2 ≅ ∠3 [tex]{}[/tex] [tex]{}[/tex] Equal angles are congruent
Step-by-step explanation:
Given [tex]{}[/tex] Reason
∠1 and ∠2 are supplementary [tex]{}[/tex] Given
Therefore;
m∠1 + m∠2 = 180° [tex]{}[/tex] Supplementary ∠s sum up to 180°
∠3 and ∠4 are supplementary [tex]{}[/tex] Given
Therefore;
m∠3 + m∠4 = 180° [tex]{}[/tex] Supplementary ∠s sum up to 180°
From which we have;
m∠1 + m∠2 = 180° = m∠3 + m∠4 [tex]{}[/tex] [tex]{}[/tex] Transitive property
m∠1 + m∠2 = m∠3 + m∠4
∠1 ≅ ∠4 [tex]{}[/tex] Given
m∠1 = m∠4 [tex]{}[/tex] Congruent ∠s have equal measure
Therefore;
m∠1 + m∠2 = m∠3 + m∠1 [tex]{}[/tex] [tex]{}[/tex] Transitive property
Therefore;
m∠1 + m∠2 - m∠1= m∠3 + m∠1 - m∠1 [tex]{}[/tex]Subtraction property
m∠1 - m∠1 + m∠2 = m∠3 + m∠1 - m∠1 [tex]{}[/tex]
0 + m∠2 = m∠3 + 0 [tex]{}[/tex] Inverse property
Therefore;
m∠2 = m∠3 [tex]{}[/tex] Identity property
∠2 ≅ ∠3 [tex]{}[/tex] [tex]{}[/tex] Equal angles are congruent.
Answer:
<1 and <2 are supp. givenm <1+ m<2 =180. def. of supplementary angles<1≅<4. given<3 and <4 are supp. givenm< 3 + m<4 = 180. def. of supplementary anglesm<1+m<2 = m< 3 + m<4. substitution propertym<1 = m<4. definition of ≅ anglesm<1+m<2 = m< 3 + m<1. Substitution propertym<2 = m< 3. subtraction property<2 ≅ < 3. definition of ≅ angle
Factor 6x^2+28x+16 Thank you so much for your help!
Answer:
2(3x+2)(x+4)
Step-by-step explanation:
6x^2+28x+16
first : 2 as a common factor:
2(3x²+14x+8) then factorize
2(3x+2)(x+4)
Midpoint of the segment with endpoints (-8, 5) and (3, -6)
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{( - 2.5 \: , \: - 0.5)}}}}}[/tex]
Step-by-step explanation:
Let the given points be A and B
Let A( -8 , 5 ) be ( x₁ , y₁ ) and B ( 3 , -6 ) be ( x₂, y₂ )
Finding the midpoint
[tex] \boxed{ \sf{midpoint = (\frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} )}}[/tex]
[tex] \dashrightarrow{ \sf{( \frac{ - 8 + 3}{2} , \: \frac{5 + ( - 6)}{2} )}}[/tex]
[tex] \dashrightarrow{ \sf{( \frac{ - 8 + 3}{2} \: , \: \frac{5 - 6}{2} )}}[/tex]
[tex] \dashrightarrow{ \sf{( \frac{ - 5}{2} \: , \: \frac{ - 1}{2} )}}[/tex]
[tex] \dashrightarrow{ \sf{( - 2.5 \: , \: - 0.5 \: )}}[/tex]
Hope I helped !
Best regards!
While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on his trip. After returning to the United States he converts his money back to US dollars. How much of the original 250 US dollars does Phelan now have? Round to the nearest cent. 1 European euro = 1.3687 US dollars
Answer:$ 44.70
Step-by-step explanation: 250/1.3687 = 182.655-150 =32.655 times 1.3687
Answer:
He has 45 USD left.
Step-by-step explanation:
250 USD = 212 Euros. 250 - 212 = 38. 38 euros - about 45 USD, rounded.
The greater of 2 consecutive odd integers is 8
more than 3 times the lesser. Find the integers.
Step-by-step explanation:
let the odd integers be a, a+2.
a+2=8+3a
collect like term
a-3a=8-2
-2a=6
a=-3
so the integers are -3, -1
SOMEONE HELP PLEASEEE !!!
Answer:
if im right its 13.09 miles since perimiter is just the total length of the outside lines.
Step-by-step explanation:
Find the inverse function (find f^-1)
[tex]f(x)=\frac{x-2}{3x+3}[/tex]
I have the correct answer, I just don't know how to get to it.
answer is: [tex]f^{-1} =\frac{-2-3x}{3x-1}[/tex]
Step-by-step explanation:
f(x) = (x-2)/(3x+3). Let y = f(x).
Then y = (x-2)/(3x+3).
y(3x+3) = x - 2
3xy + 3y = x - 2
3xy - x = -3y - 2
x(3y-1) = -(3y+2)
x = -(3y+2)/(3y-1)
Hence, the inverse of f(x) is -(3x+2)/(3x-1).
the slope of (-2,3) and (4,-5)
Answer:
-4/3
Step-by-step explanation:
Slope= - 5-3/4+2
Slope= - 8/6
Slope = - 4/3
answer:
0.75 i think i'm not really sure i hope it helps tho
Step-by-step explanation: