Step-by-step explanation:
If a number is rational, we can represent it as a fraction.
[tex] \frac{a}{b} [/tex]
Where a and b are intergers.
First, we know that
[tex] \sqrt{49} = 7[/tex]
We can represent 7 as
[tex] \frac{7}{1} ..... \frac{14}{2} .... \frac{21}{3} ..... \frac{n}{y} = 7[/tex]
Where n and y are two numbers that when divided equal 7.
So
[tex] \sqrt{49} [/tex]
is a rational number
Imran can row at 3 m/s against the current and at 6 m/s with the current. Find the speed of the current.
komhnyrtgfdedavfbfsfb
1. The hot-water tank in Rafael's house holds 17x + 11 gallons of hot water. Rafael used 4x + 1 gallons of hot water washing the dishes. Which of the following
binomials represents the number of gallons of hot water remaining in the tank?
Answer:
13x + 10
Step-by-step explanation:
Rafael's hot-water tank holds:
[tex]17x + 11[/tex]
Gallons of hot water.
Rafael used:
[tex]4x + 1[/tex]
Gallons of hot water.
And we want to determine which binomial represent the amount of hot water remaining in the tank.
The amount remaining R in the tank will be the amount taken by Rafael subtracted from the total amount. Hence:
[tex]\displaystyle R = (17x+11) - (4x + 1)[/tex]
Simplify. Distribute:
[tex]\displaystyle R = (17x + 11) + (-4x - 1)[/tex]
Rearrange:
[tex]R = (17x - 4x) + (11 - 1)[/tex]
Combine like terms:
[tex]R = 13x + 10[/tex]
In conclusion, 13x + 10 gallons remain in the tank.
what is 15% of 71.40$
Answer:
10.71
Step-by-step explanation:
0.15*71.40
Tutorial Charlie is planning a trip to Madrid. He starts with $984.20 in his savings account and uses $381.80 to buy his plane ticket. Then, he transfers 1 4 of his remaining savings into his checking account so that he has some spending money for his trip. How much money is left in Charlie's savings account?
Answer:
$150.60
Step-by-step explanation:
$984.20-$381.80= $602.40
Take $602.40 and divide by 4 which equals $150.60 which is the 1/4 $ Charlie has in his savings account.
If AB=2x BC=x+20 and AC=50 what is the value of x
Answer:
x = 10
Step-by-step explanation:
AC = AB + BC
Substitute the values for the line segments:
50 = (2x) + (x + 20)
50 = 2x + x + 20
Combine like terms:
50 = 3x + 20
Subtract 20 from both sides:
30 = 3x
Divide both sides by 3:
10 = x
Check your work:
50 = 2(10) + 10 + 20
50 = 20 + 30
50 = 50
Correct!
Garcy has 4/5 pound of bird seed she needs 3/10 pound to feed the birds daily which rectangle models below shows how many days worth
Answer:
I believe it is 2 days
Step-by-step explanation:
3/10 can be simplified into 1.5/5 and just go up by the 1.5/10 of a pound she needs each day. if she did it for 3 days she would need 4.5/5 so she has enough for 2 days
The original price of a toy was $42. If the price is reduced by 20%, what is the new price of the toy?
Write a multiplication expression without exponents that is equivalent to 3^3.
Hi! I'm happy to help!
This expression is an exponent, or repeated multiplication. 3^3 is three multiplied by itself (3), 3 times, or 3×3×3
So, our non-exponent expression will be 3×3×3.
I hope this was helpful, keep learning! :D
HELP ASAP!!!!!!!!!
Ollie is investing $15000 in an account that earns 4.75 simple interest. About how many years will it take to have a balance of $23550 his account?
Answer:
Step-by-step explanation:
23550=15000(1+.0475t)
t=12
Which expression represents the number of sides in the polygon for the nth member of the sequence?
A) n+2
B) 2n + 1
C) 4n-3
D) 3n+2
Answer:
The answer is n+2.Step-by-step explanation:
I hope U like my answer and my answer helped U....Answer:
n+2 represemts the number of sides in the polygon for the nth member of the sequence
The midpoint m of gh has coordinates ( -5, -4) point h has coordinates (-4, -7) find the coordinates of point g
Answer:
Step-by-step explanation:
The midpoint formula is
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex] and we have the coordinates of the midpoint and the coordinates of one endpoint. Filling that in we have:
[tex](-5,-4)=(\frac{-4+x_2}{2},\frac{-7+y_2}{2})[/tex] and we will solve for the missing values one at a time. x first:
[tex]-5=\frac{-4+x_2}{2}[/tex] and
-10 = -4 + x₂ so
-6 = x₂ and do the same for y:
[tex]-4=\frac{-7+y_2}{2}[/tex] and
-8 = -7 + y₂ so
-1 = y₂
Thus, the coordinates of point g are (-6, -1)
7(3w-3)=-12
HURRY PLEASE
Answer:
3/7
Step-by-step explanation:
21w - 21 = -12
21w = -12 +21
21w = 9
w = 9/21
i.e w= 3/7
Step-by-step explanation:
21w-21= -12
21w= -12 + 21
w=9/21
Expand the following:
a).
[tex]8(x - 2y)[/tex]
b).
[tex] \frac{6a + 18b - 12c}{6} [/tex]
Answer:
8x-16y
Step-by-step explanation:
b.6a/6+18b/6-12c/6Answer:
8x - 16y and a + 3b - 2c
Step-by-step explanation:
(a)
8(x - 2y) ← multiply each term in the parenthesis by 8
= 8x - 16y
(b)
[tex]\frac{6a+18b-12c}{6}[/tex] ← factor out 6 from each term in the numerator
= [tex]\frac{6(a+3b-2c)}{6}[/tex] ← cancel the 6 on numerator/ denominator
= a + 3b - 2c
Cant figure this one out help please!
Answer:x+20
Step-by-step explanation:
Mr Guru bought a second hand bike for rupees 125200 he Spent rupees 5302 repair it at what price should he sell it to gain 5% on his total investment
Answer:
137027.1 Rupees
Step-by-step explanation:
(125200+5302) * 0.05 = 6525.1
130502+6525.1 = 137027.1
A certain forest covers an area of 5000 km². Suppose that each year this area decreases by 5%. What will the area be after 10 years?
Use the calculator provided and round your answer to the nearest square kilometer.
Answer:
The forest will cover an area of approximately 2994 square kilometers after 10 years.
Step-by-step explanation:
A forest covers an area of 5000 square kilometers. Each year, the area of the forest decreases by 5%. We want to determine its area after 10 years.
We can write an exponential function to represent the situation. The standard exponential function is given by:
[tex]\displaystyle f(x) = a(r)^x[/tex]
Where a is the initial value, r is the rate, and x is the time that has passed (in this case in years).
Since the original area is 5000 square kilometers, let a = 5000.
Each year, the area decreases by 5%. In other words, for each subsequent year, the forest's area will be 100% - 5% = 95% = 0.95 of its previous year. Hence, r = 0.95.
Thus, our function is:
[tex]\displaystyle f(x) = 5000(0.95)^x[/tex]
Then after 10 years (x = 10), the area will be:
[tex]\displaystyle f(10) = 5000(0.95)^{(10)}= 2993.6846...\approx 2994\text{ km}^2[/tex]
In conclusion, the forest will cover an area of approximately 2994 square kilometers after 10 years.
write an equation in slope-intercept form for the line described. passes through (12,0) and is parallel to y=-1/2x-3
Answer:
y = -1/2x + 6
Step-by-step explanation:
The slope of a parallel line will remain the same. The only thing that is different is the y-intercept but we can solve that using the point given, the slope, and the slope intercept form equation [ y = mx + b ].
0 = -1/2(12) + b
0 = -6 + b
6 = b
Now input the data we were given and solved for back into the formula.
y = -1/2x + 6
Best of Luck!
final grades are often computed using weighted averages. Some college professors Us complicated weighted averages. Your college professor tells you he will give a 33%-67% split on grades between test and homework where whichever average is higher will be 67%. What will your final grade be if your homework average is 78 and your test average is 79?
Answer:
Your final grade will be 78.67 %
Step-by-step explanation:
67% of your grade will be from your test average which is 79 (higher)
33% of your grade will be from your homework average which is 78.
Calculating:
(67×79+33×78) / (67+33) = 7867 / 100 = 78.67
Find the missing length. The triangles are similar.
Answer:
182
Step-by-step explanation:
First, we can say that ∠ACB and ∠BCF are opposite angles because they are not next to each other and are formed by intersecting lines. Therefore, ∠ACB = ∠BCF
Next, angles correspond with the side opposite of it. This means that, for example, ∠ACB corresponds with line AB and ∠BCF corresponds with line BF. Because ∠ACB and ∠BCF are equal and the triangles are similar, we can say that their corresponding sides have a ratio with each other. Similarly, ∠CAB corresponds to CB, ∠ABC corresponds to AC, ∠CWV corresponds to CV, and ∠CVW corresponds to CB.
Because the triangle CVW is isosceles, we can say that the angles whose corresponding sides are equal are equal as well, so ∠CAB = ∠ABC and ∠CVW = ∠CVW. Next, because ∠ACB and ∠BCF are equal and correspond to each other, and the other two angles in each triangle are equal to each other, we can say that the other two angles must be equal. Another way of putting this is like this:
Say that x = ∠CAB. Then,
∠CAB + ∠ABC + ∠ACB = 180
x + x + ∠ACB = 180
2x + ∠ACB = 180
subtract ∠ACB from both sides
180 - ∠ACB = 2x
Similarly, if y = ∠CWV,
180 - ∠WCV = 2y. Therefore, 2y=2x and y=x, so ∠CAB = ∠ABC = ∠CWV = ∠CVW.
Given this, we can say that sides CV and CW correspond with BC and AC. This means that the ratio between, for example, CV and BC is equal to the ratio between CW and AC. Therefore,
CV/BC = CW/AC
84/182 = 84/?
Filling in the blank, 84/182 is equal to 84/182, so ? = 182
Integration as the Inverse of Differentiation, Integration of ax" and Integration of the Functions of the Sum or Difference of Algebraic Terms
For each of the following, find f(x).
(a) f'(x) = x³ + 4x -1 1
(b) f'(x) = 1/2x² + root x
(c) f'(x) = 3x - 4 / 2x³
Answer:
The answer is in the image above
Answer:
Step-by-step explanation:
The antiderivative for b is definitely incorrect, as stated in the comments section.
[tex]\int\limits {\frac{1}{2x^2}+\sqrt{x} } \, dx \\\frac{1}{2} \int\limits{\frac{1}{x^2} } \, dx+\int\limits {x^{\frac{1}{2}} } \, dx[/tex] That's a bit more simplified. One more important simplification and then we can integrate one term at a time:
[tex]\frac{1}{2}\int\limits{x^{-2}} \, dx +\int\limits{x^{\frac{1}{2} } \, dx[/tex] and here we go:
[tex]\frac{1}{2}(\frac{x^{-2+1}}{-2+1})+(\frac{x^{\frac{1}{2}+\frac{2}{2}} }{\frac{1}{2}+\frac{2}{2} })+C[/tex] and
[tex]\frac{1}{2}(\frac{x^{-1}}{-1})+(\frac{x^{\frac{3}{2}} }{\frac{3}{2} })+C[/tex] and finally,
[tex]-\frac{1}{2x}+\frac{2}{3}x^{\frac{3}{2}}+C[/tex]
Anyango divided her 50 hectares farm as follows.maize took 35% of the farm beans 32%;potatoes 24% and millet took the remaining part.
a). What is the area covered by each crop in hectares?
b) Anyango increased the plot for beans by 11 and quater % and reduced the plot for potatoes by 15%in the following year.
Answer:
a = Maize takes up 17.5 Hectares, Beans takes up 16 Hectares, and Potatoes takes up 12 hectares
b = Beans takes up 17.8 hectares, and Potatoes takes up 10.2 Hectares
Step-by-step explanation:
A: 50/100 = .5
.5 is = to 1% of the farm
Maize = .5*35
Maize = 17.5 Hectares
Beans = .5*32
Beans = 16 Hectares
Potatoes = .5*24
Potatoes = 12 hectares
B: Beans: 16*1.1125 = 17.8 hectares
Potatoes: 12*.85 = 10.2 Hectares
if m<8= 23° find each measure.
straight angles ( 1 , 2 , 3 , 4 ) parallel to straight angles Angles ( 5 , 6 , 7 , 8 )
m<8 = m< 6 = 23° [ Opposite angles]
m< 4 = m< 2 = 23°
m<8 + m< 5 = 180°
23° + m< 5 = 180°
m<5 = 180 - 23 = 157
m< 5 = m< 7 = 157° [ Opposite angles]
m< 1 = m< 3 = 157° [ Opposite angles]
straight angles ( 1 , 2 , 3 , 4 ) parallel to straight angles Angles ( 5 , 6 , 7 , 8 )
So;m< 1 = 157m< 2 = 23m< 3 = 157m<4 = 23m< 5 = 157m< 6 = 23m< 7 = 157m< 8 = 23I hope I helped you^_^
What is the answer? Given right triangle MNO below. how many units long is NO?
Answer:
8!
Step-by-step explanation:
Basically, you would use the phythagorean theorem to find the answer plugging in the values that you already have to find the missing side (a^2 + b^2 = c^2)
since you have the length of the hypothenuse (c in the equation) and one of the legs of the triangle (a or b, it doesn't matter, but for the sake of the equation we'll plug in 6 for a), we can insert these numbers to find b!
Plugging it into the equation:
A^2 + b^2 = c^2
(6)^2 + b^2 = (10)^2
36 + b^2 = 100
subtract both sides to get b^2 = 64
then square root both sides b = 8
a survey of 100 high school students provided this frequency table on how students get to school. find the probability that a random selected student either takes the bus or walks. need help ASAP. picture is included.
Answer:
60% or 3/5
Step-by-step explanation:
Add up how many students take the bus: 50, and how many walk:10
Put that number over 100 and simplify: 60/100=6/10=3/5
an appliance repair p person charges 55 per trip plus 15 per hour for her labor. the cost of fixing a stove was 92.50. write and solve an equation to find how many hours it took to repair the stove
(92.50-55)/15 =2.5 hours
Step-by-step explanation:
92.5 (total) -55 (trip charge) = 37.50(hour charge)
37.50(hour charge)/15{per hour charge)=2.5(hours)
[tex]Find \: H.C.F \: of \: \\ 900 \: , 270 \\ using \: e.d.l \: \\ ( \: Euclid's \: division \: lemma \: )[/tex]
H.C.F of 900 & 270
Answer:
90Step-by-step explanation:
Factorize both numbers:
900 = 2*2*3*3*5*5270 = 2*3*3*3*5Common factors are:
2*3*3*5So HCF is:
HCF(900, 270) = 2*3*3*5 = 90[tex]\Large \red \mid \: \underline {\rm {{{\color{blue}{Explanation...}}}}} \: \red \mid[/tex]
We know that ,As per Euclid Division Algorithm.
[tex] \longrightarrow \: \Large\underbrace {\rm {{{\color{red}{ \: a \: = \: bq \: + \: r \: }}}}} [/tex]
a denotes dividendb denotes divisorq denotes quotientr denotes remainder◆━━━━━▣✦▣━━━━━◆Using Euclid Division Algorithm[tex]\large\bf{\purple{ \hookrightarrow \: }} \tt \: \: 900 \: = \: 270 \: \times \: 3 \: + \: 90[/tex]
Here ,[tex]\large\bf{\orange{ \implies \: }} \: \:r \: \neq \: 0[/tex]
Again Applying Euclid Division Algorithm
[tex]\large\bf{\purple{ \hookrightarrow \: }} \tt \: 270 \: = \: 90 \: \times \: 3 \: + \: 0[/tex]
Here ,[tex]\large\bf{\orange{ \implies \: }} \: \:r \: = \: 0[/tex]
As the reminder is 0 , 90 will be the greatest common divisor for the two given numbers.
So,[tex]{\boxed{ \Large{ \blue{ \bf{ \underline{ HCF \: = \: 90}}}}}}[/tex]
◆━━━━━▣✦▣━━━━━◆Solve for c:
9x + 72°
4x + 112°
Can someone please help me with this? You've gotta prove that x=8 in a table graph thing.
Answer:
AB= AC+CB
50 = (2x – 2 ) + 4(x+1)
50 = (2x – 2) + ( 4x+4)
50 = 6x +2
6x = 50 – 2
6x = 48
x= 48/6
x= 8
So; x=8 Q.E.D.
I hope I helped you^_^
Pls help on the top question
Answer:
-13=5×1+5×4m-2m
-13=5+20m-2m
-13-5=18m
-18=18m
18m=-18
m=18÷18
m=1
Answer:
[tex]\frac{55}{4}[/tex]
Step-by-step explanation:
let the number be n the multiply by - 4 is - 4n and add 5 gives
- 4n + 5 = - 50 ( subtract 5 from both sides )
- 4n = - 55 ( divide both sides by - 4 )
n = [tex]\frac{-55}{-4}[/tex] = [tex]\frac{55}{4}[/tex]
The number is [tex]\frac{55}{4}[/tex] or 13.75 if you prefer
Insert grouping symbols to make each number sentence true 3+8-2*5=45
Insert grouping symbols to make each number sentence true 3+8-2*5=45
Answer:
3+2+8×5