Prove algebraically that the recurring decimal 0.472 can be written as
17
36
Given:
The recurring decimal is [tex]0.47\overline{2}[/tex].
To prove:
Algebraically that the recurring decimal [tex]0.47\overline{2}[/tex] can be written as [tex]\dfrac{17}{36}[/tex].
Proof:
Let,
[tex]x=0.47\overline{2}[/tex]
[tex]x=0.472222...[/tex]
Multiply both sides by 100.
[tex]100x=47.2222...[/tex] ...(i)
Multiply both sides by 10.
[tex]1000x=472.2222...[/tex] ...(ii)
Subtract (i) from (ii).
[tex]1000x-100x=472.2222...-47.2222...[/tex]
[tex]900x=425[/tex]
Divide both sides by 900.
[tex]x=\dfrac{425}{900}[/tex]
[tex]x=\dfrac{17}{36}[/tex]
So, [tex]0.47\overline{2}=\dfrac{17}{36}[/tex].
Hence proved.
use the gcf and the distributive property to find the sum of 26 + 39
Answer:= 13
Step-by-step explanation:
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yes aaaaaaaaaaaaaaaxxs
Which numbers below represents a repeating decimal? Check all the boxes that apply.*
-2/3
-3/5
3/10
11/20
Answer:
-2/3
Step-by-step explanation:
-2/3= -.066666667
-3/5= -0.6
3/10= 0.3
11/20= 0.55
Round off 3.447 g to the nearest 1/100 g
pls help
Answer: 3.55 g
Step-by-step explanation: 3.447 g rounded to the nearest 1/100 g is 3.55 g.
Hint: nearest 1/100 g also means nearest hundredth!
CL 3-115. Jermaine has a triangle with sides 8, 14, and 20. Sadio and Aisha both think that they have triangles that are similar to Jermaine's triangle. The sides of Sadie's
triangle are 2, 3.5, and 5. The sides of Aisha's triangle are 4, 10, and 16. Decide who, if anyone, has a triangle similar to Jermaine's triangle. Be sure to explain how
you know
pening
1
CL 3-116. For the points R(-2, 7) and P(2,1) determine each of the following:
9514 1404 393
Answer:
Jermaine and Sadie have similar triangles. Aisha's is not similar.
Step-by-step explanation:
The side lengths can be arranged smallest-to-largest and reduced to mutually-prime integers. If the triangles are similar, their side ratios will be the same.
Jermaine's triangle has side ratios ...
8 : 14 : 20 = 4 : 7 : 10
Sadie's triangle has side ratios ...
2 : 3.5 : 5 = 4 : 7 : 10 . . . . (same as Jermaine's)
Aisha's triangle has side ratios ...
4 : 10 : 16 = 2 : 5 : 8 . . . . . (different from Jermaine's)
Sadie and Jermaine have similar triangles.
Find the inverse of the function f(x) = 2x - 4.
Answer:
f⁻¹(x) = 1/2 x + 2
Step-by-step explanation:
f(x) = 2x - 4 y=2x - 4
swap x and y: x = 2y - 4
solve y: 2y = x + 4
y = 1/2 x + 2
Inverse notation: f⁻¹(x) = 1/2 x + 2
Just need help 1-3 because it’s not easy
help plz plz plz will mark brainliest
Step-by-step explanation:
We have Angle ZWD = Angle DWN.
=> 5v - 7 = 4v + 8, v = 15.
Therefore x = Angle ZWD = 5(15) - 7 = 68.
list all 10 possible SRSs of size n = 2, calculate the proportion of females for each sample
Answer:
10
Step-by-step explanation:
since i helped can i have brainlst please that would be greatly apericated
we have a total of 10 choices,
while we need SRS of size 2 only,
We know that,
A combination helps us to determine the number of possible arrangements that can be made through a set of data provided where the order of the selection does not matter.
where,
n is the number of choices,
r is the number of selection.
All 10 possible SRSs of size n = 2, are:
1. Abigail & Bobby
2. Abigail & Carlos
3. Abigail & DeAnna
4. Abigail & Emily
5. Bobby & Carlos
6. Bobby & DeAnna
7. Bobby & Emily
8. Carlos & DeAnna
9. Carlos & Emily
10. DeAnna & Emily
To know more visit:
https://brainly.com/question/25351212
1)Ellen wanted to buy the following items:
∙ A DVD player for $49.95 ∙ A DVD holder for $19.95 ∙ Personal stereo for $21.95
Does Ellen have enough money to buy all three items if he has $90.s
Answer:
[tex]\huge\boxed{\tt{ No.}}[/tex]
Step-by-step explanation:
DVD player = $ 49.95
DVD Holder = $ 19.95
Personal Stereo = $ 21.95
Sum of Prices = $ 49.95 + $ 19.95 + $ 21.95 = $ 91.85
Ellan has $ 90 which is less than $ 91.85 which means that Ellan does not have enough to buy all three items.
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807A soccer field is 120 yards long. Han measures the length of the field using a 30-foot-long tape measure and gets a measurement of 358 feet, 10 inches. What is the amount of the error?
Answer:
Error = 1.167 feet
Percentage error = 0.3242%
Step-by-step explanation:
The original length of the soccer field = 120 yards long
Converting to feet
1 yard = 3 feet
120 yards = x
Cross Multiply
x = 120 × 3 feet
x = 360 feet
Measured length:
Han measures the length of the field using a 30-foot-long tape measure and gets a measurement of 358 feet, 10 inches.
We convert 10 inches to feet
1 inch = 0.0833 feet
10 inches = x feet
Cross Multiply
x = 10 × 0.0833 feet
x = 0.833 feet
The measured length = 358 feet + 0.833 feet
= 358.833 feet
The Error is calculated as:
|Measured length - Original Length)
= 360 feet - 358.833 feet
= 1.167 feet
Percentage Error
= Error/Original Length × 100
= 1.167/360 × 100
= 0.3241666667%
Approximately = 0.3242%
4. An angle is 50° more than its supplement. Find the angles.
Answer:
The angles measure [tex]65[/tex]° and [tex]115[/tex]°.
Step-by-step explanation:
Supplementary angles are a pair of angles whose measures add up to [tex]180[/tex]°. In this case, we know that one angle is [tex]50[/tex]° bigger than the other one, so if we let the measure of one angle be [tex]x[/tex], then the measure of the other angle will be [tex]x+50[/tex]. Therefore, we can write the following equation to solve for
[tex]x+x+50=180[/tex]
Solving for [tex]x[/tex], we get:
[tex]x+x+50=180[/tex]
[tex]2x+50=180[/tex] (Simplify LHS)
[tex]2x+50-50=180-50[/tex] (Subtract [tex]50[/tex] from both sides of the equation to isolate [tex]x[/tex])
[tex]2x=130[/tex] (Simplify)
[tex]\frac{2x}{2}=\frac{130}{2}[/tex] (Divide both sides of the equation by [tex]2[/tex] to get rid of [tex]x[/tex]'s coefficient)
[tex]x=65[/tex]
Therefore, [tex]x+50=65+50=115[/tex], so our final answer is that the angles measure [tex]65[/tex]° and [tex]115[/tex]°. Hope this helps!
help me pleaseee pleaseee
Answer:
x = 3
m<PAW = 1
Step-by-step explanation:
☆They are supplementary angles.
☆Supplementary angles equal 180 degrees.
[tex]- 11x + 17 3 - 1x + 43 = 180 \\ - 12x + 216 = 180 \\ \frac{ \: \: \: \: \: \: \: \: \: \: \: \: \: - 216 = - 216}{ \frac{ - 12x}{ - 12} = \frac{ - 36}{ - 12} } \\ x = 3[/tex]
☆Plug in for m<AEZ
[tex] - 1(3) + 4 \\ - 3 + 4 \\ 1[/tex]
☆m<PAW is corresponding to m<AEZ
☆Corresponding angles are congruent.
☆m<PAW equals 1.
In Toronto, Canada, one liter of gasoline costs. $0.74$. There are 3.8 liters in one gallon. How much does one gallon of gas cost in Toronto? Round your answer to he nearest hundredths.
Answer:
$2.81
Step-by-step explanation:
From the above question:
1 liter of gasoline = $0.74
There are 3.8 liters in one gallon.
Hence:
1 liter of gasoline = $0.74
3.8 liters of gasoline = x
Cross Multiply
x = 3.8 × $0.74
x = $2.812
Approximately to the nearest hundredth = $2.81
Therefore , the cost of one gallon of gas(3.8 liters) in Toronto is $2.81
According to records at the guidance office, the mean GPA of all juniors is 3.45 and the mean GPA of all seniors is 3.62. Which of the following statements is true?
A. 3.45 is a statistic and 3.62 is a statistic.
B. 3.45 is a statistic and 3.62 is a parameter.
C. 3.45 is a parameter and 3.62 is a statistic.
D.3.45 is a parameter and 3.62 is a parameter.
Answer:
d, they are both parameters because they mean allllll the juniors and seniors, not just pulling out a few and taking a sample
Step-by-step explanation:
Answer:
The answer is "D".
Step-by-step explanation:
3.45 is a parameter and 3.62 is a parameter.
18. A figure is said to be regular if its sides are equal in length and angles are equal in
measure. What do you mean by a regular quadrilateral?
Answer:
If its 4 sides need to be equal and 4 angles need to be equal then it is a square.
Step-by-step explanation:
[tex]\huge\sf\fcolorbox{green}{pink}{Answer}[/tex]
Properties of regular quadrilateral :- All sides are equalAll angles are 90° ( equal)Square is only the regular quadrilateral
h(x) = –2 – 5 help pls!!!
Answer:
h(0)= -5
h(-2)= -7
Step-by-step explanation:
Answer:
-5
Step-by-step explanation:
x just represents a value, so simply plug 0 into the equation instead of x.
h(0)= -0 - 5
h(0) = -5
Determine the number of zeros of the polynomial function f(x)= x^8-x^9
Step-by-step explanation:
Determine if odd, even, or neither.
The function is neither even nor odd
Answer:
9
Step-by-step explanation:
The highest power of x is 9: x^9
and therefore this polynomial will have 9 zeros.
. What number replaces ☺ to make the sentence true? 1 + 3 + 4 + 6 + 6 + 8 + 9 + 11 = 4 × ☺.
Answer:
12
Step-by-step explanation:
1+3+4+6+6+8+9+11=48. Knowing this, we can now figure out the other side of the equation. To make both equations true, both sides must equal 48.
To this, simply divide 48 by 4.
48/4=12
Thus, your answer is 12
Answer: 12
Step-by-step explanation:
1+3+4+6+6+8+9+11 is 48 (you can double check)
48=4*X (calling x as the smiley).
Divide 4 by each side.
12=X
What is the answer?? Please
9514 1404 393
Answer:
not similar
Step-by-step explanation:
"Triangle" DPS cannot exist. Sides DP and DS are not long enough.
__
Side ratios are not the same. In the top triangle, the length ratios are ...
14 : 16 : 19
In the bottom triangle, the length ratios are ...
7 : 8 : 19 (such a triangle cannot exist)
Since the ratios are not the same, the triangles are not similar.
Write an Equation using the following arithmetic sequence: 5, _____, ______, 32
Answer:
The sequence is:
5, 14, 23, 32
Step-by-step explanation:
We know that an Arithmetic sequence with a₁ and the commo difference 'd' has the nth term such as:
aₙ = a₁ + (n-1)d
Given the arithmetic sequence
5, _____, ______, 32
here:
a₁ = 5
n = 4
aₙ
so substituting a₁ = 5, n = 4 and aₙ = 32 in the nth term
aₙ = a₁ + (n-1)d
32 = 5 + (4-1)d
32 = 5 + 3d
3d = 32-5
3d = 27
divide both sides by 3
3d/3 = 27/3
d = 9
Therefore, the common difference: d = 9
Determining the 2nd term:
Using the formula
aₙ = a₁ + (n-1)d
substitute n = 2, a₁ = 5, d = 9
a₂ = 5 + (2-1)9
a₂ = 5 + 1(9)
a₂ = 5 + 9
a₂ = 14
Determining the 3rd term:
Using the formula
aₙ = a₁ + (n-1)d
substitute n = 3, a₁ = 5, d = 9
a₃ = 5 + (3-1)9
a₃ = 5 + 2(9)
a₃ = 5 + 18
a₃ = 23
Thus, the sequence becomes:
5, 14, 23, 32
Find the area of the rectangle with: l=3m50cm b=2m20cm
I NEED HELP PLEASE!! Does anyone understand this??
Answer: 44.4
Step-by-step explanation:
We are asked to find angle V, so we are going to use our trig ratios to explain this one. They have given us the side opposite of angle v and the hypotunse. angle v. so we are going to be using sine. . SOHCAHTOA.
First, let use the ratio for sine [tex]\frac{opp}{hypo\\}[/tex] which equal to [tex]\frac{7}{10}[/tex]
then we are to take the arcsine or the sine inverse because we are trying to the angle measure not side length. ([tex]sin^{-1}[/tex](7/10) which gives us 44.4
Write the ratio in simplest form.
The ratio of green beads to blue beads is ???
3:6 but if u simplify it it will become
1:2
–15 = a/5
A. a = –3
B. a = –20
C. a = –10
D. a = –75
Answer: a = -75
Step-by-step explanation:
i just multiplied both sides by 5, in order to get "a" by itself.
-75 = a
then, just for kicks, we switch it around so that the variable is in front.
a = -75
Matt has answered the questions on a test. What percentage of the test questions have 20/25 Matt answered?
Answer:
80% complete with the test
Step-by-step explanation:
what you would do is if he does 20 out of 25 questions you would think that 25 is 100 and you would see that 20 is 80% because of you doing 5,10,5,20,25 the 20 is the 4th one and 80 is the forth of 100 so the answer is 80%.
Hope this helps :)
Which of the following rational functions is graphed below?
Answer:
there is no attached file
Step-by-step explanation:
Need help asap Pleaseee
Answer:
the answer is 144 feet and I don't really have an explanation
Answer:
Radius = 12 feet
Step-by-step explanation:
The area of a circle formula is Area = pi r^2 ("r" represents the radius)
The area of Circle Q is 144pi
You can substitute "Area" with 144pi, which would look like this:
144pi = pi x r^2
Now divide both sides with "pi", which gives:
144 = r^2
Finally, square root both sides:
sqrt(144) = sqrt(r^2) (sqrt = square root)
And that gives
12 = r
So the radius is 12 feet.
A $310 suit is marked down by 20%. Find the sale price.
Answer:
the answer is 62!
Step-by-step explanation:
multiply
Answer:
$248
Step-by-step explanation:
310/100=3.1
3.1x20=62
310-62=248$