Answer:
Decreased
Step-by-step explanation:
Renee wants to put a fence around her
square garden that has an area of
6,500 square feet. Determine the
perimeter of the garden to the nearest
tenth of a foot.
Answer:
perimeter = 322.5 ft ( to the nearest tenth of a foot)
Step-by-step explanation:
Length the length of the sides of the square be L
Area of a square = L²
∴ 6,500 = L²
L = √(6,500)
L = 80.6226
Next Let us calculate the perimeter
Perimeter of a square = L + L + L + L = 4L
perimeter = 4 × 80.6226
Perimeter = 322.4904 ft
perimeter = 322.5 ft ( to the nearest tenth of a foot)
N:B rounding to the nearest tenth of a foot is same as rounding to 1 decimal place.
What is the mixed number for (91/5?)
Answer:
18 1/5
Step-by-step explanation:
• (4xy^4)(– 2x^2y^5)
Answer:
This will be -8x^3y^9.
In the diagram, points Q, R, S and T are collinear and PR = RS. IF RS = 12 and RT = 30, find
a) QR
b) ST
c) QS
d) QT
Answer:
QR=12
ST=18
QS=24
QT=42
Step-by-step explanation:
The question tells us that PR is congruent to RS. But there's no point P in the line. So, I'm going to assume it's a typo and that they meant point Q.
So, we know that QR is congruent so RS. RS is 12 and RT is 30. With that information, we can find the other lengths:
1) QR
Since QR is congruent to RS and RS is 12, this means that QR is also 12.
2) ST
We know that RT is 30. RT is made by adding up RS and ST. In an equation, this is:
[tex]RT=RS+ST[/tex]
We know that RT is 30 and RS is 12. Thus, substitute:
[tex]30=12+ST\\ST=18[/tex]
Thus, ST is 18.
3) QS
QS is the length of QR plus RS. Since QR is 12 and RS is also 12, QS is 12+12 or 24.
4) QT is the length of the entire segment. The entire segment can be written as:
[tex]QT=QR+RT[/tex]
And since we already know that QR is 12 and RT is 30:
[tex]QT=12+30\\QT=42[/tex]
QT is 42.
somebody please help me on this!!
=======================================================
Explanation:
See the attached image below to see one way you could draw the diagram based on the given info. The drawing is not to scale.
The color coded angles hopefully let you see which angles are congruent to one another
Angle EXB = Angle DXE (in red) Angle CXD = Angle DXB (in blue) Angle AXC = Angle CXB (in green)These three pairs of congruences are possible because of the angle bisections that occur.
Since EXB is 20, this means DXE is 20 as well. They combine to 20+20 = 40, which is the measure of angle DXB (angle addition postulate).
Angle DXB is congruent to CXD, so both are 40 and they combine to 40+40 = 80. This is the measure of angle CXB.
Finally, angle CXB = 80 doubles to 160 which is the measure of angle AXB. Or you could say
angle AXB = (angle AXC) + (angle CXB) = 80 + 80 = 160.
he exponential expression 28 has a value of 256. Write two other exponential expressions that have a value of 256. Explain how you got your answers. (Begin by writing out 2 8as the product of 2s.)
Answer:
Two other exponents that results in 256 are [tex]16^2[/tex] and [tex]4^4[/tex]
Step-by-step explanation:
Given
[tex]2^8 = 256[/tex]
Required
Write two exponential expression that equals 256
[tex]2^8 = 256[/tex]
Expand 8 as 4 * 2
[tex]2^{4*2} = 256[/tex]
Using laws of indices, we have
[tex](2^4)^2 = 256[/tex]
2⁴ = 16; So, we have
[tex]16^2 = 256[/tex] --- This is one
Recall that
[tex]2^{4*2} = 256[/tex]
This can also be rewritten as
[tex]2^{2*4} = 256[/tex]
Using laws of indices, we have
[tex](2^2)^4 = 256[/tex]
2² = 4; So, we have
[tex]4^4 = 256[/tex] --- This is another one
Hence, two other exponents that results in 256 are [tex]16^2[/tex] and [tex]4^4[/tex]
Janes jogging speed is 5 kilometers per hour. What is her speed in meters per second?
Answer:
1.3888888888889 mps
Step-by-step explanation:
1 kph = 0.27777777777778 mps, so just multiply that by 5.
Rationalise the denominator and find a, b
Answer:
a = 49
b = - 20√2
Step-by-step explanation:
5 - 2√6 / 5 + 2√6
We can rationalise the denominator as follow:
5 - 2√6 / 5 + 2√6
Multiply the numerator and the denominator by the conjugate of
5 + 2√6. The conjugate of 5 + 2√6 is
5 - 2√6
(5 - 2√6 / 5 + 2√6) x (5 - 2√6 / 5 - 2√6)
(5 - 2√6) (5 - 2√6) /(5 + 2√6) (5 - 2√6)
Expand
(25 - 10√6 - 10√6 + 4×6) / (25 - 10√6 + 10√6 + 4×6)
25 - 20√6 + 24 / 25 - 24
25 + 24 - 20√6 / 1
49 - 20√6
Equating 49 - 20√6 with a + b√3, we can obtain the value of a and b as follow:
49 - 20√6 = a + b√3
From the above
a = 49
b√3 = - 20√6
Divide both side by √3
b = - 20√6/√3
Rationalise
b = - 20√6/√3 x √3/√3
b = - 20√(6×3)/ √3×√3
b = - 20√18 / 3
b = - 20√(9×2) / 3
b = - 20 × 3√2 / 3
b = - 20√2
Given info:- Rationalise the denominator and find out the value of "a" and "b"
Given expression: {(5-2√6)/(5+2√6)} = a+b√3
Explanation:-
{(5-2√6)/(5+2√6)} = a+b√3
We know that Rationalising factor of a+b√c is a-b√c.
Therefore, the rationalising factor of 5+2√6 is 5-2√6.
⇛{(5-2√6)/(5+2√6)} × {(5-2√6)/(5-2√6)} = a+b√3
⇛{(5-2√6)(5-2√6)}/{(5+2√6)/(5-2√6)} = a+b√3
⇛{(5-2√6)²}/{5+2√6)(5-2√6)} = a+b√3 [∵(a-b)(a-b)=(a-b)²]
⇛{(5-2√6)²}/{(5)²-(2√6)²} = a+b√3 [∵(a+b)(a-b)=a²-b²]
⇛{(5-2√6)²}/({5*5)-(2*2√6*6)} = a+b√3
⇛{(5-2√6)²}/(25 - 4√6) = a+b√3
⇛{(5-2√6)²}/(25-24) = a+b√3
⇛{(5-2√6)²}/1 = a+b√3
⇛(5-2√6)² = a+b√3
⇛(5)²-(2√6)²+2(5)(2√6) = a+b√3
⇛(5*5) - (2*2√6*6) - 10 - 2√6 = a+b√3
⇛25 - 10 - 4√6 - 2√6 = a+b√3
⇛15 - 4√6 - 2√6 = a+b√3
⇛15 + 6√6 = a+b√3
∴ 15 + 6√6 = a+b√3
On, comparing with both RHS we notice that:
The value of a = 15 and b = 6.
Hope this helps!!
If you have any doubt, then you can ask me in the comments.
Find the length of the side x in this right triangle.
A.5 tan 50.1
B.(tan 50.1)/5
C.tan^-1(5/50.1)
Answer:
x = 5.98
Step-by-step explanation:
Step 1: Use tangent to solve for x
tan50.1 = [tex]\frac{x}{5}[/tex]
x = 5tan50.1
x = 5.98
Therefore x is equal to 5.98
In 1000 sq. meter of land a farmer cultivated 765 kg of rice with the wastage of 23.5%. I) Find the weight of the wastage. II) Find the weight and percentage of rice cultivated. 3) If the area has been increased 40 times in size, how much rice will be cultivated (excluding the wastage)
Answer:
i. 179.775 kg
IIa)the weight=585.225 kg
IIb) percentage=75.6%
3)=30240 kg
Step-by-step explanation:
From the question were given the total area of the land as 1000 sq. meter
Amount of cultivated rice= 765 kg
the percentage of wastage rice =23.5%.
But we can convert the amount of the wastage rice from percentage to kilogram which is
23.5/100=0.235
Then to kilogram 0.235× 765 kg= 179.775 kg
Then amount of wastage rice= 179.775 kg
I)Find the weight of the wastage. ?
The amount of wastage rice is the conversion of it's percentage to kilogram which I did above
Then amount of wastage rice= 179.775 kg
II) Find the weight and percentage of rice cultivated.
Since we know amount of wastage as 179.775 kg, then the amount of cultivated will b difference between the cultivated and wastage=765 - 179. 775 = 585.225 kg
Then it's percentage is the substraction of the percentage of wastage from 100%
= 75.6%
3)If the area has been increased 40 times in size, how much rice will be cultivated (excluding the wastage)
Increase in the land in 40 times= 40×1000= 40,000sm
Then the rice cultivated= 75.6% ×40000
=30240 kg
A right angle measures
Answer:
90 degrees
Step-by-step explanation:
I don't really have an explanation but I'm 100% sure that it is
Answer:
90 degrees
Step-by-step explanation:
Jim takes great pride in decorating his float for the homecoming parade for his high school. With the $5000 he has to spend, Jim buys 5,000 carnations at $0.30 each, 4,000 tulips at $0.60 each, and 300 irises at $0.25 each. Write an inequality which describes how many roses, r, Jim can buy if roses cost $0.80 each.
Answer:
r = (5000 - [(5000 x 0.3) + (4000 x 0.6) + (300 x 0.25)])0.8
Simplified - r = 820
Step-by-step explanation:
I don't know how to explain it exactly, but I know you have to find out how much the carnations, tulips, and irises all cost,subtract that from how much money he has, and divide what left by the cost of the roses (by multiplying the 0.8 cents, because it's a decimal).
r = (5000 - [(5000 x 0.3) + (4000 x 0.6) + (300 x 0.25)])0.8
r = (5000 - [1500 + 2400 + 75])0.8
r = (5000 - 3975)0.8
r = 1025(0.8)
r = 820
Learning
Diagnostic
Analytics
See your levels
What is the area of the triangle?
7 ft.
4 ft.
6 ft.
square feet
Answer:
Area of the triangle = 12 square feet
Step-by-step explanation:
Area of a triangle is calculated by the formula,
Area = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
From the picture attached,
Height of the given triangle = Vertical distance of the top vertex = 4 feet
Base of the triangle = 6 feet
Area of this triangle = [tex]\frac{1}{2}(6)(4)[/tex]
= 12 square feet
Therefore, area of the given triangle will be 12 square feet.
Plzzz helppp!!
9-4x=17????
Answer:
[tex] \boxed{ \bold{ \boxed{ \sf{x = - 2}}}}[/tex]Step-by-step explanation:
[tex] \sf{9 - 4x = 17}[/tex]
Move 9 to right hand side and change it's sign
⇒[tex] \sf{ - 4x = 17 - 9}[/tex]
Subtract 9 from 17
⇒[tex] \sf{ - 4x = 8}[/tex]
Divide both sides of the equation by -4
⇒[tex] \sf{ \frac{ - 4x}{ - 4} = \frac{8}{ - 4}} [/tex]
Calculate
⇒[tex] \sf{x = - 2}[/tex]
Hope I helped!
Best regards!!
Please solve ASAP, 3k+16=9+6x? and show ur work please?
Answer:
[tex]\Large \boxed{k=2x + \frac{-7}{3}} \\ \\ \\ \Large \boxed{x=\frac{1}{2} k+\frac{7}{6}}[/tex]
Step-by-step explanation:
Solving for k:
[tex]\sf 3k+16=9+6x[/tex]
Subtracting 16 from both sides.
[tex]\sf 3k=6x-7[/tex]
Dividing both sides by 3.
[tex]\displaystyle \sf k=2x + \frac{-7}{3}[/tex]
Solving for x:
Flipping the original equation.
[tex]\sf 6x+9=3k+16[/tex]
Subtracting 9 from both sides.
[tex]\sf 6x=3k+7[/tex]
Dividing both sides by 6.
[tex]\sf \displaystyle x=\frac{1}{2} k+\frac{7}{6}[/tex]
Jake's water bill is $24.60 per month plus $2.00 per ccf (hundred cubic feet) of water. What is the maximum number of ccf Jake can use if he wants his bill to be no more than $64.00?
Answer:
Jake can use 19.70 ccf to not exceed $ 64.00 in water bill.
Step-by-step explanation:
The cost function of water bill is:
[tex]C = C_{f}+C_{v}[/tex]
Where:
[tex]C_{f}[/tex] - Fix costs, measured in USD.
[tex]C_{v}[/tex] - Variable costs, measured in USD.
The fix and variable costs are, respectively:
[tex]C_{f} = 24.60[/tex]
[tex]C_{v} =2\cdot \left(\frac{Q}{100} \right)[/tex]
Where [tex]Q[/tex] is the water capacity consumed within a month, measured in cubic feet. Therefore, first formula is expanded:
[tex]C = 24.60+2\cdot \left(\frac{Q}{100} \right)[/tex]
If [tex]C = 64\,USD[/tex], the maximum water capacity is:
[tex]64 = 24.60+2\cdot \left(\frac{Q}{100} \right)[/tex]
[tex]39.40 = 2\cdot \left(\frac{Q}{100} \right)[/tex]
[tex]Q = 1970\,ft^{3}[/tex]
Which is equivalent to 19.70 ccf.
WILL GIVE BRAINLIEST
A hospital did a 10 year study on patients who use his services. 1000 patients were randomly selected and followed over a period of 10 years to determine the average number of visits per year. By the end of the 10 year. Some of the patients had left the area. Identify the problem with the poll.
A) A nonresponse occurred
B) The relationship between two variables implies one causes the other
C) Some of the sample data are missing
D) The conclusion is based on a voluntary response sample
Answer:
b so it doesnt tell you how many people come to the hospital a day
Step-by-step explanation:
a--->b--->=c
Answer:
A) A nonresponse occurred
Step-by-step explanation:
We understand that in the span of 10 years, 1000 patients were monitored, and among those were some individuals who had moved. These certain individuals are not responsive anymore, and can not be a source of data, and the poll would be incorrect if the hospital decided to switch out the patients in the midst of the decade. Therefore we are to assume a nonresponse occurred. (To define nonresponse, it is simply a failure to respond, which is indeed what is defined for those who had moved.)
It is not B for the two variables have no correlation, it is not C for all patients were at first patrons and the problem did not explicitly state there was missing info, and D is incorrect for it said the sample group was selected at random. Therefore, with process of elimination, A would still be correct.
Find the product of the following. i) –5a² bc, 6ab, 8abc² ii) –3x²y and (5y – xy) iii) x²y²z² and (xy – yz + zx) iv) (p + 6) and (q – 7) v) (2x + 7) and (x² – 5x + 6) vii) (x + y + 5) and (2x – 2y – 3)
Answer:
i)-240*a^4*b^3*c^2
ii)-15*x^2*y^2+3*x^3*y^2
iii)x^4*y^3*z^2-x^2*y^3*z^3+x^3*y^2*z^3
iv)p*q+6*q-7*p-42
v)2*x^3-3*x^2-23*x+42
vii)2*x^2-2*y^2+7*x-12*y-15
Step-by-step explanation:
How many square inches are in 60 square fee
Answer:8640 square inches
Step-by-step explanation:
solve for x, x-6≤3 simplify
Answer:
x≤9
Step-by-step explanation:
x−6≤3
Add 6 to both sides.
x≤3+6
Add 3 and 6 to get 9
x≤9
Answer: x ≤ 9
Step-by-step explanation: When solving an inequality, your goal is the same as it would be if you were solving an equation – to get the variable by itself or isolated on one side of the equals sign.
Since 6 is being subtracted from x, add 6 to both sides of the inequality.
On the left, the -6 +6 cancel out and on the right, 3 + 6 is 9.
So we have x ≤ 9.
Find the slope of the line y = -4x +
9
Simplify your answer and write it as a proper fraction, improper fraction, or integer
Answer:
The slope is - 4Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
From the question the equation of the line is
y = - 4x + 9
Comparing the equation with the general equation of a line above
Slope / m = - 4
Hope this helps you
find the area of a cicle
with Radius 7cm using pie
Answer: 153.94cm
Step-by-step explanation:
Answer:
A = 49 cm ²
Step-by-step explanation:
A = πr²
= 22/7 * 7 *7
= 49 cm²
HELPPp me asap please I'm hopeless
The arithmetic progressions [tex]\{2, 5, 8, 11, \ldots\}[/tex] and[tex]3, 10, 17, 24, \ldots \}[/tex] have some common values. What is the largest value less than 500 that they have in common?
=================================================
Work Shown:
We have two sequences, which we'll call A and B
A = {2,5,8,11,14, 17 ,20,23,26,29,32,35, 38, 41,44,47,50,53,56, 59 ,62...}B = {3,10, 17 ,24,31, 38 ,45,52, 59 , 66...}Both sequences are arithmetic. The first sequence starts at 2, and increases by 3 each time. Sequence B starts at 3 and increases by 7 each time.
The terms in bold are what the two sequences have in common.
-----------
It turns out that the bold terms follow an arithmetic sequence of their own.
The sequence {17, 38, 59, ...} is arithmetic.
Call this sequence C. This sequence starts at 17 and increases by 21 each time. The nth term for sequence C is
C(n) = a+d(n-1)
C(n) = 17+21(n-1)
C(n) = 17+21n-21
C(n) = 21n-4
Plugging in n = 1 leads to C(n) = 17. Also, plug in n = 2 and you should get C(n) = 38. Plugging in n = 3 leads to C(n) = 59. And so on.
-----------
The question is now "what is the largest term in sequence C such that it is less than 500?".
In other words, we want to find the term C(n) where C(n) < 500 and C(n) is as large as possible.
Use a bit of algebra to get
C(n) < 500
21n - 4 < 500
21n < 500+4
21n < 504
n < 504/21
n < 24
So n must be smaller than 24 to get what we want.
Because n is a natural number (positive whole number), we drop to n = 23 to find that
C(n) = 21n-4
C(23) = 21(23)-4
C(23) = 479
The largest value, less than 500, the two original sequences have in common is 479.
If we didn't have the restriction "less than 500", then there would be no largest value as sequence C goes on forever.
Answer:
467
Step-by-step explanation:
We have two sequences, which we'll call A and B
A = {2,5,8,11,14, 17 ,20,23,26,29,32,35, 38, 41,44,47,50,53,56, 59 ,62...}
B = {3,10, 17 ,24,31, 38 ,45,52, 59 , 66...}
Both sequences are arithmetic. The first sequence starts at 2, and increases by 3 each time. Sequence B starts at 3 and increases by 7 each time.
The terms in bold are what the two sequences have in common.
-----------
It turns out that the bold terms follow an arithmetic sequence of their own.
The sequence {17, 38, 59, ...} is arithmetic.
Call this sequence C. This sequence starts at 17 and increases by 21 each time. The nth term for sequence C is
C(n) = a+d(n-1)
C(n) = 17+21(n-1)
C(n) = 17+21n-21
C(n) = 21n-4
Plugging in n = 1 leads to C(n) = 17. Also, plug in n = 2 and you should get C(n) = 38. Plugging in n = 3 leads to C(n) = 59. And so on.
-----------
The question is now "what is the largest term in sequence C such that it is less than 500?".
In other words, we want to find the term C(n) where C(n) < 500 and C(n) is as large as possible.
Use a bit of algebra to get
C(n) < 500
21n - 4 < 500
21n < 500+4
21n < 504
n < 504/21
n < 24
So n must be smaller than 24 to get what we want.
Because n is a natural number (positive whole number), we drop to n = 23 to find that
C(n) = 21n-4
C(23) = 21(23)-4
C(23) = 479
The largest value, less than 500, the two original sequences have in common is 479.
If we didn't have the restriction "less than 500", then there would be no largest value as sequence C goes on forever.We have two sequences, which we'll call A and B
A = {2,5,8,11,14, 17 ,20,23,26,29,32,35, 38, 41,44,47,50,53,56, 59 ,62...}
B = {3,10, 17 ,24,31, 38 ,45,52, 59 , 66...}
Both sequences are arithmetic. The first sequence starts at 2, and increases by 3 each time. Sequence B starts at 3 and increases by 7 each time.
The terms in bold are what the two sequences have in common.
-----------
It turns out that the bold terms follow an arithmetic sequence of their own.
The sequence {17, 38, 59, ...} is arithmetic.
Call this sequence C. This sequence starts at 17 and increases by 21 each time. The nth term for sequence C is
C(n) = a+d(n-1)
C(n) = 17+21(n-1)
C(n) = 17+21n-21
C(n) = 21n-4
Plugging in n = 1 leads to C(n) = 17. Also, plug in n = 2 and you should get C(n) = 38. Plugging in n = 3 leads to C(n) = 59. And so on.
-----------
The question is now "what is the largest term in sequence C such that it is less than 500?".
In other words, we want to find the term C(n) where C(n) < 500 and C(n) is as large as possible.
Use a bit of algebra to get
C(n) < 500
21n - 4 < 500
21n < 500+4
21n < 504
n < 504/21
n < 24
So n must be smaller than 24 to get what we want.
Because n is a natural number (positive whole number), we drop to n = 23 to find that
C(n) = 21n-4
C(23) = 21(23)-4
C(23) = 479
The largest value, less than 500, the two original sequences have in common is 479.
If we didn't have the restriction "less than 500", then there would be no largest value as sequence C goes on forever.
Solve for y.
2y^2 - 10y+44 =(y-7)^2
If there is more than one solution, separate them with commas.
Answer:
y = -5, 1
Step-by-step explanation:
2y² - 10y + 44 = (y - 7)²
expand (y - 7)²
(y - 7)² = y² - 14y + 49
move it to the left
(2y² - 10y + 44) - (y² - 14y + 49) = 0
distribute the (-)
2y² - 10 y + 44 - y² + 14y - 49 = 0
combine like terms
y² - 4y -5
factor with factoring X
y² + 5y - y - 5 = 0
factor by grouping ↓
factor out a y from first half of equation
y(y + 5) - y - 5 = 0
factor out a (-) from second half of equation
y(y +5) - (y + 5) = 0
(y +5)(y - 1) = 0
y = -5, 1
Make the following conversion. 0.00432 km = _____ mm 0.00000000432 0.0000000432 432 4,320
Answer:
0.00432 km = 4320 mm
Step-by-step explanation:
There are 1000000 millimeters in a kilometer. To convert kilometers to millimeters, multiply the kilometer value by 1000000.
Quick check 0.00432 * 1000000 = 4320 mm
Answer:
4320
Step-by-step explanation:
What would be the equation for "two times x subtracted by x squared"?
Answer:
[tex]\Huge \boxed{-x^2+2x}[/tex]
Step-by-step explanation:
2 times x subtracted by x².
[tex]\Rightarrow 2 \cdot x-x^2[/tex]
[tex]\Rightarrow 2x-x^2[/tex]
Rearranging the expression.
[tex]\Rightarrow -x^2+2x[/tex]
Answer:
2x -x^2
Step-by-step explanation:
[tex]2(x) - x^2\\= 2x-x^2[/tex]
5. If the area of a rectangular field is 21x - 7x and one of its sides is 7x, what is its other side?
Answer:
21x-7/7x
=7x(3x-1)/7= 3x-1
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
To find the area of a rectangle, you must multiply its length with its width.
We know that either the length or it's width is 7x.
To find the length of the other side, we essentially have to figure out what 7x you to be multiplied by to get 14x (21x-7x can be simplified to that by combining like terms)
To reverse multiplication, we can use division.
Let's set up the following expression:
14x/7x
2x/x
2
The length of its other side is 2.
Which term describes any number that cannot be expressed as a simple fraction?
real number
whole number
rational number
irrational number
Answer:
rational numbers are the number which can not expressed into simpler fraction
To solve -8p = 48, which of the following could you do to both sides of the equation? A. add -8 B. subtract -8 C. multiply by -8 D. divide by -8
Answer:
D. divide by -8
Step-by-step explanation:
true or false: the negative square root is known as the principal square root
Answer:
true
Step-by-step explanation:
Answer:
False, if you get a negitive it would be - square root symbol 9
This is just an example
Step-by-step explanation: