5 cm or 29 cm
Step-by-step explanation:
Let x length is cut off from each measurements.
Thus, the new measurements would be: 20 - x, 41 - x, 44 - x, which forms the sides of a right triangle.
Here, (44 - x) will be hypotenuse and (20 - x) and (41 - x) will be perpendicular legs of the triangle.
Therefore, by Pythagoras theorem:
[tex] {(41 - x)}^{2} + {(20 - x)}^{2} = {(44 - x)}^{2} \\ \\ \therefore \: {(41)}^{2} - 82x + {x}^{2} + {(20)}^{2} - 40x + {x}^{2} \\ = {(44)}^{2} - 88x + {x}^{2} \\ \\ \therefore \: 1681 - 122x + 2 {x}^{2} + 400 \\ = 1936 - 88x + {x}^{2} \\ \\ \therefore \: 2081 - 122x + {x}^{2} = 1936 - 88x \\ \\ \therefore \: {x}^{2} - 122x + 88x + 2081 - 1936 = 0 \\ \\ \therefore \: {x}^{2} - 34x + 145 = 0 \\ \\ \therefore \: {x}^{2} - 29x - 5x+ 145 = 0 \\ \\ \therefore \: x(x - 29) - 5(x - 29) = 0 \\ (x - 5)(x - 29) = 0 \\ x - 5 = 0 \: or \: x - 29 = 0 \\ \\ \therefore \: x = 5, \: 29[/tex]
So, the length that is cut off will be either 5 cm or 29 cm.
A Triangular Park ABC has sides 120 m, 80m and 50m. a gardener has to put a fence all around it and also plant grass inside. How much area does she need to plant? Find the cost of fencing it with barbed wire at the rate of of Rs. 20 per metre leaving a space 3m wide for a gate on one side?
The perimeter = sum of all sides
= 120 + 80 + 50
= 250
So 250 - 3
247
Left space for gate
Now cost of fencing = Rs 20/per meter
= 247 × 20
= Rs 4,940
Now the area of the triangular park can be found using heron's formula
S = (a+b+c)/2
S = (120+80+50)/2
S = 250/2
S = 125
Now
Herons formula = √s(s-a)(s-b)(s-c)
√125(125-120)(125-80)(120-50)
√125(5)(45)(70)
√5×5×5×5×5×3×3×5×14
After Making pairs
5×5×5×3√14
375√14
Therefore 375√14m is the area of the triangular park
Must click thanks and mark brainliest
$\sf\underline\bold{Answer:}$
$\sf\small\underline{\underline{Area\: planted\: by\: the\: gardener : 1452.36m^2}}$$\sf\small\underline{\underline{The\:cost\:of\:fencing\:the\:park:Rs.4940}}$$\space$
$\sf\underline\bold{Step-by-Step:}$
$\space$
$\sf\bold{Given(In \:the\:Q):}$
Sides of the triangular park are 120m,80m and 50m.$\space$
$\sf\bold{To \: find:}$
How much area of the park does she need to plant?The cost of fencing the park ?$\space$
$\sf\small{☆Area\:to\:be\:planted=Area \: of \: ∆ABC}$
$\space$
$\sf\underline\bold{Calculating\:area\:of\:∆ABC:}$
$\space$
Use heron's formula to find the area of the triangle.
$\space$
$\mapsto$ $\sf\small{Heron's\:formula=}$
[tex]\sf\sqrt{s(s-a)(s-b)(s-c)}[/tex]
$\sf{Where\:s=semi\:perimeter}$$\sf{a,b,c\: = side\:of\:the\:∆}$$\sf\small{Here\:a=120,b=80 \:and\: c=50}$$\space$
$\sf\bold{Now,find\:semi\:parameter:-}$
$\sf\small{Perimeter\:of\:the\:∆=120+80+50=250}$
$\sf\small{Semi-Perimeter:}$ $\sf\dfrac{250}{2}$ $\sf\small{=125m}$
$\space$
$\sf\small{Substitute \: the\:values\:in\:heron's\:formula:}$
$\sf{Area\:of\:the\:∆:-}$
$\mapsto$ [tex]\sf\sqrt{125(125-120)(125-80)(125-50)}[/tex]
$\space$
$\mapsto$ $\sf\sqrt{125\times(5)\times(45)\times(75)}$
$\space$
$\mapsto$ $\sf\small\sqrt{2109375}$ $\sf\small{=375}$ $\sf\small\sqrt{15}$
$\space$
$\longmapsto$ $\sf\underline\bold\purple{1452.56m^2}$
______________________________
$\sf\underline\bold{Now,find\:the\:cost\:of\:fencing:}$
$\sf{Cost\:of\:fencing-}$
$\sf{Rate = Rs.20 per \:meter}$ $\sf{Left\:space=3m}$$\space$
$\sf\underline{Hence,the\:gardener\:has\:to\:fence:}$
$\sf{= 250-3=247m.}$$\space$
So,total cost of fencing at the rate of Rs.20 per m:-
$\sf\underline\bold\purple{=247\times20=4940}$___________________________________
2 square5 + 5 square5
Answer:
=2^5+5^5
=32+3125
=3157
What is the area of a circle with a diameter of 20 inches if
[tex]\pi[/tex]
=3.1415
$\sf\underline\bold\blue{Information\:given\:in\:the\:question:}$
π =[tex]\sf{ 3.1415}[/tex]$\sf{Diameter = 20inches}$$\space$
$\sf\underline\bold\blue{What\:we\:have\:to\:find?}$
$\sf{Area\:of\:the\:circle.}$$\space$
$\sf\underline\bold\blue{Answer:}$
$\sf\small{Area\:of\:the\:circle\:is : 314.15}$$\space$
$\sf\underline\bold\blue{Calculations:}$
Here we have the value of the circle's diameter that is 20inches. So, first we have to calculate the radius of the circle using the formula :
$\mapsto$ $\sf\bold{Radius=}$ $\sf\dfrac{Diameter}{2}$
$\space$
$\sf\underline\bold\blue{Calculating\:the\:required\:values:}$
$\mapsto$ $\sf\bold{Radius=}$ $\sf\dfrac{20}{2}$
$\sf{Convert \: to \: the\:lowest\:term(Divide),}$
$\mapsto$ $\sf\underline\bold{Radius=10}$
☆Now we know the value of the radius . So now let's calculate the area of the circle.
$\space$
$\sf\bold{Area\:of\:circle:}$ π$\sf{ r \: ^{2} }$
$\sf\bold{Evaluating \: the\:required\:values:}$
$\sf\bold{Area\:of\:circle=3.1415(10)^2}$
$\space$
$\sf\bold{Area\:of\:the\:circle=3.1415\times10\times10}$
$\sf\bold{Now,}$
$\sf\bold{Area\:of\:the\:circle:3.1415\times100}$
$\space$
$\sf\underline\bold\green{Thus,Area\:of\:the\:circle\: is \: 314.15}$
____________________________
Help me! thank you so much
Answer:
Step-by-step explanation:
[tex]\frac{sinxcos^3x-cos xsin^3x}{cos^42x-sin^42x} \\=\frac{sin x cos x(cos^2x-sin ^2 x)}{(cis^2 2x+sin^2 2x)(cos^2 2x-sin ^22x)} \\=\frac{2sin x cos x cos 2x}{2(1)(cos 4x)} \\=\frac{sin 2x cos 2x}{2 cos 4x} \\=\frac{2 sin 2x cos 2x}{4 cos 4x} \\=\frac{sin 4x}{4 cos 4x} \\=\frac{1}{4} tan 4x[/tex]
pleeaseeee help me !!!
Answer 3. -7.5 is located to the left of 6.5 on a number line oriented from left to right.
Which table shows a function that is increasing only over the interval (–2, 1), and nowhere else?
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 6, negative 3, negative 1, 1, 3, 6.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 2, negative 4, negative 1, 1, 4, 3.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 3, negative 5, negative 7, negative 6, 1, negative 1.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries 5, 7, 1, 0, negative 4, negative 2.
Answer:
the answer is c
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
What is the y-intercept of the line whose equation is y=−3x ?
Answer:
y=mx+b
b is the y intercept
b=0, so 0 is the y intercept
Step-by-step explanation:
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
You can visualize data sets using ______________.
A. dot charts
B. dotgrams
C. dot graphs
D. dot plots
Answer:
Adrenaline: A stress hormone produced within the adrenal gland that quickens the heart beat, strengthens the force of the heart's contraction, and opens up the bronchioles in the lungs, among other effects. The secretion of adrenaline is part of the human 'fight or flight' response to fear, panic, or perceived threat.
Step-by-step explanation:
help lol i forgot everything of the summer time
fill in the table using this function rule
Answer:
hope it help you
Step-by-step explanation:
mark me brailiest answer
Solve the following equation for b. Be sure to take into account whether a letter is capitalized or not.
t+1/2b=Y
Answer:
b = 2(Y - t)Step-by-step explanation:
Given:
t + 1/2b = YIsolate b:
1/2b = Y - tFind b:
b = 2(Y - t)[tex]\\ \sf\longmapsto t+\dfrac{1}{2}b=Y[/tex]
take t right side[tex]\\ \sf\longmapsto \dfrac{1}{2}b=Y-t[/tex]
[tex]\\ \sf\longmapsto \dfrac{b}{2}=Y-t[/tex]
[tex]\\ \sf\longmapsto b=2(Y-t)[/tex]
[tex]\\ \sf\longmapsto b=2Y-2t[/tex]
What is the Compound interest on Rs.1000 at the rate of 20% p.a. semiannually for 1 year and 10 months?
A. Rs. 420.31
B. Rs. 400.29
C. Rs. 419.73
D. Rs. 409.13
Answer:
420.31
Step-by-step explanation:
A
.Rs.420.31
20ejjdj
Answer:
I think A rs 420.31 is right answet
3(x-5)=5x-(3-x) solve for x
Answer:
x = -4
Step-by-step explanation:
[tex]3(x-5)=5x-(3-x)\\\\3x-15=5x-3+x\\\\3x-15=6x-3\\\\-15=3x-3\\\\-12=3x\\\\-4=x[/tex]
Step-by-step explanation:
[tex]3(x - 5) = 5x - (3 - x) \\ 3x - 15 = 5x - 3 + x \\ 3x - 5x - x = - 3 + 15 \\ - 3x = 12 \\ x = \frac{12}{ - 3} \\ x = - 4[/tex]
I hope it helped U
stay safe stay happy
Solve the inequality 2x – 22 < -8.
2x - 22 < -8
Add 22 to both sides
2x < 14
Divide both sides by 2
X < 7
Answer:
[tex]2x-22<-8[/tex]
Add 22 to both sides
[tex]2x-22+22<-8+22[/tex]
[tex]2x<14[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}<\frac{14}{2}[/tex]
[tex]x<7[/tex]
OAmalOHopeO
A line of best fit predicts that when x equals 28, y will equal 27.255, but y actually equals 26. What is the residual in this case?
A. 0.745
B. -0.745
C. -1.255
D. 1.255
Answer:
C) -1.255
Step-by-step explanation:
We are tasked to solve for the residual value given that when x equals 29, y will be equals to 27.255. But, when it is tested, y actual value is 26. The formula in solving residual is shown below:
Residual value = Observed value - predicted value
Residual value = 26 - 27.255
Residual values = -1.255
The answer is -1.255 for residual value.
Find the equation of the line that is parallel
to the line y = -5x - 9 and passes
through the point (-4,-9) Write the
equation in slope-intercept form.
A parallel line would contain the same slope and have a different y-intercept.
Using the slope of the original line you would start with:
Y = -5x + b, where b is the new y-intercept.
Using the given point replace x and y and solve for b:
-9 = -5(-4) + b
Simplify:
-9 = 20 + b
Subtract 20 from both sides
-29 = b
Now replace b in the equation to get:
Y = -5x -29
if (-2/15)+(-13/5)=(-13/5)+a/b then a/b is equal to
The choose C. –2/15
(-2/15) +(-13/5) =(-13/5) +a/b
a/b = (-2/15)+(-13/5) - (-13/5)
a/b = (-2/15) - ( 39/15) +(39/15)
a/b = –2/15
I hope I helped you ^_^
Answer: option 3: a/b = (-2/15)
Step-by-step explanation:
See here when we solve this
(-2/15)+(-13/5) = (-13/5)+a/b
(-2/15) = (-13/5)+a/b-(-3/15)
(-2/15) = a/b
please click thanks and mark brainliest if you like :)
i neeeeeeed help :)))))
4. a) x2 + xy2 + y 4
Answer:
x2 + xy2 + y 4=（x+y^2)^2-xy^2
Step-by-step explanation:
Helpppp pleaseeee !!!!!!
Answer:
149 inches squared
Step-by-step explanation:
top rectangle: 25 * 7 = 175
second rectangle: 8 * (25 - 17) = 8^2 = 64
triangle in bottom right: 1/2 * (13 - 8) * (15 - 11) = 10
175 + 64 + 10 = 149 sq in
hopefully got this right!
find the missing side. Round it the nearest tenth.
Answer: x= 11√3= 19.0525 = 19.1
Step-by-step explanation:
Let the reference angle be 30
so
cos 30 = b/h
√3/2 = x/22
or, 22√3 = 2x
or. x = (22√3)/2
so, x = 11√3
Answer:
x = 19.1 cm
Step-by-step explanation:
→ Find the name of the side you are not given
Opposite
→ Find a formula without opposite in it
Cos = Adjacent ÷ Hypotenuse
→ Rearrange to make adjacent the subject
Adjacent = Cos × Hypotenuse
→ Substitute in the values
Adjacent = Cos ( 30 ) × 22
→ Simplify
Adjacent = 19.1
A bag contains 5 pieces of string. The lengths of the pieces of string are 1 inch, 3 inches, 5 inches, 7 inches, and 9 inches. Suppose you pick three pieces of string from the bag at random and all pieces are equally likely to be chosen. What is the probability you can form a triangle with the three pieces
Answer:
30%
Step-by-step explanation:
There are 10 possible combinations of sticks that can be drawn from a group of 5 strings
5C3 = (5*4*3)/(3*2) = 10 combinations, which are
1,3,5 ; 1,3,7 ; 1,3,9 ; 1,5,7 ; 1,5,9 ; 1,7,9 ; 3,5,7 ; 3,5,9 ; 3,7,9 ; 5,7,9
to make a triangle, the sum of any two sides must be greater than the third side and if you look at the possible combinations there are only three cases where that is true
so the probability for drawing three sticks that would make a triangle is 3/10 or 30%
What is the mathematical expression for seven less then a number
There is a proportional relationship between any length measured in centimeters and
the same length measured in millimeters. There are two ways of thinking about this proportional relationship. If you know the length of something in centimeters, you can calculate it’s length in millimeters
The constant of proportionality is 10.
What is constant of proportionality?The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. The constant of proportionality is the fixed or constant pace at which ratios rise and decrease. Two ratios are said to be directly proportional if they share the same constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality. The constant of proportionality is the name given to this consistent pace of growth or decline.
a)
since , 1 cm = 10mm
9cm = 90mm
12.5cm = 125mm
50cm = 500mm
88.49cm = 884.9mm
b)
The constant of proportionality is 10.
To know more about constant of proportionality please visit:
https://brainly.in/question/15971683?
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What is the decimal equivalent of 9.7x10^5
A. 0.000097
B. 970,000
C. 9,700,000
D. 97,000,000
Answer:
B. 970,000
Step-by-step explanation:
Move the decimal 5 places to the right, since the exponent is a positive 5.
9.7 x 10⁵ = 970,000.
If it is a negative exponent, you would have to move the decimal to the left.
-5 (k+4) > 2 - (3k+6)
I believe that the answer you are looking for is -8>k, or k<-8.
Solution/Explanation:
First, writing out the inequality,
-5(k+4) > 2-(3k+6)
Next, using the Distributive Property on both sides,
-5k-20 > 2-3k-6
Simplifying the right side just a little bit more,
-5k-20 > -3k-4
Adding 5k to both sides,
-5k+5k-20 > -3k+5k-4
-20 > 2k-4
Now, adding 4 to both sides,
-20+4 > 2k-4+4
-16 > 2k
Finally, dividing 2 from both sides,
So, therefore, the final answer is -8>k, or k<-8.
I hope this helped answer your question. Enjoy your day, and take care!
If 2 fligs make a flog and 3 flogs make a flug, how many fligs in 12 flugs?
Answer:
There are 72 fligs in 12 flugs
(x+4)^2-(x+2)(x-2)=20
⇒x²+ 4² - x²+ 2x - 2x + 4 = 20
⇒ x² - x² + 2x - 2x + 4² + 4 = 20
⇒ 16 + 4 = 20
⇒ 20 = 20
RHS = LHS hence proved
Answered by Gauthmath must click thanks and mark brainliest
Answer:
x = 0
Step-by-step explanation:
(a + b)² = a² +2ab + b²
(a +b)(a -b)= a² - b²
(x + 4)² - (x + 2 )(x - 2) = 20
x² + 2*4 *x + 4² - [x² - 2²] = 20
x² + 8x + 16 - [x² - 4] = 20
x² + 8x + 16 - x² + 4 = 20 {(-1) is distributed x² and (-4)²}
x² - x² + 8x + 16 + 4 = 20 {Combine like terms}
8x + 20 = 20
8x = 20 - 20
8x = 0
x = 0
5a + 18 < −27 pre algibra
Answer:
X < -9
Step-by-step explanation:
5a +18 < -27
5a < -27 -18
5a < - 45
5a/5 < - 45/5
a < - 9
Answred by Gauthmath
Answer: -9
Step-by-step explanation:
5a+18 < -27
5a< -27-18
5a<-45
a< -45/5
a< -9
If give 7 billions for 7 millions people. What is total?
Answer:
this is a very big number
Step-by-step explanation:
(7000000000)⁷⁰⁰⁰⁰⁰⁰
Find he probability of no more than 35 defective CD's in a batch of 80 CD's if the probablility of any one CD being defective is 0.1.
Answer:
0.999999
Step-by-step explanation:
Given that :
Probability of CD being defective, p = 0.1
q = 1 - p = 1 - 0.1 = 0.9
Total number of CD's = number of trials = 80
Probability, that no more than 35 CD's are defective ;
The question satisfied the requirements for a binomial probability problem ;
Recall :
P(x = x) = nCx * p^x * q^(n-x)
Hence,
P(x ≤ 35) = 80C35 * 0.1^35 * 0.9^(45)
Using calculator to save computation time :
P(x ≤ 35) = 0.999999
