Answer:
[tex]AB = 6[/tex] [tex]BC = 8[/tex] [tex]AC = 10[/tex]
Step-by-step explanation:
The picture of the triangle is missing.
Given
[tex]AC = x + 4[/tex]
[tex]BC = x + 2[/tex]
[tex]AB = x[/tex]
Required
Find x
When Pythagoras theorem is applied, we have:
[tex](AC)^2 = (BC)^2 + (AB)^2[/tex]
This is so, because AC is the hypotenuse
So, we have:
[tex](x+4)^2 = (x+2)^2 + x^2[/tex]
Open brackets
[tex]x^2 + 4x + 4x + 16 = x^2+2x + 2x + 4 + x^2[/tex]
[tex]x^2 + 8x + 16 = x^2+4x + 4 + x^2[/tex]
Collect Like Terms
[tex]x^2 -x^2 - x^2 + 8x -4x + 16 - 4 = 0[/tex]
[tex]- x^2 + 4x + 12 = 0[/tex]
Expand:
[tex]- x^2 + 6x -2x+ 12 = 0[/tex]
Factorize:
[tex]-x(x -6) -2(x- 6) = 0[/tex]
[tex](-x -2)(x- 6) = 0[/tex]
Split
[tex]-x - 2 = 0[/tex] or [tex]x - 6 = 0[/tex]
[tex]-x = 2[/tex] or [tex]x = 6[/tex]
[tex]x =-2[/tex] or [tex]x = 6[/tex]
Because [tex]BC = x + 2[/tex] and [tex]AB = x[/tex]
[tex]x =-2[/tex] can not be considered.
Hence:
[tex]x = 6[/tex]
Substitute 6 for x in
[tex]AC = x + 4[/tex]
[tex]BC = x + 2[/tex]
[tex]AB = x[/tex]
[tex]AC = 6 + 4[/tex]
[tex]AC = 10[/tex]
[tex]BC = 6 + 2[/tex]
[tex]BC = 8[/tex]
[tex]AB = 6[/tex]
Find the sum of the following series. Round to the nearest hundredth if necessary. 4 + 24 + 144 +... + 6718464
Answer:
Your answer is 264
Step-by-step explanation:
A manufacturing company has 1000 employees. 10% of the employees earn less than
Rs.500 per day, 200 earn between Rs.500 and Rs.999; 30% earn between Rs.1,000
and Rs.1,499; 250 employees earn between Rs.1,500 and 1,999 and rest earn Rs.2,000
and above. Calculate the suitable average wage. Give the reason for your choice of
average.
Answer:
heehhe
Step-by-step explanation:
vwhehehhehdhdhd
I messed up somewhere I think ugh
Answer:
¯\_(ツ)_/¯
Step-by-step explanation:
Answer:
Step-by-step explanation:
n≤-2
n≥-4
or -4≤n
combining
-4≤n≤-2
Need help with this
What inequality is true
Answer:
I'm pretty sure it c because pie is 3.14 and that time 3 would be a little over 9
On average, 3 percent of U.S. travelers do not show up for their flight. Suppose this probability is independent and constant across travelers. For a given flight from Seattle to San Francisco, an airline accepted a total of 103 reservations while the plane capacity is 100 seats. What is the probability that the airline will have to bump at least one passenger
Answer:
.3988 .
Step-by-step explanation:
We shall use Binomial distribution formula in the problem .
n = 103
The probability that a passenger will not miss the flight and show up = .97
The probability that a passenger will miss the flight = .03
n = 103 ,
probability of showing up 101 , 102 and 103 passengers so that at least 1 passenger will return or bump .
= 103C₁₀₁ .97¹⁰¹ .03² + 103C₁₀₂ .97¹⁰² .03+ 103C₁₀₃ .97¹⁰³
103 x 102 /2 .97¹⁰¹ .03² + 103 .97¹⁰² .03 + .97¹⁰³
= 5253 x .046 x .0009 + 103 x .00134 + .0434
= .2174 + .1380 + .0434
= .3988 .
The probability that the airline will have to bump at least one passenger is; 0.3988
Binomial probability distributionProbability that the travelers did not show up for the flight is; q = 3% = 0.03
Probability that they will show up for the flight is; p = 97% = 0.97
The formula for binomial probability is;P(X = r) = nCr × p^(r) × q^(n - r)
Thus, the probability that the airline will have to bump at least one passenger is;
(103C₁₀₁ × 0.97¹⁰¹ × 0.03²) + (103C₁₀₂ × 97¹⁰² × 0.03) + (103C₁₀₃ × 0.97¹⁰³ × 0.03⁰)
>> 0.2174 + 0.1380 + 0.0434
>> 0.3988
Read more on binomial probability at; https://brainly.com/question/15246027
Please help this is for another person who doesn’t know the answer :)
Answer:
The answer is,
[tex]x = \frac{4 + \sqrt{19} }{6}, \frac{4 - \sqrt{19} }{3} [/tex]
Scarlett is going to invest in an account paying an interest rate of 4% compounded daily. How much would Scarlett need to invest, to the nearest ten dollars, for the value of the account to reach $54,000 in 8 years?
Answer: 39210
Step-by-step explanation:
Find the intercepts of
y= 2x -4
Answer:
y intercept is -4
x intercept is 2
Use the theorem part 1
Answer:
(a)
Step-by-step explanation:
The base angles theorem states that if 2 sides of a triangle are congruent, that is an isosceles triangle then the angles opposite these sides are equal.
Answer:
a) Base Angle TheoremStep-by-step explanation:
The Base Angle Theorem states that in an isosceles triangle, the angles opposite the congruent sides are congruent.
Find the 8th term in the following sequence.
32, 16, 8, 4, ..
02
O 114
O 1/2
O 1
Find two consecutive whole numbers that 34 lies between.
Answer:
34 lies in between 5 and 6
5^2=25, 6^2=36, so sqrt(34) lies between 5 and 6
£5-2 x 0.81=
Answer for school and explanation please. would be great help
Answer:
3.38
Step-by-step explanation:
first do the multiplication
2×0.81
= 1.62
then the subtraction
5- 1.62= 3.38
To find the quotient of 4-5 multiply 4 by
A. 1/5
B. 1/4
C. 4
D. 5
Answer:
5
Step-by-step explanation:
when dividing number by fractions,we can simply multiply the number by the reciprocal of the decimal
so,4÷1/5=4 ×(reciprocal of 1/5 )
A reciprocal of a number is the same no.written under 1 aka.1divided by that number which simply is flipping
numerator and denominator .
reciprocal of 1/5 is 5/1 =5
so 4÷1/5 = 4×5
so answer is 5
hope this is helpful
Apply the distributive property to create an equivalent expression,
1/3(3j+ 6)
Answer:
j + 2
Step-by-step explanation:
1/3(3j) + 1/3(6)
1/3(3j) = j
1/3(6) = 2
Answer: j + 2
Please help (8th grade math)
Answer:
-1
Step-by-step explanation:
since the line increases by 1 along the x axis and goes down by 1 on the y axis, you can do rise over run, which gives you:
1 / -1 , which ultimately gives you -1.
I need help plz I will mark brainliest
What the area of the large square?
Answer:
[tex]x^{2}[/tex]
Step-by-step explanation:
x · x =[tex]x^{2}[/tex]
fill in the blanks _ + _ = 10.5
Answer:
there can be many answerrrs I guess
.
Step-by-step explanation:
5.25+5.25=10.5
2.5+8=10.5
have a great day :)
Which expressions are equivalent to 4b+12?
Answer:
4(b+3)
Step-by-step explanation:
can't really explain it sorry
it’s multiple choice please help i’ll mark brainliest !
THe answer is the third one
Answer:
C?
Step-by-step explanation:
A baseball pitcher won 60% of his games. How many did he win if he pitched 35 games?
Answer:
21 games
Step-by-step explanation:
Multiply the number of games by the percentage.
35 · 0.60 = 21
Duncan and his family are season ticket holders for their favorite baseball team. Last year, the cost of season tickets was $2,730. This year, the cost is $3,333.80. What was the percent of increase in the cost of season tickets?
Round your answer to the nearest tenth of a percent.
Answer:
10%
Step-by-step explanation:
To find the answer we need to know what percentage of $1030 is $927 and to do this we can multiply 927 by 100 and divide by 1030.
(927(100))/1030
92700/1030
90
so now that we know $927 is 90% of $1030 we can subtract 90 from 100 and it'll give us the percentage decrease. Which is 10%.
Hope this helps!!!!!!!!!!!!
///////////////////////////////////////////////////////////////////////////////////////////////////
Eli burned 1449 calories running a half marathon. If he finished in 2 hours and 6 minutes.ow many calories did he burn per minute
Which type of heat transfer causes air movement between land and ocean?
Answer:
Energy is transferred between the Earth's surface and the atmosphere in a variety of ways, including radiation, conduction, and convection. Conduction is one of the three main ways that heat energy moves from place to place.
Step-by-step explanation:
Help plz:)))I’ll mark u Brainliest
Answer:
22-18-25,
19-24-30,
7-24-25
Step-by-step explanation:
In a triangle with side lengths [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex], any two sides must have a sum larger than the third.
Using this rule, the possible side lengths out of these choices that could form a triangle are:
22-18-25,
19-24-30,
7-24-25
Please help!!!!!!!!!!
Answer: angle 1 = 51, angle 2 = 18, angle 3 = 123, angle 4 = 39
Step-by-step explanation:
72+57=129 180-129= 51 degrees for 1
90-72= 18 degrees for 2
180-57= 123 degrees for 3
123+18=141 180-141= 39 degrees for angle 4
What is the result when the number 52 is decreased by 50%?
Answer: You get 26, If this wasn't what you were looking for let me know! :)
Step-by-step explanation:
help me.... this is do in 13 min
Answer:
d
Step-by-step explanation:
What is the diameter of X?
12 cm
4 cm
8 cm
2 cm
Answer:
diameter =2xradius
diameter=2x4
diameter =8cm
Answer:8cm
Step-by-step explanation: