ABC is an isosceles triangle. Solve for x. In your final answer, include all of the necessary calculations. You may include a sketch as part of your calculations.
Answers
Answer:
x= 105
Step-by-step explanation:
Let the unknown angle at the base be y. We know the base angles of an isosceles triangle are the same
The sum of the angles of the triangles are
30 + y +y = 180
30 + 2y = 180
2y = 180-30
2y = 150
y = 75
We know that x+y = 180 since it forms a straight line
x+75 =180
x = 180-75
x = 105
Answer:The abc conjecture It is stated in terms of three positive integers, a, b and c (hence the name) that are relatively prime and satisfy a + b = c. So a conjecture is like an educated guess.
Related Questions
Which operation should you perform last in the expression 3^2 + 2?
Answers
Answer:
8
Step-by-step explanation:
Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded.
Maximize p=x+ysubject to
x+3y≤4
3x+y≤4
x≤0
y≤0
Answers
Answer:
P = 4
Step-by-step explanation:
The LP is:
Maximize p = x+y
x+3y≤4
3x+y≤4
x ≥ 0
y ≥ 0
Solving graphically using the geogebra graphing calculator which is attached, the points are A(0, 4), B(0, 1.33), C(1.33, 0), D(4, 0) and E(1, 1)
The maximum objective is:
For point A(0, 4): Maximize p = x + y = 0 + 4 = 4
For point B(0, 1.33): Maximize p = x + y = 0 + 1.33 = 1.33
For point C(1.33, 0): Maximize p = x + y = 1.33 + 0 = 1.33
For point D(4, 0): Maximize p = x + y = 4 + 0 = 4
For point E(1, 1): Maximize p = x + y = 1 + 1 = 2
Hence, the maximum point is at A(0, 4) which gives P = 4
When the system is executed, the system crashes with probability 0.05 if only Module A fails. The system crashes with probability 0.12 if only Module B fails. The system crashes with probability 0.60 if both Module A and Module B fail. The system crashes with probability 0.01 if neither fails. (a) When the system is executed, what is the probability the system will crash
Answers
Answer:
P (system will crash) = 0.101528
P(A and B jails / System crash) = 0.5390
Step-by-step explanation:
The complete question is as stated below
"Suppose a system has two modules, A and B , that function independently. Module A fails with probability 0.24 and Module B fails with probability 0.38 ,when the system is executed. When the system is executed, the system crashes with probability 0.05 if only Module A fails. The system crashes with probability 0.12 if only Module B fails. The system crashes with probability 0.60 if both Module A and Module B fail. The system crashes with probability 0.01 if neither fails.
(a) When the system is executed, what is the probability the system will crash?
(b) If the system crashes, what is the probability that both modules A and B crashed?"
Solution
P(A fails) = 0.24
P(B fails) = 0.38
P(A ∩ B) = P (A) * P (B) = 0.24 * 0.38 = 0.0912
P(only A fails) = P(A) - P(A ∩ B) =0.24 - 0.24*0.38 = 0.1488
P(only A fails) =P(B) - P(B ∩ A) = 0.38 - 0.24*0.38 = 0.2888
P(Both fails) = P(A) * P(B) = 0.24*0.38 = 0.0912
P(Neither fails) = P(A) * P(B) =1-(0.24+0.38-0.0912) = 0.4712
P(Add to 1)
a) P (system will crash) = 0.1488*0.05+0.2888*0.12+0.0912*0.6+0.4712*0.01 P (system will crash) = 0.101528
b) P(A and B jails / System crash) = 0.0912*0.6 / 0.101528
P(A and B jails / System crash) = 0.5390
If C is the part of the circle (x/5)^2 + (y/5)^2 = 1 in the first quadrant, find the following line integral with respect to arc length. integral_c (8x - 3y)ds = _______.
Answers
Convert to polar coordinates, in which the circle's equation becomes
[tex]\left(\dfrac x5\right)^2+\left(\dfrac y5\right)^2=1\implies x^2+y^2=5^2\implies r^2=5^2\implies r=5[/tex]
where [tex]x=5\cos\theta[/tex] and [tex]y=5\sin\theta[/tex], and we get the part of the circle in the first quadrant with [tex]0\le \theta\le\frac\pi2[/tex].
So the integral is
[tex]\displaystyle\int_C(8x-3y)\,\mathrm ds=\int_0^{\frac\pi2}(8x(\theta)-3y(\theta))\sqrt{\left(\dfrac{\mathrm dx}{\mathrm d\theta}\right)^2+\left(\dfrac{\mathrm dy}{\mathrm d\theta}\right)^2}\,\mathrm d\theta[/tex]
[tex]=\displaystyle\int_0^{\frac\pi2}(40\cos\theta-15\sin\theta)\sqrt{25\cos^2\theta+25\sin^2\theta}\,\mathrm d\theta[/tex]
[tex]=\displaystyle25\int_0^{\frac\pi2}(8\cos\theta-3\sin\theta)\,\mathrm d\theta[/tex]
[tex]=25(8\sin\theta+3\cos\theta)\bigg|_0^{\frac\pi2}=200-75=\boxed{125}[/tex]
Line integral involves integrating a function along a curve
The value of the line integral is 125
The equation is given as:
[tex]\mathbf{(\frac{x}{5})^2 + (\frac{y}{5})^2 = 1}[/tex]
Expand
[tex]\mathbf{\frac{x^2}{5^2} + \frac{y^2}{5^2} = 1}[/tex]
Multiply through by 5^2
[tex]\mathbf{x^2 + y^2 = 5^2}[/tex]
The equation of a circle is represented as:
[tex]\mathbf{(x - a)^2 + (y - b)^2 = r^2}[/tex]
So, by comparison
[tex]\mathbf{r^2 = 5^2}[/tex]
[tex]\mathbf{r = 5}[/tex]
Where:
[tex]\mathbf{x = rcos\theta}[/tex]
[tex]\mathbf{y = rsin\theta}[/tex]
So, we have:
[tex]\mathbf{\int_c (8x - 3y)ds}[/tex]
Because it is in the first quadrant (i.e. 0 to pi/2), the integrand becomes
[tex]\mathbf{\int_c (8x - 3y)ds = \int\limits^{\frac{\pi}{2}}_0 (8x - 3y)rd\theta}[/tex]
Convert to polar forms
[tex]\mathbf{\int_c (8x - 3y)ds = \int\limits^{\frac{\pi}{2}}_0 (8x - 3y)\sqrt{x^2 + y^2}d\theta}[/tex]
Substitute [tex]\mathbf{x = rcos\theta}[/tex] and [tex]\mathbf{y = rsin\theta}[/tex]
[tex]\mathbf{\int_c (8x - 3y)ds = \int\limits^{\frac{\pi}{2}}_c (8rcos(\theta) - 3rsin(\theta))\sqrt{(rcos(\theta))^2 + ( rsin(\theta))^2}d\theta}[/tex]
Substitute 5 for r
[tex]\mathbf{\int_c (8x - 3y)ds = \int\limits^{\frac{\pi}{2}}_c (40cos(\theta) - 15sin(\theta))\sqrt{25cos^2\theta + 25sin^2\theta}\ d\theta}[/tex]
Factor out 5
[tex]\mathbf{\int_c (8x - 3y)ds = \int\limits^{\frac{\pi}{2}}_c 5(8cos(\theta) - 3sin(\theta))\sqrt{25cos^2\theta + 25sin^2\theta}\ d\theta}[/tex]
[tex]\mathbf{\int_c (8x - 3y)ds = \int\limits^{\frac{\pi}{2}}_c 5(8cos(\theta) - 3sin(\theta))\sqrt{25(cos^2\theta + sin^2\theta)}\ d\theta}[/tex]
[tex]\mathbf{\int_c (8x - 3y)ds = \int\limits^{\frac{\pi}{2}}_c 5(8cos(\theta) - 3sin(\theta))5\sqrt{(cos^2\theta + sin^2\theta)}\ d\theta}[/tex]
[tex]\mathbf{\int_c (8x - 3y)ds = \int\limits^{\frac{\pi}{2}}_c 25(8cos(\theta) - 3sin(\theta))\sqrt{(cos^2\theta + sin^2\theta)}\ d\theta}[/tex]
[tex]\mathbf{\int_c (8x - 3y)ds =25 \int\limits^{\frac{\pi}{2}}_c (8cos(\theta) - 3sin(\theta))\sqrt{(cos^2\theta + sin^2\theta)}\ d\theta}[/tex]
In trigonometry
[tex]\mathbf{cos^2\theta + sin^2\theta = 1}[/tex]
So, we have:
[tex]\mathbf{\int_c (8x - 3y)ds =25 \int\limits^{\frac{\pi}{2}}_c (8cos(\theta) - 3sin(\theta))\sqrt{1}\ d\theta}[/tex]
[tex]\mathbf{\int_c (8x - 3y)ds =25 \int\limits^{\frac{\pi}{2}}_0 (8cos(\theta) - 3sin(\theta))\ d\theta}[/tex]
Integrate
[tex]\mathbf{\int_c (8x - 3y)ds =25 \times [ (8sin(\theta) + 3cos(\theta))\ } ]|\limits^{\frac{\pi}{2}}_0}[/tex]
Expand
[tex]\mathbf{\int_c (8x - 3y)ds =25 \times ([ 8sin(\frac{\pi}{2}) + 3cos(\frac{\pi}{2})] - ([ (8sin(0) + 3cos(0)])}[/tex]
[tex]\mathbf{\int_c (8x - 3y)ds =25 \times ([ 8\times 1 + 3\times 0)] - ([ (8\times 0 + 3\times 1])}[/tex]
[tex]\mathbf{\int_c (8x - 3y)ds =25 \times ([ 8] - [ 3])}[/tex]
[tex]\mathbf{\int_c (8x - 3y)ds =25 \times 5}[/tex]
[tex]\mathbf{\int_c (8x - 3y)ds =125}[/tex]
Hence, the value of the line integral is 125
Read more about line integrals at:
https://brainly.com/question/16571667
Show work for f(4) = 3x + 2
Answers
=3(4)+2
F(4)=14
The solution of the given function will be F(4)=14
Since we know that Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, it is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable . In physical sciences, functions are indispensable for formulating physical relationships.
We have been given a function as;
F(x)=3x+2
F(4)=3x+2
WE have to substitute the value of x as 4 then we get;
F(4)=3(4)+2
F(4)=14
Therefore, the value of the given function will be as 14.
Learn more about function here:
https://brainly.com/question/2253924
#SPJ6
Who can help me :(??
Answers
Answer:
3rd option
Step-by-step explanation:
7.6, 7.42, square 48, 79%=0.79
Answer:
C
Step-by-step explanation:
To make this easier, simplify all values to rational numbers (simplify from percentages and roots):
79% → 79÷100 → 0.79
√48 ≈ 6.9
Now order from greatest to least (descending):
[tex]7.6,7.42,6.9,0.79[/tex]
Re-insert the given values before simplification:
7.6, 7.42, √48, 79%
The correct answer is option C.
:Done
The perimeter of a rectangle is 92 cm. If the length is 16 cm, how wide is the rectangle?
Answers
Answer:
30cm
Step-by-step explanation:
2w+2L=Perimeter of rectangle
2w+2*16=92
2w+32=92
2w=92-32
2w=60
w=30
check : 16 +16 +30 +30 =92cm
You are going to buy some folders to file
your orders. After doing research, you find
that the most cost-effective price is $7.40
per
box of 100 folders. You have $15 to
spend. How many 100 count boxes can
you buy?
Answers
Which equation represents the data shown in the table below?
x
y
2
5
moll
6
7.
5
8
O A. y = 2x
B. y = x + 3
O C. y = 3x
D. y = x + 1
Answers
Answer:
the answer will be y=2x
Step-by-step explanation:
1+1 lol dats da question
Answers
Answer:
yellow?
Step-by-step explanation:
so you have 1 then add another an get yellow, bam im a genius
Answer:
i think you have to first find the first 50 numbers of pi then x that my 96,1000 then you should turn on then off the works to but if you have a switch it wont work so after that you have to tell who ever you live with that they need to keep talking and never stop being them and that they are nice person then you get the answer
Step-by-step explanation:
this only works if you are cool enough
what is the answer to 5/3x + 4 = 2/3x
Answers
Answer:
5/3x + 4 = 2/3x
Step One- Subtract 5/3x to isolate the variable
4 = -3/3x
Step Two- Divide –3/3 to make your equation easier
4 = -x
Step Three- Divide by -1 (the lone negative cannot be there. It always represents a –1)
-4 = x is your answer!
Hopefully this helped! Feel free to mark brainliest!
A school authority claims that the average height of students is 178 cm. A researcher has taken a well-designed survey and his sample mean is 177.5 cm and the sample standard deviation is 2. The sample size is 25. Which statement is correct?
a) The result of the survey is statistically significant.
b) The sample mean and population mean is the same.
c) The result of the survey is biased.
d) The difference exists due to chance since the test statistic is small
Answers
Answer:
d) The difference exists due to chance since the test statistic is small
Step-by-step explanation:
From the given information:
Population mean = 178 cm
the sample mean = 177.5 cm
the standard deviation = 2
the sample size = 25
The null hypothesis and the alternative hypothesis can be computed as:
Null hypothesis:
[tex]H_o: \mu = 178[/tex]
Alternative hypothesis:
[tex]H_1: \mu \neq 178[/tex]
The t-test statistics is determined by using the formula:
[tex]t = \dfrac{X - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \dfrac{177.5 - 178}{\dfrac{2}{\sqrt{25}}}[/tex]
[tex]t = \dfrac{-0.5}{\dfrac{2}{5}}}[/tex]
[tex]\mathbf{t= -1.25}[/tex]
Degree of freedom df = n- 1
Degree of freedom df = 25 - 1
Degree of freedom df = 24
At the level of significance ∝ = 0.05, the critical value = 2.064
Decision rule: To reject the null hypothesis if the test statistics is greater than the critical value at 0.05 level of significance
Conclusion: We fail to reject the null hypothesis since the test statistics is lesser than the critical value and we conclude that the difference exists due to chance since the test statistic is small
Answer:
d. The difference exists due to chance since the test statistic is small
Step-by-step explanation:
With a very small sample size of 25, a difference of 0.5 cm is most likely due to chance.
This applet illustrates 95% confidence intervals for samples from a normal distribution with known variance. (a) When taking 100 samples of size 30 or greater from a population, exactly 95 of them will create a confidence interval that contains the true population mean. True False (b) Which statement is the correct interpretation of the confidence interval in this illustration?
Answers
Answer:
Step-by-step explanation:
When taking 100 samples of size 30 or greater from a population, exactly 95 of them will create a confidence interval that contains the true population mean. True or false?
This statement is false, or better still, ambiguous. 100 samples of size 30 (or greater) each, means 300 total and it can't be just 95 of them that will contain the true population mean.
electricity in a dash power station
Answers
Answer:
Most of U.S. electricity generation is from electric power plants that use a turbine or similar machine to drive electricity generators. A turbine converts the potential and kinetic energy of a moving fluid (liquid or gas) to mechanical energy.
Step-by-step explanation:
pls mark brainliest
Answer:
most power stations make use of turbines which drives power generators. A turbine converts potential and kinetic of moving fluid to mechanical energy.
PART 1
A.5x=3x
B.5=3
1) How can we get Equation B from Equation A?
Choose 1 answer:
A) Add/subtract the same quantity to/from both sides
B)Add/subtract a quantity to/from only one side
C)Multiply/divide both sides by the same non-zero constant
D)Multiply divide both sides by the same variable expression
PART 2
Based on the previous answer, are the equations equivalent? In others words , do they have the same solution?
choose 1 answer:
A) yes
B) No
Answers
Answer:
не знаю Не до х#я не знаю
2a + 4c = 38.00 solve for c
Answers
Answer:
c = 19/2 - 1/2a
Step-by-step explanation:
Step 1: Write equation
2a + 4c = 38.00
Step 2: Solve for c
Subtract 2a on both sides: 4c = 38 - 2a
Divide both sides by 4: c = 19/2 - 1/2a
Step-by-step explanation:
2 (a+2c)=38
a+2c=19
c=(19-a)/2
A car travel 300 miles on 10 gallons of gas,whats the ratio
Answers
Answer:
30/1
Step-by-step explanation:
300 miles per 10 gallons or 300/10.
simplify by dividing both numbers by the greatest common denominator. which in this case is 10. so divide 300 and 10 by ten and you get 30/1. it can't be simplified any more so thats the final simplified ratio.
HELP HELP I NEED HELP PLEASE
Answers
Answer: 76 degrees
Step-by-step explanation:
m<abc = m<1 + m<2
4x+12=(2x-7)+(3x-4)
x=23
180=4x+12+m<3
m<3=76
consider the diagram. lines ac and rs are
Answers
Answer:
Skew.
Step-by-step explanation:
Answer:
D- skew
Step-by-step explanation:
Just took the test today and got it right :)
The expression 15n + 2(3p) represents the amount Isaiah spent buying gasoline and snacks, where n represents the price of each gallon of gasoline and p represents the cost of each snack that he bought. Which statement is true about the amount Isaiah spent?
He spent 6p dollars on gasoline.
He spent n + p dollars in all.
He bought 15 gallons of gasoline.
He bought 6 dollars worth of snacks.
Answers
Answer:
He bought 15 gallons of gasoline.
Step-by-step explanation:
In the expression [tex]15n+2(3p)[/tex]
[tex]n=[/tex] price of each gallon of gasoline
[tex]p=[/tex] cost of each snack bought
We can go ahead and distribute.
[tex]15n+6p[/tex]
The [tex]6p[/tex] means he bought 6 snacks. The [tex]15n[/tex] means he bought 15 gallons of gasoline.
Answer:
c
Step-by-step explanation:
9. If LK MK, LK = 7x - 10, KN = x + 3, MN = 9x - 1), and KJ = 28, find L.
Answers
Answer:LJ = 18 + 28 = 46
Step-by-step explanation:
Suppose J, K, L, M, N are points on the same line.
MK = MN + (-KN) = MN - KN = 9x - 11 - x - 3 = 8x - 14
Since LK = MK and LK = 7x - 10, then
7x - 10 = 8x - 14
8x - 7x = -10 + 14
x = 4
LJ = MK + KJ
MK = LK = 7x - 10 = 7(4) - 10 = 28 - 10 = 18
LJ = 18 + 28 = 46
Stuco wants to start a new project to help with trash removal. They need $15 to buy supplies at the local landfill and they charge 75 per pound.
How can you use this info to assess the possible cost of the service project? If the Senior Class collects 235 pounds of trash, what is the cost
going to be?
Answers
Answer:
$17,640
Step-by-step explanation:
Stuco wants to start a new project to help with trash removal. They need $15 to buy supplies at the local landfill and they charge 75 per pound. If the Senior Class collects 235 pounds of trash, the cost is going to be $17,640.
235 ⋅ 75 = 17,625
17,625 + 15 = 17,640
Therefore, the answer is $17,640.
Find two consecutive whole numbers that 141 lies between
Answers
Answer:
140 and 142?
Step-by-step explanation:
State whether the given pairs are complementary or supplementary
1) 75 °, 105 °
2) 62 ° , 28 °
3) 132 ° , 48 °
4) 76 ° , 14 °
5) 118 ° , 62 °
6) 19 ° , 71 °
Answers
Write three DIFFERENT properties that are equivalent to 3 4
Answers
Answer:
6/8
9/12
12/16
Step-by-step explanation:
A standard working day is 8 hours, if you were to work 125% of a normal day, how many total hours would you work?
Answers
Answer:
10 hours
Step-by-step explanation:
It is given that,
Standard working day is 8 hours
If you were to work 125% of a normal day, then it means that,
[tex]125\%\ \text{of}\ 8\ \text{hours}\\\\=\dfrac{125}{100}\times 8\\\\=10\ \text{hours}[/tex]
Hence, you will work for 10 hours.
Identify the segment bisector of AB¯¯¯¯¯¯¯¯. Then find AB.
Answers
Answer:
is there more to the question? this does not make seince
Step-by-step explanation:
Find the missing angle
measures marked with
question marks.
Answers
Answer:
First one- The ? across from 70 degrees is 70 degrees, and the ones on the side are both 110 degrees.
The second one- The one across 53 degrees is 53 degrees and the ones are the side are both 127 degrees.
Step-by-step explanation:
Take the shown angle and subract that by 180 degrees to get your answer for the missing angles. And the one across from the shown angle is the same number.
Hope this helped im not sure if its right though.
[tex]\frac{(2xy^2)^5}{(4x^2y)^2 (xy^2)}[/tex]
Please solve this and also mention the steps
Answers
Answer:
2 y^6
Step-by-step explanation:
Simplify the following:
(2 x y^2)^5/((4 x^2 y)^2 x y^2)
Hint: | Distribute exponents over products in (4 x^2 y)^2.
Multiply each exponent in 4 x^2 y by 2:
(2 x y^2)^5/(4^2 x^(2×2) y^2 x y^2)
Hint: | Multiply 2 and 2 together.
2×2 = 4:
(2 x y^2)^5/(4^2 x^4 y^2 x y^2)
Hint: | Evaluate 4^2.
4^2 = 16:
(2 x y^2)^5/(16 x^4 y^2 x y^2)
Hint: | Distribute exponents over products in (2 x y^2)^5.
Multiply each exponent in 2 x y^2 by 5:
(2^5 x^5 y^(5×2))/(16 x^4 y^2 x y^2)
Hint: | Multiply 5 and 2 together.
5×2 = 10:
(2^5 x^5 y^10)/(16 x^4 y^2 x y^2)
Hint: | Compute 2^5 by repeated squaring. For example a^7 = a a^6 = a (a^3)^2 = a (a a^2)^2.
2^5 = 2×2^4 = 2 (2^2)^2:
(2 (2^2)^2 x^5 y^10)/(16 x^4 y^2 x y^2)
Hint: | Evaluate 2^2.
2^2 = 4:
(2×4^2 x^5 y^10)/(16 x^4 y^2 x y^2)
Hint: | Evaluate 4^2.
4^2 = 16:
(2×16 x^5 y^10)/(16 x^4 y^2 x y^2)
Hint: | Multiply 2 and 16 together.
2×16 = 32:
(32 x^5 y^10)/(16 x^4 y^2 x y^2)
Hint: | In (32 x^5 y^10)/(16 x^4 y^2 x y^2), divide 32 in the numerator by 16 in the denominator.
32/16 = (16×2)/16 = 2:
(2 x^5 y^10)/(x^4 y^2 x y^2)
Hint: | For all exponents, a^n a^m = a^(n + m). Apply this to (2 x^5 y^10)/(x^4 y^2 x y^2).
Combine powers. (2 x^5 y^10)/(x^4 y^2 x y^2) = 2 x^(5 - 1 - 4) y^(10 - 2 - 2):
2 x^(5 - 1 - 4) y^(10 - 2 - 2)
Hint: | Evaluate 5 - 1 - 4.
5 - 1 - 4 = 0:
2 x^0 y^(10 - 2 - 2)
Hint: | Evaluate 10 - 2 - 2.
10 - 2 - 2 = 6:
2 x^0 y^6
Hint: | Any nonzero expression to the zero power is one.
x^0 = 1:
2×1 y^6
Hint: | Simplify the expression.
Write 2×1 y^6 as 2 y^6:
Answer: 2 y^6
Convert 0.4 to a percent
Answers
Answer:
0.4=40%
Step-by-step explanation:
hope this helps!!!
