Answer:
[tex] \displaystyle{ \sqrt{ \frac{1 + cos \: {30}^{ \circ} }{1 - cos \: {30}^{ \circ} } } = sec \: {60}^{ \circ} + tan \: {60}^{ \circ} }[/tex]
[tex]LHS = \displaystyle{ \sqrt{ \frac{1 + cos \: {30}^{ \circ} }{1 - cos \: {30}^{ \circ} } } }[/tex]
[tex] \displaystyle{ \sqrt{ \frac{1 + \frac{ \sqrt{3} }{2} }{1 - \frac{ \sqrt{3} }{2} } } }[/tex]
[tex] \displaystyle{ \sqrt{ \frac{ \frac{2 + \sqrt{3} }{2} }{ \frac{2 - \sqrt{3} }{2} } } }[/tex]
[tex] \displaystyle{ \sqrt{ \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } } }[/tex]
[tex] \displaystyle{ \sqrt{ \frac{(2 + \sqrt{3} {)}^{2} }{4 - 3} } }[/tex]
[tex] \displaystyle{2 + \sqrt{3} }[/tex]
[tex]RHS = sec \: {60}^{ \circ} + tan \: {60}^{ \circ} [/tex]
[tex] = 2 + \sqrt{3} [/tex]
[tex] \rm\therefore{LHS=RHS,proved. }[/tex]
-(4-x)=3/4(x-6) i need help pls
Solve for x by simplifying both sides of the equation, then isolating the variable.
x=−2
hope this is what your looking for
Answer:
x = -2
Step-by-step explanation:
[tex]-4+x=\frac{3}{4}x-\frac{9}{2}[/tex]
[tex]\mathrm{Add\:}4\mathrm{\:to\:both\:sides}[/tex]
[tex]-4+x+4=\frac{3}{4}x-\frac{9}{2}+4[/tex]
[tex]Simplify[/tex]
[tex]x=-\frac{1}{2}+\frac{3}{4}x[/tex]
[tex]\mathrm{Subtract\:}\frac{3}{4}x\mathrm{\:from\:both\:sides}[/tex]
[tex]x-\frac{3}{4}x=-\frac{1}{2}+\frac{3}{4}x-\frac{3}{4}x[/tex]
[tex]\frac{1}{4}x=-\frac{1}{2}[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}4[/tex]
[tex]4\cdot \frac{1}{4}x=4\left(-\frac{1}{2}\right)[/tex]
[tex]x=-2[/tex]
~lenvy~
The number of men and women participating in the Winter Olympic Games has been steadily increasing in recent years. In the 19th Winter Olympics, 1389 men and 787 women participated. 1660 men and 1121 women participated in the 22nd Winter Olympics.
Part A
Which system describes the number of men and women participating if x represents the number of winter games after the 22nd Winter Olympics?
Multiple choice question.
A)
y=1389x+1660y=787x+1121
B)
y=2713x+1121y=3343x+1660
C)
y=2713x+1389y=3343x+787
D)
y=2713x+1660y=3343x+1121
Using a system of equations, it is found that the correct option is:
A) 1389x+1660y=787x+1121y.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, considering the amounts in each olympics(1389 men and 787 women participated on the 19th, 1660 men and 1121 women in the 22th), the system is:
A) 1389x+1660y=787x+1121y.
More can be learned about a system of equations at https://brainly.com/question/24342899
For what values of x is x3+23x2+162x+360=0 a true statement?
Answer:
Step-by-step explanation:
x³+23x²+162x+360=0
x³+12x²+11x²+132x+30x+360=0
x²(x+12)+11x(x+12)+30(x+12)=0
(x+12)(x²+11x+30)=0
(x+12)[x²+6x+5x+30]=0
(x+12)[x(x+6)+5(x+6)]=0
(x+12)(x+6)(x+5)=0
x=-12,-6,-5
There is a red, orange, yellow, green, blue, and purple card placed in a box. (six total, one of each color). You are asked to randomly choose a card, replace it in the box, and choose another card.
Find P(Yellow, then Blue)
Answer:
Step-by-step explanation:
If you are doing probability with replacement they will all be 1/6 each time.
total there is 6/6. If you draw a yellow card first it's 1/6 then replace it and draw a blue it is still 1/6. so you take those two probabilities and multiply them (1/6)*(1/6)=1/36 1*1=1 and 6*6=36.
Your answer is 1/36
I need help, so this one question: 1/4 (4+x)=4/3
Is stopping me from being great
Answer:
if you are solving for x, x= 4/3
Step-by-step explanation:
How to solve your problem:
1. Rearrange terms
2. Combine multiplied terms into a single fraction
3. Multiply by 1
4. Multiply all terms by the same value to eliminate fraction denominators
5. Cancel multiplied terms that are in the denominator
6. Multiply the numbers
7. Subtract 4 from both sides
8.Simplify
Answer:
X= 4/3
Hopes this helps! ^^
When asked to factor the x^2 - 144, a student gives the answer (x - 12)(x - 12). What is wrong with this answer?
A. Both minus signs should be plus signs l
B. One of the minus signs should be a plus sign
C. There is nothing wrong with this answer
D. -1 is also a factor
Answer:
B
Step-by-step explanation:
because in general
(a + b)(a - b) = a² - b²
when the second term is negative, it has to be the product of a positive and a negative number.
positive × positive = positive
negative × negative = positive
In this box-and-whisker plot, what is the maximum value of the data.
A: 53 B: 56 C: 60 D: 68
Answer:
68
this will be your maximum because of where the dot ends
1) A prize is divided in the ratio 15:1 if the smaller share is £5 what is the total prize?
Answer:
£80
Step-by-step explanation:
larger ratio is 15 and smaller ratio is 1
15 + 1 = 16
£5×16=£80
what is m
ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd
Answer:
66 degrees
Step-by-step explanation:
All three angles on any given triangle have a sum of 180 degrees.
We know that the measure of angle B is the the same as angle C.
So 57 +57 = 114
180 - 114 = 66
Hope that helps!
Help picture below problem 10
Solution :-
Here, we have been given that lines f and g are parallel. Thus, the angle measuring 135° and ∠2 are vertically opposite angles.
And we know that vertically opposite angles measure same. Thus,
∠2 = 135°
And,
∠2 + ∠6 = 180° ( Co - interior angles sum up to 180° )
135° + ∠6 = 180°
∠6 = 180° - 135°
∠6 = 45°
Hope that helps :)
There are six more necromancers than there are
wizards. Write a system of equations that deter-
mines the numbers of wizards and the number of
necromancers.
Answer:
Step-by-step explanation:
let x be necromancers and y be wizards
if you know the amount of wizards and want to find the amount of necromancers. you just use y + 6
but if you know the amount of necromancers and want to find out the amount of wizards you just do x - 6
Find the Area in yards.
12 mi
6.9 mi
Answer:
82.8
Step-by-step explanation:
multiply the 2
1 2
6.9
9×2=18
9×1=9
10.8
72.0
____
82.8
Evaluate the expression 21 ÷ 3 + 8 − 4. 19 17 15 11
Answer:
Your answer is D, 11
Step-by-step explanation:
PEMDAS, first you divide, 21/3 is 7
7+8 is 15
15 - 4 is 11
Hope this helps! :)
Answer:
[tex]\boxed{\sf{11}}[/tex]
Step-by-step explanation:
Solving this problem requires an order of operations.
PEMDAS stands for:
ParenthesisExponentsMultiplyDivideAddSubtract21÷3+8-4First, divide.
[tex]\sf{21\div3+8-4}[/tex]
[tex]\sf{21\div3=7}[/tex]
Then rewrite the problem.
[tex]\sf{7+8-4}[/tex]
Add.
[tex]\sf{7+8=15}[/tex]
Subtract.
[tex]\sf{15-4=\boxed{\sf{11}}[/tex]
11
Therefore, the correct answer is 11.
I hope this helps you! Let me know if my answer is wrong or not.
3/9 and 1/2 common denominator
Given:
[tex]\frac{3}{9}[/tex] and [tex]\frac{1}{2}[/tex]
Finding a common denominator:
9 * 2 = 18
-> If you need to stop here, a common denominator is 18.
Converting [tex]\frac{3}{9}[/tex]:
[tex]\frac{3}{9}[/tex] = [tex]\frac{3*2}{9*2}[/tex] = [tex]\frac{6}{18}[/tex]
Converting [tex]\frac{1}{2}[/tex]:
[tex]\frac{1}{2}[/tex] = [tex]\frac{1*9}{2*9}[/tex] = [tex]\frac{9}{18}[/tex]
-> [tex]\frac{6}{18}[/tex] and [tex]\frac{9}{18}[/tex]
What is the slope-intercept equation for this line?
y = [?]x+ [?]
Answer:
y= -x-3
Step-by-step explanation:
Find the Perimeter of the Square with One side is 75cm
Answer:
P=300cm
Step-by-step explanation:
P=4a=4.75×4=300cm
[tex]\green{ \underline { \boxed{ \sf{Perimeter \: of \:Square = 4 \times side }}}}[/tex]
Putting Values -
[tex]\begin{gathered}\\\implies\quad \sf Perimeter \:of \:Square = 4 \times 75 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf Perimeter \: of \:Square = 300 sq. \:cm \\\end{gathered} [/tex]
>>Therefore, Perimeter of the Square is 300 sq. cm
Noah walked a family’s dog 5 times this past month and earned the same amount each time. To thank him, the family gave him an extra $6 at the end of the month. Noah earned $106 from dog walking.
1- This situation IS represented by the tape diagram.
2- This situation IS NOT represented by the tape diagram.
The situation IS NOT represented by the tape diagram.
How to represent the situationNumber of times Noah walked the dog = 5Amount earned each time = sExtra amount earned = $6Total amount earned = $106The situation can be represented by the equation:
s + s + s + s + s + 6 = 106
5s + 6 = 106
5s = 106 - 6
5s = 100
s = 100/5
s = 20
Therefore, the amount Noah earned each time he walked the dog is $20
Learn more about equation:
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please help:
A box in the shape of a right rectangular prism has a length of 8 . 58.5 inches, a width of 4 . 54.5 inches, and a height of 3 . 753.75 inches. What is the volume, in cubic inches, of the box? Do not round your answer.
Answer:
Step-by-step explanation:
Use the volume formula of a right rectangular prism!
V=whl
Just plug the values in and throw them in your calculator.
w stands for width
h stands for height
l stands for length
Hope that helps. Since it is part of a quiz, I can't give you the answer, but I believe in you!
Graph a quadratic function with a vertex at (2, -3) with a = 3.
Answer:
bottom one
Step-by-step explanation:
use (x , y)
the top one is -3,2
the bottom one is 2,-3
This graph represents function of y = 3(x−2)²-3.
What is Parabola?A parabola is a U-shaped curve this is drawn for a quadratic function,
f(x) = ax² + b x + c. The graph of the parabola is downward (or opens down), when the price of a is much less than 0, a < 0. The graph of the parabola is upward (or opens up) when the value of a is more than 0, a > 0.
The vertex form of parabola :
y=a(x−h)²+k
(h,k)is the vertex of the parabola, and
Substitute vertex(2,-3), into equation
y = a(x−2)²-3
Substitute a = 3 into equation
y = 3(x−2)²-3
Here is a graph of the y = 3(x−2)²-3
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Simplify the expression.
The cost of renting a community center is $100, with an additional cost of $10 per guest.
Which graph has the most appropriate scales and units for this situation?
Answer:
Units will be # attendees for the x axis
Units will be $ for the y axis
the graph should be y = 100 when x = 0 and then for each x increase of one the value of y will increase 10
Step-by-step explanation:
How much is it but don’t stop it fast cash x
Answer:
yes
Step-by-step explanation:
How many lines pass
through two points?
A. infinite
B. 1
C. zero
D. 2
Answer:
1
Step-by-step explanation:
Only 1 line can pass through two points.
TRUE or FALSE? The only difference between involuntary manslaughter and voluntary manslaughter is reckless conduct
Answer:
Yeah?
Step-by-step explanation:
dunno if this is and actual school related question but to me, yeah thats the only difference cuz the meaning of involuntary manslaughter is death thru recklessness/something close to that
A cone has a radius of 7 cm and a height of 12 cm what is the volume in cubic meters of the cone
Answer: 615.44 m^3.
Step-by-step explanation: To find the volume of a cone, you need to multiply the radius, pi, and height. The equation is given below:
π x r^2 x h = V, where π is pi, r is the radius squared, h is the height, and V is the volume.
Now, we need to substitute the values with the information that is given. π ≈ 3.14:
3.14 x 7^2 x 12 ≈ 1846.32.
We are not finished yet! A cone's volume is a third of a cylinder's, so you need to split 1846.32 in 1/3:
1/3 x 1846.32 ≈ 615.44 m^3.
Hope this helps! :)
Jenny brought an antique vase for $ 120 and advertises to sell it at a profit of 35% calculate the selling cost
35% of 120 is :
120 x 0.35 = 42 $ profit
selling cost 120+42=162$
Before every flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The Bombardier Dash 8 aircraft can carry 37 passengers, and a flight has fuel and baggage that allows for a total passenger load of 6200 lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 6200lb/37 = 167.6lb. What is the probability that the aircraft is overloaded? Should the pilot take any action to correct for an overloaded aircraft? Assume that weights of men are normally distributed with a mean of 185.47 lb and a standard deviation of 39 lb. make sure to include pdf
Using the normal probability distribution and the central limit theorem, it is found that the probability is of 0.9974 = 99.74%, which means that the pilot should take action.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem, for the population, the mean and the standard deviation are given by, respectively:
[tex]\mu = 185.47, \sigma = 39[/tex].
For a sample of 37 passengers, we have that:
[tex]n = 37, s = \frac{39}{\sqrt{37}} = 6.4116[/tex]
The probability that the aircraft is overloaded is one subtracted by the p-value of Z when X = 167.6, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{167.6 - 185.47}{6.4116}[/tex]
[tex]Z = -2.79[/tex]
[tex]Z = -2.79[/tex] has a p-value of 0.0026.
1 - 0.0026 = 0.9974.
There is a 0.9974 = 99.74% probability that the aircraft is overloaded. Since this is a very high probability, the pilot should take action.
To lern more about the normal probability distribution and the central limit theorem, you can check https://brainly.com/question/24663213
What would be the corresponding angles ( similar figures ). Any help with this question will be gladly appreciated . Thank you
Answer:
x=4.8
I think ur supposed to solve for x. Since the rectangles are similar, we can set a proportion for the sides
5/3 = 8/x (then just solve for x)
24=5x
4.8=x
Write an essay comparing the two arguments made about whether dodgyball should be played in school. Use textual evidence from the article to support your answer. TITLE- A Dodgy call AUTHOR Tum Jones Introduction Hook- Bridge-
Answer:
(This is not math)
Step-by-step explanation:
I think that dodgeball should be allowed un our school because it gets our legs moving and lets us extrasice and practice our swiftness
What are the domain and range of the function
Answer: The answer should be the 2nd one
Step-by-step explanation:
A sample of bacteria is decaying according to a half-life model. If the sample begins with 500 bacteria,
and after 17 minutes there are 150 bacteria, after how many minutes will there be 10 bacteria
remaining?
When solving this problem, round the value of k to four decimal places and round your final answer to
the nearest whole number.
contact +2348021312463, he can help you
after approximately 137 minutes, there will be 10 bacteria remaining.
To find the time at which there will be 10 bacteria remaining, we can use the half-life model for exponential decay, which is given by:
N(t) = N₀ * [tex](1/2)^{(t / t_{half})[/tex]
where:
N(t) = the number of bacteria at time t
N₀ = the initial number of bacteria
t = time (in minutes)
t_half = the half-life of the bacteria
We are given that the initial number of bacteria (N₀) is 500 and after 17 minutes there are 150 bacteria (N(17) = 150).
Let's use this information to find the value of k (the decay constant):
150 = 500 * [tex](1/2)^{(17 / t_{half})[/tex]
Divide both sides by 500:
[tex](1/2)^{(17 / t_{half})[/tex] = 150 / 500
[tex](1/2)^{(17 / t_{half})[/tex] = 0.3
Now, we can write the equation as an exponent:
17 / t_half = log base (1/2) of 0.3
Using logarithms:
t_half = 17 / log base (1/2) of 0.3
Now, calculate t_half:
t_half = 17 / log base 2 of 0.3 ≈ 38.555
Now, we can find the time at which there will be 10 bacteria remaining (N(t) = 10):
10 = 500 * [tex](1/2)^{(t / 38.555)[/tex]
Divide both sides by 500:
[tex](1/2)^{(t / 38.555)[/tex] = 10 / 500
[tex](1/2)^{(t / 38.555)[/tex] = 0.02
Write the equation as an exponent:
t / 38.555 = log base (1/2) of 0.02
Using logarithms:
t = 38.555 * log base 2 of 0.02 ≈ 137.08
Rounding to the nearest whole number:
t ≈ 137
So, after approximately 137 minutes, there will be 10 bacteria remaining.
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