Answer:
see explanation
Step-by-step explanation:
Given
AB + BC = 31
AB - BC = 17
Add the 2 equations
2AB = 48 ( divide both sides by 2 )
AB = 24
Substitute AB = 24 into the first equation
24 + BC = 31 ( subtract 24 from both sides )
BC = 7
Using Pythagoras' identity to find the hypotenuse AC
AC² = AB² + BC² = 24² + 7² = 576 + 49 = 625 ( take square root of both sides )
AC = [tex]\sqrt{625}[/tex] = 25
Then
sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{7}{25}[/tex]
cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{24}{25}[/tex]
sinC = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{24}{25}[/tex]
cosC = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{7}{25}[/tex]
Rewrite the fraction with the indicated denominator
Answer:
170
Step-by-step explanation:
17/7
Multiply the top and bottom by 10
17*10/ 7*10 =170/70
The fraction with the indicated denominator 70 is [tex]\frac{170}{70}[/tex].
The given fraction is[tex]\frac{17}{7}[/tex].
Convert the fraction with a denominator of 70.
To do this, multiply the numerator and denominator by 10:
[tex]\frac{17}{7} \times \frac{10}{10}[/tex]
[tex]=\frac{17 \times 10}{7 \times 10}[/tex]
[tex]=\frac{170}{70}[/tex]
Hence, the fraction with the indicated denominator 70 is [tex]\frac{170}{70}[/tex].
To learn more on Fractions click:
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A publishing company expects to sell 5000 copies of a new book from its web site, if the company charges $30 per book. The company expects that 500 more books would be sold for each price reduction of $2. What price would maximize the company's revenue?
Solution :
Let the revenue be = R
Therefore, R = price x quantity
R = (30 - 2x) ( 5000 + 500x)
= [tex]150000 + 5000x - 1000x^2[/tex]
For the maximum revenue,
[tex]$\frac{dR}{dx} = 0$[/tex]
[tex]$-2000x+5000=0$[/tex]
[tex]$x=2.5$[/tex]
[tex]$\frac{d^2R}{dx^2}=-2000<0$[/tex]
At [tex]x=2.5[/tex], the revenue is maximum.
So the price for the maximum company revenue = [tex]$30-2x$[/tex]
[tex]$=30-2(2.5)$[/tex]
= 30 - 5
= 25
Therefore, the price that will maximize the company's revenue is $25.
What is the slope of the line containing (-3, 5) and (6, -1)?
O A. -1
O B.-2/3
O C. 1
OD. 2/3
Answer:
-2/3
Step-by-step explanation:
The slope of a line can be represented as [tex]\frac{y_{2} -y_{1} }{x_{2}- x_{1} }[/tex] where (x1, y1) and (x2, y2) are points on the line. We can substitute the points given, (-3, 5) and (6, -1), to calculate the slope:
[tex]\frac{-1-5}{6-(-3)} =\frac{-6}{6+3} =\frac{-6}{9} =-\frac{2}{3}[/tex]
find tan(2x) if x=pi/3
Answer:
Wouldn't it be something along the lines of
0.03657034937430407
I used a calculator btw, but rounded for pi with 3.14159.
Step-by-step explanation:
If there are 3 people splitting a paycheck of 89 how much would each have to pay
Answer:
Around 29.67 each.
Step-by-step explanation:
The bill is being split amongst 3 people. Therefore, we must divide the total price by 3:
[tex]\frac{89}{3}[/tex]
=29.66666667
=29.67
Answer:
3÷89 it would be 36.55 each has to pay on bills
find the area of given figure
find the missing side of the triangle.
Answer:
34
Step-by-step explanation:
x² = 30² + 16²
(pythagoras theorem)
x = Square root 30² + 16²
x = 34
Please help explanation if possible
Answer:
see explanation
Step-by-step explanation:
He wants to buy at least 4 snacks , that is can be more than 4 , so
x + y ≥ 4
He only has $20 , thus total cost must be less than or equal to $20 , so
3x + 2y ≤ 20
David has a part-time job. He earns $9.40 per hour. How much will he earn when he works 9 hours?
Answer:
$84.60
Step-by-step explanation:
$84.60 is what david will earn in 9 hours becuz 9.40 times 9 is 84 dollars and 60 cents
In an experiment, colored letters flash briefly on a computer screen. On each trial, participants are asked to report the letters in their correct colors and to rate their confidence in their responses. In one condition, participants are required simultaneously to monitor the screen for the appearance of a particular digit. Which alternative correctly identifies the dependent variable(s) in this experiment
The alternatives or options aren't given.
Answer:
Kindly check explanation
Step-by-step explanation:
The dependent variable in an experiment refers to the va ibale which we intend to measure based on the outcome or values of one or more predictor variables, this variable which we intend to measure is the dependent variable while the the variables which causes a change or upon which the dependent variable relies are the independent variable. Hence, from the scenario described above, the possible dependent variables are :
The letters in their correct colors and the confidence in response Given.
Simplify the given expression below:
(1 + 3) + (2 - 5i)
Answer:
6 -5i
Step-by-step explanation:
(1 + 3) + (2 - 5i)
Combine like terms
1+3+2 -5i
6 -5i
1. A football goal post casts a shadow 120 inches long. You are 5 feet 6 inches tall and cast a shadow 16.5 inches long. Find the height of the goal post in feet. Round your answer to the nearest whole number.
Answer:
40 feets
Step-by-step explanation:
Given that :
Person's height = 5feet 6 inches ;
Person's height in inches ;
1 foot = 12 inches ;
5 feets = (12 * 5) = 60 inches
Person's height = 60 + 6 = 66 inches
Height of person's shadow = 16.5 inches
Height of post shadow = 120 inches
Height of goal post = x
(Height of goal post / height of post shadow) = (person's height / person's shadow)
x / 120 = 66 / 16.5
Cross multiply :
16.5x = 120 * 66
16.5x = 7920
x = 7920 / 16.5
x = 480 inches
To feets ;
1 foot = 12 inches
480 inches = 480/12 feets = 40 feets
A train is exactly 24km from Smalltown at 7:00p.m. It travels toward Smalltown at a constant rate of 90km per hour. At what time does the train reach Smalltown?
Answer:
7:16 P.M.
Step-by-step explanation:
24/90=4/15. There are 60 minutes in an hour, so we have 240/15=16.
Sam spent 5 of an hour at the dentist's office. He spent to of the time in the waiting room. How much time did he
spend at the dentist's office other than in the waiting room?
0 1 / 2
of an hour
25 of an hour
of an hour
o of an hour
Answer:
We know he spent 5 sixths which is 50 minutes
Ten percent of 50 is 5
This means he spent 3 quarters of an hour in the office
Answer:
Sam spent 50 minutes at the office, and 1/10 (or 5 minutes) in the waiting room.
So, he spent 3/4 of an hour at the office but not in the waiting room.
Let me know if this helps!
Cinco litros de agua se divide en cuatro partes iguales, me tomo 2 partes ¿Cuánto me queda?
Answer:
2 [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
5 ÷ 4 = 1 [tex]\frac{1}{4}[/tex]
1 [tex]\frac{1}{4}[/tex] × 2 = 2 [tex]\frac{2}{4}[/tex] = 2 [tex]\frac{1}{2}[/tex]
5 - 2 [tex]\frac{1}{2}[/tex] = 2 [tex]\frac{1}{2}[/tex]
respuesta: 2 [tex]\frac{1}{2}[/tex]
If the mortgage interest rates increase, this would be an example of changing your external environment.
Answer:
Economic conditions
Step-by-step explanation:
If the mortgage interest rates increase, this would be an example of changing Economic conditions in a company's your external environment
Mortgage is the legal agreement/arrangement between a financial institution and a debtor wherein the Financial institution lends funds to the debtor at an interest rate, and also with the title of the property owned by the debtor.
once the debtor repays the mortgage he retains the full ownership of his property.
A car accelerates from rest at 1.0 m/s2 for 20.0 seconds along a straight road. It then moves at a constant speed for half an hour. It then decelerates uniformly to a stop in 30.0 s. Find the total distance covered by the car.
HELP
Answer:
50m
Step-by-step explanation:
speed (m/s2) = distance (m) ÷ time (s)
distance = speed (m/s2) x time (s)
1x20 =20m.
30s = 30m because they do 1 meter per second (every second)
50m in total if not counting the constant for half a hour.
if f(x) = 2x/2x+1 and g(x) = 1/2x+1, find f(x) / g(x)
Answer:
2x
Step-by-step explanation:
Just solve the function operation:
f/g=(2x/2x+1)/(1/2x+1) = 2x since (2x/1)/(2x+1/2x+1) simplifies to 2x/1 the answer is 2x
Write in point-siope form, siope-intercept form, and standard form an equation that passes
through( - 1, 2) with slope 4.
Answer:
The forms are:
y - y1 = m(x - x1)y = mx + bax + by = cGiven:
m = 4Point (-1, 2)Use point slope form:
y - 2 = 4(x - (-1))y - 2 = 4(x + 1)Convert it to slope-intercept form:
y = 4x + 4 + 2y = 4x + 6Convert it to standard form:
4x - y = - 6please help me is for my homework
Answer:
0.625
Step-by-step explanation:
:) i hope this helps.
The diameter of a circle is 7 m. Find its area to the nearest tenth.
Area = pi x r^2
R = 7/2 = 3.5
Area = 3.14 x 3.5^2
Area = 38.5 m^2
Find the value of the trigonometric ratio, Make sure to simplify the fraction if needed
Answer:
Cos Z = 7/25
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj / hyp
cos Z = 14/50
Cos Z = 7/25
▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
As the [tex]\triangle\sf{XYZ}[/tex] is a right angle traingle.
we know that,
[tex]\boxed{\underline{\sf{cos\blue{\theta}=\dfrac{adjacent}{hypertension} }}}[/tex]
According to the question,
[tex]cosZ=\dfrac{adjacent}{hypertension}\\\\cosZ=\dfrac{14}{50}\\\\\pmb{\green{\sf{cosZ}=\frak{\dfrac{7}{25}}}}[/tex]
▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
Several days after a wedding, an outbreak of cyclosporiasis occurred among attendees. Of the 108 guests at the wedding, 76 were ill and met the case definition. 50 of the 76 who were ill ate the wedding cake. Three of those who were well ate the wedding cake. What is the attack rate for those who ate the wedding cake
Answer:
The answer is "94.3".
Step-by-step explanation:
Calculating the total numbers of cake eaters[tex]=50+3=53\\\\[/tex]
Calculating the total numbers of ill among them[tex]=50\\\\[/tex]
[tex]\therefore[/tex]
The attack rate for those who ate cake[tex]=\frac{50}{53}\times 100\%=94.3[/tex]
Daniel took her dog for a walk. She decided to count how many dog ears. She passed on her walk. She passed 14 dogs. How many ears did she count?
Answer:
Each dog has 2 ears (unless a dog had genetic disorder)
So-
14 x 2
= 28
So she counted of 28 Ears of total
(honestly that's a weird thing to do but ok)
Answer:
14 x 2 = 28
Step-by-step explanation:
Each dog has 2 ears
14 dogs has 28 ears
Which of the following best describe(s) the slope of a linear function?
Select all that apply.
rise over run
run over rise
average rate of change
intersection with the y-axis
A box contains 9 balls written B,E,R,N,H,E,A,R,T. Two balls are drawn at random without replacement. what is the probability of getting both balls written with R ?
Answer:
How many balls have “R” written on them initially? We can see this is 2.
How many balls are there initially? This is 9.
As a result, the probability of initially drawing a ball with an R on it is 2/9, as out of the 9 possible draws we could make, 2 of them result in a ball with R on it.
How many balls have “R” written on them now? We can see this is 1, since we just drew one ball with R on it and didn’t replace.
How many balls are there in total right now? This is 8, because we took away one.
As a result, the probability of drawing a ball with an R on it after having already done so is 1/8, as out of the 8 possible draws we could make, 1 results in a ball with R on it.
We then multiply these two values (2/9)*(1/8) = 2/72, which is our probability.
Another way to think about this is that there are 72 possible combinations of balls that we could draw, counting each ball uniquely. This is because of our denominator, since 8*9=72. Out of those 72 outcomes that could possibly happen, 2 outcomes will result in both balls being written with R.
Step-by-step explanation:
3x - 28= 80
What is the value of x?
Cual es el valor de x?
Answer:
3x-28 = 80
3x = 108
x = 36
Let me know if this helps!
CAN A KIND SOUL PLEASE HELP ME OUT??!!!!!!!!!!!!!!
The translation (x, y)->(x + 10, y – 6) is applied to triangle ABC to create a new image triangle A’B’C’. Graph triangle A’B’C’ on the coordinate plane.
please show how you got it so I can see if the answer makes sense!!!!
Answer:
First find the coordinates of the vertices. A=(-8,8), B=(-8,3) and C=(-4, 4). Next apply transformation, A'=(2, 2), B=(2, - 3) and C=(6, - 2). Next map this and join them to get the required triangle
solue for x
X(3 + X) = 3x + x²
Answer:
here,
3x-3x=
[tex] {x}^{2} - {x}^{2} [/tex]
x=0
Please answer this, Its due in a few minutes
Answer:
The final solution is 2.
y ÷ 2 + x ; use x = 1 and y = 2
(2) ÷ 2 + (1) -----> divide 2 by 2
1 + 1 ----> add the quotient of 2/2 to 1
2 ---> answer
Answer:
2
Step-by-step explanation:
(To make this easier I will put this in steps)
Step 1 : Substitute
As you can see we are given the amount the variable stands for so we can simply just substitute them out...
y / 2 + x OR 2 / 2 + 1
Step 2 : Solve
Now that there are no variables this should now be pretty simple to solve.
2/2 = 1 so...
1 + 1
Then you would add them and get 2
y / 2 + x = 2
Hope this helps :)
