Answer:
[tex]\displaystyle x=\frac{1}{5}y^2[/tex]
Step-by-step explanation:
[tex]\displaystyle r=5\cot(\theta)\csc(\theta)\\\\r=5\biggr(\frac{\cos(\theta)}{\sin(\theta)}\biggr)\biggr(\frac{1}{\sin(\theta)}\biggr)\\\\r=\frac{5\cos(\theta)}{\sin^2(\theta)}\\\\r^2=\frac{5r\cos(\theta)}{\sin^2\theta}\\\\r^2\sin^2(\theta)=5r\cos(\theta)\\\\(r\sin(\theta))^2=5x\\\\y^2=5x\\\\x=\frac{1}{5}y^2[/tex]
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answer:
The three statements that are always true regarding this diagram are:
m∠3 + m∠4 + m∠5 = 180°
m∠2 + m∠3 + m∠5 = 180°
m∠2 + m∠3 = m∠6
Here's why:
The sum of the measures of the interior angles of a triangle is always 180°. Therefore, m∠2 + m∠3 + m∠5 = 180°.
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. Therefore, m∠4 = m∠2 + m∠5, and m∠3 + m∠4 + m∠5 = 180°.
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. Therefore, m∠6 = m∠2 + m∠3.
The other two statements are not always true. For example, if m∠5 = 100° and m∠3 = 80°, then m∠5 + m∠3 = 180°, but m∠4 ≠ 0°. Similarly, if m∠5 = 100° and m∠6 = 80°, then m∠5 + m∠6 ≠ 180°.
Step-by-step explanation:
Laura, Tom and Alex share £95 in the ratio 8:7:4 find how much money each of them will receive
Answer:
Laura: £40Tom: £35Alex: £20Step-by-step explanation:
You want the amount of money each receives if Laura, Tom, and Alex share £95 in the ratio 8:7:4.
Ratio unitsThe total number of ratio units is 8+7+4 = 19, corresponding to a total amount of £95. That makes each ratio unit represent £95/19 = £5.
Multiplying the ratio units by £5, we find the distribution to be ...
Laura : Tom : Alex = £40 : £35 : £20
Answer:
Money received by Laura = 8x = 8x5 = £40
Money received by Tom = 7x = 7x5 = £35
Money received by Alex = 4x = 4x5 = £20
Step-by-step explanation:
Given ,
Laura, Tom and Alex share £95 in the ratio 8:7:4To Find : How much money will each of them receive
Let us take the variable as 'x' to find the money received by them
When we convert it to a equation
8x+7x+4x = 95
19x = 95
x = [tex]\frac{95}{19}[/tex]
x = 5
Money received by Laura = 8x = 8x5 = £40
Money received by Tom = 7x = 7x5 = £35
Money received by Alex = 4x = 4x5 = £20
Hence, the money received by each of them is £40, £35 and £20
Write the number 4,207 in expanded form
Answer:
That's easy! four thousand two hundred and seven or 4,000+200+7
Step-by-step explanation:
will mark u brainliesst
Answer:
- 7√10
Step-by-step explanation:
Step 1 : Take √10 common
2√10 - 5√10 - 4√10
= √10 ( 2 - 5 - 4 )
Step 2 : Subtract the numbers separately.
2 - 5 - 4
= 2 - 9
= - 7
Step 3 : Multiply √10 and - 7
√10 * - 7 = - 7√10
Which statement correctly compares the centers of the distributions?
Answer:
B
Step-by-step explanation:
Center of the distributions -> mean/median (preferably mean)
The option with range is eliminated
Median might not be accurate as median is the center person, not the center result.
Based on the graphs, identify the graph with the intervals of greatest frequency.
For North Heights -> between 30 and 32 (right-skewed, some higher values)
For Southview -> between 28 and 30 (most concentrated there)
Hence, mean of Southview is lower than North Heights.
hello i need help with ym math today please and thanks
The annual cost if she chooses to make monthly payment is $1920 and money saved is $170
How to determine the incomes?The given parameters that will help us to determine the incomes are
Mindley switching to insurance comapnyAnnual premium $1750/ yearMonthly premium $160*12 = $1920a) Annual cost if she chooses to make one annual monthly installment is $1920
b) Money saved is she makes one annual payment is $(1920-1750)= $170
3) Volume of gas = 60 L
Efficiency rating = 10.2km/L
Average drive = Volume / Efficiency = 60/10.2 = 5.9km/L
b) Cost of gas = 149.9⊄⊄/L
Number of liters =60
= 60*149.9
=$8994
c) Constant gas price = $149.9⊄/L
Number of weeks /year = 52
=52*149.9
= $7795
4) Morgan pay $15/hr
Number of hours per week = 40
Gross monthly income = 40*15*4
=$2400
b) Monthly income $2400
Amount left after deduction = 85%
=0.85*2400
Net income = $2040
In conclusion Mindley receives $1920 monthly and saves $170
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find the truth value Of 3+4= 12, then 3+2=6
The truth value of "If 3 + 4 = 12, then 3 + 2 = 6", is true.
What is Truth Values?Truth value is defined as whether the given proposition is either true or false, not both.
Here the proposition is of the form if p, then q.
Here p is the statement 3 + 4 = 12 and q is the statement 3 + 2 = 6.
Here, both of the propositions are false.
The truth value of 'if p, then q' is false only when p is true and q is false. In all other cases the truth value is true.
Here, since both of the statements are false, the truth value is true.
Hence the truth value of the given proposition is true.
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Find tan0, where 0 is the angle shown.
Give an exact value, not a decimal approximation.
The exact value of tan θ = 15/ 8
What are trigonometric identities?Trigonometric Identities are defined as the equalities involving trigonometry functions and also one that holds true for all the values of the variables in the given equation.
The trigonometric functions are;
sinecosinetangentcotangentsecantFrom the information given, we have;
tan θ = opposite/ adjacent
To determine the adjacent sent
17² - 15² = x²
x = √64
x = 8
Substitute the value
tan θ = 15/8
Hence, the value is 15/8
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A mechanic charges $45 per hour for labor plus $55 for a computer diagnostic test. The mechanic charges a customer $595 to repair a vehicle. How many hours did the mechanic spend on the repair?
Answer:
The mechanic spent 12 hours on the repair.
Step-by-step explanation:
$595-$55=£540. £540 is the total of the amount the mechanic charges for an hour, MINUS the computer diagnostic testTo find out how many hours the mechanic spent on the repair, we have to do $540 divided by $45, which is 12.The mechanic spent 12 hours on the repair.
I need help with this?
The first equation will be multiplied by 3 and that of the second by 4.
What is an elimination method?An elimination method is a process of solving a system of linear equation, in this we make coefficients of the one variable equal and subtract the equations.
Given that are two equations to be solved by using elimination method,
-4x+4y = 32.....(i)
3x-y = 12......(ii)
To eliminate x, we will multiply eq(i) by 3 and eq(ii) by 4
-12x+12y = 96.....(iii)
12x-4y = 48....(iv)
Solving the equations, we get,
8y = 144
y = 18
Put y = 18 in eq (ii)
3x-18 = 12
3x = 30
x = 10
Hence, the first equation will be multiplied by 3 and that of the second by 4.
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Nevaeh has $0.80 worth of nickels and dimes. She has a total of 11 nickels and dimes altogether. Graphically solve a system of equations in order to determine the number of nickels, x,x, and the number of dimes, y,y, that Nevaeh has.
Answer: We can set up a system of equations to represent this problem. The first equation represents the total value of the nickels and dimes in terms of the number of nickels and dimes that Nevaeh has:
0.05x + 0.1y = 0.80
The second equation represents the total number of nickels and dimes that Nevaeh has in terms of the number of nickels and dimes that she has:
x + y = 11
To graphically solve this system of equations, we can use the slope-intercept form of the linear equations.
y = -2x + 22
y = -1/2 x + 8
The solution would be the point where the lines intersect , which x = 4, and y = 7 .
So she has 4 nickels, and 7 dimes.
Step-by-step explanation:
3/4 divided by 3/7 in simplest form
Answer:
7/
Step-by-step explanation:
3/4 * 7/
3 can be crossed
Leaving 7/
A small business celebrates serving 5110 customers in their first year of business how many customers did they average each day
The no. of customers they serve per day is equal to 14.
It is given that the total number of customers served in first year of business was 5110.
We have to find that what will be the average of servings per day ?
What do you mean by average ?
The average is the ratio of sum of all numbers to the total no. of numbers.
As per the question ;
Total number of people served in a year = 5110
We know that ;
1 year = 365 days
So ;
To calculate the average of servings per day we need to divide total number of servings by no. of days in 1 year.
i.e.,
Average of customers per day ;
= 5110 ÷ 365
= 14 customers per day
Thus , the no. of customers they serve per day is equal to 14.
Edet took sixth at the end of term test and each test was marked out of 80. If his marks were 48, 52, 46, 46, 44 and 52. What percentage of the total marks did he get?
The percentage of the total marks that Edet gets is 60%
How to calculate the percentage?The percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.
In this situation, the score of Edet will be:
= 48 + 52 + 46 + 46 + 44 + 52
= 288
Total score = 80 × 6
= 480
The percentage will be:
= 288 / 480 × 100
= 60%
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Which of the following is equivalent to 5/20 ? *
Mark only one oval.
2/10
10/30
5/10
1/4
F(x)=2 sin (1/2x)+1
What is the midline of the functionless
Answer: 4
Step-by-step explanation:
Let me get to know you:)
please, if you write an absurd anwser i will report it
a) The function is continuous in it's entire domain.
b) The increasing and decreasing intervals for the function are given as follows:
Increasing: (0,2).Decreasing: (2,10).What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
In this problem, we have a piece-wise function which has the definition changing at x = 2, hence the continuity must be studied at x = 2.
The lateral limits for the function in this problem are defined as follows:
[tex]\lim_{x \rightarrow 2^-} A(x) = \lim_{x \rightarrow 2} x^2 + 2 = 2^2 + 2 = 6[/tex][tex]\lim_{x \rightarrow 2^+} A(x) = \lim_{x \rightarrow 2} \frac{-3x + 30}{4} = 0.25(-3(2) + 30) = 6[/tex]The second limit is also equals to the numeric value at x = 2, due to the equal sign in the definition, hence the function is continuous at x = 2 and for all other values in the domain.
The intervals of increase and decrease are given as follows:
Increasing: (0,2). -> y = x² increases for x > 0, the 2 changes just the range.Decreasing: (2,10). -> decreasing line, due to the negative slope.TranslationThe function for this problem is the piece-wise function A(x).
Item a asks if the function is continuous.
Item b asks when the function is increasing and when it is decreasing.
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please answer this with work
Answer:
Step-by-step explanation:
-38 + -12x < -200
Answer:
-38 - 12x > -200
x = 13.5 min
Step-by-step explanation:
let x = minutes of the dive
-38 ft - 12 ft/min(x) > -200 ft
-12 ft/min(x) < -162 ft
x > -162/-12 **flip the inequality when you divide by a (-) number
x > 13.5 min
Starting at -38 ft, he has to dive longer than 13.5 minutes to go deeper than -200 ft at a rate of -12 ft/min
What is the solution for the system of linear equations shown in the graph?
Graph and answers in picture below
Answer:
(d) (-1/4, 3/4)
Step-by-step explanation:
You want the solution to the graphed system of equations.
SolutionThe solution is the point that satisfies both equations, the point where the lines intersect. That point is in the 2nd quadrant, where x-values are negative.
The only suitable answer choice is ...
(x, y) = (-1/4, 3/4)
2 1/7 - 1 2/5 give your awenser as a mixed number
Answer:
dunno la saya , gak bisa bahasa ingeris
Directions: Determine whether each relation is a function. Explain your answer.
X
12)
10)
#IN
13)
x
14)
15)
10
Answer:
10. Yes
11. No
12. Yes
13. Yes
14. No
15. No
Step-by-step explanation:
Use the vertical line test to determine whether or not a relation is a function. The vertical line test is when you draw a line through a relation and if that line intersects the relation more than ONCE, the relation is not a function.
10. Is a function, the vertical line only intersects the relation once.
11. Isn't a function, intersects the relation more than once.
12. Is a function, intersects the relation only once.
13. Is a function, only intersects the relation once.
14. Isn't the function, intersects the relation more than once.
15. Isn't a function, the relation intersects the function more than once.
Hope this helps.
A scientist uses a submarine to study ocean life.
She begins at sea level, which is an elevation of 0 feet.
She travels down 4.2 feet.
She then travels directly up 3.4 feet.
Next, she descends a second time, 10 feet.
Answer:
Below
Step-by-step explanation:
0 ft -4.2 + 3.4 - 10 = -10.8 ft or 10.8 ft below the surface
Find the slope of the line that has an equation of 4x-2y=6
4x - 2y = 6
2y = 4x - 6
y = (4x - 6)/2
y = 2x - 3
Hafiz has $25. His sister has 1/5 as much as Hafiz. His father has 40% as much as Hafiz. Calculate how much money Hafiz, his sister and his father have in total.
please answer it
Answer:
Step-by-step explanation:
According to question, we know that
His Sister has "1/5*$25 which is equal to $5, and his father has "40%*$25 which is equal to 0.4 * $25 = $10". So, the money Hafiz, his sister and his father have in total
= $25+$5+$10 = $40
Hafiz = $25
Sister = [tex]\frac{1}{5}[/tex]
Father = 40%
FindTotal money of Hafiz, Sister, and Father altogether.
SolutionSister[tex]\frac{1}{5} X[/tex] $25
= $5
Father40% (0.4) x $25
= $ 10
Add all$ 25 + $ 5 + $ 10
Answer$ 40Please help me solve this
a. The model represents exponential growth.
b. The annual percentage increase is 3%.
c. After 2390 decades the population was about 590000.
What is the formula for exponential growth and exponential decaying function?The formula for exponential growth is [tex]y = y_₀.e^{(kt)}.[/tex]
The formula for exponential decay is [tex]y = y_₀.e^{(-kt)}.[/tex]
Given, The population P(in thousands) of Austin Texas during a recent decade is approximated by [tex]y = 492(1.03)^t[/tex].
The model represents exponential growth as time can not be negative.
The annual percentage increase in the model [tex]y = 492(1.03)^t[/tex] is 3%
as 1.03×100% = 103%.
The time when the population was about 590000 since the beginning of a decade is,
[tex]590000 = 492(1.03)^t[/tex].
[tex](1.03)^t = 590000/492[/tex].
[tex](1.03)^t = 1199.1869[/tex].
[tex]log_{1.03}1.03^t = log_{1.03}1199.1869[/tex].
t = 2389.84 Or 2390 decades.
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if its a linear equation in two variables
Answer:
SOLVE A SYSTEM OF LINEAR EQUATIONS BY GRAPHING.
Graph the first equation.
Graph the second equation on the same rectangular coordinate system.
Determine whether the lines intersect, are parallel, or are the same line.
Identify the solution to the system. ...
Check the solution in both equations.
Step-by-step explanation:
An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.
helo i need help with my math please thanky uo i need help with question 3
On one tank of gas Charlie will drive 612 km
At a cost of 149.9, Charlie will fill the tank with the sum of 8994
Annual cost of filling the tank 467688
How to find how far Charlie can drive on one tank of gasInformation from the problem have it that the efficiency if the Volkswagen golf is 10.2 km/L
Hence, on one liter rides 10.2 km and on a tank which is 60 L Charlie will ride
= 60 * 10.2
= 612 km
Cost of filling the tank
The cost per liter is 149.9 for 60 L we have
= 149.9 * 60
= 8994
Filling the tank once week, the cost for filling in one year is
1 year is 52 weeks
= 8994 * 52
= 467688
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You are dealt one card from a 52-card deck. Find the probability that you are not dealt a jack or a ten
If you are dealt one card from a 52-card deck. The probability that you are not dealt a jack or a ten is 12/13.
How to find the probability?Since there are 4 aces in a deck of card 52 first step is to find the number of cards not aces in a deck of 52
Number of cards not aces in a deck = 52 -4
Number of cards not aces in a deck = 48
Now let find the probability that you won't draw an ace.
Probability = 48/52
Probability = 24/26
Probability = 12/13
Therefore we can conclude that the probability is 12/13.
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2) Which of the following would be A' if A (2, -3)
was reflected over the x axis?
a. A'(-2, -3)
c. A'(-2, 3)
b. A'(2, 3)
d. A'(2, -3)
A'(-2, -3) would result if A (2, -3) was reflected over the x axis. Point (2,3)'s representation under the x-axis is (2,-3). from the y-axis P image (-a,b).
What is (2, -3) reflected over the x-axis?Changing the sign of the value on the opposite axis, in this case the y-value, is all that is required to reflect a point such as (-2,3) across the x-axis in a question. As a result, this location has a y-value of 3. A positive number, this. A negative sign produces a result of -3.
While the Y coordinate remains the same when you reflect across the Y-axis, the X coordinate changes sign. Determining the reflection of (2, 3) across the Y-axis is therefore (-2, 3). The Y-coordinate of each point must be negative while reflecting across the X axis, but the X value must remain constant.
Therefore the correct answer is option a ) A'(-2, -3)
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Consider all five-digit numbers that can be created from the digits 0-9 0 - 9 where the first and last digits must be odd and no digit can repeat. What is the probability of choosing a random number that starts with 7 7 from this group? Enter a fraction or round your answer to 4 4 decimal places, if necessary.