Please help! Need answer ASAP!
Aliya lined up the interior angles of the triangle along line p below.
When the measure of angle A increases in the triangle, what happens to angle A on line p?
A) It also increases.
B) It decreases.
C) It stays the same.
D) It may increase, or it may stay the same.
Answers
A ) It also increases.
EXPLANATION:
When the measure of angle A increases im the trianes, the measure of angle A on line p also increases. This is angle A in the triangle and angle A on line p are equivalent to each other. Hence, if there is an increase to one of the angle As then there is also an increase to the other.
Therefore, the answer must be:
A ) It also increases.
The measure of angle A increases in the triangles, the measure of angle A on line p also increases, option A is correct.
What is Coordinate System?A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
Given that Aliya lined up the interior angles of the triangle along line p .
We have to find the what happens to angle When the measure of angle A increases in the triangle.
An angle is the figure formed by two rays, called the sides of the angle, sharing
When the measure of angle A increases in the triangles, the measure of angle A on line p also increases.
Hence, the measure of angle A increases in the triangles, the measure of angle A on line p also increases, option A is correct.
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Related Questions
Help me please!!! 30 points! :)
Answers
[tex] \frac{625 {(5xy)}^{ - 3} }{ {(5x)}^{2} {y}^{7} } \: = \: 625 \times \frac{1}{ {(5xy)}^{3} } \times \frac{1}{ {(5x)}^{2} {y}^{7} } \: = \: 625 \times \frac{1}{125 {x}^{3} {y}^{3} } \times \frac{1}{25 {x}^{2} {y}^{7} } \: = \: \frac{1}{5 {x}^{5} {y}^{10} } [/tex]
Drag and drop numbers into the boxes so that the paired values are in a proportional relationship.
x 1 3 _____ 5 8
y 4 12 16 20 _____
4
12
32
8
36
Answers
Answer:
4 and 32
Step-by-step explanation:
We are given paired values for two variables x and y and we are to fill in the missing values such that they are in a proportional relationship.
For x, we have the following paired values:
[tex]1, 3, ___, 5, 8[/tex]
So from the given options, 4 fits the best here which is greater than 3 and lesser than 5.
And for y, we have:
[tex]4, 12, 16, 20, ___[/tex]
Here, 32 fits the best from all the options as it is the next (available) number after 20.
What is an equation of the line, in point-slope form, that passes through the given point and has the given slope?
Answers
Answer: [tex]y -3 = \frac{4}{11} (x - 11)[/tex]
Step-by-step explanation:
We can use the point-slope formula to write the equation of a line given a point on the line and the slope of the line:
Slope = m
Given point (x₁,y₁)
Formula = (y-y₁) = m(x-x₁)
Given point: (11,3); slope: 4/11
Answer : [tex]y - 3 = \frac{4}{11} (x - 11)[/tex]
[tex]\textit{\textbf{Spymore}}[/tex]
Order the numbers from least to greatest. A) 1.5, 1.66, 2.4, 3.25, 3.33 B) 1.5, 1.66, 2.4, 3.33, 3.25 C) 1.66, 1.5, 2.4, 3.25, 3.33 D) 3.25, 3.33, 2.4, 1.66, 1.5
Answers
The expression 1/2bh gives the area of a triangle where b is the base of the triangle and h is the height of the triangle. What is the area of a triangle with the base of 7cm and a height of 4 cm?
Answers
[tex]A_{\triangle}=\dfrac{1}{2}bh\\\\\text{We have}\ b=7cm,\ h=4cm\\\\\text{Substitute:}\\\\A_{\triangle}=\dfrac{1}{2}(7)(4)=\dfrac{28}{2}=\boxed{14\ cm^2}[/tex]
There are 65 students who walk to West Middle School each day. This is 12.5% 0f the total student at the school. How many students attend West Middle School
Answers
Equation:
65=0.125x
Divide both sides by 0.125.
520=x
There are 520 students.
Sketch the plane curve represented by the given parametric equations. Then use interval notation to give the relation's domain and range. X = 2t, y = t2 + t + 3
Answers
Answer:
Domain: [tex]( -\infty,\infty )[/tex] and Range: [tex][ -1,\infty )[/tex]
Step-by-step explanation:
We have the parametric equations [tex]x= 2t[/tex] and [tex]y=t^{2}+t+3[/tex].
Now, we will find the values of 'x' and 'y' for different values of 't'.
t : -3 -2.5 -2 -1.5 -1 0 1 1.5 2
[tex]x= 2t[/tex] : -6 -5 -4 -3 -2 0 2 3 4
[tex]y=t^{2}+t+3[/tex] : 9 6.75 5 3.75 3 3 5 6.75 9
Now, we can see that these parametric equations represents a parabola.
The general form of the parabola is [tex]y=ax^{2}+bx+c[/tex].
Now, we have the point ( x,y ) = ( 0,3 ). This gives that c = 3.
Also, we have the points ( x,y ) = ( -2,3 ) and ( 2,5 ). Substituting these in the general form gives us,
4a - 2b + 3 = 3 → 4a - 2b = 0 → b = 2a.
4a + 2b + 3 = 5 → 4a + 2b = 2 → 2a + b = 1 → 2a + 2a = 1 ( As, b = 2a ) → 4a = 1 → [tex]a=\frac{1}{4}[/tex].
So, [tex]b=\frac{1}{2}[/tex].
Therefore, the equation of the parabola obtained is [tex]y=\frac{x^{2}}{4}+\frac{x}{2}+3[/tex].
The graph of this function is given below and we can see from the graph that domain contains all real numbers and the range is [tex]y\geq -1[/tex].
Hence, in the interval form we get,
Domain is [tex]( -\infty,\infty )[/tex] and Range is [tex][ -1,\infty )[/tex]
Answer:
Domain:
[tex](-\infty,\infty)[/tex]
Range:
[tex][2.75,\infty)[/tex]
Step-by-step explanation:
we are given parametric equation as
[tex]x=2t[/tex]
[tex]y=t^2+t+3[/tex]
We can change into rectangular equation
we can eliminate t from first equation and plug into second equation
[tex]x=2t[/tex]
[tex]t=\frac{x}{2}[/tex]
now, we can plug that into second equation
[tex]y=(\frac{x}{2})^2+\frac{x}{2}+3[/tex]
now, we can draw graph
Domain:
we know that
domain is all possible values of x for which any function is defined
we can see that our equation is parabolic
and it is defined for all values of x
so, domain will be
[tex](-\infty,\infty)[/tex]
Range:
we know that
range is all possible values of y
we can see that
smallest y-value is 2.75
so, range will be
[tex][2.75,\infty)[/tex]
Can someone give 2 examples of a logarithmic equation with infinite solutions?
Answers
Assuming what is meant by "infinite solutions" are infinite number of solutions of a logarithmic equation.
[tex]\frac{1}{2}\log x^2 - \log \sqrt{x} - \log \sqrt{x} = 0[/tex]
and
[tex]\frac{1}{2}x-2\ln e^x=-\frac{3}{2}x[/tex]
Logarithmic equations with infinite solutions have graphs that look like dying-out exponentials. They can have infinite solutions because there are infinitely many values of y that satisfy the equation.
Examples of Logarithmic Equations with Infinite Solutions:
1. Logarithms to the base 10 (common logarithms):
In the equations below, y is the exponent to which 10 must be raised to equal x, so y is the common logarithm (log) of x.
x = 10^y
x = 10^y+1
2. Logarithms to the base e (natural logarithms):
In the equations below, y is the power to which e must be raised to equal x, so y is the natural logarithm (ln) of x.
x = e^y
x = e^y+1
Both of these equations have graphs that look like dying-out exponentials. They have infinite solutions because there are infinitely many values of y that satisfy the equation. Whenever the base is positive and not equal to 1, logarithmic equations can have infinite solutions.
If two angles are supplementary, which is the sum of their measurements? A. 45o B. 90o C. 120o D. 180o
Answers
Two supplementary angle when added together need to equal 180 degrees.
Answer:
Two supplementary angle when added together need to equal 180 degrees.
Step-by-step explanation:
solve 14^x+1=36
Round to the nearest ten-thousandth.
Answers
Answer:
x = 1.3472 to the nearest ten thousandth.
Step-by-step explanation:
14^x + 1 = 36
14^x = 35
Taking logarithms:-
x ln 14 = ln 35
x = ln 35 / ln 14
= 1.3472.
The solution, rounded to the nearest ten-thousandth, is x = 1.5404.
To solve the equation [tex]14^x + 1 = 36[/tex], we first isolate the exponential term by subtracting 1 from both sides of the equation, which gives us [tex]14^x = 35.[/tex]
The next step is to take the logarithm of both sides of the equation.
We could use any base for the logarithm, but it's common to use base 10 or the natural logarithm base (e). In this case, let's use the natural logarithm:
[tex]ln(14^x) = ln(35)[/tex]
We can then use the property of logarithms which allows us to bring the exponent down as a multiplier:
[tex]x * times ln(14) = ln(35)[/tex]
Now, you can solve for x by dividing both sides by ln(14):
[tex]x = ln(35) / ln(14)[/tex]
Using a calculator, we find the quotient and then round to the nearest ten-thousandth:
x = 1.5404
This value is the solution to the original equation.
You are going to flip a coin 8 times. The first 3 times you flip the coin you get tails. What is the probability that all the remaining flips will also be tails?
Answers
Answer:
So when you flip the coin 8 times and you get tails 3 of the times then you should do 3 plus 5 and you will get 8 as your total again so then the answer is 5 out of 8 total.
Step-by-step explanation:
The probability that all the remaining flips will be tails is 1/32, or approximately 0.03125.
Explanation:The probability of getting tails on each coin flip is 50 percent since a fair coin has two equally likely outcomes: heads or tails.
If the first three coin flips resulted in tails, the remaining five coin flips are independent events. The probability of getting tails on each of the remaining flips is still 50 percent.
The probability of getting all the remaining flips to be tails is calculated by multiplying the probabilities of each individual flip. Since there are five remaining flips, the probability is 0.5 raised to the power of 5, or 1/32 (approximately 0.03125).
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If a right triangle has sides of length a, b and c and if c is the largest, then it is called the "hypotenuse" and its length is the square root of the sum of the squares of the lengths of the shorter sides (a and b). assume that variables a and b have been declared as doubles and that a and bcontain the lengths of the shorter sides of a right triangle: write an expression for the length of the hypotenuse.
Answers
Assuming this is for a programming language like c++, then the expression might look like
c = sqrt(a*a + b*b)
or you can use the pow function (short for power function)
c = sqrt( pow(a,2) + pow(b,2) )
writing "pow(a,2)" means "a^2"; similarly for b as well.
the length of hypotenuse can be found using the formula [tex]c = \sqrt{a^2+b^2}[/tex]
The pytharogas theorem states that:
[tex]hypotenuse^2 = perpendicular^2+ base^2[/tex]
The Pythagorean Theorem relates the length of the legs of a right triangle, labeled a and b, with the hypotenuse, labeled c. The relationship is given by:
[tex]a^2 + b^2 = c^2[/tex]
This can be rewritten, solving for c:
[tex]c = \sqrt{a^2+b^2}\\\\[/tex]
Thus, the length of hypotenuse can be found using the formula [tex]c = \sqrt{a^2+b^2}[/tex]
River rambler charges $25 per day to rent a kayak. How much will it cost to rent a kayak for 5 days? Write and solve an equation to solve this problem.
Answers
Answer:
C=25d
Step-by-step explanation:
We write an equation where C or cost is my output and d or days is my input. I should be able to put in any number of days and find the cost. Let's gather some data:
River Ramble
Day 1 $25(1)=25 cost
Day 2 $25(2)=50 cost
Day 3 $25(3)=75 cost
Day d $25(d)=C.
Our equation is C=25d.
Please help! Write the slope-intercept form of the equation for the line.
a. y=-8/7x-3/2
b. y=-3/2x+7/8
c. y=-7/8x-3/2
d. y=7/8x-3/2
Answers
Answer:
C
Step-by-step explanation:
The slope intercept of a line is y=mx +b where
m is the slope which is calculated as the vertical distance divided by the horizontal distance between two points.b is the y-intercept for value on the y-axis for which the line crosses it.This graph crosses the y-axis (the vertical line) halfway between -1 and -2. This is -3/2. This means only answers a, c, and d are options.
The graph moves up from -3/2 to its next point at (-4,0). We calculate the slope using:
Slope:[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We substitute [tex]x_1=0\\y_1=-1.5[/tex] and [tex]x_2=-4\\y_2=2[/tex]
[tex]m=\frac{2-(-1.5)}{-4-0}[/tex]
[tex]m=\frac{2+1.5}{-4}=\frac{3.5}{-4} =-0.875[/tex]
This decimal is equivalent to -7/8. This means C is the answer.
This equation represents a line with a slope of [tex]\( -\frac{7}{8} \)[/tex](meaning the line slopes downward from left to right) and a y-intercept of [tex]\( -\frac{3}{2} \)[/tex](where the line crosses the y-axis). The correct answer is option c
The slope-intercept form of the equation of a line is [tex]\( y = mx + b \),[/tex] where m represents the slope of the line, and b represents the y-intercept (where the line crosses the y-axis).
Let's analyze each option:
a.[tex]\( y = -\frac{8}{7}x - \frac{3}{2} \):[/tex]
- Slope [tex]\( m = -\frac{8}{7} \)[/tex]
- y-intercept [tex]\( b = -\frac{3}{2} \)[/tex]
b. [tex]\( y = -\frac{3}{2}x + \frac{7}{8} \):[/tex]
- Slope [tex]\( m = -\frac{3}{2} \)[/tex]
- y-intercept[tex]\( b = \frac{7}{8} \)[/tex]
c.[tex]\( y = -\frac{7}{8}x - \frac{3}{2} \):[/tex]
- Slope [tex]\( m = -\frac{7}{8} \)[/tex]
- y-intercept [tex]\( b = -\frac{3}{2} \)[/tex]
d.[tex]\( y = \frac{7}{8}x - \frac{3}{2} \):[/tex]
- Slope[tex]\( m = \frac{7}{8} \)[/tex]
- y-intercept[tex]\( b = -\frac{3}{2} \)[/tex]
Among the given options, the correct slope-intercept form is option c:
[tex]\[ \boxed{y = -\frac{7}{8}x - \frac{3}{2}} \][/tex]
A satellite travels about 2272 miles in 8 minutes about how many miles does a satellite travel in 3 minutes
Answers
Answer:
852 miles
Step-by-step explanation:
We presume the speed is constant, so the satellite will travel 3/8 the distance in 3/8 the time.
... d = (3/8)·(2272 miles) = 852 miles
_____
1 minute is 1/8 of 8 minutes, so 3 minutes is 3/8 of 8 minutes.
What is the answer to: (51 + 11.22 + 35.92)?
Answers
Answer:
It would equal 98.14
Step-by-step explanation:
Solve for x: 5 over quantity x squared minus 4 plus 2 over x equals 2 over quantity x minus 2.
x = 8
x = –4
x = 8 and x = –4
No Solution
Answers
[tex]\text{The domain}\\\\x\neq0\ \wedge\ x\neq-2\ \wedge\ x\neq2[/tex]
[tex]\dfrac{5}{x^2-4}+\dfrac{2}{x}=\dfrac{2}{x-2}\qquad\text{subtract}\ \dfrac{2}{x-2}\ \text{from obth sides}\\\\\dfrac{5}{x^2-2^2}+\dfrac{2}{x}-\dfrac{2}{x-2}=0\\\\\dfrac{5}{(x-2)(x+2)}+\dfrac{2}{x}-\dfrac{2}{x-2}=0\\\\\dfrac{5x}{x(x-2)(x+2)}+\dfrac{2(x-2)(x+2)}{x(x-2)(x+2)}-\dfrac{2x(x+2)}{x(x-2)(x+2)}=0\\\\\dfrac{5x+2(x^2-4)-2x(x+2)}{x(x-2)(x+2)}=0\\\\\dfrac{5x+2x^2-8-2x^2-4x}{x(x-2)(x+2)}=0\\\\\dfrac{x-8}{x(x-2)(x+2)}=0\iff x-8=0\to\boxed{x=8}\in D[/tex]
Jupiter has 11 more than 4 times as many moons has Neptune. Neptune has 14 moons. Let j equal the number of moons Jupiter has.
Answers
Final answer:
Jupiter has 67 moons.
Explanation:
To solve this problem, let's define j as the number of moons Jupiter has. According to the given information, Jupiter has 11 more than 4 times as many moons as Neptune, which has 14 moons. So, we can set up an equation: j = 4n + 11, where n is the number of moons Neptune has. Since Neptune has 14 moons, we can substitute that value into the equation: j = 4(14) + 11. Simplifying further, we get j = 56 + 11 = 67. Therefore, Jupiter has 67 moons.
Shryia read a 480480-page-long book cover to cover in a single session, at a constant rate. After reading for1.51.5 hours, she had 402402 pages left to read.Let P(t)P(t) denote the number of pages to read PP as a function of time tt (measured in hours).Write the function's formula.P(t)=
Answers
Answer:
Function formula P(t) = -52t +480
Step-by-step explanation:
here, P(t) denotes the number of pages to read and t represents the time in hour.
Given the statement: Shryia read a 480-page-long book cover to cover in a single session, at a constant rate. After reading for 1.5 hours, she had 402 pages left to read.
⇒Total number of page in a long book = 480
After reading for 1.5 hours, she had 402 pages left to read.
Then,
Total number of page Shryia read in 1.5 hours is:
[tex]480-402 = 78[/tex]
Constant rate at which she is reading her book = [tex]\frac{78}{1.5} = 52[/tex] page per hour
Then, the function formula is given by:
P(t) = -52t + 480 ; where t is in hours.
Check:
P(t) = -52t + 480
P(1.5) = -52(1.5) + 480 = -78 + 480 = 402 True.
The measure of an angle is 78 less than the measure or its complement.What is the measure of the angle
Answers
Answer:
84°
Step-by-step explanation:
2 complementary angles sum to 90°
let x be the angle then complement = x - 78, hence
x + x - 78 = 90 ( add 78 to both sides )
2x = 168 ( divide both sides by 2 )
x = 84
hence the angle is 84°
someone help i cant do math bc im pretty
Answers
Answer:
52
Step-by-step explanation:
One way is to simply count the number of yellow squares.
I count 52, so the area is 52 square units.
Another way is to find the area of the larger rectangle and subtract from it the area of the smaller rectangle.
The larger rectangle is 11 by 6. Area = 11 * 6 = 66.
The smaller rectangle is 7 by 2. Area 7 * 2 = 14.
Area shaded in yellow = 66 = 14 = 52
Answer: area = 52 square units
Answer:
"i cant do math cuz im pretty" such pick me vibes LOL
Step-by-step explanation:
Ryan will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $59 and costs an additional $0.08 per mile driven. The second plan has an initial fee of $46 and costs an additional $0.10 per mile driven.A) for what amount of driving do the two plans cost the same? B) What is the cost when the two plans cost the same
Answers
1st's plan total cost = 0,08x + 59
2nd's = 0,10x + 46
(x stands for the total of miles)
a) For you two know when the costs will be the same, you set one equation equal to the other and you find out that if you drive 650 miles, you'd pay the same amount of money. It doesn't matter which plan you pick.
b) Knowing this, just place 650 into the equation and solve.
Help plz 30 points!!
Answers
900 workers : 3.2×10⁵
Dividing by 9×10² becomes
1 worker :[tex]\frac{3.2}{9}[/tex] ×10³
3.2/9 is just 0.36 rounded so it is
1 worker : 0.36×10³
or A
Answer:
the answer is a
Step-by-step explanation:
A research study is done to find the average age of all U.S. factory workers. The researchers asked every factory worker in Ohio what their birth year is. This research is an example of a ______.
census
survey
convenience sample
simple random sample
Answers
Answer: Census.
Step-by-step explanation:
Given statement:- A research study is done to find the average age of all U.S. factory workers. The researchers asked every factory worker in Ohio what their birth year is.
This research is an example of a census because research in which information is obtained through the responses that all available members of an entire population give to questions.
In other words "Census is an official survey of population in a certain area and records various details about the individuals".
The study querying every factory worker in Ohio for their birth year to determine the average age of all U.S. factory workers is a census, as it attempts to gather data from every member of the entire population of interest. (First option)
The research study done to find the average age of all U.S. factory workers where the researchers asked every factory worker in Ohio their birth year is an example of a census. A census involves gathering information about every individual in the entire population of interest.
In this case, the population of interest would be all factory workers, and by querying every one of them (assuming it was indeed every single factory worker in Ohio), it constitutes a census, not a survey, which typically involves a representative sample.
It is not a convenience sample since that would imply a non-random selection based on ease of access, and it's not a simple random sample because not all members of the larger population (nationwide factory workers) have an equal chance of being included.
Last year my family decided to put on a play It was A Great success . 200 people attended and we earned a total of 800 . If adults tickets cost 4 and children coat 2 dollar , how many adults were there
Answers
Answer:
200 adults
Step-by-step explanation:
We can set-up a system of equations to find the number of adults. We know children and adults attended. We will let c be the number of children and a be the number of adults. Since 200 people attended, then c+a=200.
We also know they made $800 and adult tickets cost $4 and child tickets cost $2. We can write 2c+4a=800.
We will solve by substituting one equation into the other. We start by solving the first equation for c. c+a=200 becomes c=200-a.
Now we substitute c=200-a into 2c+4a=800. Simplify and isolate the variable a.
2(200-a)+4a=800400-2a+4a=800400+2a=800400-400+2a=800-4002a=400a=200This means that 200 adults attended and 0 children attended.
What is the fourth term of the expansion of the binomial (2x + 5)5? A. 10x2 B. 5,000x2 C. 1,250x3 D. 2,000x3
Answers
Answer:
B would be the answer for this question.
Step-by-step explanation:
Answer: The fourth term is [tex]5000x^2.[/tex]
Step-by-step explanation: We are given to find the fourth term in the expansion of the following binomial :
[tex]B=(2x+5)^5.[/tex]
We know that
the r-th term in the expansion of the binomial [tex](a+x)^n[/tex] is given by
[tex]T_r=^nC_ra^{n-(r-1)}b^{r-1}.[/tex]
For the given term, we have
n = 5 and r = 4.
Therefore, fourth term is given by
[tex]T_4\\\\=^5C_{4-1}(2x)^{5-(4-1)}5^{4-1}\\\\=^5C_3(2x)^25^3\\\\=\dfrac{5!}{3!(5-3)!}\times4x^2\times125\\\\\\=\dfrac{5\times4}{2\times1}\times 500x^2\\\\=5000x^2.[/tex]
Thus, the fourth term is [tex]5000x^2.[/tex]
Simplify: (3–a)·2+a =
Answers
Answer:
The simplified form of the given expression is 6-a.
Step-by-step explanation:
The given expression is
[tex](3-a)\cdot 2+a[/tex]
According to distributive property.
[tex]a\cdot (b+c)=ab+ac[/tex]
Use distributive property.
[tex]3(2)-a(2)+a[/tex]
[tex]6-2a+a[/tex]
Combine like terms.
[tex]6+(-2a+a)[/tex]
[tex]6-a[/tex]
Therefore the simplified form of the given expression is 6-a.
A formula for electrical circuits states that E=P/\I where E represents the force in volts, P represents power in watts, and I represents current in amps. Solve this formula for I. Then find I when the force E = 3.6 volts and the power P = 45 watts.
Answers
Answer:
[tex]I=12.5[/tex] amp
Step-by-step explanation:
The formula is,
[tex]E=\dfrac{P}{I}[/tex]
where,
E = Electromotive force in volts,
P = Power in watts,
I = Current in amps.
Given values are,
E = 3.6 volts,
P = 45 watts,
I = ??
Putting the values,
[tex]\Rightarrow 3.6=\dfrac{45}{I}[/tex]
[tex]\Rightarrow I=\dfrac{45}{3.6}=12.5[/tex] amp
Help me with these math questions.......
Answers
Answer: 118.40, 300, $18,000
Step-by-step explanation:
a) p(x) = [tex]-\frac{1}{5} (8) + 120[/tex]
p(8) = [tex]-\frac{8}{5} + 120[/tex]
= -1.60 + 120
= 118.40
b) R(x) = x * p(x)
= [tex]x(-\frac{1}{5}x + 120)[/tex]
= [tex]-\frac{1}{5}x^{2} + 120x[/tex]
a=[tex]-\frac{1}{5}[/tex], b=120
x = [tex]\frac{-b}{2a}[/tex]
= [tex]\frac{-120}{-\frac{2}{5}}[/tex]
= [tex]\frac{-120(5)}{-2}[/tex]
= 300
c) R(x) = [tex]-\frac{1}{5}x^{2} + 120x[/tex]
R(300) = [tex]-\frac{1}{5}(300)^{2} + 120(300)[/tex]
= -18,000 + 36,000
= 18,000
***********************************************************************
sec θ = [tex]\sqrt{6}[/tex]
[tex]\frac{hypotenuse}{adjacent} = \frac{\sqrt{6}}{1}[/tex]
adjacent² + opposite² = hypotenuse²
1² + opposite² = (√6)²
1 + opposite² = 6
opposite² = 5
opposite = √5
csc θ = [tex]\frac{hypotenuse}{opposite} = \frac{\sqrt{6}}{\sqrt{5}} = \frac{\sqrt{30}}{5}[/tex]
cot θ = [tex]\frac{adjacent}{opposite} = \frac{1}{\sqrt{5}} = \frac{\sqrt{5}}{5}[/tex]
sin θ = [tex]\frac{opposite}{hypotenuse} = \frac{\sqrt{5}}{\sqrt{6}} = \frac{\sqrt{30}}{6}[/tex]
cos θ = [tex]\frac{adjacent}{hypotenuse} = \frac{1}{\sqrt{6}} = \frac{\sqrt{6}}{6}[/tex]
tan θ = [tex]\frac{opposite}{adjacent} = \frac{\sqrt{5}}{1} = \sqrt{5}[/tex]
**********************************************************************
Answer: 144°
Step-by-step explanation:
[tex]\frac{\pi}{180}=\frac{4\pi}{5(x)}[/tex]
π(5x) = 180(4π)
x = [tex]\frac{180(4\pi)}{5\pi}[/tex]
= 36(4)
= 144
PLEASE HELP ME! What is the equation of a line that passes through the point (6, 1) and is perpendicular to the line whose equation is y=−2x−6?
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Answers
Answer:
y=0.5x-2
Step-by-step explanation:
if it is perpendicular to the line y=-2x-6, then you know that its slope is the negative reciprocal of that line, and it has a different y intercept which you need to solve for using the point given. You solve by plugging in the x and y values from the point and plugging in the slope into the standard equation, and solving for b, the y intercept
y=0.5x+b
1=0.5(6)+b
1=3+b
-2=b
The equation of the line that passes through the point (6, 1) and is perpendicular to the line whose equation is y=−2x−6 is y = 0.5x - 2.
How to find equation of straight line from concept of perpendicular line ?From the classic definition of straight lines, we know that if we have to find an equation of a straight line being perpendicular to another straight line then the slope of the new equation of straight lines becomes negative reciprocal of the slope of given perpendicular line.
Finding the equation of the required straight line -Mathematically, let m1 be the slope of the new straight line and m be the slope of the given perpendicular line, then we have
m1 = -(1/m)
Now, we have given equation y = -2x - 6
Thus slope of the required equation is say (m1) = -(-1/2) = 0.5
Thus the equation formed is y = (m1)x + c [where c is the y-intercept]
∴ y = 0.5x + c
The point given is (6,1) , thus y = 1 and x = 6
Thus the given equation can be formed as
⇒ 1 = 0.5*6 + c
∴ c = 1 - 0.5*6 = -2
The value of y-intercept of the required straight line is -2
The equation of straight line formed is y = 0.5x - 2.
Thus the equation of the line that passes through the point (6, 1) and is perpendicular to the line whose equation is y = − 2x − 6 is y = 0.5x - 2.
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