For the Propositional Function each proposition ∀x∀y P(x,y) is false.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
It is given that Propositional function -
P(x,y) : x ≥ y
Universal quantifier x Universal quantifier y Propositional function
∀x∀y P(x,y)
For every positive integer = every positive integer ≥ every positive integer
But this is false.
Example - x = 1 and x = 2
x < y
Therefore, the given statement is false.
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Let P(x,y) be the propositional function x≥y. The domain of discourse is Z+×Z+. Tell whether each proposition is true or false.
∀x∀yP(x,y)
is x+y=8
and x^2+y^2=80
then what is xy?
a. 16
b. -8
c. 8
d.-16
e.-32
Answer: Given the two equations x + y = 8 and x^2 + y^2 = 80, we can use the first equation to solve for x or y and substitute that expression into the second equation.
Let's solve for y:
y = 8 - x
Now we can substitute this expression for y into the second equation:
x^2 + (8 - x)^2 = 80
Expanding the square and collecting terms gives:
x^2 + 64 - 16x + x^2 = 80
Combining like terms:
2x^2 - 16x + 16 = 80
Moving all terms to the left side:
2x^2 - 16x - 64 = 0
Using the quadratic formula, we can solve for x:
x = (-b ± √(b^2 - 4ac)) / (2a)
where a = 2, b = -16, and c = -64
x = (-(-16) ± √((-16)^2 - 4 * 2 * -64)) / (2 * 2)
x = (16 ± √(256 + 512)) / 4
x = (16 ± √768) / 4
x = (16 ± 8√6) / 4
Since x and y must be real numbers, we reject the negative square root. Therefore, x = (16 + 8√6) / 4.
Finally, substituting x into the first equation to find y:
y = 8 - x = 8 - (16 + 8√6) / 4 = (8 - 16) / 4 - 8√6 / 4 = -8 / 4 - 8√6 / 4 = -2 - 2√6.
Therefore, xy = x * y = (16 + 8√6) / 4 * (-2 - 2√6) = -16 - 16√6.
The answer is d. -16.
Step-by-step explanation:
write the degree of the given polynomials4x²-2x+1
Answer:
2
Step-by-step explanation:
the degree of polynomial is 2
the teacher has data representing the scores of thousands of students. for each student, the data contain the student name, the midterm exam score, the final exam score, and the result of the total points calculation. which of the following could be determined from the data?
From the data that teacher described, the following information could be determined:
1. The distribution of midterm and final exam scores for the students. This would allow you to see the range of scores and the overall performance of the students.
2. The average midterm and final exam scores for the students. This would give you an idea of the average performance of the students on each exam.
3. The correlation between final exam and midterm scores. This would indicate if there were a relationship between performance on the midterm and final exams.
4. The distribution of total points calculated for each student. This would allow you to see the range of total scores and the overall performance of the students.
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In a school long jump competition, A placed seventh, while B placed sixth. C, ranked above A and B, ranked above and below some friends. D does worse than E and ranks penultimate. How many of people participated in the contest?
However, we can't determine the exact number of participants with this information alone.
What's the Participated trying to say?an individual who engages in or becomes engaged in a specific action. Examples. Over three thousand people will be competing in the games, a worldwide athletic event. She has contributed significantly to the conversation.
Let's use logic to determine the possible rankings of the participants:
A placed seventh, so at least 6 people ranked higher than A.
B placed sixth, so at least 5 people ranked higher than B.
C ranked above A and B, so C must have ranked at least fifth. This means there are at least four people who ranked higher than C.
D does worse than E and ranks penultimate, which means D ranked second to last. Therefore, there must be at least two people who ranked worse than D. Also, E must have ranked higher than D, so there is at least one person who ranked higher than D.
Putting this information together, we know that there are at least 6 + 5 + 4 + 2 + 1 = 18 people who participated in the contest.
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Miya and her family are on vacation. During the drive from the airport to Bryce National Park, she saw 42 trucks and 23 blue cars. Write the ratio of blue cars to trucks three different ways.
Answer:
23 to 42
23:42
[tex]\frac{23}{42}[/tex]
Given that the height of a particular object at time t is
h(t) = 50t - 4.9t^2, find h when t = 2h (2)
40
If the Time taken by object is 2 hour then the height will be 80.4 feet.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
We have Given the function as
h(t) = 50t - 4.9t²
If time = 2 hours then put the value of t=2 in the above Equation we get
h(t) = 50t - 4.9t²
h(t) = 50(2) - 4.9(2)²
h(t) = 100 - 4.9 x 4
h(2) = 100 - 19.6
h(2)= 80.4
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Someone please help me ASAP!!! Find an equation for the sine graph
Answer:
Step-by-step explanation:
This graph goes up to 2 and down to -2, which tells us that the amplitude of the waves is 2. In the equation for the parent graph, y = sinx, we will throw the 2 out front which is where the amplitude goes in sin and cos curves:
y = 2sinx
14. G is the incenter of AABC,
AC; GR = 7, and m< BAC = 60
GT:______
m>BAG:______
In the triangle where G is the incenter of AABC, GT = 7, m>BAG = 120.
What is an incenter in a triangle?An incenter is a position within a triangle where the triangle's three angle bisectors connect. The lines that divide the angles in a triangle into two equal pieces are known as angle bisectors. The incenter is equidistant from the triangle's three sides, which means that the distance from the incenter to each side is the same. The incenter is also the core of the inscribed circle of the triangle, which is the greatest circle that can fit within the triangle. The incenter is a crucial point in trigonometry and geometry because it may be used to compute angles, sides, and other triangle features.
Given:
AABC, AC; GR = 7, and m<BAC = 60
Step 1: Since the angle bisector of any angle in a triangle divides that angle into two equal parts, m<BAC = 60 implies m<BAG = 120.
Step 2: Since the incenter of a triangle is equidistant from the three sides, GR = 7 implies GT = 7.
Therefore, GT = 7 and m>BAG = 120.
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Find each function value, if possible. (If an answer is undefined, enter UNDEFINED
g(t) = 5t² - 3t+ 6
(a) g(2)
(b) g(-1)
(c) g(t + 2)
Answer:
see below
Step-by-step explanation:
g(t) = 5t² - 3t+ 6
g(2) = 5*4 - 3*2 + 6 =20
g(-1) = 5*1 -3* (-1) +6 =5+3+6 = 14
g(t+2) = 5(t+2)² - 3(t+2) + 6
= 5*(t²+4t+4) - 3t -6+6
= 5t²+20t+20-3t
= 5t²+17t+20
What number should go in the space?
Multiplying by 0.65 is the same as decreasing by _____%.
pls show simple working out
Answer:
0.65*10=6.5
10*0.35=3.5
10-3.5=6.5
So, it is decreasing by 35%
Step-by-step explanation:
Explain why this graph does not represent a function.
A pack of cardinal flower seeds costs $4.
You spend $36 on seeds.
How many packs of seeds did you buy?
please explain how you got this answer.
Answer:
To find out how many packs of cardinal flower seeds you bought, you need to divide the total amount you spent ($36) by the cost per pack ($4).
$36 ÷ $4 = 9
Therefore, you bought 9 packs of cardinal flower seeds.
A pack of cardinal flower seeds costs $4. You spend $36 on seeds. The correct answer is 9.
What are cardinal flower seeds?Cardinals love sunflower seeds, particularly black oil sunflower seeds. Their thin shells are quite easy for cardinals to break. These songbirds can also eat hulled and heavier-shelled striped sunflower seeds due to their sturdy beaks.
So, if we spend $36 on seeds. we are going to use 36 and 4 to find are answer:
→ 36/4
→ = 9
Therefore, A pack of cardinal flower seeds costs $4. You spend $36 on seeds. The correct answer is 9.
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Please do it and show the work 10 points for brainliest answer
The rate of inflation for potatoes was 21%, for oranges it was 40%, and for ground beef it was 67%.
What do you mean by rate?The idea of rate is used in mathematics to describe how one quantity changes in relation to another. It is frequently expressed as a fraction or ratio and is a measurement of how quickly one thing is changing in relation to another.
For instance, velocity is the measure of how quickly a position changes in relation to time. Acceleration is the measure of how quickly a velocity changes with relation to time. The derivative of a function, which denotes the instantaneous rate of change at a specific location, is the rate of change of any function with regard to its independent variable.
The rate of inflation for each item can be calculated using the formula:
r = (P2/P1)¹/ⁿ - 1
where P1 is the price per pound in 2009 and P2 is the price per pound in the given year, and n is the number of years between the two prices (in this case, n = 1 year).
For Potatoes:
P1 = $0.620
P2 = $0.749
n = 1
r = (0.749/0.620)¹/¹ - 1 = 0.21 or 21%
For Oranges:
P1 = $0.910
P2 = $1.280
n = 1
r = (1.280/0.910)¹/¹ - 1 = 0.40 or 40%
For Ground beef:
P1 = $2.251
P2 = $3.775
n = 1
r = (3.775/2.251)¹/¹ - 1 = 0.67 or 67%
So, the rate of inflation for potatoes was 21%, for oranges it was 40%, and for ground beef it was 67%.
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4) Mr. Perez gives out about 2 grades
per week. Students currently have
7 grades in their gradebook. Write
a linear equation indicating the
number of grades students will
receive in Mr. Perez's class.
Slope:
Y-Intercept:
Equation:
A linear equation indicating the number of grades students will receive in Mr. Perez's class is as follows;
Slope: 2.
Y-Intercept: 7.
Equation: y = 2x + 7.
What is the slope-intercept form?In Mathematics, the slope-intercept form of a line can be calculated by using this mathematical expression:
y = mx + b
Where:
x and y represents the data points.m represents the slope of a line.b represents the y-intercept of a line.From the information provided above, we have the following slope and y-intercept on the line:
Y-intercept = 7
Slope, m = 2
Therefore, the required equation of line is given by:
y = mx + c
y = 2x + 7
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The population of a town increased from 3200 in 2008 to 5700 in 2009. Find the absolute and relative (percent) increase.
Absolute increase:
Relative increase:
%
Give answers accurate to at least 1 decimal place.
If the population of a town increased from 3200 in 2008 to 5700 in 2009, the absolute and relative (percent) increases are:
Absolute Increase = 2,500Relative Increase = 78.125%.What is the difference between absolute and relative increases?
Absolute increase refers to a numerical addition to the quantity of an item.
The absolute increase is the difference between the current value and the initial value.
On the other hand, the relative increase is expressed in percentage terms.
To compute the relative increase, divide the absolute increase by the initial value.
The population of the town in 2008 = 3,200
The population in 2009 = 5,700
The absolute increase in population = 2,500 (5,700 - 3,200)
The relative increase in population = 78.125% (2,500/3,200 x 100)
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Two mechanics worked on a car. The first mechanic charged $55 per hour, and the second mechanic charged $65 per hour. The mechanics worked for a combined total of 20 hours, and together they charged a total of $1250 . How long did each mechanic work?
The first mechanic worked for 5 hours and the second mechanic worked for 15 hours.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
Two mechanics worked on a car.
The first mechanic charged $55 per hour,
and the second mechanic charged $65 per hour.
The mechanics worked for a combined total of 20 hours,
and together they charged a total of $1250.
Let x be the number of working hours of the First mechanic and y be the
number of working hours of the second mechanic.
So
x + y = 20 {equation 1}
55x + 65y = 1250 {equation 2}
Substituting the value of y from the equation 1 to the equation 2,
55x + 65(20 - x) = 1250
55x + 1300 - 65x = 1250
-10x = -50
x = 5
And y = 15
Therefore, x = 5 and y = 15.
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5. The solar constant during the last glacial maximum was about 1363 W/m². The global
average albedo was slightly higher 0.305.
a) (3 points) Solve for the amount of solar radiation, En, available to warm the
average square meter on Earth during this time.
b) (2 point) Why do you think the albedo was higher during the last glacial maximum
than it is today?
The amount of solar radiation available is 415.4 W/m² and the albedo was higher during the last glacial maximum than it is today because there was more ice and snow on the planet.
Describe radiation.Radiation refers to the emission and transmission of energy through space or a material medium in the form of electromagnetic waves or energetic particles. Radiation can take many forms, including light, X-rays, and radio waves, and can be either ionizing (having enough energy to remove electrons from atoms and molecules) or non-ionizing (having insufficient energy to cause ionization). Radiation is a fundamental aspect of physics and plays a crucial role in many natural processes, such as nuclear reactions and the warming of the Earth by the sun.
a) The amount of solar radiation available to warm the average square meter on Earth during the last glacial maximum can be found by multiplying the solar constant by the average albedo:
En = 1363 W/m² * 0.305 = 415.4 W/m²
b) The albedo was higher during the last glacial maximum than it is today because there was more ice and snow on the planet. Ice and snow are very reflective and therefore have a high albedo, which means that they reflect more of the incoming solar radiation back into space, making the planet cooler. During the last glacial maximum, there was more ice and snow, which led to a higher average albedo and a cooler planet.
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A trapezoid has an area of 900 square meters. The height of the trapezoid is 40 meters (m), and
the length of the longer base is twice that of the shorter base. Find the length of each base of the trapezoid.
Check the picture below.
[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ A=900\\ b=2a\\ h=40 \end{cases}\implies 900=\cfrac{40(a+2a)}{2} \\\\\\ 1800=40(3a)\implies 1800=120a\implies \cfrac{1800}{120}=a\implies \boxed{15=a}~\hfill \boxed{b=30}[/tex]
8. A man started his journey at 11:57am and was scheduled to arrive at 12:49pm. If he arrived 15 minutes late, how long did his journey take?
Answer:
Below
Step-by-step explanation:
From 11:57 to 12:00 is 3 min then add 49 min to get to 12:49 then add the 15 min late = 3 + 49 + 15 = 67 MIN or 1hr 7 min
A monkey types on a 26-letter keyboard that has lowercase letters only. Each letter is chosen independently and uniformly at random from the alphabet. If the monkey types n = 1,000,004 letters. what is the expected number of times the sequence "proof" appears?
The expected number of times the sequence "proof" appears in a randomly generated string of 1,000,004 letters is approximately 36.
How to solve for the number of times that proof would appearThe expected number of times the sequence "proof" appears in a randomly generated string of n = 1,000,004 letters can be calculated using the formula:
expected_occurrences = (n - 4) / 26^4
where 26^4 is the number of possible 4-letter sequences that can be formed using a 26-letter keyboard. Plugging in n = 1,000,004, we get:
expected_occurrences = (1,000,004 - 4) / 26^4
≈ 36.08
So, the expected number of times the sequence "proof" appears in a randomly generated string of 1,000,004 letters is approximately 36.
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Your teacher tells you that the mean score for a test was a 70 and that the standard deviation was 7 for your class. You are given that the z-score for your test was 2.5. What did you score on your test?
Answer:
Check the image for the answer!
Step-by-step explanation:
Please mark me Brainliest!
can someone help me please
here is the picture
135 and 59 are the values of fog(5) and gof(5) respectively.
Composite functionsComposite functions are also known as function of a function. Given the functions below;
f(x) = x^2 + 6x
g(x) = x + 4
For fog(5)
fog(5) = f(g(5))
f(g(x)) = f(x +4)
f(g(x)) = (x+4)^2 + 6(x+4)
f(g(5)) = (9)^2 + 6(9)
f(g(5)) = 81. + 54 = 135
For gof(5))
g(f(x)) = g(x^2 + 6x)
g(f(x)) = x^2 + 6x + 4
g(f(5)) = 5^2 + 6(5) + 4
g(f(5)) = 59
Hence the value of the composite values fog(5) and gof(5) area 135 and 59
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Kerys is trying to expand the binomial using the binomial theorem expression, . What value(s) should she substitute for k? Why?Kerys is trying to expand the binomial using the binomial theorem expression, . What value(s) should she substitute for k? Why?
Kerys should substitute the values of k from 0 to 4 (inclusive) in the binomial theorem expression to expand the binomial (2x + y)⁴.
What is the Binomial Theorem?The binomial theorem states the principle for expanding the algebraic expression (x + y)ⁿ and describes it as the total of the phrases involving the unique exponents of the x and y variables. Each word in a binomial expansion has a coefficient, which is a numerical value.
here, we have,
The binomial theorem states that the expansion of the binomial (x+y)^n is given by the formula:
(x+y)n = ∑nk=0nCk xn-kyk = ∑nk=0nCk xkyn-k
The variable n represents the power to which the binomial is raised, in this case n = 4.
The variable k is the exponent of the second term in the binomial (b), in this case y.
So, with k = 0, the term will be aⁿ = (2x)⁴, with k = 1, the term will be
a^(n-1) *b = (2x)³y , and so on.
Therefore, he should substitute the values of k from 0 to 4 (inclusive) in the binomial theorem expression to expand the binomial (2x + y)⁴.
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If a rock is thrown upward on an exoplanet of a nearby star with initial velocity of……
A. The displacement is the change in position, which is given by the change in the height, so:
i. [1,2] = -5.46 m/s
ii. [1,1.1) = -1.39 m/s
iii. [1,1.01) = -0.138 m/s
iv. [1,1.001) = -0.0138 m/s
How did we get these values?(a) To find the average velocity over a time interval, we need to calculate the displacement during that time interval and divide it by the length of the interval. The displacement is the change in position, which is given by the change in the height, so:
i. [1,2]: Δs = y(2) - y(1) = [20(2) - 1.87(2)²] - [20(1) - 1.87(1)²] ≈ -5.46
Average velocity = Δs / Δt = -5.46 / (2 - 1) = -5.46 m/s
ii. [1,1.1): Δs = y(1.1) - y(1) = [20(1.1) - 1.87(1.1)²] - [20(1) - 1.87(1)²] ≈ -1.39
Average velocity = Δs / Δt = -1.39 / (1.1 - 1) = -1.39 m/s
iii. [1,1.01): Δs = y(1.01) - y(1) = [20(1.01) - 1.87(1.01)²] - [20(1) - 1.87(1)²] ≈ -0.138
Average velocity = Δs / Δt = -0.138 / (1.01 - 1) = -0.138 m/s
iv. [1,1.001): Δs = y(1.001) - y(1) = [20(1.001) - 1.87(1.001)²] - [20(1) - 1.87(1)²] ≈ -0.0138
Average velocity = Δs / Δt = -0.0138 / (1.001 - 1) = -0.0138 m/s
(b) The instantaneous velocity at t=1 is given by the derivative of the height function with respect to time, which is:
dy/dt = 20 - 3.74t
So the instantaneous velocity at t=1 is:
dy/dt(1) = 20 - 3.74(1) = 16.26 m/s (approximately)
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Sarah wants to install carpet to cover her rectangular dining room floor, which has a length of 12 feet and a width of 9 feet. The cost to install the carpet is $5 per square foot. Sarah predicts that the total cost to install the carpet will be $500. Which statement BEST explains why Sarah’s prediction is incorrect?
a.
Sarah rounded the area of the floor to 110 square feet.
b.
Sarah rounded the area of the floor to 108 square feet.
c.
Sarah rounded the area of the floor to 100 square feet.
d.
Sarah rounded the area of the floor to 98 square feet.
The solution is, c. Sarah rounded the area of the floor to 100 square feet., is statement BEST explains why Sarah’s prediction is incorrect.
What is area of a rectangle?Area of a rectangle (A) is the product of its length (l) and width (w).
A= l. w
here, we have,
rectangular dining room floor, which has a length of 12 feet and a width of 9 feet.
The cost to install the carpet is $5 per square foot.
so, area of the floor = A= l. w
= 108 ft^2
so, total cost = 108* 5
=$ 540
i.e. Sarah rounded the area of the floor to 100 square feet.
because, 100*5 = $500
Hence, The solution is, c. Sarah rounded the area of the floor to 100 square feet., is statement BEST explains why Sarah’s prediction is incorrect.
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One angle of a right triangle measures 80°. What is the measure of the other acute angle? please help i dont understand, ty!!
Answer:
10 degrees
Step-by-step explanation:
Triangle Interior Angles:In a triangle, the interior angles of a triangle (the angles in the inside) will always add up to 180 degrees.
We're given that the triangle is a right triangle which immediately gives us one angle, of 90 degrees, since that's a right angle. We're also given another angle of 80, and adding up these two angles plus the last angle, should give us 180.
Let's represent the unknown angle as "A", giving us the equation: [tex]90 + 80+ A= 180[/tex]
Now from here we can combine the 90 and 80 to get:
[tex]170+A=180[/tex]
Now from here we subtract 170 from both sides (to maintain equality and get rid of the 170):
[tex]170-170+A=180-170[/tex]
We simplify 170-170 to 0, which we don't need to put in the equation as 0 + A is just A. We also simplify 180 - 170 to 10:
[tex]A=10[/tex]
So the other acute angle is 10 degrees.
PLEASE HELP ME!
Anna is considering writing and publishing her own book She estimates her revenue equation as R = 6.56x and her cost equation as C = 10.063 + 1.09x where x is the number of books she sells. Find the minimum number of books she must sell to make a profit
Anna must sell atleast ? books to make a profit.
The sentence regarding how many books must be sold to make a profit is given as follows:
Anna must sell at least 2 books to make a profit.
How to model the profit?The profit function is given by the subtraction of the revenue function by the cost function, as follows:
P(x) = R(x) - C(x).
The revenue function and the cost function for this problem are given as follows:
R(x) = 6.56x.C(x) = 1.09x + 10.063.Hence the profit function is given as follows:
P(x) = 6.56x - 1.09x - 10.063.
P(x) = 5.47x - 10.063.
A profit is made when:
P(x) > 0.
Hence:
5.47x - 10.063 > 0
5.47x > 10.063
x > 10.063/5.47
x > 1.84.
As the number of books is a countable amount, we have that:
Anna must sell at least 2 books to make a profit.
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3x ^ -1 - x ^ -3 * (y + 2)
Drag each label to the correct location. Not all labels will be used.First, drag a value to represent the missing angle in the triangle. Then, complete the trigonometry equality statements.59°90 +33 57°90-8 62° sin(e) cos(0)Bsin(280) = cos(cos(33°) = sin(cos(31°) = sin(cos(908) =90 +0
The triangle's missing angle, according to the provided assertion, is (a) 62° (b) 57° (c) 59° (d) sin0
Trigonometry is what degree of mathematics?Trigonometry is typically included in math courses for sophomores or juniors. Trigonometry is frequently included as a unit or term emphasis in other math classes in adding to being given as a separate course.
(a) sin(28°) = cos(90° - 28°) = cos(62°)
62° is right answer.
(b) cos (33°) = sin (90° – 33°) = sin (57°)
57° is correct answer.
(c) cos (31°) = sin(90° - 31°) = sin (59°)
59° is correct answer
(d) cos(90° - 0) = sin0
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In exercises 5-12, write an equation in point slope form..
The equation of the line is y=-2x/5 -10
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here: A line that passes through (5,-12) and m=-2/5
Thus using the slope intercept form constructing it we get
y=mx+c
Putting (5,-12) and m=-2/5
-12=-2/5×5+c
c=-12+2
c=-10
The equation of the line is y=-2x/5 -10
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