Answer:
We have the measure of both angles as 55 degrees and 35 degrees
Step-by-step explanation:
We know that there are three angles in a right-angled triangle. One of which is 90. FOr now, the other two are unknown, so we would designate them to be x and y.
We now set up an equation using the information we are given about the problem.
From this statement "The measure of one of the small angles of a right triangle is 15 less than twice the measure of the other small angle." we can set up the following equation:
x =2y -15 -------- equation 1
similarly, we know that the sum of angles in a triangle = 180 degrees. Hence, we can use this to set up another equation as follows:
x + y + 90 = 180
x+ y = 90 ------------- equation 2
we can now solve the two equations simultaneously as
x -2y =-15
x+ y = 90
from this, we have that
x = 55 and y = 35
We have the measure of both angles as 55 degrees and 35 degrees
hey guys can you please help me with this. i’m really desperate please help anything helps. thank u :(
Answer:
- 29 / 20
Step-by-step explanation
The cosec (x) = 1 / sin(x)
There are 2 ways to do this:
Either using a calculator:
sin^-1(20 / 29) = 43.60281897
so inputting into 1/sin(-x) where x = 43.6.....
This gives: -29 / 20
OR
1 / sin(x) = cosec ( x)
so cosec (x) = 1/(20/29)
= 29/20
By observing the cosec(x) graph, we see that to get cosec (-x), all we need to do is to minus our answer seeing as the graph is symmetrical across the axes. Therefore x = -29/20
1. What are foci? 2. What is the first step to take to write the equation of a hyperbola? 3. How do you represent parts of a hyperbola algebraically?
Answer: see below
Step-by-step explanation:
1) Foci is plural for Focus. Since a hyperbola has two focus points, they are referred to as foci. The foci is where the sum of the distances from any point on the curve to the foci is constant.
2) When determining the equation of a hyperbola you need the following:
a) does the hyperbola open up or to the right?
b) what is the center (h, k) of the hyperbola?
c) What is the slope of the asymptotes of the hyperbola?
3) The equation of a hyperbola is:
[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1\qquad or\qquad \dfrac{(y-k)^2}{b^2}-\dfrac{(x-h)^2}{a^2}=1[/tex]
(h, k) is the center of the hyperbola± b/a is the slope of the line of the asymptotesThe equation starts with the "x" if it opens to the right and "y" if it opens upFind two numbers in a given ratio such that the difference of their squares is to the sum of the numbers in a given ratio.Ratios, respectively, are 3 to 1 and 6 to 1.
According to the given situation, the computation of two number in a given ratio is shown below:-
We assume the numbers is x and y
Given that
[tex]\frac{x}{y} = \frac{3}{1}[/tex]
x = 3y
and
[tex]\frac{x^2-y^2}{x + y} = \frac{6}{1} \\\\\frac{(x + y) (x - y)}{(x + y)} = 6[/tex]
With the help of above formula we will put the value and be able to find the values of x and y
x - y = 6
3y - y = 6
2y = 6
y = 3
x = 3y = 9
x = 9, y = 3
Therefore the correct answer is x = 9 where as y = 3
A magazine provided results from a poll of 2000 adults who were asked to identify their favorite pie. Among the 2000 respondents, 11% chose chocolate pie, and the margin of error was given as plus or minus5 percentage points. What values do ModifyingAbove p with caret, ModifyingAbove q with caret, n, E, and p represent? If the confidence level is 95%, what is the value of alpha?
Answer:
[tex]\r p = 0.11[/tex]
[tex]\r q = 0.89[/tex]
n = 2000
[tex]E = \pm 5[/tex]
p - population proportion
[tex]\alpha = 5[/tex]%
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 2000[/tex]
The proportion of the population for chocolate pie is [tex]p_c = 0.11[/tex]
The margin of error is [tex]E = \pm 5[/tex]%
Now in the question we are asked to provide the meaning of
[tex]\r p , \r q , n , E , and\ p[/tex]
Now [tex]\r p[/tex] is the sample proportion of the population that those chocolate pie as favorite pie of which is given from the question as 0.11
Now
[tex]\r q[/tex] is the sample proportion of the population that choose other pies apart from chocolate pie as their favorite and it is evaluated as
[tex]\r q = 1 - \r p[/tex]
[tex]\r q = 1 - 0.11[/tex]
[tex]\r q = 0.89[/tex]
n is the sample size which is given as n = 2000
E is the margin of error which given as [tex]E = \pm 5[/tex]%
p is the population proportion
Given that the confidence level is 95 % then the level of significance is mathematically evaluated as
[tex]\alpha =(100 - 95)[/tex]%
[tex]\alpha =[/tex]5%
A 75 lb boy and a 65 lb girl play on a seesaw. The seesaw is 14 ft long and is pivoted exactly in the middle. If the girl sits on the end of her side, where must the boy sit to make the seesaw balance?
Answer: 6 feet from the pivot point
Step-by-step explanation:
Girl's weight x distance from center = Boy's weight x distance from center
65 (7) = 75x
[tex]\dfrac{65(7)}{75}=x[/tex]
6.066 = x
The boy needs to be placed 6 feet from the center (aka pivot point) which is the same as saying 1 foot from the end of the seesaw.
Determine which type of correlation is shown in the graphed relationship
Answer:
No correlation
Step-by-step explanation:
Hey there! :)
This has no correlation because all the points are spread out throughout the graph making no correlation.
Answer:
D no correlation
Step-by-step explanation:
too many scattered dot all over the place if its some going up down its NO CORRELATION!!!
Based on the dot plot, which statements are correct? Check all that apply
Eleven students answered Mr. Chiu's question.
Twelve students answered Mr. Chiu's question.
Three people studied for two hours.
Three people studied for three hours.
Everyone who responded studied for at least one hour.
Four people studied for four or more hours
Answer: options 2,3and 6
Answer:
option
2-Twelve students answered Mr. Chiu’s question.
3-Three people studied for two hours.
6-Four people studied for four or more hours.
Step-by-step explanation:
hope this helps:)
Fine the value of x in the triangle. Then classify the triangle as acute, right,
or obtuse.
47* 45* x
Answer:
x = 88
Step-by-step explanation:
The sum of the angles in a triangle add to 180
47+45 +x = 180
Combine like terms
92+x = 180
Subtract 92 from each side
92+x-92= 180-92
x =88
P(x)=2x^5+9x^4+9x^3+3x^2+7x-6;x=i,-2
Answer:
The value of the polynomial function at P(1) and P(-2) is 24 and 0 respectively.
Step-by-step explanation:
We are given with the following polynomial function below;
[tex]\text{P}(x) = 2x^{5} +9x^{4} +9x^{3} +3x^{2}+7x-6[/tex]
Now, we have to calculate the value of P(x) at x = 1 and x = -2.
For this, we will substitute the value of x in the given polynomial and find it's value.
At x = 1;
[tex]\text{P}(1) = 2(1)^{5} +9(1)^{4} +9(1)^{3} +3(1)^{2}+7(1)-6[/tex]
[tex]\text{P}(1) = (2\times 1) +(9\times 1)+(9 \times 1)+(3\times 1)+(7\times 1)-6[/tex]
[tex]\text{P}(1) = 2 +9+9+3+7-6[/tex]
P(1) = 30 - 6
P(1) = 24
At x = -2;
[tex]\text{P}(-2) = 2(-2)^{5} +9(-2)^{4} +9(-2)^{3} +3(-2)^{2}+7(-2)-6[/tex]
[tex]\text{P}(-2) = (2\times -32) +(9\times 16)+(9 \times -8)+(3\times 4)+(7\times -2)-6[/tex]
[tex]\text{P}(-2) = -64 +144-72+12-14-6[/tex]
P(-2) = 156 - 156
P(-2) = 0
Hence, the value of the polynomial function at P(1) and P(-2) is 24 and 0 respectively.
Which of the following shapes can NOT be created by revolving a two-dimensional figure around an axis? There can be more than 1. A. come B. cube C. Rectangular pyramid D. Rectangular Prism E. Cylinder F. Sphere
PLEASE HELP
Answer:
A. Cone
D. Rectangular Prism
E. Cylinder
F. Sphere
Step-by-step explanation:
Rectangular Prism is a solid three dimensional shape. It has six faces which are sides of a rectangle. It is also known as Cuboid. The rectangular prism cannot be formed with two dimensional shapes. Sphere is a geometrical object which is a three dimensional circle. This shape has a circumference so this shape cannot be formed with two dimensional shapes.
How many solutions does the following equation have? 14(z+3)=14z+21
Answer:
No solutions
Step-by-step explanation:
14(z + 3) = 14z + 21
Expand brackets.
14z + 42 = 14z + 21
Subtract 14z on both sides.
42 = 21
There are no solutions.
Answer:
No solution
Step-by-step explanation:
First, We have to simplify the right side.
Distribute 14, 14z+42.
Now the equation stands as 14z+42=14z+21
Subtract 14z from both sides,
this makes it 42=21.
We know when the solution is #=#, our answer is no solution.
2. Look at the figure below.
Which angle is congruent to 26?
Answer:
<4 is congruent to angle <6
Step-by-step explanation:
Assuming the lines are parallel
<2 , <4 , <6 , <8 are all equal
Congruent means they are equal.
There are 3 angles that are the same as angle 6, they are 2, 4, 8
The answer would be B. angle 4
An ice sculpture is melting at a constant rate. It's weight changes -1 4/5 pounds every hour. What is the total change in weight of the sculpture after 3 1/2 hours?
Answer:
It will decrease by 6 3/10 lbs in the 3 1/2 hours
Step-by-step explanation:
The rate is -1 4/5 lbs per hour
The time is 3 1/2 hours
Multiply to find the weight change
-1 4/5 * 3 1/2
Change to improper fractions
- ( 5*1 +4) /5 * ( 2* 3+1)/2
- 9/5 * 7/2
-63/10
Changing back to a mixed number
-6 3/10
It will decrease by 6 3/10 lbs in the 3 1/2 hours
Answer:
-6 3/10 pounds
Step-by-step explanation:
The weight of ice sculpture changes -1 4/5 pounds every 1 hour.
In 3 1/2 hours, multiply the time with the weight.
-1 4/5 × 3 1/2
Multiply.
-9/5 × 7/2
-63/10 = -6 3/10
Write an equation perpendicular to 5x+6y=18 that passes through the point (10,7)
Answer:
Step-by-step explanation:
6y = -5x + 18
y = -5/6x + 3
perp slope: 6/5
y - 7 = 6/5(x - 10)
y - 7 = 6/5x - 12
y = 6/5x - 5
Here, we are required to write an equation perpendicular to 5x + 6y = 18.
The equation perpendicular to 5x+6y=18 that passes through the point (10,7) is;6x - 5y = 25.
By rearranging 5x+6y=18 to resemble the end of a straight line; y = Mx + c; we have;y = (-5/6)x +3Therefore, slope of equation 5x + 6y = 18 is -5/6.
However, the product of the slopes of 2 perpendicular lines is -1.Therefore, m1m2 = -1
Therefore, the slope of the required line, m2 is;
m2 = -1/(-5/6)m2 = 6/5
Therefore, the equation of a line perpendicular to the equation 5x+6y=18 and passes through the point (10,7) is given as;
6/5 = (y - 7)/(x - 10).
By cross product; we have;
6x - 60 = 5y - 35
6x - 5y = 25.
Read more:
https://brainly.com/question/17619748
Need Help finding the process for both of these ( due today)
Similar triangles have side lengths that are proportional to each other. To find each of the missing lengths, we need to set up proportions.
The proportions will look as follows:
(length or unknown of triangle 1) / (length or unknown of triangle 2) = (length of triangle 1) / (length of triangle 2)
-On both sides, remember to be consistent with which length/unknown you put on top! If a triangle 1 length is the numerator on the left, then it also needs to be the numerator on the right! And this also works vice versa with triangle 2.
In each proportion equation, we can only have one unknown. On the left side of the equation, we choose one length or unknown of triangle 1, and the corresponding side length of unknown of triangle 2 (whichever you did not choose from triangle 1). On the right side of the equation, we use a completed proportion. This is because all of the sides of one triangle are proportional to the other triangle, but we need to know that proportion/ratio in order to find other side lengths.
Let's start with problem a, to show how this works:
Triangle 1 side lengths - 16, a, 11
Triangle 2 side lengths - 8, 3, b
As you can tell, the side lengths match up (corresponding!) on each triangle, as in they are in the same position on each triangle. Now, we will set up a proportion to find the length of side a on triangle 1.
a / 3 = 16 / 8
48 = 8a
a = 6
Next, let's find the length of side b on triangle 2.
11 / b = 16 / 8
16b = 88
b = 5.5
Moving on to problem b, we'll apply the same concept and steps from problem a in order to find the missing side lengths.
Triangle 1 side lengths: 5, 5.5, d
Triangle 2 side lengths: 15, c, 18
5 / 15 = 5.5 / c
5c = 82.5
c = 16.5
5 / 15 = d / 18
15d = 90
d = 6
Hope this helps!! :)
Answer:
On a) you can see the shapes are simular. The blue line signatures that they are equal just reduced. You can see that 8 goes into 16 two times so for the orange line 3 must times 2. Which would mean a is 6. Now on the red line all you see is 11. So divide 11 by 2 and your answer should be 5.5 for b.
On b) it is the same thing but you have to find how the blue line is divisible. 5 divided by 15 is 3. So 3 is the number you will be using to divide or multiply. For the orange line you divide 18 by 3. The answer is 6 for d. For the red line 5.5 times 3 and you should get 11 for c.
Step-by-step explanation:
Hope this helped
what is improper sampling in statistical analysis and how can i use it in day-to-day life
Answer:
Statistical concepts are used in quality testing. Companies make many products on a daily basis and every company should make sure that they sold the best quality items.
Step-by-step explanation:
pls keep brainly questions only school related thank you!
The circumference of C is 72cm. What is the length of AB (the minor arc)
Answer:
Step-by-step explanation:
Can you please include a image?
Thanks!!!
Find the volume of the figure below. Round to the nearest tenth.
7 cm
7 cm
9 cm
20 cm
11 cm
Answer:
3057.6 cm³
Step-by-step explanation:
You have a cylinder and a rectangular prism. Solve for the area of each separately.
Cylinder
The formula for volume of a cylinder is V = πr²h. The radius is 7, and the height is 7.
V = πr²h
V = π(7)²(7)
V = π(49)(7)
V = 343π
V = 1077.57 cm³
Rectangular Prism
The formula for volume of a rectangular prism is V = lwh. The length is 20, the width is 11, and the height is 9.
V = lwh
V = (20)(11)(9)
V = (220)(9)
V = 1980 cm³
Add the areas of the two shapes.
1077.57 cm³ + 1980 cm³ = 3057.57 cm³
Round to the nearest tenth.
3057.57 cm³ ≈ 3057.6 cm³
What is the value of the fourth term in a geometric sequence for which a1 =
30 and r= 1/2
Answer:
3¾
Step-by-step explanation:
Geometric sequence also known as geometric progression, can be said to be a sequence with a constant ratio between the terms.
Formula for geometric sequence:
[tex] a^n = a ( n-1 ) * r [/tex]
Given:
First term, a1 = 30
ratio, r = ½
Required:
Find the fourth term
Where, the first term, a¹ = 30
Second term: a² = 30 * ½ = 15
Third term: a³ = 15 * ½ = 7.5
Fourth term: a⁴ = 7.5 * ½ = 3.75 = 3¾
Therfore the fourth term of the geometric sequence is 3¾
"Radon: The Problem No One Wants to Face" is the title of an article appearing in Consumer Reports. Radon is a gas emitted from the ground that can collect in houses and buildings. At certain levels it can cause lung cancer. Radon concentrations are measured in picocuries per liter (pCi/L). A radon level of 4 pCi/L is considered "acceptable." Radon levels in a house vary from week to week. In one house, a sample of 8 weeks had the following readings for radon level (in pCi/L). 1.92.45.75.51.98.23.96.9 (a) Find the mean, median, and mode. (Round your answers to two decimal places.) mean 4.55 median 4.7 mode 1.9 (b) Find the sample standard deviation, coefficient of variation, and range. (Round your answers to two decimal places.) s CV % range (c) Based on the data, would you recommend radon mitigation in this house
Answer:
a) Mean = 4.55
Median = 4.7
Mode = 1.9
b) S = 2.3952
CV = 52.64 %
Range = 6.3
c) Yes, since the average and median values are both over "acceptable" ranges.
Step-by-step explanation:
Explanation is provided in the attached document.
WHOEVER ANSWERS FIRST GETS BRAINLIEST:) Which expression represents the surface area of the cone? A cone with diameter 12 inches, height 8 inches, and slant height 10 inches. S A = pi r l + pi r squared (pi) (6) (10) + (pi) (6 squared) (pi) (8) (10) + (pi) (8 squared) (pi) (12) (10) + (pi) (12 squared) (pi) (10) (12) + (pi) (10 squared)
Answer:
Step-by-step explanation:
The surface area of a cone is:
● Sa = Pi*r^2 +Pi*r*l
r is the radius and l is the slant heigth
The diameter of this cone is 12 inches so the radius is 6 (12/2=6).
●Sa = Pi*36 +Pi*6*10
●Sa = 301.59 in^2
Answer:
pi (6) * 10+ pi ( 6)^2
Step-by-step explanation:
The surface area of a cone is given by
SA = pi rl +pi r^2 where r is the radius and l is the slant height
We know the diameter is 12 so the radius is 12/2 = 6
SA = pi (6) * 10+ pi ( 6)^2
A manufacturer claims that its rechargeable batteries are good for an average of more than 1.000 charges. A random sample of 100 batteries has a mean life of 1002 charges and a standard deviation of 14. Is there enough evidence to support this claim at a significance level of 0.01?
a. State the hypotheses.
b. State the test statistie information
c. State either the p-value or the critical information d. State your conclusion and explain your reasoning
It's 1000 charges and not 1.000 charges
Answer:
A)Null Hypothesis;H0: μ = 1000
Alternative Hypothesis;Ha: μ ≠ 1000
B) t-statistic = 1.4286
C) p-value = 0.15628
D) We conclude that we will fail to reject the manufacturers claim that its rechargeable batteries are good for an average of more than 1000 charges
Step-by-step explanation:
We are given;
x = 1002 charges
s = 14
μ = 1000 charges
n = 100
degree of freedom = n - 1 = 100 - 1 = 99
A) The hypotheses are;
Null Hypothesis;H0: μ = 1000
Alternative Hypothesis;Ha: μ ≠ 1000
B) t-statistic = (x - μ)/(s/√n)
(1002 - 1000)/(14/√100) = 1.4286
C) From the t-score calculator results attached, the p-value is approximately 0.15628
D) The P-value of 0.15628 is is greater than the significance level of 0.01, thus we fail to reject the null hypothesis, and we conclude that the result is statistically nonsignificant.
Let x represent the number of times a student visits a gym in a one month period. Assume that the probability distribution of X is as follows: x 0 1 2 3 p(x) 0.17 0.33 0.32 0.18 Determine the probability the student visits the gym at most twice in a month. Report your answer to two decimal places.
Answer: Probability of visiting at most twice = 0.82
Step-by-step explanation: The probability distribution is of the form:
X 0 1 2 3
P(X) 0.17 0.33 0.32 0.18
It wants the probability of visiting the gym at most twice in a month, which means the probability of never going to the gym, P(X=0), or going once, P(X=1), or going twice, P(X=2).
Using the "OR" probability:
P(visiting at most twice) = P(X=0) + P(X=1) + P(X=2)
P(visiting at most twice) = 0.17 + 0.33 + 0.32
P(visiting at most twice) = 0.82
Therefore, the probability of visiting the gym at most twice in a month is 0.82 or 82%
calculate the value of angle A to one decimal place. Picture Attached
Answer:
[tex] A = 50.7 [/tex] (to nearest tenth)
Step-by-step explanation:
Use the Law of Cosines to find the value of angle A as follows:
[tex] cos(A) = \frac{b^2 + c^2 - a^2}{2*b*c} [/tex]
Where,
a = 7 in
b = 5 in
c = 9 in
Plug in the values into the formula
[tex] cos(A) = \frac{5^2 + 9^2 - 7^2}{2*5*9} [/tex]
[tex] cos(A) = \frac{57}{90} [/tex]
[tex] cos(A) = 0.6333 [/tex]
[tex] A = cos^{-1}(0.6333) [/tex]
[tex] A = 50.7 [/tex] (to nearest tenth)
A father's age is 4 times as that of his son's age. in 5 years time, the father will be 3 times as old as his son. what are their present ages?
Answer:
present age of son = 10 present age of father = 40Step-by-step explanation:
Let, present age of son be 'x'
present age of father be 'y'
y = 4x→ equation ( i )
After five years,
Son's age = x + 5
father's age = y + 5
According to Question,
[tex]y + 5 = 3(x + 5)[/tex]
Put the value of y from equation ( i )
[tex]4x + 5 = 3(x + 5)[/tex]
Distribute 3 through the parentheses
[tex]4x + 5 = 3x + 15[/tex]
Move variable to L.H.S and change it's sign
Similarly, Move constant to R.H.S. and change its sign
[tex]4x - 3x = 15 - 5[/tex]
Collect like terms
[tex]x = 15 - 5[/tex]
Calculate the difference
[tex]x = 10[/tex]
Now, put the value of X in equation ( i ) in order to find the present age of father
[tex]y = 4x[/tex]
plug the value of X
[tex] = 4 \times 10[/tex]
Calculate the product
[tex] = 40[/tex]
Therefore,
Present age of son = 10
present age of father = 40
Hope this helps..
Best regards!!
Which of the following is the rule for rotating the point with coordinates (x,y), 180° clockwise about the origin? A. (x,y)→(y,−x) B. (x,y)→(−y,−x) C. (x,y)→(y,x) D. (x,y)→(−x,−y)
Hey there! I'm happy to help!
If you reflect a point across the x-axis, you have (x,y)⇒(x,-y). If you reflect across the y-axis, you have (x,y)⇒(-x,y). A 180° rotation is the same thing as reflecting across both the x and y axes. This means that the rule for rotating the point with coordinates (x,y) 180° clockwise about the origin is D. (x,y)⇒ (-x,-y).
Have a wonderful day! :D
less than 0 but greater than (−5)
Answer:
-5 < x < 0
Step-by-step explanation:
Students in management science class have just received their grades on the first test. The instructor has provided information about the first test grades in some previous classes as well as the final average for the same students. Some of these grades have been sampled and are as follow:
1st test Grade 98 77 88 80 96 61 64 95 79
Final average 93 78 84 75 84 64 66 95 86
Develop a regression model that could be used to predict the final average in the course based on the first test grade.
Predict the final average of a students who made an 83 on the first test.
Give the value of r and r2 for this model.
Interpret the value of r2 in the context of this problem.
Answer:
The regression model is:
y = 20.29 + 0.73·x
Step-by-step explanation:
In this case a regression model is to be formed to predict the final average in the course based on the first test grade.
Use Excel to form the regression model.
The output is attached below.
The regression model is:
y = 20.29 + 0.73·x
Predict the final average of a students who made an 83 on the first test as follows:
y = 20.29 + 0.73·x
= 20.29 + 0.73 × 83
= 80.88
The final average of a students who made an 83 on the first test would be 80.88.
From the output:
R² = 0.839
Then the correlation coefficient will be:
[tex]r=\sqrt{R^{2}}=\sqrt{0.839}=0.91597\approx 0.92[/tex]
The value of r is 0.92.
The coefficient of determination R² specifies the percentage of the variance in the dependent-variable (Y) that is forecasted or explained by linear regression and the forecaster variable (X, also recognized as the independent-variable).
In this case, the R² value of 0.839 implies that 83.9% of the variation in the final average can be explained by the grades in the first test.
A cash register has $10 and $50 dollars bills with total of $1080.there are 28 bills in total how many of each bills.
Hey there! I'm happy to help!
Let's set this up as a system of equations, where x is equal to the number of 10 dollar bills and y is equal to the number of 50 dollar bills.
10x+50y=1080
x+y=28
We want to solve for x or y. We can rearrange the second equation to find the value of one of the variables.
x+y=28
Subtract x from both sides.
y=28-x
Now, we have a value for y. So, we could replace the y in the first equation with 28-x and the solve for x.
10x+50(28-x)=1080
We use distributive property to undo the parentheses.
10x+1400-50x=1080
We combine like terms.
-40x+1400=1080
We subtract 1400 from both sides.
-40x=-320
We divide both sides by -40.
x=8
Since there are 28 total bills, this means that there must be 20 50 dollar ones because there are 8 10 dollar bills.
Have a wonderful day! :D
Which is the graph of linear inequality x - 2y 2-12?
10
10
10
1034
Help asappp!!!pls
It would have to have a positive slope and the bottom needs to be shaded, since -2y is negative it means we will be dividing by a negative. The inequality sign will switch.
also if it is < then the line is dotted, if it’s the “greater or equal to sign” then the line is not dotted.
dunno if I explained it very well
The shaded region common to both the inequalities represents the solution set of the inequality → x - 2y² < 12.
What is inequality?An inequality is used to compare two or more expressions or numbers.
For example -
2x > 4y + 3
x + y > 3
x - y < 6
Given is the inequality as -
x - 2y² < 12
The given inequality is -
x - 2y² < 12
2y² - x < - 12
2y² < x - 12
y² < (x/2) - 6
[tex]$y < \pm\sqrt{\frac{x}{2}-6 }[/tex]
[tex]$y < \sqrt{\frac{x}{2}-6 }[/tex]
and
[tex]$y < -\sqrt{\frac{x}{2}-6 }[/tex]
Refer to the graph of the equation attached. The shaded region common to both the inequalities represents the solution set of the inequality.
Therefore, the shaded region common to both the inequalities represents the solution set of the inequality → x - 2y² < 12.
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