Answer:
17%
Step-by-step explanation:
Let us say there are 200 people on the JV swim team. That would mean that 110 people do not wear glasses.
Of these 110 people, 30% are in 10th grade. Therefore, 33 people are in 10th grade and do not wear glasses.
This is 33 people ÷ 200 total = 16.5% ≈ 17%
Therefore, there is a 17% probability that a randomly chosen member of the jv swim team does not wear glasses and is in the 10th grade
[NOTE] You could also just do 55% × 30% = .55 × .30 = .165 ≈ .17 ⇒ 17%
Find the equation of the line, given the following information:
Passes through (-9,3) and is perpendicular to
y=1/2x+6
Answer:
y=2/5x + 33/5
Step-by-step explanation:
To find the equation of the line that passes through the point (-9,3) and is perpendicular to y = 1/2x + 6, we can first find the slope of the given line y = 1/2x + 6. The slope of a line is equal to the rise (the change in the y-coordinate) divided by the run (the change in the x-coordinate), so we can find the slope of the line y = 1/2x + 6 as follows:
Slope = (change in y) / (change in x)
= (1/2 - 6) / (1 - 0)
= -5/2
Since the line we are looking for is perpendicular to the line y = 1/2x + 6, its slope must be the negative reciprocal of the slope of y = 1/2x + 6. The negative reciprocal of a number is equal to the negative of the reciprocal of the number, so the slope of the line we are looking for is equal to -1 / (-5/2) = 2/5.
Next, we can use the point-slope form of a line to find the equation of the line that passes through the point (-9,3) and has a slope of 2/5. The point-slope form of a line is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. Substituting the values for the given point and the slope into this equation, we get:
y - 3 = 2/5(x - (-9))
y - 3 = 2/5(x + 9)
Next, we can distribute the 2/5 on the right-hand side of the equation to get:
y - 3 = 2/5x + 18/5
Finally, we can combine like terms on both sides of the equation to get the final equation of the line:
y=2/5x + 18/5 + 3
y=2/5x + 33/5
1. When renting a vehicle from Schrader car rental, a customer pays a fee up front, and is
also charged for miles driven when they return. Henry drove 85 miles and his rental bill
was $77. Marcia drove 115 miles and her rental bill was $83.
The up front payment costs $34.5 while the payment per miles driven is $0.5
How to solve Simultaneous equation word problems?We are told that when renting a vehicle from Schrader car rental, a customer pays a fee up front, and is also charged for miles driven when they return.
Let the amount paid up front be x and let the amount paid per mile driven be y.
Thus, the equation for Henry will be;
x + 85y = 77 -------(1)
The equation for Marcia will be;
x + 115y = 83 ------(2)
Subtract eq 1 from eq 2 to get;
30y = 6
y = 6/30
y = $0.5
Thus;
x + 85(0.5) = 77
x = 77 - 42.5
x = $34.5
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Complete question is;
When renting a vehicle from Schrader car rental, a customer pays a fee up front, and is
also charged for miles driven when they return. Henry drove 85 miles and his rental bill
was $77. Marcia drove 115 miles and her rental bill was $83.
What is the up fronmt cost and the cost per miles driven
Solve the equation by using the quadratic formula. 3 x squared minus 1 = 5 x a. startfraction 5 startroot 13 endroot over 6 endfraction, startfraction 5 minus startroot 13 endroot over 6 endfraction b. startfraction negative 5 startroot 13 endroot over 6 endfraction, startfraction negative 5 minus startroot 13 endroot over 6 endfraction c. startfraction negative 5 startroot 37 endroot over 6 endfraction, startfraction negative 5 minus startroot 37 endroot over 6 endfraction d. startfraction 5 startroot 37 endroot over 6 endfraction, startfraction 5 minus startroot 37 endroot over 6 endfraction
The solution to the quadratic equation 3x²-1 = 5x by formula method is
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable of x . It is expressed as ax²+bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
In the equation 3x²-1= 5x
we put the equation in standard form. i.e 3x²- 5x -1 = 0
therefore a = 3 , b = -5 and c = -1
formula method is a method of solving the root of a quadratic equation. It is given by x = (-b±√b²-4ac)/2a
=(-(-5±√-5²-4×3×-1)/2×3
=(5±√25+12)/6
=(5±√37)/12
x = 5+6.1/12 or
x= 5-6.1/12
therefore x = 11.1/12 or -1.1/12
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Answer: it's d.
StartFraction 5 + StartRoot 37 EndRoot Over 6 EndFraction, StartFraction 5 minus StartRoot 37 EndRoot Over 6 EndFraction just took the test
please help thank you!
Answer:
...…...................c = 50
What is the equation of the line that passes through the point (-4, 5) and has a
slope of o?
Answer:
y = 5
Step-by-step explanation:
A line with a slope of 0 is a horizontal line parallel to the x- axis with equation
y = c ( c is the value of the y- coordinates the line passes through )
the line passes through (- 4, 5 ) with y- coordinate 5 , then
y = 5 ← equation of line
How do you measure the size of an angle using a protractor or a compass? Explain the steps and show your work.
The size of the angles is measured in the form of degrees by using a protractor and compass.
The symbol for degrees is a little circle °.
The FULL CIRCLE is 360° (360 degrees). A half circle or a straight angle is 180°.A quarter circle or a right angle is 90°A protractor is a tool that measures the number of degrees in an angle.
To measure an angle with a protractor:
Place the midpoint of the protractor on the VERTEX of the angle.Line up one side of the angle with the zero line of the protractor.Read the protractor to see where the other side of the angle crosses the number scale.Most protractors have two number scales. It's important to use the same number scale for both sides of the angle.
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Gracie is trying to read 48 books this year. So far, she’s read 16 book. How many books does she need to read per week if there are only 18 weeks left in the year?
Answer: The answers is, 1.77777, repeated 7s
Step-by-step explanation: The explanation if you need to show your work is: Start with the goal of (48 books). Subtract the number of books already read (16 books read).
(48 - 16) = 32 books left to read.
You must then take the other given of 18 weeks left to complete said goal of (48 books) and divide the number of books left (32 books to read) by the amount of time left (18) weeks to complete the desired goal.
(32 / 18) = 1.77777
Therefore, the answer to your question is that Gracie must read 1.777 books per week to complete her goal on time.
Good Luck, Hope this helps.
y - 5 = 3 ( x + 9) in slope intercept
Answer:y=3x+32
Step-by-step explanation:Hope this helps
What
property is illustrated in: If ∠A ≅ ∠B, ∠B ≅ ∠C, then ∠A ≅ ∠C.a.
Reflexive Propertyb. Symmetric Propertyc. Transitive Propertyd. Addition
Property
The property illustrated in the statement "If ∠A ≅ ∠B, ∠B ≅ ∠C, then ∠A ≅ ∠C" is the Transitive Property.
This property states that if two elements are related by a certain relationship, and another element is related to the second element by the same relationship, then the first and third elements are related by the same relationship.
In this statement, the relationship is that of congruency, meaning that each angle has the same measure. Therefore, the Transitive Property states that if angle A is congruent to angle B, and angle B is congruent to angle C, then angle A is congruent to angle C.
The other three properties listed do not apply to this statement. The Reflexive Property states that a given element is related to itself by a certain relationship, which does not apply to this statement.
The Symmetric Property states that if two elements are related by a certain relationship, then the two elements are related to each other in the same way, which is not applicable in this statement.
Lastly, the Addition Property states that the sum of two elements related by a certain relationship is related to the two elements by the same relationship, which is not applicable in this statement.
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Enter the value of x below.
x + 9 = 12
Answer:
x = 3
Step-by-step explanation:
Enter the value of x below.
x + 9 = 12
x = 12 - 9
x = 3
-----------------------------------------------
check
3 + 9 = 12
12 = 12
the answer is good
Piper invested $990 in an account paying an interest rate of 33% compounded
continuously. Sadie invested $990 in an account paying an interest rate of 3%
compounded monthly. After 14 years, how much more money would Piper have in
her account than Sadie, to the nearest dollar?
Answer:
55
Step-by-step explanation:
that’s if you meant the interest rate is 3 3/8 for compounded continuously and 3 1/8 for compounded monthly
Which of the following propositions is tautology?
a. (p v q)→q b. p v (q→p) c. p v (p→q) d. Both (b) & (c)
From the truth table, the values for p v (p→q) are all true. Therefore, this proposition is considered a tautology.
A statement or formula that is true under every scenario is referred to as a tautology. For example, the bag is red or it is not. Whatever the color of the bag, these two statements are true.
Construct a truth table for the given propositions. From the table, we can tell that the proposition p v (p→q) is in tautology. Because whatever the value of p and q, the result is true for this proposition.
Therefore, the correct option is option c.
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HELPPPPP For a given recipe, 2 cups of flour are mixed with 4 cups of sugar. How many cups of sugar should be used if 6 cups of flour are used?
Answer: 12 cups of sugar
Step-by-step explanation:
you can set it up as a ratio
2:4 and this can be simplified to 1:2, so for every cup of flour there is 2 cups of sugar, you could count it by hand but with a ratio of 1:2 you can just multiply by 2 so 6x2=12
Answer:
Step-by-step explanation:
Can someone help me with Questions 1 and 2 on this assignment? I am not really understanding them. I would deeply appreciate it!
Add 5 to 2 = 2 will make 7 = 7 a true statement and adding 5 to 2 ≠ 3 to make 7 ≠ 8 will make a true statement.
What is a number system?A way to express or represent numbers is through the number system.
We often employ decimal numbers because they are so widely used.
The Number System includes any of the several sets of symbols and the rules for using them to represent numbers.
(1)
As per the given,
2 = 2
Add 5 on both sides of the above equation,
2 + 5 = 2 + 5
7 = 7 (True)
(2)
As per the given
2 ≠ 3
Add 5 on both sides of the above equation,
2 + 5 ≠ 3 + 5
7 ≠ 8 (True)
Hence "It is correct that if you add 5 to 2 = 2, you will get 7 = 7, and if you add 5 to 2 ≠ 3, you will get 7 ≠ 8".
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The midpoint of AB is M(3,-3). If the coordinates of A are (2, -1), what are the
coordinates of B?
Answer:
The coordinates of B is (4, 7)
Step-by-step explanation:
To find the answer for B, you have to do the inverse of the midpoint formula, which is M equals (x1 multiplied by x2, over 2; y1 multiplied by y2, over 2).
If you substitute in A's coordinates for x1 and y1, you come up with (3, 3) = (2+x, over 2; and -1+y, over 2)
If the x coordinate answer for AB was 3, you can create an equation like this to solve for B's x coordinate: 2+x over 2 equals 3.
you multiply 2 by 3 to get 6---> 2+x=6-----> x=4
If the y coordinate for AB was also three, you can create another equation to solve for B's y coordinate: -1+y over 2 equals 3.
you multiply 2 by 3 to get 6 again---->so -1+y=6---->y=7
so the answer for B's coordinates is (4, 7).
Answer:
B(4, - 5)--------------------------
Given:
A = (2, - 1), Midpoint M = (3, - 3),Find the coordinates of the other end point B.
Use midpoint equation, considering point B as (x, y):
3 = (2 + x)/2 ⇒ 2 + x = 2*3 ⇒ 2 + x = 6 ⇒ x = 4,- 3 = (- 1 + y)/2 ⇒ -1 + y = 2*(-3) ⇒ -1 + y = - 6 ⇒ y = - 5.Therefore the point B has coordinates of (4, - 5).
Earth’s distance from the sun is 1.496 x 108 km. Saturn’s distance from the sun is 1.4246 x 109 km. How many times further from the sun is Saturn?
Saturn's distance is 9.5 farther from the Sun than the earth.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Earth's distance from the sun = 1.496 x [tex]10^8[/tex] km
Saturn's distance from the sun = 1.4246 x [tex]10^9[/tex] km
Divide Saturn's distance by Earth's distance.
= 1.4246 x [tex]10^9[/tex] / 1.496 x [tex]10^8[/tex]
= 9.5
We see that,
Saturn's distance from the sun x 0.95 = Earth's distance from the sun.
Thus,
Saturn's distance is 0.95 farther from the sun.
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Hannah, Ben, Stephanie, and Brayden bought a gift for their Mom. The total cost of the gift, including tax, was $64.80. Hannah paid $21, Ben paid 1/3 of the cost, Stephanie paid 15% of the cost, and Brayden paid the remaining cost. Who paid the greatest part of the cost?
Answer: Ben paid the most
Step-by-step explanation: Okay, to find the prices of the 4, we need to follow what the problem says. So, we know Hannah paid 21, so we know that is how much she paid. Now, we need to find 1/3 of the total cost ($64.80) So, we do 1/3 divided by $64.80 and get $21.60. For Stephanie, we need to find 15% of $64.80, so we can write it as a proportional relationship, so 15 x $64.80 / 100 is 9.27. (as a decimal) Now, we subtract all of those numbers from the total cost ($64.80) to find Brayden's pay. After I subtracted all of the amounts, I got $12.93. I'll list all the amounts.
Hannah - 21
Ben - 21.60
Stephanie - 9.27
Brayden- 12.93
So, as we see Ben paid the most. I hoped this LONG explanation helped you!
it should be ben.
Hannah paid $21;
ben paid 1/3 of 64.80 and that's $21.6 (64.84÷3);
Stephanie paid 15% of $64.80 and that's $9.72 (15÷100×64.80);
Brayden paid $12.48 [64.80-(21+21.6+9.72)].
hope I helped (btw sorry for any mistake english isnt my forst language)
Am cla ha collected 52 can in a food drive. They plan to ort the can into a x bag, with an equal number of can in each bag. Write an expreion to how how many can there will be in each bag
Answer:
Math Expert Answer
Step-by-step explanation:
52 cans in total separated into x number of bags. 52/x with x being the number of bags.
Answer:
c = 52/x
Step-by-step explanation:
We have 52 total cans and x bags of with an equal amount of cans in each.
Thus, we would have c = 52/x cans per bag. This is probably the answer you are looking for.
However, this can evaluate to a fractional number of cans, so you may be looking to round that answer down to an integer. In that case, the answer would be c = ⌊52/x⌋, which is solving for the greatest integer less than the value of 52/x
A baker sells boxes of cookies this table shows the total cast, in dollars, for different numbers of boxes of cookies based on the table what is the total cost in dollars of 7 boxes of cookies
The total cost in dollars of 7 boxes of cookies is; $24.50
How to interpret Function Tables?
From the attached table, we see the following coordinates that represents number of boxes (n) and total cost (c in dollars);
(3, 10.5)
(4, 14)
(5, 17.5)
(9, 31.50)
Now, let us find the slope with two coordinates using the formula;
slope = (y₂ - y₁)/(x₂ - x₁)
Let us use the first two coordinates to get;
Slope = (14 - 10.5)/(4 - 3)
Slope = $3.5
Thus, this is the cost of each box
Thus, for 7 boxes, the cost = 3.5 * 7 = $24.5
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A giraffe heart weighs about 4×102 ounces. For comparison, a human heart weighs about 1×101 ounces.
Use these numbers to complete the sentence below. Write your answer in standard form, without using exponents.
Answer:
The heart weighs 404 ounces and a human heart compared to that is 303
Step-by-step explanation:
4 x 102 = 404 - 101
everytime adam shoots a free throw there is a 70% chance he'll make it. if adman shoots 20 free thrwos, how many do you expect him to make?
The number of free throws that adam can expect to make if he attempts 20 free throws is 14.
Probability is a metric used to express the possibility or chance that a particular event will occur. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given the probability that the person making a free throw is 70%. The question asks to estimate how many of his 20 free throw attempts will be successful.
Then, the number of free throws is calculated as follows,
[tex]\begin{aligned}\text{70\% of 20}&=\frac{70\times20}{100}\\&=14\end{aligned}[/tex]
Then, the number of successful free throws is 14.
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At center street middle school, 240 scholars voted for their middle school play. the ratio of scholars who voted for annie to scholars who voted for wicked was 5 : 2, and the ratio of scholars who voted for wicked to scholars who voted for the wizard of oz was 2 : 3. how many scholars voted for wicked?
The number of scholars who voted for the play named Wicked will be equal to 48.
This problem can be solved by using the concept of Ratio. It is given that the total number of students are 240. Now, the ratio of Annie to Wicked is equal to 5:2 and ratio of Wicked to Wizard Oz is equal to 2:3. If we assume that the number of people who voted for Annie is 'x', the number of people who voted for Wicked is 'y' and number of people who voted for Wizard Oz is 'z'. Now, we write the expressions as
x/y = 5:2; from this we get x = 5y/2 ....(1)
y/z = 2:3; from this we get z = 3y/2 ....(2)
x + y + z = 240 ....(3)
We use the above values of equation (1) and (2) in equation (3) as
5y/2 + y + 3y/2 = 240
4y + y = 240
5y = 240
y = 48
So, the number of students who voted for Wicked will be 48.
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PLEASE HELP!!! Make sure to show your work.
1)How many triangles can be constructed
with angles measuring 16˚, 38˚ and 126˚?
Circle one answer:
A) None
B) One
C) Infinite (More than one)
The angles α = 16°, β = 38° and γ = 126° can construct a triangle. (Correct choice: B)
How many triangles can be made by using three given triangles
In this problem we find the measures of three angles that must be proved to be part of a given triangle. The angles are part of a triangle if and only if the sum of the measures equals 180°. If we know that α = 16°, β = 38° and γ = 126°, then the sum of the measures is:
x = α + β + γ
x = 16° + 38° + 126°
x = 180°
As the sum of the measures of the three angles equals 180°, then the given angles can construct a triangle.
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If the toss of a coin comes down heads, you win two dollars. If it comes down tails, you lose fifty cents. How much would you expect to gain after 16 tosses (in $ dollars)? $______.
The expected gain after 16 tosses of the coin is $400.
State the term equally likely events?Equally likely denotes the probability that each experiment's result will occur. For instance, if you throw a fair, six-sided die, any of the faces (1, 2, 3, 4, 5, or 6) has the same chance of coming up. A fair coin has an equal chance of landing on its head (H) or tail (T).Let x stand in for your entire savings.
There is a 0.5 likelihood of heads and a 0.5 possibility of tails. (equally likely events).
The value of accepting this offer is 1.5. The formula is as follows:
2 heads.
0.5 = P(Heads)
Value anticipated if the coin came out heads: 2x*0.5 = x
Plus
(1 - 0.5)x = 0.5x for tails.
0.5 = P(Tails)
Value anticipated if the coin came up tails: 0.5x*0.5 = 0.25x
Total projected value is equal to 1.25x.
For x = $20
Thus,
Amount = 1.25(20) = $25.
Thus, for the 16 tosses = $25 x 16 = $400.
Therefore, the expected gain after 16 tosses of the coin is $400.
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HELPPP PLS!!!!Which of the following is equivalent to sum from n equals 1 to infinity of 10 times quantity negative seven eighths end quantity to the power of n question mark
Answer:
-14/3
Step-by-step explanation:
this is a geometric series with r = -7/8
The infinite sum of geometric series with |r| < 1 is
a1/(1-r)We already have r, but we need to find a1 which is the first term of the series.
To find it, only plug in 1 for n, 10(-7/8) and this = -35/4
Now plug in r and a1 in the formula above:
[tex]\frac{-35/4}{1+7/8}[/tex]
after simplifying it, you will get the infinite sum = -14/3
In a canoe race, the distance y (in miles) that Team A travels in x hours is represented by y = 5.5x. Team B travels 4 miles per hour and is 3 miles ahead of Team A. The teams continue traveling at their current rates for the remainder of the race. Will Team A catch up to Team B? Use a system to solve and explain your answer.
Answer:
Team A catches up to B in 2 hours, at the 11 mile mark
Step-by-step explanation:
(5.5 mi/hr)(x) = (4 mi/hr)(x) + 3 mi
(1.5 mi/hr)(x) = 3 mi
x = 3/1.5 = 2 hours
The surface area in square units of a cylinder with a volume of 18 cubic units is a function of its radius r in units where s(r)=2pi r^2 + 36/r . What is the surface area of a cylinder with a volume of 18 cubic units and a radius of 3 units?
The surface area of a cylinder with a volume of 18 cubic units and a radius of 3 units is 18π +12.
What is the surface area of the cylinder?
The quantity of space enclosing a three-dimensional shape's exterior is its surface area. The area of the cylinder is determined by adding the areas of its two circular bases and curving surface.
Here, we have
Given
The surface area in square units of a cylinder with a volume of 18 cubic units is a function of its radius r in units
where s(r)=2πr² + 36/r ....(1)
Now, we put the value of r = 3 in equation (1) and we get
s(r)=2π(3)² + 36/3
s(r) = 18π + 12
Hence, the surface area of a cylinder with a volume of 18 cubic units and a radius of 3 units is 18π +12.
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consider the equation 1 (x−1)2 + y2 + 4 (x+1)2 +y2 =2 . the graph of this curve looks like this:
The positive intercept y is [tex]\sqrt{ }(3 / 2)[/tex], the negative y intercept is y= [tex]-\sqrt{ }\left(\frac{3}{2}\right)[/tex], the equation of the tangent line at positive intercept is y=-0.48989x+1.2247, the equation of the tangent line negative intercept is y=0.48989x-1.2247.
(a). Here we have to find the positive y intercept
So letting x=0 in the given equation [tex]\frac{1}{(\mathrm{x}-1)^2+\mathrm{y}^2}+\frac{4}{(\mathrm{x}+1)^2+\mathrm{y}^2}=2[/tex]
x=0 implies
[tex]$$\begin{aligned}\frac{1}{(0-1)^2+y^2}+\frac{4}{(0+1)^2+y^2} & =2 \\\frac{1}{1+y^2}+\frac{4}{1+y^2} & =2 \\\frac{5}{1+y^2} & =2 \\5 & =2+2 y^2 \\5-2 & =2 y^2 \\\frac{3}{2} & =y^2 \\\mathrm{y} & =\sqrt{ }\left(\frac{3}{2}\right)\end{aligned}$$[/tex]
Therefore, the positive intercept y is [tex]\sqrt{ }\left(\frac{3}{2}\right)[/tex].
(b). Next we have to find the negative y intercept , the negative y intercept is y= [tex]-\sqrt{ }\left(\frac{3}{2}\right)[/tex]
(c). Next we have to find the equation of the tangent line at [tex]$(0, \sqrt{ }(3 / 2))$[/tex]using implicit differentiation Here
[tex]\frac{1}{(x-1)^2+y^2}+\frac{4}{(x+1)^2+y^2}=2 \\[/tex]
[tex]\left((x-1)^2+y^2\right)^{-1}+4 \times\left((x+1)^2+y^2\right)^{-1}=2[/tex]
Then differentiating using power rule
[tex](-1) \times\left((\mathrm{x}-1)^2+\mathrm{y}^2\right)^{-1-1} \times\left(2(\mathrm{x}-1)+2 \mathrm{y} \times \mathrm{y}^{\prime}\right)+4 \times(-1) \times\left((\mathrm{x}+1)^2+\mathrm{y}^2\right)^{-1-1} \times\left(2(\mathrm{x}+1)+2 \mathrm{yy} \mathrm{y}^{\prime}\right)=0 \\[/tex]
[tex](-1) \times\left((\mathrm{x}-1)^2+\mathrm{y}^2\right)^{-2} \times\left(2(\mathrm{x}-1)+2 \mathrm{y} \times \mathrm{y}^{\prime}\right)+(-4) \times\left((\mathrm{x}+1)^2+\mathrm{y}^2\right)^{-2} \times\left(2(\mathrm{x}+1)+2 \mathrm{yy} \mathrm{y}^{\prime}\right)=0 \\[/tex]
[tex](-1) \times\left((\mathrm{x}-1)^2+\mathrm{y}^2\right)^{-2} \times\left((\mathrm{x}-1)+\mathrm{yy} \mathrm{y}^{\prime}\right)+(-4) \times\left((\mathrm{x}+1)^2+\mathrm{y}^2\right)^{-2} \times((\mathrm{x}+1)+\mathrm{yy})=0[/tex]
Then Substituting x=0 and y= [tex]\sqrt{ }(3 / 2)$[/tex], then
[tex](-1) \times\left(1+\left(\frac{3}{2}\right)\right)^{-2} \times\left(-1+\sqrt{ }\left(\frac{3}{2}\right) \mathrm{y}^{\prime}\right. & =4\left(1+\left(\frac{3}{2}\right)\right)^{-2} \times\left(1+\sqrt{ }\left(\frac{3}{2}\right) \mathrm{y}^{\prime}\right) \\[/tex][tex]\left.-1 \times\left(\frac{2}{5}\right)^2\right) \times\left(-1+\sqrt{ }\left(\frac{3}{2}\right) \mathrm{y}^{\prime}\right) & =4\left(\frac{2}{5}\right)^2 \times\left(1+\sqrt{ }\left(\frac{3}{2}\right) \mathrm{y}^{\prime}\right) \\[/tex]
[tex]-\left(-1+\sqrt{ }\left(\frac{3}{2}\right) \mathrm{y}^{\prime}\right) & =4 \times\left(1+\sqrt{ }\left(\frac{3}{2}\right) \mathrm{y}^{\prime}\right) \\[/tex]
[tex]1-\sqrt{ }\left(\frac{3}{2}\right) \mathrm{y}^{\prime} & =4+4 \sqrt{ }\left(\frac{3}{2}\right) \mathrm{y}^{\prime} \\[/tex][tex]-3 & =5 \sqrt{ }\left(\frac{3}{2}\right) \mathrm{y}^{\prime} \\[/tex]
[tex]\mathrm{y}^{\prime} & =-0.48989[/tex]
Then the equation of the tangent line is y-y1=m(x-x1)
Here X1=0
[tex]& \mathrm{y} 1=\sqrt{ }(3 / 2)=1.2247 \\[/tex]
m=-0.48989
y=-1.2247=-0.48989x
y=-0.48989x+1.2247
(d). Next we have to find the equation of the tangent line at[tex]$(0,-\sqrt{ }(3 / 2))$[/tex] using implicit differentiation
Here [tex]\left((x-1)^2+y^2\right)^{-1}+4 \times\left((x+1)^2+y^2\right)^{-1}=2[/tex]
Then differentiating using power rule
[tex](-1) \times\left((\mathrm{x}-1)^2+\mathrm{y}^2\right)^{-2} \times\left((\mathrm{x}-1)+\mathrm{yy^{ \prime } )}+(-4) \times\left((\mathrm{x}+1)^2+\mathrm{y}^2\right)^{-2} \times\left((\mathrm{x}+1)+\mathrm{y} \mathrm{y}^{\prime}\right)=0\right.[/tex]
Then Substituting x=0 and y=[tex]-\sqrt{ }(3 / 2)$[/tex], then
[tex](-1) \times\left(1+\left(\frac{3}{2}\right)\right)^{-2} \times\left(-1-\sqrt{ }\left(\frac{3}{2}\right) y^{\prime}\right) & =4\left(1+\left(\frac{3}{2}\right)\right)^{-2} \times\left(1-\sqrt{ }\left(\frac{3}{2}\right) y^{\prime}\right) \\[/tex]
[tex](-1) \times\left(-1-\sqrt{ }\left(\frac{3}{2}\right) y^{\prime}\right) & =4 \times\left(1-\sqrt{ }\left(\frac{3}{2}\right) y^{\prime}\right) \\[/tex]
[tex]\left(1+\sqrt{ }\left(\frac{3}{2}\right) y^{\prime}\right) & =4-4 \sqrt{ }\left(\frac{3}{2}\right) y^{\prime} \\[/tex]
[tex]-3 & =-5 \sqrt{ }\left(\frac{3}{2}\right) y^{\prime} \\y^{\prime} & =\frac{3}{5 \sqrt{ }\left(\frac{3}{2}\right)}=0.48989[/tex]
Then the equation of the tangent line is
y+1.2247 =0.48989x
y=0.48989x-1.2247.
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3 x square - 5 x + 2 is equals to zero
Answer:
x=2/3 or x=1
Step-by-step explanation:
Factor 3x² and 2
a menorah holds one candle for each night of hanukkah and and extra candle called the shamash that is used to light the other candles. how many candles does a hanukkah menorah hold?
Answer: There is one candle for each night of Hanukkah, and the ninth candle, which sits in the middle, is known as the shamash, which translates to attendant or servant candle. This candle is lit first and is used to light the others.
Step-by-step explanation: