x+-2*2-3x-7
x+4-3x-7
x+1.x-7
x.x-7
2x-7
The point P(7, −2) lies on the curve y = 2/(6 − x). (a) If Q is the point (x, 2/(6 − x)), use your calculator to find the slope mPQ of the secant line PQ (correct to six decimal places) for the following values of x.
(i) 6.9
mPQ = 1
(ii) 6.99
mPQ = 2
(iii) 6.999
mPQ = 3
(iv) 6.9999
mPQ = 4
(v) 7.1
mPQ = 5
(vi) 7.01
mPQ = 6
(vii) 7.001
mPQ = 7
(viii) 7.000
mPQ = 8
(b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at
P(7, −2).
m = 9
(c) Using the slope from part (b), find an equation of the tangent line to the curve at
P(7, −2).
The equation of the tangent line to the curve at P(7, -2) is y = 2x -16.
For each given value of x, we substitute the coordinates of P and Q into the slope formula to find the slope mPQ.
(i) For x = 6.9:
mPQ = (2/(6 - 6.9) - (-2)) / (6.9 - 7)
= 2.22
(ii) For x = 6.99:
mPQ = (2/(6 - 6.99) - (-2)) / (6.99 - 7)
= 2.020
(iii) For x = 6.999:
mPQ = (2/(6 - 6.999) - (-2)) / (6.999 - 7)
= 2.002002
(iv) For x = 6.9999:
mPQ = (2/(6 - 6.9999) - (-2)) / (6.9999 - 7)
= 2.000200
(v) For x = 7.1:
mPQ = (2/(6 - 7.1) - (-2)) / (7.1 - 7)
= 1.818182
(vi) For x = 7.01:
mPQ = (2/(6 - 7.01) - (-2)) / (7.01 - 7)
= 1.980198
(vii) For x = 7.001:
mPQ = (2/(6 - 7.001) - (-2)) / (7.001 - 7)
= 1.998002
(viii) For x = 7.0001:
mPQ = (2/(6 - 7.0001) - (-2)) / (7.0001 - 7)
= 1.999800
By observing the pattern in the calculated slopes, we can see that as x approaches 7, the slope of the secant line PQ approaches 2.
Using the point-slope form, we have:
y - y₁ = m(x - x₁)
Substituting the values of P(7, -2), we have:
y - (-2) = 2(x - 7)
y = 2x -16
Therefore, the equation of the tangent line to the curve at P(7, -2) is y = 2x -16.
Learn more about the equation of the tangent line here:
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Which of the following is equivalent to the polynomial given below?
Answer:
[tex](x+(3+\sqrt{11}i)) (x+(3-\sqrt{11}i))[/tex]
Step-by-step explanation:
The first step to this problem is to look at the key features of the initial expression given to us. Namely, the middle term.
Notice that it is just [tex]+6x[/tex]. This indicates that the square root terms cancel out, meaning that their signs need to be opposite, but the threes need to have the same, positive sign. This indicates that our answer is option C, but you should always double check by multiplying the expression out to confirm. Here are the steps:
[tex](x+(3+\sqrt{11}i)) (x+(3-\sqrt{11}i))[/tex]
[tex]x^{2} +(3+\sqrt{11}i)x+(3-\sqrt{11}i)x+(3+\sqrt{11}i)(3-\sqrt{11}i)[/tex][tex]x^{2}+3x+\sqrt{11}ix+3x-\sqrt{11}ix+9+3\sqrt{11}i-3\sqrt{11}i-(\sqrt{11})^{2}(i^{2})[/tex][tex]x^{2}+6x+9-(11)(-1)[/tex]
[tex]x^{2}+6x+9+11[/tex]
[tex]x^{2}+6x+20[/tex]
Therefore as we suspected, the answer is C.
Hurrryy plzzz!!
Which linear inequality is represented by the graph?
y<1/2x+2
y>1/2x+2
y<1/3x+2
y>1/3x+2
what is the y-intersept of y=4x-6
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▹ Answer
y-intercept = -6
▹ Step-by-Step Explanation
The format of slope is:
y = mx + b
The b represents the y-intercept which is, -6.
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
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Answer: -6
Step-by-step explanation: This equation is written in slope-intercept form which is more commonly known as y = mx + b form where the multiplier or the coefficient of the x term represents the slope of the line and the b or the constant term represents the y-intercept.
So this line has a y-intercept of -6.
This means it crosses the y-axis 6 units up from origin.
I need help urgent plz someone help me solved this problem! Can someone plz help I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
Answer: L = 20.25
Step-by-step explanation:
[tex]T=2\pi \sqrt{\dfrac{L}{32}}[/tex]
Given: T = 5, π = 22/7
[tex]5=2\bigg(\dfrac{22}{7}\bigg)\sqrt{\dfrac{L}{32}}\\\\\\\dfrac{5}{2}\bigg(\dfrac{7}{22}\bigg)=\sqrt{\dfrac{L}{32}}\\\\\\\dfrac{35}{44}=\sqrt{\dfrac{L}{32}}\\\\\\\bigg(\dfrac{35}{44}\bigg)^2=\bigg(\sqrt{\dfrac{L}{32}}\bigg)^2\\\\\\\bigg(\dfrac{35}{44}\bigg)^2=\dfrac{L}{32}\\\\\\32\bigg(\dfrac{35}{44}\bigg)^2=L\\\\\\\large\boxed{20.25=L}[/tex]
Basic factoring. Please help!
Answer:
-1(3 - y)
Step-by-step explanation:
If you factor out a negative 1, you will get the opposite signs you already have, so -1(3 - y). To check, we can simply distribute again:
-3 + y
So our answer is 2nd Choice.
Can someone answer these questions dm me or just do it in the comments.
Answer:
1. 8/4+ 3= 5
2. 5/(10/2)= 1
3. 5+10/2=10
4. 8/2+5x5= 29
5. 5+3/15+2= 10.15
6. 30+6x11-11= 25.11
7. 12 + (19+2) / 3 =19
Step-by-step explanation:
---------------------------------------------
Student name : Aparna Guha
Class : 8th
Division : B
School : St. John's Marhauli
Suggested subject : Maths
Work given on : 08 : 07 : 2020
Completed on : 08 : 07 : 2020
Posted on : 08 : 07 : 2020
Topic : Worksheet 1
Teacher's name : Manish Goel
School name : St. John's Marhauli
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A Japanese garden has a circular koi pond in the middle that has a radius of 3 feet. A rectangle with length of 16 feet and width of 14 feet. A circle with radius 3 feet is cut out of the rectangle. What is the area of the Japanese garden around the koi pond? Use 3.14 for Pi. 195.74 feet squared 224.00 feet squared 252.26 feet squared 337.04 feet squared
Answer:
first, find the area of the circle cut.
r= 3 feet
π=3.14
area of a circle= πr²= 3.14×3×3= 28.26 sq.feet
Now, find the area of the rectangle and subtract it by the area of the circle.
area of rectangle = l×b
length of the rectangle= 16 feet
breadth/width of the rectangular garden= 14 feet
area= 16×14= 224 sq. feet
now, area of the garden surrounding the koi pond= 224-28.26
=195.74 sq. feet
Answer:
A. 195.74
Step-by-step explanation:
Edge2020
help asap!! will get branliest.
Answer:
C
Step-by-step explanation:
A reflection is when the original diagram or picture is fliped exactly over the x axis.
HEYA!!
Answer:
Your Answer of the Question is C
if you want to prove it you can do the same thing in real life by drawing a 'W' on a paper and see its reflection on the mirror
HOPE IT MATCHES!!
Suppose the area of a circle is 201.0624 square feet. What's the diameter of the circle? (Use π = 3.1416.)
Answer:
16
Step-by-step explanation:
Area of circle Formula: A = πr²
d = 2r
Simply plug in what you know:
201.0624 = 3.1416r²
64 = r²
r = 8
d = 2(8)
d = 16
find the common ratio of the geometric sequence: 16/3,4,3,…
Answer:
3/4
Step-by-step explanation:
r= a3/a2=3/4
or
r= a2/a1= 4÷16/3= 4×3/16= 3/4
The given equation has been solved in the table. In which step was the subtraction property of equality applied?
Answer:
Option (D)
Step-by-step explanation:
Subtraction property of equality tells that whatever subtracted from one side of the equation must be subtracted from the other side.
If x + 2 = 2,
By the property of subtraction of equality,
x + 2 - 2 = 2 - 2
x = 0
But in the given question,
[tex]\frac{x}{2}-7=-7[/tex]
[tex]\frac{x}{2}-7+7=-7+7[/tex]
shows the addition property of equality in step (2)
Therefore, subtraction property of equality was not applied.
Option (D) will be the answer.
Write an equation:
For every 2 apples there
are 6 bananas
Answer:
[tex]2a=6b\\a=3b[/tex]
Step-by-step explanation:
Let [tex]a[/tex] equal the amount of apples and [tex]b[/tex] equal the amount of bananas.
[tex]2a=6b\\a=3b[/tex]
Answer:
every 2 apples there
are 6 bananas
Step-by-step explanation:
2a=6b
Population of town was 21000 in 1980 and it was 20000 in 1990. Assuming the population is decreasing continuously at a rate proportion to the existing population, estimate the population in 2010.
Answer:
19,000
Step-by-step explanation:
Here, we are to estimate the population in the year 2010
From the question, we can see that within a period of a decade which is 10 years, 1000 was lost
So within the period of another decade, it is possible that another 1000 be lost
The estimated population in the year 2010 is thus 20,000 - 1,000 =
19,000
xpress 8/(1 - 2x)2 as a power series by differentiating the equation below. What is the radius of convergence? 4 (1 - 2x) = 4(1 + 2x + 4x2 + 8x3 + ...) = 4 [infinity] Σ n=0 (2x)n SOLUTION Differentiating each side of the equation, we get 8 (1 - 2x)2 = 4(2 + Correct: Your answer is correct. + 24x2 + ...) = 4 [infinity] Σ n=1 Incorrect: Your answer is incorrect. If we wish, we can replace
Recall that for |x| < 1, we have
[tex]\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n[/tex]
Replace x with 2x, multiply 4, and call this function f :
[tex]f(x)=\dfrac4{1-2x}=\displaystyle4\sum_{n=0}^\infty(2x)^n[/tex]
Take the derivative:
[tex]f'(x)=\dfrac8{(1-2x)^2}=\displaystyle8\sum_{n=0}^\infty n(2x)^{n-1}=\boxed{8\sum_{n=0}^\infty (n+1)(2x)^n}[/tex]
By the ratio test, the series converges for
[tex]\displaystyle\lim_{n\to\infty}\left|\frac{(n+2)(2x)^{n+1}}{(n+1)(2x)^n}\right|=|2x|\lim_{n\to\infty}\frac{n+2}{n+1}=|2x|<1[/tex]
or |x| < 1/2, so the radius of convergence is 1/2.
In math list the angles in order from smallest to the largest
Answer:
A) S,T,R
Step-by-step explanation:
Please answer this correctly
Answer:
4/5 chance
Step-by-step explanation:
There are 4 numbers that fit the rule, 1, 3, 4, 5, since all of them are either odd or greater than 3. There will be a 4/5 chance of picking one.
Answer:
4/5 is the answer.Step-by-step explanation:
Facts!This is because 5 is odd and greater than 3.
Also. 4 is greater than 3.
After that, the other odd numbers are 1 and 3
So the numbers are 1, 3, 4, and 5.
So 4 out of 5 numbers are counted in the circle.
In this way 4/5 is the answer.
4/5 is the answer.Hope this helped!
Kavitha
Find the measure of angle angle AEB in the figure below. Enter only the number. PLEASE HELP ASAP
Answer:
42°
Step-by-step explanation:
AD is a line
AEC and DEC are both 90°
AEB and CEB make up 90°
AEB+CEB=AEC substitute
AEB+48=90 Next use Subtraction property of equality
AEB=42
Hope this helps, if so please give me brainliest, it helps a lot. :)
Have a good day!
Answer:
∠AEB=42
Step-by-step explanation:
∠AEB and ∠BEC are inside of ∠AEC.
∠AEC is a right angle, Since ∠AEC and ∠CED are on a straight line, they must add to 180 degrees. ∠CED is a right angle (the little square in the corner tell us this), so ∠AEC must also be a right angle. This is because a right angle is 90 degrees (∠CED+∠AEC=180 --> 90+∠AEC=180 --> ∠AEC=90)
Therefore, the 2 angles (AEB and BEC) inside of ∠AEC must add to 90 degrees.
∠AEB+ ∠BEC= 90
We know that ∠BEC=48
∠AEB+48=90
We want to find out what ∠AEB is. We must get ∠AEB by itself. 48 is being added, and the inverse of addition is subtraction. Subtract 48 from both sides.
∠AEB+48-48=90-48
∠AEB=90-48
∠AEB=42
Which of the following is the equation of the quadratic function below?
A. y = x2 - 2x+2
B. y = x +2x-2
C. y = x2 - 8x+12
D. y = x2 +8x-12
Determine the slope of the line that has the following coordinates: (5, 9)(11, - 3)
Answer:
[tex] x_1 = 5, x_2 =11, y_1 =9, y_2 = -3[/tex]
The slope can be founded with this formula:
[tex]m =\frac{y_2 -y_1}{x_2 -x_1}[/tex]
And replacing we got:
[tex] m =\frac{-3 -9}{11-5}= -2[/tex]
And the best answer for this case would be :
[tex]m=-2[/tex]
Step-by-step explanation:
For this case we have the following two points given:
[tex] x_1 = 5, x_2 =11, y_1 =9, y_2 = -3[/tex]
The slope can be founded with this formula:
[tex]m =\frac{y_2 -y_1}{x_2 -x_1}[/tex]
And replacing we got:
[tex] m =\frac{-3 -9}{11-5}= -2[/tex]
And the best answer for this case would be :
[tex]m=-2[/tex]
Please help me and my daughter.
Answer:
you can either factorise or use tge formula method
Step-by-step explanation:
3x2−7x−20=03x2-7x-20=0
Use the quadratic formula to find the solutions.
−b±√b2−4(ac)2a-b±b2-4(ac)2a
Substitute the values a=3a=3, b=−7b=-7, and c=−20c=-20 into the quadratic formula and solve for xx.
7±√(−7)2−4⋅(3⋅−20)2⋅37±(-7)2-4⋅(3⋅-20)2⋅3
Simplify.
Tap for more steps...
x=7±176x=7±176
The final answer is the combination of both solutions.
x=4,−53
which of these is a ratio table?
Answer:
The last graph.
Step-by-step explanation:
The last graph is the only one that has a constant pattern that can have a rule, which is every number is multiplied by two.
Hope this helped ! good luck :)
a.) The perimeter of a rectangular field is 354 m. If the length of the field is 95m, what is its width? b.) The area of a rectangular painting is 8439 cm^2. If the width of the painting is 87cm, what is its length?
Answer:
a) 82
b) 97
Step-by-step explanation:
a) 354 - (95+95)
354 - 190
164
164 ÷ 2 = 82
(82+82+95+95=254)
b) 8439 cm^2 = 87x
8439 cm^2 ÷ 87 = 87x ÷ 87
97 = x
If bis the unknown number of blankets, which equation best represents the
situation described below?
Ling gave some of her blankets to charity, decreasing her
total number of blankets by 9. After she gave the blankets
away, she had 11 left.
A. 6-9 = 11
B. 6+9 = 11
C.
= 11
D. b +11 = 9
Answer:
A. b-9=11
Step-by-step explanation:
I‘m assuming the equation should say b, not 6. She had b blankets, subtracted 9, and was left with 11. b-9=11.
What is the equation of BD, simplified?
Third option is the correct answer.
Answer:
[tex] y = \bigg[ \frac{2b}{(2a - c)} \bigg]x - \bigg[ \frac{2bc}{(2a - c)} \bigg][/tex]
Step-by-step explanation:
[tex]y - y_1 = m(x - x_1) \\ \\ y - 0 = \bigg[ \frac{2b}{(2a - c)} \bigg] (x - c) \\ \\ y = \bigg[ \frac{2b}{(2a - c)} \bigg]x - \bigg[ \frac{2b}{(2a - c)} \bigg]c \\ \\ \purple { \boxed{ \bold{y = \bigg[ \frac{2b}{(2a - c)} \bigg]x - \bigg[ \frac{2bc}{(2a - c)} \bigg]}}} \\ [/tex]
Solving by fractions
Answer: Step 3
Step-by-step explanation:
x = -9 or 1. She flipped the signs.
Hope it helps <3
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▹ Answer
Step 3
▹ Step-by-Step Explanation
Juliet flipped the signs. The final answer should be (-9, 1)
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
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CAN SOMEONE HELP ME ASAP
A. 5
B. 53‾√53
C. 10
D. 103√3
Answer:
n = 5
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan 30 = n/ 5 sqrt(3)
5 sqrt(3) tan 30 = n
5 sqrt(3) * 1/ sqrt(3) = n
5 = n
1. Write down a pair of integers
(a) sum is -7
Answer:
-10, 3
Step-by-step explanation:
-10, 3 work since
-10 + 3 = -7
which of the following is a composite number? 6,1,0,19
Answer:
63
Step-by-step explanation:
A composite number is an integer which can be found by mulitplying 2 smaller integers, 7 and 9 in this case
The inclination (tilt) of an amusement park ride is accelerating at a rate of 2160 degreesmin22160\,\dfrac{\text{degrees}}{\text{min}^2} 2160 min 2 degrees 2160, start fraction, start text, d, e, g, r, e, e, s, end text, divided by, start text, m, i, n, end text, squared, end fraction . What is the ride's acceleration rate in degreess2\dfrac{\text{degrees}}{\text{s}^2} s 2 degrees start fraction, start text, d, e, g, r, e, e, s, end text, divided by, start text, s, end text, squared, end fraction ? degreess2\dfrac{\text{degrees}}{\text{s}^2} s 2 degrees
Answer:
um
Step-by-step explanation:
not sure sorry