Answer:
k=24
Step-by-step explanation:
The tangent of the function f at x=a, can be found by differentiating f w.r.t. x and then replacing x with a.
f=-x^2+8x+20
Differentiating both sides:
f'=(-x^2+8x+20)'
By sum rule:
f'=(-x^2)'+(8x)'+(20)'
By constant multiple rule:
f'=-(x^2)'+8(x)'+(20)'
By constant rule:
f'=-(x^2)+8(x)'+0
By power rule:
f'=-2x+8
f' at x=a is -2a+8
This is the slope of any tangent line to the curve f.
The slope of g is 4 if you compare it to slope intercept form y=mx+b.
So we gave -2a+8=4.
Subtracr 8 on both sides: -2a=-4
Divide both sides by -2: a=2
The tangent line to the curve at x=2 is y=4x+k.
To tind y we must first know the y-coordinate of the point of tangency.
If x=2, then
f(2)=-(2)^2+8(2)+20=-4+16+20=12+20=32
So the point is (2,32).
g(x)=4x+k and we know g(2)=32.
This gives us:
32=4(2)+k
32=8+k
k=32-8
k=24
From the tangent given, the value of k will be 24.
How to solve the tangentFrom the information given, g(x) = 4x + k and this is a tangent to f(x)= -x² +8x + 20.
f(x)= -x² +8x + 20
= f'(x) = -2x + 8
The slope of tangent = -2x + 8 at (x , y)
g(x) = 4x + k
Hence, slope = 4
-2x + 8 = 4
Collect like terms
-2x = 4 - 8
-2x = - 4
Divide both side by -2
-2x/-2 = -4/-2
x = 2
f(x)= -x² +8x +20
where, x = 2
y = -2² + 8(2) + 20
y = 32
Hence (2 , 32) lies on g(x)= 4x+k
32 = 4(2) + k
32 = 8 + k
k = 32 - 8
k = 24
In conclusion, the value of k is 24.
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Simplify: 10x+2x-3= 9
A. x=-1
B. x=-2
C. x=1
D. x=2
Answer:
C. x = 1
Step-by-step explanation:
Combine like terms
10 + 2 − 3 = 9
12 − 3 = 9
Add 3 to both sides of the equation
12 − 3 + 3 = 9 + 3
Add the numbers
12 = 9 + 3
12 = 12
[tex]\frac{12x}{12} = \frac{12}{12}[/tex]
Cancel terms that are in both the numerator and denominator
[tex]x = \frac{12}{12}[/tex]
Divide the numbers
x = 1
Therefore the correct answer is C. x = 1
Answer:
C. x = 1
Step-by-step explanation:
Have a great day
I’m timed plsss answer correctly I’ll mark u brainliest
Answer:
[tex]\sqrt{125}[/tex]
Step-by-step explanation:
Use Pythagorean theorem since you have a right triangle [tex]15^{2}[/tex] = [tex]10^{2} + x^{2}[/tex]
225 = 100 + [tex]x^{2}[/tex] so x = [tex]\sqrt{125}[/tex]
Answer:
x = 5[tex]\sqrt{5}[/tex]
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
x² + 10² = 15²
x² + 100 = 225 ( subtract 100 from both sides )
x² = 125 ( take the square root of both sides )
x = [tex]\sqrt{125}[/tex] = [tex]\sqrt{25(5)}[/tex] = 5[tex]\sqrt{5}[/tex] ← in simplest radical form
Which of ratio is equivalent to 3:4 ?
12:9
9: 20
9:12
803 : 804
Answer:
C
Step-by-step explanation:
3/4 = 9/12
This is because
3 x 3 = 9
4 x 3 = 12
3/4 = 9/12
Hope that helps!
There are 2 similar rectangles. The perimeter of the large rectangle is 75 meters, The perimeter of the small rectangle is 50 meters. Find the scale factor.
Here is my answer. I hope this is helpful.
Find the Value of X.
Answer: 80
Step-by-step explanation:
If you look at the top left and bottom right corner, you see that they are identical, so basically you would do the same to 80.
Well lets see...
Solution 1. The sum of angles of a quadrilateral is 360˚ 100˚+100˚+80˚=280 degrees 360˚-280˚=80˚.
Solution 2. Opposite angles on a parallelogram are equal so x=80˚.
HOPE THIS HELPED!!!!!!!!!!
if $45 is divided into the ratio 4:5 the smaller part is A. $1.50 B.$3.50 C.$4.50 D.$24.50 Asap
Answer:
Step-by-step explanation:
When you do 45 divided by 9 you get 5.
45 / 9 = 5
To figure out what the smaller number (in this the 4) equals,
you have to do 4 times 9 to get 36.
4 * 9 = 36
So your answer is 36.
6) Reflection: Across the line x = 1
Answer:
The coordinates of the new triangle would be (2,2), (-1,0) and (-2,4)
Write an equation of the line that passes through the points (−3,−4) and (0,2).
y=23x−2
y−3=23(x−0)
y−0=23(x−3)
y+0=23(x+3)
which one of them are it
what is (16 ÷ 8) + (24 ÷ 6)
Answer: 6
Step-by-step explanation:
2+4=6
Find the value or ratio of the following:
Answer:
see below
Step-by-step explanation:
cos = adj/ hypotenuse
Cos A = 30 /34
Simplifying
Cos A = 15/17
can someone help me do this one problem please like I need help Right now
Answer:
x= 11/12
Step-by-step explanation:
you have to make 1/3 equivalent to 7/12 so now you get 4/12+7/12= 11/12
1
Which expression can be simplified as m18?
Answer:
D : ( n^-3)6
Step-by-step explanation:
HELP ASAP!!! Please give a step-by-step explanation, or you will be reported!
The table gives the probabilities that orphaned pets in animal shelters in six cities are one of the types listed. The probability that a randomly selected orphan pet in an animal shelter in Austin is a dog is _____ %. The probability that a randomly selected orphaned dog in the same animal shelter in Austin is a Chihuahua is _____ %. (Round to the nearest hundredth.)
For all the dogs: you have 2.65+2.46+3.67+2.91 = 11.69%
Now, the probability of getting a chihuahua would be 3.44/11.69=0.2942= 24.92
Step-by-step explanation:
there ya go!!
Answer:
The probability that a randomly selected orphan pet in an animal shelter in Austin is a dog is 11.71% .
The probability that a randomly selected orphaned dog in the same animal shelter in Austin is a Chihuahua is 29.37% .
Step-by-step explanation:
2.76% + 2.86% + 3.44% + 2.65% = 11.71%
11.71 / 3.44 = .2937
.2937 = 29.37%
Point K is located at (1.5) on the coordinate plane. Point K is reflected over the Z-
acis to create point K'. What ordered pair describes the location of K"?
Answer:
hold on i'm abt to answer it
Step-by-step explanation:
PLEASE PLEASE PLEASE
HELP ME!!!!!
Answer:
3 adjacent
4. complementary
Make this into a smaller word problem
7.4z−5(−1.6z+2.4)
:D
x + 6 = -6
please help me pls
Manuel can mow 2 yards per hour. Let h represent the number of hours. Which equation best represents how long it will take him to mow 30 yards?
A=2h=30
B=30(2)=h
c 30h=2
D h/2=30
Answer:
2h = 30
Step-by-step explanation:
i hope helper
What is the midpoint of the line segment with endpoint (1,-2) and (9,8)?
A. (3,5)
B. (4,3)
C. (5,3)
D. (5,5)
There is a line that includes the point (3, 7) and has a slope of 1. What is its equation in
slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
Y=1x+7
Step-by-step explanation:
y=mx+b
m: slope
b: y axis
The interior angle sum of a convex polygon is 2.520 How many sides does the polygon
have?
Complete Question
The interior angle sum of a convex polygon is 2520.How many sides does the polygon have?
Answer:
16 sides
Step-by-step explanation:
The sum of angles in a polygon formula is given as:
(n - 2)180°
Where n = Number of sides of the polygon
Hence:
(n - 2)180°= 2520°
Divide both side by 180°
(n -2) = 2520/180
n - 2 = 14
n = 14 + 2 = 16
Therefore the number of sides the convex polygon has 16 sides.
please help i am stuck on this question!
9514 1404 393
Answer:
39 units
Step-by-step explanation:
The angle markings tell you this is an equilateral triangle, so all sides are the same length.
10x -11 = 2x +29
8x = 40
x = 5
Then the side length is ...
2x +29 = 2·5 +29 = 39
The length of side KL is 39 units.
Find the value of x.
2x
120
70
A. 70
B. 35
C. 25
D. 55
Answer:
Step-by-step explanation:
120 = 2x + 70
120 - 70 = 2x + 70 - 70
50 = 2x
50/2 = 2x/2
x = 25
On a map,1 inch represents 5 miles.joel measure 2 1/2 inches between two cities on the map. how many miles apart are the two cities?
Answer:
12.5 miles
Step-by-step explanation:
5/2 inch*5 miles/ i inch= 25/2 miles or 12.5 miles
if my anwer helps please mark as brainliest.
PLS help ASAP I DONT have time to answer this, it also detects if it’s right or wrong.
Answer:
C. 43.98
Step-by-step explanation:
(3ax + 4a) - (9x + 15a)
Answer:
3ax−11a−9x
Step-by-step explanation:
3ax+4a−(9x+15a)
Distribute the Negative Sign:
=3ax+4a+−1(9x+15a)
=3ax+4a+−1(9x)+−1(15a)
=3ax+4a+−9x+−15a
Combine Like Terms:
=3ax+4a+−9x+−15a
=(3ax)+(4a+−15a)+(−9x)
=3ax+−11a+−9x
2. Nadia has 5 pairs of jeans, 3 blouses, and 4 pairs of tennis shoes. How many different
combinations can be made of 1 pair of jeans, 1 blouse, and 1 pair of shoes?
A)12
B)11
C)60
D)90
Answer:
try to be clear enough so that the answerer can understand
Step-by-step explanation:
.
What is the reciprocal of 5/4
Answer:
That would be 4/5. A reciprocal is just a fraction inverted, pretty much.
Hello Brainliest! I need you to help! Thank you Brainliest! (You will get brainliest lol)
Answer:
2/3
Step-by-step explanation:
Answer:
2/3
Step-by-step explanation:
One equation in a system is 4x – 2y = 8. Which equation gives the system no solution?
Answer:
-8
Step-by-step explanation:
Correct me if i'm wrong